Properties

Label 980.1.bq.b.179.1
Level $980$
Weight $1$
Character 980.179
Analytic conductor $0.489$
Analytic rank $0$
Dimension $12$
Projective image $D_{21}$
CM discriminant -20
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [980,1,Mod(39,980)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(980, base_ring=CyclotomicField(42))
 
chi = DirichletCharacter(H, H._module([21, 21, 34]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("980.39");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 980.bq (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: \(0.489083712380\)
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 179.1
Root \(0.365341 - 0.930874i\) of defining polynomial
Character \(\chi\) \(=\) 980.179
Dual form 980.1.bq.b.219.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.0747301 + 0.997204i) q^{2} +(-1.40097 - 0.432142i) q^{3} +(-0.988831 + 0.149042i) q^{4} +(-0.733052 + 0.680173i) q^{5} +(0.326239 - 1.42935i) q^{6} +(-0.988831 + 0.149042i) q^{7} +(-0.222521 - 0.974928i) q^{8} +(0.949729 + 0.647514i) q^{9} +O(q^{10})\) \(q+(0.0747301 + 0.997204i) q^{2} +(-1.40097 - 0.432142i) q^{3} +(-0.988831 + 0.149042i) q^{4} +(-0.733052 + 0.680173i) q^{5} +(0.326239 - 1.42935i) q^{6} +(-0.988831 + 0.149042i) q^{7} +(-0.222521 - 0.974928i) q^{8} +(0.949729 + 0.647514i) q^{9} +(-0.733052 - 0.680173i) q^{10} +(1.44973 + 0.218511i) q^{12} +(-0.222521 - 0.974928i) q^{14} +(1.32091 - 0.636119i) q^{15} +(0.955573 - 0.294755i) q^{16} +(-0.574730 + 0.995462i) q^{18} +(0.623490 - 0.781831i) q^{20} +(1.44973 + 0.218511i) q^{21} +(0.698220 - 1.77904i) q^{23} +(-0.109562 + 1.46200i) q^{24} +(0.0747301 - 0.997204i) q^{25} +(-0.136622 - 0.171318i) q^{27} +(0.955573 - 0.294755i) q^{28} +(0.455573 - 0.571270i) q^{29} +(0.733052 + 1.26968i) q^{30} +(0.365341 + 0.930874i) q^{32} +(0.623490 - 0.781831i) q^{35} +(-1.03563 - 0.498732i) q^{36} +(0.826239 + 0.563320i) q^{40} +(-0.367711 - 1.61105i) q^{41} +(-0.109562 + 1.46200i) q^{42} +(-0.367711 + 1.61105i) q^{43} +(-1.13662 + 0.171318i) q^{45} +(1.82624 + 0.563320i) q^{46} +(-0.0332580 - 0.443797i) q^{47} -1.46610 q^{48} +(0.955573 - 0.294755i) q^{49} +1.00000 q^{50} +(0.160629 - 0.149042i) q^{54} +(0.365341 + 0.930874i) q^{56} +(0.603718 + 0.411608i) q^{58} +(-1.21135 + 0.825886i) q^{60} +(-1.88980 - 0.284841i) q^{61} +(-1.03563 - 0.498732i) q^{63} +(-0.900969 + 0.433884i) q^{64} +(0.500000 - 0.866025i) q^{67} +(-1.74698 + 2.19064i) q^{69} +(0.826239 + 0.563320i) q^{70} +(0.419945 - 1.07000i) q^{72} +(-0.535628 + 1.36476i) q^{75} +(-0.500000 + 0.866025i) q^{80} +(-0.302576 - 0.770951i) q^{81} +(1.57906 - 0.487076i) q^{82} +(1.78181 - 0.858075i) q^{83} -1.46610 q^{84} +(-1.63402 - 0.246289i) q^{86} +(-0.885113 + 0.603460i) q^{87} +(0.603718 + 0.411608i) q^{89} +(-0.255779 - 1.12064i) q^{90} +(-0.425270 + 1.86323i) q^{92} +(0.440071 - 0.0663300i) q^{94} +(-0.109562 - 1.46200i) q^{96} +(0.365341 + 0.930874i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + q^{2} - 8 q^{3} + q^{4} + q^{5} - 5 q^{6} + q^{7} - 2 q^{8} - 7 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + q^{2} - 8 q^{3} + q^{4} + q^{5} - 5 q^{6} + q^{7} - 2 q^{8} - 7 q^{9} + q^{10} - q^{12} - 2 q^{14} + 2 q^{15} + q^{16} - 7 q^{18} - 2 q^{20} - q^{21} - q^{23} - q^{24} + q^{25} + 12 q^{27} + q^{28} - 5 q^{29} - q^{30} + q^{32} - 2 q^{35} - 7 q^{36} + q^{40} + 2 q^{41} - q^{42} + 2 q^{43} + 13 q^{46} + 2 q^{47} + 2 q^{48} + q^{49} + 12 q^{50} + 15 q^{54} + q^{56} - q^{58} - q^{60} - q^{61} - 7 q^{63} - 2 q^{64} + 6 q^{67} - 2 q^{69} + q^{70} - q^{75} - 6 q^{80} - 8 q^{81} - q^{82} + 2 q^{83} + 2 q^{84} - q^{86} - 6 q^{87} - q^{89} - 5 q^{92} + 2 q^{94} - q^{96} + q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/980\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(197\) \(491\)
\(\chi(n)\) \(e\left(\frac{2}{21}\right)\) \(-1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.0747301 + 0.997204i 0.0747301 + 0.997204i
\(3\) −1.40097 0.432142i −1.40097 0.432142i −0.500000 0.866025i \(-0.666667\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(4\) −0.988831 + 0.149042i −0.988831 + 0.149042i
\(5\) −0.733052 + 0.680173i −0.733052 + 0.680173i
\(6\) 0.326239 1.42935i 0.326239 1.42935i
\(7\) −0.988831 + 0.149042i −0.988831 + 0.149042i
\(8\) −0.222521 0.974928i −0.222521 0.974928i
\(9\) 0.949729 + 0.647514i 0.949729 + 0.647514i
\(10\) −0.733052 0.680173i −0.733052 0.680173i
\(11\) 0 0 0.826239 0.563320i \(-0.190476\pi\)
−0.826239 + 0.563320i \(0.809524\pi\)
\(12\) 1.44973 + 0.218511i 1.44973 + 0.218511i
\(13\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(14\) −0.222521 0.974928i −0.222521 0.974928i
\(15\) 1.32091 0.636119i 1.32091 0.636119i
\(16\) 0.955573 0.294755i 0.955573 0.294755i
\(17\) 0 0 −0.365341 0.930874i \(-0.619048\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(18\) −0.574730 + 0.995462i −0.574730 + 0.995462i
\(19\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(20\) 0.623490 0.781831i 0.623490 0.781831i
\(21\) 1.44973 + 0.218511i 1.44973 + 0.218511i
\(22\) 0 0
\(23\) 0.698220 1.77904i 0.698220 1.77904i 0.0747301 0.997204i \(-0.476190\pi\)
0.623490 0.781831i \(-0.285714\pi\)
\(24\) −0.109562 + 1.46200i −0.109562 + 1.46200i
\(25\) 0.0747301 0.997204i 0.0747301 0.997204i
\(26\) 0 0
\(27\) −0.136622 0.171318i −0.136622 0.171318i
\(28\) 0.955573 0.294755i 0.955573 0.294755i
