Properties

Label 2352.4.a.bj.1.1
Level $2352$
Weight $4$
Character 2352.1
Self dual yes
Analytic conductor $138.772$
Analytic rank $0$
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] = [2352,4,Mod(1,2352)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2352, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("2352.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2352.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: \(138.772492334\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 168)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 2352.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+3.00000 q^{3} +16.0000 q^{5} +9.00000 q^{9} +O(q^{10})\) \(q+3.00000 q^{3} +16.0000 q^{5} +9.00000 q^{9} +18.0000 q^{11} +54.0000 q^{13} +48.0000 q^{15} +128.000 q^{17} +52.0000 q^{19} +202.000 q^{23} +131.000 q^{25} +27.0000 q^{27} +302.000 q^{29} -200.000 q^{31} +54.0000 q^{33} -150.000 q^{37} +162.000 q^{39} -172.000 q^{41} -164.000 q^{43} +144.000 q^{45} -460.000 q^{47} +384.000 q^{51} -190.000 q^{53} +288.000 q^{55} +156.000 q^{57} +96.0000 q^{59} -622.000 q^{61} +864.000 q^{65} -744.000 q^{67} +606.000 q^{69} +54.0000 q^{71} -742.000 q^{73} +393.000 q^{75} +92.0000 q^{79} +81.0000 q^{81} -228.000 q^{83} +2048.00 q^{85} +906.000 q^{87} +116.000 q^{89} -600.000 q^{93} +832.000 q^{95} +554.000 q^{97} +162.000 q^{99} +O(q^{100})\)

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
\(3\) 3.00000 0.577350
\(4\) 0 0
\(5\) 16.0000 1.43108 0.715542 0.698570i \(-0.246180\pi\)
0.715542 + 0.698570i \(0.246180\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 9.00000 0.333333
\(10\) 0 0
\(11\) 18.0000 0.493382 0.246691 0.969094i \(-0.420657\pi\)
0.246691 + 0.969094i \(0.420657\pi\)
\(12\) 0 0
\(13\) 54.0000 1.15207 0.576035 0.817425i \(-0.304599\pi\)
0.576035 + 0.817425i \(0.304599\pi\)
\(14\) 0 0
\(15\) 48.0000 0.826236
\(16\) 0 0
\(17\) 128.000 1.82615 0.913075 0.407791i \(-0.133701\pi\)
0.913075 + 0.407791i \(0.133701\pi\)
\(18\) 0 0
\(19\) 52.0000 0.627875 0.313937 0.949444i \(-0.398352\pi\)
0.313937 + 0.949444i \(0.398352\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 202.000 1.83130 0.915650 0.401976i \(-0.131676\pi\)
0.915650 + 0.401976i \(0.131676\pi\)
\(24\) 0 0
\(25\) 131.000 1.04800
\(26\) 0 0
\(27\) 27.0000 0.192450
\(28\) 0 0
\(29\) 302.000 1.93379 0.966896 0.255169i \(-0.0821312\pi\)
0.966896 + 0.255169i \(0.0821312\pi\)
\(30\) 0 0
\(31\) −200.000 −1.15874 −0.579372 0.815063i \(-0.696702\pi\)
−0.579372 + 0.815063i \(0.696702\pi\)
\(32\) 0 0
\(33\) 54.0000 0.284854
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −150.000 −0.666482 −0.333241 0.942842i \(-0.608142\pi\)
−0.333241 + 0.942842i \(0.608142\pi\)
\(38\) 0 0
\(39\) 162.000 0.665148
\(40\) 0 0
\(41\) −172.000 −0.655168 −0.327584 0.944822i \(-0.606234\pi\)
−0.327584 + 0.944822i \(0.606234\pi\)
\(42\) 0 0
\(43\) −164.000 −0.581622 −0.290811 0.956780i \(-0.593925\pi\)
−0.290811 + 0.956780i \(0.593925\pi\)
\(44\) 0 0
\(45\) 144.000 0.477028
\(46\) 0 0
\(47\) −460.000 −1.42761 −0.713807 0.700342i \(-0.753031\pi\)
−0.713807 + 0.700342i \(0.753031\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 384.000 1.05433
\(52\) 0 0
\(53\) −190.000 −0.492425 −0.246212 0.969216i \(-0.579186\pi\)
−0.246212 + 0.969216i \(0.579186\pi\)
\(54\) 0 0
\(55\) 288.000 0.706071
\(56\) 0 0
\(57\) 156.000 0.362504
\(58\) 0 0
\(59\) 96.0000 0.211833 0.105916 0.994375i \(-0.466222\pi\)
0.105916 + 0.994375i \(0.466222\pi\)
\(60\) 0 0
\(61\) −622.000 −1.30556 −0.652778 0.757549i \(-0.726397\pi\)
−0.652778 + 0.757549i \(0.726397\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 864.000 1.64871
\(66\) 0 0
\(67\) −744.000 −1.35663 −0.678314 0.734772i \(-0.737289\pi\)
−0.678314 + 0.734772i \(0.737289\pi\)
\(68\) 0 0
\(69\) 606.000 1.05730
\(70\) 0 0
\(71\) 54.0000 0.0902623 0.0451311 0.998981i \(-0.485629\pi\)
0.0451311 + 0.998981i \(0.485629\pi\)
\(72\) 0 0
\(73\) −742.000 −1.18965 −0.594826 0.803855i \(-0.702779\pi\)
−0.594826 + 0.803855i \(0.702779\pi\)
\(74\) 0 0
\(75\) 393.000 0.605063
