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Properties

Label 1008.4.a.l.1.1
Level $1008$
Weight $4$
Character 1008.1
Self dual yes
Analytic conductor $59.474$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [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: \(0\)
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 \(\chi\) \(=\) 1008.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.00000 q^{5} +7.00000 q^{7} +O(q^{10})\) \(q+2.00000 q^{5} +7.00000 q^{7} +52.0000 q^{11} +86.0000 q^{13} +30.0000 q^{17} +4.00000 q^{19} +120.000 q^{23} -121.000 q^{25} -246.000 q^{29} -80.0000 q^{31} +14.0000 q^{35} -290.000 q^{37} +374.000 q^{41} -164.000 q^{43} +464.000 q^{47} +49.0000 q^{49} +162.000 q^{53} +104.000 q^{55} +180.000 q^{59} -666.000 q^{61} +172.000 q^{65} +628.000 q^{67} +296.000 q^{71} -518.000 q^{73} +364.000 q^{77} +1184.00 q^{79} +220.000 q^{83} +60.0000 q^{85} +774.000 q^{89} +602.000 q^{91} +8.00000 q^{95} -1086.00 q^{97} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) 2.00000 0.178885 0.0894427 − 0.995992i \(-0.471491\pi\)
0.0894427 + 0.995992i \(0.471491\pi\)
\(6\) 0 0
\(7\) 7.00000 0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 52.0000 1.42533 0.712663 − 0.701506i \(-0.247489\pi\)
0.712663 + 0.701506i \(0.247489\pi\)
\(12\) 0 0
\(13\) 86.0000 1.83478 0.917389 − 0.397992i \(-0.130293\pi\)
0.917389 + 0.397992i \(0.130293\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 30.0000 0.428004 0.214002 − 0.976833i \(-0.431350\pi\)
0.214002 + 0.976833i \(0.431350\pi\)
\(18\) 0 0
\(19\) 4.00000 0.0482980 0.0241490 − 0.999708i \(-0.492312\pi\)
0.0241490 + 0.999708i \(0.492312\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 120.000 1.08790 0.543951 − 0.839117i \(-0.316928\pi\)
0.543951 + 0.839117i \(0.316928\pi\)
\(24\) 0 0
\(25\) −121.000 −0.968000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −246.000 −1.57521 −0.787604 − 0.616181i \(-0.788679\pi\)
−0.787604 + 0.616181i \(0.788679\pi\)
\(30\) 0 0
\(31\) −80.0000 −0.463498 −0.231749 − 0.972776i \(-0.574445\pi\)
−0.231749 + 0.972776i \(0.574445\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 14.0000 0.0676123
\(36\) 0 0
\(37\) −290.000 −1.28853 −0.644266 − 0.764801i \(-0.722837\pi\)
−0.644266 + 0.764801i \(0.722837\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 374.000 1.42461 0.712305 − 0.701870i \(-0.247651\pi\)
0.712305 + 0.701870i \(0.247651\pi\)
\(42\) 0 0
\(43\) −164.000 −0.581622 −0.290811 − 0.956780i \(-0.593925\pi\)
−0.290811 + 0.956780i \(0.593925\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 464.000 1.44003 0.720014 − 0.693959i \(-0.244135\pi\)
0.720014 + 0.693959i \(0.244135\pi\)
\(48\) 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
\(55\) 104.000 0.254970
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 180.000 0.397187 0.198593 − 0.980082i \(-0.436363\pi\)
0.198593 + 0.980082i \(0.436363\pi\)
\(60\) 0 0
\(61\) −666.000 −1.39791 −0.698955 − 0.715165i \(-0.746351\pi\)
−0.698955 + 0.715165i \(0.746351\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 172.000 0.328215
\(66\) 0 0
\(67\) 628.000 1.14511 0.572555 − 0.819866i \(-0.305952\pi\)
0.572555 + 0.819866i \(0.305952\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 296.000 0.494771 0.247385 − 0.968917i \(-0.420429\pi\)
0.247385 + 0.968917i \(0.420429\pi\)
\(72\) 0 0
\(73\) −518.000 −0.830511 −0.415256 − 0.909705i \(-0.636308\pi\)
−0.415256 + 0.909705i \(0.636308\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 364.000 0.538723
\(78\) 0 0
\(79\) 1184.00 1.68621 0.843104 − 0.537751i \(-0.180726\pi\)
0.843104 + 0.537751i \(0.180726\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 220.000 0.290941 0.145471 − 0.989363i \(-0.453530\pi\)
0.145471 + 0.989363i \(0.453530\pi\)
\(84\) 0 0
\(85\) 60.0000 0.0765637
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 774.000 0.921841 0.460920 − 0.887441i \(-0.347519\pi\)
0.460920 + 0.887441i \(0.347519\pi\)
\(90\) 0 0
\(91\) 602.000 0.693481
