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Properties

Label 1568.4.a.j.1.1
Level $1568$
Weight $4$
Character 1568.1
Self dual yes
Analytic conductor $92.515$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1568,4,Mod(1,1568)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1568, 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("1568.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1568 = 2^{5} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1568.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: \(92.5149948890\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1568.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.00000 q^{3} -14.0000 q^{5} -23.0000 q^{9} +O(q^{10})\) \(q+2.00000 q^{3} -14.0000 q^{5} -23.0000 q^{9} +20.0000 q^{11} +6.00000 q^{13} -28.0000 q^{15} -20.0000 q^{17} +102.000 q^{19} +124.000 q^{23} +71.0000 q^{25} -100.000 q^{27} -78.0000 q^{29} +236.000 q^{31} +40.0000 q^{33} +66.0000 q^{37} +12.0000 q^{39} -268.000 q^{41} -132.000 q^{43} +322.000 q^{45} +516.000 q^{47} -40.0000 q^{51} -354.000 q^{53} -280.000 q^{55} +204.000 q^{57} +438.000 q^{59} -486.000 q^{61} -84.0000 q^{65} -804.000 q^{67} +248.000 q^{69} -248.000 q^{71} -768.000 q^{73} +142.000 q^{75} -192.000 q^{79} +421.000 q^{81} +294.000 q^{83} +280.000 q^{85} -156.000 q^{87} -80.0000 q^{89} +472.000 q^{93} -1428.00 q^{95} -1404.00 q^{97} -460.000 q^{99} +O(q^{100})\)

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
\(3\) 2.00000 0.384900 0.192450 − 0.981307i \(-0.438357\pi\)
0.192450 + 0.981307i \(0.438357\pi\)
\(4\) 0 0
\(5\) −14.0000 −1.25220 −0.626099 − 0.779744i \(-0.715349\pi\)
−0.626099 + 0.779744i \(0.715349\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −23.0000 −0.851852
\(10\) 0 0
\(11\) 20.0000 0.548202 0.274101 − 0.961701i \(-0.411620\pi\)
0.274101 + 0.961701i \(0.411620\pi\)
\(12\) 0 0
\(13\) 6.00000 0.128008 0.0640039 − 0.997950i \(-0.479613\pi\)
0.0640039 + 0.997950i \(0.479613\pi\)
\(14\) 0 0
\(15\) −28.0000 −0.481971
\(16\) 0 0
\(17\) −20.0000 −0.285336 −0.142668 − 0.989771i \(-0.545568\pi\)
−0.142668 + 0.989771i \(0.545568\pi\)
\(18\) 0 0
\(19\) 102.000 1.23160 0.615800 − 0.787902i \(-0.288833\pi\)
0.615800 + 0.787902i \(0.288833\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 124.000 1.12416 0.562082 − 0.827081i \(-0.310000\pi\)
0.562082 + 0.827081i \(0.310000\pi\)
\(24\) 0 0
\(25\) 71.0000 0.568000
\(26\) 0 0
\(27\) −100.000 −0.712778
\(28\) 0 0
\(29\) −78.0000 −0.499456 −0.249728 − 0.968316i \(-0.580341\pi\)
−0.249728 + 0.968316i \(0.580341\pi\)
\(30\) 0 0
\(31\) 236.000 1.36732 0.683659 − 0.729802i \(-0.260388\pi\)
0.683659 + 0.729802i \(0.260388\pi\)
\(32\) 0 0
\(33\) 40.0000 0.211003
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 66.0000 0.293252 0.146626 − 0.989192i \(-0.453159\pi\)
0.146626 + 0.989192i \(0.453159\pi\)
\(38\) 0 0
\(39\) 12.0000 0.0492702
\(40\) 0 0
\(41\) −268.000 −1.02084 −0.510422 − 0.859924i \(-0.670511\pi\)
−0.510422 + 0.859924i \(0.670511\pi\)
\(42\) 0 0
\(43\) −132.000 −0.468135 −0.234068 − 0.972220i \(-0.575204\pi\)
−0.234068 + 0.972220i \(0.575204\pi\)
\(44\) 0 0
\(45\) 322.000 1.06669
\(46\) 0 0
\(47\) 516.000 1.60141 0.800706 − 0.599058i \(-0.204458\pi\)
0.800706 + 0.599058i \(0.204458\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) −40.0000 −0.109826
\(52\) 0 0
\(53\) −354.000 −0.917465 −0.458732 − 0.888574i \(-0.651696\pi\)
−0.458732 + 0.888574i \(0.651696\pi\)
\(54\) 0 0
\(55\) −280.000 −0.686458
\(56\) 0 0
\(57\) 204.000 0.474043
\(58\) 0 0
\(59\) 438.000 0.966487 0.483244 − 0.875486i \(-0.339459\pi\)
0.483244 + 0.875486i \(0.339459\pi\)
\(60\) 0 0
\(61\) −486.000 −1.02010 −0.510049 − 0.860146i \(-0.670373\pi\)
−0.510049 + 0.860146i \(0.670373\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −84.0000 −0.160291
\(66\) 0 0
\(67\) −804.000 −1.46603 −0.733017 − 0.680211i \(-0.761888\pi\)
−0.733017 + 0.680211i \(0.761888\pi\)
\(68\) 0 0
\(69\) 248.000 0.432691
\(70\) 0 0
\(71\) −248.000 −0.414538 −0.207269 − 0.978284i \(-0.566458\pi\)
−0.207269 + 0.978284i \(0.566458\pi\)
\(72\) 0 0
\(73\) −768.000 −1.23134 −0.615669 − 0.788005i \(-0.711114\pi\)
