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Properties

Label 1296.4.a.e.1.1
Level $1296$
Weight $4$
Character 1296.1
Self dual yes
Analytic conductor $76.466$
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] = [1296,4,Mod(1,1296)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1296, 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("1296.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1296 = 2^{4} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1296.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: \(76.4664753674\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 324)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1296.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+3.00000 q^{5} +4.00000 q^{7} +24.0000 q^{11} -25.0000 q^{13} -21.0000 q^{17} +52.0000 q^{19} -168.000 q^{23} -116.000 q^{25} -177.000 q^{29} +124.000 q^{31} +12.0000 q^{35} -265.000 q^{37} +426.000 q^{41} +160.000 q^{43} +540.000 q^{47} -327.000 q^{49} -258.000 q^{53} +72.0000 q^{55} -528.000 q^{59} -505.000 q^{61} -75.0000 q^{65} +244.000 q^{67} -204.000 q^{71} -397.000 q^{73} +96.0000 q^{77} -200.000 q^{79} +540.000 q^{83} -63.0000 q^{85} -453.000 q^{89} -100.000 q^{91} +156.000 q^{95} +290.000 q^{97} +O(q^{100})\)

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
\(3\) 0 0
\(4\) 0 0
\(5\) 3.00000 0.268328 0.134164 − 0.990959i \(-0.457165\pi\)
0.134164 + 0.990959i \(0.457165\pi\)
\(6\) 0 0
\(7\) 4.00000 0.215980 0.107990 − 0.994152i \(-0.465559\pi\)
0.107990 + 0.994152i \(0.465559\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 24.0000 0.657843 0.328921 − 0.944357i \(-0.393315\pi\)
0.328921 + 0.944357i \(0.393315\pi\)
\(12\) 0 0
\(13\) −25.0000 −0.533366 −0.266683 − 0.963784i \(-0.585928\pi\)
−0.266683 + 0.963784i \(0.585928\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −21.0000 −0.299603 −0.149801 − 0.988716i \(-0.547863\pi\)
−0.149801 + 0.988716i \(0.547863\pi\)
\(18\) 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
\(23\) −168.000 −1.52306 −0.761531 − 0.648129i \(-0.775552\pi\)
−0.761531 + 0.648129i \(0.775552\pi\)
\(24\) 0 0
\(25\) −116.000 −0.928000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −177.000 −1.13338 −0.566691 − 0.823930i \(-0.691777\pi\)
−0.566691 + 0.823930i \(0.691777\pi\)
\(30\) 0 0
\(31\) 124.000 0.718421 0.359211 − 0.933257i \(-0.383046\pi\)
0.359211 + 0.933257i \(0.383046\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 12.0000 0.0579534
\(36\) 0 0
\(37\) −265.000 −1.17745 −0.588726 − 0.808333i \(-0.700370\pi\)
−0.588726 + 0.808333i \(0.700370\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 426.000 1.62268 0.811342 − 0.584572i \(-0.198738\pi\)
0.811342 + 0.584572i \(0.198738\pi\)
\(42\) 0 0
\(43\) 160.000 0.567437 0.283718 − 0.958908i \(-0.408432\pi\)
0.283718 + 0.958908i \(0.408432\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 540.000 1.67590 0.837948 − 0.545750i \(-0.183755\pi\)
0.837948 + 0.545750i \(0.183755\pi\)
\(48\) 0 0
\(49\) −327.000 −0.953353
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −258.000 −0.668661 −0.334330 − 0.942456i \(-0.608510\pi\)
−0.334330 + 0.942456i \(0.608510\pi\)
\(54\) 0 0
\(55\) 72.0000 0.176518
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −528.000 −1.16508 −0.582540 − 0.812802i \(-0.697941\pi\)
−0.582540 + 0.812802i \(0.697941\pi\)
\(60\) 0 0
\(61\) −505.000 −1.05998 −0.529989 − 0.848005i \(-0.677804\pi\)
−0.529989 + 0.848005i \(0.677804\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −75.0000 −0.143117
\(66\) 0 0
\(67\) 244.000 0.444916 0.222458 − 0.974942i \(-0.428592\pi\)
0.222458 + 0.974942i \(0.428592\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −204.000 −0.340991 −0.170495 − 0.985358i \(-0.554537\pi\)
−0.170495 + 0.985358i \(0.554537\pi\)
\(72\) 0 0
\(73\) −397.000 −0.636511 −0.318256 − 0.948005i \(-0.603097\pi\)
−0.318256 + 0.948005i \(0.603097\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 96.0000 0.142081
\(78\) 0 0
\(79\) −200.000 −0.284832 −0.142416 − 0.989807i \(-0.545487\pi\)