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 8.00000 0.00863982
\(96\) 0 0
\(97\) −1086.00 −1.13677 −0.568385 − 0.822763i \(-0.692431\pi\)
−0.568385 + 0.822763i \(0.692431\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 290.000 0.285704 0.142852 − 0.989744i \(-0.454373\pi\)
0.142852 + 0.989744i \(0.454373\pi\)
\(102\) 0 0
\(103\) 88.0000 0.0841835 0.0420917 − 0.999114i \(-0.486598\pi\)
0.0420917 + 0.999114i \(0.486598\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 372.000 0.336099 0.168050 − 0.985779i \(-0.446253\pi\)
0.168050 + 0.985779i \(0.446253\pi\)
\(108\) 0 0
\(109\) 1430.00 1.25660 0.628299 − 0.777972i \(-0.283752\pi\)
0.628299 + 0.777972i \(0.283752\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −1810.00 −1.50682 −0.753409 − 0.657552i \(-0.771592\pi\)
−0.753409 + 0.657552i \(0.771592\pi\)
\(114\) 0 0
\(115\) 240.000 0.194610
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 210.000 0.161770
\(120\) 0 0
\(121\) 1373.00 1.03156
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −492.000 −0.352047
\(126\) 0 0
\(127\) −1168.00 −0.816089 −0.408044 − 0.912962i \(-0.633789\pi\)
−0.408044 + 0.912962i \(0.633789\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −1268.00 −0.845692 −0.422846 − 0.906202i \(-0.638969\pi\)
−0.422846 + 0.906202i \(0.638969\pi\)
\(132\) 0 0
\(133\) 28.0000 0.0182549
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −474.000 −0.295595 −0.147798 − 0.989018i \(-0.547218\pi\)
−0.147798 + 0.989018i \(0.547218\pi\)
\(138\) 0 0
\(139\) 2684.00 1.63780 0.818899 − 0.573938i \(-0.194585\pi\)
0.818899 + 0.573938i \(0.194585\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 4472.00 2.61516
\(144\) 0 0
\(145\) −492.000 −0.281782
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 1314.00 0.722464 0.361232 − 0.932476i \(-0.382356\pi\)
0.361232 + 0.932476i \(0.382356\pi\)
\(150\) 0 0
\(151\) −3000.00 −1.61680 −0.808399 − 0.588635i \(-0.799666\pi\)
−0.808399 + 0.588635i \(0.799666\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −160.000 −0.0829130
\(156\) 0 0
\(157\) 774.000 0.393452 0.196726 − 0.980459i \(-0.436969\pi\)
0.196726 + 0.980459i \(0.436969\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 840.000 0.411188
\(162\) 0 0
\(163\) 2292.00 1.10137 0.550685 − 0.834713i \(-0.314367\pi\)
0.550685 + 0.834713i \(0.314367\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −1672.00 −0.774750 −0.387375 − 0.921922i \(-0.626618\pi\)
−0.387375 + 0.921922i \(0.626618\pi\)
\(168\) 0 0
\(169\) 5199.00 2.36641
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 2730.00 1.19976 0.599879 − 0.800091i \(-0.295215\pi\)
0.599879 + 0.800091i \(0.295215\pi\)
\(174\) 0 0
\(175\) −847.000 −0.365870
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 2572.00 1.07397 0.536984 − 0.843592i \(-0.319564\pi\)
0.536984 + 0.843592i \(0.319564\pi\)
\(180\) 0 0
\(181\) 3214.00 1.31986 0.659930 − 0.751327i \(-0.270586\pi\)
0.659930 + 0.751327i \(0.270586\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −580.000 −0.230500
\(186\) 0 0
\(187\) 1560.00 0.610045
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −1520.00 −0.575829 −0.287915 − 0.957656i \(-0.592962\pi\)
−0.287915 + 0.957656i \(0.592962\pi\)
\(192\) 0 0
\(193\) −62.0000 −0.0231236 −0.0115618 − 0.999933i \(-0.503680\pi\)
−0.0115618 + 0.999933i \(0.503680\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 1074.00 0.388423 0.194212 − 0.980960i \(-0.437785\pi\)
0.194212 + 0.980960i \(0.437785\pi\)
\(198\) 0 0
\(199\) −552.000 −0.196634 −0.0983172 − 0.995155i \(-0.531346\pi\)
−0.0983172 + 0.995155i \(0.531346\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −1722.00 −0.595373
\(204\) 0 0
\(205\) 748.000 0.254842
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 208.000 0.0688405
\(210\) 0 0
\(211\) −1692.00 −0.552048 −0.276024 − 0.961151i \(-0.589017\pi\)
−0.276024 + 0.961151i \(0.589017\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −328.000 −0.104044
