Properties

Label 3267.1.be.a.2864.1
Level $3267$
Weight $1$
Character 3267.2864
Analytic conductor $1.630$
Analytic rank $0$
Dimension $24$
Projective image $D_{18}$
CM discriminant -11
Inner twists $16$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [3267,1,Mod(245,3267)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3267, base_ring=CyclotomicField(90))
 
chi = DirichletCharacter(H, H._module([5, 72]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3267.245");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3267 = 3^{3} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3267.be (of order \(90\), degree \(24\), not 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: \(1.63044539627\)
Analytic rank: \(0\)
Dimension: \(24\)
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: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{18}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{18} - \cdots)\)

Embedding invariants

Embedding label 2864.1
Root \(0.848048 - 0.529919i\) of defining polynomial
Character \(\chi\) \(=\) 3267.2864
Dual form 3267.1.be.a.608.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.990268 - 0.139173i) q^{3} +(0.0348995 - 0.999391i) q^{4} +(-0.663721 - 0.165484i) q^{5} +(0.961262 + 0.275637i) q^{9} +O(q^{10})\) \(q+(-0.990268 - 0.139173i) q^{3} +(0.0348995 - 0.999391i) q^{4} +(-0.663721 - 0.165484i) q^{5} +(0.961262 + 0.275637i) q^{9} +(-0.173648 + 0.984808i) q^{12} +(0.634231 + 0.256246i) q^{15} +(-0.997564 - 0.0697565i) q^{16} +(-0.188547 + 0.657542i) q^{20} +(0.592396 - 1.62760i) q^{23} +(-0.469807 - 0.249801i) q^{25} +(-0.913545 - 0.406737i) q^{27} +(-0.194206 - 0.287922i) q^{31} +(0.309017 - 0.951057i) q^{36} +(1.25755 - 1.39666i) q^{37} +(-0.592396 - 0.342020i) q^{45} +(-1.28479 + 0.0448659i) q^{47} +(0.978148 + 0.207912i) q^{48} +(0.241922 - 0.970296i) q^{49} +(-1.15771 + 1.59345i) q^{53} +(-1.04374 + 1.67033i) q^{59} +(0.278224 - 0.624902i) q^{60} +(-0.104528 + 0.994522i) q^{64} +(-0.0603074 - 0.342020i) q^{67} +(-0.813149 + 1.52931i) q^{69} +(-0.522891 + 1.17443i) q^{71} +(0.430469 + 0.312754i) q^{75} +(0.650561 + 0.211380i) q^{80} +(0.848048 + 0.529919i) q^{81} +(-1.50000 - 0.866025i) q^{89} +(-1.60593 - 0.648838i) q^{92} +(0.152245 + 0.312148i) q^{93} +(-0.370646 - 1.48658i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 3 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 3 q^{5} + 3 q^{15} + 6 q^{20} + 3 q^{25} - 3 q^{27} - 3 q^{31} - 6 q^{36} - 3 q^{47} - 3 q^{48} - 3 q^{59} + 3 q^{64} - 24 q^{67} - 6 q^{75} - 36 q^{89} - 6 q^{93} - 6 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3267\mathbb{Z}\right)^\times\).

\(n\) \(244\) \(3026\)
\(\chi(n)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{18}\right)\)

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 0 0.719340 0.694658i \(-0.244444\pi\)
−0.719340 + 0.694658i \(0.755556\pi\)
\(3\) −0.990268 0.139173i −0.990268 0.139173i
\(4\) 0.0348995 0.999391i 0.0348995 0.999391i
\(5\) −0.663721 0.165484i −0.663721 0.165484i −0.104528 0.994522i \(-0.533333\pi\)
−0.559193 + 0.829038i \(0.688889\pi\)
\(6\) 0 0
\(7\) 0 0 0.788011 0.615661i \(-0.211111\pi\)
−0.788011 + 0.615661i \(0.788889\pi\)
\(8\) 0 0
\(9\) 0.961262 + 0.275637i 0.961262 + 0.275637i
\(10\) 0 0
\(11\) 0 0
\(12\) −0.173648 + 0.984808i −0.173648 + 0.984808i
\(13\) 0 0 −0.898794 0.438371i \(-0.855556\pi\)
0.898794 + 0.438371i \(0.144444\pi\)
\(14\) 0 0
\(15\) 0.634231 + 0.256246i 0.634231 + 0.256246i
\(16\) −0.997564 0.0697565i −0.997564 0.0697565i
\(17\) 0 0 −0.913545 0.406737i \(-0.866667\pi\)
0.913545 + 0.406737i \(0.133333\pi\)
\(18\) 0 0
\(19\) 0 0 0.743145 0.669131i \(-0.233333\pi\)
−0.743145 + 0.669131i \(0.766667\pi\)
\(20\) −0.188547 + 0.657542i −0.188547 + 0.657542i
\(21\) 0 0
\(22\) 0 0
\(23\) 0.592396 1.62760i 0.592396 1.62760i −0.173648 0.984808i \(-0.555556\pi\)
0.766044 0.642788i \(-0.222222\pi\)
\(24\) 0 0
\(25\) −0.469807 0.249801i −0.469807 0.249801i
\(26\) 0 0
\(27\) −0.913545 0.406737i −0.913545 0.406737i
\(28\) 0 0
\(29\) 0 0 0.990268 0.139173i \(-0.0444444\pi\)
−0.990268 + 0.139173i \(0.955556\pi\)
\(30\) 0 0
\(31\) −0.194206 0.287922i −0.194206 0.287922i 0.719340 0.694658i \(-0.244444\pi\)
−0.913545 + 0.406737i \(0.866667\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0.309017 0.951057i 0.309017 0.951057i
\(37\) 1.25755 1.39666i 1.25755 1.39666i 0.374607 0.927184i \(-0.377778\pi\)
0.882948 0.469472i \(-0.155556\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 −0.990268 0.139173i \(-0.955556\pi\)
