Properties

Label 2717.1.db.d.1429.1
Level $2717$
Weight $1$
Character 2717.1429
Analytic conductor $1.356$
Analytic rank $0$
Dimension $24$
Projective image $D_{45}$
CM discriminant -143
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2717,1,Mod(142,2717)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2717, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([9, 9, 8]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2717.142");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2717 = 11 \cdot 13 \cdot 19 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2717.db (of order \(18\), degree \(6\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.35595963932\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(4\) over \(\Q(\zeta_{18})\)
Coefficient field: \(\Q(\zeta_{45})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{24} - x^{21} + x^{15} - x^{12} + x^{9} - x^{3} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{45}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{45} - \cdots)\)

Embedding invariants

Embedding label 1429.1
Root \(-0.882948 + 0.469472i\) of defining polynomial
Character \(\chi\) \(=\) 2717.1429
Dual form 2717.1.db.d.1715.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.59381 - 0.580099i) q^{2} +(-0.130100 - 0.737831i) q^{3} +(1.43767 + 1.20635i) q^{4} +(-0.220661 + 1.25143i) q^{6} +(0.241922 - 0.419021i) q^{7} +(-0.743520 - 1.28781i) q^{8} +(0.412224 - 0.150037i) q^{9} +O(q^{10})\) \(q+(-1.59381 - 0.580099i) q^{2} +(-0.130100 - 0.737831i) q^{3} +(1.43767 + 1.20635i) q^{4} +(-0.220661 + 1.25143i) q^{6} +(0.241922 - 0.419021i) q^{7} +(-0.743520 - 1.28781i) q^{8} +(0.412224 - 0.150037i) q^{9} +(-0.500000 - 0.866025i) q^{11} +(0.703040 - 1.21770i) q^{12} +(0.173648 - 0.984808i) q^{13} +(-0.628651 + 0.527501i) q^{14} +(0.112076 + 0.635614i) q^{16} -0.744043 q^{18} +(0.990268 - 0.139173i) q^{19} +(-0.340641 - 0.123983i) q^{21} +(0.294524 + 1.67033i) q^{22} +(0.856733 + 0.718885i) q^{23} +(-0.853457 + 0.716136i) q^{24} +(0.173648 - 0.984808i) q^{25} +(-0.848048 + 1.46886i) q^{26} +(-0.538939 - 0.933469i) q^{27} +(0.853288 - 0.310571i) q^{28} +(-0.0681302 + 0.386385i) q^{32} +(-0.573931 + 0.481585i) q^{33} +(0.773638 + 0.281581i) q^{36} +(-1.65903 - 0.352638i) q^{38} -0.749213 q^{39} +(0.333843 + 1.89332i) q^{41} +(0.470994 + 0.395211i) q^{42} +(0.325893 - 1.84823i) q^{44} +(-0.948445 - 1.64275i) q^{46} +(0.454395 - 0.165386i) q^{48} +(0.382948 + 0.663285i) q^{49} +(-0.848048 + 1.46886i) q^{50} +(1.43767 - 1.20635i) q^{52} +(-0.943248 - 0.791479i) q^{53} +(0.317461 + 1.80041i) q^{54} -0.719495 q^{56} +(-0.231520 - 0.712544i) q^{57} +(0.0368572 - 0.209028i) q^{63} +(0.655438 - 1.13525i) q^{64} +(1.19410 - 0.434618i) q^{66} +(0.418955 - 0.725651i) q^{69} +(-0.499717 - 0.419312i) q^{72} +(0.107320 + 0.608645i) q^{73} -0.749213 q^{75} +(1.59157 + 0.994522i) q^{76} -0.483844 q^{77} +(1.19410 + 0.434618i) q^{78} +(-0.282579 + 0.237112i) q^{81} +(0.566229 - 3.21125i) q^{82} +(0.997564 - 1.72783i) q^{83} +(-0.340162 - 0.589177i) q^{84} +(-0.743520 + 1.28781i) q^{88} +(-0.370646 - 0.311009i) q^{91} +(0.364474 + 2.06703i) q^{92} +0.293951 q^{96} +(-0.225575 - 1.27930i) q^{98} +(-0.336048 - 0.281978i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 3 q^{2} + 3 q^{3} + 3 q^{4} + 24 q^{6} - 3 q^{8} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 3 q^{2} + 3 q^{3} + 3 q^{4} + 24 q^{6} - 3 q^{8} + 3 q^{9} - 12 q^{11} - 3 q^{12} + 3 q^{14} - 3 q^{16} + 6 q^{18} + 3 q^{21} + 3 q^{22} + 3 q^{23} - 6 q^{24} - 3 q^{27} - 9 q^{28} - 9 q^{32} - 6 q^{33} + 30 q^{36} + 3 q^{41} + 12 q^{42} - 6 q^{44} - 3 q^{46} - 12 q^{49} + 3 q^{52} + 3 q^{53} + 21 q^{54} - 12 q^{56} + 6 q^{63} - 15 q^{64} - 12 q^{66} - 3 q^{69} + 15 q^{72} + 3 q^{76} - 12 q^{78} + 6 q^{81} + 3 q^{82} + 12 q^{84} - 3 q^{88} - 6 q^{91} - 3 q^{92} - 6 q^{96} + 6 q^{98} + 3 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2717\mathbb{Z}\right)^\times\).

