Properties

Label 3267.1.be.a.2423.1
Level $3267$
Weight $1$
Character 3267.2423
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 2423.1
Root \(0.990268 - 0.139173i\) of defining polynomial
Character \(\chi\) \(=\) 3267.2423
Dual form 3267.1.be.a.1049.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.0348995 + 0.999391i) q^{3} +(-0.374607 - 0.927184i) q^{4} +(1.15547 + 0.563559i) q^{5} +(-0.997564 - 0.0697565i) q^{9} +O(q^{10})\) \(q+(-0.0348995 + 0.999391i) q^{3} +(-0.374607 - 0.927184i) q^{4} +(1.15547 + 0.563559i) q^{5} +(-0.997564 - 0.0697565i) q^{9} +(0.939693 - 0.342020i) q^{12} +(-0.603541 + 1.13510i) q^{15} +(-0.719340 + 0.694658i) q^{16} +(0.0896772 - 1.28244i) q^{20} +(1.11334 + 1.32683i) q^{23} +(0.401844 + 0.514337i) q^{25} +(0.104528 - 0.994522i) q^{27} +(-0.454664 + 1.82356i) q^{31} +(0.309017 + 0.951057i) q^{36} +(1.49861 - 0.318539i) q^{37} +(-1.11334 - 0.642788i) q^{45} +(1.82620 + 0.737831i) q^{47} +(-0.669131 - 0.743145i) q^{48} +(-0.438371 + 0.898794i) q^{49} +(-0.402069 - 0.553400i) q^{53} +(0.0952000 - 0.677383i) q^{59} +(1.27853 + 0.134379i) q^{60} +(0.913545 + 0.406737i) q^{64} +(-1.76604 - 0.642788i) q^{67} +(-1.36487 + 1.06636i) q^{69} +(1.95883 + 0.205881i) q^{71} +(-0.528048 + 0.383650i) q^{75} +(-1.22265 + 0.397265i) q^{80} +(0.990268 + 0.139173i) q^{81} +(-1.50000 - 0.866025i) q^{89} +(0.813149 - 1.52931i) q^{92} +(-1.80658 - 0.518029i) q^{93} +(0.152245 + 0.312148i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 3 q^{5}+O(q^{10}) \) 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 \(\left(\mathbb{Z}/3267\mathbb{Z}\right)^\times\).

\(n\) \(244\) \(3026\)
\(\chi(n)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{7}{18}\right)\)

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 0.559193 0.829038i \(-0.311111\pi\)
−0.559193 + 0.829038i \(0.688889\pi\)
\(3\) −0.0348995 + 0.999391i −0.0348995 + 0.999391i
\(4\) −0.374607 0.927184i −0.374607 0.927184i
\(5\) 1.15547 + 0.563559i 1.15547 + 0.563559i 0.913545 0.406737i \(-0.133333\pi\)
0.241922 + 0.970296i \(0.422222\pi\)
\(6\) 0 0
\(7\) 0 0 −0.529919 0.848048i \(-0.677778\pi\)
0.529919 + 0.848048i \(0.322222\pi\)
\(8\) 0 0
\(9\) −0.997564 0.0697565i −0.997564 0.0697565i
\(10\) 0 0
\(11\) 0 0
\(12\) 0.939693 0.342020i 0.939693 0.342020i
\(13\) 0 0 −0.275637 0.961262i \(-0.588889\pi\)
0.275637 + 0.961262i \(0.411111\pi\)
\(14\) 0 0
\(15\) −0.603541 + 1.13510i −0.603541 + 1.13510i
\(16\) −0.719340 + 0.694658i −0.719340 + 0.694658i
\(17\) 0 0 0.104528 0.994522i \(-0.466667\pi\)
−0.104528 + 0.994522i \(0.533333\pi\)
\(18\) 0 0
\(19\) 0 0 0.207912 0.978148i \(-0.433333\pi\)
−0.207912 + 0.978148i \(0.566667\pi\)
\(20\) 0.0896772 1.28244i 0.0896772 1.28244i
\(21\) 0 0
\(22\) 0 0
\(23\) 1.11334 + 1.32683i 1.11334 + 1.32683i 0.939693 + 0.342020i \(0.111111\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(24\) 0 0
\(25\) 0.401844 + 0.514337i 0.401844 + 0.514337i
\(26\) 0 0
\(27\) 0.104528 0.994522i 0.104528 0.994522i
\(28\) 0 0
\(29\) 0 0 −0.0348995 0.999391i \(-0.511111\pi\)
0.0348995 + 0.999391i \(0.488889\pi\)
\(30\) 0 0
\(31\) −0.454664 + 1.82356i −0.454664 + 1.82356i 0.104528 + 0.994522i \(0.466667\pi\)
−0.559193 + 0.829038i \(0.688889\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(37\) 1.49861 0.318539i 1.49861 0.318539i 0.615661 0.788011i \(-0.288889\pi\)
0.882948 + 0.469472i \(0.155556\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 0.0348995 0.999391i \(-0.488889\pi\)
−0.0348995 + 0.999391i \(0.511111\pi\)
\(42\) 0 0
\(43\) 0 0 −0.984808 0.173648i \(-0.944444\pi\)
0.984808 + 0.173648i \(0.0555556\pi\)
\(44\) 0 0
\(45\) −1.11334 0.642788i −1.11334 0.642788i
\(46\) 0 0
\(47\) 1.82620 + 0.737831i 1.82620 + 0.737831i 0.978148 + 0.207912i \(0.0666667\pi\)
0.848048 + 0.529919i \(0.177778\pi\)
\(48\) −0.669131 0.743145i −0.669131 0.743145i
\(49\) −0.438371 + 0.898794i −0.438371 + 0.898794i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −0.402069 0.553400i −0.402069 0.553400i 0.559193 0.829038i \(-0.311111\pi\)
−0.961262 + 0.275637i \(0.911111\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0.0952000 0.677383i 0.0952000 0.677383i −0.882948 0.469472i \(-0.844444\pi\)
0.978148 0.207912i \(-0.0666667\pi\)
\(60\) 1.27853 + 0.134379i 1.27853 + 0.134379i
\(61\) 0 0 0.970296 0.241922i \(-0.0777778\pi\)
