Properties

Label 1008.4.a.j.1.1
Level $1008$
Weight $4$
Character 1008.1
Self dual yes
Analytic conductor $59.474$
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] = [1008,4,Mod(1,1008)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1008, 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("1008.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1008.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: \(59.4739252858\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 42)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1008.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.00000 q^{5} +7.00000 q^{7} +O(q^{10})\) \(q-2.00000 q^{5} +7.00000 q^{7} -8.00000 q^{11} -42.0000 q^{13} +2.00000 q^{17} +124.000 q^{19} +76.0000 q^{23} -121.000 q^{25} -254.000 q^{29} +72.0000 q^{31} -14.0000 q^{35} +398.000 q^{37} -462.000 q^{41} -212.000 q^{43} -264.000 q^{47} +49.0000 q^{49} +162.000 q^{53} +16.0000 q^{55} -772.000 q^{59} +30.0000 q^{61} +84.0000 q^{65} +764.000 q^{67} -236.000 q^{71} +418.000 q^{73} -56.0000 q^{77} -552.000 q^{79} +1036.00 q^{83} -4.00000 q^{85} -30.0000 q^{89} -294.000 q^{91} -248.000 q^{95} -1190.00 q^{97} +O(q^{100})\)

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
\(5\) −2.00000 −0.178885 −0.0894427 0.995992i \(-0.528509\pi\)
−0.0894427 + 0.995992i \(0.528509\pi\)
\(6\) 0 0
\(7\) 7.00000 0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −8.00000 −0.219281 −0.109640 0.993971i \(-0.534970\pi\)
−0.109640 + 0.993971i \(0.534970\pi\)
\(12\) 0 0
\(13\) −42.0000 −0.896054 −0.448027 0.894020i \(-0.647873\pi\)
−0.448027 + 0.894020i \(0.647873\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2.00000 0.0285336 0.0142668 0.999898i \(-0.495459\pi\)
0.0142668 + 0.999898i \(0.495459\pi\)
\(18\) 0 0
\(19\) 124.000 1.49724 0.748620 0.663000i \(-0.230717\pi\)
0.748620 + 0.663000i \(0.230717\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 76.0000 0.689004 0.344502 0.938786i \(-0.388048\pi\)
0.344502 + 0.938786i \(0.388048\pi\)
\(24\) 0 0
\(25\) −121.000 −0.968000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −254.000 −1.62644 −0.813218 0.581960i \(-0.802286\pi\)
−0.813218 + 0.581960i \(0.802286\pi\)
\(30\) 0 0
\(31\) 72.0000 0.417148 0.208574 0.978007i \(-0.433118\pi\)
0.208574 + 0.978007i \(0.433118\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −14.0000 −0.0676123
\(36\) 0 0
\(37\) 398.000 1.76840 0.884200 0.467109i \(-0.154704\pi\)
0.884200 + 0.467109i \(0.154704\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −462.000 −1.75981 −0.879906 0.475148i \(-0.842394\pi\)
−0.879906 + 0.475148i \(0.842394\pi\)
\(42\) 0 0
\(43\) −212.000 −0.751853 −0.375927 0.926649i \(-0.622676\pi\)
−0.375927 + 0.926649i \(0.622676\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −264.000 −0.819327 −0.409663 0.912237i \(-0.634354\pi\)
−0.409663 + 0.912237i \(0.634354\pi\)
\(48\) 0 0
\(49\) 49.0000 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 162.000 0.419857 0.209928 0.977717i \(-0.432677\pi\)
0.209928 + 0.977717i \(0.432677\pi\)
\(54\) 0 0
\(55\) 16.0000 0.0392262
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −772.000 −1.70349 −0.851744 0.523958i \(-0.824455\pi\)
−0.851744 + 0.523958i \(0.824455\pi\)
\(60\) 0 0
\(61\) 30.0000 0.0629690 0.0314845 0.999504i \(-0.489977\pi\)
0.0314845 + 0.999504i \(0.489977\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 84.0000 0.160291
\(66\) 0 0
\(67\) 764.000 1.39310 0.696548 0.717510i \(-0.254718\pi\)
0.696548 + 0.717510i \(0.254718\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −236.000 −0.394480 −0.197240 0.980355i \(-0.563198\pi\)
−0.197240 + 0.980355i \(0.563198\pi\)
\(72\) 0 0
\(73\) 418.000 0.670181 0.335090 0.942186i \(-0.391233\pi\)
0.335090 + 0.942186i \(0.391233\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −56.0000 −0.0828804
\(78\) 0 0
\(79\) −552.000 −0.786137 −0.393069 0.919509i \(-0.628587\pi\)
−0.393069 + 0.919509i \(0.628587\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 1036.00 1.37007 0.685035 0.728510i \(-0.259787\pi\)
0.685035 + 0.728510i \(0.259787\pi\)
