Properties

Label 2016.4.a.e.1.1
Level $2016$
Weight $4$
Character 2016.1
Self dual yes
Analytic conductor $118.948$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 2016 = 2^{5} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2016.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(118.947850572\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 672)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 2016.1

$q$-expansion

\(f(q)\) \(=\) \(q+18.0000 q^{5} -7.00000 q^{7} +O(q^{10})\) \(q+18.0000 q^{5} -7.00000 q^{7} -44.0000 q^{11} +58.0000 q^{13} +130.000 q^{17} +92.0000 q^{19} -84.0000 q^{23} +199.000 q^{25} +250.000 q^{29} -72.0000 q^{31} -126.000 q^{35} -354.000 q^{37} -334.000 q^{41} -416.000 q^{43} +464.000 q^{47} +49.0000 q^{49} +450.000 q^{53} -792.000 q^{55} +516.000 q^{59} +58.0000 q^{61} +1044.00 q^{65} -656.000 q^{67} +940.000 q^{71} +178.000 q^{73} +308.000 q^{77} +1072.00 q^{79} -660.000 q^{83} +2340.00 q^{85} -1254.00 q^{89} -406.000 q^{91} +1656.00 q^{95} +210.000 q^{97} +O(q^{100})\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) 18.0000 1.60997 0.804984 0.593296i \(-0.202174\pi\)
0.804984 + 0.593296i \(0.202174\pi\)
\(6\) 0 0
\(7\) −7.00000 −0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −44.0000 −1.20605 −0.603023 0.797724i \(-0.706037\pi\)
−0.603023 + 0.797724i \(0.706037\pi\)
\(12\) 0 0
\(13\) 58.0000 1.23741 0.618704 0.785624i \(-0.287658\pi\)
0.618704 + 0.785624i \(0.287658\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 130.000 1.85468 0.927342 0.374215i \(-0.122088\pi\)
0.927342 + 0.374215i \(0.122088\pi\)
\(18\) 0 0
\(19\) 92.0000 1.11086 0.555428 0.831565i \(-0.312555\pi\)
0.555428 + 0.831565i \(0.312555\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −84.0000 −0.761531 −0.380765 0.924672i \(-0.624339\pi\)
−0.380765 + 0.924672i \(0.624339\pi\)
\(24\) 0 0
\(25\) 199.000 1.59200
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 250.000 1.60082 0.800411 0.599452i \(-0.204615\pi\)
0.800411 + 0.599452i \(0.204615\pi\)
\(30\) 0 0
\(31\) −72.0000 −0.417148 −0.208574 0.978007i \(-0.566882\pi\)
−0.208574 + 0.978007i \(0.566882\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −126.000 −0.608511
\(36\) 0 0
\(37\) −354.000 −1.57290 −0.786449 0.617655i \(-0.788083\pi\)
−0.786449 + 0.617655i \(0.788083\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −334.000 −1.27224 −0.636122 0.771588i \(-0.719463\pi\)
−0.636122 + 0.771588i \(0.719463\pi\)
\(42\) 0 0
\(43\) −416.000 −1.47534 −0.737668 0.675164i \(-0.764073\pi\)
−0.737668 + 0.675164i \(0.764073\pi\)
\(44\) 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
\(53\) 450.000 1.16627 0.583134 0.812376i \(-0.301826\pi\)
0.583134 + 0.812376i \(0.301826\pi\)
\(54\) 0 0
\(55\) −792.000 −1.94170
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 516.000 1.13860 0.569301 0.822129i \(-0.307214\pi\)
0.569301 + 0.822129i \(0.307214\pi\)
\(60\) 0 0
\(61\) 58.0000 0.121740 0.0608700 0.998146i \(-0.480612\pi\)
0.0608700 + 0.998146i \(0.480612\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 1044.00 1.99219
\(66\) 0 0
\(67\) −656.000 −1.19617 −0.598083 0.801434i \(-0.704071\pi\)
−0.598083 + 0.801434i \(0.704071\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 940.000 1.57123 0.785616 0.618714i \(-0.212346\pi\)
0.785616 + 0.618714i \(0.212346\pi\)
\(72\) 0 0
\(73\) 178.000 0.285388 0.142694 0.989767i \(-0.454424\pi\)
0.142694 + 0.989767i \(0.454424\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 308.000 0.455842
\(78\) 0 0
\(79\) 1072.00 1.52670 0.763351 0.645984i \(-0.223553\pi\)
0.763351 + 0.645984i \(0.223553\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −660.000 −0.872824 −0.436412 0.899747i \(-0.643751\pi\)
−0.436412 + 0.899747i \(0.643751\pi\)
\(84\) 0 0
\(85\) 2340.00 2.98598