0.990268 + 0.139173i \(0.0444444\pi\)
\(42\) 0 0
\(43\) 0 0 0.642788 0.766044i \(-0.277778\pi\)
−0.642788 + 0.766044i \(0.722222\pi\)
\(44\) 0 0
\(45\) −0.592396 0.342020i −0.592396 0.342020i
\(46\) 0 0
\(47\) −1.28479 + 0.0448659i −1.28479 + 0.0448659i −0.669131 0.743145i \(-0.733333\pi\)
−0.615661 + 0.788011i \(0.711111\pi\)
\(48\) 0.978148 + 0.207912i 0.978148 + 0.207912i
\(49\) 0.241922 0.970296i 0.241922 0.970296i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −1.15771 + 1.59345i −1.15771 + 1.59345i −0.438371 + 0.898794i \(0.644444\pi\)
−0.719340 + 0.694658i \(0.755556\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −1.04374 + 1.67033i −1.04374 + 1.67033i −0.374607 + 0.927184i \(0.622222\pi\)
−0.669131 + 0.743145i \(0.733333\pi\)
\(60\) 0.278224 0.624902i 0.278224 0.624902i
\(61\) 0 0 −0.829038 0.559193i \(-0.811111\pi\)
0.829038 + 0.559193i \(0.188889\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −0.104528 + 0.994522i −0.104528 + 0.994522i
\(65\) 0 0
\(66\) 0 0
\(67\) −0.0603074 0.342020i −0.0603074 0.342020i 0.939693 0.342020i \(-0.111111\pi\)
−1.00000 \(\pi\)
\(68\) 0 0
\(69\) −0.813149 + 1.52931i −0.813149 + 1.52931i
\(70\) 0 0
\(71\) −0.522891 + 1.17443i −0.522891 + 1.17443i 0.438371 + 0.898794i \(0.355556\pi\)
−0.961262 + 0.275637i \(0.911111\pi\)
\(72\) 0 0
\(73\) 0 0 0.207912 0.978148i \(-0.433333\pi\)
−0.207912 + 0.978148i \(0.566667\pi\)
\(74\) 0 0
\(75\) 0.430469 + 0.312754i 0.430469 + 0.312754i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 −0.694658 0.719340i \(-0.744444\pi\)
0.694658 + 0.719340i \(0.255556\pi\)
\(80\) 0.650561 + 0.211380i 0.650561 + 0.211380i
\(81\) 0.848048 + 0.529919i 0.848048 + 0.529919i
\(82\) 0 0
\(83\) 0 0 −0.438371 0.898794i \(-0.644444\pi\)
0.438371 + 0.898794i \(0.355556\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −1.50000 0.866025i −1.50000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
−1.00000 \(\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −1.60593 0.648838i −1.60593 0.648838i
\(93\) 0.152245 + 0.312148i 0.152245 + 0.312148i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −0.370646 1.48658i −0.370646 1.48658i −0.809017 0.587785i \(-0.800000\pi\)
0.438371 0.898794i \(-0.355556\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −0.266044 + 0.460802i −0.266044 + 0.460802i
\(101\) 0 0 −0.961262 0.275637i \(-0.911111\pi\)
0.961262 + 0.275637i \(0.0888889\pi\)
\(102\) 0 0
\(103\) −1.59381 0.995922i −1.59381 0.995922i −0.978148 0.207912i \(-0.933333\pi\)
−0.615661 0.788011i \(-0.711111\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(108\) −0.438371 + 0.898794i −0.438371 + 0.898794i
\(109\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(110\) 0 0
\(111\) −1.43969 + 1.20805i −1.43969 + 1.20805i
\(112\) 0 0
\(113\) −1.19196 + 0.481585i −1.19196 + 0.481585i −0.882948 0.469472i \(-0.844444\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(114\) 0 0
\(115\) −0.662528 + 0.982238i −0.662528 + 0.982238i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 0 0
\(122\) 0 0
\(123\) 0 0
\(124\) −0.294524 + 0.184039i −0.294524 + 0.184039i
\(125\) 0.778824 + 0.701256i 0.778824 + 0.701256i
\(126\) 0 0
\(127\) 0 0 0.994522 0.104528i \(-0.0333333\pi\)
−0.994522 + 0.104528i \(0.966667\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 −0.939693 0.342020i \(-0.888889\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0.539031 + 0.421137i 0.539031 + 0.421137i
\(136\) 0 0
\(137\) 1.77028 0.863423i 1.77028 0.863423i 0.809017 0.587785i \(-0.200000\pi\)
0.961262 0.275637i \(-0.0888889\pi\)
\(138\) 0 0
\(139\) 0 0 −0.999391 0.0348995i \(-0.988889\pi\)
0.999391 + 0.0348995i \(0.0111111\pi\)
\(140\) 0 0
\(141\) 1.27853 + 0.134379i 1.27853 + 0.134379i
\(142\) 0 0
\(143\) 0 0
\(144\) −0.939693 0.342020i −0.939693 0.342020i
\(145\) 0 0
\(146\) 0 0
\(147\) −0.374607 + 0.927184i −0.374607 + 0.927184i
\(148\) −1.35192 1.30553i −1.35192 1.30553i
\(149\) 0 0 −0.719340 0.694658i \(-0.755556\pi\)
0.719340 + 0.694658i \(0.244444\pi\)
\(150\) 0 0
\(151\) 0 0 −0.529919 0.848048i \(-0.677778\pi\)
0.529919 + 0.848048i \(0.322222\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0.0812519 + 0.223238i 0.0812519 + 0.223238i
\(156\) 0 0
\(157\) 0.130100 + 0.322008i 0.130100 + 0.322008i 0.978148 0.207912i \(-0.0666667\pi\)
−0.848048 + 0.529919i \(0.822222\pi\)
\(158\) 0 0
\(159\) 1.36821 1.41682i 1.36821 1.41682i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −1.23949 0.900539i −1.23949 0.900539i −0.241922 0.970296i \(-0.577778\pi\)