\(84\) 0 0
\(85\) −4.00000 −0.00510425
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −30.0000 −0.0357303 −0.0178651 0.999840i \(-0.505687\pi\)
−0.0178651 + 0.999840i \(0.505687\pi\)
\(90\) 0 0
\(91\) −294.000 −0.338677
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −248.000 −0.267834
\(96\) 0 0
\(97\) −1190.00 −1.24563 −0.622815 0.782369i \(-0.714011\pi\)
−0.622815 + 0.782369i \(0.714011\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −1370.00 −1.34970 −0.674852 0.737953i \(-0.735793\pi\)
−0.674852 + 0.737953i \(0.735793\pi\)
\(102\) 0 0
\(103\) −464.000 −0.443876 −0.221938 0.975061i \(-0.571238\pi\)
−0.221938 + 0.975061i \(0.571238\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −2136.00 −1.92986 −0.964930 0.262509i \(-0.915450\pi\)
−0.964930 + 0.262509i \(0.915450\pi\)
\(108\) 0 0
\(109\) −1226.00 −1.07733 −0.538667 0.842518i \(-0.681072\pi\)
−0.538667 + 0.842518i \(0.681072\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −338.000 −0.281384 −0.140692 0.990053i \(-0.544933\pi\)
−0.140692 + 0.990053i \(0.544933\pi\)
\(114\) 0 0
\(115\) −152.000 −0.123253
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 14.0000 0.0107847
\(120\) 0 0
\(121\) −1267.00 −0.951916
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 492.000 0.352047
\(126\) 0 0
\(127\) −2088.00 −1.45890 −0.729449 0.684035i \(-0.760223\pi\)
−0.729449 + 0.684035i \(0.760223\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −292.000 −0.194749 −0.0973747 0.995248i \(-0.531045\pi\)
−0.0973747 + 0.995248i \(0.531045\pi\)
\(132\) 0 0
\(133\) 868.000 0.565903
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −818.000 −0.510120 −0.255060 0.966925i \(-0.582095\pi\)
−0.255060 + 0.966925i \(0.582095\pi\)
\(138\) 0 0
\(139\) 2156.00 1.31561 0.657804 0.753189i \(-0.271485\pi\)
0.657804 + 0.753189i \(0.271485\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 336.000 0.196488
\(144\) 0 0
\(145\) 508.000 0.290946
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 2850.00 1.56699 0.783494 0.621400i \(-0.213436\pi\)
0.783494 + 0.621400i \(0.213436\pi\)
\(150\) 0 0
\(151\) −1672.00 −0.901096 −0.450548 0.892752i \(-0.648771\pi\)
−0.450548 + 0.892752i \(0.648771\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −144.000 −0.0746217
\(156\) 0 0
\(157\) 446.000 0.226718 0.113359 0.993554i \(-0.463839\pi\)
0.113359 + 0.993554i \(0.463839\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 532.000 0.260419
\(162\) 0 0
\(163\) −2708.00 −1.30127 −0.650635 0.759391i \(-0.725497\pi\)
−0.650635 + 0.759391i \(0.725497\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 896.000 0.415177 0.207589 0.978216i \(-0.433439\pi\)
0.207589 + 0.978216i \(0.433439\pi\)
\(168\) 0 0
\(169\) −433.000 −0.197087
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −4034.00 −1.77283 −0.886414 0.462893i \(-0.846811\pi\)
−0.886414 + 0.462893i \(0.846811\pi\)
\(174\) 0 0
\(175\) −847.000 −0.365870
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −3480.00 −1.45311 −0.726557 0.687106i \(-0.758881\pi\)
−0.726557 + 0.687106i \(0.758881\pi\)
\(180\) 0 0
\(181\) −2898.00 −1.19009 −0.595046 0.803692i \(-0.702866\pi\)
−0.595046 + 0.803692i \(0.702866\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −796.000 −0.316341
\(186\) 0 0
\(187\) −16.0000 −0.00625688
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 2652.00 1.00467 0.502335 0.864673i \(-0.332474\pi\)
0.502335 + 0.864673i \(0.332474\pi\)
\(192\) 0 0
\(193\) 146.000 0.0544524 0.0272262 0.999629i \(-0.491333\pi\)
0.0272262 + 0.999629i \(0.491333\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 2546.00 0.920787 0.460393 0.887715i \(-0.347708\pi\)
0.460393 + 0.887715i \(0.347708\pi\)
\(198\) 0 0
\(199\) 2536.00 0.903378 0.451689 0.892175i \(-0.350822\pi\)
0.451689 + 0.892175i \(0.350822\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −1778.00 −0.614735
\(204\) 0 0
\(205\) 924.000 0.314805
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −992.000 −0.328316
\(210\) 0 0
\(211\) 1300.00 0.424150 0.212075 0.977253i \(-0.431978\pi\)
