Properties

Label 983.1.b.c.982.1
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 982.1
Root \(1.98648\) 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)
 
\(f(q)\) \(=\) \(q-1.98648 q^{2} -0.573606 q^{3} +2.94609 q^{4} +1.13946 q^{6} -1.37248 q^{7} -3.86586 q^{8} -0.670976 q^{9} +O(q^{10})\) \(q-1.98648 q^{2} -0.573606 q^{3} +2.94609 q^{4} +1.13946 q^{6} -1.37248 q^{7} -3.86586 q^{8} -0.670976 q^{9} -1.68990 q^{12} +2.72641 q^{14} +4.73336 q^{16} +1.33288 q^{18} +1.19432 q^{19} +0.787265 q^{21} -0.116290 q^{23} +2.21748 q^{24} +1.00000 q^{25} +0.958482 q^{27} -4.04346 q^{28} -1.87939 q^{31} -5.53684 q^{32} -1.97675 q^{36} +1.53209 q^{37} -2.37248 q^{38} +0.347296 q^{41} -1.56388 q^{42} +0.792160 q^{43} +0.231007 q^{46} +1.78727 q^{47} -2.71508 q^{48} +0.883710 q^{49} -1.98648 q^{50} +0.792160 q^{53} -1.90400 q^{54} +5.30583 q^{56} -0.685068 q^{57} -1.00000 q^{59} +3.73336 q^{62} +0.920903 q^{63} +6.26544 q^{64} +0.347296 q^{67} +0.0667045 q^{69} +2.59390 q^{72} -3.04346 q^{74} -0.573606 q^{75} +3.51857 q^{76} -1.00000 q^{79} +0.121184 q^{81} -0.689896 q^{82} +2.31935 q^{84} -1.57361 q^{86} +1.94609 q^{89} -0.342600 q^{92} +1.07803 q^{93} -3.55036 q^{94} +3.17597 q^{96} -1.75547 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 9 q + 9 q^{4} + 9 q^{9}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.98648 −1.98648 −0.993238 0.116093i \(-0.962963\pi\)
−0.993238 + 0.116093i \(0.962963\pi\)
\(3\) −0.573606 −0.573606 −0.286803 0.957990i \(-0.592593\pi\)
−0.286803 + 0.957990i \(0.592593\pi\)
\(4\) 2.94609 2.94609
\(5\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(6\) 1.13946 1.13946
\(7\) −1.37248 −1.37248 −0.686242 0.727374i \(-0.740741\pi\)
−0.686242 + 0.727374i \(0.740741\pi\)
\(8\) −3.86586 −3.86586
\(9\) −0.670976 −0.670976
\(10\) 0 0
\(11\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(12\) −1.68990 −1.68990
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) 2.72641 2.72641
\(15\) 0 0
\(16\) 4.73336 4.73336
\(17\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(18\) 1.33288 1.33288
\(19\) 1.19432 1.19432 0.597159 0.802123i \(-0.296296\pi\)
0.597159 + 0.802123i \(0.296296\pi\)
\(20\) 0 0
\(21\) 0.787265 0.787265
\(22\) 0 0
\(23\) −0.116290 −0.116290 −0.0581448 0.998308i \(-0.518519\pi\)
−0.0581448 + 0.998308i \(0.518519\pi\)
\(24\) 2.21748 2.21748
\(25\) 1.00000 1.00000
\(26\) 0 0
\(27\) 0.958482 0.958482
\(28\) −4.04346 −4.04346
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 0 0
\(31\) −1.87939 −1.87939 −0.939693 0.342020i \(-0.888889\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(32\) −5.53684 −5.53684
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) −1.97675 −1.97675
\(37\) 1.53209 1.53209 0.766044 0.642788i \(-0.222222\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(38\) −2.37248 −2.37248
\(39\) 0 0
\(40\) 0 0
\(41\) 0.347296 0.347296 0.173648 0.984808i \(-0.444444\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(42\) −1.56388 −1.56388
\(43\) 0.792160 0.792160 0.396080 0.918216i \(-0.370370\pi\)
0.396080 + 0.918216i \(0.370370\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0.231007 0.231007
\(47\) 1.78727 1.78727 0.893633 0.448799i \(-0.148148\pi\)
0.893633 + 0.448799i \(0.148148\pi\)
\(48\) −2.71508 −2.71508
\(49\) 0.883710 0.883710