\(29\) 0.455573 0.571270i 0.455573 0.571270i −0.500000 0.866025i \(-0.666667\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(30\) 0.733052 + 1.26968i 0.733052 + 1.26968i
\(31\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(32\) 0.365341 + 0.930874i 0.365341 + 0.930874i
\(33\) 0 0
\(34\) 0 0
\(35\) 0.623490 0.781831i 0.623490 0.781831i
\(36\) −1.03563 0.498732i −1.03563 0.498732i
\(37\) 0 0 −0.988831 0.149042i \(-0.952381\pi\)
0.988831 + 0.149042i \(0.0476190\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0.826239 + 0.563320i 0.826239 + 0.563320i
\(41\) −0.367711 1.61105i −0.367711 1.61105i −0.733052 0.680173i \(-0.761905\pi\)
0.365341 0.930874i \(-0.380952\pi\)
\(42\) −0.109562 + 1.46200i −0.109562 + 1.46200i
\(43\) −0.367711 + 1.61105i −0.367711 + 1.61105i 0.365341 + 0.930874i \(0.380952\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(44\) 0 0
\(45\) −1.13662 + 0.171318i −1.13662 + 0.171318i
\(46\) 1.82624 + 0.563320i 1.82624 + 0.563320i
\(47\) −0.0332580 0.443797i −0.0332580 0.443797i −0.988831 0.149042i \(-0.952381\pi\)
0.955573 0.294755i \(-0.0952381\pi\)
\(48\) −1.46610 −1.46610
\(49\) 0.955573 0.294755i 0.955573 0.294755i
\(50\) 1.00000 1.00000
\(51\) 0 0
\(52\) 0 0
\(53\) 0 0 0.988831 0.149042i \(-0.0476190\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(54\) 0.160629 0.149042i 0.160629 0.149042i
\(55\) 0 0
\(56\) 0.365341 + 0.930874i 0.365341 + 0.930874i
\(57\) 0 0
\(58\) 0.603718 + 0.411608i 0.603718 + 0.411608i
\(59\) 0 0 −0.733052 0.680173i \(-0.761905\pi\)
0.733052 + 0.680173i \(0.238095\pi\)
\(60\) −1.21135 + 0.825886i −1.21135 + 0.825886i
\(61\) −1.88980 0.284841i −1.88980 0.284841i −0.900969 0.433884i \(-0.857143\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(62\) 0 0
\(63\) −1.03563 0.498732i −1.03563 0.498732i
\(64\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(65\) 0 0
\(66\) 0 0
\(67\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(68\) 0 0
\(69\) −1.74698 + 2.19064i −1.74698 + 2.19064i
\(70\) 0.826239 + 0.563320i 0.826239 + 0.563320i
\(71\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(72\) 0.419945 1.07000i 0.419945 1.07000i
\(73\) 0 0 0.0747301 0.997204i \(-0.476190\pi\)
−0.0747301 + 0.997204i \(0.523810\pi\)
\(74\) 0 0
\(75\) −0.535628 + 1.36476i −0.535628 + 1.36476i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(80\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(81\) −0.302576 0.770951i −0.302576 0.770951i
\(82\) 1.57906 0.487076i 1.57906 0.487076i
\(83\) 1.78181 0.858075i 1.78181 0.858075i 0.826239 0.563320i \(-0.190476\pi\)
0.955573 0.294755i \(-0.0952381\pi\)
\(84\) −1.46610 −1.46610
\(85\) 0 0
\(86\) −1.63402 0.246289i −1.63402 0.246289i
\(87\) −0.885113 + 0.603460i −0.885113 + 0.603460i
\(88\) 0 0
\(89\) 0.603718 + 0.411608i 0.603718 + 0.411608i 0.826239 0.563320i \(-0.190476\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(90\) −0.255779 1.12064i −0.255779 1.12064i
\(91\) 0 0
\(92\) −0.425270 + 1.86323i −0.425270 + 1.86323i
\(93\) 0 0
\(94\) 0.440071 0.0663300i 0.440071 0.0663300i
\(95\) 0 0
\(96\) −0.109562 1.46200i −0.109562 1.46200i
\(97\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(98\) 0.365341 + 0.930874i 0.365341 + 0.930874i
\(99\) 0 0
\(100\) 0.0747301 + 0.997204i 0.0747301 + 0.997204i
\(101\) −1.88980 0.582926i −1.88980 0.582926i −0.988831 0.149042i \(-0.952381\pi\)
−0.900969 0.433884i \(-0.857143\pi\)
\(102\) 0 0
\(103\) 0.733052 0.680173i 0.733052 0.680173i −0.222521 0.974928i \(-0.571429\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(104\) 0 0
\(105\) −1.21135 + 0.825886i −1.21135 + 0.825886i
\(106\) 0 0
\(107\) −1.63402 1.11406i −1.63402 1.11406i −0.900969 0.433884i \(-0.857143\pi\)
−0.733052 0.680173i \(-0.761905\pi\)
\(108\) 0.160629 + 0.149042i 0.160629 + 0.149042i
\(109\) −0.826239 + 0.563320i −0.826239 + 0.563320i −0.900969 0.433884i \(-0.857143\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(113\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(114\) 0 0
\(115\) 0.698220 + 1.77904i 0.698220 + 1.77904i
\(116\) −0.365341 + 0.632789i −0.365341 + 0.632789i
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) −0.914101 1.14625i −0.914101 1.14625i
\(121\) 0.365341 0.930874i 0.365341 0.930874i
\(122\) 0.142820 1.90580i 0.142820 1.90580i
\(123\) −0.181049 + 2.41593i −0.181049 + 2.41593i
\(124\) 0 0
\(125\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(126\) 0.419945 1.07000i 0.419945 1.07000i
\(127\) −1.12349 + 1.40881i −1.12349 + 1.40881i −0.222521 + 0.974928i \(0.571429\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(128\) −0.500000 0.866025i −0.500000 0.866025i
\(129\) 1.21135 2.09812i 1.21135 2.09812i
\(130\) 0 0
\(131\) 0 0 0.955573 0.294755i \(-0.0952381\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0.900969 + 0.433884i 0.900969 + 0.433884i
\(135\) 0.216677 + 0.0326588i 0.216677 + 0.0326588i
\(136\) 0 0
\(137\) 0 0 −0.733052 0.680173i \(-0.761905\pi\)
0.733052 + 0.680173i \(0.238095\pi\)
\(138\) −2.31507 1.57839i −2.31507 1.57839i
\(139\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(140\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(141\) −0.145190 + 0.636119i −0.145190 + 0.636119i
\(142\) 0 0
\(143\) 0 0
\(144\) 1.09839 + 0.338809i 1.09839 + 0.338809i
\(145\) 0.0546039 + 0.728639i 0.0546039 + 0.728639i
\(146\) 0 0
\(147\) −1.46610 −1.46610
\(148\) 0 0
\(149\) −0.147791 1.97213i −0.147791 1.97213i −0.222521 0.974928i \(-0.571429\pi\)
