Properties

Label 983.1.b.c.982.9
Level $983$
Weight $1$
Character 983.982
Self dual yes
Analytic conductor $0.491$
Analytic rank $0$
Dimension $9$
Projective image $D_{27}$
CM discriminant -983
Inner twists $2$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [983,1,Mod(982,983)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(983, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("983.982");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 983 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 983.b (of order \(2\), degree \(1\), 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: yes
Analytic conductor: \(0.490580907418\)
Analytic rank: \(0\)
Dimension: \(9\)
Coefficient field: \(\Q(\zeta_{54})^+\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{9} - 9x^{7} + 27x^{5} - 30x^{3} + 9x - 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{27}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{27} - \cdots)\)

Embedding invariants

Embedding label 982.9
Root \(-1.94609\) of defining polynomial
Character \(\chi\) \(=\) 983.982

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.94609 q^{2} -1.67098 q^{3} +2.78727 q^{4} -3.25187 q^{6} -0.116290 q^{7} +3.47818 q^{8} +1.79216 q^{9} +O(q^{10})\) \(q+1.94609 q^{2} -1.67098 q^{3} +2.78727 q^{4} -3.25187 q^{6} -0.116290 q^{7} +3.47818 q^{8} +1.79216 q^{9} -4.65745 q^{12} -0.226310 q^{14} +3.98158 q^{16} +3.48770 q^{18} -0.573606 q^{19} +0.194317 q^{21} -1.98648 q^{23} -5.81195 q^{24} +1.00000 q^{25} -1.32368 q^{27} -0.324130 q^{28} +1.53209 q^{31} +4.27034 q^{32} +4.99522 q^{36} +0.347296 q^{37} -1.11629 q^{38} -1.87939 q^{41} +0.378159 q^{42} -1.37248 q^{43} -3.86586 q^{46} +1.19432 q^{47} -6.65313 q^{48} -0.986477 q^{49} +1.94609 q^{50} -1.37248 q^{53} -2.57600 q^{54} -0.404476 q^{56} +0.958482 q^{57} -1.00000 q^{59} +2.98158 q^{62} -0.208410 q^{63} +4.32888 q^{64} -1.87939 q^{67} +3.31935 q^{69} +6.23345 q^{72} +0.675870 q^{74} -1.67098 q^{75} -1.59879 q^{76} -1.00000 q^{79} +0.419676 q^{81} -3.65745 q^{82} +0.541614 q^{84} -2.67098 q^{86} +1.78727 q^{89} -5.53684 q^{92} -2.56008 q^{93} +2.32425 q^{94} -7.13563 q^{96} -1.91977 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 9 q + 9 q^{4} + 9 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 9 q + 9 q^{4} + 9 q^{9} - 9 q^{12} + 9 q^{16} - 9 q^{21} + 9 q^{25} - 9 q^{28} + 9 q^{36} - 9 q^{38} - 9 q^{48} + 9 q^{49} - 9 q^{59} + 9 q^{64} - 9 q^{79} + 9 q^{81} - 9 q^{84} - 9 q^{86}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/983\mathbb{Z}\right)^\times\).