\(50\) −1.98648 −1.98648
\(51\) 0 0
\(52\) 0 0
\(53\) 0.792160 0.792160 0.396080 0.918216i \(-0.370370\pi\)
0.396080 + 0.918216i \(0.370370\pi\)
\(54\) −1.90400 −1.90400
\(55\) 0 0
\(56\) 5.30583 5.30583
\(57\) −0.685068 −0.685068
\(58\) 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 \(\pi\)
\(62\) 3.73336 3.73336
\(63\) 0.920903 0.920903
\(64\) 6.26544 6.26544
\(65\) 0 0
\(66\) 0 0
\(67\) 0.347296 0.347296 0.173648 0.984808i \(-0.444444\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(68\) 0 0
\(69\) 0.0667045 0.0667045
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 2.59390 2.59390
\(73\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(74\) −3.04346 −3.04346
\(75\) −0.573606 −0.573606
\(76\) 3.51857 3.51857
\(77\) 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
\(81\) 0.121184 0.121184
\(82\) −0.689896 −0.689896
\(83\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(84\) 2.31935 2.31935
\(85\) 0 0
\(86\) −1.57361 −1.57361
\(87\) 0 0
\(88\) 0 0
\(89\) 1.94609 1.94609 0.973045 0.230616i \(-0.0740741\pi\)
0.973045 + 0.230616i \(0.0740741\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −0.342600 −0.342600
\(93\) 1.07803 1.07803
\(94\) −3.55036 −3.55036
\(95\) 0 0
\(96\) 3.17597 3.17597
\(97\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(98\) −1.75547 −1.75547
\(99\) 0 0
\(100\) 2.94609 2.94609
\(101\) 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
\(106\) −1.57361 −1.57361
\(107\) 1.94609 1.94609 0.973045 0.230616i \(-0.0740741\pi\)
0.973045 + 0.230616i \(0.0740741\pi\)
\(108\) 2.82378 2.82378
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 0 0
\(111\) −0.878816 −0.878816
\(112\) −6.49645 −6.49645
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) 1.36087 1.36087
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 1.98648 1.98648
\(119\) 0 0
\(120\) 0 0
\(121\) 1.00000 1.00000
\(122\) 0 0
\(123\) −0.199211 −0.199211
\(124\) −5.53684 −5.53684
\(125\) 0 0
\(126\) −1.82935 −1.82935
\(127\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(128\) −6.90932 −6.90932
\(129\) −0.454388 −0.454388
\(130\) 0 0
\(131\) −1.67098 −1.67098 −0.835488 0.549509i \(-0.814815\pi\)
−0.835488 + 0.549509i \(0.814815\pi\)
\(132\) 0 0
\(133\) −1.63918 −1.63918
\(134\) −0.689896 −0.689896
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) −0.132507 −0.132507
\(139\) 1.78727 1.78727 0.893633 0.448799i \(-0.148148\pi\)
0.893633 + 0.448799i \(0.148148\pi\)
\(140\) 0 0
\(141\) −1.02519 −1.02519
\(142\) 0 0
\(143\) 0 0
\(144\) −3.17597 −3.17597
\(145\) 0 0
\(146\) 0 0
\(147\) −0.506902 −0.506902
\(148\) 4.51367 4.51367
\(149\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(150\) 1.13946 1.13946
\(151\) −1.98648 −1.98648 −0.993238 0.116093i \(-0.962963\pi\)
−0.993238 + 0.116093i \(0.962963\pi\)
\(152\) −4.61707 −4.61707
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(158\) 1.98648 1.98648
\(159\) −0.454388 −0.454388
\(160\) 0 0
\(161\) 0.159606 0.159606
\(162\) −0.240729 −0.240729
\(163\) −1.67098 −1.67098 −0.835488 0.549509i \(-0.814815\pi\)
−0.835488 + 0.549509i \(0.814815\pi\)
\(164\) 1.02317 1.02317
\(165\) 0 0
\(166\) 0 0
\(167\) 0.792160 0.792160 0.396080 0.918216i \(-0.370370\pi\)
0.396080 + 0.918216i \(0.370370\pi\)
\(168\) −3.04346 −3.04346