−0.142416 + 0.989807i \(0.545487\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 540.000 0.714129 0.357064 − 0.934080i \(-0.383778\pi\)
0.357064 + 0.934080i \(0.383778\pi\)
\(84\) 0 0
\(85\) −63.0000 −0.0803919
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −453.000 −0.539527 −0.269764 − 0.962927i \(-0.586946\pi\)
−0.269764 + 0.962927i \(0.586946\pi\)
\(90\) 0 0
\(91\) −100.000 −0.115196
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 156.000 0.168476
\(96\) 0 0
\(97\) 290.000 0.303557 0.151779 − 0.988415i \(-0.451500\pi\)
0.151779 + 0.988415i \(0.451500\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 1374.00 1.35364 0.676822 − 0.736146i \(-0.263357\pi\)
0.676822 + 0.736146i \(0.263357\pi\)
\(102\) 0 0
\(103\) −1268.00 −1.21301 −0.606504 − 0.795081i \(-0.707428\pi\)
−0.606504 + 0.795081i \(0.707428\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1164.00 −1.05166 −0.525832 − 0.850588i \(-0.676246\pi\)
−0.525832 + 0.850588i \(0.676246\pi\)
\(108\) 0 0
\(109\) 587.000 0.515820 0.257910 − 0.966169i \(-0.416966\pi\)
0.257910 + 0.966169i \(0.416966\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −1233.00 −1.02647 −0.513234 − 0.858249i \(-0.671553\pi\)
−0.513234 + 0.858249i \(0.671553\pi\)
\(114\) 0 0
\(115\) −504.000 −0.408680
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −84.0000 −0.0647081
\(120\) 0 0
\(121\) −755.000 −0.567243
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −723.000 −0.517337
\(126\) 0 0
\(127\) −1496.00 −1.04526 −0.522632 − 0.852558i \(-0.675050\pi\)
−0.522632 + 0.852558i \(0.675050\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 2004.00 1.33657 0.668284 − 0.743907i \(-0.267029\pi\)
0.668284 + 0.743907i \(0.267029\pi\)
\(132\) 0 0
\(133\) 208.000 0.135608
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 2775.00 1.73054 0.865271 − 0.501304i \(-0.167146\pi\)
0.865271 + 0.501304i \(0.167146\pi\)
\(138\) 0 0
\(139\) −2012.00 −1.22774 −0.613869 − 0.789408i \(-0.710388\pi\)
−0.613869 + 0.789408i \(0.710388\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −600.000 −0.350871
\(144\) 0 0
\(145\) −531.000 −0.304118
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −2145.00 −1.17936 −0.589682 − 0.807635i \(-0.700747\pi\)
−0.589682 + 0.807635i \(0.700747\pi\)
\(150\) 0 0
\(151\) −3176.00 −1.71165 −0.855825 − 0.517265i \(-0.826950\pi\)
−0.855825 + 0.517265i \(0.826950\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 372.000 0.192773
\(156\) 0 0
\(157\) 515.000 0.261793 0.130896 − 0.991396i \(-0.458214\pi\)
0.130896 + 0.991396i \(0.458214\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −672.000 −0.328950
\(162\) 0 0
\(163\) −3272.00 −1.57229 −0.786144 − 0.618044i \(-0.787925\pi\)
−0.786144 + 0.618044i \(0.787925\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 684.000 0.316943 0.158472 − 0.987364i \(-0.449343\pi\)
0.158472 + 0.987364i \(0.449343\pi\)
\(168\) 0 0
\(169\) −1572.00 −0.715521
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 3123.00 1.37247 0.686235 − 0.727380i \(-0.259262\pi\)
0.686235 + 0.727380i \(0.259262\pi\)
\(174\) 0 0
\(175\) −464.000 −0.200429
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −2892.00 −1.20759 −0.603794 − 0.797140i \(-0.706345\pi\)
−0.603794 + 0.797140i \(0.706345\pi\)
\(180\) 0 0
\(181\) −1426.00 −0.585601 −0.292800 − 0.956174i \(-0.594587\pi\)
−0.292800 + 0.956174i \(0.594587\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −795.000 −0.315944
\(186\) 0 0
\(187\) −504.000 −0.197092
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 1596.00 0.604620 0.302310 − 0.953210i \(-0.402242\pi\)
0.302310 + 0.953210i \(0.402242\pi\)
\(192\) 0 0
\(193\) 1115.00 0.415852 0.207926 − 0.978145i \(-0.433329\pi\)
0.207926 + 0.978145i \(0.433329\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −1245.00 −0.450267 −0.225133 − 0.974328i \(-0.572282\pi\)
−0.225133 + 0.974328i \(0.572282\pi\)
\(198\) 0 0
\(199\) 700.000 0.249355 0.124678 − 0.992197i \(-0.460210\pi\)
0.124678 + 0.992197i \(0.460210\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −708.000 −0.244787
