Properties

Label 980.1.bq.a.39.1
Level $980$
Weight $1$
Character 980.39
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 39.1
Root \(-0.733052 + 0.680173i\) of defining polynomial
Character \(\chi\) \(=\) 980.39
Dual form 980.1.bq.a.779.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.988831 + 0.149042i) q^{2} +(-0.123490 + 0.0841939i) q^{3} +(0.955573 + 0.294755i) q^{4} +(0.0747301 + 0.997204i) q^{5} +(-0.134659 + 0.0648483i) q^{6} +(-0.955573 - 0.294755i) q^{7} +(0.900969 + 0.433884i) q^{8} +(-0.357180 + 0.910080i) q^{9} +O(q^{10})\) \(q+(0.988831 + 0.149042i) q^{2} +(-0.123490 + 0.0841939i) q^{3} +(0.955573 + 0.294755i) q^{4} +(0.0747301 + 0.997204i) q^{5} +(-0.134659 + 0.0648483i) q^{6} +(-0.955573 - 0.294755i) q^{7} +(0.900969 + 0.433884i) q^{8} +(-0.357180 + 0.910080i) q^{9} +(-0.0747301 + 0.997204i) q^{10} +(-0.142820 + 0.0440542i) q^{12} +(-0.900969 - 0.433884i) q^{14} +(-0.0931869 - 0.116853i) q^{15} +(0.826239 + 0.563320i) q^{16} +(-0.488831 + 0.846680i) q^{18} +(-0.222521 + 0.974928i) q^{20} +(0.142820 - 0.0440542i) q^{21} +(1.21135 - 1.12397i) q^{23} +(-0.147791 + 0.0222759i) q^{24} +(-0.988831 + 0.149042i) q^{25} +(-0.0657731 - 0.288171i) q^{27} +(-0.826239 - 0.563320i) q^{28} +(0.326239 - 1.42935i) q^{29} +(-0.0747301 - 0.129436i) q^{30} +(0.733052 + 0.680173i) q^{32} +(0.222521 - 0.974928i) q^{35} +(-0.609562 + 0.764367i) q^{36} +(-0.365341 + 0.930874i) q^{40} +(-0.658322 - 0.317031i) q^{41} +(0.147791 - 0.0222759i) q^{42} +(0.658322 - 0.317031i) q^{43} +(-0.934227 - 0.288171i) q^{45} +(1.36534 - 0.930874i) q^{46} +(-1.78181 - 0.268565i) q^{47} -0.149460 q^{48} +(0.826239 + 0.563320i) q^{49} -1.00000 q^{50} +(-0.0220888 - 0.294755i) q^{54} +(-0.733052 - 0.680173i) q^{56} +(0.535628 - 1.36476i) q^{58} +(-0.0546039 - 0.139129i) q^{60} +(1.57906 - 0.487076i) q^{61} +(0.609562 - 0.764367i) q^{63} +(0.623490 + 0.781831i) q^{64} +(-0.500000 + 0.866025i) q^{67} +(-0.0549581 + 0.240787i) q^{69} +(0.365341 - 0.930874i) q^{70} +(-0.716677 + 0.664979i) q^{72} +(0.109562 - 0.101659i) q^{75} +(-0.500000 + 0.866025i) q^{80} +(-0.684292 - 0.634930i) q^{81} +(-0.603718 - 0.411608i) q^{82} +(-1.19158 - 1.49419i) q^{83} +0.149460 q^{84} +(0.698220 - 0.215372i) q^{86} +(0.0800550 + 0.203977i) q^{87} +(-0.535628 + 1.36476i) q^{89} +(-0.880843 - 0.424191i) q^{90} +(1.48883 - 0.716983i) q^{92} +(-1.72188 - 0.531130i) q^{94} +(-0.147791 - 0.0222759i) q^{96} +(0.733052 + 0.680173i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - q^{2} + 8 q^{3} + q^{4} + q^{5} - 5 q^{6} - q^{7} + 2 q^{8} - 7 q^{9}+O(q^{10}) \) 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 \(\left(\mathbb{Z}/980\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(197\) \(491\)
\(\chi(n)\) \(e\left(\frac{17}{21}\right)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.988831 + 0.149042i 0.988831 + 0.149042i
\(3\) −0.123490 + 0.0841939i −0.123490 + 0.0841939i −0.623490 0.781831i \(-0.714286\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(4\) 0.955573 + 0.294755i 0.955573 + 0.294755i
\(5\) 0.0747301 + 0.997204i 0.0747301 + 0.997204i
\(6\) −0.134659 + 0.0648483i −0.134659 + 0.0648483i
\(7\) −0.955573 0.294755i −0.955573 0.294755i
\(8\) 0.900969 + 0.433884i 0.900969 + 0.433884i
\(9\) −0.357180 + 0.910080i −0.357180 + 0.910080i
\(10\) −0.0747301 + 0.997204i −0.0747301 + 0.997204i
\(11\) 0 0 −0.365341 0.930874i \(-0.619048\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(12\) −0.142820 + 0.0440542i −0.142820 + 0.0440542i
\(13\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(14\) −0.900969 0.433884i −0.900969 0.433884i
\(15\) −0.0931869 0.116853i −0.0931869 0.116853i
\(16\) 0.826239 + 0.563320i 0.826239 + 0.563320i
\(17\) 0 0 −0.733052 0.680173i \(-0.761905\pi\)
0.733052 + 0.680173i \(0.238095\pi\)
\(18\) −0.488831 + 0.846680i −0.488831 + 0.846680i
\(19\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(20\) −0.222521 + 0.974928i −0.222521 + 0.974928i
\(21\) 0.142820 0.0440542i 0.142820 0.0440542i
\(22\) 0 0
\(23\) 1.21135 1.12397i 1.21135 1.12397i 0.222521 0.974928i \(-0.428571\pi\)
0.988831 0.149042i \(-0.0476190\pi\)
\(24\) −0.147791 + 0.0222759i −0.147791 + 0.0222759i
\(25\) −0.988831 + 0.149042i −0.988831 + 0.149042i
\(26\) 0 0
\(27\) −0.0657731 0.288171i −0.0657731 0.288171i
\(28\) −0.826239 0.563320i −0.826239 0.563320i
\(29\) 0.326239 1.42935i 0.326239 1.42935i −0.500000 0.866025i \(-0.666667\pi\)
0.826239 0.563320i \(-0.190476\pi\)
\(30\) −0.0747301 0.129436i −0.0747301 0.129436i
\(31\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(32\) 0.733052 + 0.680173i 0.733052 + 0.680173i
\(33\) 0 0
\(34\) 0 0
\(35\) 0.222521 0.974928i 0.222521 0.974928i
\(36\) −0.609562 + 0.764367i −0.609562 + 0.764367i
\(37\) 0 0 0.955573 0.294755i \(-0.0952381\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) −0.365341 + 0.930874i −0.365341 + 0.930874i
\(41\) −0.658322 0.317031i −0.658322 0.317031i 0.0747301 0.997204i \(-0.476190\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(42\) 0.147791 0.0222759i 0.147791 0.0222759i
\(43\) 0.658322 0.317031i 0.658322 0.317031i −0.0747301 0.997204i \(-0.523810\pi\)
0.733052 + 0.680173i \(0.238095\pi\)
\(44\) 0 0
\(45\) −0.934227 0.288171i −0.934227 0.288171i
\(46\) 1.36534 0.930874i 1.36534 0.930874i