0.212075 + 0.977253i \(0.431978\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 424.000 0.134496
\(216\) 0 0
\(217\) 504.000 0.157667
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −84.0000 −0.0255677
\(222\) 0 0
\(223\) −2576.00 −0.773550 −0.386775 0.922174i \(-0.626411\pi\)
−0.386775 + 0.922174i \(0.626411\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −1836.00 −0.536826 −0.268413 0.963304i \(-0.586499\pi\)
−0.268413 + 0.963304i \(0.586499\pi\)
\(228\) 0 0
\(229\) −1874.00 −0.540775 −0.270387 0.962752i \(-0.587152\pi\)
−0.270387 + 0.962752i \(0.587152\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −3730.00 −1.04876 −0.524379 0.851485i \(-0.675702\pi\)
−0.524379 + 0.851485i \(0.675702\pi\)
\(234\) 0 0
\(235\) 528.000 0.146566
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 2004.00 0.542377 0.271188 0.962526i \(-0.412583\pi\)
0.271188 + 0.962526i \(0.412583\pi\)
\(240\) 0 0
\(241\) −646.000 −0.172666 −0.0863330 0.996266i \(-0.527515\pi\)
−0.0863330 + 0.996266i \(0.527515\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −98.0000 −0.0255551
\(246\) 0 0
\(247\) −5208.00 −1.34161
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 1260.00 0.316855 0.158427 0.987371i \(-0.449358\pi\)
0.158427 + 0.987371i \(0.449358\pi\)
\(252\) 0 0
\(253\) −608.000 −0.151086
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −5910.00 −1.43446 −0.717229 0.696838i \(-0.754590\pi\)
−0.717229 + 0.696838i \(0.754590\pi\)
\(258\) 0 0
\(259\) 2786.00 0.668392
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 2988.00 0.700563 0.350281 0.936645i \(-0.386086\pi\)
0.350281 + 0.936645i \(0.386086\pi\)
\(264\) 0 0
\(265\) −324.000 −0.0751063
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 1318.00 0.298736 0.149368 0.988782i \(-0.452276\pi\)
0.149368 + 0.988782i \(0.452276\pi\)
\(270\) 0 0
\(271\) 5640.00 1.26423 0.632114 0.774876i \(-0.282188\pi\)
0.632114 + 0.774876i \(0.282188\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 968.000 0.212264
\(276\) 0 0
\(277\) 6446.00 1.39820 0.699102 0.715022i \(-0.253583\pi\)
0.699102 + 0.715022i \(0.253583\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −4930.00 −1.04662 −0.523308 0.852144i \(-0.675302\pi\)
−0.523308 + 0.852144i \(0.675302\pi\)
\(282\) 0 0
\(283\) 6260.00 1.31491 0.657453 0.753496i \(-0.271634\pi\)
0.657453 + 0.753496i \(0.271634\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −3234.00 −0.665146
\(288\) 0 0
\(289\) −4909.00 −0.999186
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 2310.00 0.460586 0.230293 0.973121i \(-0.426032\pi\)
0.230293 + 0.973121i \(0.426032\pi\)
\(294\) 0 0
\(295\) 1544.00 0.304729
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −3192.00 −0.617385
\(300\) 0 0
\(301\) −1484.00 −0.284174
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −60.0000 −0.0112642
\(306\) 0 0
\(307\) −196.000 −0.0364375 −0.0182187 0.999834i \(-0.505800\pi\)
−0.0182187 + 0.999834i \(0.505800\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −6736.00 −1.22818 −0.614089 0.789237i \(-0.710477\pi\)
−0.614089 + 0.789237i \(0.710477\pi\)
\(312\) 0 0
\(313\) 394.000 0.0711508 0.0355754 0.999367i \(-0.488674\pi\)
0.0355754 + 0.999367i \(0.488674\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 6714.00 1.18958 0.594788 0.803882i \(-0.297236\pi\)
0.594788 + 0.803882i \(0.297236\pi\)
\(318\) 0 0
\(319\) 2032.00 0.356646
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 248.000 0.0427216
\(324\) 0 0
\(325\) 5082.00 0.867380
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −1848.00 −0.309676
\(330\) 0 0
\(331\) −692.000 −0.114912 −0.0574558 0.998348i \(-0.518299\pi\)
−0.0574558 + 0.998348i \(0.518299\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −1528.00 −0.249205
\(336\) 0 0
\(337\) −1566.00 −0.253132 −0.126566 0.991958i \(-0.540396\pi\)
−0.126566 + 0.991958i \(0.540396\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −576.000 −0.0914726
\(342\) 0 0
\(343\) 343.000 0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −5328.00 −0.824271 −0.412135 0.911123i \(-0.635217\pi\)
