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Properties

Label 11.17.b.a.10.1
Level $11$
Weight $17$
Character 11.10
Self dual yes
Analytic conductor $17.856$
Analytic rank $0$
Dimension $1$
CM discriminant -11
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [11,17,Mod(10,11)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(11, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 17, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("11.10");
 
S:= CuspForms(chi, 17);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 11 \)
Weight: \( k \) \(=\) \( 17 \)
Character orbit: \([\chi]\) \(=\) 11.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: \(17.8556998242\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label 10.1
Character \(\chi\) \(=\) 11.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-353.000 q^{3} +65536.0 q^{4} +543551. q^{5} -4.29221e7 q^{9} +O(q^{10})\) \(q-353.000 q^{3} +65536.0 q^{4} +543551. q^{5} -4.29221e7 q^{9} +2.14359e8 q^{11} -2.31342e7 q^{12} -1.91874e8 q^{15} +4.29497e9 q^{16} +3.56222e10 q^{20} +1.26182e11 q^{23} +1.42860e11 q^{25} +3.03470e10 q^{27} +6.69617e11 q^{31} -7.56687e10 q^{33} -2.81294e12 q^{36} -6.51166e12 q^{37} +1.40482e13 q^{44} -2.33304e13 q^{45} -1.06484e13 q^{47} -1.51612e12 q^{48} +3.32329e13 q^{49} +1.08514e14 q^{53} +1.16515e14 q^{55} -2.76838e14 q^{59} -1.25746e13 q^{60} +2.81475e14 q^{64} -4.19827e14 q^{67} -4.45422e13 q^{69} -1.24190e15 q^{71} -5.04295e13 q^{75} +2.33453e15 q^{80} +1.83694e15 q^{81} -8.00201e14 q^{89} +8.26945e15 q^{92} -2.36375e14 q^{93} -9.08862e15 q^{97} -9.20074e15 q^{99} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/11\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(3\) −353.000 −0.0538028 −0.0269014 − 0.999638i \(-0.508564\pi\)
−0.0269014 + 0.999638i \(0.508564\pi\)
\(4\) 65536.0 1.00000
\(5\) 543551. 1.39149 0.695745 − 0.718289i \(-0.255074\pi\)
0.695745 + 0.718289i \(0.255074\pi\)
\(6\) 0 0
\(7\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(8\) 0 0
\(9\) −4.29221e7 −0.997105
\(10\) 0 0
\(11\) 2.14359e8 1.00000
\(12\) −2.31342e7 −0.0538028
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) 0 0
\(15\) −1.91874e8 −0.0748661
\(16\) 4.29497e9 1.00000
\(17\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(18\) 0 0
\(19\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(20\) 3.56222e10 1.39149
\(21\) 0 0
\(22\) 0 0
\(23\) 1.26182e11 1.61129 0.805646 − 0.592398i \(-0.201819\pi\)
0.805646 + 0.592398i \(0.201819\pi\)
\(24\) 0 0
\(25\) 1.42860e11 0.936246
\(26\) 0 0
\(27\) 3.03470e10 0.107450
\(28\) 0 0
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 0 0
\(31\) 6.69617e11 0.785114 0.392557 − 0.919728i \(-0.371590\pi\)
0.392557 + 0.919728i \(0.371590\pi\)
\(32\) 0 0
\(33\) −7.56687e10 −0.0538028
\(34\) 0 0
\(35\) 0 0
\(36\) −2.81294e12 −0.997105
\(37\) −6.51166e12 −1.85386 −0.926932 − 0.375228i \(-0.877564\pi\)
−0.926932 + 0.375228i \(0.877564\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) 0 0
\(43\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(44\) 1.40482e13 1.00000
\(45\) −2.33304e13 −1.38746
\(46\) 0 0
\(47\) −1.06484e13 −0.447200 −0.223600 − 0.974681i \(-0.571781\pi\)
−0.223600 + 0.974681i \(0.571781\pi\)
\(48\) −1.51612e12 −0.0538028
\(49\) 3.32329e13 1.00000
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 1.08514e14 1.74293 0.871464 − 0.490459i \(-0.163171\pi\)
0.871464 + 0.490459i \(0.163171\pi\)
\(54\) 0 0
\(55\) 1.16515e14 1.39149
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −2.76838e14 −1.88543 −0.942714 − 0.333603i \(-0.891736\pi\)
−0.942714 + 0.333603i \(0.891736\pi\)
\(60\) −1.25746e13 −0.0748661
