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Properties

Label 4928.2.a.bb.1.1
Level $4928$
Weight $2$
Character 4928.1
Self dual yes
Analytic conductor $39.350$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [4928,2,Mod(1,4928)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4928, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("4928.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4928 = 2^{6} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4928.a (trivial)

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: \(39.3502781161\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 2464)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 4928.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{3} +3.00000 q^{5} -1.00000 q^{7} -2.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{3} +3.00000 q^{5} -1.00000 q^{7} -2.00000 q^{9} +1.00000 q^{11} -6.00000 q^{13} +3.00000 q^{15} -6.00000 q^{19} -1.00000 q^{21} +3.00000 q^{23} +4.00000 q^{25} -5.00000 q^{27} +3.00000 q^{31} +1.00000 q^{33} -3.00000 q^{35} +1.00000 q^{37} -6.00000 q^{39} -10.0000 q^{41} -2.00000 q^{43} -6.00000 q^{45} -12.0000 q^{47} +1.00000 q^{49} +6.00000 q^{53} +3.00000 q^{55} -6.00000 q^{57} +11.0000 q^{59} -4.00000 q^{61} +2.00000 q^{63} -18.0000 q^{65} +7.00000 q^{67} +3.00000 q^{69} +13.0000 q^{71} -14.0000 q^{73} +4.00000 q^{75} -1.00000 q^{77} +2.00000 q^{79} +1.00000 q^{81} -14.0000 q^{83} -17.0000 q^{89} +6.00000 q^{91} +3.00000 q^{93} -18.0000 q^{95} -15.0000 q^{97} -2.00000 q^{99} +O(q^{100})\)

Display 100 coefficients 10 coefficients

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
\(3\) 1.00000 0.577350 0.288675 − 0.957427i \(-0.406785\pi\)
0.288675 + 0.957427i \(0.406785\pi\)
\(4\) 0 0
\(5\) 3.00000 1.34164 0.670820 − 0.741620i \(-0.265942\pi\)
0.670820 + 0.741620i \(0.265942\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) −2.00000 −0.666667
\(10\) 0 0
\(11\) 1.00000 0.301511
\(12\) 0 0
\(13\) −6.00000 −1.66410 −0.832050 − 0.554700i \(-0.812833\pi\)
−0.832050 + 0.554700i \(0.812833\pi\)
\(14\) 0 0
\(15\) 3.00000 0.774597
\(16\) 0 0
\(17\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(18\) 0 0
\(19\) −6.00000 −1.37649 −0.688247 − 0.725476i \(-0.741620\pi\)
−0.688247 + 0.725476i \(0.741620\pi\)
\(20\) 0 0
\(21\) −1.00000 −0.218218
\(22\) 0 0
\(23\) 3.00000 0.625543 0.312772 − 0.949828i \(-0.398743\pi\)
0.312772 + 0.949828i \(0.398743\pi\)
\(24\) 0 0
\(25\) 4.00000 0.800000
\(26\) 0 0
\(27\) −5.00000 −0.962250
\(28\) 0 0
\(29\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 0 0
\(31\) 3.00000 0.538816 0.269408 − 0.963026i \(-0.413172\pi\)
0.269408 + 0.963026i \(0.413172\pi\)
\(32\) 0 0
\(33\) 1.00000 0.174078
\(34\) 0 0
\(35\) −3.00000 −0.507093
\(36\) 0 0
\(37\) 1.00000 0.164399 0.0821995 − 0.996616i \(-0.473806\pi\)
0.0821995 + 0.996616i \(0.473806\pi\)
\(38\) 0 0
\(39\) −6.00000 −0.960769
\(40\) 0 0
\(41\) −10.0000 −1.56174 −0.780869 − 0.624695i \(-0.785223\pi\)
−0.780869 + 0.624695i \(0.785223\pi\)
\(42\) 0 0
\(43\) −2.00000 −0.304997 −0.152499 − 0.988304i \(-0.548732\pi\)
−0.152499 + 0.988304i \(0.548732\pi\)
\(44\) 0 0
\(45\) −6.00000 −0.894427
\(46\) 0 0
\(47\) −12.0000 −1.75038 −0.875190 − 0.483779i \(-0.839264\pi\)
−0.875190 + 0.483779i \(0.839264\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 6.00000 0.824163 0.412082 − 0.911147i \(-0.364802\pi\)
0.412082 + 0.911147i \(0.364802\pi\)
\(54\) 0 0
\(55\) 3.00000 0.404520
\(56\) 0 0
\(57\) −6.00000 −0.794719
\(58\) 0 0
\(59\) 11.0000 1.43208 0.716039 − 0.698060i \(-0.245953\pi\)
0.716039 + 0.698060i \(0.245953\pi\)
\(60\) 0 0
\(61\) −4.00000 −0.512148 −0.256074 − 0.966657i \(-0.582429\pi\)
−0.256074 + 0.966657i \(0.582429\pi\)
\(62\) 0 0
\(63\) 2.00000 0.251976
\(64\) 0 0
\(65\) −18.0000 −2.23263
\(66\) 0 0
\(67\) 7.00000 0.855186 0.427593 − 0.903971i \(-0.359362\pi\)
0.427593 + 0.903971i \(0.359362\pi\)
\(68\) 0 0
\(69\) 3.00000 0.361158
\(70\) 0 0
\(71\) 13.0000 1.54282 0.771408 − 0.636341i \(-0.219553\pi\)
0.771408 + 0.636341i \(0.219553\pi\)
\(72\) 0 0