\(n\) \(5\)
\(\chi(n)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.94609 1.94609 0.973045 0.230616i \(-0.0740741\pi\)
0.973045 + 0.230616i \(0.0740741\pi\)
\(3\) −1.67098 −1.67098 −0.835488 0.549509i \(-0.814815\pi\)
−0.835488 + 0.549509i \(0.814815\pi\)
\(4\) 2.78727 2.78727
\(5\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(6\) −3.25187 −3.25187
\(7\) −0.116290 −0.116290 −0.0581448 0.998308i \(-0.518519\pi\)
−0.0581448 + 0.998308i \(0.518519\pi\)
\(8\) 3.47818 3.47818
\(9\) 1.79216 1.79216
\(10\) 0 0
\(11\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(12\) −4.65745 −4.65745
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) −0.226310 −0.226310
\(15\) 0 0
\(16\) 3.98158 3.98158
\(17\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(18\) 3.48770 3.48770
\(19\) −0.573606 −0.573606 −0.286803 0.957990i \(-0.592593\pi\)
−0.286803 + 0.957990i \(0.592593\pi\)
\(20\) 0 0
\(21\) 0.194317 0.194317
\(22\) 0 0
\(23\) −1.98648 −1.98648 −0.993238 0.116093i \(-0.962963\pi\)
−0.993238 + 0.116093i \(0.962963\pi\)
\(24\) −5.81195 −5.81195
\(25\) 1.00000 1.00000
\(26\) 0 0
\(27\) −1.32368 −1.32368
\(28\) −0.324130 −0.324130
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 0 0
\(31\) 1.53209 1.53209 0.766044 0.642788i \(-0.222222\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(32\) 4.27034 4.27034
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 4.99522 4.99522
\(37\) 0.347296 0.347296 0.173648 0.984808i \(-0.444444\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(38\) −1.11629 −1.11629
\(39\) 0 0
\(40\) 0 0
\(41\) −1.87939 −1.87939 −0.939693 0.342020i \(-0.888889\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(42\) 0.378159 0.378159
\(43\) −1.37248 −1.37248 −0.686242 0.727374i \(-0.740741\pi\)
−0.686242 + 0.727374i \(0.740741\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) −3.86586 −3.86586
\(47\) 1.19432 1.19432 0.597159 0.802123i \(-0.296296\pi\)
0.597159 + 0.802123i \(0.296296\pi\)
\(48\) −6.65313 −6.65313
\(49\) −0.986477 −0.986477
\(50\) 1.94609 1.94609
\(51\) 0 0
\(52\) 0 0
\(53\) −1.37248 −1.37248 −0.686242 0.727374i \(-0.740741\pi\)
−0.686242 + 0.727374i \(0.740741\pi\)
\(54\) −2.57600 −2.57600
\(55\) 0 0
\(56\) −0.404476 −0.404476
\(57\) 0.958482 0.958482
\(58\) 0 0
\(59\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(60\) 0 0
\(61\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(62\) 2.98158 2.98158
\(63\) −0.208410 −0.208410
\(64\) 4.32888 4.32888
\(65\) 0 0
\(66\) 0 0
\(67\) −1.87939 −1.87939 −0.939693 0.342020i \(-0.888889\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(68\) 0 0
\(69\) 3.31935 3.31935
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 6.23345 6.23345
\(73\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(74\) 0.675870 0.675870
\(75\) −1.67098 −1.67098
\(76\) −1.59879 −1.59879
\(77\) 0 0
\(78\) 0 0
\(79\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(80\) 0 0
\(81\) 0.419676 0.419676
\(82\) −3.65745 −3.65745
\(83\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(84\) 0.541614 0.541614
\(85\) 0 0
\(86\) −2.67098 −2.67098
\(87\) 0 0
\(88\) 0 0
\(89\) 1.78727 1.78727 0.893633 0.448799i \(-0.148148\pi\)
0.893633 + 0.448799i \(0.148148\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −5.53684 −5.53684
\(93\) −2.56008 −2.56008
\(94\) 2.32425 2.32425
\(95\) 0 0
\(96\) −7.13563 −7.13563
\(97\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(98\) −1.91977 −1.91977
\(99\) 0 0
\(100\) 2.78727 2.78727
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) 0 0
\(103\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) −2.67098 −2.67098
