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Properties

Label 11.55.b.a.10.1
Level $11$
Weight $55$
Character 11.10
Self dual yes
Analytic conductor $203.147$
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] = [11,55,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, 55, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("11.10");
 
S:= CuspForms(chi, 55);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 11 \)
Weight: \( k \) \(=\) \( 55 \)
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: \(203.146858102\)
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)
 
\(f(q)\) \(=\) \(q+1.51663e13 q^{3} +1.80144e16 q^{4} +6.30749e18 q^{5} +1.71868e26 q^{9} -1.31100e28 q^{11} +2.73212e29 q^{12} +9.56615e31 q^{15} +3.24519e32 q^{16} +1.13626e35 q^{20} +1.14140e37 q^{23} -1.57267e37 q^{25} +1.72468e39 q^{27} -3.69623e40 q^{31} -1.98830e41 q^{33} +3.09609e42 q^{36} +5.25867e41 q^{37} -2.36169e44 q^{44} +1.08405e45 q^{45} -1.50031e45 q^{47} +4.92175e45 q^{48} +4.31811e45 q^{49} +4.21092e46 q^{53} -8.26912e46 q^{55} +8.91266e47 q^{59} +1.72328e48 q^{60} +5.84601e48 q^{64} -3.03068e49 q^{67} +1.73109e50 q^{69} +1.87246e50 q^{71} -2.38516e50 q^{75} +2.04690e51 q^{80} +1.61630e52 q^{81} +1.26210e52 q^{89} +2.05617e53 q^{92} -5.60583e53 q^{93} -8.34054e53 q^{97} -2.25318e54 q^{99} +O(q^{100})\)

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 \(\pi\)
\(3\) 1.51663e13 1.98887 0.994435 − 0.105351i \(-0.0335965\pi\)
0.994435 + 0.105351i \(0.0335965\pi\)
\(4\) 1.80144e16 1.00000
\(5\) 6.30749e18 0.846578 0.423289 − 0.905995i \(-0.360876\pi\)
0.423289 + 0.905995i \(0.360876\pi\)
\(6\) 0 0
\(7\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(8\) 0 0
\(9\) 1.71868e26 2.95561
\(10\) 0 0
\(11\) −1.31100e28 −1.00000
\(12\) 2.73212e29 1.98887
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) 0 0
\(15\) 9.56615e31 1.68373
\(16\) 3.24519e32 1.00000
\(17\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(18\) 0 0
\(19\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(20\) 1.13626e35 0.846578
\(21\) 0 0
\(22\) 0 0
\(23\) 1.14140e37 1.95338 0.976690 − 0.214654i \(-0.0688625\pi\)
0.976690 + 0.214654i \(0.0688625\pi\)
\(24\) 0 0
\(25\) −1.57267e37 −0.283306
\(26\) 0 0
\(27\) 1.72468e39 3.88944
\(28\) 0 0
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 0 0
\(31\) −3.69623e40 −1.99983 −0.999916 − 0.0129364i \(-0.995882\pi\)
−0.999916 + 0.0129364i \(0.995882\pi\)
\(32\) 0 0
\(33\) −1.98830e41 −1.98887
\(34\) 0 0
\(35\) 0 0
\(36\) 3.09609e42 2.95561
\(37\) 5.25867e41 0.239569 0.119784 − 0.992800i \(-0.461780\pi\)
0.119784 + 0.992800i \(0.461780\pi\)
\(38\) 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 \(\pi\)
\(44\) −2.36169e44 −1.00000
\(45\) 1.08405e45 2.50215
\(46\) 0 0
\(47\) −1.50031e45 −1.07038 −0.535192 − 0.844730i \(-0.679761\pi\)
−0.535192 + 0.844730i \(0.679761\pi\)
\(48\) 4.92175e45 1.98887
\(49\) 4.31811e45 1.00000
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 4.21092e46 1.17200 0.586002 − 0.810310i \(-0.300701\pi\)
0.586002 + 0.810310i \(0.300701\pi\)
\(54\) 0 0
\(55\) −8.26912e46 −0.846578
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 8.91266e47 1.37089 0.685445 − 0.728124i \(-0.259608\pi\)
0.685445 + 0.728124i \(0.259608\pi\)
\(60\) 1.72328e48 1.68373
\(61\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 5.84601e48 1.00000
\(65\) 0 0
\(66\) 0 0
\(67\) −3.03068e49 −1.50494 −0.752472 − 0.658625i \(-0.771139\pi\)
−0.752472 + 0.658625i \(0.771139\pi\)
\(68\) 0 0
\(69\) 1.73109e50 3.88502
\(70\) 0 0
\(71\) 1.87246e50 1.94284 0.971418 − 0.237376i \(-0.0762874\pi\)
