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Properties

Label 8.5.d.a.3.1
Level $8$
Weight $5$
Character 8.3
Self dual yes
Analytic conductor $0.827$
Analytic rank $0$
Dimension $1$
CM discriminant -8
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] = [8,5,Mod(3,8)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("8.3");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8 = 2^{3} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 8.d (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: \(0.826959704671\)
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 3.1
Character \(\chi\) \(=\) 8.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+4.00000 q^{2} -14.0000 q^{3} +16.0000 q^{4} -56.0000 q^{6} +64.0000 q^{8} +115.000 q^{9} +O(q^{10})\) \(q+4.00000 q^{2} -14.0000 q^{3} +16.0000 q^{4} -56.0000 q^{6} +64.0000 q^{8} +115.000 q^{9} -46.0000 q^{11} -224.000 q^{12} +256.000 q^{16} -574.000 q^{17} +460.000 q^{18} +434.000 q^{19} -184.000 q^{22} -896.000 q^{24} +625.000 q^{25} -476.000 q^{27} +1024.00 q^{32} +644.000 q^{33} -2296.00 q^{34} +1840.00 q^{36} +1736.00 q^{38} -1246.00 q^{41} -3502.00 q^{43} -736.000 q^{44} -3584.00 q^{48} +2401.00 q^{49} +2500.00 q^{50} +8036.00 q^{51} -1904.00 q^{54} -6076.00 q^{57} -238.000 q^{59} +4096.00 q^{64} +2576.00 q^{66} -5134.00 q^{67} -9184.00 q^{68} +7360.00 q^{72} +9506.00 q^{73} -8750.00 q^{75} +6944.00 q^{76} -2651.00 q^{81} -4984.00 q^{82} +11186.0 q^{83} -14008.0 q^{86} -2944.00 q^{88} +5474.00 q^{89} -14336.0 q^{96} -9982.00 q^{97} +9604.00 q^{98} -5290.00 q^{99} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/8\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(7\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.00000 1.00000
\(3\) −14.0000 −1.55556 −0.777778 − 0.628539i \(-0.783653\pi\)
−0.777778 + 0.628539i \(0.783653\pi\)
\(4\) 16.0000 1.00000
\(5\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(6\) −56.0000 −1.55556
\(7\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(8\) 64.0000 1.00000
\(9\) 115.000 1.41975
\(10\) 0 0
\(11\) −46.0000 −0.380165 −0.190083 − 0.981768i \(-0.560876\pi\)
−0.190083 + 0.981768i \(0.560876\pi\)
\(12\) −224.000 −1.55556
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 256.000 1.00000
\(17\) −574.000 −1.98616 −0.993080 − 0.117443i \(-0.962530\pi\)
−0.993080 + 0.117443i \(0.962530\pi\)
\(18\) 460.000 1.41975
\(19\) 434.000 1.20222 0.601108 − 0.799168i \(-0.294726\pi\)
0.601108 + 0.799168i \(0.294726\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −184.000 −0.380165
\(23\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(24\) −896.000 −1.55556
\(25\) 625.000 1.00000
\(26\) 0 0
\(27\) −476.000 −0.652949
\(28\) 0 0
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(32\) 1024.00 1.00000
\(33\) 644.000 0.591368
\(34\) −2296.00 −1.98616
\(35\) 0 0
\(36\) 1840.00 1.41975
\(37\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(38\) 1736.00 1.20222
\(39\) 0 0
\(40\) 0 0
\(41\) −1246.00 −0.741225 −0.370613 − 0.928787i \(-0.620852\pi\)
−0.370613 + 0.928787i \(0.620852\pi\)
\(42\) 0 0
\(43\) −3502.00 −1.89400 −0.946998 − 0.321238i \(-0.895901\pi\)
−0.946998 + 0.321238i \(0.895901\pi\)
\(44\) −736.000 −0.380165
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(48\) −3584.00 −1.55556
\(49\) 2401.00 1.00000
\(50\) 2500.00 1.00000
\(51\) 8036.00 3.08958
\(52\) 0 0
\(53\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(54\) −1904.00 −0.652949
\(55\) 0 0
\(56\) 0 0