\(216\) 0 0
\(217\) −560.000 −0.175186
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 2580.00 0.785292
\(222\) 0 0
\(223\) −528.000 −0.158554 −0.0792769 − 0.996853i \(-0.525261\pi\)
−0.0792769 + 0.996853i \(0.525261\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −1876.00 −0.548522 −0.274261 − 0.961655i \(-0.588433\pi\)
−0.274261 + 0.961655i \(0.588433\pi\)
\(228\) 0 0
\(229\) −5474.00 −1.57962 −0.789808 − 0.613354i \(-0.789820\pi\)
−0.789808 + 0.613354i \(0.789820\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −3418.00 −0.961033 −0.480516 − 0.876986i \(-0.659551\pi\)
−0.480516 + 0.876986i \(0.659551\pi\)
\(234\) 0 0
\(235\) 928.000 0.257600
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 7360.00 1.99196 0.995981 − 0.0895670i \(-0.0285483\pi\)
0.995981 + 0.0895670i \(0.0285483\pi\)
\(240\) 0 0
\(241\) −2126.00 −0.568248 −0.284124 − 0.958788i \(-0.591703\pi\)
−0.284124 + 0.958788i \(0.591703\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 98.0000 0.0255551
\(246\) 0 0
\(247\) 344.000 0.0886162
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −7788.00 −1.95846 −0.979231 − 0.202745i \(-0.935014\pi\)
−0.979231 + 0.202745i \(0.935014\pi\)
\(252\) 0 0
\(253\) 6240.00 1.55061
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 3470.00 0.842228 0.421114 − 0.907008i \(-0.361639\pi\)
0.421114 + 0.907008i \(0.361639\pi\)
\(258\) 0 0
\(259\) −2030.00 −0.487020
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −3096.00 −0.725884 −0.362942 − 0.931812i \(-0.618228\pi\)
−0.362942 + 0.931812i \(0.618228\pi\)
\(264\) 0 0
\(265\) 324.000 0.0751063
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 3274.00 0.742079 0.371040 − 0.928617i \(-0.379001\pi\)
0.371040 + 0.928617i \(0.379001\pi\)
\(270\) 0 0
\(271\) −960.000 −0.215188 −0.107594 − 0.994195i \(-0.534315\pi\)
−0.107594 + 0.994195i \(0.534315\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −6292.00 −1.37972
\(276\) 0 0
\(277\) 910.000 0.197388 0.0986942 − 0.995118i \(-0.468533\pi\)
0.0986942 + 0.995118i \(0.468533\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 6486.00 1.37695 0.688474 − 0.725261i \(-0.258281\pi\)
0.688474 + 0.725261i \(0.258281\pi\)
\(282\) 0 0
\(283\) −3796.00 −0.797346 −0.398673 − 0.917093i \(-0.630529\pi\)
−0.398673 + 0.917093i \(0.630529\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 2618.00 0.538452
\(288\) 0 0
\(289\) −4013.00 −0.816813
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 6882.00 1.37219 0.686093 − 0.727513i \(-0.259324\pi\)
0.686093 + 0.727513i \(0.259324\pi\)
\(294\) 0 0
\(295\) 360.000 0.0710509
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 10320.0 1.99606
\(300\) 0 0
\(301\) −1148.00 −0.219833
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −1332.00 −0.250066
\(306\) 0 0
\(307\) −7228.00 −1.34373 −0.671863 − 0.740676i \(-0.734506\pi\)
−0.671863 + 0.740676i \(0.734506\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 7912.00 1.44260 0.721300 − 0.692623i \(-0.243545\pi\)
0.721300 + 0.692623i \(0.243545\pi\)
\(312\) 0 0
\(313\) 2218.00 0.400539 0.200270 − 0.979741i \(-0.435818\pi\)
0.200270 + 0.979741i \(0.435818\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −8118.00 −1.43834 −0.719168 − 0.694837i \(-0.755477\pi\)
−0.719168 + 0.694837i \(0.755477\pi\)
\(318\) 0 0
\(319\) −12792.0 −2.24519
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 120.000 0.0206718
\(324\) 0 0
\(325\) −10406.0 −1.77606
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 3248.00 0.544280
\(330\) 0 0
\(331\) 10780.0 1.79010 0.895049 − 0.445968i \(-0.147140\pi\)
0.895049 + 0.445968i \(0.147140\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 1256.00 0.204844
\(336\) 0 0
\(337\) 3122.00 0.504647 0.252324 − 0.967643i \(-0.418805\pi\)
0.252324 + 0.967643i \(0.418805\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −4160.00 −0.660635
\(342\) 0 0
\(343\) 343.000 0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −828.000 −0.128096 −0.0640481 − 0.997947i \(-0.520401\pi\)