0.971418 + 0.237376i \(0.0762874\pi\)
\(72\) 0 0
\(73\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(74\) 0 0
\(75\) −2.38516e50 −0.563460
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(80\) 2.04690e51 0.846578
\(81\) 1.61630e52 4.78000
\(82\) 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
\(89\) 1.26210e52 0.293469 0.146735 − 0.989176i \(-0.453124\pi\)
0.146735 + 0.989176i \(0.453124\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 2.05617e53 1.95338
\(93\) −5.60583e53 −3.97741
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −8.34054e53 −1.89827 −0.949134 − 0.314872i \(-0.898038\pi\)
−0.949134 + 0.314872i \(0.898038\pi\)
\(98\) 0 0
\(99\) −2.25318e54 −2.95561
\(100\) −2.83306e53 −0.283306
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) 0 0
\(103\) 1.24441e54 0.560219 0.280110 − 0.959968i \(-0.409629\pi\)
0.280110 + 0.959968i \(0.409629\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) 3.10691e55 3.88944
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 0 0
\(111\) 7.97548e54 0.476471
\(112\) 0 0
\(113\) −3.08203e55 −1.13689 −0.568446 − 0.822721i \(-0.692455\pi\)
−0.568446 + 0.822721i \(0.692455\pi\)
\(114\) 0 0
\(115\) 7.19938e55 1.65369
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 1.71872e56 1.00000
\(122\) 0 0
\(123\) 0 0
\(124\) −6.65854e56 −1.99983
\(125\) −4.49332e56 −1.08642
\(126\) 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 \(\pi\)
\(132\) −3.58181e57 −1.98887
\(133\) 0 0
\(134\) 0 0
\(135\) 1.08784e58 3.29272
\(136\) 0 0
\(137\) −7.78727e57 −1.58464 −0.792319 − 0.610107i \(-0.791126\pi\)
−0.792319 + 0.610107i \(0.791126\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(140\) 0 0
\(141\) −2.27542e58 −2.12886
\(142\) 0 0
\(143\) 0 0
\(144\) 5.57742e58 2.95561
\(145\) 0 0
\(146\) 0 0
\(147\) 6.54899e58 1.98887
\(148\) 9.47319e57 0.239569
\(149\) 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
\(155\) −2.33140e59 −1.69301
\(156\) 0 0
\(157\) −3.88707e59 −1.99679 −0.998395 − 0.0566425i \(-0.981960\pi\)
−0.998395 + 0.0566425i \(0.981960\pi\)
\(158\) 0 0
\(159\) 6.38642e59 2.33096
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −4.56636e59 −0.852129 −0.426064 − 0.904693i \(-0.640100\pi\)
−0.426064 + 0.904693i \(0.640100\pi\)
\(164\) 0 0
\(165\) −1.25412e60 −1.68373
\(166\) 0 0
\(167\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(168\) 0 0
\(169\) 1.42214e60 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
\(176\) −4.25444e60 −1.00000
\(177\) 1.35172e61 2.72652
\(178\) 0 0
\(179\) −4.57475e59 −0.0681296 −0.0340648 − 0.999420i \(-0.510845\pi\)
−0.0340648 + 0.999420i \(0.510845\pi\)
\(180\) 1.95286e61 2.50215
\(181\) −6.08812e59 −0.0671679 −0.0335839 − 0.999436i \(-0.510692\pi\)
−0.0335839 + 0.999436i \(0.510692\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 3.31691e60 0.202813
\(186\) 0 0
\(187\) 0 0
\(188\) −2.70272e61 −1.07038
\(189\) 0 0
\(190\) 0 0
\(191\) −7.00538e61 −1.80938 −0.904692 − 0.426066i \(-0.859899\pi\)
−0.904692 + 0.426066i \(0.859899\pi\)
\(192\) 8.86624e61 1.98887
\(193\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 7.77882e61 1.00000
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 0 0
\(199\) −3.17134e61 −0.270526 −0.135263 − 0.990810i \(-0.543188\pi\)
−0.135263 + 0.990810i \(0.543188\pi\)
\(200\) 0 0
\(201\) −4.59642e62 −2.99314
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 1.96170e63 5.77342
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(212\) 7.58572e62 1.17200
\(213\) 2.83983e63 3.86405
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) −1.48963e63 −0.846578