−0.997564 + 0.0697565i \(0.977778\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 0.997564 0.0697565i \(-0.0222222\pi\)
−0.997564 + 0.0697565i \(0.977778\pi\)
\(168\) 0 0
\(169\) 0.615661 + 0.788011i 0.615661 + 0.788011i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 0 0 0.848048 0.529919i \(-0.177778\pi\)
−0.848048 + 0.529919i \(0.822222\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 1.26604 1.50881i 1.26604 1.50881i
\(178\) 0 0
\(179\) −0.409506 1.92657i −0.409506 1.92657i −0.374607 0.927184i \(-0.622222\pi\)
−0.0348995 0.999391i \(-0.511111\pi\)
\(180\) −0.362486 + 0.580099i −0.362486 + 0.580099i
\(181\) 0.196449 + 1.86909i 0.196449 + 1.86909i 0.438371 + 0.898794i \(0.355556\pi\)
−0.241922 + 0.970296i \(0.577778\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −1.06579 + 0.718885i −1.06579 + 0.718885i
\(186\) 0 0
\(187\) 0 0
\(188\) 1.28558i 1.28558i
\(189\) 0 0
\(190\) 0 0
\(191\) −0.178917 1.27306i −0.178917 1.27306i −0.848048 0.529919i \(-0.822222\pi\)
0.669131 0.743145i \(-0.266667\pi\)
\(192\) 0.241922 0.970296i 0.241922 0.970296i
\(193\) 0 0 −0.275637 0.961262i \(-0.588889\pi\)
0.275637 + 0.961262i \(0.411111\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −0.961262 0.275637i −0.961262 0.275637i
\(197\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(198\) 0 0
\(199\) 0.766044 + 1.32683i 0.766044 + 1.32683i 0.939693 + 0.342020i \(0.111111\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(200\) 0 0
\(201\) 0.0121205 + 0.347085i 0.0121205 + 0.347085i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 1.01807 1.40126i 1.01807 1.40126i
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 −0.0697565 0.997564i \(-0.522222\pi\)
0.0697565 + 0.997564i \(0.477778\pi\)
\(212\) 1.55208 + 1.21262i 1.55208 + 1.21262i
\(213\) 0.681251 1.09023i 0.681251 1.09023i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −0.0348995 0.999391i −0.0348995 0.999391i −0.882948 0.469472i \(-0.844444\pi\)
0.848048 0.529919i \(-0.177778\pi\)
\(224\) 0 0
\(225\) −0.382753 0.369620i −0.382753 0.369620i
\(226\) 0 0
\(227\) 0 0 0.374607 0.927184i \(-0.377778\pi\)
−0.374607 + 0.927184i \(0.622222\pi\)
\(228\) 0 0
\(229\) 0.438371 0.898794i 0.438371 0.898794i −0.559193 0.829038i \(-0.688889\pi\)
0.997564 0.0697565i \(-0.0222222\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 0.104528 0.994522i \(-0.466667\pi\)
−0.104528 + 0.994522i \(0.533333\pi\)
\(234\) 0 0
\(235\) 0.860169 + 0.182834i 0.860169 + 0.182834i
\(236\) 1.63289 + 1.10140i 1.63289 + 1.10140i
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 0.615661 0.788011i \(-0.288889\pi\)
−0.615661 + 0.788011i \(0.711111\pi\)
\(240\) −0.614811 0.299864i −0.614811 0.299864i
\(241\) 0 0 −0.984808 0.173648i \(-0.944444\pi\)
0.984808 + 0.173648i \(0.0555556\pi\)
\(242\) 0 0
\(243\) −0.766044 0.642788i −0.766044 0.642788i
\(244\) 0 0
\(245\) −0.321137 + 0.603972i −0.321137 + 0.603972i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 0.913545 0.406737i \(-0.133333\pi\)
−0.913545 + 0.406737i \(0.866667\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0.990268 + 0.139173i 0.990268 + 0.139173i
\(257\) −0.813149 1.52931i −0.813149 1.52931i −0.848048 0.529919i \(-0.822222\pi\)
0.0348995 0.999391i \(-0.488889\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 0.939693 0.342020i \(-0.111111\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(264\) 0 0
\(265\) 1.03209 0.866025i 1.03209 0.866025i
\(266\) 0 0
\(267\) 1.36487 + 1.06636i 1.36487 + 1.06636i
\(268\) −0.343916 + 0.0483343i −0.343916 + 0.0483343i
\(269\) 0.755642 + 1.04005i 0.755642 + 1.04005i 0.997564 + 0.0697565i \(0.0222222\pi\)
−0.241922 + 0.970296i \(0.577778\pi\)
\(270\) 0 0
\(271\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(277\) 0 0 0.275637 0.961262i \(-0.411111\pi\)
−0.275637 + 0.961262i \(0.588889\pi\)
\(278\) 0 0
\(279\) −0.107320 0.330298i −0.107320 0.330298i
\(280\) 0 0
\(281\) 0 0 −0.997564 0.0697565i \(-0.977778\pi\)
0.997564 + 0.0697565i \(0.0222222\pi\)
\(282\) 0 0
\(283\) 0 0 0.139173 0.990268i \(-0.455556\pi\)
−0.139173 + 0.990268i \(0.544444\pi\)
\(284\) 1.15547 + 0.563559i 1.15547 + 0.563559i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 0.669131 + 0.743145i 0.669131 + 0.743145i
\(290\) 0 0
\(291\) 0.160147 + 1.52370i 0.160147 + 1.52370i
\(292\) 0 0
\(293\) 0 0 0.0348995 0.999391i \(-0.488889\pi\)
−0.0348995 + 0.999391i \(0.511111\pi\)
\(294\) 0 0
\(295\) 0.969164 0.935911i 0.969164 0.935911i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 0.327587 0.419292i 0.327587 0.419292i