\(n\) \(210\) \(287\) \(2224\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{9}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.59381 0.580099i −1.59381 0.580099i −0.615661 0.788011i \(-0.711111\pi\)
−0.978148 + 0.207912i \(0.933333\pi\)
\(3\) −0.130100 0.737831i −0.130100 0.737831i −0.978148 0.207912i \(-0.933333\pi\)
0.848048 0.529919i \(-0.177778\pi\)
\(4\) 1.43767 + 1.20635i 1.43767 + 1.20635i
\(5\) 0 0 0.766044 0.642788i \(-0.222222\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(6\) −0.220661 + 1.25143i −0.220661 + 1.25143i
\(7\) 0.241922 0.419021i 0.241922 0.419021i −0.719340 0.694658i \(-0.755556\pi\)
0.961262 + 0.275637i \(0.0888889\pi\)
\(8\) −0.743520 1.28781i −0.743520 1.28781i
\(9\) 0.412224 0.150037i 0.412224 0.150037i
\(10\) 0 0
\(11\) −0.500000 0.866025i −0.500000 0.866025i
\(12\) 0.703040 1.21770i 0.703040 1.21770i
\(13\) 0.173648 0.984808i 0.173648 0.984808i
\(14\) −0.628651 + 0.527501i −0.628651 + 0.527501i
\(15\) 0 0
\(16\) 0.112076 + 0.635614i 0.112076 + 0.635614i
\(17\) 0 0 −0.939693 0.342020i \(-0.888889\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(18\) −0.744043 −0.744043
\(19\) 0.990268 0.139173i 0.990268 0.139173i
\(20\) 0 0
\(21\) −0.340641 0.123983i −0.340641 0.123983i
\(22\) 0.294524 + 1.67033i 0.294524 + 1.67033i
\(23\) 0.856733 + 0.718885i 0.856733 + 0.718885i 0.961262 0.275637i \(-0.0888889\pi\)
−0.104528 + 0.994522i \(0.533333\pi\)
\(24\) −0.853457 + 0.716136i −0.853457 + 0.716136i
\(25\) 0.173648 0.984808i 0.173648 0.984808i
\(26\) −0.848048 + 1.46886i −0.848048 + 1.46886i
\(27\) −0.538939 0.933469i −0.538939 0.933469i
\(28\) 0.853288 0.310571i 0.853288 0.310571i
\(29\) 0 0 0.939693 0.342020i \(-0.111111\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(30\) 0 0
\(31\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(32\) −0.0681302 + 0.386385i −0.0681302 + 0.386385i
\(33\) −0.573931 + 0.481585i −0.573931 + 0.481585i
\(34\) 0 0
\(35\) 0 0
\(36\) 0.773638 + 0.281581i 0.773638 + 0.281581i
\(37\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(38\) −1.65903 0.352638i −1.65903 0.352638i
\(39\) −0.749213 −0.749213
\(40\) 0 0
\(41\) 0.333843 + 1.89332i 0.333843 + 1.89332i 0.438371 + 0.898794i \(0.355556\pi\)
−0.104528 + 0.994522i \(0.533333\pi\)
\(42\) 0.470994 + 0.395211i 0.470994 + 0.395211i
\(43\) 0 0 0.766044 0.642788i \(-0.222222\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(44\) 0.325893 1.84823i 0.325893 1.84823i
\(45\) 0 0
\(46\) −0.948445 1.64275i −0.948445 1.64275i
\(47\) 0 0 0.939693 0.342020i \(-0.111111\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(48\) 0.454395 0.165386i 0.454395 0.165386i
\(49\) 0.382948 + 0.663285i 0.382948 + 0.663285i
\(50\) −0.848048 + 1.46886i −0.848048 + 1.46886i
\(51\) 0 0
\(52\) 1.43767 1.20635i 1.43767 1.20635i
\(53\) −0.943248 0.791479i −0.943248 0.791479i 0.0348995 0.999391i \(-0.488889\pi\)
−0.978148 + 0.207912i \(0.933333\pi\)
\(54\) 0.317461 + 1.80041i 0.317461 + 1.80041i
\(55\) 0 0
\(56\) −0.719495 −0.719495
\(57\) −0.231520 0.712544i −0.231520 0.712544i
\(58\) 0 0
\(59\) 0 0 −0.939693 0.342020i \(-0.888889\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(60\) 0 0
\(61\) 0 0 −0.766044 0.642788i \(-0.777778\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(62\) 0 0
\(63\) 0.0368572 0.209028i 0.0368572 0.209028i
\(64\) 0.655438 1.13525i 0.655438 1.13525i
\(65\) 0 0
\(66\) 1.19410 0.434618i 1.19410 0.434618i
\(67\) 0 0 0.939693 0.342020i \(-0.111111\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(68\) 0 0
\(69\) 0.418955 0.725651i 0.418955 0.725651i
\(70\) 0 0
\(71\) 0 0 0.766044 0.642788i \(-0.222222\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(72\) −0.499717 0.419312i −0.499717 0.419312i
\(73\) 0.107320 + 0.608645i 0.107320 + 0.608645i 0.990268 + 0.139173i \(0.0444444\pi\)
−0.882948 + 0.469472i \(0.844444\pi\)
\(74\) 0 0
\(75\) −0.749213 −0.749213
\(76\) 1.59157 + 0.994522i 1.59157 + 0.994522i
\(77\) −0.483844 −0.483844
\(78\) 1.19410 + 0.434618i 1.19410 + 0.434618i
\(79\) 0 0 −0.173648 0.984808i \(-0.555556\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(80\) 0 0
\(81\) −0.282579 + 0.237112i −0.282579 + 0.237112i
\(82\) 0.566229 3.21125i 0.566229 3.21125i
\(83\) 0.997564 1.72783i 0.997564 1.72783i 0.438371 0.898794i \(-0.355556\pi\)
0.559193 0.829038i \(-0.311111\pi\)
\(84\) −0.340162 0.589177i −0.340162 0.589177i
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) −0.743520 + 1.28781i −0.743520 + 1.28781i
\(89\) 0 0 0.173648 0.984808i \(-0.444444\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(90\) 0 0
\(91\) −0.370646 0.311009i −0.370646 0.311009i
\(92\) 0.364474 + 2.06703i 0.364474 + 2.06703i
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0.293951 0.293951
\(97\) 0 0 −0.939693 0.342020i \(-0.888889\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(98\) −0.225575 1.27930i −0.225575 1.27930i
\(99\) −0.336048 0.281978i −0.336048 0.281978i
\(100\) 1.43767 1.20635i 1.43767 1.20635i
\(101\) 0 0 0.173648 0.984808i \(-0.444444\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(102\) 0 0
\(103\) −0.438371 0.759281i −0.438371 0.759281i 0.559193 0.829038i \(-0.311111\pi\)
−0.997564 + 0.0697565i \(0.977778\pi\)
\(104\) −1.39736 + 0.508597i −1.39736 + 0.508597i
\(105\) 0 0
\(106\) 1.04422 + 1.80864i 1.04422 + 1.80864i
\(107\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(108\) 0.351273 1.99217i 0.351273 1.99217i
\(109\) 1.02517 0.860218i 1.02517 0.860218i 0.0348995 0.999391i \(-0.488889\pi\)
0.990268 + 0.139173i \(0.0444444\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0.293449 + 0.106807i 0.293449 + 0.106807i