\(221\) 0 0
\(222\) 0 0
\(223\) 1.19400e63 0.470733 0.235366 − 0.971907i \(-0.424371\pi\)
0.235366 + 0.971907i \(0.424371\pi\)
\(224\) 0 0
\(225\) −2.70291e63 −0.837342
\(226\) 0 0
\(227\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(228\) 0 0
\(229\) 9.29718e63 1.78975 0.894877 − 0.446313i \(-0.147263\pi\)
0.894877 + 0.446313i \(0.147263\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(234\) 0 0
\(235\) −9.46322e63 −0.906163
\(236\) 1.60556e64 1.37089
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 3.10439e64 1.68373
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) 0 0
\(243\) 1.44844e65 5.61735
\(244\) 0 0
\(245\) 2.72365e64 0.846578
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −1.26631e64 −0.204810 −0.102405 − 0.994743i \(-0.532654\pi\)
−0.102405 + 0.994743i \(0.532654\pi\)
\(252\) 0 0
\(253\) −1.49638e65 −1.95338
\(254\) 0 0
\(255\) 0 0
\(256\) 1.05312e65 1.00000
\(257\) −1.67585e65 −1.43233 −0.716163 − 0.697933i \(-0.754103\pi\)
−0.716163 + 0.697933i \(0.754103\pi\)
\(258\) 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
\(265\) 2.65604e65 0.992192
\(266\) 0 0
\(267\) 1.91414e65 0.583672
\(268\) −5.45958e65 −1.50494
\(269\) −7.06986e65 −1.76238 −0.881189 − 0.472763i \(-0.843256\pi\)
−0.881189 + 0.472763i \(0.843256\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 2.06176e65 0.283306
\(276\) 3.11845e66 3.88502
\(277\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(278\) 0 0
\(279\) −6.35263e66 −5.91072
\(280\) 0 0
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) 0 0
\(283\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(284\) 3.37312e66 1.94284
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 2.78126e66 1.00000
\(290\) 0 0
\(291\) −1.26495e67 −3.77541
\(292\) 0 0
\(293\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(294\) 0 0
\(295\) 5.62165e66 1.16057
\(296\) 0 0
\(297\) −2.26106e67 −3.88944
\(298\) 0 0
\(299\) 0 0
\(300\) −4.29672e66 −0.563460
\(301\) 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
\(309\) 1.88731e67 1.11420
\(310\) 0 0
\(311\) −4.01104e67 −1.98942 −0.994710 − 0.102724i \(-0.967244\pi\)
−0.994710 + 0.102724i \(0.967244\pi\)
\(312\) 0 0
\(313\) −3.31820e67 −1.38422 −0.692110 − 0.721792i \(-0.743319\pi\)
−0.692110 + 0.721792i \(0.743319\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 5.37207e67 1.59053 0.795264 − 0.606263i \(-0.207332\pi\)
0.795264 + 0.606263i \(0.207332\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 3.68737e67 0.846578
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 2.91167e68 4.78000
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −1.58556e68 −1.46159 −0.730796 − 0.682596i \(-0.760851\pi\)
−0.730796 + 0.682596i \(0.760851\pi\)
\(332\) 0 0
\(333\) 9.03796e67 0.708070
\(334\) 0 0
\(335\) −1.91160e68 −1.27405
\(336\) 0 0
\(337\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(338\) 0 0
\(339\) −4.67431e68 −2.26113
\(340\) 0 0
\(341\) 4.84576e68 1.99983
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 1.09188e69 3.28897
\(346\) 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
\(353\) −1.08544e69 −1.76072 −0.880359 − 0.474307i \(-0.842699\pi\)
−0.880359 + 0.474307i \(0.842699\pi\)
\(354\) 0 0
\(355\) 1.18105e69 1.64476
\(356\) 2.27359e68 0.293469
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(360\) 0 0
\(361\) 1.12900e69 1.00000
\(362\) 0 0
\(363\) 2.60667e69 1.98887
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −1.71453e68 −0.0973107 −0.0486554 − 0.998816i \(-0.515494\pi\)
−0.0486554 + 0.998816i \(0.515494\pi\)