\(169\) 1.00000 1.00000
\(170\) 0 0
\(171\) −0.801358 −0.801358
\(172\) 2.33377 2.33377
\(173\) 1.19432 1.19432 0.597159 0.802123i \(-0.296296\pi\)
0.597159 + 0.802123i \(0.296296\pi\)
\(174\) 0 0
\(175\) −1.37248 −1.37248
\(176\) 0 0
\(177\) 0.573606 0.573606
\(178\) −3.86586 −3.86586
\(179\) 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
\(184\) 0.449560 0.449560
\(185\) 0 0
\(186\) −2.14148 −2.14148
\(187\) 0 0
\(188\) 5.26544 5.26544
\(189\) −1.31550 −1.31550
\(190\) 0 0
\(191\) 1.53209 1.53209 0.766044 0.642788i \(-0.222222\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(192\) −3.59390 −3.59390
\(193\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 2.60349 2.60349
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) −3.86586 −3.86586
\(201\) −0.199211 −0.199211
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0.0780275 0.0780275
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(212\) 2.33377 2.33377
\(213\) 0 0
\(214\) −3.86586 −3.86586
\(215\) 0 0
\(216\) −3.70536 −3.70536
\(217\) 2.57942 2.57942
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 1.74575 1.74575
\(223\) −1.67098 −1.67098 −0.835488 0.549509i \(-0.814815\pi\)
−0.835488 + 0.549509i \(0.814815\pi\)
\(224\) 7.59922 7.59922
\(225\) −0.670976 −0.670976
\(226\) 0 0
\(227\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(228\) −2.01827 −2.01827
\(229\) 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
\(236\) −2.94609 −2.94609
\(237\) 0.573606 0.573606
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 0 0
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) −1.98648 −1.98648
\(243\) −1.02799 −1.02799
\(244\) 0 0
\(245\) 0 0
\(246\) 0.395729 0.395729
\(247\) 0 0
\(248\) 7.26544 7.26544
\(249\) 0 0
\(250\) 0 0
\(251\) 0.347296 0.347296 0.173648 0.984808i \(-0.444444\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(252\) 2.71306 2.71306
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 7.45976 7.45976
\(257\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(258\) 0.902631 0.902631
\(259\) −2.10277 −2.10277
\(260\) 0 0
\(261\) 0 0
\(262\) 3.31935 3.31935
\(263\) 0.347296 0.347296 0.173648 0.984808i \(-0.444444\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 3.25619 3.25619
\(267\) −1.11629 −1.11629
\(268\) 1.02317 1.02317
\(269\) −1.37248 −1.37248 −0.686242 0.727374i \(-0.740741\pi\)
−0.686242 + 0.727374i \(0.740741\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0.196517 0.196517
\(277\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(278\) −3.55036 −3.55036
\(279\) 1.26102 1.26102
\(280\) 0 0
\(281\) 1.19432 1.19432 0.597159 0.802123i \(-0.296296\pi\)
0.597159 + 0.802123i \(0.296296\pi\)
\(282\) 2.03651 2.03651
\(283\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −0.476658 −0.476658
\(288\) 3.71508 3.71508
\(289\) 1.00000 1.00000
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −1.87939 −1.87939 −0.939693 0.342020i \(-0.888889\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(294\) 1.00695 1.00695
\(295\) 0 0
\(296\) −5.92284 −5.92284
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) −1.68990 −1.68990
\(301\) −1.08723 −1.08723
\(302\) 3.94609 3.94609
\(303\) 0 0
\(304\) 5.65313 5.65313
\(305\) 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
