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Properties

Label 11.47.b.a.10.1
Level $11$
Weight $47$
Character 11.10
Self dual yes
Analytic conductor $147.420$
Analytic rank $0$
Dimension $1$
CM discriminant -11
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] = [11,47,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, 47, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("11.10");
 
S:= CuspForms(chi, 47);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 11 \)
Weight: \( k \) \(=\) \( 47 \)
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: \(147.420205496\)
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)
 
\(f(q)\) \(=\) \(q-1.16391e11 q^{3} +7.03687e13 q^{4} +1.77177e16 q^{5} +4.68394e21 q^{9} -8.95430e23 q^{11} -8.19029e24 q^{12} -2.06218e27 q^{15} +4.95176e27 q^{16} +1.24677e30 q^{20} -3.59606e31 q^{23} +1.71808e32 q^{25} +4.86398e32 q^{27} +3.36821e34 q^{31} +1.04220e35 q^{33} +3.29603e35 q^{36} +2.33634e36 q^{37} -6.30103e37 q^{44} +8.29886e37 q^{45} -1.88014e38 q^{47} -5.76341e38 q^{48} +7.49048e38 q^{49} -7.03316e39 q^{53} -1.58650e40 q^{55} -8.94537e40 q^{59} -1.45113e41 q^{60} +3.48449e41 q^{64} +4.07321e41 q^{67} +4.18550e42 q^{69} +2.80432e42 q^{71} -1.99969e43 q^{75} +8.77338e43 q^{80} -9.81258e43 q^{81} +8.71600e44 q^{89} -2.53050e45 q^{92} -3.92030e45 q^{93} +7.09608e45 q^{97} -4.19414e45 q^{99} +O(q^{100})\)

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 \(\pi\)
\(3\) −1.16391e11 −1.23632 −0.618160 − 0.786052i \(-0.712122\pi\)
−0.618160 + 0.786052i \(0.712122\pi\)
\(4\) 7.03687e13 1.00000
\(5\) 1.77177e16 1.48627 0.743134 − 0.669143i \(-0.233338\pi\)
0.743134 + 0.669143i \(0.233338\pi\)
\(6\) 0 0
\(7\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(8\) 0 0
\(9\) 4.68394e21 0.528486
\(10\) 0 0
\(11\) −8.95430e23 −1.00000
\(12\) −8.19029e24 −1.23632
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) 0 0
\(15\) −2.06218e27 −1.83750
\(16\) 4.95176e27 1.00000
\(17\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(18\) 0 0
\(19\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(20\) 1.24677e30 1.48627
\(21\) 0 0
\(22\) 0 0
\(23\) −3.59606e31 −1.72221 −0.861107 − 0.508424i \(-0.830228\pi\)
−0.861107 + 0.508424i \(0.830228\pi\)
\(24\) 0 0
\(25\) 1.71808e32 1.20899
\(26\) 0 0
\(27\) 4.86398e32 0.582942
\(28\) 0 0
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 0 0
\(31\) 3.36821e34 1.68299 0.841493 − 0.540269i \(-0.181677\pi\)
0.841493 + 0.540269i \(0.181677\pi\)
\(32\) 0 0
\(33\) 1.04220e35 1.23632
\(34\) 0 0
\(35\) 0 0
\(36\) 3.29603e35 0.528486
\(37\) 2.33634e36 1.99478 0.997391 − 0.0721860i \(-0.0229975\pi\)
0.997391 + 0.0721860i \(0.0229975\pi\)
\(38\) 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 \(\pi\)
\(44\) −6.30103e37 −1.00000
\(45\) 8.29886e37 0.785472
\(46\) 0 0
\(47\) −1.88014e38 −0.654546 −0.327273 − 0.944930i \(-0.606130\pi\)
−0.327273 + 0.944930i \(0.606130\pi\)
\(48\) −5.76341e38 −1.23632
\(49\) 7.49048e38 1.00000
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −7.03316e39 −1.54456 −0.772281 − 0.635281i \(-0.780884\pi\)
−0.772281 + 0.635281i \(0.780884\pi\)
\(54\) 0 0
\(55\) −1.58650e40 −1.48627
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −8.94537e40 −1.66725 −0.833627 − 0.552328i \(-0.813740\pi\)
−0.833627 + 0.552328i \(0.813740\pi\)
\(60\) −1.45113e41 −1.83750
\(61\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 3.48449e41 1.00000
\(65\) 0 0
\(66\) 0 0
\(67\) 4.07321e41 0.407583 0.203791 − 0.979014i \(-0.434674\pi\)
0.203791 + 0.979014i \(0.434674\pi\)
\(68\) 0 0
\(69\) 4.18550e42 2.12921