\(57\) −6076.00 −1.87011
\(58\) 0 0
\(59\) −238.000 −0.0683712 −0.0341856 − 0.999416i \(-0.510884\pi\)
−0.0341856 + 0.999416i \(0.510884\pi\)
\(60\) 0 0
\(61\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 4096.00 1.00000
\(65\) 0 0
\(66\) 2576.00 0.591368
\(67\) −5134.00 −1.14368 −0.571842 − 0.820364i \(-0.693771\pi\)
−0.571842 + 0.820364i \(0.693771\pi\)
\(68\) −9184.00 −1.98616
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 7360.00 1.41975
\(73\) 9506.00 1.78382 0.891912 − 0.452209i \(-0.149364\pi\)
0.891912 + 0.452209i \(0.149364\pi\)
\(74\) 0 0
\(75\) −8750.00 −1.55556
\(76\) 6944.00 1.20222
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(80\) 0 0
\(81\) −2651.00 −0.404054
\(82\) −4984.00 −0.741225
\(83\) 11186.0 1.62375 0.811874 − 0.583833i \(-0.198448\pi\)
0.811874 + 0.583833i \(0.198448\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −14008.0 −1.89400
\(87\) 0 0
\(88\) −2944.00 −0.380165
\(89\) 5474.00 0.691074 0.345537 − 0.938405i \(-0.387697\pi\)
0.345537 + 0.938405i \(0.387697\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) −14336.0 −1.55556
\(97\) −9982.00 −1.06090 −0.530450 − 0.847716i \(-0.677977\pi\)
−0.530450 + 0.847716i \(0.677977\pi\)
\(98\) 9604.00 1.00000
\(99\) −5290.00 −0.539741
\(100\) 10000.0 1.00000
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) 32144.0 3.08958
\(103\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 8786.00 0.767403 0.383702 − 0.923457i \(-0.374649\pi\)
0.383702 + 0.923457i \(0.374649\pi\)
\(108\) −7616.00 −0.652949
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −15934.0 −1.24787 −0.623933 − 0.781478i \(-0.714466\pi\)
−0.623933 + 0.781478i \(0.714466\pi\)
\(114\) −24304.0 −1.87011
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) −952.000 −0.0683712
\(119\) 0 0
\(120\) 0 0
\(121\) −12525.0 −0.855474
\(122\) 0 0
\(123\) 17444.0 1.15302
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(128\) 16384.0 1.00000
\(129\) 49028.0 2.94622
\(130\) 0 0
\(131\) −30478.0 −1.77600 −0.888002 − 0.459840i \(-0.847907\pi\)
−0.888002 + 0.459840i \(0.847907\pi\)
\(132\) 10304.0 0.591368
\(133\) 0 0
\(134\) −20536.0 −1.14368
\(135\) 0 0
\(136\) −36736.0 −1.98616
\(137\) 19106.0 1.01796 0.508978 − 0.860780i \(-0.330024\pi\)
0.508978 + 0.860780i \(0.330024\pi\)
\(138\) 0 0
\(139\) 3794.00 0.196367 0.0981833 − 0.995168i \(-0.468697\pi\)
0.0981833 + 0.995168i \(0.468697\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 29440.0 1.41975
\(145\) 0 0
\(146\) 38024.0 1.78382
\(147\) −33614.0 −1.55556
\(148\) 0 0
\(149\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(150\) −35000.0 −1.55556
\(151\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(152\) 27776.0 1.20222
\(153\) −66010.0 −2.81986
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) −10604.0 −0.404054
\(163\) 50546.0 1.90244 0.951221 − 0.308509i \(-0.0998301\pi\)
0.951221 + 0.308509i \(0.0998301\pi\)
\(164\) −19936.0 −0.741225
\(165\) 0 0
\(166\) 44744.0 1.62375
\(167\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(168\) 0 0
\(169\) 28561.0 1.00000
\(170\) 0 0
\(171\) 49910.0 1.70685
\(172\) −56032.0 −1.89400
\(173\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −11776.0 −0.380165
\(177\) 3332.00 0.106355
\(178\) 21896.0 0.691074
\(179\) −62926.0 −1.96392 −0.981961 − 0.189086i \(-0.939448\pi\)
−0.981961 + 0.189086i \(0.939448\pi\)
\(180\) 0 0
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 26404.0 0.755069
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(192\) −57344.0 −1.55556
