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Properties

Label 1152.4.a.h.1.1
Level $1152$
Weight $4$
Character 1152.1
Self dual yes
Analytic conductor $67.970$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1152,4,Mod(1,1152)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1152, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1152.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1152 = 2^{7} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1152.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: \(67.9702003266\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 384)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1152.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+4.00000 q^{5} +10.0000 q^{7} +O(q^{10})\) \(q+4.00000 q^{5} +10.0000 q^{7} +4.00000 q^{11} -26.0000 q^{13} -14.0000 q^{17} +8.00000 q^{19} -148.000 q^{23} -109.000 q^{25} +72.0000 q^{29} +18.0000 q^{31} +40.0000 q^{35} -262.000 q^{37} +378.000 q^{41} -432.000 q^{43} -148.000 q^{47} -243.000 q^{49} +360.000 q^{53} +16.0000 q^{55} +428.000 q^{59} +442.000 q^{61} -104.000 q^{65} -692.000 q^{67} -540.000 q^{71} -1018.00 q^{73} +40.0000 q^{77} +386.000 q^{79} -108.000 q^{83} -56.0000 q^{85} +382.000 q^{89} -260.000 q^{91} +32.0000 q^{95} +298.000 q^{97} +O(q^{100})\)

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
\(3\) 0 0
\(4\) 0 0
\(5\) 4.00000 0.357771 0.178885 − 0.983870i \(-0.442751\pi\)
0.178885 + 0.983870i \(0.442751\pi\)
\(6\) 0 0
\(7\) 10.0000 0.539949 0.269975 − 0.962867i \(-0.412985\pi\)
0.269975 + 0.962867i \(0.412985\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 4.00000 0.109640 0.0548202 − 0.998496i \(-0.482541\pi\)
0.0548202 + 0.998496i \(0.482541\pi\)
\(12\) 0 0
\(13\) −26.0000 −0.554700 −0.277350 − 0.960769i \(-0.589456\pi\)
−0.277350 + 0.960769i \(0.589456\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −14.0000 −0.199735 −0.0998676 − 0.995001i \(-0.531842\pi\)
−0.0998676 + 0.995001i \(0.531842\pi\)
\(18\) 0 0
\(19\) 8.00000 0.0965961 0.0482980 − 0.998833i \(-0.484620\pi\)
0.0482980 + 0.998833i \(0.484620\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −148.000 −1.34174 −0.670872 − 0.741573i \(-0.734080\pi\)
−0.670872 + 0.741573i \(0.734080\pi\)
\(24\) 0 0
\(25\) −109.000 −0.872000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 72.0000 0.461037 0.230518 − 0.973068i \(-0.425958\pi\)
0.230518 + 0.973068i \(0.425958\pi\)
\(30\) 0 0
\(31\) 18.0000 0.104287 0.0521435 − 0.998640i \(-0.483395\pi\)
0.0521435 + 0.998640i \(0.483395\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 40.0000 0.193178
\(36\) 0 0
\(37\) −262.000 −1.16412 −0.582061 − 0.813145i \(-0.697754\pi\)
−0.582061 + 0.813145i \(0.697754\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 378.000 1.43985 0.719923 − 0.694054i \(-0.244177\pi\)
0.719923 + 0.694054i \(0.244177\pi\)
\(42\) 0 0
\(43\) −432.000 −1.53208 −0.766039 − 0.642794i \(-0.777775\pi\)
−0.766039 + 0.642794i \(0.777775\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −148.000 −0.459320 −0.229660 − 0.973271i \(-0.573761\pi\)
−0.229660 + 0.973271i \(0.573761\pi\)
\(48\) 0 0
\(49\) −243.000 −0.708455
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 360.000 0.933015 0.466508 − 0.884517i \(-0.345512\pi\)
0.466508 + 0.884517i \(0.345512\pi\)
\(54\) 0 0
\(55\) 16.0000 0.0392262
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 428.000 0.944421 0.472211 − 0.881486i \(-0.343456\pi\)
0.472211 + 0.881486i \(0.343456\pi\)
\(60\) 0 0
\(61\) 442.000 0.927743 0.463871 − 0.885903i \(-0.346460\pi\)
0.463871 + 0.885903i \(0.346460\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −104.000 −0.198456
\(66\) 0 0
\(67\) −692.000 −1.26181 −0.630905 − 0.775860i \(-0.717316\pi\)
−0.630905 + 0.775860i \(0.717316\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −540.000 −0.902623 −0.451311 − 0.892367i \(-0.649044\pi\)
−0.451311 + 0.892367i \(0.649044\pi\)
\(72\) 0 0
\(73\) −1018.00 −1.63216 −0.816081 − 0.577937i \(-0.803858\pi\)
−0.816081 + 0.577937i \(0.803858\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 40.0000 0.0592003