\(204\) 0 0
\(205\) 1278.00 0.435412
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 1248.00 0.413043
\(210\) 0 0
\(211\) −704.000 −0.229694 −0.114847 − 0.993383i \(-0.536638\pi\)
−0.114847 + 0.993383i \(0.536638\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 480.000 0.152259
\(216\) 0 0
\(217\) 496.000 0.155164
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 525.000 0.159798
\(222\) 0 0
\(223\) 880.000 0.264256 0.132128 − 0.991233i \(-0.457819\pi\)
0.132128 + 0.991233i \(0.457819\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 3924.00 1.14733 0.573667 − 0.819088i \(-0.305520\pi\)
0.573667 + 0.819088i \(0.305520\pi\)
\(228\) 0 0
\(229\) −6145.00 −1.77324 −0.886622 − 0.462494i \(-0.846955\pi\)
−0.886622 + 0.462494i \(0.846955\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −3885.00 −1.09234 −0.546169 − 0.837675i \(-0.683914\pi\)
−0.546169 + 0.837675i \(0.683914\pi\)
\(234\) 0 0
\(235\) 1620.00 0.449690
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −4860.00 −1.31534 −0.657672 − 0.753304i \(-0.728459\pi\)
−0.657672 + 0.753304i \(0.728459\pi\)
\(240\) 0 0
\(241\) −4549.00 −1.21588 −0.607940 − 0.793983i \(-0.708004\pi\)
−0.607940 + 0.793983i \(0.708004\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −981.000 −0.255811
\(246\) 0 0
\(247\) −1300.00 −0.334887
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −4800.00 −1.20706 −0.603532 − 0.797338i \(-0.706241\pi\)
−0.603532 + 0.797338i \(0.706241\pi\)
\(252\) 0 0
\(253\) −4032.00 −1.00194
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 2511.00 0.609463 0.304731 − 0.952438i \(-0.401433\pi\)
0.304731 + 0.952438i \(0.401433\pi\)
\(258\) 0 0
\(259\) −1060.00 −0.254306
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 4548.00 1.06632 0.533159 − 0.846015i \(-0.321005\pi\)
0.533159 + 0.846015i \(0.321005\pi\)
\(264\) 0 0
\(265\) −774.000 −0.179421
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −2517.00 −0.570499 −0.285249 − 0.958453i \(-0.592076\pi\)
−0.285249 + 0.958453i \(0.592076\pi\)
\(270\) 0 0
\(271\) −4040.00 −0.905581 −0.452791 − 0.891617i \(-0.649571\pi\)
−0.452791 + 0.891617i \(0.649571\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −2784.00 −0.610478
\(276\) 0 0
\(277\) −7090.00 −1.53789 −0.768947 − 0.639312i \(-0.779219\pi\)
−0.768947 + 0.639312i \(0.779219\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −3165.00 −0.671915 −0.335957 − 0.941877i \(-0.609060\pi\)
−0.335957 + 0.941877i \(0.609060\pi\)
\(282\) 0 0
\(283\) 6748.00 1.41741 0.708705 − 0.705505i \(-0.249280\pi\)
0.708705 + 0.705505i \(0.249280\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 1704.00 0.350467
\(288\) 0 0
\(289\) −4472.00 −0.910238
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 6495.00 1.29502 0.647512 − 0.762055i \(-0.275810\pi\)
0.647512 + 0.762055i \(0.275810\pi\)
\(294\) 0 0
\(295\) −1584.00 −0.312624
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 4200.00 0.812349
\(300\) 0 0
\(301\) 640.000 0.122555
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −1515.00 −0.284422
\(306\) 0 0
\(307\) 8980.00 1.66943 0.834716 − 0.550681i \(-0.185632\pi\)
0.834716 + 0.550681i \(0.185632\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −3864.00 −0.704525 −0.352263 − 0.935901i \(-0.614588\pi\)
−0.352263 + 0.935901i \(0.614588\pi\)
\(312\) 0 0
\(313\) 5495.00 0.992319 0.496159 − 0.868231i \(-0.334743\pi\)
0.496159 + 0.868231i \(0.334743\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −885.000 −0.156803 −0.0784015 − 0.996922i \(-0.524982\pi\)
−0.0784015 + 0.996922i \(0.524982\pi\)
\(318\) 0 0
\(319\) −4248.00 −0.745587
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −1092.00 −0.188113
\(324\) 0 0
\(325\) 2900.00 0.494963
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 2160.00 0.361959
\(330\) 0 0
\(331\) 10924.0 1.81401 0.907005 − 0.421120i \(-0.138363\pi\)
0.907005 + 0.421120i \(0.138363\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 732.000 0.119383
\(336\) 0 0