0.0747301 0.997204i \(-0.476190\pi\)
\(150\) −1.40097 0.432142i −1.40097 0.432142i
\(151\) 0 0 0.988831 0.149042i \(-0.0476190\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 −0.733052 0.680173i \(-0.761905\pi\)
0.733052 + 0.680173i \(0.238095\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) −0.900969 0.433884i −0.900969 0.433884i
\(161\) −0.425270 + 1.86323i −0.425270 + 1.86323i
\(162\) 0.746184 0.359343i 0.746184 0.359343i
\(163\) 1.19158 0.367554i 1.19158 0.367554i 0.365341 0.930874i \(-0.380952\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(164\) 0.603718 + 1.53825i 0.603718 + 1.53825i
\(165\) 0 0
\(166\) 0.988831 + 1.71271i 0.988831 + 1.71271i
\(167\) 0.0931869 0.116853i 0.0931869 0.116853i −0.733052 0.680173i \(-0.761905\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(168\) −0.109562 1.46200i −0.109562 1.46200i
\(169\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(170\) 0 0
\(171\) 0 0
\(172\) 0.123490 1.64786i 0.123490 1.64786i
\(173\) 0 0 0.365341 0.930874i \(-0.380952\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(174\) −0.667917 0.837541i −0.667917 0.837541i
\(175\) 0.0747301 + 0.997204i 0.0747301 + 0.997204i
\(176\) 0 0
\(177\) 0 0
\(178\) −0.365341 + 0.632789i −0.365341 + 0.632789i
\(179\) 0 0 −0.365341 0.930874i \(-0.619048\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(180\) 1.09839 0.338809i 1.09839 0.338809i
\(181\) 0.900969 0.433884i 0.900969 0.433884i 0.0747301 0.997204i \(-0.476190\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(182\) 0 0
\(183\) 2.52446 + 1.21572i 2.52446 + 1.21572i
\(184\) −1.88980 0.284841i −1.88980 0.284841i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0.0990311 + 0.433884i 0.0990311 + 0.433884i
\(189\) 0.160629 + 0.149042i 0.160629 + 0.149042i
\(190\) 0 0
\(191\) 0 0 0.733052 0.680173i \(-0.238095\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(192\) 1.44973 0.218511i 1.44973 0.218511i
\(193\) 0 0 −0.955573 0.294755i \(-0.904762\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 0 0
\(199\) 0 0 −0.955573 0.294755i \(-0.904762\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(200\) −0.988831 + 0.149042i −0.988831 + 0.149042i
\(201\) −1.07473 + 0.997204i −1.07473 + 0.997204i
\(202\) 0.440071 1.92808i 0.440071 1.92808i
\(203\) −0.365341 + 0.632789i −0.365341 + 0.632789i
\(204\) 0 0
\(205\) 1.36534 + 0.930874i 1.36534 + 0.930874i
\(206\) 0.733052 + 0.680173i 0.733052 + 0.680173i
\(207\) 1.81507 1.23749i 1.81507 1.23749i
\(208\) 0 0
\(209\) 0 0
\(210\) −0.914101 1.14625i −0.914101 1.14625i
\(211\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0.988831 1.71271i 0.988831 1.71271i
\(215\) −0.826239 1.43109i −0.826239 1.43109i
\(216\) −0.136622 + 0.171318i −0.136622 + 0.171318i
\(217\) 0 0
\(218\) −0.623490 0.781831i −0.623490 0.781831i
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −1.12349 1.40881i −1.12349 1.40881i −0.900969 0.433884i \(-0.857143\pi\)
−0.222521 0.974928i \(-0.571429\pi\)
\(224\) −0.500000 0.866025i −0.500000 0.866025i
\(225\) 0.716677 0.898684i 0.716677 0.898684i
\(226\) 0 0
\(227\) 0.900969 1.56052i 0.900969 1.56052i 0.0747301 0.997204i \(-0.476190\pi\)
0.826239 0.563320i \(-0.190476\pi\)
\(228\) 0 0
\(229\) 1.19158 0.367554i 1.19158 0.367554i 0.365341 0.930874i \(-0.380952\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(230\) −1.72188 + 0.829215i −1.72188 + 0.829215i
\(231\) 0 0
\(232\) −0.658322 0.317031i −0.658322 0.317031i
\(233\) 0 0 −0.988831 0.149042i \(-0.952381\pi\)
0.988831 + 0.149042i \(0.0476190\pi\)
\(234\) 0 0
\(235\) 0.326239 + 0.302705i 0.326239 + 0.302705i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(240\) 1.07473 0.997204i 1.07473 0.997204i
\(241\) 1.78181 0.268565i 1.78181 0.268565i 0.826239 0.563320i \(-0.190476\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(242\) 0.955573 + 0.294755i 0.955573 + 0.294755i
\(243\) 0.107115 + 1.42935i 0.107115 + 1.42935i
\(244\) 1.91115 1.91115
\(245\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(246\) −2.42270 −2.42270
\(247\) 0 0
\(248\) 0 0
\(249\) −2.86707 + 0.432142i −2.86707 + 0.432142i
\(250\) −0.733052 + 0.680173i −0.733052 + 0.680173i
\(251\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(252\) 1.09839 + 0.338809i 1.09839 + 0.338809i
\(253\) 0 0
\(254\) −1.48883 1.01507i −1.48883 1.01507i
\(255\) 0 0
\(256\) 0.826239 0.563320i 0.826239 0.563320i
\(257\) 0 0 −0.988831 0.149042i \(-0.952381\pi\)
0.988831 + 0.149042i \(0.0476190\pi\)
\(258\) 2.18278 + 1.05117i 2.18278 + 1.05117i
\(259\) 0 0
\(260\) 0 0
\(261\) 0.802576 0.247562i 0.802576 0.247562i
\(262\) 0 0
\(263\) −0.365341 + 0.632789i −0.365341 + 0.632789i −0.988831 0.149042i \(-0.952381\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −0.667917 0.837541i −0.667917 0.837541i
\(268\) −0.365341 + 0.930874i −0.365341 + 0.930874i
\(269\) 0.0111692 0.149042i 0.0111692 0.149042i −0.988831 0.149042i \(-0.952381\pi\)
1.00000 \(0\)
\(270\) −0.0163752 + 0.218511i −0.0163752 + 0.218511i
\(271\) 0 0 0.365341 0.930874i \(-0.380952\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 1.40097 2.42655i 1.40097 2.42655i
\(277\) 0 0 −0.365341 0.930874i \(-0.619048\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) −0.900969 0.433884i −0.900969 0.433884i
\(281\) 0.400969 + 0.193096i 0.400969 + 0.193096i 0.623490 0.781831i \(-0.285714\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(282\) −0.645190 0.0972467i −0.645190 0.0972467i