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 92.0000 0.131023 0.0655114 0.997852i \(-0.479132\pi\)
0.0655114 + 0.997852i \(0.479132\pi\)
\(80\) 0 0
\(81\) 81.0000 0.111111
\(82\) 0 0
\(83\) −228.000 −0.301521 −0.150761 0.988570i \(-0.548172\pi\)
−0.150761 + 0.988570i \(0.548172\pi\)
\(84\) 0 0
\(85\) 2048.00 2.61337
\(86\) 0 0
\(87\) 906.000 1.11648
\(88\) 0 0
\(89\) 116.000 0.138157 0.0690785 0.997611i \(-0.477994\pi\)
0.0690785 + 0.997611i \(0.477994\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −600.000 −0.669001
\(94\) 0 0
\(95\) 832.000 0.898541
\(96\) 0 0
\(97\) 554.000 0.579899 0.289949 0.957042i \(-0.406362\pi\)
0.289949 + 0.957042i \(0.406362\pi\)
\(98\) 0 0
\(99\) 162.000 0.164461
\(100\) 0 0
\(101\) 780.000 0.768445 0.384222 0.923241i \(-0.374470\pi\)
0.384222 + 0.923241i \(0.374470\pi\)
\(102\) 0 0
\(103\) 24.0000 0.0229591 0.0114796 0.999934i \(-0.496346\pi\)
0.0114796 + 0.999934i \(0.496346\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −78.0000 −0.0704724 −0.0352362 0.999379i \(-0.511218\pi\)
−0.0352362 + 0.999379i \(0.511218\pi\)
\(108\) 0 0
\(109\) −1034.00 −0.908617 −0.454308 0.890844i \(-0.650114\pi\)
−0.454308 + 0.890844i \(0.650114\pi\)
\(110\) 0 0
\(111\) −450.000 −0.384794
\(112\) 0 0
\(113\) 186.000 0.154844 0.0774222 0.996998i \(-0.475331\pi\)
0.0774222 + 0.996998i \(0.475331\pi\)
\(114\) 0 0
\(115\) 3232.00 2.62074
\(116\) 0 0
\(117\) 486.000 0.384023
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −1007.00 −0.756574
\(122\) 0 0
\(123\) −516.000 −0.378261
\(124\) 0 0
\(125\) 96.0000 0.0686920
\(126\) 0 0
\(127\) 316.000 0.220791 0.110396 0.993888i \(-0.464788\pi\)
0.110396 + 0.993888i \(0.464788\pi\)
\(128\) 0 0
\(129\) −492.000 −0.335800
\(130\) 0 0
\(131\) −988.000 −0.658946 −0.329473 0.944165i \(-0.606871\pi\)
−0.329473 + 0.944165i \(0.606871\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 432.000 0.275412
\(136\) 0 0
\(137\) 950.000 0.592438 0.296219 0.955120i \(-0.404274\pi\)
0.296219 + 0.955120i \(0.404274\pi\)
\(138\) 0 0
\(139\) −2124.00 −1.29608 −0.648041 0.761606i \(-0.724411\pi\)
−0.648041 + 0.761606i \(0.724411\pi\)
\(140\) 0 0
\(141\) −1380.00 −0.824234
\(142\) 0 0
\(143\) 972.000 0.568411
\(144\) 0 0
\(145\) 4832.00 2.76742
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 2242.00 1.23270 0.616348 0.787474i \(-0.288611\pi\)
0.616348 + 0.787474i \(0.288611\pi\)
\(150\) 0 0
\(151\) −2776.00 −1.49608 −0.748039 0.663655i \(-0.769004\pi\)
−0.748039 + 0.663655i \(0.769004\pi\)
\(152\) 0 0
\(153\) 1152.00 0.608717
\(154\) 0 0
\(155\) −3200.00 −1.65826
\(156\) 0 0
\(157\) 3258.00 1.65616 0.828079 0.560612i \(-0.189434\pi\)
0.828079 + 0.560612i \(0.189434\pi\)
\(158\) 0 0
\(159\) −570.000 −0.284302
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 2432.00 1.16864 0.584322 0.811522i \(-0.301361\pi\)
0.584322 + 0.811522i \(0.301361\pi\)
\(164\) 0 0
\(165\) 864.000 0.407650
\(166\) 0 0
\(167\) −3156.00 −1.46239 −0.731193 0.682170i \(-0.761036\pi\)
−0.731193 + 0.682170i \(0.761036\pi\)
\(168\) 0 0
\(169\) 719.000 0.327264
\(170\) 0 0
\(171\) 468.000 0.209292
\(172\) 0 0
\(173\) 3724.00 1.63659 0.818296 0.574797i \(-0.194919\pi\)
0.818296 + 0.574797i \(0.194919\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 288.000 0.122302
\(178\) 0 0
\(179\) 2398.00 1.00131 0.500656 0.865646i \(-0.333092\pi\)
0.500656 + 0.865646i \(0.333092\pi\)
\(180\) 0 0
\(181\) −2906.00 −1.19338 −0.596689 0.802473i \(-0.703517\pi\)
−0.596689 + 0.802473i \(0.703517\pi\)
\(182\) 0 0
\(183\) −1866.00 −0.753763
\(184\) 0 0
\(185\) −2400.00 −0.953792
\(186\) 0 0
\(187\) 2304.00 0.900990
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 1478.00 0.559918 0.279959 0.960012i \(-0.409679\pi\)
0.279959 + 0.960012i \(0.409679\pi\)
\(192\) 0 0
\(193\) −1098.00 −0.409512 −0.204756 0.978813i \(-0.565640\pi\)
−0.204756 + 0.978813i \(0.565640\pi\)
\(194\) 0 0
\(195\) 2592.00 0.951882
\(196\) 0 0
\(197\) 5058.00 1.82928 0.914639 0.404273i \(-0.132475\pi\)
0.914639 + 0.404273i \(0.132475\pi\)
\(198\) 0 0
\(199\) −4432.00 −1.57877 −0.789387 0.613895i \(-0.789602\pi\)
−0.789387 + 0.613895i \(0.789602\pi\)