\(78\) 0 0
\(79\) 386.000 0.549726 0.274863 − 0.961483i \(-0.411367\pi\)
0.274863 + 0.961483i \(0.411367\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −108.000 −0.142826 −0.0714129 − 0.997447i \(-0.522751\pi\)
−0.0714129 + 0.997447i \(0.522751\pi\)
\(84\) 0 0
\(85\) −56.0000 −0.0714594
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 382.000 0.454965 0.227483 − 0.973782i \(-0.426950\pi\)
0.227483 + 0.973782i \(0.426950\pi\)
\(90\) 0 0
\(91\) −260.000 −0.299510
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 32.0000 0.0345593
\(96\) 0 0
\(97\) 298.000 0.311931 0.155966 − 0.987762i \(-0.450151\pi\)
0.155966 + 0.987762i \(0.450151\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 1800.00 1.77333 0.886667 − 0.462409i \(-0.153015\pi\)
0.886667 + 0.462409i \(0.153015\pi\)
\(102\) 0 0
\(103\) −818.000 −0.782524 −0.391262 − 0.920279i \(-0.627961\pi\)
−0.391262 + 0.920279i \(0.627961\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −716.000 −0.646900 −0.323450 − 0.946245i \(-0.604843\pi\)
−0.323450 + 0.946245i \(0.604843\pi\)
\(108\) 0 0
\(109\) 1134.00 0.996491 0.498245 − 0.867036i \(-0.333978\pi\)
0.498245 + 0.867036i \(0.333978\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −1858.00 −1.54678 −0.773389 − 0.633932i \(-0.781440\pi\)
−0.773389 + 0.633932i \(0.781440\pi\)
\(114\) 0 0
\(115\) −592.000 −0.480037
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −140.000 −0.107847
\(120\) 0 0
\(121\) −1315.00 −0.987979
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −936.000 −0.669747
\(126\) 0 0
\(127\) −1402.00 −0.979586 −0.489793 − 0.871839i \(-0.662928\pi\)
−0.489793 + 0.871839i \(0.662928\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −1188.00 −0.792336 −0.396168 − 0.918178i \(-0.629660\pi\)
−0.396168 + 0.918178i \(0.629660\pi\)
\(132\) 0 0
\(133\) 80.0000 0.0521570
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −734.000 −0.457736 −0.228868 − 0.973457i \(-0.573502\pi\)
−0.228868 + 0.973457i \(0.573502\pi\)
\(138\) 0 0
\(139\) 404.000 0.246524 0.123262 − 0.992374i \(-0.460664\pi\)
0.123262 + 0.992374i \(0.460664\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −104.000 −0.0608176
\(144\) 0 0
\(145\) 288.000 0.164946
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −684.000 −0.376077 −0.188038 − 0.982162i \(-0.560213\pi\)
−0.188038 + 0.982162i \(0.560213\pi\)
\(150\) 0 0
\(151\) −3502.00 −1.88734 −0.943671 − 0.330885i \(-0.892653\pi\)
−0.943671 + 0.330885i \(0.892653\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 72.0000 0.0373108
\(156\) 0 0
\(157\) 3258.00 1.65616 0.828079 − 0.560612i \(-0.189434\pi\)
0.828079 + 0.560612i \(0.189434\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −1480.00 −0.724474
\(162\) 0 0
\(163\) −856.000 −0.411332 −0.205666 − 0.978622i \(-0.565936\pi\)
−0.205666 + 0.978622i \(0.565936\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −1552.00 −0.719146 −0.359573 − 0.933117i \(-0.617078\pi\)
−0.359573 + 0.933117i \(0.617078\pi\)
\(168\) 0 0
\(169\) −1521.00 −0.692308
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −1548.00 −0.680302 −0.340151 − 0.940371i \(-0.610478\pi\)
−0.340151 + 0.940371i \(0.610478\pi\)
\(174\) 0 0
\(175\) −1090.00 −0.470836
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −3420.00 −1.42806 −0.714030 − 0.700115i \(-0.753132\pi\)
−0.714030 + 0.700115i \(0.753132\pi\)
\(180\) 0 0
\(181\) 3502.00 1.43813 0.719065 − 0.694943i \(-0.244570\pi\)
0.719065 + 0.694943i \(0.244570\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −1048.00 −0.416489
\(186\) 0 0
\(187\) −56.0000 −0.0218991
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 4792.00 1.81538 0.907688 − 0.419645i \(-0.137845\pi\)
0.907688 + 0.419645i \(0.137845\pi\)
\(192\) 0 0
\(193\) −98.0000 −0.0365502 −0.0182751 − 0.999833i \(-0.505817\pi\)
−0.0182751 + 0.999833i \(0.505817\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 1184.00 0.428206 0.214103 − 0.976811i \(-0.431317\pi\)
0.214103 + 0.976811i \(0.431317\pi\)
\(198\) 0 0
\(199\) −1466.00 −0.522221 −0.261111 − 0.965309i \(-0.584089\pi\)