\(283\) −0.367711 + 0.250701i −0.367711 + 0.250701i −0.733052 0.680173i \(-0.761905\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0.603718 + 1.53825i 0.603718 + 1.53825i
\(288\) −0.255779 + 1.12064i −0.255779 + 1.12064i
\(289\) −0.733052 + 0.680173i −0.733052 + 0.680173i
\(290\) −0.722521 + 0.108903i −0.722521 + 0.108903i
\(291\) 0 0
\(292\) 0 0
\(293\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(294\) −0.109562 1.46200i −0.109562 1.46200i
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 1.95557 0.294755i 1.95557 0.294755i
\(299\) 0 0
\(300\) 0.326239 1.42935i 0.326239 1.42935i
\(301\) 0.123490 1.64786i 0.123490 1.64786i
\(302\) 0 0
\(303\) 2.39564 + 1.63332i 2.39564 + 1.63332i
\(304\) 0 0
\(305\) 1.57906 1.07659i 1.57906 1.07659i
\(306\) 0 0
\(307\) −0.134659 0.0648483i −0.134659 0.0648483i 0.365341 0.930874i \(-0.380952\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(308\) 0 0
\(309\) −1.32091 + 0.636119i −1.32091 + 0.636119i
\(310\) 0 0
\(311\) 0 0 −0.365341 0.930874i \(-0.619048\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(312\) 0 0
\(313\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(314\) 0 0
\(315\) 1.09839 0.338809i 1.09839 0.338809i
\(316\) 0 0
\(317\) 0 0 0.365341 0.930874i \(-0.380952\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0.365341 0.930874i 0.365341 0.930874i
\(321\) 1.80778 + 2.26689i 1.80778 + 2.26689i
\(322\) −1.88980 0.284841i −1.88980 0.284841i
\(323\) 0 0
\(324\) 0.414101 + 0.717244i 0.414101 + 0.717244i
\(325\) 0 0
\(326\) 0.455573 + 1.16078i 0.455573 + 1.16078i
\(327\) 1.40097 0.432142i 1.40097 0.432142i
\(328\) −1.48883 + 0.716983i −1.48883 + 0.716983i
\(329\) 0.0990311 + 0.433884i 0.0990311 + 0.433884i
\(330\) 0 0
\(331\) 0 0 −0.988831 0.149042i \(-0.952381\pi\)
0.988831 + 0.149042i \(0.0476190\pi\)
\(332\) −1.63402 + 1.11406i −1.63402 + 1.11406i
\(333\) 0 0
\(334\) 0.123490 + 0.0841939i 0.123490 + 0.0841939i
\(335\) 0.222521 + 0.974928i 0.222521 + 0.974928i
\(336\) 1.44973 0.218511i 1.44973 0.218511i
\(337\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(338\) −0.733052 + 0.680173i −0.733052 + 0.680173i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(344\) 1.65248 1.65248
\(345\) −0.209389 2.79410i −0.209389 2.79410i
\(346\) 0 0
\(347\) −1.63402 + 0.246289i −1.63402 + 0.246289i −0.900969 0.433884i \(-0.857143\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(348\) 0.785286 0.728639i 0.785286 0.728639i
\(349\) −0.367711 + 1.61105i −0.367711 + 1.61105i 0.365341 + 0.930874i \(0.380952\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(350\) −0.988831 + 0.149042i −0.988831 + 0.149042i
\(351\) 0 0
\(352\) 0 0
\(353\) 0 0 −0.733052 0.680173i \(-0.761905\pi\)
0.733052 + 0.680173i \(0.238095\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −0.658322 0.317031i −0.658322 0.317031i
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 0.955573 0.294755i \(-0.0952381\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(360\) 0.419945 + 1.07000i 0.419945 + 1.07000i
\(361\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(362\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(363\) −0.914101 + 1.14625i −0.914101 + 1.14625i
\(364\) 0 0
\(365\) 0 0
\(366\) −1.02366 + 2.60825i −1.02366 + 2.60825i
\(367\) 0.0111692 0.149042i 0.0111692 0.149042i −0.988831 0.149042i \(-0.952381\pi\)
1.00000 \(0\)
\(368\) 0.142820 1.90580i 0.142820 1.90580i
\(369\) 0.693950 1.76815i 0.693950 1.76815i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(374\) 0 0
\(375\) −0.535628 1.36476i −0.535628 1.36476i
\(376\) −0.425270 + 0.131178i −0.425270 + 0.131178i
\(377\) 0 0
\(378\) −0.136622 + 0.171318i −0.136622 + 0.171318i
\(379\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(380\) 0 0
\(381\) 2.18278 1.48819i 2.18278 1.48819i
\(382\) 0 0
\(383\) 0.603718 + 0.411608i 0.603718 + 0.411608i 0.826239 0.563320i \(-0.190476\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(384\) 0.326239 + 1.42935i 0.326239 + 1.42935i
\(385\) 0 0
\(386\) 0 0
\(387\) −1.39240 + 1.29196i −1.39240 + 1.29196i
\(388\) 0 0
\(389\) 1.19158 + 0.367554i 1.19158 + 0.367554i 0.826239 0.563320i \(-0.190476\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −0.500000 0.866025i −0.500000 0.866025i
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 0 0 0.733052 0.680173i \(-0.238095\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −0.222521 0.974928i −0.222521 0.974928i
\(401\) −1.21135 0.825886i −1.21135 0.825886i −0.222521 0.974928i \(-0.571429\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(402\) −1.07473 0.997204i −1.07473 0.997204i
\(403\) 0 0
\(404\) 1.95557 + 0.294755i 1.95557 + 0.294755i
\(405\) 0.746184 + 0.359343i 0.746184 + 0.359343i
\(406\) −0.658322 0.317031i −0.658322 0.317031i
\(407\) 0 0
\(408\) 0 0
\(409\) 0.0546039 + 0.139129i 0.0546039 + 0.139129i 0.955573 0.294755i \(-0.0952381\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(410\) −0.826239 + 1.43109i −0.826239 + 1.43109i
\(411\) 0 0
\(412\) −0.623490 + 0.781831i −0.623490 + 0.781831i
\(413\) 0 0
\(414\) 1.36967 + 1.71752i 1.36967 + 1.71752i
\(415\) −0.722521 + 1.84095i −0.722521 + 1.84095i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(420\) 1.07473 0.997204i 1.07473 0.997204i
\(421\) −0.914101 + 1.14625i −0.914101 + 1.14625i 0.0747301 + 0.997204i \(0.476190\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(422\) 0 0