−0.615669 + 0.788005i \(0.711114\pi\)
\(74\) 0 0
\(75\) 142.000 0.218623
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −192.000 −0.273439 −0.136720 − 0.990610i \(-0.543656\pi\)
−0.136720 + 0.990610i \(0.543656\pi\)
\(80\) 0 0
\(81\) 421.000 0.577503
\(82\) 0 0
\(83\) 294.000 0.388804 0.194402 − 0.980922i \(-0.437723\pi\)
0.194402 + 0.980922i \(0.437723\pi\)
\(84\) 0 0
\(85\) 280.000 0.357297
\(86\) 0 0
\(87\) −156.000 −0.192241
\(88\) 0 0
\(89\) −80.0000 −0.0952807 −0.0476404 − 0.998865i \(-0.515170\pi\)
−0.0476404 + 0.998865i \(0.515170\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 472.000 0.526281
\(94\) 0 0
\(95\) −1428.00 −1.54221
\(96\) 0 0
\(97\) −1404.00 −1.46964 −0.734818 − 0.678265i \(-0.762732\pi\)
−0.734818 + 0.678265i \(0.762732\pi\)
\(98\) 0 0
\(99\) −460.000 −0.466987
\(100\) 0 0
\(101\) 1522.00 1.49945 0.749726 − 0.661748i \(-0.230185\pi\)
0.749726 + 0.661748i \(0.230185\pi\)
\(102\) 0 0
\(103\) −524.000 −0.501274 −0.250637 − 0.968081i \(-0.580640\pi\)
−0.250637 + 0.968081i \(0.580640\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 748.000 0.675812 0.337906 − 0.941180i \(-0.390281\pi\)
0.337906 + 0.941180i \(0.390281\pi\)
\(108\) 0 0
\(109\) 506.000 0.444642 0.222321 − 0.974973i \(-0.428637\pi\)
0.222321 + 0.974973i \(0.428637\pi\)
\(110\) 0 0
\(111\) 132.000 0.112873
\(112\) 0 0
\(113\) −1146.00 −0.954041 −0.477020 − 0.878892i \(-0.658283\pi\)
−0.477020 + 0.878892i \(0.658283\pi\)
\(114\) 0 0
\(115\) −1736.00 −1.40768
\(116\) 0 0
\(117\) −138.000 −0.109044
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −931.000 −0.699474
\(122\) 0 0
\(123\) −536.000 −0.392923
\(124\) 0 0
\(125\) 756.000 0.540950
\(126\) 0 0
\(127\) −2196.00 −1.53436 −0.767179 − 0.641433i \(-0.778340\pi\)
−0.767179 + 0.641433i \(0.778340\pi\)
\(128\) 0 0
\(129\) −264.000 −0.180185
\(130\) 0 0
\(131\) −2682.00 −1.78876 −0.894379 − 0.447309i \(-0.852382\pi\)
−0.894379 + 0.447309i \(0.852382\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 1400.00 0.892539
\(136\) 0 0
\(137\) −1098.00 −0.684733 −0.342367 − 0.939566i \(-0.611229\pi\)
−0.342367 + 0.939566i \(0.611229\pi\)
\(138\) 0 0
\(139\) 610.000 0.372227 0.186113 − 0.982528i \(-0.440411\pi\)
0.186113 + 0.982528i \(0.440411\pi\)
\(140\) 0 0
\(141\) 1032.00 0.616384
\(142\) 0 0
\(143\) 120.000 0.0701742
\(144\) 0 0
\(145\) 1092.00 0.625418
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −474.000 −0.260615 −0.130307 − 0.991474i \(-0.541596\pi\)
−0.130307 + 0.991474i \(0.541596\pi\)
\(150\) 0 0
\(151\) −2316.00 −1.24817 −0.624084 − 0.781357i \(-0.714528\pi\)
−0.624084 + 0.781357i \(0.714528\pi\)
\(152\) 0 0
\(153\) 460.000 0.243064
\(154\) 0 0
\(155\) −3304.00 −1.71215
\(156\) 0 0
\(157\) −1074.00 −0.545952 −0.272976 − 0.962021i \(-0.588008\pi\)
−0.272976 + 0.962021i \(0.588008\pi\)
\(158\) 0 0
\(159\) −708.000 −0.353132
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 2844.00 1.36662 0.683311 − 0.730128i \(-0.260539\pi\)
0.683311 + 0.730128i \(0.260539\pi\)
\(164\) 0 0
\(165\) −560.000 −0.264218
\(166\) 0 0
\(167\) 1500.00 0.695051 0.347525 − 0.937671i \(-0.387022\pi\)
0.347525 + 0.937671i \(0.387022\pi\)
\(168\) 0 0
\(169\) −2161.00 −0.983614
\(170\) 0 0
\(171\) −2346.00 −1.04914
\(172\) 0 0
\(173\) −1226.00 −0.538792 −0.269396 − 0.963029i \(-0.586824\pi\)
−0.269396 + 0.963029i \(0.586824\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 876.000 0.372001
\(178\) 0 0
\(179\) −3764.00 −1.57170 −0.785851 − 0.618416i \(-0.787775\pi\)
−0.785851 + 0.618416i \(0.787775\pi\)
\(180\) 0 0
\(181\) −138.000 −0.0566710 −0.0283355 − 0.999598i \(-0.509021\pi\)
−0.0283355 + 0.999598i \(0.509021\pi\)
\(182\) 0 0
\(183\) −972.000 −0.392636
\(184\) 0 0
\(185\) −924.000 −0.367210
\(186\) 0 0
\(187\) −400.000 −0.156422
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 2168.00 0.821314 0.410657 − 0.911790i \(-0.365299\pi\)
0.410657 + 0.911790i \(0.365299\pi\)
\(192\) 0 0
\(193\) 1806.00 0.673569 0.336784 − 0.941582i \(-0.390661\pi\)
0.336784 + 0.941582i \(0.390661\pi\)
\(194\) 0 0
\(195\) −168.000 −0.0616961
\(196\) 0 0
\(197\) 3966.00 1.43434 0.717172 − 0.696896i \(-0.245436\pi\)