\(73\) −14.0000 −1.63858 −0.819288 − 0.573382i \(-0.805631\pi\)
−0.819288 + 0.573382i \(0.805631\pi\)
\(74\) 0 0
\(75\) 4.00000 0.461880
\(76\) 0 0
\(77\) −1.00000 −0.113961
\(78\) 0 0
\(79\) 2.00000 0.225018 0.112509 − 0.993651i \(-0.464111\pi\)
0.112509 + 0.993651i \(0.464111\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −14.0000 −1.53670 −0.768350 − 0.640030i \(-0.778922\pi\)
−0.768350 + 0.640030i \(0.778922\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −17.0000 −1.80200 −0.900998 − 0.433823i \(-0.857164\pi\)
−0.900998 + 0.433823i \(0.857164\pi\)
\(90\) 0 0
\(91\) 6.00000 0.628971
\(92\) 0 0
\(93\) 3.00000 0.311086
\(94\) 0 0
\(95\) −18.0000 −1.84676
\(96\) 0 0
\(97\) −15.0000 −1.52302 −0.761510 − 0.648154i \(-0.775541\pi\)
−0.761510 + 0.648154i \(0.775541\pi\)
\(98\) 0 0
\(99\) −2.00000 −0.201008
\(100\) 0 0
\(101\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(102\) 0 0
\(103\) −8.00000 −0.788263 −0.394132 − 0.919054i \(-0.628955\pi\)
−0.394132 + 0.919054i \(0.628955\pi\)
\(104\) 0 0
\(105\) −3.00000 −0.292770
\(106\) 0 0
\(107\) −16.0000 −1.54678 −0.773389 − 0.633932i \(-0.781440\pi\)
−0.773389 + 0.633932i \(0.781440\pi\)
\(108\) 0 0
\(109\) −6.00000 −0.574696 −0.287348 − 0.957826i \(-0.592774\pi\)
−0.287348 + 0.957826i \(0.592774\pi\)
\(110\) 0 0
\(111\) 1.00000 0.0949158
\(112\) 0 0
\(113\) −7.00000 −0.658505 −0.329252 − 0.944242i \(-0.606797\pi\)
−0.329252 + 0.944242i \(0.606797\pi\)
\(114\) 0 0
\(115\) 9.00000 0.839254
\(116\) 0 0
\(117\) 12.0000 1.10940
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) −10.0000 −0.901670
\(124\) 0 0
\(125\) −3.00000 −0.268328
\(126\) 0 0
\(127\) 18.0000 1.59724 0.798621 − 0.601834i \(-0.205563\pi\)
0.798621 + 0.601834i \(0.205563\pi\)
\(128\) 0 0
\(129\) −2.00000 −0.176090
\(130\) 0 0
\(131\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) 0 0
\(133\) 6.00000 0.520266
\(134\) 0 0
\(135\) −15.0000 −1.29099
\(136\) 0 0
\(137\) −19.0000 −1.62328 −0.811640 − 0.584158i \(-0.801425\pi\)
−0.811640 + 0.584158i \(0.801425\pi\)
\(138\) 0 0
\(139\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(140\) 0 0
\(141\) −12.0000 −1.01058
\(142\) 0 0
\(143\) −6.00000 −0.501745
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 1.00000 0.0824786
\(148\) 0 0
\(149\) 12.0000 0.983078 0.491539 − 0.870855i \(-0.336434\pi\)
0.491539 + 0.870855i \(0.336434\pi\)
\(150\) 0 0
\(151\) 2.00000 0.162758 0.0813788 − 0.996683i \(-0.474068\pi\)
0.0813788 + 0.996683i \(0.474068\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 9.00000 0.722897
\(156\) 0 0
\(157\) 7.00000 0.558661 0.279330 − 0.960195i \(-0.409888\pi\)
0.279330 + 0.960195i \(0.409888\pi\)
\(158\) 0 0
\(159\) 6.00000 0.475831
\(160\) 0 0
\(161\) −3.00000 −0.236433
\(162\) 0 0
\(163\) 12.0000 0.939913 0.469956 − 0.882690i \(-0.344270\pi\)
0.469956 + 0.882690i \(0.344270\pi\)
\(164\) 0 0
\(165\) 3.00000 0.233550
\(166\) 0 0
\(167\) 18.0000 1.39288 0.696441 − 0.717614i \(-0.254766\pi\)
0.696441 + 0.717614i \(0.254766\pi\)
\(168\) 0 0
\(169\) 23.0000 1.76923
\(170\) 0 0
\(171\) 12.0000 0.917663
\(172\) 0 0
\(173\) −6.00000 −0.456172 −0.228086 − 0.973641i \(-0.573247\pi\)
−0.228086 + 0.973641i \(0.573247\pi\)
\(174\) 0 0
\(175\) −4.00000 −0.302372
\(176\) 0 0
\(177\) 11.0000 0.826811
\(178\) 0 0
\(179\) −9.00000 −0.672692 −0.336346 − 0.941739i \(-0.609191\pi\)
−0.336346 + 0.941739i \(0.609191\pi\)
\(180\) 0 0
\(181\) 1.00000 0.0743294 0.0371647 − 0.999309i \(-0.488167\pi\)
0.0371647 + 0.999309i \(0.488167\pi\)
\(182\) 0 0
\(183\) −4.00000 −0.295689
\(184\) 0 0
\(185\) 3.00000 0.220564
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 5.00000 0.363696
\(190\) 0 0
\(191\) 5.00000 0.361787 0.180894 − 0.983503i \(-0.442101\pi\)
0.180894 + 0.983503i \(0.442101\pi\)
\(192\) 0 0
\(193\) 16.0000 1.15171 0.575853 − 0.817554i \(-0.304670\pi\)
0.575853 + 0.817554i \(0.304670\pi\)
\(194\) 0 0
\(195\) −18.0000 −1.28901
\(196\) 0 0
\(197\) 2.00000 0.142494 0.0712470 − 0.997459i \(-0.477302\pi\)
0.0712470 + 0.997459i \(0.477302\pi\)
\(198\) 0 0
\(199\) −16.0000 −1.13421 −0.567105 − 0.823646i \(-0.691937\pi\)