\(193\) −64894.0 −1.74217 −0.871084 − 0.491134i \(-0.836582\pi\)
−0.871084 + 0.491134i \(0.836582\pi\)
\(194\) −39928.0 −1.06090
\(195\) 0 0
\(196\) 38416.0 1.00000
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) −21160.0 −0.539741
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) 40000.0 1.00000
\(201\) 71876.0 1.77906
\(202\) 0 0
\(203\) 0 0
\(204\) 128576. 3.08958
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −19964.0 −0.457041
\(210\) 0 0
\(211\) −37966.0 −0.852766 −0.426383 − 0.904543i \(-0.640212\pi\)
−0.426383 + 0.904543i \(0.640212\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 35144.0 0.767403
\(215\) 0 0
\(216\) −30464.0 −0.652949
\(217\) 0 0
\(218\) 0 0
\(219\) −133084. −2.77484
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(224\) 0 0
\(225\) 71875.0 1.41975
\(226\) −63736.0 −1.24787
\(227\) 95858.0 1.86027 0.930136 − 0.367214i \(-0.119688\pi\)
0.930136 + 0.367214i \(0.119688\pi\)
\(228\) −97216.0 −1.87011
\(229\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 79778.0 1.46951 0.734753 − 0.678335i \(-0.237298\pi\)
0.734753 + 0.678335i \(0.237298\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −3808.00 −0.0683712
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 0 0
\(241\) −78526.0 −1.35201 −0.676004 − 0.736898i \(-0.736290\pi\)
−0.676004 + 0.736898i \(0.736290\pi\)
\(242\) −50100.0 −0.855474
\(243\) 75670.0 1.28148
\(244\) 0 0
\(245\) 0 0
\(246\) 69776.0 1.15302
\(247\) 0 0
\(248\) 0 0
\(249\) −156604. −2.52583
\(250\) 0 0
\(251\) 91154.0 1.44687 0.723433 − 0.690395i \(-0.242563\pi\)
0.723433 + 0.690395i \(0.242563\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 65536.0 1.00000
\(257\) 16898.0 0.255840 0.127920 − 0.991784i \(-0.459170\pi\)
0.127920 + 0.991784i \(0.459170\pi\)
\(258\) 196112. 2.94622
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) −121912. −1.77600
\(263\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(264\) 41216.0 0.591368
\(265\) 0 0
\(266\) 0 0
\(267\) −76636.0 −1.07500
\(268\) −82144.0 −1.14368
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) −146944. −1.98616
\(273\) 0 0
\(274\) 76424.0 1.01796
\(275\) −28750.0 −0.380165
\(276\) 0 0
\(277\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(278\) 15176.0 0.196367
\(279\) 0 0
\(280\) 0 0
\(281\) −101278. −1.28263 −0.641317 − 0.767276i \(-0.721611\pi\)
−0.641317 + 0.767276i \(0.721611\pi\)
\(282\) 0 0
\(283\) −153454. −1.91604 −0.958022 − 0.286696i \(-0.907443\pi\)
−0.958022 + 0.286696i \(0.907443\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 117760. 1.41975
\(289\) 245955. 2.94483
\(290\) 0 0
\(291\) 139748. 1.65029
\(292\) 152096. 1.78382
\(293\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(294\) −134456. −1.55556
\(295\) 0 0
\(296\) 0 0
\(297\) 21896.0 0.248229
\(298\) 0 0
\(299\) 0 0
\(300\) −140000. −1.55556
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 111104. 1.20222
\(305\) 0 0
\(306\) −264040. −2.81986
\(307\) 105266. 1.11689 0.558446 − 0.829541i \(-0.311398\pi\)
0.558446 + 0.829541i \(0.311398\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(312\) 0 0
\(313\) 80738.0 0.824118 0.412059 − 0.911157i \(-0.364810\pi\)
0.412059 + 0.911157i \(0.364810\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) −123004. −1.19374
\(322\) 0 0
\(323\) −249116. −2.38779
\(324\) −42416.0 −0.404054
\(325\) 0 0
\(326\) 202184. 1.90244
\(327\) 0 0
\(328\) −79744.0 −0.741225
\(329\) 0 0
\(330\) 0 0