\(313\) −1.98648 −1.98648 −0.993238 0.116093i \(-0.962963\pi\)
−0.993238 + 0.116093i \(0.962963\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) −2.94609 −2.94609
\(317\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(318\) 0.902631 0.902631
\(319\) 0 0
\(320\) 0 0
\(321\) −1.11629 −1.11629
\(322\) −0.317053 −0.317053
\(323\) 0 0
\(324\) 0.357019 0.357019
\(325\) 0 0
\(326\) 3.31935 3.31935
\(327\) 0 0
\(328\) −1.34260 −1.34260
\(329\) −2.45299 −2.45299
\(330\) 0 0
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) 0 0
\(333\) −1.02799 −1.02799
\(334\) −1.57361 −1.57361
\(335\) 0 0
\(336\) 3.72641 3.72641
\(337\) −1.87939 −1.87939 −0.939693 0.342020i \(-0.888889\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(338\) −1.98648 −1.98648
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 1.59188 1.59188
\(343\) 0.159606 0.159606
\(344\) −3.06238 −3.06238
\(345\) 0 0
\(346\) −2.37248 −2.37248
\(347\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(348\) 0 0
\(349\) −0.573606 −0.573606 −0.286803 0.957990i \(-0.592593\pi\)
−0.286803 + 0.957990i \(0.592593\pi\)
\(350\) 2.72641 2.72641
\(351\) 0 0
\(352\) 0 0
\(353\) 1.78727 1.78727 0.893633 0.448799i \(-0.148148\pi\)
0.893633 + 0.448799i \(0.148148\pi\)
\(354\) −1.13946 −1.13946
\(355\) 0 0
\(356\) 5.73336 5.73336
\(357\) 0 0
\(358\) 0 0
\(359\) 1.94609 1.94609 0.973045 0.230616i \(-0.0740741\pi\)
0.973045 + 0.230616i \(0.0740741\pi\)
\(360\) 0 0
\(361\) 0.426394 0.426394
\(362\) 0 0
\(363\) −0.573606 −0.573606
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 1.78727 1.78727 0.893633 0.448799i \(-0.148148\pi\)
0.893633 + 0.448799i \(0.148148\pi\)
\(368\) −0.550440 −0.550440
\(369\) −0.233027 −0.233027
\(370\) 0 0
\(371\) −1.08723 −1.08723
\(372\) 3.17597 3.17597
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −6.90932 −6.90932
\(377\) 0 0
\(378\) 2.61321 2.61321
\(379\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −3.04346 −3.04346
\(383\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(384\) 3.96323 3.96323
\(385\) 0 0
\(386\) 1.98648 1.98648
\(387\) −0.531520 −0.531520
\(388\) 0 0
\(389\) −0.116290 −0.116290 −0.0581448 0.998308i \(-0.518519\pi\)
−0.0581448 + 0.998308i \(0.518519\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −3.41630 −3.41630
\(393\) 0.958482 0.958482
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(398\) 0 0
\(399\) 0.940244 0.940244
\(400\) 4.73336 4.73336
\(401\) 1.78727 1.78727 0.893633 0.448799i \(-0.148148\pi\)
0.893633 + 0.448799i \(0.148148\pi\)
\(402\) 0.395729 0.395729
\(403\) 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
\(413\) 1.37248 1.37248
\(414\) −0.155000 −0.155000
\(415\) 0 0
\(416\) 0 0
\(417\) −1.02519 −1.02519
\(418\) 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
\(423\) −1.19921 −1.19921
\(424\) −3.06238 −3.06238
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 5.73336 5.73336
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) 4.53684 4.53684
\(433\) 0.347296 0.347296 0.173648 0.984808i \(-0.444444\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(434\) −5.12397 −5.12397
\(435\) 0 0
\(436\) 0 0
\(437\) −0.138887 −0.138887
\(438\) 0 0
\(439\) 1.53209 1.53209 0.766044 0.642788i \(-0.222222\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(440\) 0 0