−0.567105 + 0.823646i \(0.691937\pi\)
\(200\) 0 0
\(201\) 7.00000 0.493742
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −30.0000 −2.09529
\(206\) 0 0
\(207\) −6.00000 −0.417029
\(208\) 0 0
\(209\) −6.00000 −0.415029
\(210\) 0 0
\(211\) 8.00000 0.550743 0.275371 − 0.961338i \(-0.411199\pi\)
0.275371 + 0.961338i \(0.411199\pi\)
\(212\) 0 0
\(213\) 13.0000 0.890745
\(214\) 0 0
\(215\) −6.00000 −0.409197
\(216\) 0 0
\(217\) −3.00000 −0.203653
\(218\) 0 0
\(219\) −14.0000 −0.946032
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −25.0000 −1.67412 −0.837062 − 0.547108i \(-0.815729\pi\)
−0.837062 + 0.547108i \(0.815729\pi\)
\(224\) 0 0
\(225\) −8.00000 −0.533333
\(226\) 0 0
\(227\) 28.0000 1.85843 0.929213 − 0.369546i \(-0.120487\pi\)
0.929213 + 0.369546i \(0.120487\pi\)
\(228\) 0 0
\(229\) 13.0000 0.859064 0.429532 − 0.903052i \(-0.358679\pi\)
0.429532 + 0.903052i \(0.358679\pi\)
\(230\) 0 0
\(231\) −1.00000 −0.0657952
\(232\) 0 0
\(233\) 8.00000 0.524097 0.262049 − 0.965055i \(-0.415602\pi\)
0.262049 + 0.965055i \(0.415602\pi\)
\(234\) 0 0
\(235\) −36.0000 −2.34838
\(236\) 0 0
\(237\) 2.00000 0.129914
\(238\) 0 0
\(239\) −26.0000 −1.68180 −0.840900 − 0.541190i \(-0.817974\pi\)
−0.840900 + 0.541190i \(0.817974\pi\)
\(240\) 0 0
\(241\) 20.0000 1.28831 0.644157 − 0.764894i \(-0.277208\pi\)
0.644157 + 0.764894i \(0.277208\pi\)
\(242\) 0 0
\(243\) 16.0000 1.02640
\(244\) 0 0
\(245\) 3.00000 0.191663
\(246\) 0 0
\(247\) 36.0000 2.29063
\(248\) 0 0
\(249\) −14.0000 −0.887214
\(250\) 0 0
\(251\) 15.0000 0.946792 0.473396 − 0.880850i \(-0.343028\pi\)
0.473396 + 0.880850i \(0.343028\pi\)
\(252\) 0 0
\(253\) 3.00000 0.188608
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −26.0000 −1.62184 −0.810918 − 0.585160i \(-0.801032\pi\)
−0.810918 + 0.585160i \(0.801032\pi\)
\(258\) 0 0
\(259\) −1.00000 −0.0621370
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 12.0000 0.739952 0.369976 − 0.929041i \(-0.379366\pi\)
0.369976 + 0.929041i \(0.379366\pi\)
\(264\) 0 0
\(265\) 18.0000 1.10573
\(266\) 0 0
\(267\) −17.0000 −1.04038
\(268\) 0 0
\(269\) −14.0000 −0.853595 −0.426798 − 0.904347i \(-0.640358\pi\)
−0.426798 + 0.904347i \(0.640358\pi\)
\(270\) 0 0
\(271\) −2.00000 −0.121491 −0.0607457 − 0.998153i \(-0.519348\pi\)
−0.0607457 + 0.998153i \(0.519348\pi\)
\(272\) 0 0
\(273\) 6.00000 0.363137
\(274\) 0 0
\(275\) 4.00000 0.241209
\(276\) 0 0
\(277\) 2.00000 0.120168 0.0600842 − 0.998193i \(-0.480863\pi\)
0.0600842 + 0.998193i \(0.480863\pi\)
\(278\) 0 0
\(279\) −6.00000 −0.359211
\(280\) 0 0
\(281\) −10.0000 −0.596550 −0.298275 − 0.954480i \(-0.596411\pi\)
−0.298275 + 0.954480i \(0.596411\pi\)
\(282\) 0 0
\(283\) 32.0000 1.90220 0.951101 − 0.308879i \(-0.0999539\pi\)
0.951101 + 0.308879i \(0.0999539\pi\)
\(284\) 0 0
\(285\) −18.0000 −1.06623
\(286\) 0 0
\(287\) 10.0000 0.590281
\(288\) 0 0
\(289\) −17.0000 −1.00000
\(290\) 0 0
\(291\) −15.0000 −0.879316
\(292\) 0 0
\(293\) −18.0000 −1.05157 −0.525786 − 0.850617i \(-0.676229\pi\)
−0.525786 + 0.850617i \(0.676229\pi\)
\(294\) 0 0
\(295\) 33.0000 1.92133
\(296\) 0 0
\(297\) −5.00000 −0.290129
\(298\) 0 0
\(299\) −18.0000 −1.04097
\(300\) 0 0
\(301\) 2.00000 0.115278
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −12.0000 −0.687118
\(306\) 0 0
\(307\) 6.00000 0.342438 0.171219 − 0.985233i \(-0.445229\pi\)
0.171219 + 0.985233i \(0.445229\pi\)
\(308\) 0 0
\(309\) −8.00000 −0.455104
\(310\) 0 0
\(311\) −16.0000 −0.907277 −0.453638 − 0.891186i \(-0.649874\pi\)
−0.453638 + 0.891186i \(0.649874\pi\)
\(312\) 0 0
\(313\) 11.0000 0.621757 0.310878 − 0.950450i \(-0.399377\pi\)
0.310878 + 0.950450i \(0.399377\pi\)
\(314\) 0 0
\(315\) 6.00000 0.338062
\(316\) 0 0
\(317\) 15.0000 0.842484 0.421242 − 0.906948i \(-0.361594\pi\)
0.421242 + 0.906948i \(0.361594\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) −16.0000 −0.893033
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) −24.0000 −1.33128
\(326\) 0 0
\(327\) −6.00000 −0.331801
\(328\) 0 0
\(329\) 12.0000 0.661581
\(330\) 0 0
\(331\) 25.0000 1.37412 0.687062 − 0.726599i \(-0.258900\pi\)