\(61\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 2.81475e14 1.00000
\(65\) 0 0
\(66\) 0 0
\(67\) −4.19827e14 −1.03389 −0.516943 − 0.856020i \(-0.672930\pi\)
−0.516943 + 0.856020i \(0.672930\pi\)
\(68\) 0 0
\(69\) −4.45422e13 −0.0866920
\(70\) 0 0
\(71\) −1.24190e15 −1.92318 −0.961591 − 0.274485i \(-0.911493\pi\)
−0.961591 + 0.274485i \(0.911493\pi\)
\(72\) 0 0
\(73\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(74\) 0 0
\(75\) −5.04295e13 −0.0503726
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(80\) 2.33453e15 1.39149
\(81\) 1.83694e15 0.991324
\(82\) 0 0
\(83\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −8.00201e14 −0.203273 −0.101636 − 0.994822i \(-0.532408\pi\)
−0.101636 + 0.994822i \(0.532408\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 8.26945e15 1.61129
\(93\) −2.36375e14 −0.0422413
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −9.08862e15 −1.15964 −0.579821 − 0.814744i \(-0.696878\pi\)
−0.579821 + 0.814744i \(0.696878\pi\)
\(98\) 0 0
\(99\) −9.20074e15 −0.997105
\(100\) 9.36246e15 0.936246
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) 0 0
\(103\) −2.53222e16 −1.99896 −0.999481 − 0.0322287i \(-0.989740\pi\)
−0.999481 + 0.0322287i \(0.989740\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) 1.98882e15 0.107450
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 0 0
\(111\) 2.29862e15 0.0997431
\(112\) 0 0
\(113\) −4.27940e16 −1.60974 −0.804869 − 0.593453i \(-0.797764\pi\)
−0.804869 + 0.593453i \(0.797764\pi\)
\(114\) 0 0
\(115\) 6.85863e16 2.24210
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 4.59497e16 1.00000
\(122\) 0 0
\(123\) 0 0
\(124\) 4.38840e16 0.785114
\(125\) −5.28771e15 −0.0887131
\(126\) 0 0
\(127\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) −4.95902e15 −0.0538028
\(133\) 0 0
\(134\) 0 0
\(135\) 1.64951e16 0.149515
\(136\) 0 0
\(137\) −1.15780e17 −0.932977 −0.466488 − 0.884527i \(-0.654481\pi\)
−0.466488 + 0.884527i \(0.654481\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(140\) 0 0
\(141\) 3.75889e15 0.0240606
\(142\) 0 0
\(143\) 0 0
\(144\) −1.84349e17 −0.997105
\(145\) 0 0
\(146\) 0 0
\(147\) −1.17312e16 −0.0538028
\(148\) −4.26748e17 −1.85386
\(149\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(150\) 0 0
\(151\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 3.63971e17 1.09248
\(156\) 0 0
\(157\) 7.15430e17 1.93807 0.969035 − 0.246922i \(-0.0794191\pi\)
0.969035 + 0.246922i \(0.0794191\pi\)
\(158\) 0 0
\(159\) −3.83055e16 −0.0937744
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −1.59249e17 −0.319578 −0.159789 − 0.987151i \(-0.551081\pi\)
−0.159789 + 0.987151i \(0.551081\pi\)
\(164\) 0 0
\(165\) −4.11298e16 −0.0748661
\(166\) 0 0
\(167\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(168\) 0 0
\(169\) 6.65417e17 1.00000
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 9.20664e17 1.00000
\(177\) 9.77239e16 0.101441
\(178\) 0 0
\(179\) −6.24913e17 −0.592919 −0.296460 − 0.955045i \(-0.595806\pi\)
−0.296460 + 0.955045i \(0.595806\pi\)
\(180\) −1.52898e18 −1.38746
\(181\) 2.24695e18 1.95058 0.975292 − 0.220920i \(-0.0709060\pi\)
0.975292 + 0.220920i \(0.0709060\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −3.53942e18 −2.57964
\(186\) 0 0
\(187\) 0 0
\(188\) −6.97855e17 −0.447200
\(189\) 0 0
\(190\) 0 0
\(191\) −3.43509e18 −1.93941 −0.969707 − 0.244270i \(-0.921452\pi\)
−0.969707 + 0.244270i \(0.921452\pi\)
\(192\) −9.93607e16 −0.0538028
\(193\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 2.17795e18 1.00000
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 0 0
\(199\) 4.91477e18 1.99838 0.999192 − 0.0401903i \(-0.0127964\pi\)
0.999192 + 0.0401903i \(0.0127964\pi\)