\(441\) −0.592948 −0.592948
\(442\) 0 0
\(443\) −1.87939 −1.87939 −0.939693 0.342020i \(-0.888889\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(444\) −2.58907 −2.58907
\(445\) 0 0
\(446\) 3.31935 3.31935
\(447\) 0 0
\(448\) −8.59922 −8.59922
\(449\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(450\) 1.33288 1.33288
\(451\) 0 0
\(452\) 0 0
\(453\) 1.13946 1.13946
\(454\) 0 0
\(455\) 0 0
\(456\) 2.64838 2.64838
\(457\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −0.573606 −0.573606 −0.286803 0.957990i \(-0.592593\pi\)
−0.286803 + 0.957990i \(0.592593\pi\)
\(462\) 0 0
\(463\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 1.98648 1.98648
\(467\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(468\) 0 0
\(469\) −0.476658 −0.476658
\(470\) 0 0
\(471\) 0 0
\(472\) 3.86586 3.86586
\(473\) 0 0
\(474\) −1.13946 −1.13946
\(475\) 1.19432 1.19432
\(476\) 0 0
\(477\) −0.531520 −0.531520
\(478\) 0 0
\(479\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) −0.0915508 −0.0915508
\(484\) 2.94609 2.94609
\(485\) 0 0
\(486\) 2.04209 2.04209
\(487\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(488\) 0 0
\(489\) 0.958482 0.958482
\(490\) 0 0
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) −0.586895 −0.586895
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) −8.89580 −8.89580
\(497\) 0 0
\(498\) 0 0
\(499\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(500\) 0 0
\(501\) −0.454388 −0.454388
\(502\) −0.689896 −0.689896
\(503\) 1.19432 1.19432 0.597159 0.802123i \(-0.296296\pi\)
0.597159 + 0.802123i \(0.296296\pi\)
\(504\) −3.56008 −3.56008
\(505\) 0 0
\(506\) 0 0
\(507\) −0.573606 −0.573606
\(508\) 0 0
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −7.90932 −7.90932
\(513\) 1.14473 1.14473
\(514\) 0 0
\(515\) 0 0
\(516\) −1.33867 −1.33867
\(517\) 0 0
\(518\) 4.17710 4.17710
\(519\) −0.685068 −0.685068
\(520\) 0 0
\(521\) −0.116290 −0.116290 −0.0581448 0.998308i \(-0.518519\pi\)
−0.0581448 + 0.998308i \(0.518519\pi\)
\(522\) 0 0
\(523\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(524\) −4.92284 −4.92284
\(525\) 0.787265 0.787265
\(526\) −0.689896 −0.689896
\(527\) 0 0
\(528\) 0 0
\(529\) −0.986477 −0.986477
\(530\) 0 0
\(531\) 0.670976 0.670976
\(532\) −4.82917 −4.82917
\(533\) 0 0
\(534\) 2.21748 2.21748
\(535\) 0 0
\(536\) −1.34260 −1.34260
\(537\) 0 0
\(538\) 2.72641 2.72641
\(539\) 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
\(547\) −0.116290 −0.116290 −0.0581448 0.998308i \(-0.518519\pi\)
−0.0581448 + 0.998308i \(0.518519\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) −0.257870 −0.257870
\(553\) 1.37248 1.37248
\(554\) 0 0
\(555\) 0 0
\(556\) 5.26544 5.26544
\(557\) −1.37248 −1.37248 −0.686242 0.727374i \(-0.740741\pi\)
−0.686242 + 0.727374i \(0.740741\pi\)
\(558\) −2.50499 −2.50499
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) −2.37248 −2.37248
\(563\) −1.37248 −1.37248 −0.686242 0.727374i \(-0.740741\pi\)
−0.686242 + 0.727374i \(0.740741\pi\)
\(564\) −3.02029 −3.02029
\(565\) 0 0
\(566\) 0 0
\(567\) −0.166323 −0.166323
\(568\) 0 0
\(569\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(570\) 0 0
\(571\) 1.94609 1.94609 0.973045 0.230616i \(-0.0740741\pi\)
0.973045 + 0.230616i \(0.0740741\pi\)
\(572\) 0 0
\(573\) −0.878816 −0.878816