−0.412135 + 0.911123i \(0.635217\pi\)
\(348\) 0 0
\(349\) 11326.0 1.73715 0.868577 0.495554i \(-0.165035\pi\)
0.868577 + 0.495554i \(0.165035\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 2130.00 0.321157 0.160579 0.987023i \(-0.448664\pi\)
0.160579 + 0.987023i \(0.448664\pi\)
\(354\) 0 0
\(355\) 472.000 0.0705666
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 3044.00 0.447510 0.223755 0.974645i \(-0.428168\pi\)
0.223755 + 0.974645i \(0.428168\pi\)
\(360\) 0 0
\(361\) 8517.00 1.24173
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −836.000 −0.119886
\(366\) 0 0
\(367\) −12416.0 −1.76597 −0.882984 0.469404i \(-0.844469\pi\)
−0.882984 + 0.469404i \(0.844469\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 1134.00 0.158691
\(372\) 0 0
\(373\) −7442.00 −1.03306 −0.516531 0.856268i \(-0.672777\pi\)
−0.516531 + 0.856268i \(0.672777\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 10668.0 1.45737
\(378\) 0 0
\(379\) −100.000 −0.0135532 −0.00677659 0.999977i \(-0.502157\pi\)
−0.00677659 + 0.999977i \(0.502157\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 8080.00 1.07799 0.538993 0.842310i \(-0.318805\pi\)
0.538993 + 0.842310i \(0.318805\pi\)
\(384\) 0 0
\(385\) 112.000 0.0148261
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 5482.00 0.714520 0.357260 0.934005i \(-0.383711\pi\)
0.357260 + 0.934005i \(0.383711\pi\)
\(390\) 0 0
\(391\) 152.000 0.0196598
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 1104.00 0.140629
\(396\) 0 0
\(397\) 10446.0 1.32058 0.660289 0.751011i \(-0.270434\pi\)
0.660289 + 0.751011i \(0.270434\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 11334.0 1.41145 0.705727 0.708484i \(-0.250621\pi\)
0.705727 + 0.708484i \(0.250621\pi\)
\(402\) 0 0
\(403\) −3024.00 −0.373787
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −3184.00 −0.387776
\(408\) 0 0
\(409\) 8594.00 1.03899 0.519494 0.854474i \(-0.326121\pi\)
0.519494 + 0.854474i \(0.326121\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −5404.00 −0.643858
\(414\) 0 0
\(415\) −2072.00 −0.245085
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 10500.0 1.22424 0.612122 0.790763i \(-0.290316\pi\)
0.612122 + 0.790763i \(0.290316\pi\)
\(420\) 0 0
\(421\) −12066.0 −1.39682 −0.698410 0.715698i \(-0.746109\pi\)
−0.698410 + 0.715698i \(0.746109\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −242.000 −0.0276205
\(426\) 0 0
\(427\) 210.000 0.0238000
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 4332.00 0.484142 0.242071 0.970259i \(-0.422173\pi\)
0.242071 + 0.970259i \(0.422173\pi\)
\(432\) 0 0
\(433\) −1918.00 −0.212871 −0.106436 0.994320i \(-0.533944\pi\)
−0.106436 + 0.994320i \(0.533944\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 9424.00 1.03160
\(438\) 0 0
\(439\) 7992.00 0.868878 0.434439 0.900701i \(-0.356947\pi\)
0.434439 + 0.900701i \(0.356947\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 3184.00 0.341482 0.170741 0.985316i \(-0.445384\pi\)
0.170741 + 0.985316i \(0.445384\pi\)
\(444\) 0 0
\(445\) 60.0000 0.00639162
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −11426.0 −1.20095 −0.600475 0.799644i \(-0.705022\pi\)
−0.600475 + 0.799644i \(0.705022\pi\)
\(450\) 0 0
\(451\) 3696.00 0.385893
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 588.000 0.0605843
\(456\) 0 0
\(457\) −16934.0 −1.73335 −0.866673 0.498877i \(-0.833746\pi\)
−0.866673 + 0.498877i \(0.833746\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 17038.0 1.72134 0.860671 0.509161i \(-0.170044\pi\)
0.860671 + 0.509161i \(0.170044\pi\)
\(462\) 0 0
\(463\) 13592.0 1.36431 0.682153 0.731209i \(-0.261044\pi\)
0.682153 + 0.731209i \(0.261044\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 8612.00 0.853353 0.426676 0.904404i \(-0.359684\pi\)
0.426676 + 0.904404i \(0.359684\pi\)
\(468\) 0 0
\(469\) 5348.00 0.526541
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 1696.00 0.164867
\(474\) 0 0
\(475\) −15004.0 −1.44933
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 7432.00 0.708928 0.354464 0.935070i \(-0.384663\pi\)
0.354464 + 0.935070i \(0.384663\pi\)