\(331\) −218926. −1.99821 −0.999106 − 0.0422866i \(-0.986536\pi\)
−0.999106 + 0.0422866i \(0.986536\pi\)
\(332\) 178976. 1.62375
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 1346.00 0.0118518 0.00592591 − 0.999982i \(-0.498114\pi\)
0.00592591 + 0.999982i \(0.498114\pi\)
\(338\) 114244. 1.00000
\(339\) 223076. 1.94112
\(340\) 0 0
\(341\) 0 0
\(342\) 199640. 1.70685
\(343\) 0 0
\(344\) −224128. −1.89400
\(345\) 0 0
\(346\) 0 0
\(347\) 192146. 1.59578 0.797889 − 0.602805i \(-0.205950\pi\)
0.797889 + 0.602805i \(0.205950\pi\)
\(348\) 0 0
\(349\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −47104.0 −0.380165
\(353\) −211582. −1.69797 −0.848984 − 0.528419i \(-0.822785\pi\)
−0.848984 + 0.528419i \(0.822785\pi\)
\(354\) 13328.0 0.106355
\(355\) 0 0
\(356\) 87584.0 0.691074
\(357\) 0 0
\(358\) −251704. −1.96392
\(359\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(360\) 0 0
\(361\) 58035.0 0.445323
\(362\) 0 0
\(363\) 175350. 1.33074
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(368\) 0 0
\(369\) −143290. −1.05236
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) 105616. 0.755069
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 183314. 1.27620 0.638098 − 0.769955i \(-0.279722\pi\)
0.638098 + 0.769955i \(0.279722\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(384\) −229376. −1.55556
\(385\) 0 0
\(386\) −259576. −1.74217
\(387\) −402730. −2.68901
\(388\) −159712. −1.06090
\(389\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 153664. 1.00000
\(393\) 426692. 2.76267
\(394\) 0 0
\(395\) 0 0
\(396\) −84640.0 −0.539741
\(397\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 160000. 1.00000
\(401\) 265154. 1.64896 0.824479 − 0.565893i \(-0.191468\pi\)
0.824479 + 0.565893i \(0.191468\pi\)
\(402\) 287504. 1.77906
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 514304. 3.08958
\(409\) −223006. −1.33312 −0.666561 − 0.745450i \(-0.732234\pi\)
−0.666561 + 0.745450i \(0.732234\pi\)
\(410\) 0 0
\(411\) −267484. −1.58349
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −53116.0 −0.305459
\(418\) −79856.0 −0.457041
\(419\) −86926.0 −0.495133 −0.247566 − 0.968871i \(-0.579631\pi\)
−0.247566 + 0.968871i \(0.579631\pi\)
\(420\) 0 0
\(421\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(422\) −151864. −0.852766
\(423\) 0 0
\(424\) 0 0
\(425\) −358750. −1.98616
\(426\) 0 0
\(427\) 0 0
\(428\) 140576. 0.767403
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) −121856. −0.652949
\(433\) −40894.0 −0.218114 −0.109057 − 0.994035i \(-0.534783\pi\)
−0.109057 + 0.994035i \(0.534783\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) −532336. −2.77484
\(439\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(440\) 0 0
\(441\) 276115. 1.41975
\(442\) 0 0
\(443\) 378386. 1.92809 0.964046 − 0.265737i \(-0.0856151\pi\)
0.964046 + 0.265737i \(0.0856151\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 346754. 1.72000 0.860001 − 0.510293i \(-0.170463\pi\)
0.860001 + 0.510293i \(0.170463\pi\)
\(450\) 287500. 1.41975
\(451\) 57316.0 0.281788
\(452\) −254944. −1.24787
\(453\) 0 0
\(454\) 383432. 1.86027
\(455\) 0 0
\(456\) −388864. −1.87011
\(457\) −361054. −1.72878 −0.864390 − 0.502822i \(-0.832295\pi\)
−0.864390 + 0.502822i \(0.832295\pi\)
\(458\) 0 0
\(459\) 273224. 1.29686
\(460\) 0 0
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 319112. 1.46951
\(467\) −435022. −1.99470 −0.997350 − 0.0727569i \(-0.976820\pi\)
−0.997350 + 0.0727569i \(0.976820\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) −15232.0 −0.0683712