\(337\) −7870.00 −1.27213 −0.636063 − 0.771637i \(-0.719438\pi\)
−0.636063 + 0.771637i \(0.719438\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 2976.00 0.472608
\(342\) 0 0
\(343\) −2680.00 −0.421885
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 4716.00 0.729591 0.364796 − 0.931088i \(-0.381139\pi\)
0.364796 + 0.931088i \(0.381139\pi\)
\(348\) 0 0
\(349\) −1642.00 −0.251846 −0.125923 − 0.992040i \(-0.540189\pi\)
−0.125923 + 0.992040i \(0.540189\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 3090.00 0.465904 0.232952 − 0.972488i \(-0.425161\pi\)
0.232952 + 0.972488i \(0.425161\pi\)
\(354\) 0 0
\(355\) −612.000 −0.0914974
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 5688.00 0.836215 0.418107 − 0.908398i \(-0.362694\pi\)
0.418107 + 0.908398i \(0.362694\pi\)
\(360\) 0 0
\(361\) −4155.00 −0.605773
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −1191.00 −0.170794
\(366\) 0 0
\(367\) −6776.00 −0.963772 −0.481886 − 0.876234i \(-0.660048\pi\)
−0.481886 + 0.876234i \(0.660048\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −1032.00 −0.144417
\(372\) 0 0
\(373\) 6158.00 0.854823 0.427412 − 0.904057i \(-0.359425\pi\)
0.427412 + 0.904057i \(0.359425\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 4425.00 0.604507
\(378\) 0 0
\(379\) −7484.00 −1.01432 −0.507160 − 0.861852i \(-0.669305\pi\)
−0.507160 + 0.861852i \(0.669305\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −4620.00 −0.616373 −0.308187 − 0.951326i \(-0.599722\pi\)
−0.308187 + 0.951326i \(0.599722\pi\)
\(384\) 0 0
\(385\) 288.000 0.0381243
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −930.000 −0.121216 −0.0606078 − 0.998162i \(-0.519304\pi\)
−0.0606078 + 0.998162i \(0.519304\pi\)
\(390\) 0 0
\(391\) 3528.00 0.456314
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −600.000 −0.0764285
\(396\) 0 0
\(397\) 1919.00 0.242599 0.121300 − 0.992616i \(-0.461294\pi\)
0.121300 + 0.992616i \(0.461294\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −10005.0 −1.24595 −0.622975 − 0.782242i \(-0.714076\pi\)
−0.622975 + 0.782242i \(0.714076\pi\)
\(402\) 0 0
\(403\) −3100.00 −0.383181
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −6360.00 −0.774579
\(408\) 0 0
\(409\) 7655.00 0.925465 0.462733 − 0.886498i \(-0.346869\pi\)
0.462733 + 0.886498i \(0.346869\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −2112.00 −0.251634
\(414\) 0 0
\(415\) 1620.00 0.191621
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 14040.0 1.63699 0.818495 − 0.574514i \(-0.194809\pi\)
0.818495 + 0.574514i \(0.194809\pi\)
\(420\) 0 0
\(421\) 11219.0 1.29877 0.649383 − 0.760461i \(-0.275027\pi\)
0.649383 + 0.760461i \(0.275027\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 2436.00 0.278031
\(426\) 0 0
\(427\) −2020.00 −0.228934
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 1884.00 0.210555 0.105277 − 0.994443i \(-0.466427\pi\)
0.105277 + 0.994443i \(0.466427\pi\)
\(432\) 0 0
\(433\) 17507.0 1.94303 0.971516 − 0.236975i \(-0.0761558\pi\)
0.971516 + 0.236975i \(0.0761558\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −8736.00 −0.956292
\(438\) 0 0
\(439\) 3508.00 0.381384 0.190692 − 0.981650i \(-0.438927\pi\)
0.190692 + 0.981650i \(0.438927\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −12420.0 −1.33204 −0.666018 − 0.745936i \(-0.732003\pi\)
−0.666018 + 0.745936i \(0.732003\pi\)
\(444\) 0 0
\(445\) −1359.00 −0.144770
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 8658.00 0.910014 0.455007 − 0.890488i \(-0.349637\pi\)
0.455007 + 0.890488i \(0.349637\pi\)
\(450\) 0 0
\(451\) 10224.0 1.06747
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −300.000 −0.0309104
\(456\) 0 0
\(457\) 335.000 0.0342902 0.0171451 − 0.999853i \(-0.494542\pi\)
0.0171451 + 0.999853i \(0.494542\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 246.000 0.0248533 0.0124266 − 0.999923i \(-0.496044\pi\)
0.0124266 + 0.999923i \(0.496044\pi\)
\(462\) 0 0
\(463\) −14312.0 −1.43658 −0.718288 − 0.695745i \(-0.755074\pi\)