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(308\) 0 0
\(309\) 1.43969 + 1.20805i 1.43969 + 1.20805i
\(310\) 0 0
\(311\) 0.274117 1.95045i 0.274117 1.95045i −0.0348995 0.999391i \(-0.511111\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(312\) 0 0
\(313\) −0.997564 0.0697565i −0.997564 0.0697565i −0.438371 0.898794i \(-0.644444\pi\)
−0.559193 + 0.829038i \(0.688889\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 −0.961262 0.275637i \(-0.911111\pi\)
0.961262 + 0.275637i \(0.0888889\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0.233956 0.642788i 0.233956 0.642788i
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0.559193 0.829038i 0.559193 0.829038i
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −1.43969 + 0.524005i −1.43969 + 0.524005i −0.939693 0.342020i \(-0.888889\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(332\) 0 0
\(333\) 1.59381 0.995922i 1.59381 0.995922i
\(334\) 0 0
\(335\) −0.0165717 + 0.236986i −0.0165717 + 0.236986i
\(336\) 0 0
\(337\) 0 0 −0.469472 0.882948i \(-0.655556\pi\)
0.469472 + 0.882948i \(0.344444\pi\)
\(338\) 0 0
\(339\) 1.24739 0.311009i 1.24739 0.311009i
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0.792781 0.880472i 0.792781 0.880472i
\(346\) 0 0
\(347\) 0 0 0.961262 0.275637i \(-0.0888889\pi\)
−0.961262 + 0.275637i \(0.911111\pi\)
\(348\) 0 0
\(349\) 0 0 0.469472 0.882948i \(-0.344444\pi\)
−0.469472 + 0.882948i \(0.655556\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 1.70574 + 0.300767i 1.70574 + 0.300767i 0.939693 0.342020i \(-0.111111\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(354\) 0 0
\(355\) 0.541404 0.692965i 0.541404 0.692965i
\(356\) −0.917847 + 1.46886i −0.917847 + 1.46886i
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 −0.978148 0.207912i \(-0.933333\pi\)
0.978148 + 0.207912i \(0.0666667\pi\)
\(360\) 0 0
\(361\) 0.104528 0.994522i 0.104528 0.994522i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −0.573931 + 1.42053i −0.573931 + 1.42053i 0.309017 + 0.951057i \(0.400000\pi\)
−0.882948 + 0.469472i \(0.844444\pi\)
\(368\) −0.704489 + 1.58231i −0.704489 + 1.58231i
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0.317271 0.141258i 0.317271 0.141258i
\(373\) 0 0 −0.642788 0.766044i \(-0.722222\pi\)
0.642788 + 0.766044i \(0.277778\pi\)
\(374\) 0 0
\(375\) −0.673648 0.802823i −0.673648 0.802823i
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 0.809017 0.587785i 0.809017 0.587785i −0.104528 0.994522i \(-0.533333\pi\)
0.913545 + 0.406737i \(0.133333\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −0.137393 1.96482i −0.137393 1.96482i −0.241922 0.970296i \(-0.577778\pi\)
0.104528 0.994522i \(-0.466667\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) −1.49861 + 0.318539i −1.49861 + 0.318539i
\(389\) 1.19196 + 0.481585i 1.19196 + 0.481585i 0.882948 0.469472i \(-0.155556\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −0.173648 + 0.300767i −0.173648 + 0.300767i −0.939693 0.342020i \(-0.888889\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0.451237 + 0.281964i 0.451237 + 0.281964i
\(401\) −0.188547 0.657542i −0.188547 0.657542i −0.997564 0.0697565i \(-0.977778\pi\)
0.809017 0.587785i \(-0.200000\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) −0.475174 0.492057i −0.475174 0.492057i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0 0 0.829038 0.559193i \(-0.188889\pi\)
−0.829038 + 0.559193i \(0.811111\pi\)
\(410\) 0 0
\(411\) −1.87322 + 0.608645i −1.87322 + 0.608645i
\(412\) −1.05094 + 1.55808i −1.05094 + 1.55808i
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −0.673648 + 0.118782i −0.673648 + 0.118782i −0.500000 0.866025i \(-0.666667\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(420\) 0 0
\(421\) 1.59381 0.995922i 1.59381 0.995922i 0.615661 0.788011i \(-0.288889\pi\)
0.978148 0.207912i \(-0.0666667\pi\)
\(422\) 0 0
\(423\) −1.24739 0.311009i −1.24739 0.311009i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(432\) 0.882948 + 0.469472i 0.882948 + 0.469472i
\(433\) −0.309017 0.951057i −0.309017 0.951057i −0.978148 0.207912i \(-0.933333\pi\)
0.669131 0.743145i \(-0.266667\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 −0.342020 0.939693i \(-0.611111\pi\)
0.342020 + 0.939693i \(0.388889\pi\)
\(440\) 0 0
\(441\) 0.500000 0.866025i 0.500000 0.866025i
\(442\) 0 0
\(443\) −0.362486 0.580099i −0.362486 0.580099i 0.615661 0.788011i \(-0.288889\pi\)
−0.978148 + 0.207912i \(0.933333\pi\)