\(47\) −1.78181 0.268565i −1.78181 0.268565i −0.826239 0.563320i \(-0.809524\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(48\) −0.149460 −0.149460
\(49\) 0.826239 + 0.563320i 0.826239 + 0.563320i
\(50\) −1.00000 −1.00000
\(51\) 0 0
\(52\) 0 0
\(53\) 0 0 −0.955573 0.294755i \(-0.904762\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(54\) −0.0220888 0.294755i −0.0220888 0.294755i
\(55\) 0 0
\(56\) −0.733052 0.680173i −0.733052 0.680173i
\(57\) 0 0
\(58\) 0.535628 1.36476i 0.535628 1.36476i
\(59\) 0 0 0.0747301 0.997204i \(-0.476190\pi\)
−0.0747301 + 0.997204i \(0.523810\pi\)
\(60\) −0.0546039 0.139129i −0.0546039 0.139129i
\(61\) 1.57906 0.487076i 1.57906 0.487076i 0.623490 0.781831i \(-0.285714\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(62\) 0 0
\(63\) 0.609562 0.764367i 0.609562 0.764367i
\(64\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(65\) 0 0
\(66\) 0 0
\(67\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(68\) 0 0
\(69\) −0.0549581 + 0.240787i −0.0549581 + 0.240787i
\(70\) 0.365341 0.930874i 0.365341 0.930874i
\(71\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(72\) −0.716677 + 0.664979i −0.716677 + 0.664979i
\(73\) 0 0 0.988831 0.149042i \(-0.0476190\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(74\) 0 0
\(75\) 0.109562 0.101659i 0.109562 0.101659i
\(76\) 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
\(81\) −0.684292 0.634930i −0.684292 0.634930i
\(82\) −0.603718 0.411608i −0.603718 0.411608i
\(83\) −1.19158 1.49419i −1.19158 1.49419i −0.826239 0.563320i \(-0.809524\pi\)
−0.365341 0.930874i \(-0.619048\pi\)
\(84\) 0.149460 0.149460
\(85\) 0 0
\(86\) 0.698220 0.215372i 0.698220 0.215372i
\(87\) 0.0800550 + 0.203977i 0.0800550 + 0.203977i
\(88\) 0 0
\(89\) −0.535628 + 1.36476i −0.535628 + 1.36476i 0.365341 + 0.930874i \(0.380952\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(90\) −0.880843 0.424191i −0.880843 0.424191i
\(91\) 0 0
\(92\) 1.48883 0.716983i 1.48883 0.716983i
\(93\) 0 0
\(94\) −1.72188 0.531130i −1.72188 0.531130i
\(95\) 0 0
\(96\) −0.147791 0.0222759i −0.147791 0.0222759i
\(97\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(98\) 0.733052 + 0.680173i 0.733052 + 0.680173i
\(99\) 0 0
\(100\) −0.988831 0.149042i −0.988831 0.149042i
\(101\) 1.57906 1.07659i 1.57906 1.07659i 0.623490 0.781831i \(-0.285714\pi\)
0.955573 0.294755i \(-0.0952381\pi\)
\(102\) 0 0
\(103\) 0.0747301 + 0.997204i 0.0747301 + 0.997204i 0.900969 + 0.433884i \(0.142857\pi\)
−0.826239 + 0.563320i \(0.809524\pi\)
\(104\) 0 0
\(105\) 0.0546039 + 0.139129i 0.0546039 + 0.139129i
\(106\) 0 0
\(107\) −0.698220 + 1.77904i −0.698220 + 1.77904i −0.0747301 + 0.997204i \(0.523810\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(108\) 0.0220888 0.294755i 0.0220888 0.294755i
\(109\) −0.365341 0.930874i −0.365341 0.930874i −0.988831 0.149042i \(-0.952381\pi\)
0.623490 0.781831i \(-0.285714\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −0.623490 0.781831i −0.623490 0.781831i
\(113\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(114\) 0 0
\(115\) 1.21135 + 1.12397i 1.21135 + 1.12397i
\(116\) 0.733052 1.26968i 0.733052 1.26968i
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) −0.0332580 0.145713i −0.0332580 0.145713i
\(121\) −0.733052 + 0.680173i −0.733052 + 0.680173i
\(122\) 1.63402 0.246289i 1.63402 0.246289i
\(123\) 0.107988 0.0162766i 0.107988 0.0162766i
\(124\) 0 0
\(125\) −0.222521 0.974928i −0.222521 0.974928i
\(126\) 0.716677 0.664979i 0.716677 0.664979i
\(127\) 0.277479 1.21572i 0.277479 1.21572i −0.623490 0.781831i \(-0.714286\pi\)
0.900969 0.433884i \(-0.142857\pi\)
\(128\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(129\) −0.0546039 + 0.0945768i −0.0546039 + 0.0945768i
\(130\) 0 0
\(131\) 0 0 −0.826239 0.563320i \(-0.809524\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −0.623490 + 0.781831i −0.623490 + 0.781831i
\(135\) 0.282450 0.0871242i 0.282450 0.0871242i
\(136\) 0 0
\(137\) 0 0 0.0747301 0.997204i \(-0.476190\pi\)
−0.0747301 + 0.997204i \(0.523810\pi\)
\(138\) −0.0902318 + 0.229907i −0.0902318 + 0.229907i
\(139\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(140\) 0.500000 0.866025i 0.500000 0.866025i
\(141\) 0.242647 0.116853i 0.242647 0.116853i
\(142\) 0 0
\(143\) 0 0
\(144\) −0.807782 + 0.550736i −0.807782 + 0.550736i
\(145\) 1.44973 + 0.218511i 1.44973 + 0.218511i
\(146\) 0 0
\(147\) −0.149460 −0.149460
\(148\) 0 0
\(149\) −1.88980 0.284841i −1.88980 0.284841i −0.900969 0.433884i \(-0.857143\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(150\) 0.123490 0.0841939i 0.123490 0.0841939i
\(151\) 0 0 −0.955573 0.294755i \(-0.904762\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 0.0747301 0.997204i \(-0.476190\pi\)
−0.0747301 + 0.997204i \(0.523810\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) −0.623490 + 0.781831i −0.623490 + 0.781831i
\(161\) −1.48883 + 0.716983i −1.48883 + 0.716983i
\(162\) −0.582018 0.729827i −0.582018 0.729827i
\(163\) 0.367711 + 0.250701i 0.367711 + 0.250701i 0.733052 0.680173i \(-0.238095\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(164\) −0.535628 0.496990i −0.535628 0.496990i
\(165\) 0 0
\(166\) −0.955573 1.65510i −0.955573 1.65510i
\(167\) −0.440071 + 1.92808i −0.440071 + 1.92808i −0.0747301 + 0.997204i \(0.523810\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(168\) 0.147791 + 0.0222759i 0.147791 + 0.0222759i