\(113\) −1.76590 −1.76590 −0.882948 0.469472i \(-0.844444\pi\)
−0.882948 + 0.469472i \(0.844444\pi\)
\(114\) −0.0443481 + 1.26996i −0.0443481 + 1.26996i
\(115\) 0 0
\(116\) 0 0
\(117\) −0.0761759 0.432015i −0.0761759 0.432015i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(122\) 0 0
\(123\) 1.35351 0.492639i 1.35351 0.492639i
\(124\) 0 0
\(125\) 0 0
\(126\) −0.180000 + 0.311770i −0.180000 + 0.311770i
\(127\) 0 0 0.173648 0.984808i \(-0.444444\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(128\) −1.40265 + 1.17696i −1.40265 + 1.17696i
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 −0.939693 0.342020i \(-0.888889\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(132\) −1.40608 −1.40608
\(133\) 0.181251 0.448612i 0.181251 0.448612i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 −0.766044 0.642788i \(-0.777778\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(138\) −1.08868 + 0.913514i −1.08868 + 0.913514i
\(139\) 0 0 0.173648 0.984808i \(-0.444444\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −0.939693 + 0.342020i −0.939693 + 0.342020i
\(144\) 0.141566 + 0.245200i 0.141566 + 0.245200i
\(145\) 0 0
\(146\) 0.182026 1.03232i 0.182026 1.03232i
\(147\) 0.439571 0.368844i 0.439571 0.368844i
\(148\) 0 0
\(149\) 0.317271 + 1.79933i 0.317271 + 1.79933i 0.559193 + 0.829038i \(0.311111\pi\)
−0.241922 + 0.970296i \(0.577778\pi\)
\(150\) 1.19410 + 0.434618i 1.19410 + 0.434618i
\(151\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(152\) −0.915513 1.17180i −0.915513 1.17180i
\(153\) 0 0
\(154\) 0.771155 + 0.280677i 0.771155 + 0.280677i
\(155\) 0 0
\(156\) −1.07712 0.903811i −1.07712 0.903811i
\(157\) −0.160147 + 0.134379i −0.160147 + 0.134379i −0.719340 0.694658i \(-0.755556\pi\)
0.559193 + 0.829038i \(0.311111\pi\)
\(158\) 0 0
\(159\) −0.461262 + 0.798929i −0.461262 + 0.798929i
\(160\) 0 0
\(161\) 0.508490 0.185075i 0.508490 0.185075i
\(162\) 0.587925 0.213987i 0.587925 0.213987i
\(163\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(164\) −1.80404 + 3.12469i −1.80404 + 3.12469i
\(165\) 0 0
\(166\) −2.59224 + 2.17515i −2.59224 + 2.17515i
\(167\) −1.35275 1.13510i −1.35275 1.13510i −0.978148 0.207912i \(-0.933333\pi\)
−0.374607 0.927184i \(-0.622222\pi\)
\(168\) 0.0936059 + 0.530865i 0.0936059 + 0.530865i
\(169\) −0.939693 0.342020i −0.939693 0.342020i
\(170\) 0 0
\(171\) 0.387331 0.205948i 0.387331 0.205948i
\(172\) 0 0
\(173\) 0 0 −0.939693 0.342020i \(-0.888889\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(174\) 0 0
\(175\) −0.370646 0.311009i −0.370646 0.311009i
\(176\) 0.494420 0.414868i 0.494420 0.414868i
\(177\) 0 0
\(178\) 0 0
\(179\) −0.173648 0.300767i −0.173648 0.300767i 0.766044 0.642788i \(-0.222222\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(180\) 0 0
\(181\) −0.0655896 + 0.0238727i −0.0655896 + 0.0238727i −0.374607 0.927184i \(-0.622222\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(182\) 0.410323 + 0.710700i 0.410323 + 0.710700i
\(183\) 0 0
\(184\) 0.288791 1.63782i 0.288791 1.63782i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) −0.521524 −0.521524
\(190\) 0 0
\(191\) 1.33826 1.33826 0.669131 0.743145i \(-0.266667\pi\)
0.669131 + 0.743145i \(0.266667\pi\)
\(192\) −0.922896 0.335907i −0.922896 0.335907i
\(193\) 0.194206 + 1.10140i 0.194206 + 1.10140i 0.913545 + 0.406737i \(0.133333\pi\)
−0.719340 + 0.694658i \(0.755556\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −0.249600 + 1.41555i −0.249600 + 1.41555i
\(197\) −0.0348995 + 0.0604477i −0.0348995 + 0.0604477i −0.882948 0.469472i \(-0.844444\pi\)
0.848048 + 0.529919i \(0.177778\pi\)
\(198\) 0.372021 + 0.644360i 0.372021 + 0.644360i
\(199\) −1.86110 + 0.677383i −1.86110 + 0.677383i −0.882948 + 0.469472i \(0.844444\pi\)
−0.978148 + 0.207912i \(0.933333\pi\)
\(200\) −1.39736 + 0.508597i −1.39736 + 0.508597i
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0.258222 + 1.46445i 0.258222 + 1.46445i
\(207\) 0.461025 + 0.167800i 0.461025 + 0.167800i
\(208\) 0.645419 0.645419
\(209\) −0.615661 0.788011i −0.615661 0.788011i
\(210\) 0 0
\(211\) 0 0 −0.939693 0.342020i \(-0.888889\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(212\) −0.401279 2.27577i −0.401279 2.27577i
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) −0.801423 + 1.38811i −0.801423 + 1.38811i
\(217\) 0 0
\(218\) −2.13293 + 0.776324i −2.13293 + 0.776324i
\(219\) 0.435115 0.158369i 0.435115 0.158369i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 0.766044 0.642788i \(-0.222222\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(224\) 0.145421 + 0.122023i 0.145421 + 0.122023i
\(225\) −0.0761759 0.432015i −0.0761759 0.432015i
\(226\) 2.81450 + 1.02439i 2.81450 + 1.02439i
\(227\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(228\) 0.526727 1.30369i 0.526727 1.30369i
\(229\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(230\) 0 0
\(231\) 0.0629478 + 0.356995i 0.0629478 + 0.356995i
\(232\) 0 0
\(233\) 0 0 0.766044 0.642788i \(-0.222222\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(234\) −0.129202 + 0.732739i −0.129202 + 0.732739i
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −0.990268 1.71519i −0.990268 1.71519i −0.615661 0.788011i \(-0.711111\pi\)
−0.374607 0.927184i \(-0.622222\pi\)
\(240\) 0 0
\(241\) −0.346450 + 1.96482i −0.346450 + 1.96482i −0.104528 + 0.994522i \(0.533333\pi\)
−0.241922 + 0.970296i \(0.577778\pi\)
\(242\) 1.29929 1.09023i 1.29929 1.09023i
\(243\) −0.613990 0.515199i −0.613990 0.515199i
\(244\) 0 0
\(245\) 0 0
\(246\) −2.44302 −2.44302
\(247\) 0.0348995 0.999391i 0.0348995 0.999391i
\(248\) 0 0
\(249\) −1.40463 0.511244i −1.40463 0.511244i