0.717172 + 0.696896i \(0.245436\pi\)
\(198\) 0 0
\(199\) −36.0000 −0.0128240 −0.00641199 − 0.999979i \(-0.502041\pi\)
−0.00641199 + 0.999979i \(0.502041\pi\)
\(200\) 0 0
\(201\) −1608.00 −0.564276
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 3752.00 1.27830
\(206\) 0 0
\(207\) −2852.00 −0.957622
\(208\) 0 0
\(209\) 2040.00 0.675166
\(210\) 0 0
\(211\) −3684.00 −1.20198 −0.600988 − 0.799258i \(-0.705226\pi\)
−0.600988 + 0.799258i \(0.705226\pi\)
\(212\) 0 0
\(213\) −496.000 −0.159556
\(214\) 0 0
\(215\) 1848.00 0.586198
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −1536.00 −0.473942
\(220\) 0 0
\(221\) −120.000 −0.0365252
\(222\) 0 0
\(223\) −2808.00 −0.843218 −0.421609 − 0.906778i \(-0.638534\pi\)
−0.421609 + 0.906778i \(0.638534\pi\)
\(224\) 0 0
\(225\) −1633.00 −0.483852
\(226\) 0 0
\(227\) 5358.00 1.56662 0.783310 − 0.621631i \(-0.213530\pi\)
0.783310 + 0.621631i \(0.213530\pi\)
\(228\) 0 0
\(229\) 6102.00 1.76084 0.880418 − 0.474198i \(-0.157262\pi\)
0.880418 + 0.474198i \(0.157262\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −5130.00 −1.44239 −0.721196 − 0.692731i \(-0.756407\pi\)
−0.721196 + 0.692731i \(0.756407\pi\)
\(234\) 0 0
\(235\) −7224.00 −2.00528
\(236\) 0 0
\(237\) −384.000 −0.105247
\(238\) 0 0
\(239\) −4796.00 −1.29802 −0.649011 − 0.760779i \(-0.724817\pi\)
−0.649011 + 0.760779i \(0.724817\pi\)
\(240\) 0 0
\(241\) 5700.00 1.52352 0.761762 − 0.647857i \(-0.224335\pi\)
0.761762 + 0.647857i \(0.224335\pi\)
\(242\) 0 0
\(243\) 3542.00 0.935059
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 612.000 0.157654
\(248\) 0 0
\(249\) 588.000 0.149651
\(250\) 0 0
\(251\) 1674.00 0.420964 0.210482 − 0.977598i \(-0.432497\pi\)
0.210482 + 0.977598i \(0.432497\pi\)
\(252\) 0 0
\(253\) 2480.00 0.616270
\(254\) 0 0
\(255\) 560.000 0.137524
\(256\) 0 0
\(257\) 3536.00 0.858248 0.429124 − 0.903246i \(-0.358822\pi\)
0.429124 + 0.903246i \(0.358822\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 1794.00 0.425463
\(262\) 0 0
\(263\) −7816.00 −1.83253 −0.916265 − 0.400573i \(-0.868811\pi\)
−0.916265 + 0.400573i \(0.868811\pi\)
\(264\) 0 0
\(265\) 4956.00 1.14885
\(266\) 0 0
\(267\) −160.000 −0.0366736
\(268\) 0 0
\(269\) −6658.00 −1.50909 −0.754545 − 0.656248i \(-0.772143\pi\)
−0.754545 + 0.656248i \(0.772143\pi\)
\(270\) 0 0
\(271\) 5168.00 1.15843 0.579213 − 0.815176i \(-0.303360\pi\)
0.579213 + 0.815176i \(0.303360\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 1420.00 0.311379
\(276\) 0 0
\(277\) −5994.00 −1.30016 −0.650080 − 0.759865i \(-0.725265\pi\)
−0.650080 + 0.759865i \(0.725265\pi\)
\(278\) 0 0
\(279\) −5428.00 −1.16475
\(280\) 0 0
\(281\) −4074.00 −0.864891 −0.432446 − 0.901660i \(-0.642349\pi\)
−0.432446 + 0.901660i \(0.642349\pi\)
\(282\) 0 0
\(283\) 222.000 0.0466308 0.0233154 − 0.999728i \(-0.492578\pi\)
0.0233154 + 0.999728i \(0.492578\pi\)
\(284\) 0 0
\(285\) −2856.00 −0.593596
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −4513.00 −0.918583
\(290\) 0 0
\(291\) −2808.00 −0.565663
\(292\) 0 0
\(293\) −5558.00 −1.10820 −0.554099 − 0.832451i \(-0.686937\pi\)
−0.554099 + 0.832451i \(0.686937\pi\)
\(294\) 0 0
\(295\) −6132.00 −1.21023
\(296\) 0 0
\(297\) −2000.00 −0.390747
\(298\) 0 0
\(299\) 744.000 0.143902
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 3044.00 0.577139
\(304\) 0 0
\(305\) 6804.00 1.27736
\(306\) 0 0
\(307\) −5274.00 −0.980466 −0.490233 − 0.871591i \(-0.663088\pi\)
−0.490233 + 0.871591i \(0.663088\pi\)
\(308\) 0 0
\(309\) −1048.00 −0.192941
\(310\) 0 0
\(311\) 8832.00 1.61034 0.805172 − 0.593042i \(-0.202073\pi\)
0.805172 + 0.593042i \(0.202073\pi\)
\(312\) 0 0
\(313\) −9372.00 −1.69245 −0.846225 − 0.532826i \(-0.821130\pi\)
−0.846225 + 0.532826i \(0.821130\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 6294.00 1.11516 0.557581 − 0.830123i \(-0.311730\pi\)
0.557581 + 0.830123i \(0.311730\pi\)
\(318\) 0 0
\(319\) −1560.00 −0.273803
\(320\) 0 0
\(321\) 1496.00 0.260120
\(322\) 0 0
\(323\) −2040.00 −0.351420
\(324\) 0 0
\(325\) 426.000 0.0727084
\(326\) 0 0
\(327\) 1012.00 0.171143