\(473\) 161092. 0.720032
\(474\) 0 0
\(475\) 271250. 1.20222
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) −314104. −1.35201
\(483\) 0 0
\(484\) −200400. −0.855474
\(485\) 0 0
\(486\) 302680. 1.28148
\(487\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(488\) 0 0
\(489\) −707644. −2.95936
\(490\) 0 0
\(491\) 129362. 0.536591 0.268296 − 0.963337i \(-0.413540\pi\)
0.268296 + 0.963337i \(0.413540\pi\)
\(492\) 279104. 1.15302
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) −626416. −2.52583
\(499\) 145202. 0.583138 0.291569 − 0.956550i \(-0.405823\pi\)
0.291569 + 0.956550i \(0.405823\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 364616. 1.44687
\(503\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −399854. −1.55556
\(508\) 0 0
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 262144. 1.00000
\(513\) −206584. −0.784986
\(514\) 67592.0 0.255840
\(515\) 0 0
\(516\) 784448. 2.94622
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 469154. 1.72838 0.864191 − 0.503163i \(-0.167830\pi\)
0.864191 + 0.503163i \(0.167830\pi\)
\(522\) 0 0
\(523\) −388654. −1.42089 −0.710444 − 0.703754i \(-0.751506\pi\)
−0.710444 + 0.703754i \(0.751506\pi\)
\(524\) −487648. −1.77600
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 164864. 0.591368
\(529\) 279841. 1.00000
\(530\) 0 0
\(531\) −27370.0 −0.0970702
\(532\) 0 0
\(533\) 0 0
\(534\) −306544. −1.07500
\(535\) 0 0
\(536\) −328576. −1.14368
\(537\) 880964. 3.05499
\(538\) 0 0
\(539\) −110446. −0.380165
\(540\) 0 0
\(541\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) −587776. −1.98616
\(545\) 0 0
\(546\) 0 0
\(547\) 446066. 1.49082 0.745409 − 0.666608i \(-0.232254\pi\)
0.745409 + 0.666608i \(0.232254\pi\)
\(548\) 305696. 1.01796
\(549\) 0 0
\(550\) −115000. −0.380165
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 60704.0 0.196367
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) −369656. −1.17455
\(562\) −405112. −1.28263
\(563\) −582862. −1.83886 −0.919431 − 0.393252i \(-0.871350\pi\)
−0.919431 + 0.393252i \(0.871350\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −613816. −1.91604
\(567\) 0 0
\(568\) 0 0
\(569\) −255646. −0.789613 −0.394807 − 0.918764i \(-0.629188\pi\)
−0.394807 + 0.918764i \(0.629188\pi\)
\(570\) 0 0
\(571\) −219118. −0.672057 −0.336028 − 0.941852i \(-0.609084\pi\)
−0.336028 + 0.941852i \(0.609084\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 471040. 1.41975
\(577\) −665854. −1.99999 −0.999994 − 0.00346620i \(-0.998897\pi\)
−0.999994 + 0.00346620i \(0.998897\pi\)
\(578\) 983820. 2.94483
\(579\) 908516. 2.71004
\(580\) 0 0
\(581\) 0 0
\(582\) 558992. 1.65029
\(583\) 0 0
\(584\) 608384. 1.78382
\(585\) 0 0
\(586\) 0 0
\(587\) 605906. 1.75845 0.879223 − 0.476410i \(-0.158062\pi\)
0.879223 + 0.476410i \(0.158062\pi\)
\(588\) −537824. −1.55556
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 39746.0 0.113027 0.0565137 − 0.998402i \(-0.482002\pi\)
0.0565137 + 0.998402i \(0.482002\pi\)
\(594\) 87584.0 0.248229
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(600\) −560000. −1.55556
\(601\) 112994. 0.312829 0.156414 − 0.987692i \(-0.450007\pi\)
0.156414 + 0.987692i \(0.450007\pi\)
\(602\) 0 0
\(603\) −590410. −1.62375
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(608\) 444416. 1.20222
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) −1.05616e6 −2.81986
\(613\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(614\) 421064. 1.11689