\(250\) 0 0
\(251\) −1.23949 1.04005i −1.23949 1.04005i −0.997564 0.0697565i \(-0.977778\pi\)
−0.241922 0.970296i \(-0.577778\pi\)
\(252\) 0.305148 0.256050i 0.305148 0.256050i
\(253\) 0.194206 1.10140i 0.194206 1.10140i
\(254\) 0 0
\(255\) 0 0
\(256\) 1.68648 0.613830i 1.68648 0.613830i
\(257\) 1.52045 0.553400i 1.52045 0.553400i 0.559193 0.829038i \(-0.311111\pi\)
0.961262 + 0.275637i \(0.0888889\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 −0.173648 0.984808i \(-0.555556\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(264\) 1.04692 + 0.381048i 1.04692 + 0.381048i
\(265\) 0 0
\(266\) −0.549119 + 0.609859i −0.549119 + 0.609859i
\(267\) 0 0
\(268\) 0 0
\(269\) 0.333843 + 1.89332i 0.333843 + 1.89332i 0.438371 + 0.898794i \(0.355556\pi\)
−0.104528 + 0.994522i \(0.533333\pi\)
\(270\) 0 0
\(271\) 0.0534691 0.0448659i 0.0534691 0.0448659i −0.615661 0.788011i \(-0.711111\pi\)
0.669131 + 0.743145i \(0.266667\pi\)
\(272\) 0 0
\(273\) −0.181251 + 0.313936i −0.181251 + 0.313936i
\(274\) 0 0
\(275\) −0.939693 + 0.342020i −0.939693 + 0.342020i
\(276\) 1.47770 0.537840i 1.47770 0.537840i
\(277\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 0.0534691 + 0.0448659i 0.0534691 + 0.0448659i 0.669131 0.743145i \(-0.266667\pi\)
−0.615661 + 0.788011i \(0.711111\pi\)
\(282\) 0 0
\(283\) 0 0 −0.939693 0.342020i \(-0.888889\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 1.69610 1.69610
\(287\) 0.874103 + 0.318147i 0.874103 + 0.318147i
\(288\) 0.0298873 + 0.169499i 0.0298873 + 0.169499i
\(289\) 0.766044 + 0.642788i 0.766044 + 0.642788i
\(290\) 0 0
\(291\) 0 0
\(292\) −0.579945 + 1.00449i −0.579945 + 1.00449i
\(293\) −0.766044 1.32683i −0.766044 1.32683i −0.939693 0.342020i \(-0.888889\pi\)
0.173648 0.984808i \(-0.444444\pi\)
\(294\) −0.914558 + 0.332872i −0.914558 + 0.332872i
\(295\) 0 0
\(296\) 0 0
\(297\) −0.538939 + 0.933469i −0.538939 + 0.933469i
\(298\) 0.538122 3.05184i 0.538122 3.05184i
\(299\) 0.856733 0.718885i 0.856733 0.718885i
\(300\) −1.07712 0.903811i −1.07712 0.903811i
\(301\) 0 0
\(302\) 1.59381 + 0.580099i 1.59381 + 0.580099i
\(303\) 0 0
\(304\) 0.199446 + 0.613830i 0.199446 + 0.613830i
\(305\) 0 0
\(306\) 0 0
\(307\) 0.0603074 + 0.342020i 0.0603074 + 0.342020i 1.00000 \(0\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(308\) −0.695607 0.583683i −0.695607 0.583683i
\(309\) −0.503189 + 0.422226i −0.503189 + 0.422226i
\(310\) 0 0
\(311\) 0.374607 0.648838i 0.374607 0.648838i −0.615661 0.788011i \(-0.711111\pi\)
0.990268 + 0.139173i \(0.0444444\pi\)
\(312\) 0.557055 + 0.964847i 0.557055 + 0.964847i
\(313\) −1.71690 + 0.624902i −1.71690 + 0.624902i −0.997564 0.0697565i \(-0.977778\pi\)
−0.719340 + 0.694658i \(0.755556\pi\)
\(314\) 0.333197 0.121274i 0.333197 0.121274i
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 0.173648 0.984808i \(-0.444444\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(318\) 1.19862 1.00576i 1.19862 1.00576i
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) −0.917798 −0.917798
\(323\) 0 0
\(324\) −0.692294 −0.692294
\(325\) −0.939693 0.342020i −0.939693 0.342020i
\(326\) 0 0
\(327\) −0.768069 0.644486i −0.768069 0.644486i
\(328\) 2.19002 1.83764i 2.19002 1.83764i
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(332\) 3.51853 1.28064i 3.51853 1.28064i
\(333\) 0 0
\(334\) 1.49756 + 2.59386i 1.49756 + 2.59386i
\(335\) 0 0
\(336\) 0.0406278 0.230411i 0.0406278 0.230411i
\(337\) 0 0 0.766044 0.642788i \(-0.222222\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(338\) 1.29929 + 1.09023i 1.29929 + 1.09023i
\(339\) 0.229742 + 1.30293i 0.229742 + 1.30293i
\(340\) 0 0
\(341\) 0 0
\(342\) −0.736802 + 0.103551i −0.736802 + 0.103551i
\(343\) 0.854417 0.854417
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 0.766044 0.642788i \(-0.222222\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(348\) 0 0
\(349\) −0.438371 + 0.759281i −0.438371 + 0.759281i −0.997564 0.0697565i \(-0.977778\pi\)
0.559193 + 0.829038i \(0.311111\pi\)
\(350\) 0.410323 + 0.710700i 0.410323 + 0.710700i
\(351\) −1.01287 + 0.368656i −1.01287 + 0.368656i
\(352\) 0.368685 0.134190i 0.368685 0.134190i
\(353\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0.102287 + 0.580099i 0.102287 + 0.580099i
\(359\) −1.05094 0.382510i −1.05094 0.382510i −0.241922 0.970296i \(-0.577778\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(360\) 0 0
\(361\) 0.961262 0.275637i 0.961262 0.275637i
\(362\) 0.118386 0.118386
\(363\) 0.704030 + 0.256246i 0.704030 + 0.256246i
\(364\) −0.157681 0.894255i −0.157681 0.894255i
\(365\) 0 0
\(366\) 0 0
\(367\) 0.107320 0.608645i 0.107320 0.608645i −0.882948 0.469472i \(-0.844444\pi\)
0.990268 0.139173i \(-0.0444444\pi\)
\(368\) −0.360914 + 0.625121i −0.360914 + 0.625121i
\(369\) 0.421686 + 0.730381i 0.421686 + 0.730381i
\(370\) 0 0
\(371\) −0.559839 + 0.203765i −0.559839 + 0.203765i
\(372\) 0 0
\(373\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0.831210 + 0.302536i 0.831210 + 0.302536i
\(379\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −2.13293 0.776324i −2.13293 0.776324i
\(383\) 0 0 −0.173648 0.984808i \(-0.555556\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(384\) 1.05088 + 0.881794i 1.05088 + 0.881794i
\(385\) 0 0
\(386\) 0.329391 1.86807i 0.329391 1.86807i
\(387\) 0 0
\(388\) 0 0
\(389\) 1.83832 0.669092i 1.83832 0.669092i 0.848048 0.529919i \(-0.177778\pi\)
0.990268 0.139173i \(-0.0444444\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0.569458 0.986330i 0.569458 0.986330i
\(393\) 0 0
\(394\) 0.0906888 0.0760969i 0.0906888 0.0760969i
\(395\) 0 0
\(396\) −0.142963 0.810781i −0.142963 0.810781i