\(423\) 0.255779 0.443022i 0.255779 0.443022i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 1.91115 1.91115
\(428\) 1.78181 + 0.858075i 1.78181 + 0.858075i
\(429\) 0 0
\(430\) 1.36534 0.930874i 1.36534 0.930874i
\(431\) 0 0 −0.733052 0.680173i \(-0.761905\pi\)
0.733052 + 0.680173i \(0.238095\pi\)
\(432\) −0.181049 0.123437i −0.181049 0.123437i
\(433\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(434\) 0 0
\(435\) 0.238377 1.04440i 0.238377 1.04440i
\(436\) 0.733052 0.680173i 0.733052 0.680173i
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 −0.0747301 0.997204i \(-0.523810\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(440\) 0 0
\(441\) 1.09839 + 0.338809i 1.09839 + 0.338809i
\(442\) 0 0
\(443\) 0.0546039 + 0.728639i 0.0546039 + 0.728639i 0.955573 + 0.294755i \(0.0952381\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(444\) 0 0
\(445\) −0.722521 + 0.108903i −0.722521 + 0.108903i
\(446\) 1.32091 1.22563i 1.32091 1.22563i
\(447\) −0.645190 + 2.82676i −0.645190 + 2.82676i
\(448\) 0.826239 0.563320i 0.826239 0.563320i
\(449\) −0.425270 1.86323i −0.425270 1.86323i −0.500000 0.866025i \(-0.666667\pi\)
0.0747301 0.997204i \(-0.476190\pi\)
\(450\) 0.949729 + 0.647514i 0.949729 + 0.647514i
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 1.62349 + 0.781831i 1.62349 + 0.781831i
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 0.955573 0.294755i \(-0.0952381\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(458\) 0.455573 + 1.16078i 0.455573 + 1.16078i
\(459\) 0 0
\(460\) −0.955573 1.65510i −0.955573 1.65510i
\(461\) −0.277479 + 0.347948i −0.277479 + 0.347948i −0.900969 0.433884i \(-0.857143\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(462\) 0 0
\(463\) −1.23305 1.54620i −1.23305 1.54620i −0.733052 0.680173i \(-0.761905\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(464\) 0.266948 0.680173i 0.266948 0.680173i
\(465\) 0 0
\(466\) 0 0
\(467\) −0.365341 + 0.930874i −0.365341 + 0.930874i 0.623490 + 0.781831i \(0.285714\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(468\) 0 0
\(469\) −0.365341 + 0.930874i −0.365341 + 0.930874i
\(470\) −0.277479 + 0.347948i −0.277479 + 0.347948i
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 0.826239 0.563320i \(-0.190476\pi\)
−0.826239 + 0.563320i \(0.809524\pi\)
\(480\) 1.07473 + 0.997204i 1.07473 + 0.997204i
\(481\) 0 0
\(482\) 0.400969 + 1.75676i 0.400969 + 1.75676i
\(483\) 1.40097 2.42655i 1.40097 2.42655i
\(484\) −0.222521 + 0.974928i −0.222521 + 0.974928i
\(485\) 0 0
\(486\) −1.41734 + 0.213630i −1.41734 + 0.213630i
\(487\) −0.425270 0.131178i −0.425270 0.131178i 0.0747301 0.997204i \(-0.476190\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(488\) 0.142820 + 1.90580i 0.142820 + 1.90580i
\(489\) −1.82820 −1.82820
\(490\) −0.900969 0.433884i −0.900969 0.433884i
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) −0.181049 2.41593i −0.181049 2.41593i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) −0.645190 2.82676i −0.645190 2.82676i
\(499\) 0 0 −0.826239 0.563320i \(-0.809524\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(500\) −0.733052 0.680173i −0.733052 0.680173i
\(501\) −0.181049 + 0.123437i −0.181049 + 0.123437i
\(502\) 0 0
\(503\) −1.48883 0.716983i −1.48883 0.716983i −0.500000 0.866025i \(-0.666667\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(504\) −0.255779 + 1.12064i −0.255779 + 1.12064i
\(505\) 1.78181 0.858075i 1.78181 0.858075i
\(506\) 0 0
\(507\) −0.535628 1.36476i −0.535628 1.36476i
\(508\) 0.900969 1.56052i 0.900969 1.56052i
\(509\) −0.955573 1.65510i −0.955573 1.65510i −0.733052 0.680173i \(-0.761905\pi\)
−0.222521 0.974928i \(-0.571429\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(513\) 0 0
\(514\) 0 0
\(515\) −0.0747301 + 0.997204i −0.0747301 + 0.997204i
\(516\) −0.885113 + 2.25523i −0.885113 + 2.25523i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −0.623490 + 1.07992i −0.623490 + 1.07992i 0.365341 + 0.930874i \(0.380952\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(522\) 0.306846 + 0.781831i 0.306846 + 0.781831i
\(523\) 1.19158 0.367554i 1.19158 0.367554i 0.365341 0.930874i \(-0.380952\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(524\) 0 0
\(525\) 0.326239 1.42935i 0.326239 1.42935i
\(526\) −0.658322 0.317031i −0.658322 0.317031i
\(527\) 0 0
\(528\) 0 0
\(529\) −1.94440 1.80414i −1.94440 1.80414i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0.785286 0.728639i 0.785286 0.728639i
\(535\) 1.95557 0.294755i 1.95557 0.294755i
\(536\) −0.955573 0.294755i −0.955573 0.294755i
\(537\) 0 0
\(538\) 0.149460 0.149460
\(539\) 0 0
\(540\) −0.219124 −0.219124
\(541\) −0.109562 1.46200i −0.109562 1.46200i −0.733052 0.680173i \(-0.761905\pi\)
0.623490 0.781831i \(-0.285714\pi\)
\(542\) 0 0
\(543\) −1.44973 + 0.218511i −1.44973 + 0.218511i
\(544\) 0 0
\(545\) 0.222521 0.974928i 0.222521 0.974928i
\(546\) 0 0
\(547\) −0.425270 1.86323i −0.425270 1.86323i −0.500000 0.866025i \(-0.666667\pi\)
0.0747301 0.997204i \(-0.476190\pi\)
\(548\) 0 0
\(549\) −1.61036 1.49419i −1.61036 1.49419i
\(550\) 0 0
\(551\) 0 0
\(552\) 2.52446 + 1.21572i 2.52446 + 1.21572i
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0.365341 0.930874i 0.365341 0.930874i
\(561\) 0 0
\(562\) −0.162592 + 0.414278i −0.162592 + 0.414278i
\(563\) 0.0546039 0.728639i 0.0546039 0.728639i −0.900969 0.433884i \(-0.857143\pi\)