\(107\) 1.78727 1.78727 0.893633 0.448799i \(-0.148148\pi\)
0.893633 + 0.448799i \(0.148148\pi\)
\(108\) −3.68945 −3.68945
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 0 0
\(111\) −0.580324 −0.580324
\(112\) −0.463017 −0.463017
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) 1.86529 1.86529
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) −1.94609 −1.94609
\(119\) 0 0
\(120\) 0 0
\(121\) 1.00000 1.00000
\(122\) 0 0
\(123\) 3.14041 3.14041
\(124\) 4.27034 4.27034
\(125\) 0 0
\(126\) −0.405584 −0.405584
\(127\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(128\) 4.15405 4.15405
\(129\) 2.29339 2.29339
\(130\) 0 0
\(131\) 0.792160 0.792160 0.396080 0.918216i \(-0.370370\pi\)
0.396080 + 0.918216i \(0.370370\pi\)
\(132\) 0 0
\(133\) 0.0667045 0.0667045
\(134\) −3.65745 −3.65745
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) 6.45976 6.45976
\(139\) 1.19432 1.19432 0.597159 0.802123i \(-0.296296\pi\)
0.597159 + 0.802123i \(0.296296\pi\)
\(140\) 0 0
\(141\) −1.99567 −1.99567
\(142\) 0 0
\(143\) 0 0
\(144\) 7.13563 7.13563
\(145\) 0 0
\(146\) 0 0
\(147\) 1.64838 1.64838
\(148\) 0.968007 0.968007
\(149\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(150\) −3.25187 −3.25187
\(151\) 1.94609 1.94609 0.973045 0.230616i \(-0.0740741\pi\)
0.973045 + 0.230616i \(0.0740741\pi\)
\(152\) −1.99511 −1.99511
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(158\) −1.94609 −1.94609
\(159\) 2.29339 2.29339
\(160\) 0 0
\(161\) 0.231007 0.231007
\(162\) 0.816728 0.816728
\(163\) 0.792160 0.792160 0.396080 0.918216i \(-0.370370\pi\)
0.396080 + 0.918216i \(0.370370\pi\)
\(164\) −5.23835 −5.23835
\(165\) 0 0
\(166\) 0 0
\(167\) −1.37248 −1.37248 −0.686242 0.727374i \(-0.740741\pi\)
−0.686242 + 0.727374i \(0.740741\pi\)
\(168\) 0.675870 0.675870
\(169\) 1.00000 1.00000
\(170\) 0 0
\(171\) −1.02799 −1.02799
\(172\) −3.82547 −3.82547
\(173\) −0.573606 −0.573606 −0.286803 0.957990i \(-0.592593\pi\)
−0.286803 + 0.957990i \(0.592593\pi\)
\(174\) 0 0
\(175\) −0.116290 −0.116290
\(176\) 0 0
\(177\) 1.67098 1.67098
\(178\) 3.47818 3.47818
\(179\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(180\) 0 0
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −6.90932 −6.90932
\(185\) 0 0
\(186\) −4.98215 −4.98215
\(187\) 0 0
\(188\) 3.32888 3.32888
\(189\) 0.153930 0.153930
\(190\) 0 0
\(191\) 0.347296 0.347296 0.173648 0.984808i \(-0.444444\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(192\) −7.23345 −7.23345
\(193\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −2.74957 −2.74957
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) 3.47818 3.47818
\(201\) 3.14041 3.14041
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −3.56008 −3.56008
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(212\) −3.82547 −3.82547
\(213\) 0 0
\(214\) 3.47818 3.47818
\(215\) 0 0
\(216\) −4.60399 −4.60399
\(217\) −0.178166 −0.178166
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) −1.12936 −1.12936
\(223\) 0.792160 0.792160 0.396080 0.918216i \(-0.370370\pi\)
0.396080 + 0.918216i \(0.370370\pi\)
\(224\) −0.496596 −0.496596
\(225\) 1.79216 1.79216
\(226\) 0 0
\(227\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(228\) 2.67154 2.67154
\(229\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −2.78727 −2.78727
\(237\) 1.67098 1.67098
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 0 0
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) 1.94609 1.94609
\(243\) 0.622410 0.622410
\(244\) 0 0
\(245\) 0 0
\(246\) 6.11151 6.11151
\(247\) 0 0