\(397\) 0 0 −0.939693 0.342020i \(-0.888889\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(398\) 3.35918 3.35918
\(399\) −0.354581 0.0753684i −0.354581 0.0753684i
\(400\) 0.645419 0.645419
\(401\) 0 0 −0.939693 0.342020i \(-0.888889\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 1.76604 0.642788i 1.76604 0.642788i 0.766044 0.642788i \(-0.222222\pi\)
1.00000 \(0\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0.285724 1.62042i 0.285724 1.62042i
\(413\) 0 0
\(414\) −0.637446 0.534881i −0.637446 0.534881i
\(415\) 0 0
\(416\) 0.368685 + 0.134190i 0.368685 + 0.134190i
\(417\) 0 0
\(418\) 0.524123 + 1.61308i 0.524123 + 1.61308i
\(419\) 1.82709 1.82709 0.913545 0.406737i \(-0.133333\pi\)
0.913545 + 0.406737i \(0.133333\pi\)
\(420\) 0 0
\(421\) 0 0 −0.173648 0.984808i \(-0.555556\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) −0.317954 + 1.80321i −0.317954 + 1.80321i
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0.374607 + 0.648838i 0.374607 + 0.648838i
\(430\) 0 0
\(431\) 0.152245 0.863423i 0.152245 0.863423i −0.809017 0.587785i \(-0.800000\pi\)
0.961262 0.275637i \(-0.0888889\pi\)
\(432\) 0.532924 0.447176i 0.532924 0.447176i
\(433\) 1.51718 + 1.27306i 1.51718 + 1.27306i 0.848048 + 0.529919i \(0.177778\pi\)
0.669131 + 0.743145i \(0.266667\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 2.51157 2.51157
\(437\) 0.948445 + 0.592654i 0.948445 + 0.592654i
\(438\) −0.785359 −0.785359
\(439\) 0 0 −0.939693 0.342020i \(-0.888889\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(440\) 0 0
\(441\) 0.257378 + 0.215965i 0.257378 + 0.215965i
\(442\) 0 0
\(443\) −0.346450 + 1.96482i −0.346450 + 1.96482i −0.104528 + 0.994522i \(0.533333\pi\)
−0.241922 + 0.970296i \(0.577778\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 1.28633 0.468185i 1.28633 0.468185i
\(448\) −0.317130 0.549285i −0.317130 0.549285i
\(449\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(450\) −0.129202 + 0.732739i −0.129202 + 0.732739i
\(451\) 1.47274 1.23577i 1.47274 1.23577i
\(452\) −2.53877 2.13028i −2.53877 2.13028i
\(453\) 0.130100 + 0.737831i 0.130100 + 0.737831i
\(454\) −0.985028 0.358521i −0.985028 0.358521i
\(455\) 0 0
\(456\) −0.745485 + 0.827945i −0.745485 + 0.827945i
\(457\) 1.98054 1.98054 0.990268 0.139173i \(-0.0444444\pi\)
0.990268 + 0.139173i \(0.0444444\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −1.49861 + 1.25748i −1.49861 + 1.25748i −0.615661 + 0.788011i \(0.711111\pi\)
−0.882948 + 0.469472i \(0.844444\pi\)
\(462\) 0.106766 0.605498i 0.106766 0.605498i
\(463\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0.939693 + 1.62760i 0.939693 + 1.62760i 0.766044 + 0.642788i \(0.222222\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(468\) 0.411644 0.712989i 0.411644 0.712989i
\(469\) 0 0
\(470\) 0 0
\(471\) 0.119984 + 0.100679i 0.119984 + 0.100679i
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0.0348995 0.999391i 0.0348995 0.999391i
\(476\) 0 0
\(477\) −0.507581 0.184744i −0.507581 0.184744i
\(478\) 0.583315 + 3.30815i 0.583315 + 3.30815i
\(479\) 1.17365 + 0.984808i 1.17365 + 0.984808i 1.00000 \(0\)
0.173648 + 0.984808i \(0.444444\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 1.69196 2.93057i 1.69196 2.93057i
\(483\) −0.202709 0.351102i −0.202709 0.351102i
\(484\) −1.76356 + 0.641884i −1.76356 + 0.641884i
\(485\) 0 0
\(486\) 0.679717 + 1.17730i 0.679717 + 1.17730i
\(487\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 0 0 −0.173648 0.984808i \(-0.555556\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(492\) 2.54020 + 0.924556i 2.54020 + 0.924556i
\(493\) 0 0
\(494\) −0.635369 + 1.57259i −0.635369 + 1.57259i
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 1.94214 + 1.62965i 1.94214 + 1.62965i
\(499\) 0 0 0.766044 0.642788i \(-0.222222\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(500\) 0 0
\(501\) −0.661516 + 1.14578i −0.661516 + 1.14578i
\(502\) 1.37217 + 2.37667i 1.37217 + 2.37667i
\(503\) 0 0 0.939693 0.342020i \(-0.111111\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(504\) −0.296593 + 0.107951i −0.296593 + 0.107951i
\(505\) 0 0
\(506\) −0.948445 + 1.64275i −0.948445 + 1.64275i
\(507\) −0.130100 + 0.737831i −0.130100 + 0.737831i
\(508\) 0 0
\(509\) 0 0 −0.766044 0.642788i \(-0.777778\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(510\) 0 0
\(511\) 0.280998 + 0.102275i 0.280998 + 0.102275i
\(512\) −1.21299 −1.21299
\(513\) −0.663608 0.849379i −0.663608 0.849379i
\(514\) −2.74434 −2.74434
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0.104528 + 0.181049i 0.104528 + 0.181049i 0.913545 0.406737i \(-0.133333\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(522\) 0 0
\(523\) 0 0 0.939693 0.342020i \(-0.111111\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(524\) 0 0
\(525\) −0.181251 + 0.313936i −0.181251 + 0.313936i
\(526\) 0 0
\(527\) 0 0
\(528\) −0.370426 0.310824i −0.370426 0.310824i
\(529\) 0.0435487 + 0.246977i 0.0435487 + 0.246977i
\(530\) 0 0
\(531\) 0 0
\(532\) 0.801761 0.426304i 0.801761 0.426304i
\(533\) 1.92252 1.92252
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −0.199324 + 0.167253i −0.199324 + 0.167253i
\(538\) 0.566229 3.21125i 0.566229 3.21125i
\(539\) 0.382948 0.663285i 0.382948 0.663285i
\(540\) 0 0
\(541\) 1.35192 0.492057i 1.35192 0.492057i 0.438371 0.898794i \(-0.355556\pi\)
0.913545 + 0.406737i \(0.133333\pi\)
\(542\) −0.111246 + 0.0404903i −0.111246 + 0.0404903i
\(543\) 0.0261472 + 0.0452882i 0.0261472 + 0.0452882i
\(544\) 0 0
\(545\) 0 0
\(546\) 0.470994 0.395211i 0.470994 0.395211i
\(547\) 0 0 −0.766044 0.642788i \(-0.777778\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 1.69610 1.69610