0.955573 0.294755i \(-0.0952381\pi\)
\(564\) 0.0487597 0.650653i 0.0487597 0.650653i
\(565\) 0 0
\(566\) −0.277479 0.347948i −0.277479 0.347948i
\(567\) 0.414101 + 0.717244i 0.414101 + 0.717244i
\(568\) 0 0
\(569\) 0.900969 + 1.56052i 0.900969 + 1.56052i 0.826239 + 0.563320i \(0.190476\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(570\) 0 0
\(571\) 0 0 −0.365341 0.930874i \(-0.619048\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) −1.48883 + 0.716983i −1.48883 + 0.716983i
\(575\) −1.72188 0.829215i −1.72188 0.829215i
\(576\) −1.13662 0.171318i −1.13662 0.171318i
\(577\) 0 0 0.826239 0.563320i \(-0.190476\pi\)
−0.826239 + 0.563320i \(0.809524\pi\)
\(578\) −0.733052 0.680173i −0.733052 0.680173i
\(579\) 0 0
\(580\) −0.162592 0.712362i −0.162592 0.712362i
\(581\) −1.63402 + 1.11406i −1.63402 + 1.11406i
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(588\) 1.44973 0.218511i 1.44973 0.218511i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 0.733052 0.680173i \(-0.238095\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0.440071 + 1.92808i 0.440071 + 1.92808i
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 0.826239 0.563320i \(-0.190476\pi\)
−0.826239 + 0.563320i \(0.809524\pi\)
\(600\) 1.44973 + 0.218511i 1.44973 + 0.218511i
\(601\) −1.12349 0.541044i −1.12349 0.541044i −0.222521 0.974928i \(-0.571429\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(602\) 1.65248 1.65248
\(603\) 1.03563 0.498732i 1.03563 0.498732i
\(604\) 0 0
\(605\) 0.365341 + 0.930874i 0.365341 + 0.930874i
\(606\) −1.44973 + 2.51100i −1.44973 + 2.51100i
\(607\) −0.365341 0.632789i −0.365341 0.632789i 0.623490 0.781831i \(-0.285714\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(608\) 0 0
\(609\) 0.785286 0.728639i 0.785286 0.728639i
\(610\) 1.19158 + 1.49419i 1.19158 + 1.49419i
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 0.0747301 0.997204i \(-0.476190\pi\)
−0.0747301 + 0.997204i \(0.523810\pi\)
\(614\) 0.0546039 0.139129i 0.0546039 0.139129i
\(615\) −1.51053 1.89415i −1.51053 1.89415i
\(616\) 0 0
\(617\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(618\) −0.733052 1.26968i −0.733052 1.26968i
\(619\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(620\) 0 0
\(621\) −0.400173 + 0.123437i −0.400173 + 0.123437i
\(622\) 0 0
\(623\) −0.658322 0.317031i −0.658322 0.317031i
\(624\) 0 0
\(625\) −0.988831 0.149042i −0.988831 0.149042i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0.419945 + 1.07000i 0.419945 + 1.07000i
\(631\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −0.134659 1.79690i −0.134659 1.79690i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0.955573 + 0.294755i 0.955573 + 0.294755i
\(641\) 1.44973 0.218511i 1.44973 0.218511i 0.623490 0.781831i \(-0.285714\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(642\) −2.12545 + 1.97213i −2.12545 + 1.97213i
\(643\) 0.400969 1.75676i 0.400969 1.75676i −0.222521 0.974928i \(-0.571429\pi\)
0.623490 0.781831i \(-0.285714\pi\)
\(644\) 0.142820 1.90580i 0.142820 1.90580i
\(645\) 0.539102 + 2.36196i 0.539102 + 2.36196i
\(646\) 0 0
\(647\) −0.109562 0.101659i −0.109562 0.101659i 0.623490 0.781831i \(-0.285714\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(648\) −0.684292 + 0.466542i −0.684292 + 0.466542i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) −1.12349 + 0.541044i −1.12349 + 0.541044i
\(653\) 0 0 0.955573 0.294755i \(-0.0952381\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(654\) 0.535628 + 1.36476i 0.535628 + 1.36476i
\(655\) 0 0
\(656\) −0.826239 1.43109i −0.826239 1.43109i
\(657\) 0 0
\(658\) −0.425270 + 0.131178i −0.425270 + 0.131178i
\(659\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(660\) 0 0
\(661\) −0.147791 + 1.97213i −0.147791 + 1.97213i 0.0747301 + 0.997204i \(0.476190\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) −1.23305 1.54620i −1.23305 1.54620i
\(665\) 0 0
\(666\) 0 0
\(667\) −0.698220 1.20935i −0.698220 1.20935i
\(668\) −0.0747301 + 0.129436i −0.0747301 + 0.129436i
\(669\) 0.965168 + 2.45921i 0.965168 + 2.45921i
\(670\) −0.955573 + 0.294755i −0.955573 + 0.294755i
\(671\) 0 0
\(672\) 0.326239 + 1.42935i 0.326239 + 1.42935i
\(673\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(674\) 0 0
\(675\) −0.181049 + 0.123437i −0.181049 + 0.123437i
\(676\) −0.733052 0.680173i −0.733052 0.680173i
\(677\) 0 0 −0.826239 0.563320i \(-0.809524\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −1.93660 + 1.79690i −1.93660 + 1.79690i
\(682\) 0 0
\(683\) 0.142820 + 0.0440542i 0.142820 + 0.0440542i 0.365341 0.930874i \(-0.380952\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −0.500000 0.866025i −0.500000 0.866025i
\(687\) −1.82820 −1.82820
\(688\) 0.123490 + 1.64786i 0.123490 + 1.64786i
\(689\) 0 0
\(690\) 2.77064 0.417607i 2.77064 0.417607i
\(691\) 0 0 0.733052 0.680173i \(-0.238095\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) −0.367711 1.61105i −0.367711 1.61105i
\(695\) 0 0
\(696\) 0.785286 + 0.728639i 0.785286 + 0.728639i
\(697\) 0 0
\(698\) −1.63402 0.246289i −1.63402 0.246289i
\(699\) 0 0
\(700\) −0.222521 0.974928i −0.222521 0.974928i
\(701\) 1.32091 0.636119i 1.32091 0.636119i 0.365341 0.930874i \(-0.380952\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) −0.326239 0.565062i −0.326239 0.565062i
\(706\) 0 0
\(707\) 1.95557 + 0.294755i 1.95557 + 0.294755i
\(708\) 0 0