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −1254.00 −1.49353 −0.746763 0.665091i \(-0.768393\pi\)
−0.746763 + 0.665091i \(0.768393\pi\)
\(90\) 0 0
\(91\) −406.000 −0.467696
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 1656.00 1.78844
\(96\) 0 0
\(97\) 210.000 0.219817 0.109909 0.993942i \(-0.464944\pi\)
0.109909 + 0.993942i \(0.464944\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 186.000 0.183244 0.0916222 0.995794i \(-0.470795\pi\)
0.0916222 + 0.995794i \(0.470795\pi\)
\(102\) 0 0
\(103\) 472.000 0.451530 0.225765 0.974182i \(-0.427512\pi\)
0.225765 + 0.974182i \(0.427512\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1212.00 1.09503 0.547516 0.836795i \(-0.315573\pi\)
0.547516 + 0.836795i \(0.315573\pi\)
\(108\) 0 0
\(109\) −1386.00 −1.21793 −0.608967 0.793196i \(-0.708416\pi\)
−0.608967 + 0.793196i \(0.708416\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −114.000 −0.0949046 −0.0474523 0.998874i \(-0.515110\pi\)
−0.0474523 + 0.998874i \(0.515110\pi\)
\(114\) 0 0
\(115\) −1512.00 −1.22604
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −910.000 −0.701005
\(120\) 0 0
\(121\) 605.000 0.454545
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 1332.00 0.953102
\(126\) 0 0
\(127\) 792.000 0.553375 0.276688 0.960960i \(-0.410763\pi\)
0.276688 + 0.960960i \(0.410763\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 428.000 0.285454 0.142727 0.989762i \(-0.454413\pi\)
0.142727 + 0.989762i \(0.454413\pi\)
\(132\) 0 0
\(133\) −644.000 −0.419864
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 2238.00 1.39566 0.697829 0.716264i \(-0.254149\pi\)
0.697829 + 0.716264i \(0.254149\pi\)
\(138\) 0 0
\(139\) 300.000 0.183062 0.0915312 0.995802i \(-0.470824\pi\)
0.0915312 + 0.995802i \(0.470824\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −2552.00 −1.49237
\(144\) 0 0
\(145\) 4500.00 2.57727
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −1646.00 −0.905004 −0.452502 0.891763i \(-0.649468\pi\)
−0.452502 + 0.891763i \(0.649468\pi\)
\(150\) 0 0
\(151\) −1184.00 −0.638096 −0.319048 0.947738i \(-0.603363\pi\)
−0.319048 + 0.947738i \(0.603363\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −1296.00 −0.671595
\(156\) 0 0
\(157\) −1150.00 −0.584586 −0.292293 0.956329i \(-0.594418\pi\)
−0.292293 + 0.956329i \(0.594418\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 588.000 0.287832
\(162\) 0 0
\(163\) −344.000 −0.165302 −0.0826508 0.996579i \(-0.526339\pi\)
−0.0826508 + 0.996579i \(0.526339\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 2304.00 1.06760 0.533799 0.845611i \(-0.320764\pi\)
0.533799 + 0.845611i \(0.320764\pi\)
\(168\) 0 0
\(169\) 1167.00 0.531179
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −2742.00 −1.20503 −0.602516 0.798107i \(-0.705835\pi\)
−0.602516 + 0.798107i \(0.705835\pi\)
\(174\) 0 0
\(175\) −1393.00 −0.601719
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 3940.00 1.64519 0.822596 0.568626i \(-0.192525\pi\)
0.822596 + 0.568626i \(0.192525\pi\)
\(180\) 0 0
\(181\) 1970.00 0.809000 0.404500 0.914538i \(-0.367446\pi\)
0.404500 + 0.914538i \(0.367446\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −6372.00 −2.53232
\(186\) 0 0
\(187\) −5720.00 −2.23683
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 476.000 0.180325 0.0901627 0.995927i \(-0.471261\pi\)
0.0901627 + 0.995927i \(0.471261\pi\)
\(192\) 0 0
\(193\) −782.000 −0.291656 −0.145828 0.989310i \(-0.546585\pi\)
−0.145828 + 0.989310i \(0.546585\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 2066.00 0.747190 0.373595 0.927592i \(-0.378125\pi\)
0.373595 + 0.927592i \(0.378125\pi\)
\(198\) 0 0
\(199\) 768.000 0.273578 0.136789 0.990600i \(-0.456322\pi\)
0.136789 + 0.990600i \(0.456322\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −1750.00 −0.605054