\(200\) 0 0
\(201\) 1.48199e17 0.0556259
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −5.41599e18 −1.60663
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(212\) 7.11159e18 1.74293
\(213\) 4.38391e17 0.103473
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 7.63593e18 1.39149
\(221\) 0 0
\(222\) 0 0
\(223\) 1.05170e19 1.71970 0.859850 − 0.510546i \(-0.170557\pi\)
0.859850 + 0.510546i \(0.170557\pi\)
\(224\) 0 0
\(225\) −6.13184e18 −0.933536
\(226\) 0 0
\(227\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(228\) 0 0
\(229\) −1.33732e19 −1.76828 −0.884141 − 0.467221i \(-0.845255\pi\)
−0.884141 + 0.467221i \(0.845255\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(234\) 0 0
\(235\) −5.78796e18 −0.622275
\(236\) −1.81429e19 −1.88543
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) −8.24090e17 −0.0748661
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) 0 0
\(243\) −1.95478e18 −0.160786
\(244\) 0 0
\(245\) 1.80638e19 1.39149
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −2.57861e19 −1.63680 −0.818402 − 0.574646i \(-0.805140\pi\)
−0.818402 + 0.574646i \(0.805140\pi\)
\(252\) 0 0
\(253\) 2.70482e19 1.61129
\(254\) 0 0
\(255\) 0 0
\(256\) 1.84467e19 1.00000
\(257\) −3.78215e19 −1.98735 −0.993675 − 0.112298i \(-0.964179\pi\)
−0.993675 + 0.112298i \(0.964179\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(264\) 0 0
\(265\) 5.89830e19 2.42527
\(266\) 0 0
\(267\) 2.82471e17 0.0109366
\(268\) −2.75138e19 −1.03389
\(269\) 5.09503e19 1.85836 0.929178 − 0.369633i \(-0.120517\pi\)
0.929178 + 0.369633i \(0.120517\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 3.06233e19 0.936246
\(276\) −2.91912e18 −0.0866920
\(277\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(278\) 0 0
\(279\) −2.87414e19 −0.782842
\(280\) 0 0
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) 0 0
\(283\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(284\) −8.13893e19 −1.92318
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 4.86612e19 1.00000
\(290\) 0 0
\(291\) 3.20828e18 0.0623920
\(292\) 0 0
\(293\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(294\) 0 0
\(295\) −1.50476e20 −2.62355
\(296\) 0 0
\(297\) 6.50515e18 0.107450
\(298\) 0 0
\(299\) 0 0
\(300\) −3.30495e18 −0.0503726
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 0 0
\(309\) 8.93875e18 0.107550
\(310\) 0 0
\(311\) 1.30589e20 1.49218 0.746092 − 0.665842i \(-0.231928\pi\)
0.746092 + 0.665842i \(0.231928\pi\)
\(312\) 0 0
\(313\) −1.72734e20 −1.87509 −0.937547 − 0.347858i \(-0.886909\pi\)
−0.937547 + 0.347858i \(0.886909\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 7.32776e19 0.718616 0.359308 − 0.933219i \(-0.383013\pi\)
0.359308 + 0.933219i \(0.383013\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 1.52996e20 1.39149
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 1.20386e20 0.991324
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −7.98565e19 −0.554225 −0.277113 − 0.960837i \(-0.589377\pi\)
−0.277113 + 0.960837i \(0.589377\pi\)
\(332\) 0 0
\(333\) 2.79494e20 1.84850
\(334\) 0 0
\(335\) −2.28198e20 −1.43864
\(336\) 0 0
\(337\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(338\) 0 0
\(339\) 1.51063e19 0.0866084
\(340\) 0 0
\(341\) 1.43538e20 0.785114
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −2.42109e19 −0.120631
\(346\) 0 0
\(347\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(348\) 0 0
\(349\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −3.59902e20 −1.49275 −0.746374 − 0.665527i \(-0.768207\pi\)
−0.746374 + 0.665527i \(0.768207\pi\)
\(354\) 0 0
\(355\) −6.75037e20 −2.67609
\(356\) −5.24419e19 −0.203273
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(360\) 0 0