\(480\) 0 0
\(481\) −16716.0 −1.58458
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 2380.00 0.222825
\(486\) 0 0
\(487\) 6616.00 0.615605 0.307802 0.951450i \(-0.400406\pi\)
0.307802 + 0.951450i \(0.400406\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 17040.0 1.56620 0.783100 0.621896i \(-0.213637\pi\)
0.783100 + 0.621896i \(0.213637\pi\)
\(492\) 0 0
\(493\) −508.000 −0.0464081
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −1652.00 −0.149099
\(498\) 0 0
\(499\) 2948.00 0.264470 0.132235 0.991218i \(-0.457785\pi\)
0.132235 + 0.991218i \(0.457785\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 17304.0 1.53389 0.766946 0.641712i \(-0.221776\pi\)
0.766946 + 0.641712i \(0.221776\pi\)
\(504\) 0 0
\(505\) 2740.00 0.241442
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −4650.00 −0.404927 −0.202463 0.979290i \(-0.564895\pi\)
−0.202463 + 0.979290i \(0.564895\pi\)
\(510\) 0 0
\(511\) 2926.00 0.253305
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 928.000 0.0794030
\(516\) 0 0
\(517\) 2112.00 0.179663
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −16854.0 −1.41725 −0.708625 0.705585i \(-0.750684\pi\)
−0.708625 + 0.705585i \(0.750684\pi\)
\(522\) 0 0
\(523\) 124.000 0.0103674 0.00518369 0.999987i \(-0.498350\pi\)
0.00518369 + 0.999987i \(0.498350\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 144.000 0.0119027
\(528\) 0 0
\(529\) −6391.00 −0.525273
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 19404.0 1.57689
\(534\) 0 0
\(535\) 4272.00 0.345224
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −392.000 −0.0313259
\(540\) 0 0
\(541\) 5382.00 0.427708 0.213854 0.976866i \(-0.431398\pi\)
0.213854 + 0.976866i \(0.431398\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 2452.00 0.192720
\(546\) 0 0
\(547\) −17460.0 −1.36478 −0.682391 0.730987i \(-0.739060\pi\)
−0.682391 + 0.730987i \(0.739060\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −31496.0 −2.43516
\(552\) 0 0
\(553\) −3864.00 −0.297132
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 9514.00 0.723736 0.361868 0.932229i \(-0.382139\pi\)
0.361868 + 0.932229i \(0.382139\pi\)
\(558\) 0 0
\(559\) 8904.00 0.673701
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 3988.00 0.298533 0.149267 0.988797i \(-0.452309\pi\)
0.149267 + 0.988797i \(0.452309\pi\)
\(564\) 0 0
\(565\) 676.000 0.0503355
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −11346.0 −0.835939 −0.417969 0.908461i \(-0.637258\pi\)
−0.417969 + 0.908461i \(0.637258\pi\)
\(570\) 0 0
\(571\) 8436.00 0.618276 0.309138 0.951017i \(-0.399959\pi\)
0.309138 + 0.951017i \(0.399959\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −9196.00 −0.666956
\(576\) 0 0
\(577\) 2098.00 0.151371 0.0756853 0.997132i \(-0.475886\pi\)
0.0756853 + 0.997132i \(0.475886\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 7252.00 0.517838
\(582\) 0 0
\(583\) −1296.00 −0.0920666
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 9436.00 0.663484 0.331742 0.943370i \(-0.392364\pi\)
0.331742 + 0.943370i \(0.392364\pi\)
\(588\) 0 0
\(589\) 8928.00 0.624570
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 1314.00 0.0909941 0.0454971 0.998964i \(-0.485513\pi\)
0.0454971 + 0.998964i \(0.485513\pi\)
\(594\) 0 0
\(595\) −28.0000 −0.00192922
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −8940.00 −0.609814 −0.304907 0.952382i \(-0.598625\pi\)
−0.304907 + 0.952382i \(0.598625\pi\)
\(600\) 0 0
\(601\) 16058.0 1.08988 0.544941 0.838474i \(-0.316552\pi\)
0.544941 + 0.838474i \(0.316552\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 2534.00 0.170284
\(606\) 0 0
\(607\) −3936.00 −0.263192 −0.131596 0.991303i \(-0.542010\pi\)
−0.131596 + 0.991303i \(0.542010\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 11088.0 0.734161
\(612\) 0 0
\(613\) 174.000 0.0114646 0.00573230 0.999984i \(-0.498175\pi\)
0.00573230 + 0.999984i \(0.498175\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −16018.0 −1.04515 −0.522577 0.852592i \(-0.675029\pi\)
−0.522577 + 0.852592i \(0.675029\pi\)
\(618\) 0 0