\(204\) 0 0
\(205\) −6012.00 −2.04827
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −4048.00 −1.33974
\(210\) 0 0
\(211\) 4248.00 1.38599 0.692996 0.720941i \(-0.256290\pi\)
0.692996 + 0.720941i \(0.256290\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −7488.00 −2.37524
\(216\) 0 0
\(217\) 504.000 0.157667
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 7540.00 2.29500
\(222\) 0 0
\(223\) −3496.00 −1.04982 −0.524909 0.851158i \(-0.675901\pi\)
−0.524909 + 0.851158i \(0.675901\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 5620.00 1.64323 0.821613 0.570045i \(-0.193074\pi\)
0.821613 + 0.570045i \(0.193074\pi\)
\(228\) 0 0
\(229\) −1982.00 −0.571940 −0.285970 0.958239i \(-0.592316\pi\)
−0.285970 + 0.958239i \(0.592316\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 1342.00 0.377328 0.188664 0.982042i \(-0.439584\pi\)
0.188664 + 0.982042i \(0.439584\pi\)
\(234\) 0 0
\(235\) 8352.00 2.31840
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 2828.00 0.765390 0.382695 0.923875i \(-0.374996\pi\)
0.382695 + 0.923875i \(0.374996\pi\)
\(240\) 0 0
\(241\) 2002.00 0.535104 0.267552 0.963543i \(-0.413785\pi\)
0.267552 + 0.963543i \(0.413785\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 882.000 0.229996
\(246\) 0 0
\(247\) 5336.00 1.37458
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −1188.00 −0.298749 −0.149374 0.988781i \(-0.547726\pi\)
−0.149374 + 0.988781i \(0.547726\pi\)
\(252\) 0 0
\(253\) 3696.00 0.918441
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 5506.00 1.33640 0.668200 0.743982i \(-0.267065\pi\)
0.668200 + 0.743982i \(0.267065\pi\)
\(258\) 0 0
\(259\) 2478.00 0.594500
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −4076.00 −0.955654 −0.477827 0.878454i \(-0.658575\pi\)
−0.477827 + 0.878454i \(0.658575\pi\)
\(264\) 0 0
\(265\) 8100.00 1.87766
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 5938.00 1.34590 0.672948 0.739689i \(-0.265028\pi\)
0.672948 + 0.739689i \(0.265028\pi\)
\(270\) 0 0
\(271\) 592.000 0.132699 0.0663495 0.997796i \(-0.478865\pi\)
0.0663495 + 0.997796i \(0.478865\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −8756.00 −1.92002
\(276\) 0 0
\(277\) 5254.00 1.13965 0.569824 0.821767i \(-0.307012\pi\)
0.569824 + 0.821767i \(0.307012\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −3410.00 −0.723927 −0.361964 0.932192i \(-0.617894\pi\)
−0.361964 + 0.932192i \(0.617894\pi\)
\(282\) 0 0
\(283\) −2212.00 −0.464628 −0.232314 0.972641i \(-0.574630\pi\)
−0.232314 + 0.972641i \(0.574630\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 2338.00 0.480863
\(288\) 0 0
\(289\) 11987.0 2.43985
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 2122.00 0.423101 0.211550 0.977367i \(-0.432149\pi\)
0.211550 + 0.977367i \(0.432149\pi\)
\(294\) 0 0
\(295\) 9288.00 1.83311
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −4872.00 −0.942325
\(300\) 0 0
\(301\) 2912.00 0.557624
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 1044.00 0.195998
\(306\) 0 0
\(307\) 2588.00 0.481124 0.240562 0.970634i \(-0.422668\pi\)
0.240562 + 0.970634i \(0.422668\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −2728.00 −0.497398 −0.248699 0.968581i \(-0.580003\pi\)
−0.248699 + 0.968581i \(0.580003\pi\)
\(312\) 0 0
\(313\) −6446.00 −1.16406 −0.582028 0.813169i \(-0.697741\pi\)
−0.582028 + 0.813169i \(0.697741\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 4234.00 0.750174 0.375087 0.926990i \(-0.377613\pi\)
0.375087 + 0.926990i \(0.377613\pi\)
\(318\) 0 0
\(319\) −11000.0 −1.93066
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 11960.0 2.06029
\(324\) 0 0
\(325\) 11542.0 1.96995
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −3248.00 −0.544280
\(330\) 0 0