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 5244.00 0.870805 0.435402 − 0.900236i \(-0.356606\pi\)
0.435402 + 0.900236i \(0.356606\pi\)
\(332\) 0 0
\(333\) −1518.00 −0.249807
\(334\) 0 0
\(335\) 11256.0 1.83576
\(336\) 0 0
\(337\) −5974.00 −0.965651 −0.482826 − 0.875716i \(-0.660390\pi\)
−0.482826 + 0.875716i \(0.660390\pi\)
\(338\) 0 0
\(339\) −2292.00 −0.367210
\(340\) 0 0
\(341\) 4720.00 0.749567
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −3472.00 −0.541815
\(346\) 0 0
\(347\) −1556.00 −0.240722 −0.120361 − 0.992730i \(-0.538405\pi\)
−0.120361 + 0.992730i \(0.538405\pi\)
\(348\) 0 0
\(349\) 4158.00 0.637744 0.318872 − 0.947798i \(-0.396696\pi\)
0.318872 + 0.947798i \(0.396696\pi\)
\(350\) 0 0
\(351\) −600.000 −0.0912411
\(352\) 0 0
\(353\) 6872.00 1.03615 0.518073 − 0.855336i \(-0.326649\pi\)
0.518073 + 0.855336i \(0.326649\pi\)
\(354\) 0 0
\(355\) 3472.00 0.519083
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 3004.00 0.441630 0.220815 − 0.975316i \(-0.429128\pi\)
0.220815 + 0.975316i \(0.429128\pi\)
\(360\) 0 0
\(361\) 3545.00 0.516839
\(362\) 0 0
\(363\) −1862.00 −0.269228
\(364\) 0 0
\(365\) 10752.0 1.54188
\(366\) 0 0
\(367\) −7944.00 −1.12990 −0.564950 − 0.825125i \(-0.691105\pi\)
−0.564950 + 0.825125i \(0.691105\pi\)
\(368\) 0 0
\(369\) 6164.00 0.869607
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 6662.00 0.924786 0.462393 − 0.886675i \(-0.346991\pi\)
0.462393 + 0.886675i \(0.346991\pi\)
\(374\) 0 0
\(375\) 1512.00 0.208212
\(376\) 0 0
\(377\) −468.000 −0.0639343
\(378\) 0 0
\(379\) −10308.0 −1.39706 −0.698531 − 0.715580i \(-0.746163\pi\)
−0.698531 + 0.715580i \(0.746163\pi\)
\(380\) 0 0
\(381\) −4392.00 −0.590575
\(382\) 0 0
\(383\) −11196.0 −1.49370 −0.746852 − 0.664990i \(-0.768436\pi\)
−0.746852 + 0.664990i \(0.768436\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 3036.00 0.398782
\(388\) 0 0
\(389\) −6654.00 −0.867278 −0.433639 − 0.901087i \(-0.642771\pi\)
−0.433639 + 0.901087i \(0.642771\pi\)
\(390\) 0 0
\(391\) −2480.00 −0.320765
\(392\) 0 0
\(393\) −5364.00 −0.688494
\(394\) 0 0
\(395\) 2688.00 0.342400
\(396\) 0 0
\(397\) −3642.00 −0.460420 −0.230210 − 0.973141i \(-0.573941\pi\)
−0.230210 + 0.973141i \(0.573941\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −8430.00 −1.04981 −0.524905 − 0.851161i \(-0.675899\pi\)
−0.524905 + 0.851161i \(0.675899\pi\)
\(402\) 0 0
\(403\) 1416.00 0.175027
\(404\) 0 0
\(405\) −5894.00 −0.723149
\(406\) 0 0
\(407\) 1320.00 0.160762
\(408\) 0 0
\(409\) −300.000 −0.0362691 −0.0181345 − 0.999836i \(-0.505773\pi\)
−0.0181345 + 0.999836i \(0.505773\pi\)
\(410\) 0 0
\(411\) −2196.00 −0.263554
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −4116.00 −0.486859
\(416\) 0 0
\(417\) 1220.00 0.143270
\(418\) 0 0
\(419\) 6306.00 0.735246 0.367623 − 0.929975i \(-0.380172\pi\)
0.367623 + 0.929975i \(0.380172\pi\)
\(420\) 0 0
\(421\) 15606.0 1.80663 0.903313 − 0.428981i \(-0.141127\pi\)
0.903313 + 0.428981i \(0.141127\pi\)
\(422\) 0 0
\(423\) −11868.0 −1.36417
\(424\) 0 0
\(425\) −1420.00 −0.162071
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 240.000 0.0270100
\(430\) 0 0
\(431\) −2164.00 −0.241847 −0.120924 − 0.992662i \(-0.538586\pi\)
−0.120924 + 0.992662i \(0.538586\pi\)
\(432\) 0 0
\(433\) −13884.0 −1.54093 −0.770465 − 0.637483i \(-0.779976\pi\)
−0.770465 + 0.637483i \(0.779976\pi\)
\(434\) 0 0
\(435\) 2184.00 0.240724
\(436\) 0 0
\(437\) 12648.0 1.38452
\(438\) 0 0
\(439\) −10752.0 −1.16894 −0.584470 − 0.811415i \(-0.698698\pi\)
−0.584470 + 0.811415i \(0.698698\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 3092.00 0.331615 0.165807 − 0.986158i \(-0.446977\pi\)
0.165807 + 0.986158i \(0.446977\pi\)
\(444\) 0 0
\(445\) 1120.00 0.119310
\(446\) 0 0
\(447\) −948.000 −0.100311
\(448\) 0 0
\(449\) −10014.0 −1.05254 −0.526269 − 0.850318i \(-0.676410\pi\)
−0.526269 + 0.850318i \(0.676410\pi\)
\(450\) 0 0
\(451\) −5360.00 −0.559629
\(452\) 0 0
\(453\) −4632.00 −0.480420
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −2378.00 −0.243410 −0.121705 − 0.992566i \(-0.538836\pi\)
−0.121705 + 0.992566i \(0.538836\pi\)
\(458\) 0 0
\(459\) 2000.00 0.203381
\(460\) 0 0