\(368\) 3.70406e69 1.95338
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) −1.00986e70 −3.97741
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) 0 0
\(375\) −6.81472e69 −2.16075
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −8.38980e69 −1.99753 −0.998764 − 0.0497092i \(-0.984171\pi\)
−0.998764 + 0.0497092i \(0.984171\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −1.45868e69 −0.261572 −0.130786 − 0.991411i \(-0.541750\pi\)
−0.130786 + 0.991411i \(0.541750\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) −1.50250e70 −1.89827
\(389\) 1.01902e70 1.20100 0.600499 − 0.799626i \(-0.294969\pi\)
0.600499 + 0.799626i \(0.294969\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) −4.05898e70 −2.95561
\(397\) 2.67219e70 1.81771 0.908853 − 0.417117i \(-0.136960\pi\)
0.908853 + 0.417117i \(0.136960\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −5.10359e69 −0.283306
\(401\) 6.36570e69 0.330330 0.165165 − 0.986266i \(-0.447184\pi\)
0.165165 + 0.986266i \(0.447184\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 1.01948e71 4.04664
\(406\) 0 0
\(407\) −6.89412e69 −0.239569
\(408\) 0 0
\(409\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(410\) 0 0
\(411\) −1.18104e71 −3.15164
\(412\) 2.24173e70 0.560219
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 9.38606e70 1.48835 0.744174 − 0.667985i \(-0.232843\pi\)
0.744174 + 0.667985i \(0.232843\pi\)
\(420\) 0 0
\(421\) −1.07219e71 −1.49505 −0.747525 − 0.664234i \(-0.768758\pi\)
−0.747525 + 0.664234i \(0.768758\pi\)
\(422\) 0 0
\(423\) −2.57855e71 −3.16363
\(424\) 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 \(\pi\)
\(432\) 5.59692e71 3.88944
\(433\) 2.15345e71 1.40592 0.702962 − 0.711227i \(-0.251860\pi\)
0.702962 + 0.711227i \(0.251860\pi\)
\(434\) 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
\(441\) 7.42144e71 2.95561
\(442\) 0 0
\(443\) 5.66047e71 1.99504 0.997521 − 0.0703717i \(-0.0224185\pi\)
0.997521 + 0.0703717i \(0.0224185\pi\)
\(444\) 1.43673e71 0.476471
\(445\) 7.96067e70 0.248444
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −7.84068e71 −1.92178 −0.960888 − 0.276939i \(-0.910680\pi\)
−0.960888 + 0.276939i \(0.910680\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) −5.55209e71 −1.13689
\(453\) 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
\(460\) 1.29693e72 1.65369
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) −1.59373e72 −1.70501 −0.852506 − 0.522717i \(-0.824918\pi\)
−0.852506 + 0.522717i \(0.824918\pi\)
\(464\) 0 0
\(465\) −3.53587e72 −3.36718
\(466\) 0 0
\(467\) 1.93338e72 1.63969 0.819845 − 0.572586i \(-0.194060\pi\)
0.819845 + 0.572586i \(0.194060\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −5.89526e72 −3.97135
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 7.23721e72 3.46398
\(478\) 0 0
\(479\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 3.09617e72 1.00000
\(485\) −5.26079e72 −1.60703
\(486\) 0 0
\(487\) 7.01678e72 1.91803 0.959016 − 0.283351i \(-0.0914460\pi\)
0.959016 + 0.283351i \(0.0914460\pi\)
\(488\) 0 0
\(489\) −6.92550e72 −1.69477
\(490\) 0 0
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) −1.42119e73 −2.50215
\(496\) −1.19950e73 −1.99983
\(497\) 0 0
\(498\) 0 0
\(499\) 1.38239e73 1.95847 0.979234 − 0.202735i \(-0.0649830\pi\)
0.979234 + 0.202735i \(0.0649830\pi\)
\(500\) −8.09445e72 −1.08642
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 2.15686e73 1.98887
\(508\) 0 0
\(509\) −1.62583e73 −1.34802 −0.674009 − 0.738723i \(-0.735429\pi\)
−0.674009 + 0.738723i \(0.735429\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 7.84911e72 0.474269