0.687062 + 0.726599i \(0.258900\pi\)
\(332\) 0 0
\(333\) −2.00000 −0.109599
\(334\) 0 0
\(335\) 21.0000 1.14735
\(336\) 0 0
\(337\) −12.0000 −0.653682 −0.326841 − 0.945079i \(-0.605984\pi\)
−0.326841 + 0.945079i \(0.605984\pi\)
\(338\) 0 0
\(339\) −7.00000 −0.380188
\(340\) 0 0
\(341\) 3.00000 0.162459
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) 9.00000 0.484544
\(346\) 0 0
\(347\) −14.0000 −0.751559 −0.375780 − 0.926709i \(-0.622625\pi\)
−0.375780 + 0.926709i \(0.622625\pi\)
\(348\) 0 0
\(349\) 16.0000 0.856460 0.428230 − 0.903670i \(-0.359137\pi\)
0.428230 + 0.903670i \(0.359137\pi\)
\(350\) 0 0
\(351\) 30.0000 1.60128
\(352\) 0 0
\(353\) 15.0000 0.798369 0.399185 − 0.916871i \(-0.369293\pi\)
0.399185 + 0.916871i \(0.369293\pi\)
\(354\) 0 0
\(355\) 39.0000 2.06991
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 6.00000 0.316668 0.158334 − 0.987386i \(-0.449388\pi\)
0.158334 + 0.987386i \(0.449388\pi\)
\(360\) 0 0
\(361\) 17.0000 0.894737
\(362\) 0 0
\(363\) 1.00000 0.0524864
\(364\) 0 0
\(365\) −42.0000 −2.19838
\(366\) 0 0
\(367\) −5.00000 −0.260998 −0.130499 − 0.991448i \(-0.541658\pi\)
−0.130499 + 0.991448i \(0.541658\pi\)
\(368\) 0 0
\(369\) 20.0000 1.04116
\(370\) 0 0
\(371\) −6.00000 −0.311504
\(372\) 0 0
\(373\) −20.0000 −1.03556 −0.517780 − 0.855514i \(-0.673242\pi\)
−0.517780 + 0.855514i \(0.673242\pi\)
\(374\) 0 0
\(375\) −3.00000 −0.154919
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −3.00000 −0.154100 −0.0770498 − 0.997027i \(-0.524550\pi\)
−0.0770498 + 0.997027i \(0.524550\pi\)
\(380\) 0 0
\(381\) 18.0000 0.922168
\(382\) 0 0
\(383\) 23.0000 1.17525 0.587623 − 0.809135i \(-0.300064\pi\)
0.587623 + 0.809135i \(0.300064\pi\)
\(384\) 0 0
\(385\) −3.00000 −0.152894
\(386\) 0 0
\(387\) 4.00000 0.203331
\(388\) 0 0
\(389\) −5.00000 −0.253510 −0.126755 − 0.991934i \(-0.540456\pi\)
−0.126755 + 0.991934i \(0.540456\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 6.00000 0.301893
\(396\) 0 0
\(397\) 2.00000 0.100377 0.0501886 − 0.998740i \(-0.484018\pi\)
0.0501886 + 0.998740i \(0.484018\pi\)
\(398\) 0 0
\(399\) 6.00000 0.300376
\(400\) 0 0
\(401\) −30.0000 −1.49813 −0.749064 − 0.662497i \(-0.769497\pi\)
−0.749064 + 0.662497i \(0.769497\pi\)
\(402\) 0 0
\(403\) −18.0000 −0.896644
\(404\) 0 0
\(405\) 3.00000 0.149071
\(406\) 0 0
\(407\) 1.00000 0.0495682
\(408\) 0 0
\(409\) 10.0000 0.494468 0.247234 − 0.968956i \(-0.420478\pi\)
0.247234 + 0.968956i \(0.420478\pi\)
\(410\) 0 0
\(411\) −19.0000 −0.937201
\(412\) 0 0
\(413\) −11.0000 −0.541275
\(414\) 0 0
\(415\) −42.0000 −2.06170
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 24.0000 1.17248 0.586238 − 0.810139i \(-0.300608\pi\)
0.586238 + 0.810139i \(0.300608\pi\)
\(420\) 0 0
\(421\) −22.0000 −1.07221 −0.536107 − 0.844150i \(-0.680106\pi\)
−0.536107 + 0.844150i \(0.680106\pi\)
\(422\) 0 0
\(423\) 24.0000 1.16692
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 4.00000 0.193574
\(428\) 0 0
\(429\) −6.00000 −0.289683
\(430\) 0 0
\(431\) −20.0000 −0.963366 −0.481683 − 0.876346i \(-0.659974\pi\)
−0.481683 + 0.876346i \(0.659974\pi\)
\(432\) 0 0
\(433\) −15.0000 −0.720854 −0.360427 − 0.932787i \(-0.617369\pi\)
−0.360427 + 0.932787i \(0.617369\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −18.0000 −0.861057
\(438\) 0 0
\(439\) −16.0000 −0.763638 −0.381819 − 0.924237i \(-0.624702\pi\)
−0.381819 + 0.924237i \(0.624702\pi\)
\(440\) 0 0
\(441\) −2.00000 −0.0952381
\(442\) 0 0
\(443\) −9.00000 −0.427603 −0.213801 − 0.976877i \(-0.568585\pi\)
−0.213801 + 0.976877i \(0.568585\pi\)
\(444\) 0 0
\(445\) −51.0000 −2.41763
\(446\) 0 0
\(447\) 12.0000 0.567581
\(448\) 0 0
\(449\) 15.0000 0.707894 0.353947 − 0.935266i \(-0.384839\pi\)
0.353947 + 0.935266i \(0.384839\pi\)
\(450\) 0 0
\(451\) −10.0000 −0.470882
\(452\) 0 0
\(453\) 2.00000 0.0939682
\(454\) 0 0
\(455\) 18.0000 0.843853
\(456\) 0 0
\(457\) −40.0000 −1.87112 −0.935561 − 0.353166i \(-0.885105\pi\)
−0.935561 + 0.353166i \(0.885105\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 20.0000 0.931493 0.465746 − 0.884918i \(-0.345786\pi\)