\(248\) 5.32888 5.32888
\(249\) 0 0
\(250\) 0 0
\(251\) −1.87939 −1.87939 −0.939693 0.342020i \(-0.888889\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(252\) −0.580893 −0.580893
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 3.75527 3.75527
\(257\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(258\) 4.46314 4.46314
\(259\) −0.0403870 −0.0403870
\(260\) 0 0
\(261\) 0 0
\(262\) 1.54161 1.54161
\(263\) −1.87939 −1.87939 −0.939693 0.342020i \(-0.888889\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0.129813 0.129813
\(267\) −2.98648 −2.98648
\(268\) −5.23835 −5.23835
\(269\) −0.116290 −0.116290 −0.0581448 0.998308i \(-0.518519\pi\)
−0.0581448 + 0.998308i \(0.518519\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 9.25192 9.25192
\(277\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(278\) 2.32425 2.32425
\(279\) 2.74575 2.74575
\(280\) 0 0
\(281\) −0.573606 −0.573606 −0.286803 0.957990i \(-0.592593\pi\)
−0.286803 + 0.957990i \(0.592593\pi\)
\(282\) −3.88376 −3.88376
\(283\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0.218553 0.218553
\(288\) 7.65313 7.65313
\(289\) 1.00000 1.00000
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 1.53209 1.53209 0.766044 0.642788i \(-0.222222\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(294\) 3.20789 3.20789
\(295\) 0 0
\(296\) 1.20796 1.20796
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) −4.65745 −4.65745
\(301\) 0.159606 0.159606
\(302\) 3.78727 3.78727
\(303\) 0 0
\(304\) −2.28386 −2.28386
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(312\) 0 0
\(313\) 1.94609 1.94609 0.973045 0.230616i \(-0.0740741\pi\)
0.973045 + 0.230616i \(0.0740741\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) −2.78727 −2.78727
\(317\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(318\) 4.46314 4.46314
\(319\) 0 0
\(320\) 0 0
\(321\) −2.98648 −2.98648
\(322\) 0.449560 0.449560
\(323\) 0 0
\(324\) 1.16975 1.16975
\(325\) 0 0
\(326\) 1.54161 1.54161
\(327\) 0 0
\(328\) −6.53684 −6.53684
\(329\) −0.138887 −0.138887
\(330\) 0 0
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) 0 0
\(333\) 0.622410 0.622410
\(334\) −2.67098 −2.67098
\(335\) 0 0
\(336\) 0.773690 0.773690
\(337\) 1.53209 1.53209 0.766044 0.642788i \(-0.222222\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(338\) 1.94609 1.94609
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) −2.00057 −2.00057
\(343\) 0.231007 0.231007
\(344\) −4.77374 −4.77374
\(345\) 0 0
\(346\) −1.11629 −1.11629
\(347\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(348\) 0 0
\(349\) −1.67098 −1.67098 −0.835488 0.549509i \(-0.814815\pi\)
−0.835488 + 0.549509i \(0.814815\pi\)
\(350\) −0.226310 −0.226310
\(351\) 0 0
\(352\) 0 0
\(353\) 1.19432 1.19432 0.597159 0.802123i \(-0.296296\pi\)
0.597159 + 0.802123i \(0.296296\pi\)
\(354\) 3.25187 3.25187
\(355\) 0 0
\(356\) 4.98158 4.98158
\(357\) 0 0
\(358\) 0 0
\(359\) 1.78727 1.78727 0.893633 0.448799i \(-0.148148\pi\)
0.893633 + 0.448799i \(0.148148\pi\)
\(360\) 0 0
\(361\) −0.670976 −0.670976
\(362\) 0 0
\(363\) −1.67098 −1.67098
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 1.19432 1.19432 0.597159 0.802123i \(-0.296296\pi\)
0.597159 + 0.802123i \(0.296296\pi\)
\(368\) −7.90932 −7.90932
\(369\) −3.36816 −3.36816
\(370\) 0 0
\(371\) 0.159606 0.159606
\(372\) −7.13563 −7.13563
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 4.15405 4.15405
\(377\) 0 0
\(378\) 0.299562 0.299562
\(379\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0.675870 0.675870
\(383\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(384\) −6.94131 −6.94131