−0.261111 + 0.965309i \(0.584089\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 720.000 0.248936
\(204\) 0 0
\(205\) 1512.00 0.515135
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 32.0000 0.0105908
\(210\) 0 0
\(211\) −2692.00 −0.878317 −0.439159 − 0.898410i \(-0.644723\pi\)
−0.439159 + 0.898410i \(0.644723\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −1728.00 −0.548133
\(216\) 0 0
\(217\) 180.000 0.0563097
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 364.000 0.110793
\(222\) 0 0
\(223\) −4554.00 −1.36753 −0.683763 − 0.729704i \(-0.739658\pi\)
−0.683763 + 0.729704i \(0.739658\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −5580.00 −1.63153 −0.815766 − 0.578383i \(-0.803684\pi\)
−0.815766 + 0.578383i \(0.803684\pi\)
\(228\) 0 0
\(229\) 902.000 0.260288 0.130144 − 0.991495i \(-0.458456\pi\)
0.130144 + 0.991495i \(0.458456\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −1962.00 −0.551652 −0.275826 − 0.961208i \(-0.588951\pi\)
−0.275826 + 0.961208i \(0.588951\pi\)
\(234\) 0 0
\(235\) −592.000 −0.164331
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −2016.00 −0.545624 −0.272812 − 0.962067i \(-0.587954\pi\)
−0.272812 + 0.962067i \(0.587954\pi\)
\(240\) 0 0
\(241\) −1826.00 −0.488062 −0.244031 − 0.969767i \(-0.578470\pi\)
−0.244031 + 0.969767i \(0.578470\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −972.000 −0.253464
\(246\) 0 0
\(247\) −208.000 −0.0535819
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 3060.00 0.769504 0.384752 − 0.923020i \(-0.374287\pi\)
0.384752 + 0.923020i \(0.374287\pi\)
\(252\) 0 0
\(253\) −592.000 −0.147110
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 558.000 0.135436 0.0677181 − 0.997704i \(-0.478428\pi\)
0.0677181 + 0.997704i \(0.478428\pi\)
\(258\) 0 0
\(259\) −2620.00 −0.628567
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −5544.00 −1.29984 −0.649920 − 0.760003i \(-0.725197\pi\)
−0.649920 + 0.760003i \(0.725197\pi\)
\(264\) 0 0
\(265\) 1440.00 0.333806
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 4856.00 1.10065 0.550326 − 0.834950i \(-0.314503\pi\)
0.550326 + 0.834950i \(0.314503\pi\)
\(270\) 0 0
\(271\) 7030.00 1.57580 0.787901 − 0.615803i \(-0.211168\pi\)
0.787901 + 0.615803i \(0.211168\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −436.000 −0.0956065
\(276\) 0 0
\(277\) −738.000 −0.160080 −0.0800399 − 0.996792i \(-0.525505\pi\)
−0.0800399 + 0.996792i \(0.525505\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 1854.00 0.393596 0.196798 − 0.980444i \(-0.436946\pi\)
0.196798 + 0.980444i \(0.436946\pi\)
\(282\) 0 0
\(283\) 1404.00 0.294909 0.147454 − 0.989069i \(-0.452892\pi\)
0.147454 + 0.989069i \(0.452892\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 3780.00 0.777444
\(288\) 0 0
\(289\) −4717.00 −0.960106
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −2056.00 −0.409941 −0.204971 − 0.978768i \(-0.565710\pi\)
−0.204971 + 0.978768i \(0.565710\pi\)
\(294\) 0 0
\(295\) 1712.00 0.337886
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 3848.00 0.744266
\(300\) 0 0
\(301\) −4320.00 −0.827245
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 1768.00 0.331919
\(306\) 0 0
\(307\) −2340.00 −0.435019 −0.217510 − 0.976058i \(-0.569793\pi\)
−0.217510 + 0.976058i \(0.569793\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −1616.00 −0.294646 −0.147323 − 0.989088i \(-0.547066\pi\)
−0.147323 + 0.989088i \(0.547066\pi\)
\(312\) 0 0
\(313\) 3286.00 0.593405 0.296702 − 0.954970i \(-0.404113\pi\)
0.296702 + 0.954970i \(0.404113\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 9936.00 1.76045 0.880223 − 0.474560i \(-0.157393\pi\)
0.880223 + 0.474560i \(0.157393\pi\)
\(318\) 0 0
\(319\) 288.000 0.0505483
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −112.000 −0.0192936
\(324\) 0 0
\(325\) 2834.00 0.483699
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −1480.00 −0.248009
\(330\) 0 0
\(331\) −2116.00 −0.351377 −0.175689 − 0.984446i \(-0.556215\pi\)
−0.175689 + 0.984446i \(0.556215\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −2768.00 −0.451439
\(336\) 0 0