\(200\) 0 0
\(201\) −2232.00 −0.783249
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −2752.00 −0.937600
\(206\) 0 0
\(207\) 1818.00 0.610434
\(208\) 0 0
\(209\) 936.000 0.309782
\(210\) 0 0
\(211\) −5444.00 −1.77621 −0.888105 0.459640i \(-0.847978\pi\)
−0.888105 + 0.459640i \(0.847978\pi\)
\(212\) 0 0
\(213\) 162.000 0.0521129
\(214\) 0 0
\(215\) −2624.00 −0.832350
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −2226.00 −0.686845
\(220\) 0 0
\(221\) 6912.00 2.10385
\(222\) 0 0
\(223\) −5352.00 −1.60716 −0.803579 0.595198i \(-0.797074\pi\)
−0.803579 + 0.595198i \(0.797074\pi\)
\(224\) 0 0
\(225\) 1179.00 0.349333
\(226\) 0 0
\(227\) 3752.00 1.09704 0.548522 0.836136i \(-0.315191\pi\)
0.548522 + 0.836136i \(0.315191\pi\)
\(228\) 0 0
\(229\) 5446.00 1.57154 0.785768 0.618521i \(-0.212268\pi\)
0.785768 + 0.618521i \(0.212268\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −2602.00 −0.731600 −0.365800 0.930694i \(-0.619204\pi\)
−0.365800 + 0.930694i \(0.619204\pi\)
\(234\) 0 0
\(235\) −7360.00 −2.04304
\(236\) 0 0
\(237\) 276.000 0.0756461
\(238\) 0 0
\(239\) 1810.00 0.489871 0.244935 0.969539i \(-0.421233\pi\)
0.244935 + 0.969539i \(0.421233\pi\)
\(240\) 0 0
\(241\) −310.000 −0.0828583 −0.0414292 0.999141i \(-0.513191\pi\)
−0.0414292 + 0.999141i \(0.513191\pi\)
\(242\) 0 0
\(243\) 243.000 0.0641500
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 2808.00 0.723355
\(248\) 0 0
\(249\) −684.000 −0.174083
\(250\) 0 0
\(251\) −32.0000 −0.00804710 −0.00402355 0.999992i \(-0.501281\pi\)
−0.00402355 + 0.999992i \(0.501281\pi\)
\(252\) 0 0
\(253\) 3636.00 0.903531
\(254\) 0 0
\(255\) 6144.00 1.50883
\(256\) 0 0
\(257\) −3348.00 −0.812617 −0.406308 0.913736i \(-0.633184\pi\)
−0.406308 + 0.913736i \(0.633184\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 2718.00 0.644598
\(262\) 0 0
\(263\) −4086.00 −0.957998 −0.478999 0.877815i \(-0.659000\pi\)
−0.478999 + 0.877815i \(0.659000\pi\)
\(264\) 0 0
\(265\) −3040.00 −0.704701
\(266\) 0 0
\(267\) 348.000 0.0797650
\(268\) 0 0
\(269\) −1416.00 −0.320948 −0.160474 0.987040i \(-0.551302\pi\)
−0.160474 + 0.987040i \(0.551302\pi\)
\(270\) 0 0
\(271\) −3856.00 −0.864337 −0.432168 0.901793i \(-0.642251\pi\)
−0.432168 + 0.901793i \(0.642251\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 2358.00 0.517065
\(276\) 0 0
\(277\) −1358.00 −0.294564 −0.147282 0.989095i \(-0.547053\pi\)
−0.147282 + 0.989095i \(0.547053\pi\)
\(278\) 0 0
\(279\) −1800.00 −0.386248
\(280\) 0 0
\(281\) −1698.00 −0.360478 −0.180239 0.983623i \(-0.557687\pi\)
−0.180239 + 0.983623i \(0.557687\pi\)
\(282\) 0 0
\(283\) −6340.00 −1.33171 −0.665855 0.746081i \(-0.731933\pi\)
−0.665855 + 0.746081i \(0.731933\pi\)
\(284\) 0 0
\(285\) 2496.00 0.518773
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 11471.0 2.33483
\(290\) 0 0
\(291\) 1662.00 0.334805
\(292\) 0 0
\(293\) −9204.00 −1.83517 −0.917583 0.397545i \(-0.869862\pi\)
−0.917583 + 0.397545i \(0.869862\pi\)
\(294\) 0 0
\(295\) 1536.00 0.303150
\(296\) 0 0
\(297\) 486.000 0.0949514
\(298\) 0 0
\(299\) 10908.0 2.10979
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 2340.00 0.443662
\(304\) 0 0
\(305\) −9952.00 −1.86836
\(306\) 0 0
\(307\) −2180.00 −0.405274 −0.202637 0.979254i \(-0.564951\pi\)
−0.202637 + 0.979254i \(0.564951\pi\)
\(308\) 0 0
\(309\) 72.0000 0.0132555
\(310\) 0 0
\(311\) 7212.00 1.31497 0.657484 0.753469i \(-0.271621\pi\)
0.657484 + 0.753469i \(0.271621\pi\)
\(312\) 0 0
\(313\) −1322.00 −0.238734 −0.119367 0.992850i \(-0.538087\pi\)
−0.119367 + 0.992850i \(0.538087\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 474.000 0.0839826 0.0419913 0.999118i \(-0.486630\pi\)
0.0419913 + 0.999118i \(0.486630\pi\)
\(318\) 0 0
\(319\) 5436.00 0.954099
\(320\) 0 0
\(321\) −234.000 −0.0406872
\(322\) 0 0
\(323\) 6656.00 1.14659
\(324\) 0 0
\(325\) 7074.00 1.20737
\(326\) 0 0
\(327\) −3102.00 −0.524590
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 11284.0 1.87379 0.936895 0.349610i \(-0.113686\pi\)
0.936895 + 0.349610i \(0.113686\pi\)
\(332\) 0 0
\(333\) −1350.00 −0.222161
\(334\) 0 0