\(70\) 0 0
\(71\) 2.80432e42 0.739409 0.369705 − 0.929149i \(-0.379459\pi\)
0.369705 + 0.929149i \(0.379459\pi\)
\(72\) 0 0
\(73\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(74\) 0 0
\(75\) −1.99969e43 −1.49470
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(80\) 8.77338e43 1.48627
\(81\) −9.81258e43 −1.24919
\(82\) 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
\(89\) 8.71600e44 1.27159 0.635795 − 0.771858i \(-0.280672\pi\)
0.635795 + 0.771858i \(0.280672\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −2.53050e45 −1.72221
\(93\) −3.92030e45 −2.08071
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 7.09608e45 1.42978 0.714889 − 0.699238i \(-0.246477\pi\)
0.714889 + 0.699238i \(0.246477\pi\)
\(98\) 0 0
\(99\) −4.19414e45 −0.528486
\(100\) 1.20899e46 1.20899
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) 0 0
\(103\) 3.77085e46 1.91066 0.955329 − 0.295545i \(-0.0955011\pi\)
0.955329 + 0.295545i \(0.0955011\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) 3.42272e46 0.582942
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 0 0
\(111\) −2.71929e47 −2.46619
\(112\) 0 0
\(113\) 2.00850e47 1.20800 0.604000 − 0.796985i \(-0.293573\pi\)
0.604000 + 0.796985i \(0.293573\pi\)
\(114\) 0 0
\(115\) −6.37140e47 −2.55967
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 8.01795e47 1.00000
\(122\) 0 0
\(123\) 0 0
\(124\) 2.37017e48 1.68299
\(125\) 5.26210e47 0.310620
\(126\) 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 \(\pi\)
\(132\) 7.33384e48 1.23632
\(133\) 0 0
\(134\) 0 0
\(135\) 8.61785e48 0.866408
\(136\) 0 0
\(137\) −2.59930e49 −1.86331 −0.931653 − 0.363350i \(-0.881633\pi\)
−0.931653 + 0.363350i \(0.881633\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(140\) 0 0
\(141\) 2.18832e49 0.809228
\(142\) 0 0
\(143\) 0 0
\(144\) 2.31937e49 0.528486
\(145\) 0 0
\(146\) 0 0
\(147\) −8.71825e49 −1.23632
\(148\) 1.64405e50 1.99478
\(149\) 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
\(155\) 5.96769e50 2.50137
\(156\) 0 0
\(157\) 6.39315e50 1.99537 0.997684 − 0.0680259i \(-0.0216700\pi\)
0.997684 + 0.0680259i \(0.0216700\pi\)
\(158\) 0 0
\(159\) 8.18596e50 1.90957
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −1.46525e51 −1.93017 −0.965087 − 0.261930i \(-0.915641\pi\)
−0.965087 + 0.261930i \(0.915641\pi\)
\(164\) 0 0
\(165\) 1.84654e51 1.83750
\(166\) 0 0
\(167\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(168\) 0 0
\(169\) 1.74339e51 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
\(176\) −4.43396e51 −1.00000
\(177\) 1.04116e52 2.06126
\(178\) 0 0
\(179\) 1.02617e52 1.56891 0.784456 − 0.620184i \(-0.212942\pi\)
0.784456 + 0.620184i \(0.212942\pi\)
\(180\) 5.83980e51 0.785472
\(181\) 2.44000e51 0.288924 0.144462 − 0.989510i \(-0.453855\pi\)
0.144462 + 0.989510i \(0.453855\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 4.13945e52 2.96478
\(186\) 0 0
\(187\) 0 0
\(188\) −1.32303e52 −0.654546
\(189\) 0 0
\(190\) 0 0
\(191\) −1.81233e52 −0.622972 −0.311486 − 0.950251i \(-0.600827\pi\)
−0.311486 + 0.950251i \(0.600827\pi\)
\(192\) −4.05564e52 −1.23632
\(193\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 5.27096e52 1.00000
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 0 0
\(199\) −1.72409e52 −0.230642 −0.115321 − 0.993328i \(-0.536790\pi\)
−0.115321 + 0.993328i \(0.536790\pi\)
\(200\) 0 0
\(201\) −4.74085e52 −0.503903
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −1.68437e53 −0.910166
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(212\) −4.94914e53 −1.54456
\(213\) −3.26397e53 −0.914146