\(461\) 422.000 0.0426345 0.0213172 − 0.999773i \(-0.493214\pi\)
0.0213172 + 0.999773i \(0.493214\pi\)
\(462\) 0 0
\(463\) 10392.0 1.04310 0.521552 − 0.853219i \(-0.325353\pi\)
0.521552 + 0.853219i \(0.325353\pi\)
\(464\) 0 0
\(465\) −6608.00 −0.659008
\(466\) 0 0
\(467\) −14082.0 −1.39537 −0.697684 − 0.716405i \(-0.745786\pi\)
−0.697684 + 0.716405i \(0.745786\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −2148.00 −0.210137
\(472\) 0 0
\(473\) −2640.00 −0.256633
\(474\) 0 0
\(475\) 7242.00 0.699549
\(476\) 0 0
\(477\) 8142.00 0.781544
\(478\) 0 0
\(479\) 1740.00 0.165976 0.0829881 − 0.996551i \(-0.473554\pi\)
0.0829881 + 0.996551i \(0.473554\pi\)
\(480\) 0 0
\(481\) 396.000 0.0375386
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 19656.0 1.84027
\(486\) 0 0
\(487\) 3276.00 0.304825 0.152412 − 0.988317i \(-0.451296\pi\)
0.152412 + 0.988317i \(0.451296\pi\)
\(488\) 0 0
\(489\) 5688.00 0.526013
\(490\) 0 0
\(491\) 14420.0 1.32539 0.662694 − 0.748890i \(-0.269413\pi\)
0.662694 + 0.748890i \(0.269413\pi\)
\(492\) 0 0
\(493\) 1560.00 0.142513
\(494\) 0 0
\(495\) 6440.00 0.584761
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −21228.0 −1.90440 −0.952200 − 0.305475i \(-0.901185\pi\)
−0.952200 + 0.305475i \(0.901185\pi\)
\(500\) 0 0
\(501\) 3000.00 0.267525
\(502\) 0 0
\(503\) 3528.00 0.312735 0.156368 − 0.987699i \(-0.450022\pi\)
0.156368 + 0.987699i \(0.450022\pi\)
\(504\) 0 0
\(505\) −21308.0 −1.87761
\(506\) 0 0
\(507\) −4322.00 −0.378593
\(508\) 0 0
\(509\) −13498.0 −1.17542 −0.587710 − 0.809072i \(-0.699970\pi\)
−0.587710 + 0.809072i \(0.699970\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −10200.0 −0.877858
\(514\) 0 0
\(515\) 7336.00 0.627695
\(516\) 0 0
\(517\) 10320.0 0.877898
\(518\) 0 0
\(519\) −2452.00 −0.207381
\(520\) 0 0
\(521\) −15316.0 −1.28792 −0.643960 − 0.765059i \(-0.722710\pi\)
−0.643960 + 0.765059i \(0.722710\pi\)
\(522\) 0 0
\(523\) 7670.00 0.641273 0.320636 − 0.947202i \(-0.396103\pi\)
0.320636 + 0.947202i \(0.396103\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −4720.00 −0.390145
\(528\) 0 0
\(529\) 3209.00 0.263746
\(530\) 0 0
\(531\) −10074.0 −0.823304
\(532\) 0 0
\(533\) −1608.00 −0.130676
\(534\) 0 0
\(535\) −10472.0 −0.846251
\(536\) 0 0
\(537\) −7528.00 −0.604948
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −5298.00 −0.421033 −0.210516 − 0.977590i \(-0.567515\pi\)
−0.210516 + 0.977590i \(0.567515\pi\)
\(542\) 0 0
\(543\) −276.000 −0.0218127
\(544\) 0 0
\(545\) −7084.00 −0.556780
\(546\) 0 0
\(547\) 3612.00 0.282336 0.141168 − 0.989986i \(-0.454914\pi\)
0.141168 + 0.989986i \(0.454914\pi\)
\(548\) 0 0
\(549\) 11178.0 0.868972
\(550\) 0 0
\(551\) −7956.00 −0.615131
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −1848.00 −0.141339
\(556\) 0 0
\(557\) −3018.00 −0.229581 −0.114791 − 0.993390i \(-0.536620\pi\)
−0.114791 + 0.993390i \(0.536620\pi\)
\(558\) 0 0
\(559\) −792.000 −0.0599249
\(560\) 0 0
\(561\) −800.000 −0.0602068
\(562\) 0 0
\(563\) 16986.0 1.27154 0.635768 − 0.771880i \(-0.280684\pi\)
0.635768 + 0.771880i \(0.280684\pi\)
\(564\) 0 0
\(565\) 16044.0 1.19465
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −1782.00 −0.131292 −0.0656462 − 0.997843i \(-0.520911\pi\)
−0.0656462 + 0.997843i \(0.520911\pi\)
\(570\) 0 0
\(571\) 14028.0 1.02811 0.514057 − 0.857756i \(-0.328142\pi\)
0.514057 + 0.857756i \(0.328142\pi\)
\(572\) 0 0
\(573\) 4336.00 0.316124
\(574\) 0 0
\(575\) 8804.00 0.638526
\(576\) 0 0
\(577\) 2952.00 0.212987 0.106493 − 0.994313i \(-0.466038\pi\)
0.106493 + 0.994313i \(0.466038\pi\)
\(578\) 0 0
\(579\) 3612.00 0.259257
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −7080.00 −0.502957
\(584\) 0 0
\(585\) 1932.00 0.136544
\(586\) 0 0
\(587\) 3882.00 0.272960 0.136480 − 0.990643i \(-0.456421\pi\)
0.136480 + 0.990643i \(0.456421\pi\)
\(588\) 0 0
\(589\) 24072.0 1.68399
\(590\) 0 0
\(591\) 7932.00 0.552079
\(592\) 0 0
\(593\) 18088.0 1.25259 0.626294 − 0.779587i \(-0.284571\pi\)
0.626294 + 0.779587i \(0.284571\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −72.0000 −0.00493595
\(598\) 0 0
\(599\) 28192.0 1.92303 0.961514 − 0.274756i \(-0.0885969\pi\)