\(551\) 0 0
\(552\) −1.24600 −1.24600
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0.333843 1.89332i 0.333843 1.89332i −0.104528 0.994522i \(-0.533333\pi\)
0.438371 0.898794i \(-0.355556\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) −0.0591929 0.102525i −0.0591929 0.102525i
\(563\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0.0309928 + 0.175769i 0.0309928 + 0.175769i
\(568\) 0 0
\(569\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(572\) −1.76356 0.641884i −1.76356 0.641884i
\(573\) −0.174107 0.987411i −0.174107 0.987411i
\(574\) −1.20860 1.01413i −1.20860 1.01413i
\(575\) 0.856733 0.718885i 0.856733 0.718885i
\(576\) 0.0998572 0.566318i 0.0998572 0.566318i
\(577\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(578\) −0.848048 1.46886i −0.848048 1.46886i
\(579\) 0.787377 0.286582i 0.787377 0.286582i
\(580\) 0 0
\(581\) −0.482665 0.836001i −0.482665 0.836001i
\(582\) 0 0
\(583\) −0.213817 + 1.21262i −0.213817 + 1.21262i
\(584\) 0.704026 0.590748i 0.704026 0.590748i
\(585\) 0 0
\(586\) 0.451237 + 2.55909i 0.451237 + 2.55909i
\(587\) 0 0 −0.939693 0.342020i \(-0.888889\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(588\) 1.07691 1.07691
\(589\) 0 0
\(590\) 0 0
\(591\) 0.0491406 + 0.0178857i 0.0491406 + 0.0178857i
\(592\) 0 0
\(593\) −0.160147 0.134379i −0.160147 0.134379i 0.559193 0.829038i \(-0.311111\pi\)
−0.719340 + 0.694658i \(0.755556\pi\)
\(594\) 1.40047 1.17513i 1.40047 1.17513i
\(595\) 0 0
\(596\) −1.71449 + 2.96958i −1.71449 + 2.96958i
\(597\) 0.741922 + 1.28505i 0.741922 + 1.28505i
\(598\) −1.78249 + 0.648775i −1.78249 + 0.648775i
\(599\) −1.59381 + 0.580099i −1.59381 + 0.580099i −0.978148 0.207912i \(-0.933333\pi\)
−0.615661 + 0.788011i \(0.711111\pi\)
\(600\) 0.557055 + 0.964847i 0.557055 + 0.964847i
\(601\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −1.43767 1.20635i −1.43767 1.20635i
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(608\) −0.0136927 + 0.392107i −0.0136927 + 0.392107i
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) −1.35275 + 1.13510i −1.35275 + 1.13510i −0.374607 + 0.927184i \(0.622222\pi\)
−0.978148 + 0.207912i \(0.933333\pi\)
\(614\) 0.102287 0.580099i 0.102287 0.580099i
\(615\) 0 0
\(616\) 0.359747 + 0.623101i 0.359747 + 0.623101i
\(617\) 0 0 0.939693 0.342020i \(-0.111111\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(618\) 1.04692 0.381048i 1.04692 0.381048i
\(619\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(620\) 0 0
\(621\) 0.209330 1.18717i 0.209330 1.18717i
\(622\) −0.973442 + 0.816814i −0.973442 + 0.816814i
\(623\) 0 0
\(624\) −0.0839687 0.476210i −0.0839687 0.476210i
\(625\) −0.939693 0.342020i −0.939693 0.342020i
\(626\) 3.09892 3.09892
\(627\) −0.501321 + 0.556774i −0.501321 + 0.556774i
\(628\) −0.392346 −0.392346
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 −0.766044 0.642788i \(-0.777778\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) −1.62693 + 0.592153i −1.62693 + 0.592153i
\(637\) 0.719706 0.261952i 0.719706 0.261952i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0.671624 0.563559i 0.671624 0.563559i −0.241922 0.970296i \(-0.577778\pi\)
0.913545 + 0.406737i \(0.133333\pi\)
\(642\) 0 0
\(643\) 0 0 −0.173648 0.984808i \(-0.555556\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(644\) 0.954305 + 0.347339i 0.954305 + 0.347339i
\(645\) 0 0
\(646\) 0 0
\(647\) 0.0697990 0.0697990 0.0348995 0.999391i \(-0.488889\pi\)
0.0348995 + 0.999391i \(0.488889\pi\)
\(648\) 0.515459 + 0.187612i 0.515459 + 0.187612i
\(649\) 0 0
\(650\) 1.29929 + 1.09023i 1.29929 + 1.09023i
\(651\) 0 0
\(652\) 0 0
\(653\) −0.766044 + 1.32683i −0.766044 + 1.32683i 0.173648 + 0.984808i \(0.444444\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(654\) 0.850289 + 1.47274i 0.850289 + 1.47274i
\(655\) 0 0
\(656\) −1.16600 + 0.424390i −1.16600 + 0.424390i
\(657\) 0.135559 + 0.234796i 0.135559 + 0.234796i
\(658\) 0 0
\(659\) 0 0 0.173648 0.984808i \(-0.444444\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(660\) 0 0
\(661\) 0 0 −0.766044 0.642788i \(-0.777778\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) −2.96683 −2.96683
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) −0.575493 3.26378i −0.575493 3.26378i
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0.0711131 0.123172i 0.0711131 0.123172i
\(673\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(674\) 0 0
\(675\) −1.01287 + 0.368656i −1.01287 + 0.368656i
\(676\) −0.938371 1.62531i −0.938371 1.62531i
\(677\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(678\) 0.389665 2.20990i 0.389665 2.20990i
\(679\) 0 0
\(680\) 0 0
\(681\) −0.0804059 0.456005i −0.0804059 0.456005i
\(682\) 0 0
\(683\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(684\) 0.805298 + 0.171171i 0.805298 + 0.171171i
\(685\) 0 0
\(686\) −1.36178 0.495647i −1.36178 0.495647i
\(687\) 0 0
\(688\) 0 0
\(689\) −0.943248 + 0.791479i −0.943248 + 0.791479i
\(690\) 0 0
\(691\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(692\) 0 0
\(693\) −0.199452 + 0.0725946i −0.199452 + 0.0725946i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 1.13914 0.955850i 1.13914 0.955850i
\(699\) 0 0
\(700\) −0.157681 0.894255i −0.157681 0.894255i
\(701\) 0 0 −0.939693 0.342020i \(-0.888889\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(702\) 1.82818 1.82818
\(703\) 0 0
\(704\) −1.31088 −1.31088
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 0 0 0.173648 0.984808i \(-0.444444\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0.113181 0.641884i 0.113181 0.641884i
\(717\) −1.13669 + 0.953796i −1.13669 + 0.953796i