\(709\) −0.722521 + 1.84095i −0.722521 + 1.84095i −0.222521 + 0.974928i \(0.571429\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0.266948 0.680173i 0.266948 0.680173i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 0.955573 0.294755i \(-0.0952381\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(720\) −1.03563 + 0.498732i −1.03563 + 0.498732i
\(721\) −0.623490 + 0.781831i −0.623490 + 0.781831i
\(722\) −0.900969 0.433884i −0.900969 0.433884i
\(723\) −2.61232 0.393744i −2.61232 0.393744i
\(724\) −0.826239 + 0.563320i −0.826239 + 0.563320i
\(725\) −0.535628 0.496990i −0.535628 0.496990i
\(726\) −1.21135 0.825886i −1.21135 0.825886i
\(727\) 0.440071 + 1.92808i 0.440071 + 1.92808i 0.365341 + 0.930874i \(0.380952\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(728\) 0 0
\(729\) 0.283323 1.24132i 0.283323 1.24132i
\(730\) 0 0
\(731\) 0 0
\(732\) −2.67746 0.825886i −2.67746 0.825886i
\(733\) 0 0 −0.0747301 0.997204i \(-0.523810\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(734\) 0.149460 0.149460
\(735\) 1.07473 0.997204i 1.07473 0.997204i
\(736\) 1.91115 1.91115
\(737\) 0 0
\(738\) 1.81507 + 0.559875i 1.81507 + 0.559875i
\(739\) 0 0 0.988831 0.149042i \(-0.0476190\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −0.0332580 0.145713i −0.0332580 0.145713i 0.955573 0.294755i \(-0.0952381\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(744\) 0 0
\(745\) 1.44973 + 1.34515i 1.44973 + 1.34515i
\(746\) 0 0
\(747\) 2.24785 + 0.338809i 2.24785 + 0.338809i
\(748\) 0 0
\(749\) 1.78181 + 0.858075i 1.78181 + 0.858075i
\(750\) 1.32091 0.636119i 1.32091 0.636119i
\(751\) 0 0 0.955573 0.294755i \(-0.0952381\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(752\) −0.162592 0.414278i −0.162592 0.414278i
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) −0.181049 0.123437i −0.181049 0.123437i
\(757\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −0.658322 + 1.67738i −0.658322 + 1.67738i 0.0747301 + 0.997204i \(0.476190\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(762\) 1.64715 + 2.06546i 1.64715 + 2.06546i
\(763\) 0.733052 0.680173i 0.733052 0.680173i
\(764\) 0 0
\(765\) 0 0
\(766\) −0.365341 + 0.632789i −0.365341 + 0.632789i
\(767\) 0 0
\(768\) −1.40097 + 0.432142i −1.40097 + 0.432142i
\(769\) 1.62349 0.781831i 1.62349 0.781831i 0.623490 0.781831i \(-0.285714\pi\)
1.00000 \(0\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0 0 0.826239 0.563320i \(-0.190476\pi\)
−0.826239 + 0.563320i \(0.809524\pi\)
\(774\) −1.39240 1.29196i −1.39240 1.29196i
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) −0.277479 + 1.21572i −0.277479 + 1.21572i
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) −0.160110 −0.160110
\(784\) 0.826239 0.563320i 0.826239 0.563320i
\(785\) 0 0
\(786\) 0 0
\(787\) 0.698220 + 0.215372i 0.698220 + 0.215372i 0.623490 0.781831i \(-0.285714\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(788\) 0 0
\(789\) 0.785286 0.728639i 0.785286 0.728639i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0.955573 0.294755i 0.955573 0.294755i
\(801\) 0.306846 + 0.781831i 0.306846 + 0.781831i
\(802\) 0.733052 1.26968i 0.733052 1.26968i
\(803\) 0 0
\(804\) 0.914101 1.14625i 0.914101 1.14625i
\(805\) −0.955573 1.65510i −0.955573 1.65510i
\(806\) 0 0
\(807\) −0.0800550 + 0.203977i −0.0800550 + 0.203977i
\(808\) −0.147791 + 1.97213i −0.147791 + 1.97213i
\(809\) −0.0747301 + 0.997204i −0.0747301 + 0.997204i 0.826239 + 0.563320i \(0.190476\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(810\) −0.302576 + 0.770951i −0.302576 + 0.770951i
\(811\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(812\) 0.266948 0.680173i 0.266948 0.680173i
\(813\) 0 0
\(814\) 0 0
\(815\) −0.623490 + 1.07992i −0.623490 + 1.07992i
\(816\) 0 0
\(817\) 0 0
\(818\) −0.134659 + 0.0648483i −0.134659 + 0.0648483i
\(819\) 0 0
\(820\) −1.48883 0.716983i −1.48883 0.716983i
\(821\) 1.78181 + 0.268565i 1.78181 + 0.268565i 0.955573 0.294755i \(-0.0952381\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(822\) 0 0
\(823\) −0.109562 0.101659i −0.109562 0.101659i 0.623490 0.781831i \(-0.285714\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(824\) −0.826239 0.563320i −0.826239 0.563320i
\(825\) 0 0
\(826\) 0 0
\(827\) 0.326239 1.42935i 0.326239 1.42935i −0.500000 0.866025i \(-0.666667\pi\)
0.826239 0.563320i \(-0.190476\pi\)
\(828\) −1.61036 + 1.49419i −1.61036 + 1.49419i
\(829\) −1.23305 + 0.185853i −1.23305 + 0.185853i −0.733052 0.680173i \(-0.761905\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(830\) −1.88980 0.582926i −1.88980 0.582926i
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0.0111692 + 0.149042i 0.0111692 + 0.149042i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(840\) 1.07473 + 0.997204i 1.07473 + 0.997204i
\(841\) 0.103718 + 0.454418i 0.103718 + 0.454418i
\(842\) −1.21135 0.825886i −1.21135 0.825886i
\(843\) −0.478300 0.443797i −0.478300 0.443797i
\(844\) 0 0
\(845\) −0.988831 0.149042i −0.988831 0.149042i
\(846\) 0.460898 + 0.221957i 0.460898 + 0.221957i
\(847\) −0.222521 + 0.974928i −0.222521 + 0.974928i
\(848\) 0 0
\(849\) 0.623490 0.192321i 0.623490 0.192321i
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(854\) 0.142820 + 1.90580i 0.142820 + 1.90580i
\(855\) 0 0
\(856\) −0.722521 + 1.84095i −0.722521 + 1.84095i
\(857\) 0 0 0.0747301 0.997204i \(-0.476190\pi\)
−0.0747301 + 0.997204i \(0.523810\pi\)