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) −1.11640e54 −1.48627
\(221\) 0 0
\(222\) 0 0
\(223\) −6.21764e52 −0.0606197 −0.0303098 − 0.999541i \(-0.509649\pi\)
−0.0303098 + 0.999541i \(0.509649\pi\)
\(224\) 0 0
\(225\) 8.04739e53 0.638936
\(226\) 0 0
\(227\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(228\) 0 0
\(229\) −8.22849e53 −0.435616 −0.217808 − 0.975992i \(-0.569891\pi\)
−0.217808 + 0.975992i \(0.569891\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(234\) 0 0
\(235\) −3.33118e54 −0.972831
\(236\) −6.29474e54 −1.66725
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) −1.02114e55 −1.83750
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) 0 0
\(243\) 7.11005e54 0.961454
\(244\) 0 0
\(245\) 1.32714e55 1.48627
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 3.05120e55 1.95873 0.979365 − 0.202099i \(-0.0647764\pi\)
0.979365 + 0.202099i \(0.0647764\pi\)
\(252\) 0 0
\(253\) 3.22002e55 1.72221
\(254\) 0 0
\(255\) 0 0
\(256\) 2.45199e55 1.00000
\(257\) 3.52177e55 1.31311 0.656553 − 0.754280i \(-0.272014\pi\)
0.656553 + 0.754280i \(0.272014\pi\)
\(258\) 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
\(265\) −1.24611e56 −2.29563
\(266\) 0 0
\(267\) −1.01446e56 −1.57209
\(268\) 2.86626e55 0.407583
\(269\) 1.46241e56 1.90882 0.954411 − 0.298497i \(-0.0964852\pi\)
0.954411 + 0.298497i \(0.0964852\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −1.53842e56 −1.20899
\(276\) 2.94528e56 2.12921
\(277\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(278\) 0 0
\(279\) 1.57765e56 0.889434
\(280\) 0 0
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) 0 0
\(283\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(284\) 1.97336e56 0.739409
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 3.98704e56 1.00000
\(290\) 0 0
\(291\) −8.25920e56 −1.76766
\(292\) 0 0
\(293\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(294\) 0 0
\(295\) −1.58491e57 −2.47799
\(296\) 0 0
\(297\) −4.35536e56 −0.582942
\(298\) 0 0
\(299\) 0 0
\(300\) −1.40716e57 −1.49470
\(301\) 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
\(309\) −4.38893e57 −2.36218
\(310\) 0 0
\(311\) 4.16398e57 1.93206 0.966028 − 0.258438i \(-0.0832079\pi\)
0.966028 + 0.258438i \(0.0832079\pi\)
\(312\) 0 0
\(313\) −2.93781e57 −1.17626 −0.588130 − 0.808766i \(-0.700136\pi\)
−0.588130 + 0.808766i \(0.700136\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 2.09037e57 0.624971 0.312485 − 0.949923i \(-0.398838\pi\)
0.312485 + 0.949923i \(0.398838\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 6.17372e57 1.48627
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) −6.90499e57 −1.24919
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 1.78004e58 1.96963 0.984816 − 0.173599i \(-0.0555398\pi\)
0.984816 + 0.173599i \(0.0555398\pi\)
\(332\) 0 0
\(333\) 1.09433e58 1.05421
\(334\) 0 0
\(335\) 7.21678e57 0.605777
\(336\) 0 0
\(337\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(338\) 0 0
\(339\) −2.33771e58 −1.49347
\(340\) 0 0
\(341\) −3.01600e58 −1.68299
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 7.41573e58 3.16457
\(346\) 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
\(353\) −1.02997e58 −0.259421 −0.129711 − 0.991552i \(-0.541405\pi\)
−0.129711 + 0.991552i \(0.541405\pi\)
\(354\) 0 0
\(355\) 4.96860e58 1.09896
\(356\) 6.13334e58 1.27159
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(360\) 0 0
\(361\) 6.64761e58 1.00000
\(362\) 0 0
\(363\) −9.33218e58 −1.23632
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 1.72102e59 1.77201 0.886007 − 0.463672i \(-0.153468\pi\)