0.465746 + 0.884918i \(0.345786\pi\)
\(462\) 0 0
\(463\) 17.0000 0.790057 0.395029 − 0.918669i \(-0.370735\pi\)
0.395029 + 0.918669i \(0.370735\pi\)
\(464\) 0 0
\(465\) 9.00000 0.417365
\(466\) 0 0
\(467\) 11.0000 0.509019 0.254510 − 0.967070i \(-0.418086\pi\)
0.254510 + 0.967070i \(0.418086\pi\)
\(468\) 0 0
\(469\) −7.00000 −0.323230
\(470\) 0 0
\(471\) 7.00000 0.322543
\(472\) 0 0
\(473\) −2.00000 −0.0919601
\(474\) 0 0
\(475\) −24.0000 −1.10120
\(476\) 0 0
\(477\) −12.0000 −0.549442
\(478\) 0 0
\(479\) −6.00000 −0.274147 −0.137073 − 0.990561i \(-0.543770\pi\)
−0.137073 + 0.990561i \(0.543770\pi\)
\(480\) 0 0
\(481\) −6.00000 −0.273576
\(482\) 0 0
\(483\) −3.00000 −0.136505
\(484\) 0 0
\(485\) −45.0000 −2.04334
\(486\) 0 0
\(487\) 19.0000 0.860972 0.430486 − 0.902597i \(-0.358342\pi\)
0.430486 + 0.902597i \(0.358342\pi\)
\(488\) 0 0
\(489\) 12.0000 0.542659
\(490\) 0 0
\(491\) 28.0000 1.26362 0.631811 − 0.775122i \(-0.282312\pi\)
0.631811 + 0.775122i \(0.282312\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) −6.00000 −0.269680
\(496\) 0 0
\(497\) −13.0000 −0.583130
\(498\) 0 0
\(499\) 12.0000 0.537194 0.268597 − 0.963253i \(-0.413440\pi\)
0.268597 + 0.963253i \(0.413440\pi\)
\(500\) 0 0
\(501\) 18.0000 0.804181
\(502\) 0 0
\(503\) −10.0000 −0.445878 −0.222939 − 0.974832i \(-0.571565\pi\)
−0.222939 + 0.974832i \(0.571565\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 23.0000 1.02147
\(508\) 0 0
\(509\) 21.0000 0.930809 0.465404 − 0.885098i \(-0.345909\pi\)
0.465404 + 0.885098i \(0.345909\pi\)
\(510\) 0 0
\(511\) 14.0000 0.619324
\(512\) 0 0
\(513\) 30.0000 1.32453
\(514\) 0 0
\(515\) −24.0000 −1.05757
\(516\) 0 0
\(517\) −12.0000 −0.527759
\(518\) 0 0
\(519\) −6.00000 −0.263371
\(520\) 0 0
\(521\) −3.00000 −0.131432 −0.0657162 − 0.997838i \(-0.520933\pi\)
−0.0657162 + 0.997838i \(0.520933\pi\)
\(522\) 0 0
\(523\) −22.0000 −0.961993 −0.480996 − 0.876723i \(-0.659725\pi\)
−0.480996 + 0.876723i \(0.659725\pi\)
\(524\) 0 0
\(525\) −4.00000 −0.174574
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −14.0000 −0.608696
\(530\) 0 0
\(531\) −22.0000 −0.954719
\(532\) 0 0
\(533\) 60.0000 2.59889
\(534\) 0 0
\(535\) −48.0000 −2.07522
\(536\) 0 0
\(537\) −9.00000 −0.388379
\(538\) 0 0
\(539\) 1.00000 0.0430730
\(540\) 0 0
\(541\) 26.0000 1.11783 0.558914 − 0.829226i \(-0.311218\pi\)
0.558914 + 0.829226i \(0.311218\pi\)
\(542\) 0 0
\(543\) 1.00000 0.0429141
\(544\) 0 0
\(545\) −18.0000 −0.771035
\(546\) 0 0
\(547\) 4.00000 0.171028 0.0855138 − 0.996337i \(-0.472747\pi\)
0.0855138 + 0.996337i \(0.472747\pi\)
\(548\) 0 0
\(549\) 8.00000 0.341432
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) −2.00000 −0.0850487
\(554\) 0 0
\(555\) 3.00000 0.127343
\(556\) 0 0
\(557\) 4.00000 0.169485 0.0847427 − 0.996403i \(-0.472993\pi\)
0.0847427 + 0.996403i \(0.472993\pi\)
\(558\) 0 0
\(559\) 12.0000 0.507546
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −24.0000 −1.01148 −0.505740 − 0.862686i \(-0.668780\pi\)
−0.505740 + 0.862686i \(0.668780\pi\)
\(564\) 0 0
\(565\) −21.0000 −0.883477
\(566\) 0 0
\(567\) −1.00000 −0.0419961
\(568\) 0 0
\(569\) −24.0000 −1.00613 −0.503066 − 0.864248i \(-0.667795\pi\)
−0.503066 + 0.864248i \(0.667795\pi\)
\(570\) 0 0
\(571\) −20.0000 −0.836974 −0.418487 − 0.908223i \(-0.637439\pi\)
−0.418487 + 0.908223i \(0.637439\pi\)
\(572\) 0 0
\(573\) 5.00000 0.208878
\(574\) 0 0
\(575\) 12.0000 0.500435
\(576\) 0 0
\(577\) −7.00000 −0.291414 −0.145707 − 0.989328i \(-0.546546\pi\)
−0.145707 + 0.989328i \(0.546546\pi\)
\(578\) 0 0
\(579\) 16.0000 0.664937
\(580\) 0 0
\(581\) 14.0000 0.580818
\(582\) 0 0
\(583\) 6.00000 0.248495
\(584\) 0 0
\(585\) 36.0000 1.48842
\(586\) 0 0
\(587\) −36.0000 −1.48588 −0.742940 − 0.669359i \(-0.766569\pi\)
−0.742940 + 0.669359i \(0.766569\pi\)
\(588\) 0 0
\(589\) −18.0000 −0.741677
\(590\) 0 0
\(591\) 2.00000 0.0822690
\(592\) 0 0
\(593\) 24.0000 0.985562 0.492781 − 0.870153i \(-0.335980\pi\)
0.492781 + 0.870153i \(0.335980\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −16.0000 −0.654836
\(598\) 0 0
\(599\) 16.0000 0.653742 0.326871 − 0.945069i \(-0.394006\pi\)