\(335\) −11904.0 −1.94145
\(336\) 0 0
\(337\) 6986.00 1.12923 0.564617 0.825353i \(-0.309024\pi\)
0.564617 + 0.825353i \(0.309024\pi\)
\(338\) 0 0
\(339\) 558.000 0.0893994
\(340\) 0 0
\(341\) −3600.00 −0.571704
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 9696.00 1.51309
\(346\) 0 0
\(347\) 7926.00 1.22620 0.613098 0.790007i \(-0.289923\pi\)
0.613098 + 0.790007i \(0.289923\pi\)
\(348\) 0 0
\(349\) 3058.00 0.469029 0.234514 0.972113i \(-0.424650\pi\)
0.234514 + 0.972113i \(0.424650\pi\)
\(350\) 0 0
\(351\) 1458.00 0.221716
\(352\) 0 0
\(353\) −7008.00 −1.05665 −0.528326 0.849042i \(-0.677180\pi\)
−0.528326 + 0.849042i \(0.677180\pi\)
\(354\) 0 0
\(355\) 864.000 0.129173
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 11286.0 1.65920 0.829599 0.558359i \(-0.188569\pi\)
0.829599 + 0.558359i \(0.188569\pi\)
\(360\) 0 0
\(361\) −4155.00 −0.605773
\(362\) 0 0
\(363\) −3021.00 −0.436808
\(364\) 0 0
\(365\) −11872.0 −1.70249
\(366\) 0 0
\(367\) −2752.00 −0.391426 −0.195713 0.980661i \(-0.562702\pi\)
−0.195713 + 0.980661i \(0.562702\pi\)
\(368\) 0 0
\(369\) −1548.00 −0.218389
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 206.000 0.0285959 0.0142980 0.999898i \(-0.495449\pi\)
0.0142980 + 0.999898i \(0.495449\pi\)
\(374\) 0 0
\(375\) 288.000 0.0396593
\(376\) 0 0
\(377\) 16308.0 2.22786
\(378\) 0 0
\(379\) −684.000 −0.0927037 −0.0463519 0.998925i \(-0.514760\pi\)
−0.0463519 + 0.998925i \(0.514760\pi\)
\(380\) 0 0
\(381\) 948.000 0.127474
\(382\) 0 0
\(383\) 9048.00 1.20713 0.603566 0.797313i \(-0.293746\pi\)
0.603566 + 0.797313i \(0.293746\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −1476.00 −0.193874
\(388\) 0 0
\(389\) −3242.00 −0.422560 −0.211280 0.977426i \(-0.567763\pi\)
−0.211280 + 0.977426i \(0.567763\pi\)
\(390\) 0 0
\(391\) 25856.0 3.34423
\(392\) 0 0
\(393\) −2964.00 −0.380443
\(394\) 0 0
\(395\) 1472.00 0.187505
\(396\) 0 0
\(397\) −1702.00 −0.215166 −0.107583 0.994196i \(-0.534311\pi\)
−0.107583 + 0.994196i \(0.534311\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 8742.00 1.08866 0.544332 0.838870i \(-0.316783\pi\)
0.544332 + 0.838870i \(0.316783\pi\)
\(402\) 0 0
\(403\) −10800.0 −1.33495
\(404\) 0 0
\(405\) 1296.00 0.159009
\(406\) 0 0
\(407\) −2700.00 −0.328831
\(408\) 0 0
\(409\) −510.000 −0.0616574 −0.0308287 0.999525i \(-0.509815\pi\)
−0.0308287 + 0.999525i \(0.509815\pi\)
\(410\) 0 0
\(411\) 2850.00 0.342044
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −3648.00 −0.431502
\(416\) 0 0
\(417\) −6372.00 −0.748293
\(418\) 0 0
\(419\) 5144.00 0.599763 0.299882 0.953976i \(-0.403053\pi\)
0.299882 + 0.953976i \(0.403053\pi\)
\(420\) 0 0
\(421\) 514.000 0.0595032 0.0297516 0.999557i \(-0.490528\pi\)
0.0297516 + 0.999557i \(0.490528\pi\)
\(422\) 0 0
\(423\) −4140.00 −0.475872
\(424\) 0 0
\(425\) 16768.0 1.91381
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 2916.00 0.328172
\(430\) 0 0
\(431\) −13626.0 −1.52283 −0.761417 0.648263i \(-0.775496\pi\)
−0.761417 + 0.648263i \(0.775496\pi\)
\(432\) 0 0
\(433\) −8794.00 −0.976011 −0.488005 0.872841i \(-0.662275\pi\)
−0.488005 + 0.872841i \(0.662275\pi\)
\(434\) 0 0
\(435\) 14496.0 1.59777
\(436\) 0 0
\(437\) 10504.0 1.14983
\(438\) 0 0
\(439\) 2616.00 0.284407 0.142204 0.989837i \(-0.454581\pi\)
0.142204 + 0.989837i \(0.454581\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 838.000 0.0898749 0.0449375 0.998990i \(-0.485691\pi\)
0.0449375 + 0.998990i \(0.485691\pi\)
\(444\) 0 0
\(445\) 1856.00 0.197714
\(446\) 0 0
\(447\) 6726.00 0.711698
\(448\) 0 0
\(449\) −9662.00 −1.01554 −0.507771 0.861492i \(-0.669530\pi\)
−0.507771 + 0.861492i \(0.669530\pi\)
\(450\) 0 0
\(451\) −3096.00 −0.323248
\(452\) 0 0
\(453\) −8328.00 −0.863761
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −3590.00 −0.367469 −0.183734 0.982976i \(-0.558819\pi\)
−0.183734 + 0.982976i \(0.558819\pi\)
\(458\) 0 0
\(459\) 3456.00 0.351443
\(460\) 0 0
\(461\) −11628.0 −1.17477 −0.587386 0.809307i \(-0.699843\pi\)
−0.587386 + 0.809307i \(0.699843\pi\)
\(462\) 0 0
\(463\) 2116.00 0.212395 0.106197 0.994345i \(-0.466132\pi\)