\(444\) 1.15707 + 1.48098i 1.15707 + 1.48098i
\(445\) 0.852268 + 0.823026i 0.852268 + 0.823026i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 0.680293 + 0.0715017i 0.680293 + 0.0715017i 0.438371 0.898794i \(-0.355556\pi\)
0.241922 + 0.970296i \(0.422222\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0.439693 + 1.20805i 0.439693 + 1.20805i
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 0.898794 0.438371i \(-0.144444\pi\)
−0.898794 + 0.438371i \(0.855556\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0.958517 + 0.696404i 0.958517 + 0.696404i
\(461\) 0 0 0.173648 0.984808i \(-0.444444\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(462\) 0 0
\(463\) 0.939693 + 0.342020i 0.939693 + 0.342020i 0.766044 0.642788i \(-0.222222\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(464\) 0 0
\(465\) −0.0493925 0.232373i −0.0493925 0.232373i
\(466\) 0 0
\(467\) 1.27853 0.134379i 1.27853 0.134379i 0.559193 0.829038i \(-0.311111\pi\)
0.719340 + 0.694658i \(0.244444\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −0.0840186 0.336980i −0.0840186 0.336980i
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −1.55208 + 1.21262i −1.55208 + 1.21262i
\(478\) 0 0
\(479\) 0 0 0.559193 0.829038i \(-0.311111\pi\)
−0.559193 + 0.829038i \(0.688889\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 1.04801i 1.04801i
\(486\) 0 0
\(487\) 0.580762 1.78740i 0.580762 1.78740i −0.0348995 0.999391i \(-0.511111\pi\)
0.615661 0.788011i \(-0.288889\pi\)
\(488\) 0 0
\(489\) 1.10209 + 1.06428i 1.10209 + 1.06428i
\(490\) 0 0
\(491\) 0 0 −0.848048 0.529919i \(-0.822222\pi\)
0.848048 + 0.529919i \(0.177778\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0.173648 + 0.300767i 0.173648 + 0.300767i
\(497\) 0 0
\(498\) 0 0
\(499\) −1.65940 + 0.882318i −1.65940 + 0.882318i −0.669131 + 0.743145i \(0.733333\pi\)
−0.990268 + 0.139173i \(0.955556\pi\)
\(500\) 0.728009 0.753876i 0.728009 0.753876i
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 0.978148 0.207912i \(-0.0666667\pi\)
−0.978148 + 0.207912i \(0.933333\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −0.500000 0.866025i −0.500000 0.866025i
\(508\) 0 0
\(509\) 1.36487 + 1.06636i 1.36487 + 1.06636i 0.990268 + 0.139173i \(0.0444444\pi\)
0.374607 + 0.927184i \(0.377778\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0.893036 + 0.924765i 0.893036 + 0.924765i
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −0.142220 + 0.669092i −0.142220 + 0.669092i 0.848048 + 0.529919i \(0.177778\pi\)
−0.990268 + 0.139173i \(0.955556\pi\)
\(522\) 0 0
\(523\) 0 0 0.406737 0.913545i \(-0.366667\pi\)
−0.406737 + 0.913545i \(0.633333\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −1.53209 1.28558i −1.53209 1.28558i
\(530\) 0 0
\(531\) −1.46371 + 1.31793i −1.46371 + 1.31793i
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0.137393 + 1.96482i 0.137393 + 1.96482i
\(538\) 0 0
\(539\) 0 0
\(540\) 0.439693 0.524005i 0.439693 0.524005i
\(541\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(542\) 0 0
\(543\) 0.0655896 1.87824i 0.0655896 1.87824i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 0.999391 0.0348995i \(-0.0111111\pi\)
−0.999391 + 0.0348995i \(0.988889\pi\)
\(548\) −0.801115 1.79933i −0.801115 1.79933i
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 1.15547 0.563559i 1.15547 0.563559i
\(556\) 0 0
\(557\) 0 0 0.669131 0.743145i \(-0.266667\pi\)
−0.669131 + 0.743145i \(0.733333\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 −0.559193 0.829038i \(-0.688889\pi\)
0.559193 + 0.829038i \(0.311111\pi\)
\(564\) 0.178917 1.27306i 0.178917 1.27306i
\(565\) 0.870827 0.122387i 0.870827 0.122387i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 0 0 −0.882948 0.469472i \(-0.844444\pi\)
0.882948 + 0.469472i \(0.155556\pi\)
\(570\) 0 0
\(571\) 0 0 0.342020 0.939693i \(-0.388889\pi\)
−0.342020 + 0.939693i \(0.611111\pi\)
\(572\) 0 0
\(573\) 1.28558i 1.28558i
\(574\) 0 0
\(575\) −0.684886 + 0.616674i −0.684886 + 0.616674i
\(576\) −0.374607 + 0.927184i −0.374607 + 0.927184i
\(577\) 1.71690 + 0.764415i 1.71690 + 0.764415i 0.997564 + 0.0697565i \(0.0222222\pi\)
0.719340 + 0.694658i \(0.244444\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0.539031 0.421137i 0.539031 0.421137i −0.309017 0.951057i \(-0.600000\pi\)
0.848048 + 0.529919i \(0.177778\pi\)
\(588\) 0.913545 + 0.406737i 0.913545 + 0.406737i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) −1.35192 + 1.30553i −1.35192 + 1.30553i