\(361\) 2.88441e20 1.00000
\(362\) 0 0
\(363\) −1.62203e19 −0.0538028
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −3.20846e20 −0.974917 −0.487459 − 0.873146i \(-0.662076\pi\)
−0.487459 + 0.873146i \(0.662076\pi\)
\(368\) 5.41947e20 1.61129
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) −1.54911e19 −0.0422413
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) 0 0
\(375\) 1.86656e18 0.00477301
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 1.35477e20 0.318238 0.159119 − 0.987259i \(-0.449135\pi\)
0.159119 + 0.987259i \(0.449135\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 1.96112e20 0.423560 0.211780 − 0.977317i \(-0.432074\pi\)
0.211780 + 0.977317i \(0.432074\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) −5.95632e20 −1.15964
\(389\) 1.04772e21 1.99825 0.999124 − 0.0418466i \(-0.0133241\pi\)
0.999124 + 0.0418466i \(0.0133241\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) −6.02979e20 −0.997105
\(397\) 8.56839e20 1.38859 0.694296 − 0.719689i \(-0.255716\pi\)
0.694296 + 0.719689i \(0.255716\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 6.13578e20 0.936246
\(401\) 7.44825e20 1.11404 0.557018 − 0.830500i \(-0.311945\pi\)
0.557018 + 0.830500i \(0.311945\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 9.98473e20 1.37942
\(406\) 0 0
\(407\) −1.39583e21 −1.85386
\(408\) 0 0
\(409\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(410\) 0 0
\(411\) 4.08705e19 0.0501967
\(412\) −1.65952e21 −1.99896
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −1.57051e21 −1.65321 −0.826606 − 0.562781i \(-0.809731\pi\)
−0.826606 + 0.562781i \(0.809731\pi\)
\(420\) 0 0
\(421\) −1.37931e21 −1.39767 −0.698837 − 0.715281i \(-0.746299\pi\)
−0.698837 + 0.715281i \(0.746299\pi\)
\(422\) 0 0
\(423\) 4.57052e20 0.445906
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) 1.30339e20 0.107450
\(433\) 2.40571e21 1.94689 0.973443 − 0.228931i \(-0.0735229\pi\)
0.973443 + 0.228931i \(0.0735229\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(440\) 0 0
\(441\) −1.42643e21 −0.997105
\(442\) 0 0
\(443\) −1.42937e21 −0.963640 −0.481820 − 0.876270i \(-0.660024\pi\)
−0.481820 + 0.876270i \(0.660024\pi\)
\(444\) 1.50642e20 0.0997431
\(445\) −4.34950e20 −0.282852
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 3.26682e21 1.97767 0.988836 − 0.149011i \(-0.0476089\pi\)
0.988836 + 0.149011i \(0.0476089\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) −2.80455e21 −1.60974
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 4.49487e21 2.24210
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) 4.03185e21 1.90922 0.954610 − 0.297858i \(-0.0962721\pi\)
0.954610 + 0.297858i \(0.0962721\pi\)
\(464\) 0 0
\(465\) −1.28482e20 −0.0587784
\(466\) 0 0
\(467\) 2.00584e21 0.886668 0.443334 − 0.896356i \(-0.353795\pi\)
0.443334 + 0.896356i \(0.353795\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −2.52547e20 −0.104274
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −4.65766e21 −1.73788
\(478\) 0 0
\(479\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 3.01136e21 1.00000
\(485\) −4.94013e21 −1.61363
\(486\) 0 0
\(487\) −5.56340e21 −1.75836 −0.879182 − 0.476487i \(-0.841910\pi\)
−0.879182 + 0.476487i \(0.841910\pi\)
\(488\) 0 0
\(489\) 5.62150e19 0.0171942
\(490\) 0 0
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) −5.00107e21 −1.38746
\(496\) 2.87598e21 0.785114
\(497\) 0 0
\(498\) 0 0
\(499\) 3.46641e21 0.901727 0.450863 − 0.892593i \(-0.351116\pi\)
0.450863 + 0.892593i \(0.351116\pi\)
\(500\) −3.46536e20 −0.0887131
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −2.34892e20 −0.0538028
\(508\) 0 0