−0.970296 + 0.241922i \(0.922222\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0.913545 + 0.406737i 0.913545 + 0.406737i
\(65\) 0 0
\(66\) 0 0
\(67\) −1.76604 0.642788i −1.76604 0.642788i −0.766044 0.642788i \(-0.777778\pi\)
−1.00000 \(\pi\)
\(68\) 0 0
\(69\) −1.36487 + 1.06636i −1.36487 + 1.06636i
\(70\) 0 0
\(71\) 1.95883 + 0.205881i 1.95883 + 0.205881i 0.997564 0.0697565i \(-0.0222222\pi\)
0.961262 + 0.275637i \(0.0888889\pi\)
\(72\) 0 0
\(73\) 0 0 0.743145 0.669131i \(-0.233333\pi\)
−0.743145 + 0.669131i \(0.766667\pi\)
\(74\) 0 0
\(75\) −0.528048 + 0.383650i −0.528048 + 0.383650i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 −0.829038 0.559193i \(-0.811111\pi\)
0.829038 + 0.559193i \(0.188889\pi\)
\(80\) −1.22265 + 0.397265i −1.22265 + 0.397265i
\(81\) 0.990268 + 0.139173i 0.990268 + 0.139173i
\(82\) 0 0
\(83\) 0 0 −0.961262 0.275637i \(-0.911111\pi\)
0.961262 + 0.275637i \(0.0888889\pi\)
\(84\) 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
\(92\) 0.813149 1.52931i 0.813149 1.52931i
\(93\) −1.80658 0.518029i −1.80658 0.518029i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 0.152245 + 0.312148i 0.152245 + 0.312148i 0.961262 0.275637i \(-0.0888889\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0.326352 0.565258i 0.326352 0.565258i
\(101\) 0 0 −0.997564 0.0697565i \(-0.977778\pi\)
0.997564 + 0.0697565i \(0.0222222\pi\)
\(102\) 0 0
\(103\) 1.51718 + 0.213226i 1.51718 + 0.213226i 0.848048 0.529919i \(-0.177778\pi\)
0.669131 + 0.743145i \(0.266667\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(108\) −0.961262 + 0.275637i −0.961262 + 0.275637i
\(109\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(110\) 0 0
\(111\) 0.266044 + 1.50881i 0.266044 + 1.50881i
\(112\) 0 0
\(113\) −0.924678 1.73907i −0.924678 1.73907i −0.615661 0.788011i \(-0.711111\pi\)
−0.309017 0.951057i \(-0.600000\pi\)
\(114\) 0 0
\(115\) 0.538683 + 2.16054i 0.538683 + 2.16054i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 0 0
\(122\) 0 0
\(123\) 0 0
\(124\) 1.86110 0.261560i 1.86110 0.261560i
\(125\) −0.0928275 0.436719i −0.0928275 0.436719i
\(126\) 0 0
\(127\) 0 0 −0.406737 0.913545i \(-0.633333\pi\)
0.406737 + 0.913545i \(0.366667\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 0.766044 0.642788i \(-0.222222\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0.681251 1.09023i 0.681251 1.09023i
\(136\) 0 0
\(137\) −0.188547 + 0.657542i −0.188547 + 0.657542i 0.809017 + 0.587785i \(0.200000\pi\)
−0.997564 + 0.0697565i \(0.977778\pi\)
\(138\) 0 0
\(139\) 0 0 0.927184 0.374607i \(-0.122222\pi\)
−0.927184 + 0.374607i \(0.877778\pi\)
\(140\) 0 0
\(141\) −0.801115 + 1.79933i −0.801115 + 1.79933i
\(142\) 0 0
\(143\) 0 0
\(144\) 0.766044 0.642788i 0.766044 0.642788i
\(145\) 0 0
\(146\) 0 0
\(147\) −0.882948 0.469472i −0.882948 0.469472i
\(148\) −0.856733 1.27016i −0.856733 1.27016i
\(149\) 0 0 −0.559193 0.829038i \(-0.688889\pi\)
0.559193 + 0.829038i \(0.311111\pi\)
\(150\) 0 0
\(151\) 0 0 −0.139173 0.990268i \(-0.544444\pi\)
0.139173 + 0.990268i \(0.455556\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −1.55303 + 1.85083i −1.55303 + 1.85083i
\(156\) 0 0
\(157\) −1.65940 + 0.882318i −1.65940 + 0.882318i −0.669131 + 0.743145i \(0.733333\pi\)
−0.990268 + 0.139173i \(0.955556\pi\)
\(158\) 0 0
\(159\) 0.567095 0.382510i 0.567095 0.382510i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −0.280969 + 0.204136i −0.280969 + 0.204136i −0.719340 0.694658i \(-0.755556\pi\)
0.438371 + 0.898794i \(0.355556\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 −0.719340 0.694658i \(-0.755556\pi\)
0.719340 + 0.694658i \(0.244444\pi\)
\(168\) 0 0
\(169\) −0.848048 + 0.529919i −0.848048 + 0.529919i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 0 0 0.990268 0.139173i \(-0.0444444\pi\)
−0.990268 + 0.139173i \(0.955556\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0.673648 + 0.118782i 0.673648 + 0.118782i
\(178\) 0 0
\(179\) −0.508341 0.457712i −0.508341 0.457712i 0.374607 0.927184i \(-0.377778\pi\)
−0.882948 + 0.469472i \(0.844444\pi\)
\(180\) −0.178917 + 1.27306i −0.178917 + 1.27306i
\(181\) 1.39963 0.623157i 1.39963 0.623157i 0.438371 0.898794i \(-0.355556\pi\)
0.961262 + 0.275637i \(0.0888889\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 1.91111 + 0.476493i 1.91111 + 0.476493i
\(186\) 0 0
\(187\) 0 0
\(188\) 1.96962i 1.96962i
\(189\) 0 0
\(190\) 0 0