0.326871 + 0.945069i \(0.394006\pi\)
\(600\) 0 0
\(601\) 44.0000 1.79480 0.897399 − 0.441221i \(-0.145454\pi\)
0.897399 + 0.441221i \(0.145454\pi\)
\(602\) 0 0
\(603\) −14.0000 −0.570124
\(604\) 0 0
\(605\) 3.00000 0.121967
\(606\) 0 0
\(607\) −2.00000 −0.0811775 −0.0405887 − 0.999176i \(-0.512923\pi\)
−0.0405887 + 0.999176i \(0.512923\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 72.0000 2.91281
\(612\) 0 0
\(613\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(614\) 0 0
\(615\) −30.0000 −1.20972
\(616\) 0 0
\(617\) 22.0000 0.885687 0.442843 − 0.896599i \(-0.353970\pi\)
0.442843 + 0.896599i \(0.353970\pi\)
\(618\) 0 0
\(619\) −19.0000 −0.763674 −0.381837 − 0.924230i \(-0.624709\pi\)
−0.381837 + 0.924230i \(0.624709\pi\)
\(620\) 0 0
\(621\) −15.0000 −0.601929
\(622\) 0 0
\(623\) 17.0000 0.681091
\(624\) 0 0
\(625\) −29.0000 −1.16000
\(626\) 0 0
\(627\) −6.00000 −0.239617
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) −17.0000 −0.676759 −0.338380 − 0.941010i \(-0.609879\pi\)
−0.338380 + 0.941010i \(0.609879\pi\)
\(632\) 0 0
\(633\) 8.00000 0.317971
\(634\) 0 0
\(635\) 54.0000 2.14292
\(636\) 0 0
\(637\) −6.00000 −0.237729
\(638\) 0 0
\(639\) −26.0000 −1.02854
\(640\) 0 0
\(641\) 3.00000 0.118493 0.0592464 − 0.998243i \(-0.481130\pi\)
0.0592464 + 0.998243i \(0.481130\pi\)
\(642\) 0 0
\(643\) −9.00000 −0.354925 −0.177463 − 0.984128i \(-0.556789\pi\)
−0.177463 + 0.984128i \(0.556789\pi\)
\(644\) 0 0
\(645\) −6.00000 −0.236250
\(646\) 0 0
\(647\) −47.0000 −1.84776 −0.923880 − 0.382682i \(-0.875001\pi\)
−0.923880 + 0.382682i \(0.875001\pi\)
\(648\) 0 0
\(649\) 11.0000 0.431788
\(650\) 0 0
\(651\) −3.00000 −0.117579
\(652\) 0 0
\(653\) −15.0000 −0.586995 −0.293498 − 0.955960i \(-0.594819\pi\)
−0.293498 + 0.955960i \(0.594819\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 28.0000 1.09238
\(658\) 0 0
\(659\) −30.0000 −1.16863 −0.584317 − 0.811525i \(-0.698638\pi\)
−0.584317 + 0.811525i \(0.698638\pi\)
\(660\) 0 0
\(661\) 43.0000 1.67251 0.836253 − 0.548344i \(-0.184741\pi\)
0.836253 + 0.548344i \(0.184741\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 18.0000 0.698010
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) −25.0000 −0.966556
\(670\) 0 0
\(671\) −4.00000 −0.154418
\(672\) 0 0
\(673\) 26.0000 1.00223 0.501113 − 0.865382i \(-0.332924\pi\)
0.501113 + 0.865382i \(0.332924\pi\)
\(674\) 0 0
\(675\) −20.0000 −0.769800
\(676\) 0 0
\(677\) −12.0000 −0.461197 −0.230599 − 0.973049i \(-0.574068\pi\)
−0.230599 + 0.973049i \(0.574068\pi\)
\(678\) 0 0
\(679\) 15.0000 0.575647
\(680\) 0 0
\(681\) 28.0000 1.07296
\(682\) 0 0
\(683\) 28.0000 1.07139 0.535695 − 0.844411i \(-0.320050\pi\)
0.535695 + 0.844411i \(0.320050\pi\)
\(684\) 0 0
\(685\) −57.0000 −2.17786
\(686\) 0 0
\(687\) 13.0000 0.495981
\(688\) 0 0
\(689\) −36.0000 −1.37149
\(690\) 0 0
\(691\) −29.0000 −1.10321 −0.551606 − 0.834105i \(-0.685985\pi\)
−0.551606 + 0.834105i \(0.685985\pi\)
\(692\) 0 0
\(693\) 2.00000 0.0759737
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 8.00000 0.302588
\(700\) 0 0
\(701\) 16.0000 0.604312 0.302156 − 0.953259i \(-0.402294\pi\)
0.302156 + 0.953259i \(0.402294\pi\)
\(702\) 0 0
\(703\) −6.00000 −0.226294
\(704\) 0 0
\(705\) −36.0000 −1.35584
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −7.00000 −0.262891 −0.131445 − 0.991323i \(-0.541962\pi\)
−0.131445 + 0.991323i \(0.541962\pi\)
\(710\) 0 0
\(711\) −4.00000 −0.150012
\(712\) 0 0
\(713\) 9.00000 0.337053
\(714\) 0 0
\(715\) −18.0000 −0.673162
\(716\) 0 0
\(717\) −26.0000 −0.970988
\(718\) 0 0
\(719\) 31.0000 1.15610 0.578052 − 0.816000i \(-0.303813\pi\)
0.578052 + 0.816000i \(0.303813\pi\)
\(720\) 0 0
\(721\) 8.00000 0.297936
\(722\) 0 0
\(723\) 20.0000 0.743808
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 23.0000 0.853023 0.426511 − 0.904482i \(-0.359742\pi\)
0.426511 + 0.904482i \(0.359742\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) −40.0000 −1.47743 −0.738717 − 0.674016i \(-0.764568\pi\)
−0.738717 + 0.674016i \(0.764568\pi\)
\(734\) 0 0
\(735\) 3.00000 0.110657