\(516\) 0 0
\(517\) 1.96691e73 1.07038
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −3.24777e73 −1.43538 −0.717690 − 0.696363i \(-0.754801\pi\)
−0.717690 + 0.696363i \(0.754801\pi\)
\(522\) 0 0
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) −6.45242e73 −1.98887
\(529\) 9.61366e73 2.81569
\(530\) 0 0
\(531\) 1.53180e74 4.05181
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −6.93822e72 −0.135501
\(538\) 0 0
\(539\) −5.66105e73 −1.00000
\(540\) 1.95968e74 3.29272
\(541\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(542\) 0 0
\(543\) −9.23344e72 −0.133588
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(548\) −1.40283e74 −1.58464
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 5.03053e73 0.403369
\(556\) 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 \(\pi\)
\(564\) −4.09904e74 −2.12886
\(565\) −1.94399e74 −0.962467
\(566\) 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
\(573\) −1.06246e75 −3.59863
\(574\) 0 0
\(575\) −1.79504e74 −0.553405
\(576\) 1.00474e75 2.95561
\(577\) 1.89952e74 0.533209 0.266605 − 0.963806i \(-0.414098\pi\)
0.266605 + 0.963806i \(0.414098\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −5.52052e74 −1.17200
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 4.81127e74 0.849241 0.424620 − 0.905371i \(-0.360408\pi\)
0.424620 + 0.905371i \(0.360408\pi\)
\(588\) 1.17976e75 1.98887
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 1.70654e74 0.239569
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −4.80975e74 −0.538041
\(598\) 0 0
\(599\) −1.56915e75 −1.60377 −0.801883 − 0.597481i \(-0.796168\pi\)
−0.801883 + 0.597481i \(0.796168\pi\)
\(600\) 0 0
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) 0 0
\(603\) −5.20876e75 −4.44802
\(604\) 0 0
\(605\) 1.08408e75 0.846578
\(606\) 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
\(617\) 2.38555e75 1.09620 0.548099 − 0.836414i \(-0.315352\pi\)
0.548099 + 0.836414i \(0.315352\pi\)
\(618\) 0 0
\(619\) −2.21652e75 −0.933304 −0.466652 − 0.884441i \(-0.654540\pi\)
−0.466652 + 0.884441i \(0.654540\pi\)
\(620\) −4.19987e75 −1.69301
\(621\) 1.96856e76 7.59756
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −1.96115e75 −0.636431
\(626\) 0 0
\(627\) 0 0
\(628\) −7.00233e75 −1.99679
\(629\) 0 0
\(630\) 0 0
\(631\) −2.39877e75 −0.601446 −0.300723 − 0.953712i \(-0.597228\pi\)
−0.300723 + 0.953712i \(0.597228\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 1.15048e76 2.33096
\(637\) 0 0
\(638\) 0 0
\(639\) 3.21815e76 5.74225
\(640\) 0 0
\(641\) 1.01502e76 1.66459 0.832296 − 0.554332i \(-0.187026\pi\)
0.832296 + 0.554332i \(0.187026\pi\)
\(642\) 0 0
\(643\) −1.11292e76 −1.67790 −0.838950 − 0.544208i \(-0.816830\pi\)
−0.838950 + 0.544208i \(0.816830\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −5.61906e75 −0.716553 −0.358276 − 0.933616i \(-0.616635\pi\)
−0.358276 + 0.933616i \(0.616635\pi\)
\(648\) 0 0
\(649\) −1.16845e76 −1.37089
\(650\) 0 0
\(651\) 0 0
\(652\) −8.22603e75 −0.852129
\(653\) −1.87957e76 −1.86811 −0.934056 − 0.357127i \(-0.883757\pi\)
−0.934056 + 0.357127i \(0.883757\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) −2.25922e76 −1.68373
\(661\) −9.19255e75 −0.657653 −0.328826 − 0.944390i \(-0.606653\pi\)
−0.328826 + 0.944390i \(0.606653\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 1.81086e76 0.936226
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(674\) 0 0
\(675\) −2.71235e76 −1.10190
\(676\) 2.56189e76 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