\(337\) −7874.00 −1.27277 −0.636386 − 0.771371i \(-0.719571\pi\)
−0.636386 + 0.771371i \(0.719571\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 72.0000 0.0114341
\(342\) 0 0
\(343\) −5860.00 −0.922479
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 10476.0 1.62069 0.810347 − 0.585950i \(-0.199278\pi\)
0.810347 + 0.585950i \(0.199278\pi\)
\(348\) 0 0
\(349\) −7030.00 −1.07824 −0.539122 − 0.842228i \(-0.681244\pi\)
−0.539122 + 0.842228i \(0.681244\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 5310.00 0.800631 0.400316 − 0.916377i \(-0.368901\pi\)
0.400316 + 0.916377i \(0.368901\pi\)
\(354\) 0 0
\(355\) −2160.00 −0.322932
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −7628.00 −1.12142 −0.560711 − 0.828012i \(-0.689472\pi\)
−0.560711 + 0.828012i \(0.689472\pi\)
\(360\) 0 0
\(361\) −6795.00 −0.990669
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −4072.00 −0.583940
\(366\) 0 0
\(367\) 13778.0 1.95969 0.979844 − 0.199763i \(-0.0640171\pi\)
0.979844 + 0.199763i \(0.0640171\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 3600.00 0.503781
\(372\) 0 0
\(373\) −2566.00 −0.356200 −0.178100 − 0.984012i \(-0.556995\pi\)
−0.178100 + 0.984012i \(0.556995\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −1872.00 −0.255737
\(378\) 0 0
\(379\) 7120.00 0.964986 0.482493 − 0.875900i \(-0.339731\pi\)
0.482493 + 0.875900i \(0.339731\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 14040.0 1.87313 0.936567 − 0.350488i \(-0.113984\pi\)
0.936567 + 0.350488i \(0.113984\pi\)
\(384\) 0 0
\(385\) 160.000 0.0211801
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −4972.00 −0.648047 −0.324024 − 0.946049i \(-0.605036\pi\)
−0.324024 + 0.946049i \(0.605036\pi\)
\(390\) 0 0
\(391\) 2072.00 0.267994
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 1544.00 0.196676
\(396\) 0 0
\(397\) −8766.00 −1.10819 −0.554097 − 0.832452i \(-0.686936\pi\)
−0.554097 + 0.832452i \(0.686936\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 12042.0 1.49962 0.749811 − 0.661652i \(-0.230144\pi\)
0.749811 + 0.661652i \(0.230144\pi\)
\(402\) 0 0
\(403\) −468.000 −0.0578480
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −1048.00 −0.127635
\(408\) 0 0
\(409\) 8002.00 0.967417 0.483708 − 0.875229i \(-0.339290\pi\)
0.483708 + 0.875229i \(0.339290\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 4280.00 0.509940
\(414\) 0 0
\(415\) −432.000 −0.0510989
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −364.000 −0.0424405 −0.0212202 − 0.999775i \(-0.506755\pi\)
−0.0212202 + 0.999775i \(0.506755\pi\)
\(420\) 0 0
\(421\) 1502.00 0.173879 0.0869394 − 0.996214i \(-0.472291\pi\)
0.0869394 + 0.996214i \(0.472291\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 1526.00 0.174169
\(426\) 0 0
\(427\) 4420.00 0.500934
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −3532.00 −0.394734 −0.197367 − 0.980330i \(-0.563239\pi\)
−0.197367 + 0.980330i \(0.563239\pi\)
\(432\) 0 0
\(433\) 8946.00 0.992881 0.496440 − 0.868071i \(-0.334640\pi\)
0.496440 + 0.868071i \(0.334640\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −1184.00 −0.129607
\(438\) 0 0
\(439\) −1602.00 −0.174167 −0.0870835 − 0.996201i \(-0.527755\pi\)
−0.0870835 + 0.996201i \(0.527755\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −4356.00 −0.467178 −0.233589 − 0.972335i \(-0.575047\pi\)
−0.233589 + 0.972335i \(0.575047\pi\)
\(444\) 0 0
\(445\) 1528.00 0.162773
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −2110.00 −0.221775 −0.110888 − 0.993833i \(-0.535369\pi\)
−0.110888 + 0.993833i \(0.535369\pi\)
\(450\) 0 0
\(451\) 1512.00 0.157865
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −1040.00 −0.107156
\(456\) 0 0
\(457\) 13698.0 1.40211 0.701056 − 0.713106i \(-0.252712\pi\)
0.701056 + 0.713106i \(0.252712\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −12028.0 −1.21518 −0.607592 − 0.794249i \(-0.707864\pi\)
−0.607592 + 0.794249i \(0.707864\pi\)
\(462\) 0 0
\(463\) 10286.0 1.03246 0.516232 − 0.856449i \(-0.327334\pi\)
0.516232 + 0.856449i \(0.327334\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −11516.0 −1.14111 −0.570553 − 0.821260i \(-0.693271\pi\)