\(736\) 0 0
\(737\) 7.00000 0.257848
\(738\) 0 0
\(739\) −50.0000 −1.83928 −0.919640 − 0.392763i \(-0.871519\pi\)
−0.919640 + 0.392763i \(0.871519\pi\)
\(740\) 0 0
\(741\) 36.0000 1.32249
\(742\) 0 0
\(743\) −12.0000 −0.440237 −0.220119 − 0.975473i \(-0.570644\pi\)
−0.220119 + 0.975473i \(0.570644\pi\)
\(744\) 0 0
\(745\) 36.0000 1.31894
\(746\) 0 0
\(747\) 28.0000 1.02447
\(748\) 0 0
\(749\) 16.0000 0.584627
\(750\) 0 0
\(751\) −43.0000 −1.56909 −0.784546 − 0.620070i \(-0.787104\pi\)
−0.784546 + 0.620070i \(0.787104\pi\)
\(752\) 0 0
\(753\) 15.0000 0.546630
\(754\) 0 0
\(755\) 6.00000 0.218362
\(756\) 0 0
\(757\) 18.0000 0.654221 0.327111 − 0.944986i \(-0.393925\pi\)
0.327111 + 0.944986i \(0.393925\pi\)
\(758\) 0 0
\(759\) 3.00000 0.108893
\(760\) 0 0
\(761\) 34.0000 1.23250 0.616250 − 0.787551i \(-0.288651\pi\)
0.616250 + 0.787551i \(0.288651\pi\)
\(762\) 0 0
\(763\) 6.00000 0.217215
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −66.0000 −2.38312
\(768\) 0 0
\(769\) −34.0000 −1.22607 −0.613036 − 0.790055i \(-0.710052\pi\)
−0.613036 + 0.790055i \(0.710052\pi\)
\(770\) 0 0
\(771\) −26.0000 −0.936367
\(772\) 0 0
\(773\) 30.0000 1.07903 0.539513 − 0.841978i \(-0.318609\pi\)
0.539513 + 0.841978i \(0.318609\pi\)
\(774\) 0 0
\(775\) 12.0000 0.431053
\(776\) 0 0
\(777\) −1.00000 −0.0358748
\(778\) 0 0
\(779\) 60.0000 2.14972
\(780\) 0 0
\(781\) 13.0000 0.465177
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 21.0000 0.749522
\(786\) 0 0
\(787\) 40.0000 1.42585 0.712923 − 0.701242i \(-0.247371\pi\)
0.712923 + 0.701242i \(0.247371\pi\)
\(788\) 0 0
\(789\) 12.0000 0.427211
\(790\) 0 0
\(791\) 7.00000 0.248891
\(792\) 0 0
\(793\) 24.0000 0.852265
\(794\) 0 0
\(795\) 18.0000 0.638394
\(796\) 0 0
\(797\) −37.0000 −1.31061 −0.655304 − 0.755366i \(-0.727459\pi\)
−0.655304 + 0.755366i \(0.727459\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 34.0000 1.20133
\(802\) 0 0
\(803\) −14.0000 −0.494049
\(804\) 0 0
\(805\) −9.00000 −0.317208
\(806\) 0 0
\(807\) −14.0000 −0.492823
\(808\) 0 0
\(809\) 54.0000 1.89854 0.949269 − 0.314464i \(-0.101825\pi\)
0.949269 + 0.314464i \(0.101825\pi\)
\(810\) 0 0
\(811\) 26.0000 0.912983 0.456492 − 0.889728i \(-0.349106\pi\)
0.456492 + 0.889728i \(0.349106\pi\)
\(812\) 0 0
\(813\) −2.00000 −0.0701431
\(814\) 0 0
\(815\) 36.0000 1.26102
\(816\) 0 0
\(817\) 12.0000 0.419827
\(818\) 0 0
\(819\) −12.0000 −0.419314
\(820\) 0 0
\(821\) 18.0000 0.628204 0.314102 − 0.949389i \(-0.398297\pi\)
0.314102 + 0.949389i \(0.398297\pi\)
\(822\) 0 0
\(823\) 31.0000 1.08059 0.540296 − 0.841475i \(-0.318312\pi\)
0.540296 + 0.841475i \(0.318312\pi\)
\(824\) 0 0
\(825\) 4.00000 0.139262
\(826\) 0 0
\(827\) −42.0000 −1.46048 −0.730242 − 0.683189i \(-0.760592\pi\)
−0.730242 + 0.683189i \(0.760592\pi\)
\(828\) 0 0
\(829\) −33.0000 −1.14614 −0.573069 − 0.819507i \(-0.694247\pi\)
−0.573069 + 0.819507i \(0.694247\pi\)
\(830\) 0 0
\(831\) 2.00000 0.0693792
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 54.0000 1.86875
\(836\) 0 0
\(837\) −15.0000 −0.518476
\(838\) 0 0
\(839\) −21.0000 −0.725001 −0.362500 − 0.931984i \(-0.618077\pi\)
−0.362500 + 0.931984i \(0.618077\pi\)
\(840\) 0 0
\(841\) −29.0000 −1.00000
\(842\) 0 0
\(843\) −10.0000 −0.344418
\(844\) 0 0
\(845\) 69.0000 2.37367
\(846\) 0 0
\(847\) −1.00000 −0.0343604
\(848\) 0 0
\(849\) 32.0000 1.09824
\(850\) 0 0
\(851\) 3.00000 0.102839
\(852\) 0 0
\(853\) −46.0000 −1.57501 −0.787505 − 0.616308i \(-0.788628\pi\)
−0.787505 + 0.616308i \(0.788628\pi\)
\(854\) 0 0
\(855\) 36.0000 1.23117
\(856\) 0 0
\(857\) 8.00000 0.273275 0.136637 − 0.990621i \(-0.456370\pi\)
0.136637 + 0.990621i \(0.456370\pi\)
\(858\) 0 0
\(859\) −17.0000 −0.580033 −0.290016 − 0.957022i \(-0.593661\pi\)
−0.290016 + 0.957022i \(0.593661\pi\)
\(860\) 0 0
\(861\) 10.0000 0.340799
\(862\) 0 0
\(863\) −8.00000 −0.272323 −0.136162 − 0.990687i \(-0.543477\pi\)
−0.136162 + 0.990687i \(0.543477\pi\)
\(864\) 0 0
\(865\) −18.0000 −0.612018
\(866\) 0 0
\(867\) −17.0000 −0.577350
\(868\) 0 0
\(869\) 2.00000 0.0678454
\(870\) 0 0
\(871\) −42.0000 −1.42312