\(385\) 0 0
\(386\) −1.94609 −1.94609
\(387\) −2.45971 −2.45971
\(388\) 0 0
\(389\) −1.98648 −1.98648 −0.993238 0.116093i \(-0.962963\pi\)
−0.993238 + 0.116093i \(0.962963\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −3.43114 −3.43114
\(393\) −1.32368 −1.32368
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(398\) 0 0
\(399\) −0.111462 −0.111462
\(400\) 3.98158 3.98158
\(401\) 1.19432 1.19432 0.597159 0.802123i \(-0.296296\pi\)
0.597159 + 0.802123i \(0.296296\pi\)
\(402\) 6.11151 6.11151
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0.116290 0.116290
\(414\) −6.92824 −6.92824
\(415\) 0 0
\(416\) 0 0
\(417\) −1.99567 −1.99567
\(418\) 0 0
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(422\) 0 0
\(423\) 2.14041 2.14041
\(424\) −4.77374 −4.77374
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 4.98158 4.98158
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) −5.27034 −5.27034
\(433\) −1.87939 −1.87939 −0.939693 0.342020i \(-0.888889\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(434\) −0.346727 −0.346727
\(435\) 0 0
\(436\) 0 0
\(437\) 1.13946 1.13946
\(438\) 0 0
\(439\) 0.347296 0.347296 0.173648 0.984808i \(-0.444444\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(440\) 0 0
\(441\) −1.76792 −1.76792
\(442\) 0 0
\(443\) 1.53209 1.53209 0.766044 0.642788i \(-0.222222\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(444\) −1.61752 −1.61752
\(445\) 0 0
\(446\) 1.54161 1.54161
\(447\) 0 0
\(448\) −0.503404 −0.503404
\(449\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(450\) 3.48770 3.48770
\(451\) 0 0
\(452\) 0 0
\(453\) −3.25187 −3.25187
\(454\) 0 0
\(455\) 0 0
\(456\) 3.33377 3.33377
\(457\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −1.67098 −1.67098 −0.835488 0.549509i \(-0.814815\pi\)
−0.835488 + 0.549509i \(0.814815\pi\)
\(462\) 0 0
\(463\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) −1.94609 −1.94609
\(467\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(468\) 0 0
\(469\) 0.218553 0.218553
\(470\) 0 0
\(471\) 0 0
\(472\) −3.47818 −3.47818
\(473\) 0 0
\(474\) 3.25187 3.25187
\(475\) −0.573606 −0.573606
\(476\) 0 0
\(477\) −2.45971 −2.45971
\(478\) 0 0
\(479\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) −0.386007 −0.386007
\(484\) 2.78727 2.78727
\(485\) 0 0
\(486\) 1.21127 1.21127
\(487\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(488\) 0 0
\(489\) −1.32368 −1.32368
\(490\) 0 0
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 8.75315 8.75315
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 6.10014 6.10014
\(497\) 0 0
\(498\) 0 0
\(499\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(500\) 0 0
\(501\) 2.29339 2.29339
\(502\) −3.65745 −3.65745
\(503\) −0.573606 −0.573606 −0.286803 0.957990i \(-0.592593\pi\)
−0.286803 + 0.957990i \(0.592593\pi\)
\(504\) −0.724886 −0.724886
\(505\) 0 0
\(506\) 0 0
\(507\) −1.67098 −1.67098
\(508\) 0 0
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 3.15405 3.15405
\(513\) 0.759271 0.759271
\(514\) 0 0
\(515\) 0 0
\(516\) 6.39228 6.39228
\(517\) 0 0
\(518\) −0.0785967 −0.0785967
\(519\) 0.958482 0.958482
\(520\) 0 0
\(521\) −1.98648 −1.98648 −0.993238 0.116093i \(-0.962963\pi\)
−0.993238 + 0.116093i \(0.962963\pi\)
\(522\) 0 0
\(523\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(524\) 2.20796 2.20796
\(525\) 0.194317 0.194317
\(526\) −3.65745 −3.65745
\(527\) 0 0
\(528\) 0 0
\(529\) 2.94609 2.94609
\(530\) 0 0
\(531\) −1.79216 −1.79216
\(532\) 0.185923 0.185923
\(533\) 0 0
\(534\) −5.81195 −5.81195
\(535\) 0 0