\(191\) −1.96842 + 0.0687386i −1.96842 + 0.0687386i −0.990268 0.139173i \(-0.955556\pi\)
−0.978148 + 0.207912i \(0.933333\pi\)
\(192\) −0.438371 + 0.898794i −0.438371 + 0.898794i
\(193\) 0 0 −0.0697565 0.997564i \(-0.522222\pi\)
0.0697565 + 0.997564i \(0.477778\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0.997564 + 0.0697565i 0.997564 + 0.0697565i
\(197\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(198\) 0 0
\(199\) 0.173648 + 0.300767i 0.173648 + 0.300767i 0.939693 0.342020i \(-0.111111\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(200\) 0 0
\(201\) 0.704030 1.74254i 0.704030 1.74254i
\(202\) 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 0.694658 0.719340i \(-0.255556\pi\)
−0.694658 + 0.719340i \(0.744444\pi\)
\(212\) −0.362486 + 0.580099i −0.362486 + 0.580099i
\(213\) −0.274117 + 1.95045i −0.274117 + 1.95045i
\(214\) 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
\(223\) 0.374607 0.927184i 0.374607 0.927184i −0.615661 0.788011i \(-0.711111\pi\)
0.990268 0.139173i \(-0.0444444\pi\)
\(224\) 0 0
\(225\) −0.364987 0.541116i −0.364987 0.541116i
\(226\) 0 0
\(227\) 0 0 −0.882948 0.469472i \(-0.844444\pi\)
0.882948 + 0.469472i \(0.155556\pi\)
\(228\) 0 0
\(229\) 0.961262 0.275637i 0.961262 0.275637i 0.241922 0.970296i \(-0.422222\pi\)
0.719340 + 0.694658i \(0.244444\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 −0.913545 0.406737i \(-0.866667\pi\)
0.913545 + 0.406737i \(0.133333\pi\)
\(234\) 0 0
\(235\) 1.69430 + 1.88171i 1.69430 + 1.88171i
\(236\) −0.663721 + 0.165484i −0.663721 + 0.165484i
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 −0.848048 0.529919i \(-0.822222\pi\)
0.848048 + 0.529919i \(0.177778\pi\)
\(240\) −0.354353 1.23577i −0.354353 1.23577i
\(241\) 0 0 −0.342020 0.939693i \(-0.611111\pi\)
0.342020 + 0.939693i \(0.388889\pi\)
\(242\) 0 0
\(243\) −0.173648 + 0.984808i −0.173648 + 0.984808i
\(244\) 0 0
\(245\) −1.01305 + 0.791479i −1.01305 + 0.791479i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 −0.104528 0.994522i \(-0.533333\pi\)
0.104528 + 0.994522i \(0.466667\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0.0348995 0.999391i 0.0348995 0.999391i
\(257\) −1.36487 1.06636i −1.36487 1.06636i −0.990268 0.139173i \(-0.955556\pi\)
−0.374607 0.927184i \(-0.622222\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 −0.766044 0.642788i \(-0.777778\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(264\) 0 0
\(265\) −0.152704 0.866025i −0.152704 0.866025i
\(266\) 0 0
\(267\) 0.917847 1.46886i 0.917847 1.46886i
\(268\) 0.0655896 + 1.87824i 0.0655896 + 1.87824i
\(269\) 1.15771 1.59345i 1.15771 1.59345i 0.438371 0.898794i \(-0.355556\pi\)
0.719340 0.694658i \(-0.244444\pi\)
\(270\) 0 0
\(271\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(277\) 0 0 0.0697565 0.997564i \(-0.477778\pi\)
−0.0697565 + 0.997564i \(0.522222\pi\)
\(278\) 0 0
\(279\) 0.580762 1.78740i 0.580762 1.78740i
\(280\) 0 0
\(281\) 0 0 0.719340 0.694658i \(-0.244444\pi\)
−0.719340 + 0.694658i \(0.755556\pi\)
\(282\) 0 0
\(283\) 0 0 −0.999391 0.0348995i \(-0.988889\pi\)
0.999391 + 0.0348995i \(0.0111111\pi\)
\(284\) −0.542900 1.89332i −0.542900 1.89332i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −0.978148 0.207912i −0.978148 0.207912i
\(290\) 0 0
\(291\) −0.317271 + 0.141258i −0.317271 + 0.141258i
\(292\) 0 0
\(293\) 0 0 −0.374607 0.927184i \(-0.622222\pi\)
0.374607 + 0.927184i \(0.377778\pi\)
\(294\) 0 0
\(295\) 0.491746 0.729043i 0.491746 0.729043i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 0.553524 + 0.345880i 0.553524 + 0.345880i
\(301\) 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
\(309\) −0.266044 + 1.50881i −0.266044 + 1.50881i
\(310\) 0 0
\(311\) 0.683624 + 0.0238727i 0.683624 + 0.0238727i 0.374607 0.927184i \(-0.377778\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(312\) 0 0
\(313\) −0.719340 + 0.694658i −0.719340 + 0.694658i −0.961262 0.275637i \(-0.911111\pi\)
0.241922 + 0.970296i \(0.422222\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 −0.997564 0.0697565i \(-0.977778\pi\)
0.997564 + 0.0697565i \(0.0222222\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0.826352 + 0.984808i 0.826352 + 0.984808i
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) −0.241922 0.970296i −0.241922 0.970296i