−0.718288 + 0.695745i \(0.755074\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −8184.00 −0.810943 −0.405471 − 0.914108i \(-0.632893\pi\)
−0.405471 + 0.914108i \(0.632893\pi\)
\(468\) 0 0
\(469\) 976.000 0.0960927
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 3840.00 0.373284
\(474\) 0 0
\(475\) −6032.00 −0.582668
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −18108.0 −1.72730 −0.863649 − 0.504094i \(-0.831827\pi\)
−0.863649 + 0.504094i \(0.831827\pi\)
\(480\) 0 0
\(481\) 6625.00 0.628012
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 870.000 0.0814529
\(486\) 0 0
\(487\) −13700.0 −1.27476 −0.637378 − 0.770551i \(-0.719981\pi\)
−0.637378 + 0.770551i \(0.719981\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 20136.0 1.85076 0.925382 − 0.379036i \(-0.123744\pi\)
0.925382 + 0.379036i \(0.123744\pi\)
\(492\) 0 0
\(493\) 3717.00 0.339564
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −816.000 −0.0736471
\(498\) 0 0
\(499\) 13408.0 1.20285 0.601427 − 0.798927i \(-0.294599\pi\)
0.601427 + 0.798927i \(0.294599\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 21600.0 1.91470 0.957352 − 0.288923i \(-0.0932972\pi\)
0.957352 + 0.288923i \(0.0932972\pi\)
\(504\) 0 0
\(505\) 4122.00 0.363221
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −5946.00 −0.517784 −0.258892 − 0.965906i \(-0.583357\pi\)
−0.258892 + 0.965906i \(0.583357\pi\)
\(510\) 0 0
\(511\) −1588.00 −0.137474
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −3804.00 −0.325484
\(516\) 0 0
\(517\) 12960.0 1.10248
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 8970.00 0.754286 0.377143 − 0.926155i \(-0.376907\pi\)
0.377143 + 0.926155i \(0.376907\pi\)
\(522\) 0 0
\(523\) 12520.0 1.04677 0.523386 − 0.852096i \(-0.324669\pi\)
0.523386 + 0.852096i \(0.324669\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −2604.00 −0.215241
\(528\) 0 0
\(529\) 16057.0 1.31972
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −10650.0 −0.865484
\(534\) 0 0
\(535\) −3492.00 −0.282191
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −7848.00 −0.627156
\(540\) 0 0
\(541\) 3911.00 0.310808 0.155404 − 0.987851i \(-0.450332\pi\)
0.155404 + 0.987851i \(0.450332\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 1761.00 0.138409
\(546\) 0 0
\(547\) 17020.0 1.33039 0.665194 − 0.746670i \(-0.268349\pi\)
0.665194 + 0.746670i \(0.268349\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −9204.00 −0.711622
\(552\) 0 0
\(553\) −800.000 −0.0615180
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 13875.0 1.05548 0.527740 − 0.849406i \(-0.323039\pi\)
0.527740 + 0.849406i \(0.323039\pi\)
\(558\) 0 0
\(559\) −4000.00 −0.302651
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −540.000 −0.0404232 −0.0202116 − 0.999796i \(-0.506434\pi\)
−0.0202116 + 0.999796i \(0.506434\pi\)
\(564\) 0 0
\(565\) −3699.00 −0.275430
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −12513.0 −0.921920 −0.460960 − 0.887421i \(-0.652495\pi\)
−0.460960 + 0.887421i \(0.652495\pi\)
\(570\) 0 0
\(571\) 20416.0 1.49629 0.748146 − 0.663534i \(-0.230944\pi\)
0.748146 + 0.663534i \(0.230944\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 19488.0 1.41340
\(576\) 0 0
\(577\) −1801.00 −0.129942 −0.0649711 − 0.997887i \(-0.520696\pi\)
−0.0649711 + 0.997887i \(0.520696\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 2160.00 0.154237
\(582\) 0 0
\(583\) −6192.00 −0.439874
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 5520.00 0.388134 0.194067 − 0.980988i \(-0.437832\pi\)
0.194067 + 0.980988i \(0.437832\pi\)
\(588\) 0 0
\(589\) 6448.00 0.451078
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −11937.0 −0.826634 −0.413317 − 0.910587i \(-0.635630\pi\)
−0.413317 + 0.910587i \(0.635630\pi\)
\(594\) 0 0
\(595\) −252.000 −0.0173630
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −16188.0 −1.10421 −0.552107 − 0.833774i \(-0.686176\pi\)
−0.552107 + 0.833774i \(0.686176\pi\)
\(600\) 0 0
\(601\) −11941.0 −0.810455 −0.405228 − 0.914216i \(-0.632808\pi\)
−0.405228 + 0.914216i \(0.632808\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −2265.00 −0.152207