0.886007 + 0.463672i \(0.153468\pi\)
\(368\) −1.78068e59 −1.72221
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) −2.75866e59 −2.08071
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) 0 0
\(375\) −6.12461e58 −0.384025
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −3.22682e59 −1.58516 −0.792579 − 0.609769i \(-0.791262\pi\)
−0.792579 + 0.609769i \(0.791262\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −3.75367e59 −1.44838 −0.724192 − 0.689598i \(-0.757787\pi\)
−0.724192 + 0.689598i \(0.757787\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 4.99342e59 1.42978
\(389\) −4.57328e59 −1.23420 −0.617102 − 0.786883i \(-0.711693\pi\)
−0.617102 + 0.786883i \(0.711693\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) −2.95136e59 −0.528486
\(397\) 7.97092e59 1.34687 0.673437 − 0.739245i \(-0.264817\pi\)
0.673437 + 0.739245i \(0.264817\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 8.50753e59 1.20899
\(401\) −4.74647e59 −0.636869 −0.318434 − 0.947945i \(-0.603157\pi\)
−0.318434 + 0.947945i \(0.603157\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) −1.73856e60 −1.85663
\(406\) 0 0
\(407\) −2.09203e60 −1.99478
\(408\) 0 0
\(409\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(410\) 0 0
\(411\) 3.02536e60 2.30364
\(412\) 2.65350e60 1.91066
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 3.50899e60 1.71498 0.857490 − 0.514500i \(-0.172023\pi\)
0.857490 + 0.514500i \(0.172023\pi\)
\(420\) 0 0
\(421\) −1.47068e60 −0.644215 −0.322108 − 0.946703i \(-0.604391\pi\)
−0.322108 + 0.946703i \(0.604391\pi\)
\(422\) 0 0
\(423\) −8.80648e59 −0.345918
\(424\) 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 \(\pi\)
\(432\) 2.40853e60 0.582942
\(433\) 5.37106e60 1.23265 0.616323 − 0.787494i \(-0.288622\pi\)
0.616323 + 0.787494i \(0.288622\pi\)
\(434\) 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
\(441\) 3.50850e60 0.528486
\(442\) 0 0
\(443\) −6.58858e60 −0.894347 −0.447174 − 0.894447i \(-0.647569\pi\)
−0.447174 + 0.894447i \(0.647569\pi\)
\(444\) −1.91353e61 −2.46619
\(445\) 1.54427e61 1.88992
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 1.88223e61 1.87502 0.937511 − 0.347957i \(-0.113124\pi\)
0.937511 + 0.347957i \(0.113124\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 1.41335e61 1.20800
\(453\) 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
\(460\) −4.48347e61 −2.55967
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) −3.10816e61 −1.52806 −0.764031 − 0.645180i \(-0.776782\pi\)
−0.764031 + 0.645180i \(0.776782\pi\)
\(464\) 0 0
\(465\) −6.94586e61 −3.09249
\(466\) 0 0
\(467\) 4.95093e61 1.99709 0.998547 − 0.0538899i \(-0.0171620\pi\)
0.998547 + 0.0538899i \(0.0171620\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −7.44105e61 −2.46691
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −3.29429e61 −0.816279
\(478\) 0 0
\(479\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 5.64213e61 1.00000
\(485\) 1.25726e62 2.12503
\(486\) 0 0
\(487\) −6.63865e61 −1.02074 −0.510369 − 0.859956i \(-0.670491\pi\)
−0.510369 + 0.859956i \(0.670491\pi\)
\(488\) 0 0
\(489\) 1.70542e62 2.38631
\(490\) 0 0
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) −7.43105e61 −0.785472
\(496\) 1.66786e62 1.68299
\(497\) 0 0
\(498\) 0 0
\(499\) −1.65713e62 −1.45561 −0.727804 − 0.685785i \(-0.759459\pi\)
−0.727804 + 0.685785i \(0.759459\pi\)
\(500\) 3.70287e61 0.310620
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −2.02915e62 −1.23632
\(508\) 0 0
\(509\) −3.48843e62 −1.94143 −0.970713 − 0.240243i \(-0.922773\pi\)