\(872\) 0 0
\(873\) 30.0000 1.01535
\(874\) 0 0
\(875\) 3.00000 0.101419
\(876\) 0 0
\(877\) 34.0000 1.14810 0.574049 − 0.818821i \(-0.305372\pi\)
0.574049 + 0.818821i \(0.305372\pi\)
\(878\) 0 0
\(879\) −18.0000 −0.607125
\(880\) 0 0
\(881\) 9.00000 0.303218 0.151609 − 0.988441i \(-0.451555\pi\)
0.151609 + 0.988441i \(0.451555\pi\)
\(882\) 0 0
\(883\) 44.0000 1.48072 0.740359 − 0.672212i \(-0.234656\pi\)
0.740359 + 0.672212i \(0.234656\pi\)
\(884\) 0 0
\(885\) 33.0000 1.10928
\(886\) 0 0
\(887\) 22.0000 0.738688 0.369344 − 0.929293i \(-0.379582\pi\)
0.369344 + 0.929293i \(0.379582\pi\)
\(888\) 0 0
\(889\) −18.0000 −0.603701
\(890\) 0 0
\(891\) 1.00000 0.0335013
\(892\) 0 0
\(893\) 72.0000 2.40939
\(894\) 0 0
\(895\) −27.0000 −0.902510
\(896\) 0 0
\(897\) −18.0000 −0.601003
\(898\) 0 0
\(899\) 0 0
\(900\) 0 0
\(901\) 0 0
\(902\) 0 0
\(903\) 2.00000 0.0665558
\(904\) 0 0
\(905\) 3.00000 0.0997234
\(906\) 0 0
\(907\) −20.0000 −0.664089 −0.332045 − 0.943264i \(-0.607738\pi\)
−0.332045 + 0.943264i \(0.607738\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −24.0000 −0.795155 −0.397578 − 0.917568i \(-0.630149\pi\)
−0.397578 + 0.917568i \(0.630149\pi\)
\(912\) 0 0
\(913\) −14.0000 −0.463332
\(914\) 0 0
\(915\) −12.0000 −0.396708
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 26.0000 0.857661 0.428830 − 0.903385i \(-0.358926\pi\)
0.428830 + 0.903385i \(0.358926\pi\)
\(920\) 0 0
\(921\) 6.00000 0.197707
\(922\) 0 0
\(923\) −78.0000 −2.56740
\(924\) 0 0
\(925\) 4.00000 0.131519
\(926\) 0 0
\(927\) 16.0000 0.525509
\(928\) 0 0
\(929\) −6.00000 −0.196854 −0.0984268 − 0.995144i \(-0.531381\pi\)
−0.0984268 + 0.995144i \(0.531381\pi\)
\(930\) 0 0
\(931\) −6.00000 −0.196642
\(932\) 0 0
\(933\) −16.0000 −0.523816
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −14.0000 −0.457360 −0.228680 − 0.973502i \(-0.573441\pi\)
−0.228680 + 0.973502i \(0.573441\pi\)
\(938\) 0 0
\(939\) 11.0000 0.358971
\(940\) 0 0
\(941\) 2.00000 0.0651981 0.0325991 − 0.999469i \(-0.489622\pi\)
0.0325991 + 0.999469i \(0.489622\pi\)
\(942\) 0 0
\(943\) −30.0000 −0.976934
\(944\) 0 0
\(945\) 15.0000 0.487950
\(946\) 0 0
\(947\) −9.00000 −0.292461 −0.146230 − 0.989251i \(-0.546714\pi\)
−0.146230 + 0.989251i \(0.546714\pi\)
\(948\) 0 0
\(949\) 84.0000 2.72676
\(950\) 0 0
\(951\) 15.0000 0.486408
\(952\) 0 0
\(953\) −56.0000 −1.81402 −0.907009 − 0.421111i \(-0.861640\pi\)
−0.907009 + 0.421111i \(0.861640\pi\)
\(954\) 0 0
\(955\) 15.0000 0.485389
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 19.0000 0.613542
\(960\) 0 0
\(961\) −22.0000 −0.709677
\(962\) 0 0
\(963\) 32.0000 1.03119
\(964\) 0 0
\(965\) 48.0000 1.54517
\(966\) 0 0
\(967\) −8.00000 −0.257263 −0.128631 − 0.991692i \(-0.541058\pi\)
−0.128631 + 0.991692i \(0.541058\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 29.0000 0.930654 0.465327 − 0.885139i \(-0.345937\pi\)
0.465327 + 0.885139i \(0.345937\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) −24.0000 −0.768615
\(976\) 0 0
\(977\) −31.0000 −0.991778 −0.495889 − 0.868386i \(-0.665158\pi\)
−0.495889 + 0.868386i \(0.665158\pi\)
\(978\) 0 0
\(979\) −17.0000 −0.543322
\(980\) 0 0
\(981\) 12.0000 0.383131
\(982\) 0 0
\(983\) −57.0000 −1.81802 −0.909009 − 0.416777i \(-0.863160\pi\)
−0.909009 + 0.416777i \(0.863160\pi\)
\(984\) 0 0
\(985\) 6.00000 0.191176
\(986\) 0 0
\(987\) 12.0000 0.381964
\(988\) 0 0
\(989\) −6.00000 −0.190789
\(990\) 0 0
\(991\) 56.0000 1.77890 0.889449 − 0.457034i \(-0.151088\pi\)
0.889449 + 0.457034i \(0.151088\pi\)
\(992\) 0 0
\(993\) 25.0000 0.793351
\(994\) 0 0
\(995\) −48.0000 −1.52170
\(996\) 0 0
\(997\) −8.00000 −0.253363 −0.126681 − 0.991943i \(-0.540433\pi\)
−0.126681 + 0.991943i \(0.540433\pi\)
\(998\) 0 0
\(999\) −5.00000 −0.158193
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 4928.2.a.bb.1.1 1
4.3 odd 2 4928.2.a.m.1.1 1
8.3 odd 2 2464.2.a.h.1.1 yes 1
8.5 even 2 2464.2.a.d.1.1 ✓ 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2464.2.a.d.1.1 ✓ 1 8.5 even 2
2464.2.a.h.1.1 yes 1 8.3 odd 2
4928.2.a.m.1.1 1 4.3 odd 2
4928.2.a.bb.1.1 1 1.1 even 1 trivial