\(169\) −0.222521 0.974928i −0.222521 0.974928i
\(170\) 0 0
\(171\) 0 0
\(172\) 0.722521 0.108903i 0.722521 0.108903i
\(173\) 0 0 0.733052 0.680173i \(-0.238095\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(174\) 0.0487597 + 0.213630i 0.0487597 + 0.213630i
\(175\) 0.988831 + 0.149042i 0.988831 + 0.149042i
\(176\) 0 0
\(177\) 0 0
\(178\) −0.733052 + 1.26968i −0.733052 + 1.26968i
\(179\) 0 0 −0.733052 0.680173i \(-0.761905\pi\)
0.733052 + 0.680173i \(0.238095\pi\)
\(180\) −0.807782 0.550736i −0.807782 0.550736i
\(181\) −0.623490 0.781831i −0.623490 0.781831i 0.365341 0.930874i \(-0.380952\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(182\) 0 0
\(183\) −0.153989 + 0.193096i −0.153989 + 0.193096i
\(184\) 1.57906 0.487076i 1.57906 0.487076i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) −1.62349 0.781831i −1.62349 0.781831i
\(189\) −0.0220888 + 0.294755i −0.0220888 + 0.294755i
\(190\) 0 0
\(191\) 0 0 −0.0747301 0.997204i \(-0.523810\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(192\) −0.142820 0.0440542i −0.142820 0.0440542i
\(193\) 0 0 0.826239 0.563320i \(-0.190476\pi\)
−0.826239 + 0.563320i \(0.809524\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 0 0
\(199\) 0 0 0.826239 0.563320i \(-0.190476\pi\)
−0.826239 + 0.563320i \(0.809524\pi\)
\(200\) −0.955573 0.294755i −0.955573 0.294755i
\(201\) −0.0111692 0.149042i −0.0111692 0.149042i
\(202\) 1.72188 0.829215i 1.72188 0.829215i
\(203\) −0.733052 + 1.26968i −0.733052 + 1.26968i
\(204\) 0 0
\(205\) 0.266948 0.680173i 0.266948 0.680173i
\(206\) −0.0747301 + 0.997204i −0.0747301 + 0.997204i
\(207\) 0.590232 + 1.50389i 0.590232 + 1.50389i
\(208\) 0 0
\(209\) 0 0
\(210\) 0.0332580 + 0.145713i 0.0332580 + 0.145713i
\(211\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) −0.955573 + 1.65510i −0.955573 + 1.65510i
\(215\) 0.365341 + 0.632789i 0.365341 + 0.632789i
\(216\) 0.0657731 0.288171i 0.0657731 0.288171i
\(217\) 0 0
\(218\) −0.222521 0.974928i −0.222521 0.974928i
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0.277479 + 1.21572i 0.277479 + 1.21572i 0.900969 + 0.433884i \(0.142857\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(224\) −0.500000 0.866025i −0.500000 0.866025i
\(225\) 0.217550 0.953150i 0.217550 0.953150i
\(226\) 0 0
\(227\) 0.623490 1.07992i 0.623490 1.07992i −0.365341 0.930874i \(-0.619048\pi\)
0.988831 0.149042i \(-0.0476190\pi\)
\(228\) 0 0
\(229\) −0.367711 0.250701i −0.367711 0.250701i 0.365341 0.930874i \(-0.380952\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(230\) 1.03030 + 1.29196i 1.03030 + 1.29196i
\(231\) 0 0
\(232\) 0.914101 1.14625i 0.914101 1.14625i
\(233\) 0 0 0.955573 0.294755i \(-0.0952381\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(234\) 0 0
\(235\) 0.134659 1.79690i 0.134659 1.79690i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(240\) −0.0111692 0.149042i −0.0111692 0.149042i
\(241\) 1.19158 + 0.367554i 1.19158 + 0.367554i 0.826239 0.563320i \(-0.190476\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(242\) −0.826239 + 0.563320i −0.826239 + 0.563320i
\(243\) 0.430241 + 0.0648483i 0.430241 + 0.0648483i
\(244\) 1.65248 1.65248
\(245\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(246\) 0.109208 0.109208
\(247\) 0 0
\(248\) 0 0
\(249\) 0.272950 + 0.0841939i 0.272950 + 0.0841939i
\(250\) −0.0747301 0.997204i −0.0747301 0.997204i
\(251\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(252\) 0.807782 0.550736i 0.807782 0.550736i
\(253\) 0 0
\(254\) 0.455573 1.16078i 0.455573 1.16078i
\(255\) 0 0
\(256\) 0.365341 + 0.930874i 0.365341 + 0.930874i
\(257\) 0 0 0.955573 0.294755i \(-0.0952381\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(258\) −0.0680900 + 0.0853822i −0.0680900 + 0.0853822i
\(259\) 0 0
\(260\) 0 0
\(261\) 1.18429 + 0.807437i 1.18429 + 0.807437i
\(262\) 0 0
\(263\) −0.733052 + 1.26968i −0.733052 + 1.26968i 0.222521 + 0.974928i \(0.428571\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −0.0487597 0.213630i −0.0487597 0.213630i
\(268\) −0.733052 + 0.680173i −0.733052 + 0.680173i
\(269\) 1.95557 0.294755i 1.95557 0.294755i 0.955573 0.294755i \(-0.0952381\pi\)
1.00000 \(0\)
\(270\) 0.292280 0.0440542i 0.292280 0.0440542i
\(271\) 0 0 0.733052 0.680173i \(-0.238095\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) −0.123490 + 0.213891i −0.123490 + 0.213891i
\(277\) 0 0 −0.733052 0.680173i \(-0.761905\pi\)
0.733052 + 0.680173i \(0.238095\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0.623490 0.781831i 0.623490 0.781831i
\(281\) −1.12349 + 1.40881i −1.12349 + 1.40881i −0.222521 + 0.974928i \(0.571429\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(282\) 0.257353 0.0793829i 0.257353 0.0793829i
\(283\) 0.658322 + 1.67738i 0.658322 + 1.67738i 0.733052 + 0.680173i \(0.238095\pi\)
−0.0747301 + 0.997204i \(0.523810\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0.535628 + 0.496990i 0.535628 + 0.496990i
\(288\) −0.880843 + 0.424191i −0.880843 + 0.424191i
\(289\) 0.0747301 + 0.997204i 0.0747301 + 0.997204i
\(290\) 1.40097 + 0.432142i 1.40097 + 0.432142i
\(291\) 0 0
\(292\) 0 0
\(293\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(294\) −0.147791 0.0222759i −0.147791 0.0222759i
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) −1.82624 0.563320i −1.82624 0.563320i
\(299\) 0 0
\(300\) 0.134659 0.0648483i 0.134659 0.0648483i