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0.266044 + 0.223238i 0.266044 + 0.223238i 0.766044 0.642788i \(-0.222222\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(332\) 0 0
\(333\) −1.51718 + 0.213226i −1.51718 + 0.213226i
\(334\) 0 0
\(335\) −1.67836 1.73799i −1.67836 1.73799i
\(336\) 0 0
\(337\) 0 0 −0.788011 0.615661i \(-0.788889\pi\)
0.788011 + 0.615661i \(0.211111\pi\)
\(338\) 0 0
\(339\) 1.77028 0.863423i 1.77028 0.863423i
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −2.17802 + 0.462953i −2.17802 + 0.462953i
\(346\) 0 0
\(347\) 0 0 0.997564 0.0697565i \(-0.0222222\pi\)
−0.997564 + 0.0697565i \(0.977778\pi\)
\(348\) 0 0
\(349\) 0 0 0.788011 0.615661i \(-0.211111\pi\)
−0.788011 + 0.615661i \(0.788889\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −0.592396 1.62760i −0.592396 1.62760i −0.766044 0.642788i \(-0.777778\pi\)
0.173648 0.984808i \(-0.444444\pi\)
\(354\) 0 0
\(355\) 2.14733 + 1.34180i 2.14733 + 1.34180i
\(356\) −0.241055 + 1.71519i −0.241055 + 1.71519i
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 −0.669131 0.743145i \(-0.733333\pi\)
0.669131 + 0.743145i \(0.266667\pi\)
\(360\) 0 0
\(361\) −0.913545 0.406737i −0.913545 0.406737i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −0.306644 0.163046i −0.306644 0.163046i 0.309017 0.951057i \(-0.400000\pi\)
−0.615661 + 0.788011i \(0.711111\pi\)
\(368\) −1.72256 0.181049i −1.72256 0.181049i
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0.196449 + 1.86909i 0.196449 + 1.86909i
\(373\) 0 0 0.984808 0.173648i \(-0.0555556\pi\)
−0.984808 + 0.173648i \(0.944444\pi\)
\(374\) 0 0
\(375\) 0.439693 0.0775297i 0.439693 0.0775297i
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 0.809017 + 0.587785i 0.809017 + 0.587785i 0.913545 0.406737i \(-0.133333\pi\)
−0.104528 + 0.994522i \(0.533333\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −0.475174 + 0.492057i −0.475174 + 0.492057i −0.913545 0.406737i \(-0.866667\pi\)
0.438371 + 0.898794i \(0.355556\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0.232387 0.258091i 0.232387 0.258091i
\(389\) 0.924678 1.73907i 0.924678 1.73907i 0.309017 0.951057i \(-0.400000\pi\)
0.615661 0.788011i \(-0.288889\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 0.939693 1.62760i 0.939693 1.62760i 0.173648 0.984808i \(-0.444444\pi\)
0.766044 0.642788i \(-0.222222\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −0.646352 0.0908388i −0.646352 0.0908388i
\(401\) 0.0896772 + 1.28244i 0.0896772 + 1.28244i 0.809017 + 0.587785i \(0.200000\pi\)
−0.719340 + 0.694658i \(0.755556\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 1.06579 + 0.718885i 1.06579 + 0.718885i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0 0 −0.970296 0.241922i \(-0.922222\pi\)
0.970296 + 0.241922i \(0.0777778\pi\)
\(410\) 0 0
\(411\) −0.650561 0.211380i −0.650561 0.211380i
\(412\) −0.370646 1.48658i −0.370646 1.48658i
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0.439693 1.20805i 0.439693 1.20805i −0.500000 0.866025i \(-0.666667\pi\)
0.939693 0.342020i \(-0.111111\pi\)
\(420\) 0 0
\(421\) −1.51718 + 0.213226i −1.51718 + 0.213226i −0.848048 0.529919i \(-0.822222\pi\)
−0.669131 + 0.743145i \(0.733333\pi\)
\(422\) 0 0
\(423\) −1.77028 0.863423i −1.77028 0.863423i
\(424\) 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 \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(432\) 0.615661 + 0.788011i 0.615661 + 0.788011i
\(433\) −0.309017 + 0.951057i −0.309017 + 0.951057i 0.669131 + 0.743145i \(0.266667\pi\)
−0.978148 + 0.207912i \(0.933333\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 0.642788 0.766044i \(-0.277778\pi\)
−0.642788 + 0.766044i \(0.722222\pi\)
\(440\) 0 0
\(441\) 0.500000 0.866025i 0.500000 0.866025i
\(442\) 0 0
\(443\) −0.178917 1.27306i −0.178917 1.27306i −0.848048 0.529919i \(-0.822222\pi\)
0.669131 0.743145i \(-0.266667\pi\)
\(444\) 1.29929 0.811883i 1.29929 0.811883i
\(445\) −1.24514 1.84600i −1.24514 1.84600i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 0.522891 1.17443i 0.522891 1.17443i −0.438371 0.898794i \(-0.644444\pi\)
0.961262 0.275637i \(-0.0888889\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) −1.26604 + 1.50881i −1.26604 + 1.50881i
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 0.275637 0.961262i \(-0.411111\pi\)
−0.275637 + 0.961262i \(0.588889\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 1.80142 1.30881i 1.80142 1.30881i