0.106197 + 0.994345i \(0.466132\pi\)
\(464\) 0 0
\(465\) −9600.00 −0.957396
\(466\) 0 0
\(467\) −5088.00 −0.504164 −0.252082 0.967706i \(-0.581115\pi\)
−0.252082 + 0.967706i \(0.581115\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 9774.00 0.956183
\(472\) 0 0
\(473\) −2952.00 −0.286962
\(474\) 0 0
\(475\) 6812.00 0.658013
\(476\) 0 0
\(477\) −1710.00 −0.164142
\(478\) 0 0
\(479\) 5068.00 0.483430 0.241715 0.970347i \(-0.422290\pi\)
0.241715 + 0.970347i \(0.422290\pi\)
\(480\) 0 0
\(481\) −8100.00 −0.767834
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 8864.00 0.829884
\(486\) 0 0
\(487\) −11008.0 −1.02427 −0.512136 0.858905i \(-0.671145\pi\)
−0.512136 + 0.858905i \(0.671145\pi\)
\(488\) 0 0
\(489\) 7296.00 0.674717
\(490\) 0 0
\(491\) −11466.0 −1.05388 −0.526938 0.849904i \(-0.676660\pi\)
−0.526938 + 0.849904i \(0.676660\pi\)
\(492\) 0 0
\(493\) 38656.0 3.53140
\(494\) 0 0
\(495\) 2592.00 0.235357
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 11900.0 1.06757 0.533785 0.845620i \(-0.320769\pi\)
0.533785 + 0.845620i \(0.320769\pi\)
\(500\) 0 0
\(501\) −9468.00 −0.844309
\(502\) 0 0
\(503\) −1832.00 −0.162395 −0.0811977 0.996698i \(-0.525875\pi\)
−0.0811977 + 0.996698i \(0.525875\pi\)
\(504\) 0 0
\(505\) 12480.0 1.09971
\(506\) 0 0
\(507\) 2157.00 0.188946
\(508\) 0 0
\(509\) −16968.0 −1.47759 −0.738795 0.673930i \(-0.764605\pi\)
−0.738795 + 0.673930i \(0.764605\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 1404.00 0.120835
\(514\) 0 0
\(515\) 384.000 0.0328564
\(516\) 0 0
\(517\) −8280.00 −0.704360
\(518\) 0 0
\(519\) 11172.0 0.944887
\(520\) 0 0
\(521\) 14976.0 1.25933 0.629665 0.776867i \(-0.283192\pi\)
0.629665 + 0.776867i \(0.283192\pi\)
\(522\) 0 0
\(523\) 9812.00 0.820361 0.410181 0.912004i \(-0.365466\pi\)
0.410181 + 0.912004i \(0.365466\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −25600.0 −2.11604
\(528\) 0 0
\(529\) 28637.0 2.35366
\(530\) 0 0
\(531\) 864.000 0.0706109
\(532\) 0 0
\(533\) −9288.00 −0.754799
\(534\) 0 0
\(535\) −1248.00 −0.100852
\(536\) 0 0
\(537\) 7194.00 0.578108
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 21370.0 1.69828 0.849139 0.528170i \(-0.177122\pi\)
0.849139 + 0.528170i \(0.177122\pi\)
\(542\) 0 0
\(543\) −8718.00 −0.688997
\(544\) 0 0
\(545\) −16544.0 −1.30031
\(546\) 0 0
\(547\) 8120.00 0.634710 0.317355 0.948307i \(-0.397205\pi\)
0.317355 + 0.948307i \(0.397205\pi\)
\(548\) 0 0
\(549\) −5598.00 −0.435185
\(550\) 0 0
\(551\) 15704.0 1.21418
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −7200.00 −0.550672
\(556\) 0 0
\(557\) −19934.0 −1.51639 −0.758196 0.652026i \(-0.773919\pi\)
−0.758196 + 0.652026i \(0.773919\pi\)
\(558\) 0 0
\(559\) −8856.00 −0.670070
\(560\) 0 0
\(561\) 6912.00 0.520187
\(562\) 0 0
\(563\) 352.000 0.0263500 0.0131750 0.999913i \(-0.495806\pi\)
0.0131750 + 0.999913i \(0.495806\pi\)
\(564\) 0 0
\(565\) 2976.00 0.221595
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −10698.0 −0.788196 −0.394098 0.919068i \(-0.628943\pi\)
−0.394098 + 0.919068i \(0.628943\pi\)
\(570\) 0 0
\(571\) 14824.0 1.08645 0.543227 0.839586i \(-0.317202\pi\)
0.543227 + 0.839586i \(0.317202\pi\)
\(572\) 0 0
\(573\) 4434.00 0.323269
\(574\) 0 0
\(575\) 26462.0 1.91920
\(576\) 0 0
\(577\) 15318.0 1.10519 0.552597 0.833449i \(-0.313637\pi\)
0.552597 + 0.833449i \(0.313637\pi\)
\(578\) 0 0
\(579\) −3294.00 −0.236432
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −3420.00 −0.242954
\(584\) 0 0
\(585\) 7776.00 0.549569
\(586\) 0 0
\(587\) −5672.00 −0.398822 −0.199411 0.979916i \(-0.563903\pi\)
−0.199411 + 0.979916i \(0.563903\pi\)
\(588\) 0 0
\(589\) −10400.0 −0.727546
\(590\) 0 0
\(591\) 15174.0 1.05613
\(592\) 0 0
\(593\) 25968.0 1.79828 0.899138 0.437665i \(-0.144194\pi\)
0.899138 + 0.437665i \(0.144194\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −13296.0 −0.911506
\(598\) 0 0
\(599\) 20846.0 1.42194 0.710972 0.703220i \(-0.248255\pi\)
0.710972 + 0.703220i \(0.248255\pi\)
\(600\) 0 0
\(601\) 4430.00 0.300671 0.150336 0.988635i \(-0.451965\pi\)
0.150336 + 0.988635i \(0.451965\pi\)
\(602\) 0 0