\(301\) −0.722521 + 0.108903i −0.722521 + 0.108903i
\(302\) 0 0
\(303\) −0.104356 + 0.265895i −0.104356 + 0.265895i
\(304\) 0 0
\(305\) 0.603718 + 1.53825i 0.603718 + 1.53825i
\(306\) 0 0
\(307\) 1.23305 1.54620i 1.23305 1.54620i 0.500000 0.866025i \(-0.333333\pi\)
0.733052 0.680173i \(-0.238095\pi\)
\(308\) 0 0
\(309\) −0.0931869 0.116853i −0.0931869 0.116853i
\(310\) 0 0
\(311\) 0 0 −0.733052 0.680173i \(-0.761905\pi\)
0.733052 + 0.680173i \(0.238095\pi\)
\(312\) 0 0
\(313\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(314\) 0 0
\(315\) 0.807782 + 0.550736i 0.807782 + 0.550736i
\(316\) 0 0
\(317\) 0 0 0.733052 0.680173i \(-0.238095\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −0.733052 + 0.680173i −0.733052 + 0.680173i
\(321\) −0.0635609 0.278479i −0.0635609 0.278479i
\(322\) −1.57906 + 0.487076i −1.57906 + 0.487076i
\(323\) 0 0
\(324\) −0.466742 0.808421i −0.466742 0.808421i
\(325\) 0 0
\(326\) 0.326239 + 0.302705i 0.326239 + 0.302705i
\(327\) 0.123490 + 0.0841939i 0.123490 + 0.0841939i
\(328\) −0.455573 0.571270i −0.455573 0.571270i
\(329\) 1.62349 + 0.781831i 1.62349 + 0.781831i
\(330\) 0 0
\(331\) 0 0 0.955573 0.294755i \(-0.0952381\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(332\) −0.698220 1.77904i −0.698220 1.77904i
\(333\) 0 0
\(334\) −0.722521 + 1.84095i −0.722521 + 1.84095i
\(335\) −0.900969 0.433884i −0.900969 0.433884i
\(336\) 0.142820 + 0.0440542i 0.142820 + 0.0440542i
\(337\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(338\) −0.0747301 0.997204i −0.0747301 0.997204i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −0.623490 0.781831i −0.623490 0.781831i
\(344\) 0.730682 0.730682
\(345\) −0.244221 0.0368104i −0.244221 0.0368104i
\(346\) 0 0
\(347\) −0.698220 0.215372i −0.698220 0.215372i −0.0747301 0.997204i \(-0.523810\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(348\) 0.0163752 + 0.218511i 0.0163752 + 0.218511i
\(349\) −0.658322 + 0.317031i −0.658322 + 0.317031i −0.733052 0.680173i \(-0.761905\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(350\) 0.955573 + 0.294755i 0.955573 + 0.294755i
\(351\) 0 0
\(352\) 0 0
\(353\) 0 0 0.0747301 0.997204i \(-0.476190\pi\)
−0.0747301 + 0.997204i \(0.523810\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −0.914101 + 1.14625i −0.914101 + 1.14625i
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 −0.826239 0.563320i \(-0.809524\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(360\) −0.716677 0.664979i −0.716677 0.664979i
\(361\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(362\) −0.500000 0.866025i −0.500000 0.866025i
\(363\) 0.0332580 0.145713i 0.0332580 0.145713i
\(364\) 0 0
\(365\) 0 0
\(366\) −0.181049 + 0.167989i −0.181049 + 0.167989i
\(367\) −1.95557 + 0.294755i −1.95557 + 0.294755i −0.955573 + 0.294755i \(0.904762\pi\)
−1.00000 \(1.00000\pi\)
\(368\) 1.63402 0.246289i 1.63402 0.246289i
\(369\) 0.523663 0.485888i 0.523663 0.485888i
\(370\) 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
\(375\) 0.109562 + 0.101659i 0.109562 + 0.101659i
\(376\) −1.48883 1.01507i −1.48883 1.01507i
\(377\) 0 0
\(378\) −0.0657731 + 0.288171i −0.0657731 + 0.288171i
\(379\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(380\) 0 0
\(381\) 0.0680900 + 0.173490i 0.0680900 + 0.173490i
\(382\) 0 0
\(383\) 0.535628 1.36476i 0.535628 1.36476i −0.365341 0.930874i \(-0.619048\pi\)
0.900969 0.433884i \(-0.142857\pi\)
\(384\) −0.134659 0.0648483i −0.134659 0.0648483i
\(385\) 0 0
\(386\) 0 0
\(387\) 0.0533842 + 0.712362i 0.0533842 + 0.712362i
\(388\) 0 0
\(389\) −0.367711 + 0.250701i −0.367711 + 0.250701i −0.733052 0.680173i \(-0.761905\pi\)
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 −0.0747301 0.997204i \(-0.523810\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −0.900969 0.433884i −0.900969 0.433884i
\(401\) 0.0546039 0.139129i 0.0546039 0.139129i −0.900969 0.433884i \(-0.857143\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(402\) 0.0111692 0.149042i 0.0111692 0.149042i
\(403\) 0 0
\(404\) 1.82624 0.563320i 1.82624 0.563320i
\(405\) 0.582018 0.729827i 0.582018 0.729827i
\(406\) −0.914101 + 1.14625i −0.914101 + 1.14625i
\(407\) 0 0
\(408\) 0 0
\(409\) 1.44973 + 1.34515i 1.44973 + 1.34515i 0.826239 + 0.563320i \(0.190476\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(410\) 0.365341 0.632789i 0.365341 0.632789i
\(411\) 0 0
\(412\) −0.222521 + 0.974928i −0.222521 + 0.974928i
\(413\) 0 0
\(414\) 0.359497 + 1.57506i 0.359497 + 1.57506i
\(415\) 1.40097 1.29991i 1.40097 1.29991i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(420\) 0.0111692 + 0.149042i 0.0111692 + 0.149042i
\(421\) −0.0332580 + 0.145713i −0.0332580 + 0.145713i −0.988831 0.149042i \(-0.952381\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(422\) 0 0
\(423\) 0.880843 1.52566i 0.880843 1.52566i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −1.65248 −1.65248
\(428\) −1.19158 + 1.49419i −1.19158 + 1.49419i
\(429\) 0 0
\(430\) 0.266948 + 0.680173i 0.266948 + 0.680173i
\(431\) 0 0 0.0747301 0.997204i \(-0.476190\pi\)
−0.0747301 + 0.997204i \(0.523810\pi\)
\(432\) 0.107988 0.275149i 0.107988 0.275149i
\(433\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(434\) 0 0
\(435\) −0.197424 + 0.0950744i −0.197424 + 0.0950744i
\(436\) −0.0747301 0.997204i −0.0747301 0.997204i