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −0.573931 1.42053i −0.573931 1.42053i
\(598\) 0 0
\(599\) −1.68060 0.419021i −1.68060 0.419021i −0.719340 0.694658i \(-0.755556\pi\)
−0.961262 + 0.275637i \(0.911111\pi\)
\(600\) 0 0
\(601\) 0 0 0.788011 0.615661i \(-0.211111\pi\)
−0.788011 + 0.615661i \(0.788889\pi\)
\(602\) 0 0
\(603\) 0.0363024 0.345394i 0.0363024 0.345394i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 −0.898794 0.438371i \(-0.855556\pi\)
0.898794 + 0.438371i \(0.144444\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 0.743145 0.669131i \(-0.233333\pi\)
−0.743145 + 0.669131i \(0.766667\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0.673648 1.85083i 0.673648 1.85083i 0.173648 0.984808i \(-0.444444\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(618\) 0 0
\(619\) 1.65940 + 0.882318i 1.65940 + 0.882318i 0.990268 + 0.139173i \(0.0444444\pi\)
0.669131 + 0.743145i \(0.266667\pi\)
\(620\) 0.225937 0.0734115i 0.225937 0.0734115i
\(621\) −1.20318 + 1.24593i −1.20318 + 1.24593i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −0.103335 0.153200i −0.103335 0.153200i
\(626\) 0 0
\(627\) 0 0
\(628\) 0.326352 0.118782i 0.326352 0.118782i
\(629\) 0 0
\(630\) 0 0
\(631\) −0.232387 + 0.258091i −0.232387 + 0.258091i −0.848048 0.529919i \(-0.822222\pi\)
0.615661 + 0.788011i \(0.288889\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) −1.36821 1.41682i −1.36821 1.41682i
\(637\) 0 0
\(638\) 0 0
\(639\) −0.826352 + 0.984808i −0.826352 + 0.984808i
\(640\) 0 0
\(641\) 1.73100 0.0604477i 1.73100 0.0604477i 0.848048 0.529919i \(-0.177778\pi\)
0.882948 + 0.469472i \(0.155556\pi\)
\(642\) 0 0
\(643\) 0.241922 0.970296i 0.241922 0.970296i −0.719340 0.694658i \(-0.755556\pi\)
0.961262 0.275637i \(-0.0888889\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) −0.943248 + 1.20730i −0.943248 + 1.20730i
\(653\) −0.362486 + 0.580099i −0.362486 + 0.580099i −0.978148 0.207912i \(-0.933333\pi\)
0.615661 + 0.788011i \(0.288889\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 −0.766044 0.642788i \(-0.777778\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(660\) 0 0
\(661\) −0.266044 1.50881i −0.266044 1.50881i −0.766044 0.642788i \(-0.777778\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) −0.104528 + 0.994522i −0.104528 + 0.994522i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 −0.694658 0.719340i \(-0.744444\pi\)
0.694658 + 0.719340i \(0.255556\pi\)
\(674\) 0 0
\(675\) 0.327587 + 0.419292i 0.327587 + 0.419292i
\(676\) 0.809017 0.587785i 0.809017 0.587785i
\(677\) 0 0 −0.438371 0.898794i \(-0.644444\pi\)
0.438371 + 0.898794i \(0.355556\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −1.11334 0.642788i −1.11334 0.642788i −0.173648 0.984808i \(-0.555556\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(684\) 0 0
\(685\) −1.31785 + 0.280119i −1.31785 + 0.280119i
\(686\) 0 0
\(687\) −0.559193 + 0.829038i −0.559193 + 0.829038i
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0.454664 + 1.82356i 0.454664 + 1.82356i 0.559193 + 0.829038i \(0.311111\pi\)
−0.104528 + 0.994522i \(0.533333\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) −0.826352 0.300767i −0.826352 0.300767i
\(706\) 0 0
\(707\) 0 0
\(708\) −1.46371 1.31793i −1.46371 1.31793i
\(709\) 1.05094 1.55808i 1.05094 1.55808i 0.241922 0.970296i \(-0.422222\pi\)
0.809017 0.587785i \(-0.200000\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −0.583667 + 0.145524i −0.583667 + 0.145524i
\(714\) 0 0
\(715\) 0 0
\(716\) −1.93969 + 0.342020i −1.93969 + 0.342020i
\(717\) 0 0
\(718\) 0 0
\(719\) 0.955369 + 0.860218i 0.955369 + 0.860218i 0.990268 0.139173i \(-0.0444444\pi\)
−0.0348995 + 0.999391i \(0.511111\pi\)
\(720\) 0.567095 + 0.382510i 0.567095 + 0.382510i
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) 1.87481 0.131099i 1.87481 0.131099i
\(725\) 0 0
\(726\) 0 0
\(727\) −0.266044 + 1.50881i −0.266044 + 1.50881i 0.500000 + 0.866025i \(0.333333\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(728\) 0 0
\(729\) 0.669131 + 0.743145i 0.669131 + 0.743145i
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 −0.999391 0.0348995i \(-0.988889\pi\)
0.999391 + 0.0348995i \(0.0111111\pi\)
\(734\) 0 0
\(735\) 0.402069 0.553400i 0.402069 0.553400i
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 −0.994522 0.104528i \(-0.966667\pi\)
0.994522 + 0.104528i \(0.0333333\pi\)
\(740\) 0.681251 + 1.09023i 0.681251 + 1.09023i
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 −0.719340 0.694658i \(-0.755556\pi\)