\(619\) 3068.00 0.199214 0.0996069 0.995027i \(-0.468241\pi\)
0.0996069 + 0.995027i \(0.468241\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −210.000 −0.0135048
\(624\) 0 0
\(625\) 14141.0 0.905024
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 796.000 0.0504588
\(630\) 0 0
\(631\) −24656.0 −1.55553 −0.777765 0.628555i \(-0.783647\pi\)
−0.777765 + 0.628555i \(0.783647\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 4176.00 0.260976
\(636\) 0 0
\(637\) −2058.00 −0.128008
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −7594.00 −0.467933 −0.233966 0.972245i \(-0.575171\pi\)
−0.233966 + 0.972245i \(0.575171\pi\)
\(642\) 0 0
\(643\) 3724.00 0.228398 0.114199 0.993458i \(-0.463570\pi\)
0.114199 + 0.993458i \(0.463570\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 3792.00 0.230416 0.115208 0.993341i \(-0.463247\pi\)
0.115208 + 0.993341i \(0.463247\pi\)
\(648\) 0 0
\(649\) 6176.00 0.373543
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −24702.0 −1.48034 −0.740171 0.672418i \(-0.765256\pi\)
−0.740171 + 0.672418i \(0.765256\pi\)
\(654\) 0 0
\(655\) 584.000 0.0348378
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −20144.0 −1.19074 −0.595371 0.803451i \(-0.702995\pi\)
−0.595371 + 0.803451i \(0.702995\pi\)
\(660\) 0 0
\(661\) −2522.00 −0.148403 −0.0742015 0.997243i \(-0.523641\pi\)
−0.0742015 + 0.997243i \(0.523641\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −1736.00 −0.101232
\(666\) 0 0
\(667\) −19304.0 −1.12062
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −240.000 −0.0138079
\(672\) 0 0
\(673\) −10414.0 −0.596479 −0.298239 0.954491i \(-0.596399\pi\)
−0.298239 + 0.954491i \(0.596399\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 22230.0 1.26199 0.630996 0.775786i \(-0.282647\pi\)
0.630996 + 0.775786i \(0.282647\pi\)
\(678\) 0 0
\(679\) −8330.00 −0.470804
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 18192.0 1.01918 0.509588 0.860418i \(-0.329798\pi\)
0.509588 + 0.860418i \(0.329798\pi\)
\(684\) 0 0
\(685\) 1636.00 0.0912531
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −6804.00 −0.376214
\(690\) 0 0
\(691\) −8108.00 −0.446372 −0.223186 0.974776i \(-0.571646\pi\)
−0.223186 + 0.974776i \(0.571646\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −4312.00 −0.235343
\(696\) 0 0
\(697\) −924.000 −0.0502138
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 5794.00 0.312177 0.156089 0.987743i \(-0.450111\pi\)
0.156089 + 0.987743i \(0.450111\pi\)
\(702\) 0 0
\(703\) 49352.0 2.64772
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −9590.00 −0.510140
\(708\) 0 0
\(709\) −1954.00 −0.103504 −0.0517518 0.998660i \(-0.516480\pi\)
−0.0517518 + 0.998660i \(0.516480\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 5472.00 0.287417
\(714\) 0 0
\(715\) −672.000 −0.0351488
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −32016.0 −1.66063 −0.830317 0.557292i \(-0.811840\pi\)
−0.830317 + 0.557292i \(0.811840\pi\)
\(720\) 0 0
\(721\) −3248.00 −0.167770
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 30734.0 1.57439
\(726\) 0 0
\(727\) 23072.0 1.17702 0.588510 0.808490i \(-0.299715\pi\)
0.588510 + 0.808490i \(0.299715\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −424.000 −0.0214531
\(732\) 0 0
\(733\) 31782.0 1.60149 0.800747 0.599003i \(-0.204436\pi\)
0.800747 + 0.599003i \(0.204436\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −6112.00 −0.305480
\(738\) 0 0
\(739\) 24396.0 1.21437 0.607186 0.794559i \(-0.292298\pi\)
0.607186 + 0.794559i \(0.292298\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −32604.0 −1.60986 −0.804929 0.593371i \(-0.797797\pi\)
−0.804929 + 0.593371i \(0.797797\pi\)
\(744\) 0 0
\(745\) −5700.00 −0.280311
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −14952.0 −0.729418
\(750\) 0 0
\(751\) 7680.00 0.373165 0.186583 0.982439i \(-0.440259\pi\)
0.186583 + 0.982439i \(0.440259\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 3344.00 0.161193
\(756\) 0 0
\(757\) 366.000 0.0175727 0.00878633 0.999961i \(-0.497203\pi\)