0.961514 + 0.274756i \(0.0885969\pi\)
\(600\) 0 0
\(601\) −25728.0 −1.74620 −0.873101 − 0.487540i \(-0.837894\pi\)
−0.873101 + 0.487540i \(0.837894\pi\)
\(602\) 0 0
\(603\) 18492.0 1.24884
\(604\) 0 0
\(605\) 13034.0 0.875880
\(606\) 0 0
\(607\) 14208.0 0.950058 0.475029 − 0.879970i \(-0.342438\pi\)
0.475029 + 0.879970i \(0.342438\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 3096.00 0.204993
\(612\) 0 0
\(613\) −11734.0 −0.773135 −0.386568 − 0.922261i \(-0.626339\pi\)
−0.386568 + 0.922261i \(0.626339\pi\)
\(614\) 0 0
\(615\) 7504.00 0.492017
\(616\) 0 0
\(617\) −18222.0 −1.18896 −0.594481 − 0.804109i \(-0.702643\pi\)
−0.594481 + 0.804109i \(0.702643\pi\)
\(618\) 0 0
\(619\) 4934.00 0.320378 0.160189 − 0.987086i \(-0.448790\pi\)
0.160189 + 0.987086i \(0.448790\pi\)
\(620\) 0 0
\(621\) −12400.0 −0.801280
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −19459.0 −1.24538
\(626\) 0 0
\(627\) 4080.00 0.259872
\(628\) 0 0
\(629\) −1320.00 −0.0836754
\(630\) 0 0
\(631\) 9648.00 0.608686 0.304343 − 0.952563i \(-0.401563\pi\)
0.304343 + 0.952563i \(0.401563\pi\)
\(632\) 0 0
\(633\) −7368.00 −0.462641
\(634\) 0 0
\(635\) 30744.0 1.92132
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 5704.00 0.353125
\(640\) 0 0
\(641\) 16242.0 1.00081 0.500406 − 0.865791i \(-0.333184\pi\)
0.500406 + 0.865791i \(0.333184\pi\)
\(642\) 0 0
\(643\) −20166.0 −1.23681 −0.618405 − 0.785859i \(-0.712221\pi\)
−0.618405 + 0.785859i \(0.712221\pi\)
\(644\) 0 0
\(645\) 3696.00 0.225628
\(646\) 0 0
\(647\) 23772.0 1.44447 0.722236 − 0.691646i \(-0.243114\pi\)
0.722236 + 0.691646i \(0.243114\pi\)
\(648\) 0 0
\(649\) 8760.00 0.529831
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 12930.0 0.774870 0.387435 − 0.921897i \(-0.373361\pi\)
0.387435 + 0.921897i \(0.373361\pi\)
\(654\) 0 0
\(655\) 37548.0 2.23988
\(656\) 0 0
\(657\) 17664.0 1.04892
\(658\) 0 0
\(659\) 11404.0 0.674107 0.337054 − 0.941485i \(-0.390570\pi\)
0.337054 + 0.941485i \(0.390570\pi\)
\(660\) 0 0
\(661\) −9678.00 −0.569486 −0.284743 − 0.958604i \(-0.591908\pi\)
−0.284743 + 0.958604i \(0.591908\pi\)
\(662\) 0 0
\(663\) −240.000 −0.0140586
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −9672.00 −0.561471
\(668\) 0 0
\(669\) −5616.00 −0.324555
\(670\) 0 0
\(671\) −9720.00 −0.559220
\(672\) 0 0
\(673\) 10542.0 0.603810 0.301905 − 0.953338i \(-0.402377\pi\)
0.301905 + 0.953338i \(0.402377\pi\)
\(674\) 0 0
\(675\) −7100.00 −0.404858
\(676\) 0 0
\(677\) −3418.00 −0.194039 −0.0970195 − 0.995282i \(-0.530931\pi\)
−0.0970195 + 0.995282i \(0.530931\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 10716.0 0.602993
\(682\) 0 0
\(683\) 17036.0 0.954414 0.477207 − 0.878791i \(-0.341649\pi\)
0.477207 + 0.878791i \(0.341649\pi\)
\(684\) 0 0
\(685\) 15372.0 0.857422
\(686\) 0 0
\(687\) 12204.0 0.677746
\(688\) 0 0
\(689\) −2124.00 −0.117443
\(690\) 0 0
\(691\) −3386.00 −0.186410 −0.0932051 − 0.995647i \(-0.529711\pi\)
−0.0932051 + 0.995647i \(0.529711\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −8540.00 −0.466102
\(696\) 0 0
\(697\) 5360.00 0.291283
\(698\) 0 0
\(699\) −10260.0 −0.555177
\(700\) 0 0
\(701\) 9954.00 0.536316 0.268158 − 0.963375i \(-0.413585\pi\)
0.268158 + 0.963375i \(0.413585\pi\)
\(702\) 0 0
\(703\) 6732.00 0.361170
\(704\) 0 0
\(705\) −14448.0 −0.771834
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 29266.0 1.55022 0.775111 − 0.631825i \(-0.217694\pi\)
0.775111 + 0.631825i \(0.217694\pi\)
\(710\) 0 0
\(711\) 4416.00 0.232930
\(712\) 0 0
\(713\) 29264.0 1.53709
\(714\) 0 0
\(715\) −1680.00 −0.0878719
\(716\) 0 0
\(717\) −9592.00 −0.499609
\(718\) 0 0
\(719\) 12540.0 0.650435 0.325218 − 0.945639i \(-0.394562\pi\)
0.325218 + 0.945639i \(0.394562\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 11400.0 0.586405
\(724\) 0 0
\(725\) −5538.00 −0.283691
\(726\) 0 0
\(727\) −14956.0 −0.762981 −0.381491 − 0.924373i \(-0.624589\pi\)
−0.381491 + 0.924373i \(0.624589\pi\)
\(728\) 0 0
\(729\) −4283.00 −0.217599
\(730\) 0 0
\(731\) 2640.00 0.133576
\(732\) 0 0
\(733\) 24690.0 1.24413 0.622064 − 0.782966i \(-0.286294\pi\)