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 −0.988831 0.149042i \(-0.952381\pi\)
0.988831 + 0.149042i \(0.0476190\pi\)
\(440\) 0 0
\(441\) −0.807782 + 0.550736i −0.807782 + 0.550736i
\(442\) 0 0
\(443\) −1.44973 0.218511i −1.44973 0.218511i −0.623490 0.781831i \(-0.714286\pi\)
−0.826239 + 0.563320i \(0.809524\pi\)
\(444\) 0 0
\(445\) −1.40097 0.432142i −1.40097 0.432142i
\(446\) 0.0931869 + 1.24349i 0.0931869 + 1.24349i
\(447\) 0.257353 0.123935i 0.257353 0.123935i
\(448\) −0.365341 0.930874i −0.365341 0.930874i
\(449\) −1.48883 0.716983i −1.48883 0.716983i −0.500000 0.866025i \(-0.666667\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(450\) 0.357180 0.910080i 0.357180 0.910080i
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0.777479 0.974928i 0.777479 0.974928i
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 −0.826239 0.563320i \(-0.809524\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(458\) −0.326239 0.302705i −0.326239 0.302705i
\(459\) 0 0
\(460\) 0.826239 + 1.43109i 0.826239 + 1.43109i
\(461\) 0.400969 1.75676i 0.400969 1.75676i −0.222521 0.974928i \(-0.571429\pi\)
0.623490 0.781831i \(-0.285714\pi\)
\(462\) 0 0
\(463\) 0.425270 + 1.86323i 0.425270 + 1.86323i 0.500000 + 0.866025i \(0.333333\pi\)
−0.0747301 + 0.997204i \(0.523810\pi\)
\(464\) 1.07473 0.997204i 1.07473 0.997204i
\(465\) 0 0
\(466\) 0 0
\(467\) −0.733052 + 0.680173i −0.733052 + 0.680173i −0.955573 0.294755i \(-0.904762\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(468\) 0 0
\(469\) 0.733052 0.680173i 0.733052 0.680173i
\(470\) 0.400969 1.75676i 0.400969 1.75676i
\(471\) 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 −0.365341 0.930874i \(-0.619048\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(480\) 0.0111692 0.149042i 0.0111692 0.149042i
\(481\) 0 0
\(482\) 1.12349 + 0.541044i 1.12349 + 0.541044i
\(483\) 0.123490 0.213891i 0.123490 0.213891i
\(484\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(485\) 0 0
\(486\) 0.415770 + 0.128248i 0.415770 + 0.128248i
\(487\) 1.48883 1.01507i 1.48883 1.01507i 0.500000 0.866025i \(-0.333333\pi\)
0.988831 0.149042i \(-0.0476190\pi\)
\(488\) 1.63402 + 0.246289i 1.63402 + 0.246289i
\(489\) −0.0665160 −0.0665160
\(490\) −0.623490 + 0.781831i −0.623490 + 0.781831i
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0.107988 + 0.0162766i 0.107988 + 0.0162766i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0.257353 + 0.123935i 0.257353 + 0.123935i
\(499\) 0 0 0.365341 0.930874i \(-0.380952\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(500\) 0.0747301 0.997204i 0.0747301 0.997204i
\(501\) −0.107988 0.275149i −0.107988 0.275149i
\(502\) 0 0
\(503\) −0.455573 + 0.571270i −0.455573 + 0.571270i −0.955573 0.294755i \(-0.904762\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(504\) 0.880843 0.424191i 0.880843 0.424191i
\(505\) 1.19158 + 1.49419i 1.19158 + 1.49419i
\(506\) 0 0
\(507\) 0.109562 + 0.101659i 0.109562 + 0.101659i
\(508\) 0.623490 1.07992i 0.623490 1.07992i
\(509\) −0.826239 1.43109i −0.826239 1.43109i −0.900969 0.433884i \(-0.857143\pi\)
0.0747301 0.997204i \(-0.476190\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0.222521 + 0.974928i 0.222521 + 0.974928i
\(513\) 0 0
\(514\) 0 0
\(515\) −0.988831 + 0.149042i −0.988831 + 0.149042i
\(516\) −0.0800550 + 0.0742802i −0.0800550 + 0.0742802i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0.222521 0.385418i 0.222521 0.385418i −0.733052 0.680173i \(-0.761905\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(522\) 1.05072 + 0.974928i 1.05072 + 0.974928i
\(523\) 0.367711 + 0.250701i 0.367711 + 0.250701i 0.733052 0.680173i \(-0.238095\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(524\) 0 0
\(525\) −0.134659 + 0.0648483i −0.134659 + 0.0648483i
\(526\) −0.914101 + 1.14625i −0.914101 + 1.14625i
\(527\) 0 0
\(528\) 0 0
\(529\) 0.129334 1.72584i 0.129334 1.72584i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) −0.0163752 0.218511i −0.0163752 0.218511i
\(535\) −1.82624 0.563320i −1.82624 0.563320i
\(536\) −0.826239 + 0.563320i −0.826239 + 0.563320i
\(537\) 0 0
\(538\) 1.97766 1.97766
\(539\) 0 0
\(540\) 0.295582 0.295582
\(541\) −0.147791 0.0222759i −0.147791 0.0222759i 0.0747301 0.997204i \(-0.476190\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(542\) 0 0
\(543\) 0.142820 + 0.0440542i 0.142820 + 0.0440542i
\(544\) 0 0
\(545\) 0.900969 0.433884i 0.900969 0.433884i
\(546\) 0 0
\(547\) 1.48883 + 0.716983i 1.48883 + 0.716983i 0.988831 0.149042i \(-0.0476190\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(548\) 0 0
\(549\) −0.120731 + 1.61105i −0.120731 + 1.61105i
\(550\) 0 0
\(551\) 0 0
\(552\) −0.153989 + 0.193096i −0.153989 + 0.193096i
\(553\) 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
\(560\) 0.733052 0.680173i 0.733052 0.680173i
\(561\) 0 0
\(562\) −1.32091 + 1.22563i −1.32091 + 1.22563i
\(563\) −1.44973 + 0.218511i −1.44973 + 0.218511i −0.826239 0.563320i \(-0.809524\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(564\) 0.266310 0.0401398i 0.266310 0.0401398i
\(565\) 0 0
\(566\) 0.400969 + 1.75676i 0.400969 + 1.75676i
\(567\) 0.466742 + 0.808421i 0.466742 + 0.808421i
\(568\) 0 0
\(569\) −0.623490 1.07992i −0.623490 1.07992i −0.988831 0.149042i \(-0.952381\pi\)
0.365341 0.930874i \(-0.380952\pi\)
\(570\) 0 0
\(571\) 0 0 −0.733052 0.680173i \(-0.761905\pi\)