−0.0640481 + 0.997947i \(0.520401\pi\)
\(348\) 0 0
\(349\) 4614.00 0.707684 0.353842 − 0.935305i \(-0.384875\pi\)
0.353842 + 0.935305i \(0.384875\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −9458.00 −1.42606 −0.713029 − 0.701134i \(-0.752677\pi\)
−0.713029 + 0.701134i \(0.752677\pi\)
\(354\) 0 0
\(355\) 592.000 0.0885073
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 2952.00 0.433985 0.216992 − 0.976173i \(-0.430375\pi\)
0.216992 + 0.976173i \(0.430375\pi\)
\(360\) 0 0
\(361\) −6843.00 −0.997667
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −1036.00 −0.148566
\(366\) 0 0
\(367\) 10592.0 1.50653 0.753267 − 0.657715i \(-0.228477\pi\)
0.753267 + 0.657715i \(0.228477\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 1134.00 0.158691
\(372\) 0 0
\(373\) 6478.00 0.899244 0.449622 − 0.893219i \(-0.351559\pi\)
0.449622 + 0.893219i \(0.351559\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −21156.0 −2.89016
\(378\) 0 0
\(379\) −5780.00 −0.783374 −0.391687 − 0.920099i \(-0.628108\pi\)
−0.391687 + 0.920099i \(0.628108\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −6912.00 −0.922158 −0.461079 − 0.887359i \(-0.652538\pi\)
−0.461079 + 0.887359i \(0.652538\pi\)
\(384\) 0 0
\(385\) 728.000 0.0963697
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 9010.00 1.17436 0.587179 − 0.809457i \(-0.300239\pi\)
0.587179 + 0.809457i \(0.300239\pi\)
\(390\) 0 0
\(391\) 3600.00 0.465626
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 2368.00 0.301638
\(396\) 0 0
\(397\) 10774.0 1.36204 0.681022 − 0.732263i \(-0.261536\pi\)
0.681022 + 0.732263i \(0.261536\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 78.0000 0.00971355 0.00485678 − 0.999988i \(-0.498454\pi\)
0.00485678 + 0.999988i \(0.498454\pi\)
\(402\) 0 0
\(403\) −6880.00 −0.850415
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −15080.0 −1.83658
\(408\) 0 0
\(409\) −15254.0 −1.84416 −0.922080 − 0.386998i \(-0.873512\pi\)
−0.922080 + 0.386998i \(0.873512\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 1260.00 0.150122
\(414\) 0 0
\(415\) 440.000 0.0520452
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −7316.00 −0.853007 −0.426504 − 0.904486i \(-0.640255\pi\)
−0.426504 + 0.904486i \(0.640255\pi\)
\(420\) 0 0
\(421\) −11330.0 −1.31162 −0.655808 − 0.754928i \(-0.727672\pi\)
−0.655808 + 0.754928i \(0.727672\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −3630.00 −0.414308
\(426\) 0 0
\(427\) −4662.00 −0.528361
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −6016.00 −0.672345 −0.336172 − 0.941801i \(-0.609132\pi\)
−0.336172 + 0.941801i \(0.609132\pi\)
\(432\) 0 0
\(433\) −13550.0 −1.50386 −0.751930 − 0.659243i \(-0.770877\pi\)
−0.751930 + 0.659243i \(0.770877\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 480.000 0.0525435
\(438\) 0 0
\(439\) 2760.00 0.300063 0.150031 − 0.988681i \(-0.452063\pi\)
0.150031 + 0.988681i \(0.452063\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −3036.00 −0.325609 −0.162804 − 0.986658i \(-0.552054\pi\)
−0.162804 + 0.986658i \(0.552054\pi\)
\(444\) 0 0
\(445\) 1548.00 0.164904
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −12962.0 −1.36239 −0.681197 − 0.732100i \(-0.738540\pi\)
−0.681197 + 0.732100i \(0.738540\pi\)
\(450\) 0 0
\(451\) 19448.0 2.03053
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 1204.00 0.124054
\(456\) 0 0
\(457\) 11866.0 1.21459 0.607295 − 0.794476i \(-0.292254\pi\)
0.607295 + 0.794476i \(0.292254\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −10998.0 −1.11112 −0.555562 − 0.831475i \(-0.687497\pi\)
−0.555562 + 0.831475i \(0.687497\pi\)
\(462\) 0 0
\(463\) 9088.00 0.912214 0.456107 − 0.889925i \(-0.349243\pi\)
0.456107 + 0.889925i \(0.349243\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 18236.0 1.80698 0.903492 − 0.428605i \(-0.140995\pi\)
0.903492 + 0.428605i \(0.140995\pi\)
\(468\) 0 0
\(469\) 4396.00 0.432811
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −8528.00 −0.829002