0.00878633 + 0.999961i \(0.497203\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −29374.0 −1.39922 −0.699610 0.714525i \(-0.746643\pi\)
−0.699610 + 0.714525i \(0.746643\pi\)
\(762\) 0 0
\(763\) −8582.00 −0.407194
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 32424.0 1.52642
\(768\) 0 0
\(769\) −38990.0 −1.82837 −0.914184 0.405299i \(-0.867167\pi\)
−0.914184 + 0.405299i \(0.867167\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 20470.0 0.952464 0.476232 0.879320i \(-0.342002\pi\)
0.476232 + 0.879320i \(0.342002\pi\)
\(774\) 0 0
\(775\) −8712.00 −0.403799
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −57288.0 −2.63486
\(780\) 0 0
\(781\) 1888.00 0.0865019
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −892.000 −0.0405565
\(786\) 0 0
\(787\) −29916.0 −1.35501 −0.677503 0.735520i \(-0.736938\pi\)
−0.677503 + 0.735520i \(0.736938\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −2366.00 −0.106353
\(792\) 0 0
\(793\) −1260.00 −0.0564236
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −4914.00 −0.218398 −0.109199 0.994020i \(-0.534828\pi\)
−0.109199 + 0.994020i \(0.534828\pi\)
\(798\) 0 0
\(799\) −528.000 −0.0233783
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −3344.00 −0.146958
\(804\) 0 0
\(805\) −1064.00 −0.0465852
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −34250.0 −1.48846 −0.744231 0.667922i \(-0.767184\pi\)
−0.744231 + 0.667922i \(0.767184\pi\)
\(810\) 0 0
\(811\) 41804.0 1.81003 0.905017 0.425376i \(-0.139858\pi\)
0.905017 + 0.425376i \(0.139858\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 5416.00 0.232778
\(816\) 0 0
\(817\) −26288.0 −1.12570
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −30862.0 −1.31193 −0.655963 0.754793i \(-0.727737\pi\)
−0.655963 + 0.754793i \(0.727737\pi\)
\(822\) 0 0
\(823\) −10576.0 −0.447942 −0.223971 0.974596i \(-0.571902\pi\)
−0.223971 + 0.974596i \(0.571902\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −10680.0 −0.449069 −0.224534 0.974466i \(-0.572086\pi\)
−0.224534 + 0.974466i \(0.572086\pi\)
\(828\) 0 0
\(829\) −1178.00 −0.0493530 −0.0246765 0.999695i \(-0.507856\pi\)
−0.0246765 + 0.999695i \(0.507856\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 98.0000 0.00407623
\(834\) 0 0
\(835\) −1792.00 −0.0742691
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −5600.00 −0.230433 −0.115217 0.993340i \(-0.536756\pi\)
−0.115217 + 0.993340i \(0.536756\pi\)
\(840\) 0 0
\(841\) 40127.0 1.64529
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 866.000 0.0352560
\(846\) 0 0
\(847\) −8869.00 −0.359790
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 30248.0 1.21843
\(852\) 0 0
\(853\) −826.000 −0.0331556 −0.0165778 0.999863i \(-0.505277\pi\)
−0.0165778 + 0.999863i \(0.505277\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −45918.0 −1.83026 −0.915128 0.403164i \(-0.867910\pi\)
−0.915128 + 0.403164i \(0.867910\pi\)
\(858\) 0 0
\(859\) −42380.0 −1.68334 −0.841669 0.539994i \(-0.818426\pi\)
−0.841669 + 0.539994i \(0.818426\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −26524.0 −1.04622 −0.523110 0.852265i \(-0.675228\pi\)
−0.523110 + 0.852265i \(0.675228\pi\)
\(864\) 0 0
\(865\) 8068.00 0.317133
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 4416.00 0.172385
\(870\) 0 0
\(871\) −32088.0 −1.24829
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 3444.00 0.133061
\(876\) 0 0
\(877\) 20614.0 0.793712 0.396856 0.917881i \(-0.370101\pi\)
0.396856 + 0.917881i \(0.370101\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 23730.0 0.907473 0.453737 0.891136i \(-0.350091\pi\)
0.453737 + 0.891136i \(0.350091\pi\)
\(882\) 0 0
\(883\) 9028.00 0.344073 0.172036 0.985091i \(-0.444965\pi\)
0.172036 + 0.985091i \(0.444965\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 37200.0 1.40818 0.704089 0.710112i \(-0.251356\pi\)
0.704089 + 0.710112i \(0.251356\pi\)
\(888\) 0 0
\(889\) −14616.0 −0.551412
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −32736.0 −1.22673
\(894\) 0 0
\(895\) 6960.00 0.259941
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −18288.0 −0.678464
\(900\) 0 0
\(901\) 324.000 0.0119800