\(606\) 0 0
\(607\) 12460.0 0.833173 0.416586 − 0.909096i \(-0.363226\pi\)
0.416586 + 0.909096i \(0.363226\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −13500.0 −0.893865
\(612\) 0 0
\(613\) 4670.00 0.307699 0.153850 − 0.988094i \(-0.450833\pi\)
0.153850 + 0.988094i \(0.450833\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 9435.00 0.615622 0.307811 − 0.951448i \(-0.400404\pi\)
0.307811 + 0.951448i \(0.400404\pi\)
\(618\) 0 0
\(619\) 13960.0 0.906462 0.453231 − 0.891393i \(-0.350271\pi\)
0.453231 + 0.891393i \(0.350271\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −1812.00 −0.116527
\(624\) 0 0
\(625\) 12331.0 0.789184
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 5565.00 0.352768
\(630\) 0 0
\(631\) 18904.0 1.19264 0.596320 − 0.802747i \(-0.296629\pi\)
0.596320 + 0.802747i \(0.296629\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −4488.00 −0.280474
\(636\) 0 0
\(637\) 8175.00 0.508486
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −21381.0 −1.31747 −0.658735 − 0.752375i \(-0.728908\pi\)
−0.658735 + 0.752375i \(0.728908\pi\)
\(642\) 0 0
\(643\) 1420.00 0.0870907 0.0435454 − 0.999051i \(-0.486135\pi\)
0.0435454 + 0.999051i \(0.486135\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 21204.0 1.28843 0.644216 − 0.764844i \(-0.277184\pi\)
0.644216 + 0.764844i \(0.277184\pi\)
\(648\) 0 0
\(649\) −12672.0 −0.766440
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 23190.0 1.38973 0.694866 − 0.719139i \(-0.255464\pi\)
0.694866 + 0.719139i \(0.255464\pi\)
\(654\) 0 0
\(655\) 6012.00 0.358639
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 9804.00 0.579529 0.289765 − 0.957098i \(-0.406423\pi\)
0.289765 + 0.957098i \(0.406423\pi\)
\(660\) 0 0
\(661\) −30241.0 −1.77948 −0.889742 − 0.456464i \(-0.849116\pi\)
−0.889742 + 0.456464i \(0.849116\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 624.000 0.0363875
\(666\) 0 0
\(667\) 29736.0 1.72621
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −12120.0 −0.697299
\(672\) 0 0
\(673\) 803.000 0.0459931 0.0229966 − 0.999736i \(-0.492679\pi\)
0.0229966 + 0.999736i \(0.492679\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −14466.0 −0.821231 −0.410616 − 0.911809i \(-0.634686\pi\)
−0.410616 + 0.911809i \(0.634686\pi\)
\(678\) 0 0
\(679\) 1160.00 0.0655622
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 7020.00 0.393284 0.196642 − 0.980475i \(-0.436996\pi\)
0.196642 + 0.980475i \(0.436996\pi\)
\(684\) 0 0
\(685\) 8325.00 0.464353
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 6450.00 0.356641
\(690\) 0 0
\(691\) 24460.0 1.34660 0.673301 − 0.739368i \(-0.264876\pi\)
0.673301 + 0.739368i \(0.264876\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −6036.00 −0.329437
\(696\) 0 0
\(697\) −8946.00 −0.486161
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 27651.0 1.48982 0.744910 − 0.667165i \(-0.232492\pi\)
0.744910 + 0.667165i \(0.232492\pi\)
\(702\) 0 0
\(703\) −13780.0 −0.739292
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 5496.00 0.292360
\(708\) 0 0
\(709\) −4921.00 −0.260666 −0.130333 − 0.991470i \(-0.541605\pi\)
−0.130333 + 0.991470i \(0.541605\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −20832.0 −1.09420
\(714\) 0 0
\(715\) −1800.00 −0.0941485
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 20232.0 1.04941 0.524705 − 0.851284i \(-0.324176\pi\)
0.524705 + 0.851284i \(0.324176\pi\)
\(720\) 0 0
\(721\) −5072.00 −0.261985
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 20532.0 1.05178
\(726\) 0 0
\(727\) −6500.00 −0.331598 −0.165799 − 0.986160i \(-0.553020\pi\)
−0.165799 + 0.986160i \(0.553020\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −3360.00 −0.170006
\(732\) 0 0
\(733\) 13718.0 0.691250 0.345625 − 0.938373i \(-0.387667\pi\)
0.345625 + 0.938373i \(0.387667\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 5856.00 0.292685
\(738\) 0 0
\(739\) 13588.0 0.676377 0.338189 − 0.941078i \(-0.390186\pi\)