\(474\) 0 0
\(475\) −484.000 −0.0467525
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −11424.0 −1.08972 −0.544860 − 0.838527i \(-0.683417\pi\)
−0.544860 + 0.838527i \(0.683417\pi\)
\(480\) 0 0
\(481\) −24940.0 −2.36417
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −2172.00 −0.203351
\(486\) 0 0
\(487\) 8536.00 0.794257 0.397128 − 0.917763i \(-0.370007\pi\)
0.397128 + 0.917763i \(0.370007\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −18732.0 −1.72172 −0.860859 − 0.508844i \(-0.830073\pi\)
−0.860859 + 0.508844i \(0.830073\pi\)
\(492\) 0 0
\(493\) −7380.00 −0.674196
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 2072.00 0.187006
\(498\) 0 0
\(499\) 21700.0 1.94674 0.973372 − 0.229231i \(-0.0736210\pi\)
0.973372 + 0.229231i \(0.0736210\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −1048.00 −0.0928986 −0.0464493 − 0.998921i \(-0.514791\pi\)
−0.0464493 + 0.998921i \(0.514791\pi\)
\(504\) 0 0
\(505\) 580.000 0.0511082
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 8890.00 0.774150 0.387075 − 0.922048i \(-0.373485\pi\)
0.387075 + 0.922048i \(0.373485\pi\)
\(510\) 0 0
\(511\) −3626.00 −0.313904
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 176.000 0.0150592
\(516\) 0 0
\(517\) 24128.0 2.05251
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −13962.0 −1.17406 −0.587031 − 0.809564i \(-0.699703\pi\)
−0.587031 + 0.809564i \(0.699703\pi\)
\(522\) 0 0
\(523\) −16420.0 −1.37284 −0.686421 − 0.727204i \(-0.740819\pi\)
−0.686421 + 0.727204i \(0.740819\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −2400.00 −0.198379
\(528\) 0 0
\(529\) 2233.00 0.183529
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 32164.0 2.61384
\(534\) 0 0
\(535\) 744.000 0.0601232
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 2548.00 0.203618
\(540\) 0 0
\(541\) −14554.0 −1.15661 −0.578304 − 0.815821i \(-0.696285\pi\)
−0.578304 + 0.815821i \(0.696285\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 2860.00 0.224787
\(546\) 0 0
\(547\) −588.000 −0.0459617 −0.0229809 − 0.999736i \(-0.507316\pi\)
−0.0229809 + 0.999736i \(0.507316\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −984.000 −0.0760795
\(552\) 0 0
\(553\) 8288.00 0.637327
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −10726.0 −0.815934 −0.407967 − 0.912997i \(-0.633762\pi\)
−0.407967 + 0.912997i \(0.633762\pi\)
\(558\) 0 0
\(559\) −14104.0 −1.06715
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −740.000 −0.0553948 −0.0276974 − 0.999616i \(-0.508817\pi\)
−0.0276974 + 0.999616i \(0.508817\pi\)
\(564\) 0 0
\(565\) −3620.00 −0.269548
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −17386.0 −1.28095 −0.640474 − 0.767980i \(-0.721262\pi\)
−0.640474 + 0.767980i \(0.721262\pi\)
\(570\) 0 0
\(571\) −1108.00 −0.0812055 −0.0406028 − 0.999175i \(-0.512928\pi\)
−0.0406028 + 0.999175i \(0.512928\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −14520.0 −1.05309
\(576\) 0 0
\(577\) −13694.0 −0.988022 −0.494011 − 0.869456i \(-0.664470\pi\)
−0.494011 + 0.869456i \(0.664470\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 1540.00 0.109966
\(582\) 0 0
\(583\) 8424.00 0.598433
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −2844.00 −0.199973 −0.0999867 − 0.994989i \(-0.531880\pi\)
−0.0999867 + 0.994989i \(0.531880\pi\)
\(588\) 0 0
\(589\) −320.000 −0.0223860
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −9410.00 −0.651640 −0.325820 − 0.945432i \(-0.605640\pi\)
−0.325820 + 0.945432i \(0.605640\pi\)
\(594\) 0 0
\(595\) 420.000 0.0289384
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −14952.0 −1.01990 −0.509952 − 0.860203i \(-0.670337\pi\)
−0.509952 + 0.860203i \(0.670337\pi\)
\(600\) 0 0
\(601\) 2570.00 0.174430 0.0872150 − 0.996190i \(-0.472203\pi\)
0.0872150 + 0.996190i \(0.472203\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 2746.00 0.184530
\(606\) 0 0
\(607\) 8176.00 0.546711 0.273356 − 0.961913i \(-0.411866\pi\)