0.622064 + 0.782966i \(0.286294\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −16080.0 −0.803683
\(738\) 0 0
\(739\) 33564.0 1.67073 0.835367 − 0.549693i \(-0.185255\pi\)
0.835367 + 0.549693i \(0.185255\pi\)
\(740\) 0 0
\(741\) 1224.00 0.0606812
\(742\) 0 0
\(743\) 28460.0 1.40524 0.702622 − 0.711563i \(-0.252013\pi\)
0.702622 + 0.711563i \(0.252013\pi\)
\(744\) 0 0
\(745\) 6636.00 0.326341
\(746\) 0 0
\(747\) −6762.00 −0.331203
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −10884.0 −0.528845 −0.264423 − 0.964407i \(-0.585181\pi\)
−0.264423 + 0.964407i \(0.585181\pi\)
\(752\) 0 0
\(753\) 3348.00 0.162029
\(754\) 0 0
\(755\) 32424.0 1.56295
\(756\) 0 0
\(757\) −27542.0 −1.32237 −0.661183 − 0.750225i \(-0.729945\pi\)
−0.661183 + 0.750225i \(0.729945\pi\)
\(758\) 0 0
\(759\) 4960.00 0.237202
\(760\) 0 0
\(761\) 4076.00 0.194159 0.0970794 − 0.995277i \(-0.469050\pi\)
0.0970794 + 0.995277i \(0.469050\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −6440.00 −0.304364
\(766\) 0 0
\(767\) 2628.00 0.123718
\(768\) 0 0
\(769\) −17796.0 −0.834513 −0.417256 − 0.908789i \(-0.637008\pi\)
−0.417256 + 0.908789i \(0.637008\pi\)
\(770\) 0 0
\(771\) 7072.00 0.330340
\(772\) 0 0
\(773\) −13510.0 −0.628617 −0.314308 − 0.949321i \(-0.601773\pi\)
−0.314308 + 0.949321i \(0.601773\pi\)
\(774\) 0 0
\(775\) 16756.0 0.776637
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −27336.0 −1.25727
\(780\) 0 0
\(781\) −4960.00 −0.227251
\(782\) 0 0
\(783\) 7800.00 0.356002
\(784\) 0 0
\(785\) 15036.0 0.683641
\(786\) 0 0
\(787\) 5870.00 0.265874 0.132937 − 0.991124i \(-0.457559\pi\)
0.132937 + 0.991124i \(0.457559\pi\)
\(788\) 0 0
\(789\) −15632.0 −0.705341
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −2916.00 −0.130580
\(794\) 0 0
\(795\) 9912.00 0.442192
\(796\) 0 0
\(797\) −21538.0 −0.957234 −0.478617 − 0.878024i \(-0.658862\pi\)
−0.478617 + 0.878024i \(0.658862\pi\)
\(798\) 0 0
\(799\) −10320.0 −0.456940
\(800\) 0 0
\(801\) 1840.00 0.0811650
\(802\) 0 0
\(803\) −15360.0 −0.675022
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −13316.0 −0.580849
\(808\) 0 0
\(809\) −12474.0 −0.542104 −0.271052 − 0.962565i \(-0.587372\pi\)
−0.271052 + 0.962565i \(0.587372\pi\)
\(810\) 0 0
\(811\) 12278.0 0.531614 0.265807 − 0.964026i \(-0.414362\pi\)
0.265807 + 0.964026i \(0.414362\pi\)
\(812\) 0 0
\(813\) 10336.0 0.445879
\(814\) 0 0
\(815\) −39816.0 −1.71128
\(816\) 0 0
\(817\) −13464.0 −0.576555
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −11034.0 −0.469049 −0.234525 − 0.972110i \(-0.575353\pi\)
−0.234525 + 0.972110i \(0.575353\pi\)
\(822\) 0 0
\(823\) 3096.00 0.131130 0.0655649 − 0.997848i \(-0.479115\pi\)
0.0655649 + 0.997848i \(0.479115\pi\)
\(824\) 0 0
\(825\) 2840.00 0.119850
\(826\) 0 0
\(827\) 33884.0 1.42474 0.712371 − 0.701803i \(-0.247621\pi\)
0.712371 + 0.701803i \(0.247621\pi\)
\(828\) 0 0
\(829\) −10038.0 −0.420548 −0.210274 − 0.977643i \(-0.567436\pi\)
−0.210274 + 0.977643i \(0.567436\pi\)
\(830\) 0 0
\(831\) −11988.0 −0.500432
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) −21000.0 −0.870341
\(836\) 0 0
\(837\) −23600.0 −0.974594
\(838\) 0 0
\(839\) −25308.0 −1.04139 −0.520697 − 0.853742i \(-0.674328\pi\)
−0.520697 + 0.853742i \(0.674328\pi\)
\(840\) 0 0
\(841\) −18305.0 −0.750543
\(842\) 0 0
\(843\) −8148.00 −0.332897
\(844\) 0 0
\(845\) 30254.0 1.23168
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 444.000 0.0179482
\(850\) 0 0
\(851\) 8184.00 0.329664
\(852\) 0 0
\(853\) 11382.0 0.456873 0.228436 − 0.973559i \(-0.426639\pi\)
0.228436 + 0.973559i \(0.426639\pi\)
\(854\) 0 0
\(855\) 32844.0 1.31373
\(856\) 0 0
\(857\) 38468.0 1.53330 0.766652 − 0.642063i \(-0.221921\pi\)
0.766652 + 0.642063i \(0.221921\pi\)
\(858\) 0 0
\(859\) −40590.0 −1.61224 −0.806119 − 0.591753i \(-0.798436\pi\)
−0.806119 + 0.591753i \(0.798436\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −680.000 −0.0268221 −0.0134110 − 0.999910i \(-0.504269\pi\)
−0.0134110 + 0.999910i \(0.504269\pi\)
\(864\) 0 0
\(865\) 17164.0 0.674675
\(866\) 0 0
\(867\) −9026.00 −0.353563
\(868\) 0 0
\(869\) −3840.00 −0.149900
\(870\) 0 0
\(871\) −4824.00 −0.187664