−0.970713 + 0.240243i \(0.922773\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 6.68108e62 2.83975
\(516\) 0 0
\(517\) 1.68354e62 0.654546
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 5.85442e62 1.90641 0.953205 − 0.302324i \(-0.0977625\pi\)
0.953205 + 0.302324i \(0.0977625\pi\)
\(522\) 0 0
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 5.16073e62 1.23632
\(529\) 8.57173e62 1.96602
\(530\) 0 0
\(531\) −4.18995e62 −0.881121
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −1.19437e63 −1.93968
\(538\) 0 0
\(539\) −6.70721e62 −1.00000
\(540\) 6.06428e62 0.866408
\(541\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(542\) 0 0
\(543\) −2.83995e62 −0.357202
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(548\) −1.82910e63 −1.86331
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −4.81795e63 −3.66542
\(556\) 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 \(\pi\)
\(564\) 1.53989e63 0.809228
\(565\) 3.55859e63 1.79541
\(566\) 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
\(573\) 2.10938e63 0.770193
\(574\) 0 0
\(575\) −6.17833e63 −2.08214
\(576\) 1.63211e63 0.528486
\(577\) −6.33344e63 −1.97059 −0.985294 − 0.170868i \(-0.945343\pi\)
−0.985294 + 0.170868i \(0.945343\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 6.29770e63 1.54456
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 9.53806e63 1.99887 0.999433 − 0.0336638i \(-0.0107175\pi\)
0.999433 + 0.0336638i \(0.0107175\pi\)
\(588\) −6.13492e63 −1.23632
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 1.15690e64 1.99478
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 2.00669e63 0.285148
\(598\) 0 0
\(599\) −1.44626e64 −1.90297 −0.951483 − 0.307703i \(-0.900440\pi\)
−0.951483 + 0.307703i \(0.900440\pi\)
\(600\) 0 0
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) 0 0
\(603\) 1.90786e63 0.215402
\(604\) 0 0
\(605\) 1.42060e64 1.48627
\(606\) 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
\(617\) 2.12437e64 1.41472 0.707361 − 0.706852i \(-0.249885\pi\)
0.707361 + 0.706852i \(0.249885\pi\)
\(618\) 0 0
\(619\) −1.94838e64 −1.20445 −0.602226 − 0.798326i \(-0.705719\pi\)
−0.602226 + 0.798326i \(0.705719\pi\)
\(620\) 4.19939e64 2.50137
\(621\) −1.74912e64 −1.00395
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −1.50922e64 −0.747329
\(626\) 0 0
\(627\) 0 0
\(628\) 4.49878e64 1.99537
\(629\) 0 0
\(630\) 0 0
\(631\) −4.97729e64 −1.97842 −0.989208 − 0.146515i \(-0.953194\pi\)
−0.989208 + 0.146515i \(0.953194\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 5.76036e64 1.90957
\(637\) 0 0
\(638\) 0 0
\(639\) 1.31352e64 0.390767
\(640\) 0 0
\(641\) −7.19994e64 −1.99340 −0.996700 − 0.0811727i \(-0.974133\pi\)
−0.996700 + 0.0811727i \(0.974133\pi\)
\(642\) 0 0
\(643\) −6.06652e64 −1.56346 −0.781731 − 0.623615i \(-0.785663\pi\)
−0.781731 + 0.623615i \(0.785663\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −7.37153e64 −1.64725 −0.823624 − 0.567136i \(-0.808051\pi\)
−0.823624 + 0.567136i \(0.808051\pi\)
\(648\) 0 0
\(649\) 8.00995e64 1.66725
\(650\) 0 0
\(651\) 0 0
\(652\) −1.03108e65 −1.93017
\(653\) −1.09355e65 −1.97623 −0.988114 − 0.153722i \(-0.950874\pi\)
−0.988114 + 0.153722i \(0.950874\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 1.29939e65 1.83750
\(661\) −1.01075e65 −1.38041 −0.690207 − 0.723612i \(-0.742481\pi\)
−0.690207 + 0.723612i \(0.742481\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 7.23678e63 0.0749453
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(674\) 0 0
\(675\) 8.35672e64 0.704773
\(676\) 1.22680e65 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