\(574\) 0.946871 0.946871
\(575\) −0.116290 −0.116290
\(576\) −4.20396 −4.20396
\(577\) 1.19432 1.19432 0.597159 0.802123i \(-0.296296\pi\)
0.597159 + 0.802123i \(0.296296\pi\)
\(578\) −1.98648 −1.98648
\(579\) 0.573606 0.573606
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 3.73336 3.73336
\(587\) 1.53209 1.53209 0.766044 0.642788i \(-0.222222\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(588\) −1.49338 −1.49338
\(589\) −2.24458 −2.24458
\(590\) 0 0
\(591\) 0 0
\(592\) 7.25192 7.25192
\(593\) 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 \(\pi\)
\(600\) 2.21748 2.21748
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) 2.15975 2.15975
\(603\) −0.233027 −0.233027
\(604\) −5.85234 −5.85234
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(608\) −6.61274 −6.61274
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 1.94609 1.94609 0.973045 0.230616i \(-0.0740741\pi\)
0.973045 + 0.230616i \(0.0740741\pi\)
\(614\) 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
\(619\) −1.98648 −1.98648 −0.993238 0.116093i \(-0.962963\pi\)
−0.993238 + 0.116093i \(0.962963\pi\)
\(620\) 0 0
\(621\) −0.111462 −0.111462
\(622\) 0 0
\(623\) −2.67098 −2.67098
\(624\) 0 0
\(625\) 1.00000 1.00000
\(626\) 3.94609 3.94609
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0.347296 0.347296 0.173648 0.984808i \(-0.444444\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(632\) 3.86586 3.86586
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) −1.33867 −1.33867
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(642\) 2.21748 2.21748
\(643\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(644\) 0.470212 0.470212
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(648\) −0.468480 −0.468480
\(649\) 0 0
\(650\) 0 0
\(651\) −1.47957 −1.47957
\(652\) −4.92284 −4.92284
\(653\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 1.64388 1.64388
\(657\) 0 0
\(658\) 4.87281 4.87281
\(659\) 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
\(666\) 2.04209 2.04209
\(667\) 0 0
\(668\) 2.33377 2.33377
\(669\) 0.958482 0.958482
\(670\) 0 0
\(671\) 0 0
\(672\) −4.35896 −4.35896
\(673\) 1.78727 1.78727 0.893633 0.448799i \(-0.148148\pi\)
0.893633 + 0.448799i \(0.148148\pi\)
\(674\) 3.73336 3.73336
\(675\) 0.958482 0.958482
\(676\) 2.94609 2.94609
\(677\) −0.116290 −0.116290 −0.0581448 0.998308i \(-0.518519\pi\)
−0.0581448 + 0.998308i \(0.518519\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(684\) −2.36087 −2.36087
\(685\) 0 0
\(686\) −0.317053 −0.317053
\(687\) 0 0
\(688\) 3.74957 3.74957
\(689\) 0 0
\(690\) 0 0
\(691\) 1.94609 1.94609 0.973045 0.230616i \(-0.0740741\pi\)
0.973045 + 0.230616i \(0.0740741\pi\)
\(692\) 3.51857 3.51857
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 1.13946 1.13946
\(699\) 0.573606 0.573606
\(700\) −4.04346 −4.04346
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 0 0
\(703\) 1.82980 1.82980
\(704\) 0 0
\(705\) 0 0
\(706\) −3.55036 −3.55036
\(707\) 0 0
\(708\) 1.68990 1.68990
\(709\) 1.19432 1.19432 0.597159 0.802123i \(-0.296296\pi\)
0.597159 + 0.802123i \(0.296296\pi\)
\(710\) 0 0
\(711\) 0.670976 0.670976
\(712\) −7.52331 −7.52331
\(713\) 0.218553 0.218553
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) −3.86586 −3.86586