\(331\) −4592.00 −0.762535 −0.381268 0.924465i \(-0.624512\pi\)
−0.381268 + 0.924465i \(0.624512\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −11808.0 −1.92579
\(336\) 0 0
\(337\) −1006.00 −0.162612 −0.0813061 0.996689i \(-0.525909\pi\)
−0.0813061 + 0.996689i \(0.525909\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 3168.00 0.503099
\(342\) 0 0
\(343\) −343.000 −0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −4644.00 −0.718452 −0.359226 0.933251i \(-0.616959\pi\)
−0.359226 + 0.933251i \(0.616959\pi\)
\(348\) 0 0
\(349\) 4786.00 0.734065 0.367033 0.930208i \(-0.380374\pi\)
0.367033 + 0.930208i \(0.380374\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −1302.00 −0.196313 −0.0981565 0.995171i \(-0.531295\pi\)
−0.0981565 + 0.995171i \(0.531295\pi\)
\(354\) 0 0
\(355\) 16920.0 2.52963
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −11260.0 −1.65538 −0.827688 0.561188i \(-0.810344\pi\)
−0.827688 + 0.561188i \(0.810344\pi\)
\(360\) 0 0
\(361\) 1605.00 0.233999
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 3204.00 0.459466
\(366\) 0 0
\(367\) 2792.00 0.397115 0.198558 0.980089i \(-0.436374\pi\)
0.198558 + 0.980089i \(0.436374\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −3150.00 −0.440808
\(372\) 0 0
\(373\) 4118.00 0.571641 0.285820 0.958283i \(-0.407734\pi\)
0.285820 + 0.958283i \(0.407734\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 14500.0 1.98087
\(378\) 0 0
\(379\) 8624.00 1.16883 0.584413 0.811456i \(-0.301325\pi\)
0.584413 + 0.811456i \(0.301325\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −6488.00 −0.865591 −0.432795 0.901492i \(-0.642473\pi\)
−0.432795 + 0.901492i \(0.642473\pi\)
\(384\) 0 0
\(385\) 5544.00 0.733892
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −1406.00 −0.183257 −0.0916286 0.995793i \(-0.529207\pi\)
−0.0916286 + 0.995793i \(0.529207\pi\)
\(390\) 0 0
\(391\) −10920.0 −1.41240
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 19296.0 2.45794
\(396\) 0 0
\(397\) 9378.00 1.18556 0.592781 0.805363i \(-0.298030\pi\)
0.592781 + 0.805363i \(0.298030\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −2890.00 −0.359900 −0.179950 0.983676i \(-0.557594\pi\)
−0.179950 + 0.983676i \(0.557594\pi\)
\(402\) 0 0
\(403\) −4176.00 −0.516182
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 15576.0 1.89699
\(408\) 0 0
\(409\) −10582.0 −1.27933 −0.639665 0.768654i \(-0.720927\pi\)
−0.639665 + 0.768654i \(0.720927\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −3612.00 −0.430351
\(414\) 0 0
\(415\) −11880.0 −1.40522
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 9500.00 1.10765 0.553825 0.832633i \(-0.313168\pi\)
0.553825 + 0.832633i \(0.313168\pi\)
\(420\) 0 0
\(421\) 598.000 0.0692274 0.0346137 0.999401i \(-0.488980\pi\)
0.0346137 + 0.999401i \(0.488980\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 25870.0 2.95266
\(426\) 0 0
\(427\) −406.000 −0.0460134
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −3708.00 −0.414404 −0.207202 0.978298i \(-0.566436\pi\)
−0.207202 + 0.978298i \(0.566436\pi\)
\(432\) 0 0
\(433\) 13706.0 1.52117 0.760587 0.649236i \(-0.224911\pi\)
0.760587 + 0.649236i \(0.224911\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −7728.00 −0.845951
\(438\) 0 0
\(439\) −8232.00 −0.894970 −0.447485 0.894291i \(-0.647680\pi\)
−0.447485 + 0.894291i \(0.647680\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −2524.00 −0.270697 −0.135349 0.990798i \(-0.543215\pi\)
−0.135349 + 0.990798i \(0.543215\pi\)
\(444\) 0 0
\(445\) −22572.0 −2.40453
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 3630.00 0.381537 0.190769 0.981635i \(-0.438902\pi\)
0.190769 + 0.981635i \(0.438902\pi\)
\(450\) 0 0
\(451\) 14696.0 1.53438
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −7308.00 −0.752977
\(456\) 0 0