\(858\) 0 0
\(859\) 0 0 0.365341 0.930874i \(-0.380952\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(860\) 1.03030 + 1.29196i 1.03030 + 1.29196i
\(861\) −0.181049 2.41593i −0.181049 2.41593i
\(862\) 0 0
\(863\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(864\) 0.109562 0.189767i 0.109562 0.189767i
\(865\) 0 0
\(866\) 0 0
\(867\) 1.32091 0.636119i 1.32091 0.636119i
\(868\) 0 0
\(869\) 0 0
\(870\) 1.05929 + 0.159662i 1.05929 + 0.159662i
\(871\) 0 0
\(872\) 0.733052 + 0.680173i 0.733052 + 0.680173i
\(873\) 0 0
\(874\) 0 0
\(875\) −0.733052 0.680173i −0.733052 0.680173i
\(876\) 0 0
\(877\) 0 0 0.733052 0.680173i \(-0.238095\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(882\) −0.255779 + 1.12064i −0.255779 + 1.12064i
\(883\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) −0.722521 + 0.108903i −0.722521 + 0.108903i
\(887\) −1.40097 + 1.29991i −1.40097 + 1.29991i −0.500000 + 0.866025i \(0.666667\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(888\) 0 0
\(889\) 0.900969 1.56052i 0.900969 1.56052i
\(890\) −0.162592 0.712362i −0.162592 0.712362i
\(891\) 0 0
\(892\) 1.32091 + 1.22563i 1.32091 + 1.22563i
\(893\) 0 0
\(894\) −2.86707 0.432142i −2.86707 0.432142i
\(895\) 0 0
\(896\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(897\) 0 0
\(898\) 1.82624 0.563320i 1.82624 0.563320i
\(899\) 0 0
\(900\) −0.574730 + 0.995462i −0.574730 + 0.995462i
\(901\) 0 0
\(902\) 0 0
\(903\) −0.885113 + 2.25523i −0.885113 + 2.25523i
\(904\) 0 0
\(905\) −0.365341 + 0.930874i −0.365341 + 0.930874i
\(906\) 0 0
\(907\) −0.109562 + 1.46200i −0.109562 + 1.46200i 0.623490 + 0.781831i \(0.285714\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(908\) −0.658322 + 1.67738i −0.658322 + 1.67738i
\(909\) −1.41734 1.77729i −1.41734 1.77729i
\(910\) 0 0
\(911\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) −2.67746 + 0.825886i −2.67746 + 0.825886i
\(916\) −1.12349 + 0.541044i −1.12349 + 0.541044i
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 −0.988831 0.149042i \(-0.952381\pi\)
0.988831 + 0.149042i \(0.0476190\pi\)
\(920\) 1.57906 1.07659i 1.57906 1.07659i
\(921\) 0.160629 + 0.149042i 0.160629 + 0.149042i
\(922\) −0.367711 0.250701i −0.367711 0.250701i
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) 1.44973 1.34515i 1.44973 1.34515i
\(927\) 1.13662 0.171318i 1.13662 0.171318i
\(928\) 0.698220 + 0.215372i 0.698220 + 0.215372i
\(929\) 0.142820 + 1.90580i 0.142820 + 1.90580i 0.365341 + 0.930874i \(0.380952\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 0 0
\(934\) −0.955573 0.294755i −0.955573 0.294755i
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(938\) −0.955573 0.294755i −0.955573 0.294755i
\(939\) 0 0
\(940\) −0.367711 0.250701i −0.367711 0.250701i
\(941\) −0.914101 0.848162i −0.914101 0.848162i 0.0747301 0.997204i \(-0.476190\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(942\) 0 0
\(943\) −3.12285 0.470694i −3.12285 0.470694i
\(944\) 0 0
\(945\) −0.219124 −0.219124
\(946\) 0 0
\(947\) 0.142820 0.0440542i 0.142820 0.0440542i −0.222521 0.974928i \(-0.571429\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) −0.914101 + 1.14625i −0.914101 + 1.14625i
\(961\) −0.500000 0.866025i −0.500000 0.866025i
\(962\) 0 0
\(963\) −0.830509 2.11610i −0.830509 2.11610i
\(964\) −1.72188 + 0.531130i −1.72188 + 0.531130i
\(965\) 0 0
\(966\) 2.52446 + 1.21572i 2.52446 + 1.21572i
\(967\) 1.32091 + 0.636119i 1.32091 + 0.636119i 0.955573 0.294755i \(-0.0952381\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(968\) −0.988831 0.149042i −0.988831 0.149042i
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 −0.826239 0.563320i \(-0.809524\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(972\) −0.318951 1.39742i −0.318951 1.39742i
\(973\) 0 0
\(974\) 0.0990311 0.433884i 0.0990311 0.433884i
\(975\) 0 0
\(976\) −1.88980 + 0.284841i −1.88980 + 0.284841i
\(977\) 0 0 −0.955573 0.294755i \(-0.904762\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(978\) −0.136622 1.82309i −0.136622 1.82309i
\(979\) 0 0
\(980\) 0.365341 0.930874i 0.365341 0.930874i
\(981\) −1.14946 −1.14946
\(982\) 0 0
\(983\) 1.82624 + 0.563320i 1.82624 + 0.563320i 1.00000 \(0\)
0.826239 + 0.563320i \(0.190476\pi\)
\(984\) 2.39564 0.361085i 2.39564 0.361085i
\(985\) 0 0
\(986\) 0 0
\(987\) 0.0487597 0.650653i 0.0487597 0.650653i
\(988\) 0 0
\(989\) 2.60937 + 1.77904i 2.60937 + 1.77904i
\(990\) 0 0
\(991\) 0 0 0.826239 0.563320i \(-0.190476\pi\)
−0.826239 + 0.563320i \(0.809524\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 2.77064 0.854630i 2.77064 0.854630i
\(997\) 0 0 −0.365341 0.930874i \(-0.619048\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(998\) 0 0
\(999\) 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 980.1.bq.b.179.1 yes 12
4.3 odd 2 980.1.bq.a.179.1 12
5.4 even 2 980.1.bq.a.179.1 12
20.19 odd 2 CM 980.1.bq.b.179.1 yes 12
49.23 even 21 inner 980.1.bq.b.219.1 yes 12
196.23 odd 42 980.1.bq.a.219.1 yes 12
245.219 even 42 980.1.bq.a.219.1 yes 12
980.219 odd 42 inner 980.1.bq.b.219.1 yes 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
980.1.bq.a.179.1 12 4.3 odd 2
980.1.bq.a.179.1 12 5.4 even 2
980.1.bq.a.219.1 yes 12 196.23 odd 42
980.1.bq.a.219.1 yes 12 245.219 even 42
980.1.bq.b.179.1 yes 12 1.1 even 1 trivial
980.1.bq.b.179.1 yes 12 20.19 odd 2 CM
980.1.bq.b.219.1 yes 12 49.23 even 21 inner
980.1.bq.b.219.1 yes 12 980.219 odd 42 inner