\(461\) 0 0 0.939693 0.342020i \(-0.111111\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(462\) 0 0
\(463\) −0.766044 + 0.642788i −0.766044 + 0.642788i −0.939693 0.342020i \(-0.888889\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(464\) 0 0
\(465\) −1.79551 1.61668i −1.79551 1.61668i
\(466\) 0 0
\(467\) −0.801115 1.79933i −0.801115 1.79933i −0.559193 0.829038i \(-0.688889\pi\)
−0.241922 0.970296i \(-0.577778\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −0.823868 1.68918i −0.823868 1.68918i
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0.362486 + 0.580099i 0.362486 + 0.580099i
\(478\) 0 0
\(479\) 0 0 −0.241922 0.970296i \(-0.577778\pi\)
0.241922 + 0.970296i \(0.422222\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0.446476i 0.446476i
\(486\) 0 0
\(487\) −0.473442 1.45710i −0.473442 1.45710i −0.848048 0.529919i \(-0.822222\pi\)
0.374607 0.927184i \(-0.377778\pi\)
\(488\) 0 0
\(489\) −0.194206 0.287922i −0.194206 0.287922i
\(490\) 0 0
\(491\) 0 0 −0.990268 0.139173i \(-0.955556\pi\)
0.990268 + 0.139173i \(0.0444444\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) −0.939693 1.62760i −0.939693 1.62760i
\(497\) 0 0
\(498\) 0 0
\(499\) 0.943248 1.20730i 0.943248 1.20730i −0.0348995 0.999391i \(-0.511111\pi\)
0.978148 0.207912i \(-0.0666667\pi\)
\(500\) −0.370145 + 0.249666i −0.370145 + 0.249666i
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 0.669131 0.743145i \(-0.266667\pi\)
−0.669131 + 0.743145i \(0.733333\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −0.500000 0.866025i −0.500000 0.866025i
\(508\) 0 0
\(509\) 0.917847 1.46886i 0.917847 1.46886i 0.0348995 0.999391i \(-0.488889\pi\)
0.882948 0.469472i \(-0.155556\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 1.63289 + 1.10140i 1.63289 + 1.10140i
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0.955369 0.860218i 0.955369 0.860218i −0.0348995 0.999391i \(-0.511111\pi\)
0.990268 + 0.139173i \(0.0444444\pi\)
\(522\) 0 0
\(523\) 0 0 −0.994522 0.104528i \(-0.966667\pi\)
0.994522 + 0.104528i \(0.0333333\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −0.347296 + 1.96962i −0.347296 + 1.96962i
\(530\) 0 0
\(531\) −0.142220 + 0.669092i −0.142220 + 0.669092i
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0.475174 0.492057i 0.475174 0.492057i
\(538\) 0 0
\(539\) 0 0
\(540\) −1.26604 0.223238i −1.26604 0.223238i
\(541\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(542\) 0 0
\(543\) 0.573931 + 1.42053i 0.573931 + 1.42053i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 −0.927184 0.374607i \(-0.877778\pi\)
0.927184 + 0.374607i \(0.122222\pi\)
\(548\) 0.680293 0.0715017i 0.680293 0.0715017i
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −0.542900 + 1.89332i −0.542900 + 1.89332i
\(556\) 0 0
\(557\) 0 0 0.978148 0.207912i \(-0.0666667\pi\)
−0.978148 + 0.207912i \(0.933333\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 0.241922 0.970296i \(-0.422222\pi\)
−0.241922 + 0.970296i \(0.577778\pi\)
\(564\) 1.96842 + 0.0687386i 1.96842 + 0.0687386i
\(565\) −0.0883686 2.53055i −0.0883686 2.53055i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 0 0 −0.615661 0.788011i \(-0.711111\pi\)
0.615661 + 0.788011i \(0.288889\pi\)
\(570\) 0 0
\(571\) 0 0 −0.642788 0.766044i \(-0.722222\pi\)
0.642788 + 0.766044i \(0.277778\pi\)
\(572\) 0 0
\(573\) 1.96962i 1.96962i
\(574\) 0 0
\(575\) −0.235047 + 1.10581i −0.235047 + 1.10581i
\(576\) −0.882948 0.469472i −0.882948 0.469472i
\(577\) 0.160147 1.52370i 0.160147 1.52370i −0.559193 0.829038i \(-0.688889\pi\)
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
\(587\) 0.681251 + 1.09023i 0.681251 + 1.09023i 0.990268 + 0.139173i \(0.0444444\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(588\) −0.104528 + 0.994522i −0.104528 + 0.994522i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) −0.856733 + 1.27016i −0.856733 + 1.27016i
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −0.306644 + 0.163046i −0.306644 + 0.163046i
\(598\) 0 0
\(599\) 1.55676 + 0.759281i 1.55676 + 0.759281i 0.997564 0.0697565i \(-0.0222222\pi\)
0.559193 + 0.829038i \(0.311111\pi\)
\(600\) 0 0
\(601\) 0 0 −0.529919 0.848048i \(-0.677778\pi\)
0.529919 + 0.848048i \(0.322222\pi\)
\(602\) 0 0
\(603\) 1.71690 + 0.764415i 1.71690 + 0.764415i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 −0.275637 0.961262i \(-0.588889\pi\)