\(509\) 3.45652e21 0.767180 0.383590 − 0.923504i \(-0.374688\pi\)
0.383590 + 0.923504i \(0.374688\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −1.37639e22 −2.78154
\(516\) 0 0
\(517\) −2.28258e21 −0.447200
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 6.52253e21 1.20147 0.600737 − 0.799447i \(-0.294874\pi\)
0.600737 + 0.799447i \(0.294874\pi\)
\(522\) 0 0
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) −3.24995e20 −0.0538028
\(529\) 9.78924e21 1.59626
\(530\) 0 0
\(531\) 1.18825e22 1.87997
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 2.20594e20 0.0319007
\(538\) 0 0
\(539\) 7.12377e21 1.00000
\(540\) 1.08103e21 0.149515
\(541\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(542\) 0 0
\(543\) −7.93173e20 −0.104947
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(548\) −7.58779e21 −0.932977
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 1.24942e21 0.138792
\(556\) 0 0
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(564\) 2.46343e20 0.0240606
\(565\) −2.32607e22 −2.23994
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(572\) 0 0
\(573\) 1.21259e21 0.104346
\(574\) 0 0
\(575\) 1.80263e22 1.50857
\(576\) −1.20815e22 −0.997105
\(577\) −2.40998e22 −1.96158 −0.980792 − 0.195058i \(-0.937511\pi\)
−0.980792 + 0.195058i \(0.937511\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 2.32610e22 1.74293
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −1.65267e22 −1.17242 −0.586208 − 0.810160i \(-0.699380\pi\)
−0.586208 + 0.810160i \(0.699380\pi\)
\(588\) −7.68818e20 −0.0538028
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) −2.79674e22 −1.85386
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −1.73492e21 −0.107519
\(598\) 0 0
\(599\) 2.62840e22 1.58591 0.792953 − 0.609283i \(-0.208543\pi\)
0.792953 + 0.609283i \(0.208543\pi\)
\(600\) 0 0
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) 0 0
\(603\) 1.80199e22 1.03089
\(604\) 0 0
\(605\) 2.49760e22 1.39149
\(606\) 0 0
\(607\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −3.85263e22 −1.83432 −0.917161 − 0.398516i \(-0.869525\pi\)
−0.917161 + 0.398516i \(0.869525\pi\)
\(618\) 0 0
\(619\) 4.08981e22 1.89748 0.948741 − 0.316055i \(-0.102359\pi\)
0.948741 + 0.316055i \(0.102359\pi\)
\(620\) 2.38532e22 1.09248
\(621\) 3.82924e21 0.173133
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −2.46728e22 −1.05969
\(626\) 0 0
\(627\) 0 0
\(628\) 4.68864e22 1.93807
\(629\) 0 0
\(630\) 0 0
\(631\) −3.10483e22 −1.23539 −0.617693 − 0.786420i \(-0.711932\pi\)
−0.617693 + 0.786420i \(0.711932\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) −2.51039e21 −0.0937744
\(637\) 0 0
\(638\) 0 0
\(639\) 5.33051e22 1.91762
\(640\) 0 0
\(641\) 1.31702e22 0.462090 0.231045 − 0.972943i \(-0.425786\pi\)
0.231045 + 0.972943i \(0.425786\pi\)
\(642\) 0 0
\(643\) −4.67358e22 −1.59942 −0.799710 − 0.600387i \(-0.795013\pi\)
−0.799710 + 0.600387i \(0.795013\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −5.46649e22 −1.78022 −0.890111 − 0.455743i \(-0.849373\pi\)
−0.890111 + 0.455743i \(0.849373\pi\)
\(648\) 0 0
\(649\) −5.93427e22 −1.88543
\(650\) 0 0
\(651\) 0 0
\(652\) −1.04366e22 −0.319578
\(653\) 3.35258e22 1.01408 0.507042 − 0.861921i \(-0.330739\pi\)
0.507042 + 0.861921i \(0.330739\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) −2.69548e21 −0.0748661
\(661\) −4.25195e22 −1.16675 −0.583373 − 0.812204i \(-0.698268\pi\)
−0.583373 + 0.812204i \(0.698268\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) −3.71250e21 −0.0925247
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(674\) 0 0
\(675\) 4.33537e21 0.100599
\(676\) 4.36087e22 1.00000