−0.570553 + 0.821260i \(0.693271\pi\)
\(468\) 0 0
\(469\) −6920.00 −0.681313
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −1728.00 −0.167978
\(474\) 0 0
\(475\) −872.000 −0.0842318
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 13932.0 1.32895 0.664477 − 0.747308i \(-0.268654\pi\)
0.664477 + 0.747308i \(0.268654\pi\)
\(480\) 0 0
\(481\) 6812.00 0.645739
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 1192.00 0.111600
\(486\) 0 0
\(487\) 10682.0 0.993938 0.496969 − 0.867768i \(-0.334446\pi\)
0.496969 + 0.867768i \(0.334446\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 11660.0 1.07171 0.535854 − 0.844311i \(-0.319990\pi\)
0.535854 + 0.844311i \(0.319990\pi\)
\(492\) 0 0
\(493\) −1008.00 −0.0920853
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −5400.00 −0.487370
\(498\) 0 0
\(499\) 12404.0 1.11278 0.556392 − 0.830920i \(-0.312185\pi\)
0.556392 + 0.830920i \(0.312185\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 2308.00 0.204590 0.102295 − 0.994754i \(-0.467381\pi\)
0.102295 + 0.994754i \(0.467381\pi\)
\(504\) 0 0
\(505\) 7200.00 0.634447
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −1984.00 −0.172769 −0.0863843 − 0.996262i \(-0.527531\pi\)
−0.0863843 + 0.996262i \(0.527531\pi\)
\(510\) 0 0
\(511\) −10180.0 −0.881285
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −3272.00 −0.279964
\(516\) 0 0
\(517\) −592.000 −0.0503600
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −3982.00 −0.334846 −0.167423 − 0.985885i \(-0.553545\pi\)
−0.167423 + 0.985885i \(0.553545\pi\)
\(522\) 0 0
\(523\) 18368.0 1.53571 0.767855 − 0.640623i \(-0.221324\pi\)
0.767855 + 0.640623i \(0.221324\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −252.000 −0.0208298
\(528\) 0 0
\(529\) 9737.00 0.800279
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −9828.00 −0.798683
\(534\) 0 0
\(535\) −2864.00 −0.231442
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −972.000 −0.0776753
\(540\) 0 0
\(541\) 2870.00 0.228079 0.114040 − 0.993476i \(-0.463621\pi\)
0.114040 + 0.993476i \(0.463621\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 4536.00 0.356515
\(546\) 0 0
\(547\) 14176.0 1.10808 0.554042 − 0.832489i \(-0.313085\pi\)
0.554042 + 0.832489i \(0.313085\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 576.000 0.0445343
\(552\) 0 0
\(553\) 3860.00 0.296824
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −12884.0 −0.980094 −0.490047 − 0.871696i \(-0.663020\pi\)
−0.490047 + 0.871696i \(0.663020\pi\)
\(558\) 0 0
\(559\) 11232.0 0.849844
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −15588.0 −1.16688 −0.583442 − 0.812155i \(-0.698295\pi\)
−0.583442 + 0.812155i \(0.698295\pi\)
\(564\) 0 0
\(565\) −7432.00 −0.553392
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 4730.00 0.348492 0.174246 − 0.984702i \(-0.444251\pi\)
0.174246 + 0.984702i \(0.444251\pi\)
\(570\) 0 0
\(571\) 4724.00 0.346223 0.173111 − 0.984902i \(-0.444618\pi\)
0.173111 + 0.984902i \(0.444618\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 16132.0 1.17000
\(576\) 0 0
\(577\) 16838.0 1.21486 0.607431 − 0.794373i \(-0.292200\pi\)
0.607431 + 0.794373i \(0.292200\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −1080.00 −0.0771187
\(582\) 0 0
\(583\) 1440.00 0.102296
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 9932.00 0.698360 0.349180 − 0.937056i \(-0.386460\pi\)
0.349180 + 0.937056i \(0.386460\pi\)
\(588\) 0 0
\(589\) 144.000 0.0100737
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −15714.0 −1.08819 −0.544095 − 0.839024i \(-0.683127\pi\)
−0.544095 + 0.839024i \(0.683127\pi\)
\(594\) 0 0
\(595\) −560.000 −0.0385845
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 20340.0 1.38743 0.693714 − 0.720250i \(-0.255973\pi\)
0.693714 + 0.720250i \(0.255973\pi\)
\(600\) 0 0
\(601\) −16434.0 −1.11540 −0.557701 − 0.830042i \(-0.688316\pi\)
−0.557701 + 0.830042i \(0.688316\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −5260.00 −0.353470
\(606\) 0 0
\(607\) −8234.00 −0.550589 −0.275295 − 0.961360i \(-0.588775\pi\)