0.733052 + 0.680173i \(0.238095\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0.455573 + 0.571270i 0.455573 + 0.571270i
\(575\) −1.03030 + 1.29196i −1.03030 + 1.29196i
\(576\) −0.934227 + 0.288171i −0.934227 + 0.288171i
\(577\) 0 0 −0.365341 0.930874i \(-0.619048\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(578\) −0.0747301 + 0.997204i −0.0747301 + 0.997204i
\(579\) 0 0
\(580\) 1.32091 + 0.636119i 1.32091 + 0.636119i
\(581\) 0.698220 + 1.77904i 0.698220 + 1.77904i
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0.445042 0.445042 0.222521 0.974928i \(-0.428571\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(588\) −0.142820 0.0440542i −0.142820 0.0440542i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 −0.0747301 0.997204i \(-0.523810\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −1.72188 0.829215i −1.72188 0.829215i
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 −0.365341 0.930874i \(-0.619048\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(600\) 0.142820 0.0440542i 0.142820 0.0440542i
\(601\) −0.277479 + 0.347948i −0.277479 + 0.347948i −0.900969 0.433884i \(-0.857143\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(602\) −0.730682 −0.730682
\(603\) −0.609562 0.764367i −0.609562 0.764367i
\(604\) 0 0
\(605\) −0.733052 0.680173i −0.733052 0.680173i
\(606\) −0.142820 + 0.247372i −0.142820 + 0.247372i
\(607\) −0.733052 1.26968i −0.733052 1.26968i −0.955573 0.294755i \(-0.904762\pi\)
0.222521 0.974928i \(-0.428571\pi\)
\(608\) 0 0
\(609\) −0.0163752 0.218511i −0.0163752 0.218511i
\(610\) 0.367711 + 1.61105i 0.367711 + 1.61105i
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 0.988831 0.149042i \(-0.0476190\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(614\) 1.44973 1.34515i 1.44973 1.34515i
\(615\) 0.0243010 + 0.106470i 0.0243010 + 0.106470i
\(616\) 0 0
\(617\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(618\) −0.0747301 0.129436i −0.0747301 0.129436i
\(619\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(620\) 0 0
\(621\) −0.403570 0.275149i −0.403570 0.275149i
\(622\) 0 0
\(623\) 0.914101 1.14625i 0.914101 1.14625i
\(624\) 0 0
\(625\) 0.955573 0.294755i 0.955573 0.294755i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0.716677 + 0.664979i 0.716677 + 0.664979i
\(631\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 1.23305 + 0.185853i 1.23305 + 0.185853i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) −0.826239 + 0.563320i −0.826239 + 0.563320i
\(641\) 0.142820 + 0.0440542i 0.142820 + 0.0440542i 0.365341 0.930874i \(-0.380952\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(642\) −0.0213459 0.284841i −0.0213459 0.284841i
\(643\) 1.12349 0.541044i 1.12349 0.541044i 0.222521 0.974928i \(-0.428571\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(644\) −1.63402 + 0.246289i −1.63402 + 0.246289i
\(645\) −0.0983929 0.0473835i −0.0983929 0.0473835i
\(646\) 0 0
\(647\) 0.147791 1.97213i 0.147791 1.97213i −0.0747301 0.997204i \(-0.523810\pi\)
0.222521 0.974928i \(-0.428571\pi\)
\(648\) −0.341040 0.868956i −0.341040 0.868956i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0.277479 + 0.347948i 0.277479 + 0.347948i
\(653\) 0 0 −0.826239 0.563320i \(-0.809524\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(654\) 0.109562 + 0.101659i 0.109562 + 0.101659i
\(655\) 0 0
\(656\) −0.365341 0.632789i −0.365341 0.632789i
\(657\) 0 0
\(658\) 1.48883 + 1.01507i 1.48883 + 1.01507i
\(659\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(660\) 0 0
\(661\) −1.88980 + 0.284841i −1.88980 + 0.284841i −0.988831 0.149042i \(-0.952381\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) −0.425270 1.86323i −0.425270 1.86323i
\(665\) 0 0
\(666\) 0 0
\(667\) −1.21135 2.09812i −1.21135 2.09812i
\(668\) −0.988831 + 1.71271i −0.988831 + 1.71271i
\(669\) −0.136622 0.126766i −0.136622 0.126766i
\(670\) −0.826239 0.563320i −0.826239 0.563320i
\(671\) 0 0
\(672\) 0.134659 + 0.0648483i 0.134659 + 0.0648483i
\(673\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(674\) 0 0
\(675\) 0.107988 + 0.275149i 0.107988 + 0.275149i
\(676\) 0.0747301 0.997204i 0.0747301 0.997204i
\(677\) 0 0 0.365341 0.930874i \(-0.380952\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0.0139277 + 0.185853i 0.0139277 + 0.185853i
\(682\) 0 0
\(683\) 1.63402 1.11406i 1.63402 1.11406i 0.733052 0.680173i \(-0.238095\pi\)
0.900969 0.433884i \(-0.142857\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −0.500000 0.866025i −0.500000 0.866025i
\(687\) 0.0665160 0.0665160
\(688\) 0.722521 + 0.108903i 0.722521 + 0.108903i
\(689\) 0 0
\(690\) −0.236007 0.0727985i −0.236007 0.0727985i
\(691\) 0 0 −0.0747301 0.997204i \(-0.523810\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) −0.658322 0.317031i −0.658322 0.317031i
\(695\) 0 0
\(696\) −0.0163752 + 0.218511i −0.0163752 + 0.218511i
\(697\) 0 0
\(698\) −0.698220 + 0.215372i −0.698220 + 0.215372i
\(699\) 0 0
\(700\) 0.900969 + 0.433884i 0.900969 + 0.433884i
\(701\) 0.0931869 + 0.116853i 0.0931869 + 0.116853i 0.826239 0.563320i \(-0.190476\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0.134659 + 0.233236i 0.134659 + 0.233236i
\(706\) 0 0
\(707\) −1.82624 + 0.563320i −1.82624 + 0.563320i
\(708\) 0 0