\(677\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 2.07666e22 0.438530 0.219265 − 0.975665i \(-0.429634\pi\)
0.219265 + 0.975665i \(0.429634\pi\)
\(684\) 0 0
\(685\) −6.29326e22 −1.29823
\(686\) 0 0
\(687\) 4.72074e21 0.0951385
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 5.48661e22 1.05555 0.527776 − 0.849384i \(-0.323026\pi\)
0.527776 + 0.849384i \(0.323026\pi\)
\(692\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 6.03367e22 1.00000
\(705\) 2.04315e21 0.0334801
\(706\) 0 0
\(707\) 0 0
\(708\) 6.40443e21 0.101441
\(709\) 1.15206e23 1.80429 0.902143 − 0.431437i \(-0.141993\pi\)
0.902143 + 0.431437i \(0.141993\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 8.44935e22 1.26505
\(714\) 0 0
\(715\) 0 0
\(716\) −4.09543e22 −0.592919
\(717\) 0 0
\(718\) 0 0
\(719\) 4.46119e22 0.624625 0.312313 − 0.949979i \(-0.398896\pi\)
0.312313 + 0.949979i \(0.398896\pi\)
\(720\) −1.00203e23 −1.38746
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) 1.47256e23 1.95058
\(725\) 0 0
\(726\) 0 0
\(727\) −1.53751e23 −1.97035 −0.985173 − 0.171564i \(-0.945118\pi\)
−0.985173 + 0.171564i \(0.945118\pi\)
\(728\) 0 0
\(729\) −7.83844e22 −0.982673
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(734\) 0 0
\(735\) −6.37652e21 −0.0748661
\(736\) 0 0
\(737\) −8.99937e22 −1.03389
\(738\) 0 0
\(739\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(740\) −2.31959e23 −2.57964
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 1.61641e23 1.59747 0.798733 − 0.601686i \(-0.205504\pi\)
0.798733 + 0.601686i \(0.205504\pi\)
\(752\) −4.57346e22 −0.447200
\(753\) 9.10251e21 0.0880646
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 2.01077e23 1.86465 0.932323 − 0.361628i \(-0.117779\pi\)
0.932323 + 0.361628i \(0.117779\pi\)
\(758\) 0 0
\(759\) −9.54801e21 −0.0866920
\(760\) 0 0
\(761\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −2.25122e23 −1.93941
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) −6.51170e21 −0.0538028
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 1.33510e22 0.106925
\(772\) 0 0
\(773\) −1.92869e23 −1.51296 −0.756479 − 0.654018i \(-0.773082\pi\)
−0.756479 + 0.654018i \(0.773082\pi\)
\(774\) 0 0
\(775\) 9.56614e22 0.735060
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) −2.66213e23 −1.92318
\(782\) 0 0
\(783\) 0 0
\(784\) 1.42734e23 1.00000
\(785\) 3.88872e23 2.69681
\(786\) 0 0
\(787\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) −2.08210e22 −0.130486
\(796\) 3.22095e23 1.99838
\(797\) 2.14768e23 1.31918 0.659589 − 0.751626i \(-0.270730\pi\)
0.659589 + 0.751626i \(0.270730\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 3.43463e22 0.202684
\(802\) 0 0
\(803\) 0 0
\(804\) 9.71237e21 0.0556259
\(805\) 0 0
\(806\) 0 0
\(807\) −1.79855e22 −0.0999847
\(808\) 0 0
\(809\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(810\) 0 0
\(811\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −8.65602e22 −0.444690
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(822\) 0 0
\(823\) −3.29804e23 −1.56696 −0.783480 − 0.621417i \(-0.786557\pi\)
−0.783480 + 0.621417i \(0.786557\pi\)
\(824\) 0 0
\(825\) −1.08100e22 −0.0503726
\(826\) 0 0
\(827\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(828\) −3.54942e23 −1.60663
\(829\) −2.48322e23 −1.11322 −0.556608 − 0.830775i \(-0.687898\pi\)
−0.556608 + 0.830775i \(0.687898\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 2.03209e22 0.0843604
\(838\) 0 0
\(839\) −4.68621e22 −0.190865 −0.0954325 − 0.995436i \(-0.530423\pi\)
−0.0954325 + 0.995436i \(0.530423\pi\)
\(840\) 0 0
\(841\) 2.50246e23 1.00000
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 3.61688e23 1.39149
\(846\) 0 0
\(847\) 0 0
\(848\) 4.66065e23 1.74293
\(849\) 0 0