\(683\) 3.10625e65 1.99784 0.998919 − 0.0464847i \(-0.0148019\pi\)
0.998919 + 0.0464847i \(0.0148019\pi\)
\(684\) 0 0
\(685\) −4.60537e65 −2.76937
\(686\) 0 0
\(687\) 9.57723e64 0.538561
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 3.44078e65 1.69302 0.846510 − 0.532373i \(-0.178700\pi\)
0.846510 + 0.532373i \(0.178700\pi\)
\(692\) 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
\(704\) −3.12012e65 −1.00000
\(705\) 3.87720e65 1.20273
\(706\) 0 0
\(707\) 0 0
\(708\) 7.32652e65 2.06126
\(709\) 3.50186e65 0.953751 0.476876 − 0.878971i \(-0.341769\pi\)
0.476876 + 0.878971i \(0.341769\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −1.21123e66 −2.89846
\(714\) 0 0
\(715\) 0 0
\(716\) 7.22101e65 1.56891
\(717\) 0 0
\(718\) 0 0
\(719\) −3.22760e65 −0.636964 −0.318482 − 0.947929i \(-0.603173\pi\)
−0.318482 + 0.947929i \(0.603173\pi\)
\(720\) 4.10940e65 0.785472
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) 1.71700e65 0.288924
\(725\) 0 0
\(726\) 0 0
\(727\) −8.24355e65 −1.26131 −0.630657 − 0.776062i \(-0.717214\pi\)
−0.630657 + 0.776062i \(0.717214\pi\)
\(728\) 0 0
\(729\) 4.21366e64 0.0605239
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(734\) 0 0
\(735\) −1.54467e66 −1.83750
\(736\) 0 0
\(737\) −3.64727e65 −0.407583
\(738\) 0 0
\(739\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(740\) 2.91288e66 2.96478
\(741\) 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
\(751\) −1.32288e66 −0.958965 −0.479482 − 0.877552i \(-0.659176\pi\)
−0.479482 + 0.877552i \(0.659176\pi\)
\(752\) −9.31002e65 −0.654546
\(753\) −3.55132e66 −2.42162
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 2.89632e66 1.74840 0.874201 − 0.485565i \(-0.161386\pi\)
0.874201 + 0.485565i \(0.161386\pi\)
\(758\) 0 0
\(759\) −3.74782e66 −2.12921
\(760\) 0 0
\(761\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −1.27531e66 −0.622972
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) −2.85390e66 −1.23632
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) −4.09903e66 −1.62342
\(772\) 0 0
\(773\) 4.60636e65 0.171882 0.0859408 − 0.996300i \(-0.472610\pi\)
0.0859408 + 0.996300i \(0.472610\pi\)
\(774\) 0 0
\(775\) 5.78686e66 2.03472
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) −2.51107e66 −0.739409
\(782\) 0 0
\(783\) 0 0
\(784\) 3.70911e66 1.00000
\(785\) 1.13272e67 2.96565
\(786\) 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
\(795\) 1.45036e67 2.83814
\(796\) −1.21322e66 −0.230642
\(797\) 8.30766e66 1.53440 0.767198 − 0.641411i \(-0.221651\pi\)
0.767198 + 0.641411i \(0.221651\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 4.08252e66 0.672017
\(802\) 0 0
\(803\) 0 0
\(804\) −3.33608e66 −0.503903
\(805\) 0 0
\(806\) 0 0
\(807\) −1.70211e67 −2.35991
\(808\) 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
\(815\) −2.59608e67 −2.86876
\(816\) 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
\(823\) 2.26438e67 1.99873 0.999364 − 0.0356563i \(-0.0113522\pi\)
0.999364 + 0.0356563i \(0.0113522\pi\)
\(824\) 0 0
\(825\) 1.79059e67 1.49470
\(826\) 0 0
\(827\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(828\) −1.18527e67 −0.910166
\(829\) −1.75636e67 −1.31177 −0.655887 − 0.754859i \(-0.727705\pi\)
−0.655887 + 0.754859i \(0.727705\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 1.63829e67 0.981083
\(838\) 0 0
\(839\) 3.51737e67 1.99385 0.996925 − 0.0783567i \(-0.0249673\pi\)
0.996925 + 0.0783567i \(0.0249673\pi\)
\(840\) 0 0
\(841\) 1.86341e67 1.00000
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 3.08888e67 1.48627
\(846\) 0 0
\(847\) 0 0
\(848\) −3.48265e67 −1.54456