\(615\) 0 0
\(616\) 0 0
\(617\) −649822. −1.70696 −0.853481 − 0.521123i \(-0.825513\pi\)
−0.853481 + 0.521123i \(0.825513\pi\)
\(618\) 0 0
\(619\) −450478. −1.17569 −0.587844 − 0.808974i \(-0.700023\pi\)
−0.587844 + 0.808974i \(0.700023\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 390625. 1.00000
\(626\) 322952. 0.824118
\(627\) 279496. 0.710952
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(632\) 0 0
\(633\) 531524. 1.32653
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −589438. −1.43457 −0.717286 − 0.696779i \(-0.754616\pi\)
−0.717286 + 0.696779i \(0.754616\pi\)
\(642\) −492016. −1.19374
\(643\) 646898. 1.56464 0.782319 − 0.622878i \(-0.214037\pi\)
0.782319 + 0.622878i \(0.214037\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −996464. −2.38779
\(647\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(648\) −169664. −0.404054
\(649\) 10948.0 0.0259923
\(650\) 0 0
\(651\) 0 0
\(652\) 808736. 1.90244
\(653\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −318976. −0.741225
\(657\) 1.09319e6 2.53259
\(658\) 0 0
\(659\) 119474. 0.275108 0.137554 − 0.990494i \(-0.456076\pi\)
0.137554 + 0.990494i \(0.456076\pi\)
\(660\) 0 0
\(661\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(662\) −875704. −1.99821
\(663\) 0 0
\(664\) 715904. 1.62375
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 646658. 1.42772 0.713862 − 0.700286i \(-0.246944\pi\)
0.713862 + 0.700286i \(0.246944\pi\)
\(674\) 5384.00 0.0118518
\(675\) −297500. −0.652949
\(676\) 456976. 1.00000
\(677\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(678\) 892304. 1.94112
\(679\) 0 0
\(680\) 0 0
\(681\) −1.34201e6 −2.89376
\(682\) 0 0
\(683\) −774574. −1.66043 −0.830217 − 0.557441i \(-0.811783\pi\)
−0.830217 + 0.557441i \(0.811783\pi\)
\(684\) 798560. 1.70685
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) −896512. −1.89400
\(689\) 0 0
\(690\) 0 0
\(691\) −416206. −0.871670 −0.435835 − 0.900027i \(-0.643547\pi\)
−0.435835 + 0.900027i \(0.643547\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 768584. 1.59578
\(695\) 0 0
\(696\) 0 0
\(697\) 715204. 1.47219
\(698\) 0 0
\(699\) −1.11689e6 −2.28590
\(700\) 0 0
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) −188416. −0.380165
\(705\) 0 0
\(706\) −846328. −1.69797
\(707\) 0 0
\(708\) 53312.0 0.106355
\(709\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 350336. 0.691074
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) −1.00682e6 −1.96392
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 232140. 0.445323
\(723\) 1.09936e6 2.10312
\(724\) 0 0
\(725\) 0 0
\(726\) 701400. 1.33074
\(727\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(728\) 0 0
\(729\) −844649. −1.58936
\(730\) 0 0
\(731\) 2.01015e6 3.76178
\(732\) 0 0
\(733\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 236164. 0.434789
\(738\) −573160. −1.05236
\(739\) −988558. −1.81014 −0.905072 − 0.425258i \(-0.860183\pi\)
−0.905072 + 0.425258i \(0.860183\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 1.28639e6 2.30532
\(748\) 422464. 0.755069
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(752\) 0 0
\(753\) −1.27616e6 −2.25068
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(758\) 733256. 1.27620
\(759\) 0 0
\(760\) 0 0
\(761\) 784994. 1.35549 0.677746 − 0.735296i \(-0.262957\pi\)
0.677746 + 0.735296i \(0.262957\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) −917504. −1.55556
\(769\) −71806.0 −0.121425 −0.0607125 − 0.998155i \(-0.519337\pi\)