−0.275295 + 0.961360i \(0.588775\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 3848.00 0.254785
\(612\) 0 0
\(613\) 6506.00 0.428670 0.214335 − 0.976760i \(-0.431242\pi\)
0.214335 + 0.976760i \(0.431242\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 20542.0 1.34034 0.670170 − 0.742208i \(-0.266221\pi\)
0.670170 + 0.742208i \(0.266221\pi\)
\(618\) 0 0
\(619\) 11116.0 0.721793 0.360896 − 0.932606i \(-0.382471\pi\)
0.360896 + 0.932606i \(0.382471\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 3820.00 0.245658
\(624\) 0 0
\(625\) 9881.00 0.632384
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 3668.00 0.232516
\(630\) 0 0
\(631\) −3574.00 −0.225481 −0.112741 − 0.993624i \(-0.535963\pi\)
−0.112741 + 0.993624i \(0.535963\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −5608.00 −0.350467
\(636\) 0 0
\(637\) 6318.00 0.392980
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −7110.00 −0.438109 −0.219055 − 0.975713i \(-0.570297\pi\)
−0.219055 + 0.975713i \(0.570297\pi\)
\(642\) 0 0
\(643\) −1728.00 −0.105981 −0.0529904 − 0.998595i \(-0.516875\pi\)
−0.0529904 + 0.998595i \(0.516875\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −14724.0 −0.894683 −0.447342 − 0.894363i \(-0.647629\pi\)
−0.447342 + 0.894363i \(0.647629\pi\)
\(648\) 0 0
\(649\) 1712.00 0.103547
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −23076.0 −1.38290 −0.691450 − 0.722424i \(-0.743028\pi\)
−0.691450 + 0.722424i \(0.743028\pi\)
\(654\) 0 0
\(655\) −4752.00 −0.283475
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 27252.0 1.61091 0.805453 − 0.592660i \(-0.201922\pi\)
0.805453 + 0.592660i \(0.201922\pi\)
\(660\) 0 0
\(661\) −18910.0 −1.11273 −0.556364 − 0.830938i \(-0.687804\pi\)
−0.556364 + 0.830938i \(0.687804\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 320.000 0.0186603
\(666\) 0 0
\(667\) −10656.0 −0.618594
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 1768.00 0.101718
\(672\) 0 0
\(673\) −350.000 −0.0200468 −0.0100234 − 0.999950i \(-0.503191\pi\)
−0.0100234 + 0.999950i \(0.503191\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 13468.0 0.764575 0.382288 − 0.924043i \(-0.375136\pi\)
0.382288 + 0.924043i \(0.375136\pi\)
\(678\) 0 0
\(679\) 2980.00 0.168427
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −12852.0 −0.720012 −0.360006 − 0.932950i \(-0.617225\pi\)
−0.360006 + 0.932950i \(0.617225\pi\)
\(684\) 0 0
\(685\) −2936.00 −0.163765
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −9360.00 −0.517544
\(690\) 0 0
\(691\) −1080.00 −0.0594575 −0.0297288 − 0.999558i \(-0.509464\pi\)
−0.0297288 + 0.999558i \(0.509464\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 1616.00 0.0881991
\(696\) 0 0
\(697\) −5292.00 −0.287588
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 22720.0 1.22414 0.612070 − 0.790803i \(-0.290337\pi\)
0.612070 + 0.790803i \(0.290337\pi\)
\(702\) 0 0
\(703\) −2096.00 −0.112450
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 18000.0 0.957510
\(708\) 0 0
\(709\) −22346.0 −1.18367 −0.591835 − 0.806059i \(-0.701596\pi\)
−0.591835 + 0.806059i \(0.701596\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −2664.00 −0.139926
\(714\) 0 0
\(715\) −416.000 −0.0217588
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −35244.0 −1.82807 −0.914033 − 0.405640i \(-0.867049\pi\)
−0.914033 + 0.405640i \(0.867049\pi\)
\(720\) 0 0
\(721\) −8180.00 −0.422523
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −7848.00 −0.402024
\(726\) 0 0
\(727\) 25074.0 1.27915 0.639576 − 0.768728i \(-0.279110\pi\)
0.639576 + 0.768728i \(0.279110\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 6048.00 0.306010
\(732\) 0 0
\(733\) 23742.0 1.19636 0.598179 − 0.801362i \(-0.295891\pi\)
0.598179 + 0.801362i \(0.295891\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −2768.00 −0.138345
\(738\) 0 0
\(739\) −4932.00 −0.245503 −0.122751 − 0.992437i \(-0.539172\pi\)
−0.122751 + 0.992437i \(0.539172\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 26248.0 1.29602 0.648012 − 0.761630i \(-0.275601\pi\)
0.648012 + 0.761630i \(0.275601\pi\)
\(744\) 0 0