0.273356 + 0.961913i \(0.411866\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 39904.0 2.64213
\(612\) 0 0
\(613\) 8862.00 0.583903 0.291952 − 0.956433i \(-0.405695\pi\)
0.291952 + 0.956433i \(0.405695\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 1126.00 0.0734701 0.0367351 − 0.999325i \(-0.488304\pi\)
0.0367351 + 0.999325i \(0.488304\pi\)
\(618\) 0 0
\(619\) −9892.00 −0.642315 −0.321158 − 0.947026i \(-0.604072\pi\)
−0.321158 + 0.947026i \(0.604072\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 5418.00 0.348423
\(624\) 0 0
\(625\) 14141.0 0.905024
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −8700.00 −0.551497
\(630\) 0 0
\(631\) −11256.0 −0.710134 −0.355067 − 0.934841i \(-0.615542\pi\)
−0.355067 + 0.934841i \(0.615542\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −2336.00 −0.145986
\(636\) 0 0
\(637\) 4214.00 0.262111
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 5694.00 0.350857 0.175429 − 0.984492i \(-0.443869\pi\)
0.175429 + 0.984492i \(0.443869\pi\)
\(642\) 0 0
\(643\) −30028.0 −1.84166 −0.920831 − 0.389962i \(-0.872488\pi\)
−0.920831 + 0.389962i \(0.872488\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 18680.0 1.13506 0.567532 − 0.823351i \(-0.307898\pi\)
0.567532 + 0.823351i \(0.307898\pi\)
\(648\) 0 0
\(649\) 9360.00 0.566120
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 3034.00 0.181822 0.0909109 − 0.995859i \(-0.471022\pi\)
0.0909109 + 0.995859i \(0.471022\pi\)
\(654\) 0 0
\(655\) −2536.00 −0.151282
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 26508.0 1.56693 0.783464 − 0.621438i \(-0.213451\pi\)
0.783464 + 0.621438i \(0.213451\pi\)
\(660\) 0 0
\(661\) −24658.0 −1.45096 −0.725480 − 0.688243i \(-0.758382\pi\)
−0.725480 + 0.688243i \(0.758382\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 56.0000 0.00326554
\(666\) 0 0
\(667\) −29520.0 −1.71367
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −34632.0 −1.99248
\(672\) 0 0
\(673\) 23266.0 1.33260 0.666299 − 0.745685i \(-0.267877\pi\)
0.666299 + 0.745685i \(0.267877\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −5694.00 −0.323247 −0.161623 − 0.986852i \(-0.551673\pi\)
−0.161623 + 0.986852i \(0.551673\pi\)
\(678\) 0 0
\(679\) −7602.00 −0.429658
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −14796.0 −0.828921 −0.414461 − 0.910067i \(-0.636030\pi\)
−0.414461 + 0.910067i \(0.636030\pi\)
\(684\) 0 0
\(685\) −948.000 −0.0528777
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 13932.0 0.770344
\(690\) 0 0
\(691\) −4540.00 −0.249942 −0.124971 − 0.992160i \(-0.539884\pi\)
−0.124971 + 0.992160i \(0.539884\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 5368.00 0.292978
\(696\) 0 0
\(697\) 11220.0 0.609739
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 18666.0 1.00571 0.502857 − 0.864370i \(-0.332282\pi\)
0.502857 + 0.864370i \(0.332282\pi\)
\(702\) 0 0
\(703\) −1160.00 −0.0622336
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 2030.00 0.107986
\(708\) 0 0
\(709\) 10974.0 0.581294 0.290647 − 0.956830i \(-0.406130\pi\)
0.290647 + 0.956830i \(0.406130\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −9600.00 −0.504240
\(714\) 0 0
\(715\) 8944.00 0.467813
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 28240.0 1.46478 0.732388 − 0.680887i \(-0.238406\pi\)
0.732388 + 0.680887i \(0.238406\pi\)
\(720\) 0 0
\(721\) 616.000 0.0318184
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 29766.0 1.52480
\(726\) 0 0
\(727\) −6232.00 −0.317926 −0.158963 − 0.987285i \(-0.550815\pi\)
−0.158963 + 0.987285i \(0.550815\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −4920.00 −0.248937
\(732\) 0 0
\(733\) 21638.0 1.09034 0.545169 − 0.838326i \(-0.316465\pi\)
0.545169 + 0.838326i \(0.316465\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 32656.0 1.63216
\(738\) 0 0
\(739\) −24364.0 −1.21278 −0.606390 − 0.795167i \(-0.707383\pi\)
−0.606390 + 0.795167i \(0.707383\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 3112.00 0.153658 0.0768292 − 0.997044i \(-0.475520\pi\)