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 5796.00 0.212890
\(906\) 0 0
\(907\) −23988.0 −0.878179 −0.439090 0.898443i \(-0.644699\pi\)
−0.439090 + 0.898443i \(0.644699\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 15276.0 0.555561 0.277781 0.960645i \(-0.410401\pi\)
0.277781 + 0.960645i \(0.410401\pi\)
\(912\) 0 0
\(913\) −8288.00 −0.300430
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −2044.00 −0.0736083
\(918\) 0 0
\(919\) 10760.0 0.386224 0.193112 0.981177i \(-0.438142\pi\)
0.193112 + 0.981177i \(0.438142\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 9912.00 0.353475
\(924\) 0 0
\(925\) −48158.0 −1.71181
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 52890.0 1.86788 0.933942 0.357424i \(-0.116345\pi\)
0.933942 + 0.357424i \(0.116345\pi\)
\(930\) 0 0
\(931\) 6076.00 0.213891
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 32.0000 0.00111926
\(936\) 0 0
\(937\) −6118.00 −0.213305 −0.106652 0.994296i \(-0.534013\pi\)
−0.106652 + 0.994296i \(0.534013\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 32230.0 1.11654 0.558272 0.829658i \(-0.311465\pi\)
0.558272 + 0.829658i \(0.311465\pi\)
\(942\) 0 0
\(943\) −35112.0 −1.21252
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −18544.0 −0.636324 −0.318162 0.948036i \(-0.603066\pi\)
−0.318162 + 0.948036i \(0.603066\pi\)
\(948\) 0 0
\(949\) −17556.0 −0.600518
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −25930.0 −0.881380 −0.440690 0.897659i \(-0.645266\pi\)
−0.440690 + 0.897659i \(0.645266\pi\)
\(954\) 0 0
\(955\) −5304.00 −0.179721
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −5726.00 −0.192807
\(960\) 0 0
\(961\) −24607.0 −0.825988
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −292.000 −0.00974074
\(966\) 0 0
\(967\) −8192.00 −0.272427 −0.136214 0.990680i \(-0.543493\pi\)
−0.136214 + 0.990680i \(0.543493\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −54444.0 −1.79937 −0.899686 0.436537i \(-0.856205\pi\)
−0.899686 + 0.436537i \(0.856205\pi\)
\(972\) 0 0
\(973\) 15092.0 0.497253
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 25446.0 0.833255 0.416627 0.909077i \(-0.363212\pi\)
0.416627 + 0.909077i \(0.363212\pi\)
\(978\) 0 0
\(979\) 240.000 0.00783497
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 33192.0 1.07697 0.538484 0.842635i \(-0.318997\pi\)
0.538484 + 0.842635i \(0.318997\pi\)
\(984\) 0 0
\(985\) −5092.00 −0.164715
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −16112.0 −0.518030
\(990\) 0 0
\(991\) −11024.0 −0.353369 −0.176685 0.984268i \(-0.556537\pi\)
−0.176685 + 0.984268i \(0.556537\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −5072.00 −0.161601
\(996\) 0 0
\(997\) −40714.0 −1.29331 −0.646653 0.762785i \(-0.723832\pi\)
−0.646653 + 0.762785i \(0.723832\pi\)
\(998\) 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 1008.4.a.j.1.1 1
3.2 odd 2 336.4.a.d.1.1 1
4.3 odd 2 126.4.a.c.1.1 1
12.11 even 2 42.4.a.b.1.1 1
21.20 even 2 2352.4.a.ba.1.1 1
24.5 odd 2 1344.4.a.t.1.1 1
24.11 even 2 1344.4.a.f.1.1 1
28.3 even 6 882.4.g.r.667.1 2
28.11 odd 6 882.4.g.s.667.1 2
28.19 even 6 882.4.g.r.361.1 2
28.23 odd 6 882.4.g.s.361.1 2
28.27 even 2 882.4.a.d.1.1 1
60.23 odd 4 1050.4.g.n.799.1 2
60.47 odd 4 1050.4.g.n.799.2 2
60.59 even 2 1050.4.a.d.1.1 1
84.11 even 6 294.4.e.a.79.1 2
84.23 even 6 294.4.e.a.67.1 2
84.47 odd 6 294.4.e.d.67.1 2
84.59 odd 6 294.4.e.d.79.1 2
84.83 odd 2 294.4.a.h.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
42.4.a.b.1.1 1 12.11 even 2
126.4.a.c.1.1 1 4.3 odd 2
294.4.a.h.1.1 1 84.83 odd 2
294.4.e.a.67.1 2 84.23 even 6
294.4.e.a.79.1 2 84.11 even 6
294.4.e.d.67.1 2 84.47 odd 6
294.4.e.d.79.1 2 84.59 odd 6
336.4.a.d.1.1 1 3.2 odd 2
882.4.a.d.1.1 1 28.27 even 2
882.4.g.r.361.1 2 28.19 even 6
882.4.g.r.667.1 2 28.3 even 6
882.4.g.s.361.1 2 28.23 odd 6
882.4.g.s.667.1 2 28.11 odd 6
1008.4.a.j.1.1 1 1.1 even 1 trivial
1050.4.a.d.1.1 1 60.59 even 2
1050.4.g.n.799.1 2 60.23 odd 4
1050.4.g.n.799.2 2 60.47 odd 4
1344.4.a.f.1.1 1 24.11 even 2
1344.4.a.t.1.1 1 24.5 odd 2
2352.4.a.ba.1.1 1 21.20 even 2