0.338189 + 0.941078i \(0.390186\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −34092.0 −1.68333 −0.841665 − 0.540000i \(-0.818424\pi\)
−0.841665 + 0.540000i \(0.818424\pi\)
\(744\) 0 0
\(745\) −6435.00 −0.316457
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −4656.00 −0.227138
\(750\) 0 0
\(751\) 940.000 0.0456739 0.0228369 − 0.999739i \(-0.492730\pi\)
0.0228369 + 0.999739i \(0.492730\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −9528.00 −0.459284
\(756\) 0 0
\(757\) −5410.00 −0.259749 −0.129874 − 0.991530i \(-0.541457\pi\)
−0.129874 + 0.991530i \(0.541457\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −6849.00 −0.326250 −0.163125 − 0.986605i \(-0.552157\pi\)
−0.163125 + 0.986605i \(0.552157\pi\)
\(762\) 0 0
\(763\) 2348.00 0.111407
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 13200.0 0.621414
\(768\) 0 0
\(769\) −9133.00 −0.428276 −0.214138 − 0.976803i \(-0.568694\pi\)
−0.214138 + 0.976803i \(0.568694\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −37845.0 −1.76092 −0.880459 − 0.474122i \(-0.842766\pi\)
−0.880459 + 0.474122i \(0.842766\pi\)
\(774\) 0 0
\(775\) −14384.0 −0.666695
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 22152.0 1.01884
\(780\) 0 0
\(781\) −4896.00 −0.224318
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 1545.00 0.0702464
\(786\) 0 0
\(787\) 33976.0 1.53890 0.769450 − 0.638708i \(-0.220531\pi\)
0.769450 + 0.638708i \(0.220531\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −4932.00 −0.221696
\(792\) 0 0
\(793\) 12625.0 0.565355
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −23805.0 −1.05799 −0.528994 − 0.848626i \(-0.677431\pi\)
−0.528994 + 0.848626i \(0.677431\pi\)
\(798\) 0 0
\(799\) −11340.0 −0.502103
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −9528.00 −0.418725
\(804\) 0 0
\(805\) −2016.00 −0.0882667
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 6567.00 0.285394 0.142697 − 0.989766i \(-0.454423\pi\)
0.142697 + 0.989766i \(0.454423\pi\)
\(810\) 0 0
\(811\) 8656.00 0.374788 0.187394 − 0.982285i \(-0.439996\pi\)
0.187394 + 0.982285i \(0.439996\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −9816.00 −0.421889
\(816\) 0 0
\(817\) 8320.00 0.356279
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 5991.00 0.254674 0.127337 − 0.991860i \(-0.459357\pi\)
0.127337 + 0.991860i \(0.459357\pi\)
\(822\) 0 0
\(823\) −45812.0 −1.94035 −0.970174 − 0.242411i \(-0.922062\pi\)
−0.970174 + 0.242411i \(0.922062\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −35160.0 −1.47840 −0.739198 − 0.673489i \(-0.764795\pi\)
−0.739198 + 0.673489i \(0.764795\pi\)
\(828\) 0 0
\(829\) −9898.00 −0.414682 −0.207341 − 0.978269i \(-0.566481\pi\)
−0.207341 + 0.978269i \(0.566481\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 6867.00 0.285627
\(834\) 0 0
\(835\) 2052.00 0.0850448
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −4032.00 −0.165912 −0.0829560 − 0.996553i \(-0.526436\pi\)
−0.0829560 + 0.996553i \(0.526436\pi\)
\(840\) 0 0
\(841\) 6940.00 0.284555
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −4716.00 −0.191994
\(846\) 0 0
\(847\) −3020.00 −0.122513
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 44520.0 1.79333
\(852\) 0 0
\(853\) 18638.0 0.748128 0.374064 − 0.927403i \(-0.377964\pi\)
0.374064 + 0.927403i \(0.377964\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 37575.0 1.49771 0.748855 − 0.662734i \(-0.230604\pi\)
0.748855 + 0.662734i \(0.230604\pi\)
\(858\) 0 0
\(859\) 6268.00 0.248966 0.124483 − 0.992222i \(-0.460273\pi\)
0.124483 + 0.992222i \(0.460273\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 44832.0 1.76837 0.884183 − 0.467142i \(-0.154716\pi\)
0.884183 + 0.467142i \(0.154716\pi\)
\(864\) 0 0
\(865\) 9369.00 0.368272
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −4800.00 −0.187375
\(870\) 0 0
\(871\) −6100.00 −0.237303
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −2892.00 −0.111734
\(876\) 0 0
\(877\) 14495.0 0.558109 0.279054 − 0.960275i \(-0.409979\pi\)