−0.0607125 + 0.998155i \(0.519337\pi\)
\(770\) 0 0
\(771\) −236572. −0.397974
\(772\) −1.03830e6 −1.74217
\(773\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(774\) −1.61092e6 −2.68901
\(775\) 0 0
\(776\) −638848. −1.06090
\(777\) 0 0
\(778\) 0 0
\(779\) −540764. −0.891113
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 614656. 1.00000
\(785\) 0 0
\(786\) 1.70677e6 2.76267
\(787\) −381262. −0.615565 −0.307783 − 0.951457i \(-0.599587\pi\)
−0.307783 + 0.951457i \(0.599587\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) −338560. −0.539741
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 640000. 1.00000
\(801\) 629510. 0.981155
\(802\) 1.06062e6 1.64896
\(803\) −437276. −0.678148
\(804\) 1.15002e6 1.77906
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 1.19376e6 1.82398 0.911991 − 0.410209i \(-0.134544\pi\)
0.911991 + 0.410209i \(0.134544\pi\)
\(810\) 0 0
\(811\) −1.28376e6 −1.95183 −0.975914 − 0.218156i \(-0.929996\pi\)
−0.975914 + 0.218156i \(0.929996\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 2.05722e6 3.08958
\(817\) −1.51987e6 −2.27699
\(818\) −892024. −1.33312
\(819\) 0 0
\(820\) 0 0
\(821\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(822\) −1.06994e6 −1.58349
\(823\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(824\) 0 0
\(825\) 402500. 0.591368
\(826\) 0 0
\(827\) 224786. 0.328669 0.164334 − 0.986405i \(-0.447452\pi\)
0.164334 + 0.986405i \(0.447452\pi\)
\(828\) 0 0
\(829\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −1.37817e6 −1.98616
\(834\) −212464. −0.305459
\(835\) 0 0
\(836\) −319424. −0.457041
\(837\) 0 0
\(838\) −347704. −0.495133
\(839\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(840\) 0 0
\(841\) 707281. 1.00000
\(842\) 0 0
\(843\) 1.41789e6 1.99521
\(844\) −607456. −0.852766
\(845\) 0 0
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 2.14836e6 2.98051
\(850\) −1.43500e6 −1.98616
\(851\) 0 0
\(852\) 0 0
\(853\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 562304. 0.767403
\(857\) −24094.0 −0.0328055 −0.0164028 − 0.999865i \(-0.505221\pi\)
−0.0164028 + 0.999865i \(0.505221\pi\)
\(858\) 0 0
\(859\) 1.23355e6 1.67175 0.835876 − 0.548918i \(-0.184960\pi\)
0.835876 + 0.548918i \(0.184960\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(864\) −487424. −0.652949
\(865\) 0 0
\(866\) −163576. −0.218114
\(867\) −3.44337e6 −4.58084
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) −1.14793e6 −1.50621
\(874\) 0 0
\(875\) 0 0
\(876\) −2.12934e6 −2.77484
\(877\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 515522. 0.664195 0.332097 − 0.943245i \(-0.392244\pi\)
0.332097 + 0.943245i \(0.392244\pi\)
\(882\) 1.10446e6 1.41975
\(883\) 1.54527e6 1.98190 0.990950 − 0.134230i \(-0.0428560\pi\)
0.990950 + 0.134230i \(0.0428560\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 1.51354e6 1.92809
\(887\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 121946. 0.153607
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 1.38702e6 1.72000
\(899\) 0 0
\(900\) 1.15000e6 1.41975
\(901\) 0 0
\(902\) 229264. 0.281788
\(903\) 0 0
\(904\) −1.01978e6 −1.24787
\(905\) 0 0
\(906\) 0 0
\(907\) 1.29250e6 1.57114 0.785571 − 0.618772i \(-0.212369\pi\)
0.785571 + 0.618772i \(0.212369\pi\)
\(908\) 1.53373e6 1.86027
\(909\) 0 0
\(910\) 0 0
\(911\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(912\) −1.55546e6 −1.87011
\(913\) −514556. −0.617293
\(914\) −1.44422e6 −1.72878