\(603\) −6696.00 −0.452209
\(604\) 0 0
\(605\) −16112.0 −1.08272
\(606\) 0 0
\(607\) −23744.0 −1.58771 −0.793854 0.608108i \(-0.791929\pi\)
−0.793854 + 0.608108i \(0.791929\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −24840.0 −1.64471
\(612\) 0 0
\(613\) 9982.00 0.657699 0.328849 0.944382i \(-0.393339\pi\)
0.328849 + 0.944382i \(0.393339\pi\)
\(614\) 0 0
\(615\) −8256.00 −0.541324
\(616\) 0 0
\(617\) −21090.0 −1.37610 −0.688048 0.725665i \(-0.741532\pi\)
−0.688048 + 0.725665i \(0.741532\pi\)
\(618\) 0 0
\(619\) −12900.0 −0.837633 −0.418816 0.908071i \(-0.637555\pi\)
−0.418816 + 0.908071i \(0.637555\pi\)
\(620\) 0 0
\(621\) 5454.00 0.352434
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −14839.0 −0.949696
\(626\) 0 0
\(627\) 2808.00 0.178853
\(628\) 0 0
\(629\) −19200.0 −1.21710
\(630\) 0 0
\(631\) −140.000 −0.00883251 −0.00441625 0.999990i \(-0.501406\pi\)
−0.00441625 + 0.999990i \(0.501406\pi\)
\(632\) 0 0
\(633\) −16332.0 −1.02550
\(634\) 0 0
\(635\) 5056.00 0.315970
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 486.000 0.0300874
\(640\) 0 0
\(641\) −2642.00 −0.162797 −0.0813984 0.996682i \(-0.525939\pi\)
−0.0813984 + 0.996682i \(0.525939\pi\)
\(642\) 0 0
\(643\) −1388.00 −0.0851281 −0.0425641 0.999094i \(-0.513553\pi\)
−0.0425641 + 0.999094i \(0.513553\pi\)
\(644\) 0 0
\(645\) −7872.00 −0.480558
\(646\) 0 0
\(647\) −11196.0 −0.680309 −0.340155 0.940369i \(-0.610479\pi\)
−0.340155 + 0.940369i \(0.610479\pi\)
\(648\) 0 0
\(649\) 1728.00 0.104515
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 9398.00 0.563204 0.281602 0.959531i \(-0.409134\pi\)
0.281602 + 0.959531i \(0.409134\pi\)
\(654\) 0 0
\(655\) −15808.0 −0.943007
\(656\) 0 0
\(657\) −6678.00 −0.396550
\(658\) 0 0
\(659\) 14050.0 0.830516 0.415258 0.909704i \(-0.363691\pi\)
0.415258 + 0.909704i \(0.363691\pi\)
\(660\) 0 0
\(661\) −22382.0 −1.31703 −0.658517 0.752566i \(-0.728816\pi\)
−0.658517 + 0.752566i \(0.728816\pi\)
\(662\) 0 0
\(663\) 20736.0 1.21466
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 61004.0 3.54136
\(668\) 0 0
\(669\) −16056.0 −0.927894
\(670\) 0 0
\(671\) −11196.0 −0.644138
\(672\) 0 0
\(673\) −6050.00 −0.346524 −0.173262 0.984876i \(-0.555431\pi\)
−0.173262 + 0.984876i \(0.555431\pi\)
\(674\) 0 0
\(675\) 3537.00 0.201688
\(676\) 0 0
\(677\) −7500.00 −0.425773 −0.212887 0.977077i \(-0.568286\pi\)
−0.212887 + 0.977077i \(0.568286\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 11256.0 0.633379
\(682\) 0 0
\(683\) 26430.0 1.48070 0.740348 0.672223i \(-0.234661\pi\)
0.740348 + 0.672223i \(0.234661\pi\)
\(684\) 0 0
\(685\) 15200.0 0.847828
\(686\) 0 0
\(687\) 16338.0 0.907327
\(688\) 0 0
\(689\) −10260.0 −0.567308
\(690\) 0 0
\(691\) 14228.0 0.783298 0.391649 0.920115i \(-0.371905\pi\)
0.391649 + 0.920115i \(0.371905\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −33984.0 −1.85480
\(696\) 0 0
\(697\) −22016.0 −1.19644
\(698\) 0 0
\(699\) −7806.00 −0.422389
\(700\) 0 0
\(701\) −12338.0 −0.664764 −0.332382 0.943145i \(-0.607852\pi\)
−0.332382 + 0.943145i \(0.607852\pi\)
\(702\) 0 0
\(703\) −7800.00 −0.418467
\(704\) 0 0
\(705\) −22080.0 −1.17955
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 7054.00 0.373651 0.186825 0.982393i \(-0.440180\pi\)
0.186825 + 0.982393i \(0.440180\pi\)
\(710\) 0 0
\(711\) 828.000 0.0436743
\(712\) 0 0
\(713\) −40400.0 −2.12201
\(714\) 0 0
\(715\) 15552.0 0.813443
\(716\) 0 0
\(717\) 5430.00 0.282827
\(718\) 0 0
\(719\) 8640.00 0.448147 0.224073 0.974572i \(-0.428064\pi\)
0.224073 + 0.974572i \(0.428064\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −930.000 −0.0478383
\(724\) 0 0
\(725\) 39562.0 2.02661
\(726\) 0 0
\(727\) 20120.0 1.02642 0.513211 0.858262i \(-0.328456\pi\)
0.513211 + 0.858262i \(0.328456\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) 0 0
\(731\) −20992.0 −1.06213
\(732\) 0 0
\(733\) −14554.0 −0.733376 −0.366688 0.930344i \(-0.619508\pi\)
−0.366688 + 0.930344i \(0.619508\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −13392.0 −0.669336
\(738\) 0 0
\(739\) 23600.0 1.17475 0.587375 0.809315i \(-0.300161\pi\)