\(719\) −1.87939 −1.87939 −0.939693 0.342020i \(-0.888889\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −0.847021 −0.847021
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 1.13946 1.13946
\(727\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(728\) 0 0
\(729\) 0.468480 0.468480
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) −0.116290 −0.116290 −0.0581448 0.998308i \(-0.518519\pi\)
−0.0581448 + 0.998308i \(0.518519\pi\)
\(734\) −3.55036 −3.55036
\(735\) 0 0
\(736\) 0.643877 0.643877
\(737\) 0 0
\(738\) 0.462903 0.462903
\(739\) 1.53209 1.53209 0.766044 0.642788i \(-0.222222\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 2.15975 2.15975
\(743\) 1.53209 1.53209 0.766044 0.642788i \(-0.222222\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(744\) −4.16751 −4.16751
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −2.67098 −2.67098
\(750\) 0 0
\(751\) −1.67098 −1.67098 −0.835488 0.549509i \(-0.814815\pi\)
−0.835488 + 0.549509i \(0.814815\pi\)
\(752\) 8.45976 8.45976
\(753\) −0.199211 −0.199211
\(754\) 0 0
\(755\) 0 0
\(756\) −3.87558 −3.87558
\(757\) 1.78727 1.78727 0.893633 0.448799i \(-0.148148\pi\)
0.893633 + 0.448799i \(0.148148\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 4.51367 4.51367
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) −4.27897 −4.27897
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −2.94609 −2.94609
\(773\) −1.67098 −1.67098 −0.835488 0.549509i \(-0.814815\pi\)
−0.835488 + 0.549509i \(0.814815\pi\)
\(774\) 1.05585 1.05585
\(775\) −1.87939 −1.87939
\(776\) 0 0
\(777\) 1.20616 1.20616
\(778\) 0.231007 0.231007
\(779\) 0.414782 0.414782
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 4.18291 4.18291
\(785\) 0 0
\(786\) −1.90400 −1.90400
\(787\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(788\) 0 0
\(789\) −0.199211 −0.199211
\(790\) 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 \(\pi\)
\(798\) −1.86777 −1.86777
\(799\) 0 0
\(800\) −5.53684 −5.53684
\(801\) −1.30578 −1.30578
\(802\) −3.55036 −3.55036
\(803\) 0 0
\(804\) −0.586895 −0.586895
\(805\) 0 0
\(806\) 0 0
\(807\) 0.787265 0.787265
\(808\) 0 0
\(809\) −0.573606 −0.573606 −0.286803 0.957990i \(-0.592593\pi\)
−0.286803 + 0.957990i \(0.592593\pi\)
\(810\) 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
\(817\) 0.946090 0.946090
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(822\) 0 0
\(823\) 0.792160 0.792160 0.396080 0.918216i \(-0.370370\pi\)
0.396080 + 0.918216i \(0.370370\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) −2.72641 −2.72641
\(827\) 1.78727 1.78727 0.893633 0.448799i \(-0.148148\pi\)
0.893633 + 0.448799i \(0.148148\pi\)
\(828\) 0.229876 0.229876
\(829\) −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
\(834\) 2.03651 2.03651
\(835\) 0 0
\(836\) 0 0
\(837\) −1.80136 −1.80136
\(838\) 0 0
\(839\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(840\) 0 0
\(841\) 1.00000 1.00000
\(842\) 0 0
\(843\) −0.685068 −0.685068
\(844\) 0 0
\(845\) 0 0
\(846\) 2.38221 2.38221
\(847\) −1.37248 −1.37248
\(848\) 3.74957 3.74957
\(849\) 0 0
\(850\) 0 0
\(851\) −0.178166 −0.178166
\(852\) 0 0
\(853\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) −7.52331 −7.52331
\(857\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(858\) 0 0