0.719340 + 0.694658i \(0.244444\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0.573931 + 1.42053i 0.573931 + 1.42053i 0.882948 + 0.469472i \(0.155556\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(752\) 1.28479 + 0.0448659i 1.28479 + 0.0448659i
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0.280969 + 0.204136i 0.280969 + 0.204136i 0.719340 0.694658i \(-0.244444\pi\)
−0.438371 + 0.898794i \(0.644444\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 0.997564 0.0697565i \(-0.0222222\pi\)
−0.997564 + 0.0697565i \(0.977778\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −1.27853 + 0.134379i −1.27853 + 0.134379i
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) −0.961262 0.275637i −0.961262 0.275637i
\(769\) 0 0 0.984808 0.173648i \(-0.0555556\pi\)
−0.984808 + 0.173648i \(0.944444\pi\)
\(770\) 0 0
\(771\) 0.592396 + 1.62760i 0.592396 + 1.62760i
\(772\) 0 0
\(773\) 0 0 0.978148 0.207912i \(-0.0666667\pi\)
−0.978148 + 0.207912i \(0.933333\pi\)
\(774\) 0 0
\(775\) 0.0193161 + 0.183780i 0.0193161 + 0.183780i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(785\) −0.0330626 0.235253i −0.0330626 0.235253i
\(786\) 0 0
\(787\) 0 0 −0.275637 0.961262i \(-0.588889\pi\)
0.275637 + 0.961262i \(0.411111\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) −1.14257 + 0.713958i −1.14257 + 0.713958i
\(796\) 1.35275 0.719272i 1.35275 0.719272i
\(797\) 0.475174 0.492057i 0.475174 0.492057i −0.438371 0.898794i \(-0.644444\pi\)
0.913545 + 0.406737i \(0.133333\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) −1.20318 1.24593i −1.20318 1.24593i
\(802\) 0 0
\(803\) 0 0
\(804\) 0.347296 0.347296
\(805\) 0 0
\(806\) 0 0
\(807\) −0.603541 1.13510i −0.603541 1.13510i
\(808\) 0 0
\(809\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(810\) 0 0
\(811\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0.673648 + 0.802823i 0.673648 + 0.802823i
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 0 0 0.374607 0.927184i \(-0.377778\pi\)
−0.374607 + 0.927184i \(0.622222\pi\)
\(822\) 0 0
\(823\) −0.438371 + 0.898794i −0.438371 + 0.898794i 0.559193 + 0.829038i \(0.311111\pi\)
−0.997564 + 0.0697565i \(0.977778\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 0.104528 0.994522i \(-0.466667\pi\)
−0.104528 + 0.994522i \(0.533333\pi\)
\(828\) −1.36487 1.06636i −1.36487 1.06636i
\(829\) −0.339707 0.0722070i −0.339707 0.0722070i 0.0348995 0.999391i \(-0.488889\pi\)
−0.374607 + 0.927184i \(0.622222\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0.0603074 + 0.342020i 0.0603074 + 0.342020i
\(838\) 0 0
\(839\) −0.813149 + 1.52931i −0.813149 + 1.52931i 0.0348995 + 0.999391i \(0.488889\pi\)
−0.848048 + 0.529919i \(0.822222\pi\)
\(840\) 0 0
\(841\) 0.961262 0.275637i 0.961262 0.275637i
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −0.278224 0.624902i −0.278224 0.624902i
\(846\) 0 0
\(847\) 0 0
\(848\) 1.26604 1.50881i 1.26604 1.50881i
\(849\) 0 0
\(850\) 0 0
\(851\) −1.52822 2.87416i −1.52822 2.87416i
\(852\) −1.06579 0.718885i −1.06579 0.718885i
\(853\) 0 0 0.0697565 0.997564i \(-0.477778\pi\)
−0.0697565 + 0.997564i \(0.522222\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 0.939693 0.342020i \(-0.111111\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(858\) 0 0
\(859\) 1.17365 0.984808i 1.17365 0.984808i 0.173648 0.984808i \(-0.444444\pi\)
1.00000 \(0\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −1.01807 1.40126i −1.01807 1.40126i −0.913545 0.406737i \(-0.866667\pi\)
−0.104528 0.994522i \(-0.533333\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −0.559193 0.829038i −0.559193 0.829038i
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 0.0534691 1.53116i 0.0534691 1.53116i
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 0 0 0.139173 0.990268i \(-0.455556\pi\)
−0.139173 + 0.990268i \(0.544444\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −1.11334 + 0.642788i −1.11334 + 0.642788i −0.939693 0.342020i \(-0.888889\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(882\) 0 0
\(883\) −1.02517 1.13856i −1.02517 1.13856i −0.990268 0.139173i \(-0.955556\pi\)
−0.0348995 0.999391i \(-0.511111\pi\)
\(884\) 0 0
\(885\) −1.08999 + 0.791921i −1.08999 + 0.791921i
\(886\) 0 0
\(887\) 0 0 0.0348995 0.999391i \(-0.488889\pi\)
−0.0348995 + 0.999391i \(0.511111\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 0 0
\(892\) −1.00000 −1.00000
\(893\) 0 0
\(894\) 0 0
\(895\) −0.0470200 + 1.34648i −0.0470200 + 1.34648i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) −0.382753 + 0.369620i −0.382753 + 0.369620i