0.275637 + 0.961262i \(0.411111\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 0.207912 0.978148i \(-0.433333\pi\)
−0.207912 + 0.978148i \(0.566667\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −0.439693 0.524005i −0.439693 0.524005i 0.500000 0.866025i \(-0.333333\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(618\) 0 0
\(619\) −0.943248 1.20730i −0.943248 1.20730i −0.978148 0.207912i \(-0.933333\pi\)
0.0348995 0.999391i \(-0.488889\pi\)
\(620\) 2.29784 + 0.746613i 2.29784 + 0.746613i
\(621\) 1.43594 0.968551i 1.43594 0.968551i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0.296761 1.19024i 0.296761 1.19024i
\(626\) 0 0
\(627\) 0 0
\(628\) 1.43969 + 1.20805i 1.43969 + 1.20805i
\(629\) 0 0
\(630\) 0 0
\(631\) −1.83832 + 0.390746i −1.83832 + 0.390746i −0.990268 0.139173i \(-0.955556\pi\)
−0.848048 + 0.529919i \(0.822222\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) −0.567095 0.382510i −0.567095 0.382510i
\(637\) 0 0
\(638\) 0 0
\(639\) −1.93969 0.342020i −1.93969 0.342020i
\(640\) 0 0
\(641\) 1.60593 + 0.648838i 1.60593 + 0.648838i 0.990268 0.139173i \(-0.0444444\pi\)
0.615661 + 0.788011i \(0.288889\pi\)
\(642\) 0 0
\(643\) −0.438371 + 0.898794i −0.438371 + 0.898794i 0.559193 + 0.829038i \(0.311111\pi\)
−0.997564 + 0.0697565i \(0.977778\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0.294524 + 0.184039i 0.294524 + 0.184039i
\(653\) −0.178917 + 1.27306i −0.178917 + 1.27306i 0.669131 + 0.743145i \(0.266667\pi\)
−0.848048 + 0.529919i \(0.822222\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 0.173648 0.984808i \(-0.444444\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(660\) 0 0
\(661\) 0.326352 + 0.118782i 0.326352 + 0.118782i 0.500000 0.866025i \(-0.333333\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0.913545 + 0.406737i 0.913545 + 0.406737i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 −0.829038 0.559193i \(-0.811111\pi\)
0.829038 + 0.559193i \(0.188889\pi\)
\(674\) 0 0
\(675\) 0.553524 0.345880i 0.553524 0.345880i
\(676\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(677\) 0 0 −0.961262 0.275637i \(-0.911111\pi\)
0.961262 + 0.275637i \(0.0888889\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 1.70574 + 0.984808i 1.70574 + 0.984808i 0.939693 + 0.342020i \(0.111111\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(684\) 0 0
\(685\) −0.588424 + 0.653511i −0.588424 + 0.653511i
\(686\) 0 0
\(687\) 0.241922 + 0.970296i 0.241922 + 0.970296i
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0.671624 + 1.37703i 0.671624 + 1.37703i 0.913545 + 0.406737i \(0.133333\pi\)
−0.241922 + 0.970296i \(0.577778\pi\)
\(692\) 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 \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) −1.93969 + 1.62760i −1.93969 + 1.62760i
\(706\) 0 0
\(707\) 0 0
\(708\) −0.142220 0.669092i −0.142220 0.669092i
\(709\) 0.370646 + 1.48658i 0.370646 + 1.48658i 0.809017 + 0.587785i \(0.200000\pi\)
−0.438371 + 0.898794i \(0.644444\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −2.92575 + 1.42698i −2.92575 + 1.42698i
\(714\) 0 0
\(715\) 0 0
\(716\) −0.233956 + 0.642788i −0.233956 + 0.642788i
\(717\) 0 0
\(718\) 0 0
\(719\) 0.409506 + 1.92657i 0.409506 + 1.92657i 0.374607 + 0.927184i \(0.377778\pi\)
0.0348995 + 0.999391i \(0.488889\pi\)
\(720\) 1.24739 0.311009i 1.24739 0.311009i
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) −1.10209 1.06428i −1.10209 1.06428i
\(725\) 0 0
\(726\) 0 0
\(727\) 0.326352 0.118782i 0.326352 0.118782i −0.173648 0.984808i \(-0.555556\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(728\) 0 0
\(729\) −0.978148 0.207912i −0.978148 0.207912i
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 0.927184 0.374607i \(-0.122222\pi\)
−0.927184 + 0.374607i \(0.877778\pi\)
\(734\) 0 0
\(735\) −0.755642 1.04005i −0.755642 1.04005i
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 0.406737 0.913545i \(-0.366667\pi\)
−0.406737 + 0.913545i \(0.633333\pi\)
\(740\) −0.274117 1.95045i −0.274117 1.95045i
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 −0.559193 0.829038i \(-0.688889\pi\)
0.559193 + 0.829038i \(0.311111\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0.306644 0.163046i 0.306644 0.163046i −0.309017 0.951057i \(-0.600000\pi\)
0.615661 + 0.788011i \(0.288889\pi\)