\(683\) −5.47434e76 −1.61798 −0.808989 − 0.587824i \(-0.799985\pi\)
−0.808989 + 0.587824i \(0.799985\pi\)
\(684\) 0 0
\(685\) −4.91182e76 −1.34152
\(686\) 0 0
\(687\) 1.41004e77 3.55959
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) −4.45896e76 −0.962336 −0.481168 − 0.876629i \(-0.659787\pi\)
−0.481168 + 0.876629i \(0.659787\pi\)
\(692\) 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
\(704\) −7.66411e76 −1.00000
\(705\) −1.43522e77 −1.80224
\(706\) 0 0
\(707\) 0 0
\(708\) 2.43505e77 2.72652
\(709\) −1.22373e77 −1.31898 −0.659489 − 0.751714i \(-0.729227\pi\)
−0.659489 + 0.751714i \(0.729227\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −4.21889e77 −3.90643
\(714\) 0 0
\(715\) 0 0
\(716\) −8.24114e75 −0.0681296
\(717\) 0 0
\(718\) 0 0
\(719\) −8.06738e76 −0.595734 −0.297867 − 0.954607i \(-0.596275\pi\)
−0.297867 + 0.954607i \(0.596275\pi\)
\(720\) 3.51796e77 2.50215
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) −1.09674e76 −0.0671679
\(725\) 0 0
\(726\) 0 0
\(727\) −3.02146e77 −1.65496 −0.827481 − 0.561494i \(-0.810227\pi\)
−0.827481 + 0.561494i \(0.810227\pi\)
\(728\) 0 0
\(729\) 1.25688e78 6.39218
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(734\) 0 0
\(735\) 4.13077e77 1.68373
\(736\) 0 0
\(737\) 3.97322e77 1.50494
\(738\) 0 0
\(739\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(740\) 5.97521e76 0.202813
\(741\) 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
\(751\) 1.54754e77 0.352665 0.176333 − 0.984331i \(-0.443577\pi\)
0.176333 + 0.984331i \(0.443577\pi\)
\(752\) −4.86879e77 −1.07038
\(753\) −1.92053e77 −0.407341
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 1.03206e78 1.89721 0.948604 − 0.316467i \(-0.102497\pi\)
0.948604 + 0.316467i \(0.102497\pi\)
\(758\) 0 0
\(759\) −2.26945e78 −3.88502
\(760\) 0 0
\(761\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −1.26198e78 −1.80938
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 1.59720e78 1.98887
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) −2.54165e78 −2.84871
\(772\) 0 0
\(773\) 1.72940e78 1.80738 0.903689 − 0.428190i \(-0.140849\pi\)
0.903689 + 0.428190i \(0.140849\pi\)
\(774\) 0 0
\(775\) 5.81294e77 0.566565
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) −2.45479e78 −1.94284
\(782\) 0 0
\(783\) 0 0
\(784\) 1.40131e78 1.00000
\(785\) −2.45177e78 −1.69044
\(786\) 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
\(795\) 4.02823e78 1.97334
\(796\) −5.71297e77 −0.270526
\(797\) 4.20968e78 1.92697 0.963484 − 0.267766i \(-0.0862855\pi\)
0.963484 + 0.267766i \(0.0862855\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 2.16914e78 0.867379
\(802\) 0 0
\(803\) 0 0
\(804\) −8.28018e78 −2.99314
\(805\) 0 0
\(806\) 0 0
\(807\) −1.07224e79 −3.50514
\(808\) 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
\(815\) −2.88023e78 −0.721393
\(816\) 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
\(823\) −3.06808e78 −0.590297 −0.295149 − 0.955451i \(-0.595369\pi\)
−0.295149 + 0.955451i \(0.595369\pi\)
\(824\) 0 0
\(825\) 3.12694e78 0.563460
\(826\) 0 0
\(827\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(828\) 3.53388e79 5.77342
\(829\) 1.23283e79 1.94954 0.974770 − 0.223212i \(-0.0716541\pi\)
0.974770 + 0.223212i \(0.0716541\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −6.37483e79 −7.77824
\(838\) 0 0
\(839\) 1.07074e79 1.22493 0.612463 − 0.790500i \(-0.290179\pi\)
0.612463 + 0.790500i \(0.290179\pi\)
\(840\) 0 0
\(841\) 9.32163e78 1.00000
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 8.97011e78 0.846578
\(846\) 0 0
\(847\) 0 0
\(848\) 1.36652e79 1.17200
\(849\) 0 0