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0.178917 1.27306i 0.178917 1.27306i
\(906\) 0 0
\(907\) 0.997564 + 0.0697565i 0.997564 + 0.0697565i 0.559193 0.829038i \(-0.311111\pi\)
0.438371 + 0.898794i \(0.355556\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 0.188547 0.657542i 0.188547 0.657542i −0.809017 0.587785i \(-0.800000\pi\)
0.997564 0.0697565i \(-0.0222222\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) −0.882948 0.469472i −0.882948 0.469472i
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) −0.939693 + 0.342020i −0.939693 + 0.342020i
\(926\) 0 0
\(927\) −1.25755 1.39666i −1.25755 1.39666i
\(928\) 0 0
\(929\) 0.137393 1.96482i 0.137393 1.96482i −0.104528 0.994522i \(-0.533333\pi\)
0.241922 0.970296i \(-0.422222\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) −0.542900 + 1.89332i −0.542900 + 1.89332i
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 −0.406737 0.913545i \(-0.633333\pi\)
0.406737 + 0.913545i \(0.366667\pi\)
\(938\) 0 0
\(939\) 0.978148 + 0.207912i 0.978148 + 0.207912i
\(940\) 0.212743 0.853264i 0.212743 0.853264i
\(941\) 0 0 0.961262 0.275637i \(-0.0888889\pi\)
−0.961262 + 0.275637i \(0.911111\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 1.15771 1.59345i 1.15771 1.59345i
\(945\) 0 0
\(946\) 0 0
\(947\) 1.93969 + 0.342020i 1.93969 + 0.342020i 1.00000 \(0\)
0.939693 + 0.342020i \(0.111111\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 0 0 −0.978148 0.207912i \(-0.933333\pi\)
0.978148 + 0.207912i \(0.0666667\pi\)
\(954\) 0 0
\(955\) −0.0919208 + 0.874568i −0.0919208 + 0.874568i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) −0.321137 + 0.603972i −0.321137 + 0.603972i
\(961\) 0.329424 0.815352i 0.329424 0.815352i
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 0 0 −0.642788 0.766044i \(-0.722222\pi\)
0.642788 + 0.766044i \(0.277778\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −1.64728 0.535233i −1.64728 0.535233i −0.669131 0.743145i \(-0.733333\pi\)
−0.978148 + 0.207912i \(0.933333\pi\)
\(972\) −0.669131 + 0.743145i −0.669131 + 0.743145i
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 0 0 0.997564 0.0697565i \(-0.0222222\pi\)
−0.997564 + 0.0697565i \(0.977778\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0.592396 + 0.342020i 0.592396 + 0.342020i
\(981\) 0 0
\(982\) 0 0
\(983\) 1.82620 + 0.737831i 1.82620 + 0.737831i 0.978148 + 0.207912i \(0.0666667\pi\)
0.848048 + 0.529919i \(0.177778\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(992\) 0 0
\(993\) 1.49861 0.318539i 1.49861 0.318539i
\(994\) 0 0
\(995\) −0.288871 1.00741i −0.288871 1.00741i
\(996\) 0 0
\(997\) 0 0 −0.139173 0.990268i \(-0.544444\pi\)
0.139173 + 0.990268i \(0.455556\pi\)
\(998\) 0 0
\(999\) −1.71690 + 0.764415i −1.71690 + 0.764415i
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 3267.1.be.a.2864.1 24
11.2 odd 10 inner 3267.1.be.a.2810.1 24
11.3 even 5 inner 3267.1.be.a.245.1 24
11.4 even 5 inner 3267.1.be.a.1703.1 24
11.5 even 5 3267.1.q.a.3026.1 yes 6
11.6 odd 10 3267.1.q.a.3026.1 yes 6
11.7 odd 10 inner 3267.1.be.a.1703.1 24
11.8 odd 10 inner 3267.1.be.a.245.1 24
11.9 even 5 inner 3267.1.be.a.2810.1 24
11.10 odd 2 CM 3267.1.be.a.2864.1 24
27.14 odd 18 inner 3267.1.be.a.3227.1 24
297.14 odd 90 inner 3267.1.be.a.608.1 24
297.41 even 90 inner 3267.1.be.a.608.1 24
297.68 even 90 inner 3267.1.be.a.3173.1 24
297.95 even 90 inner 3267.1.be.a.2066.1 24
297.149 even 90 3267.1.q.a.122.1 6
297.203 odd 90 3267.1.q.a.122.1 6
297.230 even 18 inner 3267.1.be.a.3227.1 24
297.257 odd 90 inner 3267.1.be.a.2066.1 24
297.284 odd 90 inner 3267.1.be.a.3173.1 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3267.1.q.a.122.1 6 297.149 even 90
3267.1.q.a.122.1 6 297.203 odd 90
3267.1.q.a.3026.1 yes 6 11.5 even 5
3267.1.q.a.3026.1 yes 6 11.6 odd 10
3267.1.be.a.245.1 24 11.3 even 5 inner
3267.1.be.a.245.1 24 11.8 odd 10 inner
3267.1.be.a.608.1 24 297.14 odd 90 inner
3267.1.be.a.608.1 24 297.41 even 90 inner
3267.1.be.a.1703.1 24 11.4 even 5 inner
3267.1.be.a.1703.1 24 11.7 odd 10 inner
3267.1.be.a.2066.1 24 297.95 even 90 inner
3267.1.be.a.2066.1 24 297.257 odd 90 inner
3267.1.be.a.2810.1 24 11.2 odd 10 inner
3267.1.be.a.2810.1 24 11.9 even 5 inner
3267.1.be.a.2864.1 24 1.1 even 1 trivial
3267.1.be.a.2864.1 24 11.10 odd 2 CM
3267.1.be.a.3173.1 24 297.68 even 90 inner
3267.1.be.a.3173.1 24 297.284 odd 90 inner
3267.1.be.a.3227.1 24 27.14 odd 18 inner
3267.1.be.a.3227.1 24 297.230 even 18 inner