\(752\) −1.82620 + 0.737831i −1.82620 + 0.737831i
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −1.52045 + 1.10467i −1.52045 + 1.10467i −0.559193 + 0.829038i \(0.688889\pi\)
−0.961262 + 0.275637i \(0.911111\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 −0.719340 0.694658i \(-0.755556\pi\)
0.719340 + 0.694658i \(0.244444\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0.801115 + 1.79933i 0.801115 + 1.79933i
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0.997564 + 0.0697565i 0.997564 + 0.0697565i
\(769\) 0 0 0.342020 0.939693i \(-0.388889\pi\)
−0.342020 + 0.939693i \(0.611111\pi\)
\(770\) 0 0
\(771\) 1.11334 1.32683i 1.11334 1.32683i
\(772\) 0 0
\(773\) 0 0 0.669131 0.743145i \(-0.266667\pi\)
−0.669131 + 0.743145i \(0.733333\pi\)
\(774\) 0 0
\(775\) −1.12063 + 0.498936i −1.12063 + 0.498936i
\(776\) 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
\(785\) −2.41462 + 0.0843204i −2.41462 + 0.0843204i
\(786\) 0 0
\(787\) 0 0 −0.0697565 0.997564i \(-0.522222\pi\)
0.0697565 + 0.997564i \(0.477778\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0.870827 0.122387i 0.870827 0.122387i
\(796\) 0.213817 0.273673i 0.213817 0.273673i
\(797\) −1.06579 + 0.718885i −1.06579 + 0.718885i −0.961262 0.275637i \(-0.911111\pi\)
−0.104528 + 0.994522i \(0.533333\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 1.43594 + 0.968551i 1.43594 + 0.968551i
\(802\) 0 0
\(803\) 0 0
\(804\) −1.87939 −1.87939
\(805\) 0 0
\(806\) 0 0
\(807\) 1.55208 + 1.21262i 1.55208 + 1.21262i
\(808\) 0 0
\(809\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(810\) 0 0
\(811\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −0.439693 + 0.0775297i −0.439693 + 0.0775297i
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 0 0 −0.882948 0.469472i \(-0.844444\pi\)
0.882948 + 0.469472i \(0.155556\pi\)
\(822\) 0 0
\(823\) −0.961262 + 0.275637i −0.961262 + 0.275637i −0.719340 0.694658i \(-0.755556\pi\)
−0.241922 + 0.970296i \(0.577778\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 −0.913545 0.406737i \(-0.866667\pi\)
0.913545 + 0.406737i \(0.133333\pi\)
\(828\) −0.917847 + 1.46886i −0.917847 + 1.46886i
\(829\) −1.25755 1.39666i −1.25755 1.39666i −0.882948 0.469472i \(-0.844444\pi\)
−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
\(837\) 1.76604 + 0.642788i 1.76604 + 0.642788i
\(838\) 0 0
\(839\) −1.36487 + 1.06636i −1.36487 + 1.06636i −0.374607 + 0.927184i \(0.622222\pi\)
−0.990268 + 0.139173i \(0.955556\pi\)
\(840\) 0 0
\(841\) −0.997564 + 0.0697565i −0.997564 + 0.0697565i
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −1.27853 + 0.134379i −1.27853 + 0.134379i
\(846\) 0 0
\(847\) 0 0
\(848\) 0.673648 + 0.118782i 0.673648 + 0.118782i
\(849\) 0 0
\(850\) 0 0
\(851\) 2.09111 + 1.63375i 2.09111 + 1.63375i
\(852\) 1.91111 0.476493i 1.91111 0.476493i
\(853\) 0 0 −0.694658 0.719340i \(-0.744444\pi\)
0.694658 + 0.719340i \(0.255556\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 −0.766044 0.642788i \(-0.777778\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(858\) 0 0
\(859\) 0.0603074 + 0.342020i 0.0603074 + 0.342020i 1.00000 \(0\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 1.01807 1.40126i 1.01807 1.40126i 0.104528 0.994522i \(-0.466667\pi\)
0.913545 0.406737i \(-0.133333\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 0.241922 0.970296i 0.241922 0.970296i
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) −0.130100 0.322008i −0.130100 0.322008i
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 0 0 −0.999391 0.0348995i \(-0.988889\pi\)
0.999391 + 0.0348995i \(0.0111111\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 1.70574 0.984808i 1.70574 0.984808i 0.766044 0.642788i \(-0.222222\pi\)
0.939693 0.342020i \(-0.111111\pi\)
\(882\) 0 0
\(883\) 0.339707 + 0.0722070i 0.339707 + 0.0722070i 0.374607 0.927184i \(-0.377778\pi\)
−0.0348995 + 0.999391i \(0.511111\pi\)
\(884\) 0 0
\(885\) 0.711438 + 0.516890i 0.711438 + 0.516890i
\(886\) 0 0
\(887\) 0 0 −0.374607 0.927184i \(-0.622222\pi\)
0.374607 + 0.927184i \(0.377778\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 0 0
\(892\) −1.00000 −1.00000
\(893\) 0 0
\(894\) 0 0
\(895\) −0.329424 0.815352i −0.329424 0.815352i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) −0.364987 + 0.541116i −0.364987 + 0.541116i
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 1.96842 + 0.0687386i 1.96842 + 0.0687386i