\(849\) 0 0
\(850\) 0 0
\(851\) −8.40161e67 −3.43544
\(852\) −2.29682e67 −0.914146
\(853\) 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
\(859\) −5.32101e67 −1.75449 −0.877246 − 0.480041i \(-0.840622\pi\)
−0.877246 + 0.480041i \(0.840622\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −3.18952e67 −0.945098 −0.472549 − 0.881304i \(-0.656666\pi\)
−0.472549 + 0.881304i \(0.656666\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −4.64056e67 −1.23632
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 3.32376e67 0.755618
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) −7.85595e67 −1.48627
\(881\) 9.73758e67 1.79475 0.897377 − 0.441264i \(-0.145470\pi\)
0.897377 + 0.441264i \(0.145470\pi\)
\(882\) 0 0
\(883\) −1.14321e68 −2.00000 −0.999998 − 0.00193710i \(-0.999383\pi\)
−0.999998 + 0.00193710i \(0.999383\pi\)
\(884\) 0 0
\(885\) 1.84470e68 3.06358
\(886\) 0 0
\(887\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 8.78649e67 1.24919
\(892\) −4.37527e66 −0.0606197
\(893\) 0 0
\(894\) 0 0
\(895\) 1.81813e68 2.33182
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) 5.66285e67 0.638936
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 4.32313e67 0.429418
\(906\) 0 0
\(907\) −2.09280e68 −1.97588 −0.987941 − 0.154833i \(-0.950516\pi\)
−0.987941 + 0.154833i \(0.950516\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 8.09321e67 0.690555 0.345277 − 0.938501i \(-0.387785\pi\)
0.345277 + 0.938501i \(0.387785\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) −5.79029e67 −0.435616
\(917\) 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
\(925\) 4.01402e68 2.41168
\(926\) 0 0
\(927\) 1.76624e68 1.00976
\(928\) 0 0
\(929\) −3.92131e67 −0.213339 −0.106669 − 0.994295i \(-0.534019\pi\)
−0.106669 + 0.994295i \(0.534019\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) −4.84650e68 −2.38864
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(938\) 0 0
\(939\) 3.41934e68 1.45423
\(940\) −2.34411e68 −0.972831
\(941\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) −4.42953e68 −1.66725
\(945\) 0 0
\(946\) 0 0
\(947\) 2.80766e68 0.982414 0.491207 − 0.871043i \(-0.336556\pi\)
0.491207 + 0.871043i \(0.336556\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) −2.43300e68 −0.772664
\(952\) 0 0
\(953\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(954\) 0 0
\(955\) −3.21102e68 −0.925904
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) −7.18565e68 −1.83750
\(961\) 7.33952e68 1.83244
\(962\) 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
\(971\) −8.46000e68 −1.66467 −0.832335 − 0.554273i \(-0.812996\pi\)
−0.832335 + 0.554273i \(0.812996\pi\)
\(972\) 5.00326e68 0.961454
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 1.44078e68 0.246050 0.123025 − 0.992404i \(-0.460740\pi\)
0.123025 + 0.992404i \(0.460740\pi\)
\(978\) 0 0
\(979\) −7.80457e68 −1.27159
\(980\) 9.33893e68 1.48627
\(981\) 0 0
\(982\) 0 0
\(983\) −1.29209e69 −1.91674 −0.958370 − 0.285528i \(-0.907831\pi\)
−0.958370 + 0.285528i \(0.907831\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 1.08678e69 1.33797 0.668987 − 0.743274i \(-0.266728\pi\)
0.668987 + 0.743274i \(0.266728\pi\)
\(992\) 0 0
\(993\) −2.07180e69 −2.43510
\(994\) 0 0
\(995\) −3.05469e68 −0.342797
\(996\) 0 0
\(997\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(998\) 0 0
\(999\) 1.13639e69 1.16284
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 11.47.b.a.10.1 ✓ 1
11.10 odd 2 CM 11.47.b.a.10.1 ✓ 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
11.47.b.a.10.1 ✓ 1 1.1 even 1 trivial
11.47.b.a.10.1 ✓ 1 11.10 odd 2 CM