\(859\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(860\) 0 0
\(861\) 0.273414 0.273414
\(862\) 0 0
\(863\) −1.87939 −1.87939 −0.939693 0.342020i \(-0.888889\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(864\) −5.30696 −5.30696
\(865\) 0 0
\(866\) −0.689896 −0.689896
\(867\) −0.573606 −0.573606
\(868\) 7.59922 7.59922
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 0 0
\(874\) 0.275895 0.275895
\(875\) 0 0
\(876\) 0 0
\(877\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(878\) −3.04346 −3.04346
\(879\) 1.07803 1.07803
\(880\) 0 0
\(881\) −1.37248 −1.37248 −0.686242 0.727374i \(-0.740741\pi\)
−0.686242 + 0.727374i \(0.740741\pi\)
\(882\) 1.17788 1.17788
\(883\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 3.73336 3.73336
\(887\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(888\) 3.39738 3.39738
\(889\) 0 0
\(890\) 0 0
\(891\) 0 0
\(892\) −4.92284 −4.92284
\(893\) 2.13456 2.13456
\(894\) 0 0
\(895\) 0 0
\(896\) 9.48293 9.48293
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) −1.97675 −1.97675
\(901\) 0 0
\(902\) 0 0
\(903\) 0.623640 0.623640
\(904\) 0 0
\(905\) 0 0
\(906\) −2.26350 −2.26350
\(907\) 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 \(\pi\)
\(912\) −3.24267 −3.24267
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 2.29339 2.29339
\(918\) 0 0
\(919\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 1.13946 1.13946
\(923\) 0 0
\(924\) 0 0
\(925\) 1.53209 1.53209
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(930\) 0 0
\(931\) 1.05543 1.05543
\(932\) −2.94609 −2.94609
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(938\) 0.946871 0.946871
\(939\) 1.13946 1.13946
\(940\) 0 0
\(941\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(942\) 0 0
\(943\) −0.0403870 −0.0403870
\(944\) −4.73336 −4.73336
\(945\) 0 0
\(946\) 0 0
\(947\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(948\) 1.68990 1.68990
\(949\) 0 0
\(950\) −2.37248 −2.37248
\(951\) 0 0
\(952\) 0 0
\(953\) 1.53209 1.53209 0.766044 0.642788i \(-0.222222\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(954\) 1.05585 1.05585
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 2.53209 2.53209
\(962\) 0 0
\(963\) −1.30578 −1.30578
\(964\) 0 0
\(965\) 0 0
\(966\) 0.181864 0.181864
\(967\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(968\) −3.86586 −3.86586
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(972\) −3.02856 −3.02856
\(973\) −2.45299 −2.45299
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(978\) −1.90400 −1.90400
\(979\) 0 0
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 1.00000 1.00000
\(984\) 0.770124 0.770124
\(985\) 0 0
\(986\) 0 0
\(987\) 1.40705 1.40705
\(988\) 0 0
\(989\) −0.0921200 −0.0921200
\(990\) 0 0
\(991\) 0.792160 0.792160 0.396080 0.918216i \(-0.370370\pi\)
0.396080 + 0.918216i \(0.370370\pi\)
\(992\) 10.4059 10.4059
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −1.67098 −1.67098 −0.835488 0.549509i \(-0.814815\pi\)
−0.835488 + 0.549509i \(0.814815\pi\)
\(998\) 0 0
\(999\) 1.46848 1.46848
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.982.1 9
983.982 odd 2 CM 983.1.b.c.982.1 9
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
983.1.b.c.982.1 9 1.1 even 1 trivial
983.1.b.c.982.1 9 983.982 odd 2 CM