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 1.09290e6 1.29686
\(919\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(920\) 0 0
\(921\) −1.47372e6 −1.73739
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −606718. −0.703000 −0.351500 − 0.936188i \(-0.614328\pi\)
−0.351500 + 0.936188i \(0.614328\pi\)
\(930\) 0 0
\(931\) 1.04203e6 1.20222
\(932\) 1.27645e6 1.46951
\(933\) 0 0
\(934\) −1.74009e6 −1.99470
\(935\) 0 0
\(936\) 0 0
\(937\) −1.24041e6 −1.41282 −0.706411 − 0.707802i \(-0.749687\pi\)
−0.706411 + 0.707802i \(0.749687\pi\)
\(938\) 0 0
\(939\) −1.13033e6 −1.28196
\(940\) 0 0
\(941\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) −60928.0 −0.0683712
\(945\) 0 0
\(946\) 644368. 0.720032
\(947\) −805582. −0.898276 −0.449138 − 0.893462i \(-0.648269\pi\)
−0.449138 + 0.893462i \(0.648269\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 1.08500e6 1.20222
\(951\) 0 0
\(952\) 0 0
\(953\) −1.79625e6 −1.97780 −0.988899 − 0.148589i \(-0.952527\pi\)
−0.988899 + 0.148589i \(0.952527\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 923521. 1.00000
\(962\) 0 0
\(963\) 1.01039e6 1.08952
\(964\) −1.25642e6 −1.35201
\(965\) 0 0
\(966\) 0 0
\(967\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(968\) −801600. −0.855474
\(969\) 3.48762e6 3.71434
\(970\) 0 0
\(971\) −937006. −0.993811 −0.496906 − 0.867805i \(-0.665530\pi\)
−0.496906 + 0.867805i \(0.665530\pi\)
\(972\) 1.21072e6 1.28148
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 1.76967e6 1.85397 0.926984 − 0.375101i \(-0.122392\pi\)
0.926984 + 0.375101i \(0.122392\pi\)
\(978\) −2.83058e6 −2.95936
\(979\) −251804. −0.262722
\(980\) 0 0
\(981\) 0 0
\(982\) 517448. 0.536591
\(983\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(984\) 1.11642e6 1.15302
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(992\) 0 0
\(993\) 3.06496e6 3.10833
\(994\) 0 0
\(995\) 0 0
\(996\) −2.50566e6 −2.52583
\(997\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(998\) 580808. 0.583138
\(999\) 0 0
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 8.5.d.a.3.1 ✓ 1
3.2 odd 2 72.5.b.a.19.1 1
4.3 odd 2 32.5.d.a.15.1 1
5.2 odd 4 200.5.e.a.99.2 2
5.3 odd 4 200.5.e.a.99.1 2
5.4 even 2 200.5.g.a.51.1 1
8.3 odd 2 CM 8.5.d.a.3.1 ✓ 1
8.5 even 2 32.5.d.a.15.1 1
12.11 even 2 288.5.b.a.271.1 1
16.3 odd 4 256.5.c.d.255.2 2
16.5 even 4 256.5.c.d.255.2 2
16.11 odd 4 256.5.c.d.255.1 2
16.13 even 4 256.5.c.d.255.1 2
20.3 even 4 800.5.e.a.399.2 2
20.7 even 4 800.5.e.a.399.1 2
20.19 odd 2 800.5.g.a.751.1 1
24.5 odd 2 288.5.b.a.271.1 1
24.11 even 2 72.5.b.a.19.1 1
40.3 even 4 200.5.e.a.99.1 2
40.13 odd 4 800.5.e.a.399.2 2
40.19 odd 2 200.5.g.a.51.1 1
40.27 even 4 200.5.e.a.99.2 2
40.29 even 2 800.5.g.a.751.1 1
40.37 odd 4 800.5.e.a.399.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8.5.d.a.3.1 ✓ 1 1.1 even 1 trivial
8.5.d.a.3.1 ✓ 1 8.3 odd 2 CM
32.5.d.a.15.1 1 4.3 odd 2
32.5.d.a.15.1 1 8.5 even 2
72.5.b.a.19.1 1 3.2 odd 2
72.5.b.a.19.1 1 24.11 even 2
200.5.e.a.99.1 2 5.3 odd 4
200.5.e.a.99.1 2 40.3 even 4
200.5.e.a.99.2 2 5.2 odd 4
200.5.e.a.99.2 2 40.27 even 4
200.5.g.a.51.1 1 5.4 even 2
200.5.g.a.51.1 1 40.19 odd 2
256.5.c.d.255.1 2 16.11 odd 4
256.5.c.d.255.1 2 16.13 even 4
256.5.c.d.255.2 2 16.3 odd 4
256.5.c.d.255.2 2 16.5 even 4
288.5.b.a.271.1 1 12.11 even 2
288.5.b.a.271.1 1 24.5 odd 2
800.5.e.a.399.1 2 20.7 even 4
800.5.e.a.399.1 2 40.37 odd 4
800.5.e.a.399.2 2 20.3 even 4
800.5.e.a.399.2 2 40.13 odd 4
800.5.g.a.751.1 1 20.19 odd 2
800.5.g.a.751.1 1 40.29 even 2