0.587375 + 0.809315i \(0.300161\pi\)
\(740\) 0 0
\(741\) 8424.00 0.417629
\(742\) 0 0
\(743\) −28970.0 −1.43043 −0.715213 0.698907i \(-0.753670\pi\)
−0.715213 + 0.698907i \(0.753670\pi\)
\(744\) 0 0
\(745\) 35872.0 1.76409
\(746\) 0 0
\(747\) −2052.00 −0.100507
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −18848.0 −0.915810 −0.457905 0.889001i \(-0.651400\pi\)
−0.457905 + 0.889001i \(0.651400\pi\)
\(752\) 0 0
\(753\) −96.0000 −0.00464600
\(754\) 0 0
\(755\) −44416.0 −2.14101
\(756\) 0 0
\(757\) −26594.0 −1.27685 −0.638425 0.769684i \(-0.720414\pi\)
−0.638425 + 0.769684i \(0.720414\pi\)
\(758\) 0 0
\(759\) 10908.0 0.521654
\(760\) 0 0
\(761\) 3012.00 0.143476 0.0717378 0.997424i \(-0.477146\pi\)
0.0717378 + 0.997424i \(0.477146\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 18432.0 0.871125
\(766\) 0 0
\(767\) 5184.00 0.244046
\(768\) 0 0
\(769\) 12614.0 0.591512 0.295756 0.955264i \(-0.404429\pi\)
0.295756 + 0.955264i \(0.404429\pi\)
\(770\) 0 0
\(771\) −10044.0 −0.469164
\(772\) 0 0
\(773\) −40684.0 −1.89302 −0.946508 0.322680i \(-0.895416\pi\)
−0.946508 + 0.322680i \(0.895416\pi\)
\(774\) 0 0
\(775\) −26200.0 −1.21436
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −8944.00 −0.411363
\(780\) 0 0
\(781\) 972.000 0.0445338
\(782\) 0 0
\(783\) 8154.00 0.372159
\(784\) 0 0
\(785\) 52128.0 2.37010
\(786\) 0 0
\(787\) 28564.0 1.29377 0.646885 0.762588i \(-0.276071\pi\)
0.646885 + 0.762588i \(0.276071\pi\)
\(788\) 0 0
\(789\) −12258.0 −0.553101
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −33588.0 −1.50409
\(794\) 0 0
\(795\) −9120.00 −0.406859
\(796\) 0 0
\(797\) −7140.00 −0.317330 −0.158665 0.987332i \(-0.550719\pi\)
−0.158665 + 0.987332i \(0.550719\pi\)
\(798\) 0 0
\(799\) −58880.0 −2.60704
\(800\) 0 0
\(801\) 1044.00 0.0460523
\(802\) 0 0
\(803\) −13356.0 −0.586953
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −4248.00 −0.185299
\(808\) 0 0
\(809\) 26682.0 1.15957 0.579783 0.814771i \(-0.303137\pi\)
0.579783 + 0.814771i \(0.303137\pi\)
\(810\) 0 0
\(811\) 18012.0 0.779885 0.389943 0.920839i \(-0.372495\pi\)
0.389943 + 0.920839i \(0.372495\pi\)
\(812\) 0 0
\(813\) −11568.0 −0.499025
\(814\) 0 0
\(815\) 38912.0 1.67243
\(816\) 0 0
\(817\) −8528.00 −0.365186
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −3270.00 −0.139006 −0.0695029 0.997582i \(-0.522141\pi\)
−0.0695029 + 0.997582i \(0.522141\pi\)
\(822\) 0 0
\(823\) 41692.0 1.76585 0.882923 0.469517i \(-0.155572\pi\)
0.882923 + 0.469517i \(0.155572\pi\)
\(824\) 0 0
\(825\) 7074.00 0.298527
\(826\) 0 0
\(827\) −12078.0 −0.507852 −0.253926 0.967224i \(-0.581722\pi\)
−0.253926 + 0.967224i \(0.581722\pi\)
\(828\) 0 0
\(829\) 24046.0 1.00742 0.503711 0.863872i \(-0.331968\pi\)
0.503711 + 0.863872i \(0.331968\pi\)
\(830\) 0 0
\(831\) −4074.00 −0.170067
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) −50496.0 −2.09280
\(836\) 0 0
\(837\) −5400.00 −0.223000
\(838\) 0 0
\(839\) −12204.0 −0.502180 −0.251090 0.967964i \(-0.580789\pi\)
−0.251090 + 0.967964i \(0.580789\pi\)
\(840\) 0 0
\(841\) 66815.0 2.73955
\(842\) 0 0
\(843\) −5094.00 −0.208122
\(844\) 0 0
\(845\) 11504.0 0.468343
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) −19020.0 −0.768863
\(850\) 0 0
\(851\) −30300.0 −1.22053
\(852\) 0 0
\(853\) 5930.00 0.238030 0.119015 0.992892i \(-0.462026\pi\)
0.119015 + 0.992892i \(0.462026\pi\)
\(854\) 0 0
\(855\) 7488.00 0.299514
\(856\) 0 0
\(857\) 5268.00 0.209978 0.104989 0.994473i \(-0.466519\pi\)
0.104989 + 0.994473i \(0.466519\pi\)
\(858\) 0 0
\(859\) −10028.0 −0.398313 −0.199157 0.979968i \(-0.563820\pi\)
−0.199157 + 0.979968i \(0.563820\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 37306.0 1.47151 0.735754 0.677249i \(-0.236828\pi\)
0.735754 + 0.677249i \(0.236828\pi\)
\(864\) 0 0
\(865\) 59584.0 2.34210
\(866\) 0 0
\(867\) 34413.0 1.34801
\(868\) 0 0
\(869\) 1656.00 0.0646444
\(870\) 0 0
\(871\) −40176.0 −1.56293
\(872\) 0 0
\(873\) 4986.00 0.193300
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −39178.0 −1.50849 −0.754246 0.656592i \(-0.771997\pi\)
−0.754246 + 0.656592i \(0.771997\pi\)