\(536\) −6.53684 −6.53684
\(537\) 0 0
\(538\) −0.226310 −0.226310
\(539\) 0 0
\(540\) 0 0
\(541\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −1.98648 −1.98648 −0.993238 0.116093i \(-0.962963\pi\)
−0.993238 + 0.116093i \(0.962963\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 11.5453 11.5453
\(553\) 0.116290 0.116290
\(554\) 0 0
\(555\) 0 0
\(556\) 3.32888 3.32888
\(557\) −0.116290 −0.116290 −0.0581448 0.998308i \(-0.518519\pi\)
−0.0581448 + 0.998308i \(0.518519\pi\)
\(558\) 5.34347 5.34347
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) −1.11629 −1.11629
\(563\) −0.116290 −0.116290 −0.0581448 0.998308i \(-0.518519\pi\)
−0.0581448 + 0.998308i \(0.518519\pi\)
\(564\) −5.56248 −5.56248
\(565\) 0 0
\(566\) 0 0
\(567\) −0.0488040 −0.0488040
\(568\) 0 0
\(569\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(570\) 0 0
\(571\) 1.78727 1.78727 0.893633 0.448799i \(-0.148148\pi\)
0.893633 + 0.448799i \(0.148148\pi\)
\(572\) 0 0
\(573\) −0.580324 −0.580324
\(574\) 0.425324 0.425324
\(575\) −1.98648 −1.98648
\(576\) 7.75804 7.75804
\(577\) −0.573606 −0.573606 −0.286803 0.957990i \(-0.592593\pi\)
−0.286803 + 0.957990i \(0.592593\pi\)
\(578\) 1.94609 1.94609
\(579\) 1.67098 1.67098
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 2.98158 2.98158
\(587\) 0.347296 0.347296 0.173648 0.984808i \(-0.444444\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(588\) 4.59447 4.59447
\(589\) −0.878816 −0.878816
\(590\) 0 0
\(591\) 0 0
\(592\) 1.38279 1.38279
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(600\) −5.81195 −5.81195
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) 0.310607 0.310607
\(603\) −3.36816 −3.36816
\(604\) 5.42427 5.42427
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(608\) −2.44949 −2.44949
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 1.78727 1.78727 0.893633 0.448799i \(-0.148148\pi\)
0.893633 + 0.448799i \(0.148148\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(618\) 0 0
\(619\) 1.94609 1.94609 0.973045 0.230616i \(-0.0740741\pi\)
0.973045 + 0.230616i \(0.0740741\pi\)
\(620\) 0 0
\(621\) 2.62946 2.62946
\(622\) 0 0
\(623\) −0.207840 −0.207840
\(624\) 0 0
\(625\) 1.00000 1.00000
\(626\) 3.78727 3.78727
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) −1.87939 −1.87939 −0.939693 0.342020i \(-0.888889\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(632\) −3.47818 −3.47818
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 6.39228 6.39228
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(642\) −5.81195 −5.81195
\(643\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(644\) 0.643877 0.643877
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(648\) 1.45971 1.45971
\(649\) 0 0
\(650\) 0 0
\(651\) 0.297711 0.297711
\(652\) 2.20796 2.20796
\(653\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −7.48293 −7.48293
\(657\) 0 0
\(658\) −0.270286 −0.270286
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 1.21127 1.21127
\(667\) 0 0
\(668\) −3.82547 −3.82547
\(669\) −1.32368 −1.32368
\(670\) 0 0
\(671\) 0 0
\(672\) 0.829800 0.829800
\(673\) 1.19432 1.19432 0.597159 0.802123i \(-0.296296\pi\)
0.597159 + 0.802123i \(0.296296\pi\)
\(674\) 2.98158 2.98158
\(675\) −1.32368 −1.32368
\(676\) 2.78727 2.78727
\(677\) −1.98648 −1.98648 −0.993238 0.116093i \(-0.962963\pi\)
−0.993238 + 0.116093i \(0.962963\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(684\) −2.86529 −2.86529
\(685\) 0 0
\(686\) 0.449560 0.449560
\(687\) 0 0
\(688\) −5.46466 −5.46466
\(689\) 0 0
\(690\) 0 0
\(691\) 1.78727 1.78727 0.893633 0.448799i \(-0.148148\pi\)