\(745\) −2736.00 −0.134549
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −7160.00 −0.349293
\(750\) 0 0
\(751\) 26146.0 1.27041 0.635207 − 0.772342i \(-0.280915\pi\)
0.635207 + 0.772342i \(0.280915\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −14008.0 −0.675236
\(756\) 0 0
\(757\) −4202.00 −0.201749 −0.100875 − 0.994899i \(-0.532164\pi\)
−0.100875 + 0.994899i \(0.532164\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 31018.0 1.47753 0.738766 − 0.673962i \(-0.235409\pi\)
0.738766 + 0.673962i \(0.235409\pi\)
\(762\) 0 0
\(763\) 11340.0 0.538054
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −11128.0 −0.523871
\(768\) 0 0
\(769\) −7570.00 −0.354982 −0.177491 − 0.984122i \(-0.556798\pi\)
−0.177491 + 0.984122i \(0.556798\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 31392.0 1.46066 0.730331 − 0.683093i \(-0.239366\pi\)
0.730331 + 0.683093i \(0.239366\pi\)
\(774\) 0 0
\(775\) −1962.00 −0.0909382
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 3024.00 0.139083
\(780\) 0 0
\(781\) −2160.00 −0.0989640
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 13032.0 0.592525
\(786\) 0 0
\(787\) −14608.0 −0.661651 −0.330825 − 0.943692i \(-0.607327\pi\)
−0.330825 + 0.943692i \(0.607327\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −18580.0 −0.835182
\(792\) 0 0
\(793\) −11492.0 −0.514619
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 30204.0 1.34238 0.671192 − 0.741283i \(-0.265782\pi\)
0.671192 + 0.741283i \(0.265782\pi\)
\(798\) 0 0
\(799\) 2072.00 0.0917423
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −4072.00 −0.178951
\(804\) 0 0
\(805\) −5920.00 −0.259196
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 306.000 0.0132984 0.00664919 − 0.999978i \(-0.497883\pi\)
0.00664919 + 0.999978i \(0.497883\pi\)
\(810\) 0 0
\(811\) −34920.0 −1.51197 −0.755985 − 0.654589i \(-0.772842\pi\)
−0.755985 + 0.654589i \(0.772842\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −3424.00 −0.147163
\(816\) 0 0
\(817\) −3456.00 −0.147993
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 14720.0 0.625739 0.312869 − 0.949796i \(-0.398710\pi\)
0.312869 + 0.949796i \(0.398710\pi\)
\(822\) 0 0
\(823\) −14030.0 −0.594235 −0.297117 − 0.954841i \(-0.596025\pi\)
−0.297117 + 0.954841i \(0.596025\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −24764.0 −1.04127 −0.520634 − 0.853780i \(-0.674304\pi\)
−0.520634 + 0.853780i \(0.674304\pi\)
\(828\) 0 0
\(829\) −1810.00 −0.0758310 −0.0379155 − 0.999281i \(-0.512072\pi\)
−0.0379155 + 0.999281i \(0.512072\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 3402.00 0.141503
\(834\) 0 0
\(835\) −6208.00 −0.257289
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −4500.00 −0.185170 −0.0925848 − 0.995705i \(-0.529513\pi\)
−0.0925848 + 0.995705i \(0.529513\pi\)
\(840\) 0 0
\(841\) −19205.0 −0.787445
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −6084.00 −0.247688
\(846\) 0 0
\(847\) −13150.0 −0.533458
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 38776.0 1.56196
\(852\) 0 0
\(853\) 29458.0 1.18244 0.591221 − 0.806510i \(-0.298646\pi\)
0.591221 + 0.806510i \(0.298646\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −15030.0 −0.599084 −0.299542 − 0.954083i \(-0.596834\pi\)
−0.299542 + 0.954083i \(0.596834\pi\)
\(858\) 0 0
\(859\) −27368.0 −1.08706 −0.543530 − 0.839390i \(-0.682912\pi\)
−0.543530 + 0.839390i \(0.682912\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −39352.0 −1.55221 −0.776105 − 0.630603i \(-0.782807\pi\)
−0.776105 + 0.630603i \(0.782807\pi\)
\(864\) 0 0
\(865\) −6192.00 −0.243392
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 1544.00 0.0602723
\(870\) 0 0
\(871\) 17992.0 0.699926
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −9360.00 −0.361629
\(876\) 0 0
\(877\) −32246.0 −1.24159 −0.620793 − 0.783975i \(-0.713189\pi\)
−0.620793 + 0.783975i \(0.713189\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −1714.00 −0.0655461 −0.0327731 − 0.999463i \(-0.510434\pi\)
−0.0327731 + 0.999463i \(0.510434\pi\)
\(882\) 0 0
\(883\) 1288.00 0.0490879 0.0245440 − 0.999699i \(-0.492187\pi\)