0.0768292 + 0.997044i \(0.475520\pi\)
\(744\) 0 0
\(745\) 2628.00 0.129238
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 2604.00 0.127033
\(750\) 0 0
\(751\) 20576.0 0.999772 0.499886 − 0.866091i \(-0.333375\pi\)
0.499886 + 0.866091i \(0.333375\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −6000.00 −0.289222
\(756\) 0 0
\(757\) −4754.00 −0.228252 −0.114126 − 0.993466i \(-0.536407\pi\)
−0.114126 + 0.993466i \(0.536407\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 10950.0 0.521599 0.260800 − 0.965393i \(-0.416014\pi\)
0.260800 + 0.965393i \(0.416014\pi\)
\(762\) 0 0
\(763\) 10010.0 0.474949
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 15480.0 0.728749
\(768\) 0 0
\(769\) −28798.0 −1.35043 −0.675216 − 0.737620i \(-0.735950\pi\)
−0.675216 + 0.737620i \(0.735950\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 12866.0 0.598652 0.299326 − 0.954151i \(-0.403238\pi\)
0.299326 + 0.954151i \(0.403238\pi\)
\(774\) 0 0
\(775\) 9680.00 0.448666
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 1496.00 0.0688059
\(780\) 0 0
\(781\) 15392.0 0.705210
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 1548.00 0.0703828
\(786\) 0 0
\(787\) 13156.0 0.595884 0.297942 − 0.954584i \(-0.403700\pi\)
0.297942 + 0.954584i \(0.403700\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −12670.0 −0.569524
\(792\) 0 0
\(793\) −57276.0 −2.56486
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −20454.0 −0.909056 −0.454528 − 0.890732i \(-0.650192\pi\)
−0.454528 + 0.890732i \(0.650192\pi\)
\(798\) 0 0
\(799\) 13920.0 0.616338
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −26936.0 −1.18375
\(804\) 0 0
\(805\) 1680.00 0.0735556
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −15706.0 −0.682563 −0.341282 − 0.939961i \(-0.610861\pi\)
−0.341282 + 0.939961i \(0.610861\pi\)
\(810\) 0 0
\(811\) −6532.00 −0.282823 −0.141412 − 0.989951i \(-0.545164\pi\)
−0.141412 + 0.989951i \(0.545164\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 4584.00 0.197019
\(816\) 0 0
\(817\) −656.000 −0.0280912
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 46754.0 1.98749 0.993743 − 0.111692i \(-0.0356269\pi\)
0.993743 + 0.111692i \(0.0356269\pi\)
\(822\) 0 0
\(823\) −22008.0 −0.932139 −0.466070 − 0.884748i \(-0.654330\pi\)
−0.466070 + 0.884748i \(0.654330\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 45412.0 1.90947 0.954734 − 0.297461i \(-0.0961398\pi\)
0.954734 + 0.297461i \(0.0961398\pi\)
\(828\) 0 0
\(829\) 13670.0 0.572713 0.286356 − 0.958123i \(-0.407556\pi\)
0.286356 + 0.958123i \(0.407556\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 1470.00 0.0611434
\(834\) 0 0
\(835\) −3344.00 −0.138591
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −26568.0 −1.09324 −0.546621 − 0.837380i \(-0.684086\pi\)
−0.546621 + 0.837380i \(0.684086\pi\)
\(840\) 0 0
\(841\) 36127.0 1.48128
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 10398.0 0.423316
\(846\) 0 0
\(847\) 9611.00 0.389891
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −34800.0 −1.40180
\(852\) 0 0
\(853\) 1070.00 0.0429497 0.0214749 − 0.999769i \(-0.493164\pi\)
0.0214749 + 0.999769i \(0.493164\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −42906.0 −1.71020 −0.855100 − 0.518463i \(-0.826504\pi\)
−0.855100 + 0.518463i \(0.826504\pi\)
\(858\) 0 0
\(859\) −11252.0 −0.446930 −0.223465 − 0.974712i \(-0.571737\pi\)
−0.223465 + 0.974712i \(0.571737\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 29264.0 1.15430 0.577148 − 0.816639i \(-0.304165\pi\)
0.577148 + 0.816639i \(0.304165\pi\)
\(864\) 0 0
\(865\) 5460.00 0.214619
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 61568.0 2.40340
\(870\) 0 0
\(871\) 54008.0 2.10102
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −3444.00 −0.133061
\(876\) 0 0
\(877\) 25782.0 0.992698 0.496349 − 0.868123i \(-0.334674\pi\)
0.496349 + 0.868123i \(0.334674\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 9054.00 0.346240 0.173120 − 0.984901i \(-0.444615\pi\)