\(718\) 1.45310 + 1.21930i 1.45310 + 1.21930i
\(719\) 0.266044 + 1.50881i 0.266044 + 1.50881i 0.766044 + 0.642788i \(0.222222\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(720\) 0 0
\(721\) −0.424206 −0.424206
\(722\) −1.69196 0.118314i −1.69196 0.118314i
\(723\) 1.49478 1.49478
\(724\) −0.123095 0.0448028i −0.123095 0.0448028i
\(725\) 0 0
\(726\) −0.973442 0.816814i −0.973442 0.816814i
\(727\) −0.370646 + 0.311009i −0.370646 + 0.311009i −0.809017 0.587785i \(-0.800000\pi\)
0.438371 + 0.898794i \(0.355556\pi\)
\(728\) −0.124939 + 0.708564i −0.124939 + 0.708564i
\(729\) −0.484690 + 0.839508i −0.484690 + 0.839508i
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0.997564 + 1.72783i 0.997564 + 1.72783i 0.559193 + 0.829038i \(0.311111\pi\)
0.438371 + 0.898794i \(0.355556\pi\)
\(734\) −0.524123 + 0.907807i −0.524123 + 0.907807i
\(735\) 0 0
\(736\) −0.336136 + 0.282051i −0.336136 + 0.282051i
\(737\) 0 0
\(738\) −0.248393 1.40871i −0.248393 1.40871i
\(739\) −1.80658 0.657542i −1.80658 0.657542i −0.997564 0.0697565i \(-0.977778\pi\)
−0.809017 0.587785i \(-0.800000\pi\)
\(740\) 0 0
\(741\) −0.741922 + 0.104270i −0.741922 + 0.104270i
\(742\) 1.01048 1.01048
\(743\) −0.326352 0.118782i −0.326352 0.118782i 0.173648 0.984808i \(-0.444444\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0.151981 0.861925i 0.151981 0.861925i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 1.83832 0.669092i 1.83832 0.669092i 0.848048 0.529919i \(-0.177778\pi\)
0.990268 0.139173i \(-0.0444444\pi\)
\(752\) 0 0
\(753\) −0.606126 + 1.04984i −0.606126 + 1.04984i
\(754\) 0 0
\(755\) 0 0
\(756\) −0.749779 0.629139i −0.749779 0.629139i
\(757\) −0.280969 1.59345i −0.280969 1.59345i −0.719340 0.694658i \(-0.755556\pi\)
0.438371 0.898794i \(-0.355556\pi\)
\(758\) 0 0
\(759\) −0.837909 −0.837909
\(760\) 0 0
\(761\) −1.43868 −1.43868 −0.719340 0.694658i \(-0.755556\pi\)
−0.719340 + 0.694658i \(0.755556\pi\)
\(762\) 0 0
\(763\) −0.112439 0.637672i −0.112439 0.637672i
\(764\) 1.92398 + 1.61441i 1.92398 + 1.61441i
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) −0.672314 1.16448i −0.672314 1.16448i
\(769\) −1.80658 + 0.657542i −1.80658 + 0.657542i −0.809017 + 0.587785i \(0.800000\pi\)
−0.997564 + 0.0697565i \(0.977778\pi\)
\(770\) 0 0
\(771\) −0.606126 1.04984i −0.606126 1.04984i
\(772\) −1.04946 + 1.81772i −1.04946 + 1.81772i
\(773\) 0 0 0.173648 0.984808i \(-0.444444\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) −3.31806 −3.31806
\(779\) 0.594092 + 1.82843i 0.594092 + 1.82843i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −0.378674 + 0.317745i −0.378674 + 0.317745i
\(785\) 0 0
\(786\) 0 0
\(787\) 0.241922 + 0.419021i 0.241922 + 0.419021i 0.961262 0.275637i \(-0.0888889\pi\)
−0.719340 + 0.694658i \(0.755556\pi\)
\(788\) −0.123095 + 0.0448028i −0.123095 + 0.0448028i
\(789\) 0 0
\(790\) 0 0
\(791\) −0.427209 + 0.739947i −0.427209 + 0.739947i
\(792\) −0.113277 + 0.642423i −0.113277 + 0.642423i
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) −3.49280 1.27127i −3.49280 1.27127i
\(797\) 1.53209 1.53209 0.766044 0.642788i \(-0.222222\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(798\) 0.521413 + 0.325815i 0.521413 + 0.325815i
\(799\) 0 0
\(800\) 0.368685 + 0.134190i 0.368685 + 0.134190i
\(801\) 0 0
\(802\) 0 0
\(803\) 0.473442 0.397265i 0.473442 0.397265i
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 1.35351 0.492639i 1.35351 0.492639i
\(808\) 0 0
\(809\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(810\) 0 0
\(811\) −0.249824 + 1.41682i −0.249824 + 1.41682i 0.559193 + 0.829038i \(0.311111\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(812\) 0 0
\(813\) −0.0400598 0.0336141i −0.0400598 0.0336141i
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) −3.18762 −3.18762
\(819\) −0.199452 0.0725946i −0.199452 0.0725946i
\(820\) 0 0
\(821\) −0.766044 0.642788i −0.766044 0.642788i 0.173648 0.984808i \(-0.444444\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(822\) 0 0
\(823\) −0.280969 + 1.59345i −0.280969 + 1.59345i 0.438371 + 0.898794i \(0.355556\pi\)
−0.719340 + 0.694658i \(0.755556\pi\)
\(824\) −0.651875 + 1.12908i −0.651875 + 1.12908i
\(825\) 0.374607 + 0.648838i 0.374607 + 0.648838i
\(826\) 0 0
\(827\) 1.83832 0.669092i 1.83832 0.669092i 0.848048 0.529919i \(-0.177778\pi\)
0.990268 0.139173i \(-0.0444444\pi\)
\(828\) 0.460377 + 0.797397i 0.460377 + 0.797397i
\(829\) 0.809017 1.40126i 0.809017 1.40126i −0.104528 0.994522i \(-0.533333\pi\)
0.913545 0.406737i \(-0.133333\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) −1.00419 0.842615i −1.00419 0.842615i
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0.0654974 1.87560i 0.0654974 1.87560i
\(837\) 0 0
\(838\) −2.91203 1.05989i −2.91203 1.05989i
\(839\) 0 0 −0.173648 0.984808i \(-0.555556\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(840\) 0 0
\(841\) 0.766044 0.642788i 0.766044 0.642788i
\(842\) 0 0
\(843\) 0.0261472 0.0452882i 0.0261472 0.0452882i
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 0.241922 + 0.419021i 0.241922 + 0.419021i
\(848\) 0.397360 0.688247i 0.397360 0.688247i
\(849\) 0 0
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) −1.59381 0.580099i −1.59381 0.580099i −0.615661 0.788011i \(-0.711111\pi\)
−0.978148 + 0.207912i \(0.933333\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 −0.939693 0.342020i \(-0.888889\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(858\) −0.220661 1.25143i −0.220661 1.25143i
\(859\) 0.0534691 + 0.0448659i 0.0534691 + 0.0448659i 0.669131 0.743145i \(-0.266667\pi\)
−0.615661 + 0.788011i \(0.711111\pi\)
\(860\) 0 0