0.0245440 + 0.999699i \(0.492187\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 12888.0 0.487865 0.243933 − 0.969792i \(-0.421562\pi\)
0.243933 + 0.969792i \(0.421562\pi\)
\(888\) 0 0
\(889\) −14020.0 −0.528927
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −1184.00 −0.0443685
\(894\) 0 0
\(895\) −13680.0 −0.510918
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 1296.00 0.0480801
\(900\) 0 0
\(901\) −5040.00 −0.186356
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 14008.0 0.514521
\(906\) 0 0
\(907\) −44920.0 −1.64448 −0.822240 − 0.569140i \(-0.807276\pi\)
−0.822240 + 0.569140i \(0.807276\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −12384.0 −0.450384 −0.225192 − 0.974314i \(-0.572301\pi\)
−0.225192 + 0.974314i \(0.572301\pi\)
\(912\) 0 0
\(913\) −432.000 −0.0156595
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −11880.0 −0.427821
\(918\) 0 0
\(919\) −8190.00 −0.293975 −0.146988 − 0.989138i \(-0.546958\pi\)
−0.146988 + 0.989138i \(0.546958\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 14040.0 0.500685
\(924\) 0 0
\(925\) 28558.0 1.01511
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 4698.00 0.165916 0.0829582 − 0.996553i \(-0.473563\pi\)
0.0829582 + 0.996553i \(0.473563\pi\)
\(930\) 0 0
\(931\) −1944.00 −0.0684340
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −224.000 −0.00783485
\(936\) 0 0
\(937\) −10646.0 −0.371174 −0.185587 − 0.982628i \(-0.559419\pi\)
−0.185587 + 0.982628i \(0.559419\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −25852.0 −0.895591 −0.447795 − 0.894136i \(-0.647791\pi\)
−0.447795 + 0.894136i \(0.647791\pi\)
\(942\) 0 0
\(943\) −55944.0 −1.93191
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 3172.00 0.108845 0.0544225 − 0.998518i \(-0.482668\pi\)
0.0544225 + 0.998518i \(0.482668\pi\)
\(948\) 0 0
\(949\) 26468.0 0.905361
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −53150.0 −1.80661 −0.903304 − 0.429001i \(-0.858866\pi\)
−0.903304 + 0.429001i \(0.858866\pi\)
\(954\) 0 0
\(955\) 19168.0 0.649489
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −7340.00 −0.247154
\(960\) 0 0
\(961\) −29467.0 −0.989124
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −392.000 −0.0130766
\(966\) 0 0
\(967\) −9802.00 −0.325968 −0.162984 − 0.986629i \(-0.552112\pi\)
−0.162984 + 0.986629i \(0.552112\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −46660.0 −1.54211 −0.771056 − 0.636767i \(-0.780271\pi\)
−0.771056 + 0.636767i \(0.780271\pi\)
\(972\) 0 0
\(973\) 4040.00 0.133110
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 41994.0 1.37514 0.687568 − 0.726120i \(-0.258678\pi\)
0.687568 + 0.726120i \(0.258678\pi\)
\(978\) 0 0
\(979\) 1528.00 0.0498826
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 11848.0 0.384428 0.192214 − 0.981353i \(-0.438433\pi\)
0.192214 + 0.981353i \(0.438433\pi\)
\(984\) 0 0
\(985\) 4736.00 0.153200
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 63936.0 2.05566
\(990\) 0 0
\(991\) −7390.00 −0.236883 −0.118442 − 0.992961i \(-0.537790\pi\)
−0.118442 + 0.992961i \(0.537790\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −5864.00 −0.186835
\(996\) 0 0
\(997\) 47682.0 1.51465 0.757324 − 0.653039i \(-0.226506\pi\)
0.757324 + 0.653039i \(0.226506\pi\)
\(998\) 0 0
\(999\) 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 1152.4.a.h.1.1 1
3.2 odd 2 384.4.a.b.1.1 ✓ 1
4.3 odd 2 1152.4.a.g.1.1 1
8.3 odd 2 1152.4.a.e.1.1 1
8.5 even 2 1152.4.a.f.1.1 1
12.11 even 2 384.4.a.f.1.1 yes 1
24.5 odd 2 384.4.a.g.1.1 yes 1
24.11 even 2 384.4.a.c.1.1 yes 1
48.5 odd 4 768.4.d.f.385.2 2
48.11 even 4 768.4.d.k.385.1 2
48.29 odd 4 768.4.d.f.385.1 2
48.35 even 4 768.4.d.k.385.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
384.4.a.b.1.1 ✓ 1 3.2 odd 2
384.4.a.c.1.1 yes 1 24.11 even 2
384.4.a.f.1.1 yes 1 12.11 even 2
384.4.a.g.1.1 yes 1 24.5 odd 2
768.4.d.f.385.1 2 48.29 odd 4
768.4.d.f.385.2 2 48.5 odd 4
768.4.d.k.385.1 2 48.11 even 4
768.4.d.k.385.2 2 48.35 even 4
1152.4.a.e.1.1 1 8.3 odd 2
1152.4.a.f.1.1 1 8.5 even 2
1152.4.a.g.1.1 1 4.3 odd 2
1152.4.a.h.1.1 1 1.1 even 1 trivial