\(850\) 0 0
\(851\) 6.00226e78 0.467968
\(852\) 5.11578e79 3.86405
\(853\) 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
\(859\) −8.05218e78 −0.487638 −0.243819 − 0.969821i \(-0.578400\pi\)
−0.243819 + 0.969821i \(0.578400\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 1.84383e79 0.984983 0.492492 − 0.870317i \(-0.336086\pi\)
0.492492 + 0.870317i \(0.336086\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 4.21815e79 1.98887
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) −1.43347e80 −5.61053
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) −2.68348e79 −0.846578
\(881\) −5.96981e79 −1.82646 −0.913231 − 0.407441i \(-0.866421\pi\)
−0.913231 + 0.407441i \(0.866421\pi\)
\(882\) 0 0
\(883\) 6.36807e79 1.83261 0.916303 − 0.400486i \(-0.131159\pi\)
0.916303 + 0.400486i \(0.131159\pi\)
\(884\) 0 0
\(885\) 8.52598e79 2.30821
\(886\) 0 0
\(887\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −2.11897e80 −4.78000
\(892\) 2.15093e79 0.470733
\(893\) 0 0
\(894\) 0 0
\(895\) −2.88552e78 −0.0576770
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) −4.86912e79 −0.837342
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −3.84008e78 −0.0568628
\(906\) 0 0
\(907\) −8.79600e79 −1.22712 −0.613562 − 0.789647i \(-0.710264\pi\)
−0.613562 + 0.789647i \(0.710264\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 1.52343e80 1.88723 0.943617 − 0.331040i \(-0.107400\pi\)
0.943617 + 0.331040i \(0.107400\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) 1.67483e80 1.78975
\(917\) 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
\(925\) −8.27014e78 −0.0678713
\(926\) 0 0
\(927\) 2.13874e80 1.65579
\(928\) 0 0
\(929\) 2.41697e80 1.76542 0.882709 − 0.469920i \(-0.155717\pi\)
0.882709 + 0.469920i \(0.155717\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) −6.08327e80 −3.95670
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(938\) 0 0
\(939\) −5.03249e80 −2.75304
\(940\) −1.70474e80 −0.906163
\(941\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 2.89232e80 1.37089
\(945\) 0 0
\(946\) 0 0
\(947\) −2.06629e80 −0.898962 −0.449481 − 0.893290i \(-0.648391\pi\)
−0.449481 + 0.893290i \(0.648391\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 8.14745e80 3.16335
\(952\) 0 0
\(953\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(954\) 0 0
\(955\) −4.41864e80 −1.53178
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 5.59238e80 1.68373
\(961\) 1.02460e81 2.99933
\(962\) 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
\(971\) −8.26308e80 −1.82904 −0.914519 − 0.404544i \(-0.867430\pi\)
−0.914519 + 0.404544i \(0.867430\pi\)
\(972\) 2.60928e81 5.61735
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −5.61874e80 −1.05314 −0.526570 − 0.850132i \(-0.676522\pi\)
−0.526570 + 0.850132i \(0.676522\pi\)
\(978\) 0 0
\(979\) −1.65461e80 −0.293469
\(980\) 4.90649e80 0.846578
\(981\) 0 0
\(982\) 0 0
\(983\) −6.52398e80 −1.03650 −0.518248 − 0.855230i \(-0.673416\pi\)
−0.518248 + 0.855230i \(0.673416\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) −2.76408e80 −0.352827 −0.176414 − 0.984316i \(-0.556450\pi\)
−0.176414 + 0.984316i \(0.556450\pi\)
\(992\) 0 0
\(993\) −2.40471e81 −2.90692
\(994\) 0 0
\(995\) −2.00032e80 −0.229021
\(996\) 0 0
\(997\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(998\) 0 0
\(999\) 9.06955e80 0.931788
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 11.55.b.a.10.1 ✓ 1
11.10 odd 2 CM 11.55.b.a.10.1 ✓ 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
11.55.b.a.10.1 ✓ 1 1.1 even 1 trivial
11.55.b.a.10.1 ✓ 1 11.10 odd 2 CM