\(878\) 0 0
\(879\) −27612.0 −1.05953
\(880\) 0 0
\(881\) 36872.0 1.41004 0.705022 0.709185i \(-0.250937\pi\)
0.705022 + 0.709185i \(0.250937\pi\)
\(882\) 0 0
\(883\) 19964.0 0.760863 0.380432 0.924809i \(-0.375775\pi\)
0.380432 + 0.924809i \(0.375775\pi\)
\(884\) 0 0
\(885\) 4608.00 0.175024
\(886\) 0 0
\(887\) 12924.0 0.489228 0.244614 0.969621i \(-0.421339\pi\)
0.244614 + 0.969621i \(0.421339\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 1458.00 0.0548202
\(892\) 0 0
\(893\) −23920.0 −0.896363
\(894\) 0 0
\(895\) 38368.0 1.43296
\(896\) 0 0
\(897\) 32724.0 1.21809
\(898\) 0 0
\(899\) −60400.0 −2.24077
\(900\) 0 0
\(901\) −24320.0 −0.899242
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −46496.0 −1.70782
\(906\) 0 0
\(907\) −44804.0 −1.64023 −0.820117 0.572196i \(-0.806092\pi\)
−0.820117 + 0.572196i \(0.806092\pi\)
\(908\) 0 0
\(909\) 7020.00 0.256148
\(910\) 0 0
\(911\) 26102.0 0.949284 0.474642 0.880179i \(-0.342578\pi\)
0.474642 + 0.880179i \(0.342578\pi\)
\(912\) 0 0
\(913\) −4104.00 −0.148765
\(914\) 0 0
\(915\) −29856.0 −1.07870
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 176.000 0.00631741 0.00315871 0.999995i \(-0.498995\pi\)
0.00315871 + 0.999995i \(0.498995\pi\)
\(920\) 0 0
\(921\) −6540.00 −0.233985
\(922\) 0 0
\(923\) 2916.00 0.103988
\(924\) 0 0
\(925\) −19650.0 −0.698474
\(926\) 0 0
\(927\) 216.000 0.00765304
\(928\) 0 0
\(929\) −23116.0 −0.816374 −0.408187 0.912898i \(-0.633839\pi\)
−0.408187 + 0.912898i \(0.633839\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 21636.0 0.759197
\(934\) 0 0
\(935\) 36864.0 1.28939
\(936\) 0 0
\(937\) 20142.0 0.702252 0.351126 0.936328i \(-0.385799\pi\)
0.351126 + 0.936328i \(0.385799\pi\)
\(938\) 0 0
\(939\) −3966.00 −0.137833
\(940\) 0 0
\(941\) −19896.0 −0.689257 −0.344629 0.938739i \(-0.611995\pi\)
−0.344629 + 0.938739i \(0.611995\pi\)
\(942\) 0 0
\(943\) −34744.0 −1.19981
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 7658.00 0.262779 0.131389 0.991331i \(-0.458056\pi\)
0.131389 + 0.991331i \(0.458056\pi\)
\(948\) 0 0
\(949\) −40068.0 −1.37056
\(950\) 0 0
\(951\) 1422.00 0.0484874
\(952\) 0 0
\(953\) 12826.0 0.435965 0.217983 0.975953i \(-0.430052\pi\)
0.217983 + 0.975953i \(0.430052\pi\)
\(954\) 0 0
\(955\) 23648.0 0.801289
\(956\) 0 0
\(957\) 16308.0 0.550849
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 10209.0 0.342687
\(962\) 0 0
\(963\) −702.000 −0.0234908
\(964\) 0 0
\(965\) −17568.0 −0.586046
\(966\) 0 0
\(967\) −53148.0 −1.76745 −0.883725 0.468006i \(-0.844972\pi\)
−0.883725 + 0.468006i \(0.844972\pi\)
\(968\) 0 0
\(969\) 19968.0 0.661986
\(970\) 0 0
\(971\) 30340.0 1.00274 0.501368 0.865234i \(-0.332830\pi\)
0.501368 + 0.865234i \(0.332830\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 21222.0 0.697075
\(976\) 0 0
\(977\) −6714.00 −0.219857 −0.109928 0.993940i \(-0.535062\pi\)
−0.109928 + 0.993940i \(0.535062\pi\)
\(978\) 0 0
\(979\) 2088.00 0.0681642
\(980\) 0 0
\(981\) −9306.00 −0.302872
\(982\) 0 0
\(983\) 22128.0 0.717979 0.358990 0.933342i \(-0.383121\pi\)
0.358990 + 0.933342i \(0.383121\pi\)
\(984\) 0 0
\(985\) 80928.0 2.61785
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −33128.0 −1.06513
\(990\) 0 0
\(991\) −41928.0 −1.34398 −0.671991 0.740559i \(-0.734561\pi\)
−0.671991 + 0.740559i \(0.734561\pi\)
\(992\) 0 0
\(993\) 33852.0 1.08183
\(994\) 0 0
\(995\) −70912.0 −2.25936
\(996\) 0 0
\(997\) −28894.0 −0.917836 −0.458918 0.888479i \(-0.651763\pi\)
−0.458918 + 0.888479i \(0.651763\pi\)
\(998\) 0 0
\(999\) −4050.00 −0.128265
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 2352.4.a.bj.1.1 1
4.3 odd 2 1176.4.a.h.1.1 1
7.6 odd 2 336.4.a.a.1.1 1
21.20 even 2 1008.4.a.t.1.1 1
28.27 even 2 168.4.a.d.1.1 1
56.13 odd 2 1344.4.a.z.1.1 1
56.27 even 2 1344.4.a.l.1.1 1
84.83 odd 2 504.4.a.h.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
168.4.a.d.1.1 1 28.27 even 2
336.4.a.a.1.1 1 7.6 odd 2
504.4.a.h.1.1 1 84.83 odd 2
1008.4.a.t.1.1 1 21.20 even 2
1176.4.a.h.1.1 1 4.3 odd 2
1344.4.a.l.1.1 1 56.27 even 2
1344.4.a.z.1.1 1 56.13 odd 2
2352.4.a.bj.1.1 1 1.1 even 1 trivial