0.173120 + 0.984901i \(0.444615\pi\)
\(882\) 0 0
\(883\) −8092.00 −0.308400 −0.154200 − 0.988040i \(-0.549280\pi\)
−0.154200 + 0.988040i \(0.549280\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 11944.0 0.452131 0.226066 − 0.974112i \(-0.427414\pi\)
0.226066 + 0.974112i \(0.427414\pi\)
\(888\) 0 0
\(889\) −8176.00 −0.308452
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 1856.00 0.0695506
\(894\) 0 0
\(895\) 5144.00 0.192117
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 19680.0 0.730105
\(900\) 0 0
\(901\) 4860.00 0.179700
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 6428.00 0.236104
\(906\) 0 0
\(907\) 31804.0 1.16432 0.582158 − 0.813076i \(-0.302209\pi\)
0.582158 + 0.813076i \(0.302209\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 27840.0 1.01249 0.506246 − 0.862389i \(-0.331033\pi\)
0.506246 + 0.862389i \(0.331033\pi\)
\(912\) 0 0
\(913\) 11440.0 0.414686
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −8876.00 −0.319642
\(918\) 0 0
\(919\) −12536.0 −0.449972 −0.224986 − 0.974362i \(-0.572234\pi\)
−0.224986 + 0.974362i \(0.572234\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 25456.0 0.907795
\(924\) 0 0
\(925\) 35090.0 1.24730
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 25870.0 0.913635 0.456818 − 0.889560i \(-0.348989\pi\)
0.456818 + 0.889560i \(0.348989\pi\)
\(930\) 0 0
\(931\) 196.000 0.00689972
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 3120.00 0.109128
\(936\) 0 0
\(937\) −6086.00 −0.212189 −0.106094 − 0.994356i \(-0.533835\pi\)
−0.106094 + 0.994356i \(0.533835\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −3894.00 −0.134900 −0.0674499 − 0.997723i \(-0.521486\pi\)
−0.0674499 + 0.997723i \(0.521486\pi\)
\(942\) 0 0
\(943\) 44880.0 1.54983
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −20692.0 −0.710031 −0.355016 − 0.934860i \(-0.615524\pi\)
−0.355016 + 0.934860i \(0.615524\pi\)
\(948\) 0 0
\(949\) −44548.0 −1.52380
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −46986.0 −1.59709 −0.798545 − 0.601936i \(-0.794396\pi\)
−0.798545 + 0.601936i \(0.794396\pi\)
\(954\) 0 0
\(955\) −3040.00 −0.103007
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −3318.00 −0.111725
\(960\) 0 0
\(961\) −23391.0 −0.785170
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −124.000 −0.00413648
\(966\) 0 0
\(967\) −53960.0 −1.79445 −0.897227 − 0.441570i \(-0.854422\pi\)
−0.897227 + 0.441570i \(0.854422\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −7068.00 −0.233597 −0.116799 − 0.993156i \(-0.537263\pi\)
−0.116799 + 0.993156i \(0.537263\pi\)
\(972\) 0 0
\(973\) 18788.0 0.619029
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −54130.0 −1.77254 −0.886270 − 0.463168i \(-0.846712\pi\)
−0.886270 + 0.463168i \(0.846712\pi\)
\(978\) 0 0
\(979\) 40248.0 1.31392
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −23064.0 −0.748349 −0.374175 − 0.927358i \(-0.622074\pi\)
−0.374175 + 0.927358i \(0.622074\pi\)
\(984\) 0 0
\(985\) 2148.00 0.0694832
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −19680.0 −0.632748
\(990\) 0 0
\(991\) 10768.0 0.345163 0.172582 − 0.984995i \(-0.444789\pi\)
0.172582 + 0.984995i \(0.444789\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −1104.00 −0.0351750
\(996\) 0 0
\(997\) 12766.0 0.405520 0.202760 − 0.979228i \(-0.435009\pi\)
0.202760 + 0.979228i \(0.435009\pi\)
\(998\) 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.l.1.1 1
3.2 odd 2 336.4.a.c.1.1 1
4.3 odd 2 504.4.a.c.1.1 1
12.11 even 2 168.4.a.f.1.1 ✓ 1
21.20 even 2 2352.4.a.bb.1.1 1
24.5 odd 2 1344.4.a.v.1.1 1
24.11 even 2 1344.4.a.g.1.1 1
84.83 odd 2 1176.4.a.e.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
168.4.a.f.1.1 ✓ 1 12.11 even 2
336.4.a.c.1.1 1 3.2 odd 2
504.4.a.c.1.1 1 4.3 odd 2
1008.4.a.l.1.1 1 1.1 even 1 trivial
1176.4.a.e.1.1 1 84.83 odd 2
1344.4.a.g.1.1 1 24.11 even 2
1344.4.a.v.1.1 1 24.5 odd 2
2352.4.a.bb.1.1 1 21.20 even 2