0.893633 + 0.448799i \(0.148148\pi\)
\(692\) −1.59879 −1.59879
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) −3.25187 −3.25187
\(699\) 1.67098 1.67098
\(700\) −0.324130 −0.324130
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 0 0
\(703\) −0.199211 −0.199211
\(704\) 0 0
\(705\) 0 0
\(706\) 2.32425 2.32425
\(707\) 0 0
\(708\) 4.65745 4.65745
\(709\) −0.573606 −0.573606 −0.286803 0.957990i \(-0.592593\pi\)
−0.286803 + 0.957990i \(0.592593\pi\)
\(710\) 0 0
\(711\) −1.79216 −1.79216
\(712\) 6.21643 6.21643
\(713\) −3.04346 −3.04346
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 3.47818 3.47818
\(719\) 1.53209 1.53209 0.766044 0.642788i \(-0.222222\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −1.30578 −1.30578
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) −3.25187 −3.25187
\(727\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(728\) 0 0
\(729\) −1.45971 −1.45971
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) −1.98648 −1.98648 −0.993238 0.116093i \(-0.962963\pi\)
−0.993238 + 0.116093i \(0.962963\pi\)
\(734\) 2.32425 2.32425
\(735\) 0 0
\(736\) −8.48293 −8.48293
\(737\) 0 0
\(738\) −6.55474 −6.55474
\(739\) 0.347296 0.347296 0.173648 0.984808i \(-0.444444\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0.310607 0.310607
\(743\) 0.347296 0.347296 0.173648 0.984808i \(-0.444444\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(744\) −8.90443 −8.90443
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −0.207840 −0.207840
\(750\) 0 0
\(751\) 0.792160 0.792160 0.396080 0.918216i \(-0.370370\pi\)
0.396080 + 0.918216i \(0.370370\pi\)
\(752\) 4.75527 4.75527
\(753\) 3.14041 3.14041
\(754\) 0 0
\(755\) 0 0
\(756\) 0.429044 0.429044
\(757\) 1.19432 1.19432 0.597159 0.802123i \(-0.296296\pi\)
0.597159 + 0.802123i \(0.296296\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0.968007 0.968007
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) −6.27497 −6.27497
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −2.78727 −2.78727
\(773\) 0.792160 0.792160 0.396080 0.918216i \(-0.370370\pi\)
0.396080 + 0.918216i \(0.370370\pi\)
\(774\) −4.78681 −4.78681
\(775\) 1.53209 1.53209
\(776\) 0 0
\(777\) 0.0674856 0.0674856
\(778\) −3.86586 −3.86586
\(779\) 1.07803 1.07803
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −3.92774 −3.92774
\(785\) 0 0
\(786\) −2.57600 −2.57600
\(787\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(788\) 0 0
\(789\) 3.14041 3.14041
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(798\) −0.216914 −0.216914
\(799\) 0 0
\(800\) 4.27034 4.27034
\(801\) 3.20306 3.20306
\(802\) 2.32425 2.32425
\(803\) 0 0
\(804\) 8.75315 8.75315
\(805\) 0 0
\(806\) 0 0
\(807\) 0.194317 0.194317
\(808\) 0 0
\(809\) −1.67098 −1.67098 −0.835488 0.549509i \(-0.814815\pi\)
−0.835488 + 0.549509i \(0.814815\pi\)
\(810\) 0 0
\(811\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0.787265 0.787265
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(822\) 0 0
\(823\) −1.37248 −1.37248 −0.686242 0.727374i \(-0.740741\pi\)
−0.686242 + 0.727374i \(0.740741\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0.226310 0.226310
\(827\) 1.19432 1.19432 0.597159 0.802123i \(-0.296296\pi\)
0.597159 + 0.802123i \(0.296296\pi\)
\(828\) −9.92290 −9.92290
\(829\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) −3.88376 −3.88376
\(835\) 0 0
\(836\) 0 0
\(837\) −2.02799 −2.02799
\(838\) 0 0
\(839\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(840\) 0 0
\(841\) 1.00000 1.00000
\(842\) 0 0
\(843\) 0.958482 0.958482
\(844\) 0 0
\(845\) 0 0