\(861\) 0.121019 0.686331i 0.121019 0.686331i
\(862\) −0.743520 + 1.28781i −0.743520 + 1.28781i
\(863\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(864\) 0.397397 0.144641i 0.397397 0.144641i
\(865\) 0 0
\(866\) −1.67959 2.90914i −1.67959 2.90914i
\(867\) 0.374607 0.648838i 0.374607 0.648838i
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) −1.87003 0.680636i −1.87003 0.680636i
\(873\) 0 0
\(874\) −1.16784 1.49477i −1.16784 1.49477i
\(875\) 0 0
\(876\) 0.816598 + 0.297217i 0.816598 + 0.297217i
\(877\) 0.107320 + 0.608645i 0.107320 + 0.608645i 0.990268 + 0.139173i \(0.0444444\pi\)
−0.882948 + 0.469472i \(0.844444\pi\)
\(878\) 0 0
\(879\) −0.879313 + 0.737831i −0.879313 + 0.737831i
\(880\) 0 0
\(881\) 0.615661 1.06636i 0.615661 1.06636i −0.374607 0.927184i \(-0.622222\pi\)
0.990268 0.139173i \(-0.0444444\pi\)
\(882\) −0.284929 0.493512i −0.284929 0.493512i
\(883\) 0.704030 0.256246i 0.704030 0.256246i 0.0348995 0.999391i \(-0.488889\pi\)
0.669131 + 0.743145i \(0.266667\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 1.69196 2.93057i 1.69196 2.93057i
\(887\) 0 0 0.173648 0.984808i \(-0.444444\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 0.346634 + 0.126165i 0.346634 + 0.126165i
\(892\) 0 0
\(893\) 0 0
\(894\) −2.32175 −2.32175
\(895\) 0 0
\(896\) 0.153840 + 0.872471i 0.153840 + 0.872471i
\(897\) −0.641876 0.538598i −0.641876 0.538598i
\(898\) 0 0
\(899\) 0 0
\(900\) 0.411644 0.712989i 0.411644 0.712989i
\(901\) 0 0
\(902\) −3.06414 + 1.11525i −3.06414 + 1.11525i
\(903\) 0 0
\(904\) 1.31298 + 2.27414i 1.31298 + 2.27414i
\(905\) 0 0
\(906\) 0.220661 1.25143i 0.220661 1.25143i
\(907\) −1.23949 + 1.04005i −1.23949 + 1.04005i −0.241922 + 0.970296i \(0.577778\pi\)
−0.997564 + 0.0697565i \(0.977778\pi\)
\(908\) 0.888528 + 0.745563i 0.888528 + 0.745563i
\(909\) 0 0
\(910\) 0 0
\(911\) 1.11839 1.11839 0.559193 0.829038i \(-0.311111\pi\)
0.559193 + 0.829038i \(0.311111\pi\)
\(912\) 0.426955 0.227016i 0.426955 0.227016i
\(913\) −1.99513 −1.99513
\(914\) −3.15660 1.14891i −3.15660 1.14891i
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(920\) 0 0
\(921\) 0.244507 0.0889933i 0.244507 0.0889933i
\(922\) 3.11796 1.13485i 3.11796 1.13485i
\(923\) 0 0
\(924\) −0.340162 + 0.589177i −0.340162 + 0.589177i
\(925\) 0 0
\(926\) 0 0
\(927\) −0.294628 0.247222i −0.294628 0.247222i
\(928\) 0 0
\(929\) 0 0 −0.939693 0.342020i \(-0.888889\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(930\) 0 0
\(931\) 0.471532 + 0.603534i 0.471532 + 0.603534i
\(932\) 0 0
\(933\) −0.527469 0.191983i −0.527469 0.191983i
\(934\) −0.553524 3.13919i −0.553524 3.13919i
\(935\) 0 0
\(936\) −0.499717 + 0.419312i −0.499717 + 0.419312i
\(937\) 0 0 0.173648 0.984808i \(-0.444444\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(938\) 0 0
\(939\) 0.684440 + 1.18549i 0.684440 + 1.18549i
\(940\) 0 0
\(941\) 1.83832 0.669092i 1.83832 0.669092i 0.848048 0.529919i \(-0.177778\pi\)
0.990268 0.139173i \(-0.0444444\pi\)
\(942\) −0.132828 0.230065i −0.132828 0.230065i
\(943\) −1.07506 + 1.86206i −1.07506 + 1.86206i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 0 0 −0.173648 0.984808i \(-0.555556\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(948\) 0 0
\(949\) 0.618034 0.618034
\(950\) −0.635369 + 1.57259i −0.635369 + 1.57259i
\(951\) 0 0
\(952\) 0 0
\(953\) 0 0 −0.173648 0.984808i \(-0.555556\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(954\) 0.701817 + 0.588894i 0.701817 + 0.588894i
\(955\) 0 0
\(956\) 0.645443 3.66049i 0.645443 3.66049i
\(957\) 0 0
\(958\) −1.29929 2.25043i −1.29929 2.25043i
\(959\) 0 0
\(960\) 0 0
\(961\) −0.500000 0.866025i −0.500000 0.866025i
\(962\) 0 0
\(963\) 0 0
\(964\) −2.86833 + 2.40682i −2.86833 + 2.40682i
\(965\) 0 0
\(966\) 0.119405 + 0.677180i 0.119405 + 0.677180i
\(967\) 1.65940 + 0.603972i 1.65940 + 0.603972i 0.990268 0.139173i \(-0.0444444\pi\)
0.669131 + 0.743145i \(0.266667\pi\)
\(968\) 1.48704 1.48704
\(969\) 0 0
\(970\) 0 0
\(971\) 1.83832 + 0.669092i 1.83832 + 0.669092i 0.990268 + 0.139173i \(0.0444444\pi\)
0.848048 + 0.529919i \(0.177778\pi\)
\(972\) −0.261206 1.48137i −0.261206 1.48137i
\(973\) 0 0
\(974\) 0 0
\(975\) −0.130100 + 0.737831i −0.130100 + 0.737831i
\(976\) 0 0
\(977\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 0.293534 0.508416i 0.293534 0.508416i
\(982\) 0 0
\(983\) 0 0 0.766044 0.642788i \(-0.222222\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(984\) −1.64079 1.37679i −1.64079 1.37679i
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 1.25579 1.39469i 1.25579 1.39469i
\(989\) 0 0
\(990\) 0 0
\(991\) −0.213817 1.21262i −0.213817 1.21262i −0.882948 0.469472i \(-0.844444\pi\)
0.669131 0.743145i \(-0.266667\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) −1.40265 2.42947i −1.40265 2.42947i
\(997\) 0 0 0.939693 0.342020i \(-0.111111\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(998\) 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 2717.1.db.d.1429.1 yes 24
11.10 odd 2 2717.1.db.c.1429.4 24
13.12 even 2 2717.1.db.c.1429.4 24
19.5 even 9 inner 2717.1.db.d.1715.1 yes 24
143.142 odd 2 CM 2717.1.db.d.1429.1 yes 24
209.43 odd 18 2717.1.db.c.1715.4 yes 24
247.233 even 18 2717.1.db.c.1715.4 yes 24
2717.1715 odd 18 inner 2717.1.db.d.1715.1 yes 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2717.1.db.c.1429.4 24 11.10 odd 2
2717.1.db.c.1429.4 24 13.12 even 2
2717.1.db.c.1715.4 yes 24 209.43 odd 18
2717.1.db.c.1715.4 yes 24 247.233 even 18
2717.1.db.d.1429.1 yes 24 1.1 even 1 trivial
2717.1.db.d.1429.1 yes 24 143.142 odd 2 CM
2717.1.db.d.1715.1 yes 24 19.5 even 9 inner
2717.1.db.d.1715.1 yes 24 2717.1715 odd 18 inner