\(906\) 0 0
\(907\) 0.719340 0.694658i 0.719340 0.694658i −0.241922 0.970296i \(-0.577778\pi\)
0.961262 + 0.275637i \(0.0888889\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −0.0896772 + 1.28244i −0.0896772 + 1.28244i 0.719340 + 0.694658i \(0.244444\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) −0.615661 0.788011i −0.615661 0.788011i
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 0.766044 + 0.642788i 0.766044 + 0.642788i
\(926\) 0 0
\(927\) −1.49861 0.318539i −1.49861 0.318539i
\(928\) 0 0
\(929\) 0.475174 + 0.492057i 0.475174 + 0.492057i 0.913545 0.406737i \(-0.133333\pi\)
−0.438371 + 0.898794i \(0.644444\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) −0.0477162 + 0.682374i −0.0477162 + 0.682374i
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 0.994522 0.104528i \(-0.0333333\pi\)
−0.994522 + 0.104528i \(0.966667\pi\)
\(938\) 0 0
\(939\) −0.669131 0.743145i −0.669131 0.743145i
\(940\) 1.10999 2.27583i 1.10999 2.27583i
\(941\) 0 0 0.997564 0.0697565i \(-0.0222222\pi\)
−0.997564 + 0.0697565i \(0.977778\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0.402069 + 0.553400i 0.402069 + 0.553400i
\(945\) 0 0
\(946\) 0 0
\(947\) 0.233956 + 0.642788i 0.233956 + 0.642788i 1.00000 \(0\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 0 0 −0.669131 0.743145i \(-0.733333\pi\)
0.669131 + 0.743145i \(0.266667\pi\)
\(954\) 0 0
\(955\) −2.31318 1.02989i −2.31318 1.02989i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) −1.01305 + 0.791479i −1.01305 + 0.791479i
\(961\) −2.23570 1.18874i −2.23570 1.18874i
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 0 0 0.984808 0.173648i \(-0.0555556\pi\)
−0.984808 + 0.173648i \(0.944444\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 1.64728 0.535233i 1.64728 0.535233i 0.669131 0.743145i \(-0.266667\pi\)
0.978148 + 0.207912i \(0.0666667\pi\)
\(972\) 0.978148 0.207912i 0.978148 0.207912i
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 0 0 −0.719340 0.694658i \(-0.755556\pi\)
0.719340 + 0.694658i \(0.244444\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 1.11334 + 0.642788i 1.11334 + 0.642788i
\(981\) 0 0
\(982\) 0 0
\(983\) 0.321137 0.603972i 0.321137 0.603972i −0.669131 0.743145i \(-0.733333\pi\)
0.990268 + 0.139173i \(0.0444444\pi\)
\(984\) 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
\(993\) −0.232387 + 0.258091i −0.232387 + 0.258091i
\(994\) 0 0
\(995\) 0.0311446 + 0.445388i 0.0311446 + 0.445388i
\(996\) 0 0
\(997\) 0 0 0.999391 0.0348995i \(-0.0111111\pi\)
−0.999391 + 0.0348995i \(0.988889\pi\)
\(998\) 0 0
\(999\) −0.160147 1.52370i −0.160147 1.52370i
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.2423.1 24
11.2 odd 10 3267.1.q.a.1937.1 yes 6
11.3 even 5 inner 3267.1.be.a.1721.1 24
11.4 even 5 inner 3267.1.be.a.1775.1 24
11.5 even 5 inner 3267.1.be.a.614.1 24
11.6 odd 10 inner 3267.1.be.a.614.1 24
11.7 odd 10 inner 3267.1.be.a.1775.1 24
11.8 odd 10 inner 3267.1.be.a.1721.1 24
11.9 even 5 3267.1.q.a.1937.1 yes 6
11.10 odd 2 CM 3267.1.be.a.2423.1 24
27.23 odd 18 inner 3267.1.be.a.1697.1 24
297.50 even 90 inner 3267.1.be.a.3155.1 24
297.104 odd 90 inner 3267.1.be.a.3155.1 24
297.131 even 18 inner 3267.1.be.a.1697.1 24
297.158 odd 90 inner 3267.1.be.a.1049.1 24
297.185 odd 90 3267.1.q.a.1211.1 6
297.212 odd 90 inner 3267.1.be.a.995.1 24
297.239 even 90 inner 3267.1.be.a.995.1 24
297.266 even 90 3267.1.q.a.1211.1 6
297.293 even 90 inner 3267.1.be.a.1049.1 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3267.1.q.a.1211.1 6 297.185 odd 90
3267.1.q.a.1211.1 6 297.266 even 90
3267.1.q.a.1937.1 yes 6 11.2 odd 10
3267.1.q.a.1937.1 yes 6 11.9 even 5
3267.1.be.a.614.1 24 11.5 even 5 inner
3267.1.be.a.614.1 24 11.6 odd 10 inner
3267.1.be.a.995.1 24 297.212 odd 90 inner
3267.1.be.a.995.1 24 297.239 even 90 inner
3267.1.be.a.1049.1 24 297.158 odd 90 inner
3267.1.be.a.1049.1 24 297.293 even 90 inner
3267.1.be.a.1697.1 24 27.23 odd 18 inner
3267.1.be.a.1697.1 24 297.131 even 18 inner
3267.1.be.a.1721.1 24 11.3 even 5 inner
3267.1.be.a.1721.1 24 11.8 odd 10 inner
3267.1.be.a.1775.1 24 11.4 even 5 inner
3267.1.be.a.1775.1 24 11.7 odd 10 inner
3267.1.be.a.2423.1 24 1.1 even 1 trivial
3267.1.be.a.2423.1 24 11.10 odd 2 CM
3267.1.be.a.3155.1 24 297.50 even 90 inner
3267.1.be.a.3155.1 24 297.104 odd 90 inner