\(872\) 0 0
\(873\) 32292.0 1.25191
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −21526.0 −0.828827 −0.414414 − 0.910089i \(-0.636013\pi\)
−0.414414 + 0.910089i \(0.636013\pi\)
\(878\) 0 0
\(879\) −11116.0 −0.426545
\(880\) 0 0
\(881\) 39632.0 1.51559 0.757796 − 0.652492i \(-0.226276\pi\)
0.757796 + 0.652492i \(0.226276\pi\)
\(882\) 0 0
\(883\) 7572.00 0.288582 0.144291 − 0.989535i \(-0.453910\pi\)
0.144291 + 0.989535i \(0.453910\pi\)
\(884\) 0 0
\(885\) −12264.0 −0.465819
\(886\) 0 0
\(887\) −15276.0 −0.578261 −0.289131 − 0.957290i \(-0.593366\pi\)
−0.289131 + 0.957290i \(0.593366\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 8420.00 0.316589
\(892\) 0 0
\(893\) 52632.0 1.97230
\(894\) 0 0
\(895\) 52696.0 1.96808
\(896\) 0 0
\(897\) 1488.00 0.0553878
\(898\) 0 0
\(899\) −18408.0 −0.682916
\(900\) 0 0
\(901\) 7080.00 0.261786
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 1932.00 0.0709634
\(906\) 0 0
\(907\) 13044.0 0.477529 0.238765 − 0.971077i \(-0.423258\pi\)
0.238765 + 0.971077i \(0.423258\pi\)
\(908\) 0 0
\(909\) −35006.0 −1.27731
\(910\) 0 0
\(911\) 13684.0 0.497663 0.248832 − 0.968547i \(-0.419953\pi\)
0.248832 + 0.968547i \(0.419953\pi\)
\(912\) 0 0
\(913\) 5880.00 0.213143
\(914\) 0 0
\(915\) 13608.0 0.491657
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −25704.0 −0.922630 −0.461315 − 0.887236i \(-0.652622\pi\)
−0.461315 + 0.887236i \(0.652622\pi\)
\(920\) 0 0
\(921\) −10548.0 −0.377382
\(922\) 0 0
\(923\) −1488.00 −0.0530640
\(924\) 0 0
\(925\) 4686.00 0.166567
\(926\) 0 0
\(927\) 12052.0 0.427011
\(928\) 0 0
\(929\) −22564.0 −0.796879 −0.398440 − 0.917195i \(-0.630448\pi\)
−0.398440 + 0.917195i \(0.630448\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 17664.0 0.619821
\(934\) 0 0
\(935\) 5600.00 0.195871
\(936\) 0 0
\(937\) 14208.0 0.495363 0.247681 − 0.968842i \(-0.420331\pi\)
0.247681 + 0.968842i \(0.420331\pi\)
\(938\) 0 0
\(939\) −18744.0 −0.651424
\(940\) 0 0
\(941\) 2626.00 0.0909725 0.0454863 − 0.998965i \(-0.485516\pi\)
0.0454863 + 0.998965i \(0.485516\pi\)
\(942\) 0 0
\(943\) −33232.0 −1.14760
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 18860.0 0.647168 0.323584 − 0.946200i \(-0.395112\pi\)
0.323584 + 0.946200i \(0.395112\pi\)
\(948\) 0 0
\(949\) −4608.00 −0.157621
\(950\) 0 0
\(951\) 12588.0 0.429226
\(952\) 0 0
\(953\) 42.0000 0.00142761 0.000713806 − 1.00000i \(-0.499773\pi\)
0.000713806 1.00000i \(0.499773\pi\)
\(954\) 0 0
\(955\) −30352.0 −1.02845
\(956\) 0 0
\(957\) −3120.00 −0.105387
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 25905.0 0.869558
\(962\) 0 0
\(963\) −17204.0 −0.575692
\(964\) 0 0
\(965\) −25284.0 −0.843441
\(966\) 0 0
\(967\) −42804.0 −1.42346 −0.711729 − 0.702454i \(-0.752088\pi\)
−0.711729 + 0.702454i \(0.752088\pi\)
\(968\) 0 0
\(969\) −4080.00 −0.135262
\(970\) 0 0
\(971\) −25770.0 −0.851698 −0.425849 − 0.904794i \(-0.640025\pi\)
−0.425849 + 0.904794i \(0.640025\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 852.000 0.0279855
\(976\) 0 0
\(977\) 2766.00 0.0905754 0.0452877 − 0.998974i \(-0.485580\pi\)
0.0452877 + 0.998974i \(0.485580\pi\)
\(978\) 0 0
\(979\) −1600.00 −0.0522331
\(980\) 0 0
\(981\) −11638.0 −0.378769
\(982\) 0 0
\(983\) −2988.00 −0.0969506 −0.0484753 − 0.998824i \(-0.515436\pi\)
−0.0484753 + 0.998824i \(0.515436\pi\)
\(984\) 0 0
\(985\) −55524.0 −1.79608
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −16368.0 −0.526261
\(990\) 0 0
\(991\) 32400.0 1.03857 0.519284 − 0.854602i \(-0.326199\pi\)
0.519284 + 0.854602i \(0.326199\pi\)
\(992\) 0 0
\(993\) 10488.0 0.335173
\(994\) 0 0
\(995\) 504.000 0.0160582
\(996\) 0 0
\(997\) −24294.0 −0.771714 −0.385857 − 0.922559i \(-0.626094\pi\)
−0.385857 + 0.922559i \(0.626094\pi\)
\(998\) 0 0
\(999\) −6600.00 −0.209024
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 1568.4.a.j.1.1 yes 1
4.3 odd 2 1568.4.a.d.1.1 ✓ 1
7.6 odd 2 1568.4.a.f.1.1 yes 1
28.27 even 2 1568.4.a.l.1.1 yes 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1568.4.a.d.1.1 ✓ 1 4.3 odd 2
1568.4.a.f.1.1 yes 1 7.6 odd 2
1568.4.a.j.1.1 yes 1 1.1 even 1 trivial
1568.4.a.l.1.1 yes 1 28.27 even 2