\(850\) 0 0
\(851\) −8.21653e23 −2.98712
\(852\) 2.87304e22 0.103473
\(853\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(858\) 0 0
\(859\) −5.17790e23 −1.74666 −0.873331 − 0.487128i \(-0.838045\pi\)
−0.873331 + 0.487128i \(0.838045\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −2.64026e23 −0.858146 −0.429073 − 0.903270i \(-0.641160\pi\)
−0.429073 + 0.903270i \(0.641160\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −1.71774e22 −0.0538028
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 3.90103e23 1.15629
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 5.00428e23 1.39149
\(881\) −1.31744e23 −0.363014 −0.181507 − 0.983390i \(-0.558097\pi\)
−0.181507 + 0.983390i \(0.558097\pi\)
\(882\) 0 0
\(883\) 5.04125e23 1.36412 0.682061 − 0.731296i \(-0.261084\pi\)
0.682061 + 0.731296i \(0.261084\pi\)
\(884\) 0 0
\(885\) 5.31179e22 0.141155
\(886\) 0 0
\(887\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 3.93765e23 0.991324
\(892\) 6.89242e23 1.71970
\(893\) 0 0
\(894\) 0 0
\(895\) −3.39672e23 −0.825041
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) −4.01857e23 −0.933536
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 1.22133e24 2.71422
\(906\) 0 0
\(907\) −4.87014e23 −1.06337 −0.531683 − 0.846943i \(-0.678440\pi\)
−0.531683 + 0.846943i \(0.678440\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −1.80044e23 −0.379517 −0.189758 − 0.981831i \(-0.560770\pi\)
−0.189758 + 0.981831i \(0.560770\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) −8.76426e23 −1.76828
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) −9.30255e23 −1.73567
\(926\) 0 0
\(927\) 1.08688e24 1.99317
\(928\) 0 0
\(929\) −4.10172e23 −0.739334 −0.369667 − 0.929164i \(-0.620528\pi\)
−0.369667 + 0.929164i \(0.620528\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) −4.60978e22 −0.0802837
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(938\) 0 0
\(939\) 6.09751e22 0.100885
\(940\) −3.79320e23 −0.622275
\(941\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) −1.18901e24 −1.88543
\(945\) 0 0
\(946\) 0 0
\(947\) 1.28791e24 1.99106 0.995530 − 0.0944410i \(-0.0301064\pi\)
0.995530 + 0.0944410i \(0.0301064\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) −2.58670e22 −0.0386635
\(952\) 0 0
\(953\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(954\) 0 0
\(955\) −1.86714e24 −2.69868
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) −5.40076e22 −0.0748661
\(961\) −2.79036e23 −0.383595
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 1.48892e24 1.88416 0.942079 − 0.335391i \(-0.108868\pi\)
0.942079 + 0.335391i \(0.108868\pi\)
\(972\) −1.28108e23 −0.160786
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 1.08016e24 1.30116 0.650582 − 0.759436i \(-0.274525\pi\)
0.650582 + 0.759436i \(0.274525\pi\)
\(978\) 0 0
\(979\) −1.71530e23 −0.203273
\(980\) 1.18383e24 1.39149
\(981\) 0 0
\(982\) 0 0
\(983\) −1.52134e24 −1.74501 −0.872506 − 0.488604i \(-0.837506\pi\)
−0.872506 + 0.488604i \(0.837506\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 8.25594e23 0.887518 0.443759 − 0.896146i \(-0.353645\pi\)
0.443759 + 0.896146i \(0.353645\pi\)
\(992\) 0 0
\(993\) 2.81893e22 0.0298188
\(994\) 0 0
\(995\) 2.67143e24 2.78073
\(996\) 0 0
\(997\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(998\) 0 0
\(999\) −1.97609e23 −0.199197
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 11.17.b.a.10.1 ✓ 1
3.2 odd 2 99.17.c.a.10.1 1
11.10 odd 2 CM 11.17.b.a.10.1 ✓ 1
33.32 even 2 99.17.c.a.10.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
11.17.b.a.10.1 ✓ 1 1.1 even 1 trivial
11.17.b.a.10.1 ✓ 1 11.10 odd 2 CM
99.17.c.a.10.1 1 3.2 odd 2
99.17.c.a.10.1 1 33.32 even 2