\(709\) −1.40097 + 1.29991i −1.40097 + 1.29991i −0.500000 + 0.866025i \(0.666667\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −1.07473 + 0.997204i −1.07473 + 0.997204i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 −0.826239 0.563320i \(-0.809524\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(720\) −0.609562 0.764367i −0.609562 0.764367i
\(721\) 0.222521 0.974928i 0.222521 0.974928i
\(722\) −0.623490 + 0.781831i −0.623490 + 0.781831i
\(723\) −0.178094 + 0.0549346i −0.178094 + 0.0549346i
\(724\) −0.365341 0.930874i −0.365341 0.930874i
\(725\) −0.109562 + 1.46200i −0.109562 + 1.46200i
\(726\) 0.0546039 0.139129i 0.0546039 0.139129i
\(727\) 1.72188 + 0.829215i 1.72188 + 0.829215i 0.988831 + 0.149042i \(0.0476190\pi\)
0.733052 + 0.680173i \(0.238095\pi\)
\(728\) 0 0
\(729\) 0.782450 0.376808i 0.782450 0.376808i
\(730\) 0 0
\(731\) 0 0
\(732\) −0.204064 + 0.139129i −0.204064 + 0.139129i
\(733\) 0 0 −0.988831 0.149042i \(-0.952381\pi\)
0.988831 + 0.149042i \(0.0476190\pi\)
\(734\) −1.97766 −1.97766
\(735\) −0.0111692 0.149042i −0.0111692 0.149042i
\(736\) 1.65248 1.65248
\(737\) 0 0
\(738\) 0.590232 0.402413i 0.590232 0.402413i
\(739\) 0 0 −0.955573 0.294755i \(-0.904762\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −1.78181 0.858075i −1.78181 0.858075i −0.955573 0.294755i \(-0.904762\pi\)
−0.826239 0.563320i \(-0.809524\pi\)
\(744\) 0 0
\(745\) 0.142820 1.90580i 0.142820 1.90580i
\(746\) 0 0
\(747\) 1.78544 0.550736i 1.78544 0.550736i
\(748\) 0 0
\(749\) 1.19158 1.49419i 1.19158 1.49419i
\(750\) 0.0931869 + 0.116853i 0.0931869 + 0.116853i
\(751\) 0 0 −0.826239 0.563320i \(-0.809524\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(752\) −1.32091 1.22563i −1.32091 1.22563i
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) −0.107988 + 0.275149i −0.107988 + 0.275149i
\(757\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −0.914101 + 0.848162i −0.914101 + 0.848162i −0.988831 0.149042i \(-0.952381\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(762\) 0.0414721 + 0.181701i 0.0414721 + 0.181701i
\(763\) 0.0747301 + 0.997204i 0.0747301 + 0.997204i
\(764\) 0 0
\(765\) 0 0
\(766\) 0.733052 1.26968i 0.733052 1.26968i
\(767\) 0 0
\(768\) −0.123490 0.0841939i −0.123490 0.0841939i
\(769\) 0.777479 + 0.974928i 0.777479 + 0.974928i 1.00000 \(0\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0 0 −0.365341 0.930874i \(-0.619048\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(774\) −0.0533842 + 0.712362i −0.0533842 + 0.712362i
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) −0.400969 + 0.193096i −0.400969 + 0.193096i
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) −0.433353 −0.433353
\(784\) 0.365341 + 0.930874i 0.365341 + 0.930874i
\(785\) 0 0
\(786\) 0 0
\(787\) 1.21135 0.825886i 1.21135 0.825886i 0.222521 0.974928i \(-0.428571\pi\)
0.988831 + 0.149042i \(0.0476190\pi\)
\(788\) 0 0
\(789\) −0.0163752 0.218511i −0.0163752 0.218511i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) −0.826239 0.563320i −0.826239 0.563320i
\(801\) −1.05072 0.974928i −1.05072 0.974928i
\(802\) 0.0747301 0.129436i 0.0747301 0.129436i
\(803\) 0 0
\(804\) 0.0332580 0.145713i 0.0332580 0.145713i
\(805\) −0.826239 1.43109i −0.826239 1.43109i
\(806\) 0 0
\(807\) −0.216677 + 0.201047i −0.216677 + 0.201047i
\(808\) 1.88980 0.284841i 1.88980 0.284841i
\(809\) 0.988831 0.149042i 0.988831 0.149042i 0.365341 0.930874i \(-0.380952\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(810\) 0.684292 0.634930i 0.684292 0.634930i
\(811\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(812\) −1.07473 + 0.997204i −1.07473 + 0.997204i
\(813\) 0 0
\(814\) 0 0
\(815\) −0.222521 + 0.385418i −0.222521 + 0.385418i
\(816\) 0 0
\(817\) 0 0
\(818\) 1.23305 + 1.54620i 1.23305 + 1.54620i
\(819\) 0 0
\(820\) 0.455573 0.571270i 0.455573 0.571270i
\(821\) 1.19158 0.367554i 1.19158 0.367554i 0.365341 0.930874i \(-0.380952\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(822\) 0 0
\(823\) 0.147791 1.97213i 0.147791 1.97213i −0.0747301 0.997204i \(-0.523810\pi\)
0.222521 0.974928i \(-0.428571\pi\)
\(824\) −0.365341 + 0.930874i −0.365341 + 0.930874i
\(825\) 0 0
\(826\) 0 0
\(827\) 0.134659 0.0648483i 0.134659 0.0648483i −0.365341 0.930874i \(-0.619048\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(828\) 0.120731 + 1.61105i 0.120731 + 1.61105i
\(829\) −0.425270 0.131178i −0.425270 0.131178i 0.0747301 0.997204i \(-0.476190\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(830\) 1.57906 1.07659i 1.57906 1.07659i
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) −1.95557 0.294755i −1.95557 0.294755i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(840\) −0.0111692 + 0.149042i −0.0111692 + 0.149042i
\(841\) −1.03563 0.498732i −1.03563 0.498732i
\(842\) −0.0546039 + 0.139129i −0.0546039 + 0.139129i
\(843\) 0.0201262 0.268565i 0.0201262 0.268565i
\(844\) 0 0
\(845\) 0.955573 0.294755i 0.955573 0.294755i
\(846\) 1.09839 1.37734i 1.09839 1.37734i
\(847\) 0.900969 0.433884i 0.900969 0.433884i
\(848\) 0 0
\(849\) −0.222521 0.151712i −0.222521 0.151712i
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(854\) −1.63402 0.246289i −1.63402 0.246289i
\(855\) 0 0
\(856\) −1.40097 + 1.29991i −1.40097 + 1.29991i
\(857\) 0 0 0.988831 0.149042i \(-0.0476190\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(858\) 0 0
\(859\) 0 0 0.733052 0.680173i \(-0.238095\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(860\) 0.162592 + 0.712362i 0.162592 + 0.712362i