0.279054 + 0.960275i \(0.409979\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 25986.0 0.993746 0.496873 − 0.867823i \(-0.334481\pi\)
0.496873 + 0.867823i \(0.334481\pi\)
\(882\) 0 0
\(883\) −34868.0 −1.32888 −0.664440 − 0.747341i \(-0.731330\pi\)
−0.664440 + 0.747341i \(0.731330\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 6720.00 0.254381 0.127190 − 0.991878i \(-0.459404\pi\)
0.127190 + 0.991878i \(0.459404\pi\)
\(888\) 0 0
\(889\) −5984.00 −0.225756
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 28080.0 1.05225
\(894\) 0 0
\(895\) −8676.00 −0.324030
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −21948.0 −0.814246
\(900\) 0 0
\(901\) 5418.00 0.200333
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −4278.00 −0.157133
\(906\) 0 0
\(907\) 17296.0 0.633191 0.316596 − 0.948561i \(-0.397460\pi\)
0.316596 + 0.948561i \(0.397460\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 14256.0 0.518466 0.259233 − 0.965815i \(-0.416530\pi\)
0.259233 + 0.965815i \(0.416530\pi\)
\(912\) 0 0
\(913\) 12960.0 0.469785
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 8016.00 0.288671
\(918\) 0 0
\(919\) −15752.0 −0.565409 −0.282704 − 0.959207i \(-0.591232\pi\)
−0.282704 + 0.959207i \(0.591232\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 5100.00 0.181873
\(924\) 0 0
\(925\) 30740.0 1.09268
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 31563.0 1.11469 0.557346 − 0.830280i \(-0.311820\pi\)
0.557346 + 0.830280i \(0.311820\pi\)
\(930\) 0 0
\(931\) −17004.0 −0.598586
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −1512.00 −0.0528852
\(936\) 0 0
\(937\) −3901.00 −0.136009 −0.0680043 − 0.997685i \(-0.521663\pi\)
−0.0680043 + 0.997685i \(0.521663\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −53445.0 −1.85150 −0.925748 − 0.378142i \(-0.876563\pi\)
−0.925748 + 0.378142i \(0.876563\pi\)
\(942\) 0 0
\(943\) −71568.0 −2.47145
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −9036.00 −0.310064 −0.155032 − 0.987909i \(-0.549548\pi\)
−0.155032 + 0.987909i \(0.549548\pi\)
\(948\) 0 0
\(949\) 9925.00 0.339493
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −25065.0 −0.851978 −0.425989 − 0.904728i \(-0.640074\pi\)
−0.425989 + 0.904728i \(0.640074\pi\)
\(954\) 0 0
\(955\) 4788.00 0.162237
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 11100.0 0.373762
\(960\) 0 0
\(961\) −14415.0 −0.483871
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 3345.00 0.111585
\(966\) 0 0
\(967\) −14444.0 −0.480339 −0.240169 − 0.970731i \(-0.577203\pi\)
−0.240169 + 0.970731i \(0.577203\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −50004.0 −1.65263 −0.826316 − 0.563207i \(-0.809567\pi\)
−0.826316 + 0.563207i \(0.809567\pi\)
\(972\) 0 0
\(973\) −8048.00 −0.265167
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −45390.0 −1.48634 −0.743170 − 0.669102i \(-0.766679\pi\)
−0.743170 + 0.669102i \(0.766679\pi\)
\(978\) 0 0
\(979\) −10872.0 −0.354924
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −35952.0 −1.16652 −0.583261 − 0.812285i \(-0.698223\pi\)
−0.583261 + 0.812285i \(0.698223\pi\)
\(984\) 0 0
\(985\) −3735.00 −0.120819
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −26880.0 −0.864241
\(990\) 0 0
\(991\) −14156.0 −0.453764 −0.226882 − 0.973922i \(-0.572853\pi\)
−0.226882 + 0.973922i \(0.572853\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 2100.00 0.0669090
\(996\) 0 0
\(997\) −51541.0 −1.63723 −0.818616 − 0.574342i \(-0.805258\pi\)
−0.818616 + 0.574342i \(0.805258\pi\)
\(998\) 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 1296.4.a.e.1.1 1
3.2 odd 2 1296.4.a.d.1.1 1
4.3 odd 2 324.4.a.b.1.1 yes 1
12.11 even 2 324.4.a.a.1.1 ✓ 1
36.7 odd 6 324.4.e.c.109.1 2
36.11 even 6 324.4.e.f.109.1 2
36.23 even 6 324.4.e.f.217.1 2
36.31 odd 6 324.4.e.c.217.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
324.4.a.a.1.1 ✓ 1 12.11 even 2
324.4.a.b.1.1 yes 1 4.3 odd 2
324.4.e.c.109.1 2 36.7 odd 6
324.4.e.c.217.1 2 36.31 odd 6
324.4.e.f.109.1 2 36.11 even 6
324.4.e.f.217.1 2 36.23 even 6
1296.4.a.d.1.1 1 3.2 odd 2
1296.4.a.e.1.1 1 1.1 even 1 trivial