\(846\) 4.16542 4.16542
\(847\) −0.116290 −0.116290
\(848\) −5.46466 −5.46466
\(849\) 0 0
\(850\) 0 0
\(851\) −0.689896 −0.689896
\(852\) 0 0
\(853\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 6.21643 6.21643
\(857\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(858\) 0 0
\(859\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(860\) 0 0
\(861\) −0.365197 −0.365197
\(862\) 0 0
\(863\) 1.53209 1.53209 0.766044 0.642788i \(-0.222222\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(864\) −5.65256 −5.65256
\(865\) 0 0
\(866\) −3.65745 −3.65745
\(867\) −1.67098 −1.67098
\(868\) −0.496596 −0.496596
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 0 0
\(874\) 2.21748 2.21748
\(875\) 0 0
\(876\) 0 0
\(877\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(878\) 0.675870 0.675870
\(879\) −2.56008 −2.56008
\(880\) 0 0
\(881\) −0.116290 −0.116290 −0.0581448 0.998308i \(-0.518519\pi\)
−0.0581448 + 0.998308i \(0.518519\pi\)
\(882\) −3.44054 −3.44054
\(883\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 2.98158 2.98158
\(887\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(888\) −2.01847 −2.01847
\(889\) 0 0
\(890\) 0 0
\(891\) 0 0
\(892\) 2.20796 2.20796
\(893\) −0.685068 −0.685068
\(894\) 0 0
\(895\) 0 0
\(896\) −0.483073 −0.483073
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) 4.99522 4.99522
\(901\) 0 0
\(902\) 0 0
\(903\) −0.266697 −0.266697
\(904\) 0 0
\(905\) 0 0
\(906\) −6.32843 −6.32843
\(907\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(912\) 3.81628 3.81628
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −0.0921200 −0.0921200
\(918\) 0 0
\(919\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) −3.25187 −3.25187
\(923\) 0 0
\(924\) 0 0
\(925\) 0.347296 0.347296
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(930\) 0 0
\(931\) 0.565849 0.565849
\(932\) −2.78727 −2.78727
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(938\) 0.425324 0.425324
\(939\) −3.25187 −3.25187
\(940\) 0 0
\(941\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(942\) 0 0
\(943\) 3.73336 3.73336
\(944\) −3.98158 −3.98158
\(945\) 0 0
\(946\) 0 0
\(947\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(948\) 4.65745 4.65745
\(949\) 0 0
\(950\) −1.11629 −1.11629
\(951\) 0 0
\(952\) 0 0
\(953\) 0.347296 0.347296 0.173648 0.984808i \(-0.444444\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(954\) −4.78681 −4.78681
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 1.34730 1.34730
\(962\) 0 0
\(963\) 3.20306 3.20306
\(964\) 0 0
\(965\) 0 0
\(966\) −0.751203 −0.751203
\(967\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(968\) 3.47818 3.47818
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(972\) 1.73482 1.73482
\(973\) −0.138887 −0.138887
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(978\) −2.57600 −2.57600
\(979\) 0 0
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 1.00000 1.00000
\(984\) 10.9229 10.9229
\(985\) 0 0
\(986\) 0 0
\(987\) 0.232076 0.232076
\(988\) 0 0
\(989\) 2.72641 2.72641
\(990\) 0 0
\(991\) −1.37248 −1.37248 −0.686242 0.727374i \(-0.740741\pi\)
−0.686242 + 0.727374i \(0.740741\pi\)
\(992\) 6.54254 6.54254
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 0.792160 0.792160 0.396080 0.918216i \(-0.370370\pi\)
0.396080 + 0.918216i \(0.370370\pi\)
\(998\) 0 0
\(999\) −0.459709 −0.459709
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 983.1.b.c.982.9 9
983.982 odd 2 CM 983.1.b.c.982.9 9
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
983.1.b.c.982.9 9 1.1 even 1 trivial
983.1.b.c.982.9 9 983.982 odd 2 CM