\(861\) −0.107988 0.0162766i −0.107988 0.0162766i
\(862\) 0 0
\(863\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(864\) 0.147791 0.255981i 0.147791 0.255981i
\(865\) 0 0
\(866\) 0 0
\(867\) −0.0931869 0.116853i −0.0931869 0.116853i
\(868\) 0 0
\(869\) 0 0
\(870\) −0.209389 + 0.0645880i −0.209389 + 0.0645880i
\(871\) 0 0
\(872\) 0.0747301 0.997204i 0.0747301 0.997204i
\(873\) 0 0
\(874\) 0 0
\(875\) −0.0747301 + 0.997204i −0.0747301 + 0.997204i
\(876\) 0 0
\(877\) 0 0 −0.0747301 0.997204i \(-0.523810\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(882\) −0.880843 + 0.424191i −0.880843 + 0.424191i
\(883\) −1.24698 −1.24698 −0.623490 0.781831i \(-0.714286\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) −1.40097 0.432142i −1.40097 0.432142i
\(887\) −0.123490 1.64786i −0.123490 1.64786i −0.623490 0.781831i \(-0.714286\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(888\) 0 0
\(889\) −0.623490 + 1.07992i −0.623490 + 1.07992i
\(890\) −1.32091 0.636119i −1.32091 0.636119i
\(891\) 0 0
\(892\) −0.0931869 + 1.24349i −0.0931869 + 1.24349i
\(893\) 0 0
\(894\) 0.272950 0.0841939i 0.272950 0.0841939i
\(895\) 0 0
\(896\) −0.222521 0.974928i −0.222521 0.974928i
\(897\) 0 0
\(898\) −1.36534 0.930874i −1.36534 0.930874i
\(899\) 0 0
\(900\) 0.488831 0.846680i 0.488831 0.846680i
\(901\) 0 0
\(902\) 0 0
\(903\) 0.0800550 0.0742802i 0.0800550 0.0742802i
\(904\) 0 0
\(905\) 0.733052 0.680173i 0.733052 0.680173i
\(906\) 0 0
\(907\) 0.147791 0.0222759i 0.147791 0.0222759i −0.0747301 0.997204i \(-0.523810\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(908\) 0.914101 0.848162i 0.914101 0.848162i
\(909\) 0.415770 + 1.82161i 0.415770 + 1.82161i
\(910\) 0 0
\(911\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) −0.204064 0.139129i −0.204064 0.139129i
\(916\) −0.277479 0.347948i −0.277479 0.347948i
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 0.955573 0.294755i \(-0.0952381\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(920\) 0.603718 + 1.53825i 0.603718 + 1.53825i
\(921\) −0.0220888 + 0.294755i −0.0220888 + 0.294755i
\(922\) 0.658322 1.67738i 0.658322 1.67738i
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) 0.142820 + 1.90580i 0.142820 + 1.90580i
\(927\) −0.934227 0.288171i −0.934227 0.288171i
\(928\) 1.21135 0.825886i 1.21135 0.825886i
\(929\) −1.63402 0.246289i −1.63402 0.246289i −0.733052 0.680173i \(-0.761905\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 0 0
\(934\) −0.826239 + 0.563320i −0.826239 + 0.563320i
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(938\) 0.826239 0.563320i 0.826239 0.563320i
\(939\) 0 0
\(940\) 0.658322 1.67738i 0.658322 1.67738i
\(941\) −0.0332580 + 0.443797i −0.0332580 + 0.443797i 0.955573 + 0.294755i \(0.0952381\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(942\) 0 0
\(943\) −1.15379 + 0.355898i −1.15379 + 0.355898i
\(944\) 0 0
\(945\) −0.295582 −0.295582
\(946\) 0 0
\(947\) 1.63402 + 1.11406i 1.63402 + 1.11406i 0.900969 + 0.433884i \(0.142857\pi\)
0.733052 + 0.680173i \(0.238095\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0.0332580 0.145713i 0.0332580 0.145713i
\(961\) −0.500000 0.866025i −0.500000 0.866025i
\(962\) 0 0
\(963\) −1.36967 1.27087i −1.36967 1.27087i
\(964\) 1.03030 + 0.702449i 1.03030 + 0.702449i
\(965\) 0 0
\(966\) 0.153989 0.193096i 0.153989 0.193096i
\(967\) −0.0931869 + 0.116853i −0.0931869 + 0.116853i −0.826239 0.563320i \(-0.809524\pi\)
0.733052 + 0.680173i \(0.238095\pi\)
\(968\) −0.955573 + 0.294755i −0.955573 + 0.294755i
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 0.365341 0.930874i \(-0.380952\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(972\) 0.392012 + 0.188783i 0.392012 + 0.188783i
\(973\) 0 0
\(974\) 1.62349 0.781831i 1.62349 0.781831i
\(975\) 0 0
\(976\) 1.57906 + 0.487076i 1.57906 + 0.487076i
\(977\) 0 0 0.826239 0.563320i \(-0.190476\pi\)
−0.826239 + 0.563320i \(0.809524\pi\)
\(978\) −0.0657731 0.00991370i −0.0657731 0.00991370i
\(979\) 0 0
\(980\) −0.733052 + 0.680173i −0.733052 + 0.680173i
\(981\) 0.977662 0.977662
\(982\) 0 0
\(983\) −1.36534 + 0.930874i −1.36534 + 0.930874i −0.365341 + 0.930874i \(0.619048\pi\)
−1.00000 \(\pi\)
\(984\) 0.104356 + 0.0321896i 0.104356 + 0.0321896i
\(985\) 0 0
\(986\) 0 0
\(987\) −0.266310 + 0.0401398i −0.266310 + 0.0401398i
\(988\) 0 0
\(989\) 0.441126 1.12397i 0.441126 1.12397i
\(990\) 0 0
\(991\) 0 0 −0.365341 0.930874i \(-0.619048\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0.236007 + 0.160907i 0.236007 + 0.160907i
\(997\) 0 0 −0.733052 0.680173i \(-0.761905\pi\)
0.733052 + 0.680173i \(0.238095\pi\)
\(998\) 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.a.39.1 12
4.3 odd 2 980.1.bq.b.39.1 yes 12
5.4 even 2 980.1.bq.b.39.1 yes 12
20.19 odd 2 CM 980.1.bq.a.39.1 12
49.44 even 21 inner 980.1.bq.a.779.1 yes 12
196.191 odd 42 980.1.bq.b.779.1 yes 12
245.44 even 42 980.1.bq.b.779.1 yes 12
980.779 odd 42 inner 980.1.bq.a.779.1 yes 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
980.1.bq.a.39.1 12 1.1 even 1 trivial
980.1.bq.a.39.1 12 20.19 odd 2 CM
980.1.bq.a.779.1 yes 12 49.44 even 21 inner
980.1.bq.a.779.1 yes 12 980.779 odd 42 inner
980.1.bq.b.39.1 yes 12 4.3 odd 2
980.1.bq.b.39.1 yes 12 5.4 even 2
980.1.bq.b.779.1 yes 12 196.191 odd 42
980.1.bq.b.779.1 yes 12 245.44 even 42