\(457\) 5386.00 0.551305 0.275653 0.961257i \(-0.411106\pi\)
0.275653 + 0.961257i \(0.411106\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −11766.0 −1.18871 −0.594357 0.804201i \(-0.702593\pi\)
−0.594357 + 0.804201i \(0.702593\pi\)
\(462\) 0 0
\(463\) −10240.0 −1.02785 −0.513923 0.857836i \(-0.671808\pi\)
−0.513923 + 0.857836i \(0.671808\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −6076.00 −0.602064 −0.301032 0.953614i \(-0.597331\pi\)
−0.301032 + 0.953614i \(0.597331\pi\)
\(468\) 0 0
\(469\) 4592.00 0.452108
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 18304.0 1.77932
\(474\) 0 0
\(475\) 18308.0 1.76848
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −6480.00 −0.618118 −0.309059 0.951043i \(-0.600014\pi\)
−0.309059 + 0.951043i \(0.600014\pi\)
\(480\) 0 0
\(481\) −20532.0 −1.94632
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 3780.00 0.353899
\(486\) 0 0
\(487\) 4240.00 0.394523 0.197262 0.980351i \(-0.436795\pi\)
0.197262 + 0.980351i \(0.436795\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 17892.0 1.64451 0.822255 0.569119i \(-0.192716\pi\)
0.822255 + 0.569119i \(0.192716\pi\)
\(492\) 0 0
\(493\) 32500.0 2.96902
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −6580.00 −0.593870
\(498\) 0 0
\(499\) −4616.00 −0.414109 −0.207055 0.978329i \(-0.566388\pi\)
−0.207055 + 0.978329i \(0.566388\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −3696.00 −0.327627 −0.163814 0.986491i \(-0.552380\pi\)
−0.163814 + 0.986491i \(0.552380\pi\)
\(504\) 0 0
\(505\) 3348.00 0.295018
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 16738.0 1.45756 0.728781 0.684747i \(-0.240087\pi\)
0.728781 + 0.684747i \(0.240087\pi\)
\(510\) 0 0
\(511\) −1246.00 −0.107867
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 8496.00 0.726949
\(516\) 0 0
\(517\) −20416.0 −1.73674
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −19062.0 −1.60292 −0.801460 0.598048i \(-0.795943\pi\)
−0.801460 + 0.598048i \(0.795943\pi\)
\(522\) 0 0
\(523\) −12268.0 −1.02570 −0.512851 0.858478i \(-0.671411\pi\)
−0.512851 + 0.858478i \(0.671411\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −9360.00 −0.773677
\(528\) 0 0
\(529\) −5111.00 −0.420071
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −19372.0 −1.57429
\(534\) 0 0
\(535\) 21816.0 1.76297
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −2156.00 −0.172292
\(540\) 0 0
\(541\) −17042.0 −1.35433 −0.677165 0.735831i \(-0.736792\pi\)
−0.677165 + 0.735831i \(0.736792\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −24948.0 −1.96083
\(546\) 0 0
\(547\) −3656.00 −0.285776 −0.142888 0.989739i \(-0.545639\pi\)
−0.142888 + 0.989739i \(0.545639\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 23000.0 1.77828
\(552\) 0 0
\(553\) −7504.00 −0.577039
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −14038.0 −1.06788 −0.533940 0.845522i \(-0.679289\pi\)
−0.533940 + 0.845522i \(0.679289\pi\)
\(558\) 0 0
\(559\) −24128.0 −1.82559
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 18332.0 1.37229 0.686147 0.727463i \(-0.259301\pi\)
0.686147 + 0.727463i \(0.259301\pi\)
\(564\) 0 0
\(565\) −2052.00 −0.152793
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 10046.0 0.740159 0.370079 0.929000i \(-0.379331\pi\)
0.370079 + 0.929000i \(0.379331\pi\)
\(570\) 0 0
\(571\) −5704.00 −0.418047 −0.209024 0.977911i \(-0.567029\pi\)
−0.209024 + 0.977911i \(0.567029\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −16716.0 −1.21236
\(576\) 0 0
\(577\) 24610.0 1.77561 0.887806 0.460219i \(-0.152229\pi\)
0.887806 + 0.460219i \(0.152229\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 4620.00 0.329897
\(582\) 0 0
\(583\) −19800.0 −1.40657
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −18516.0 −1.30194 −0.650969 0.759105i \(-0.725637\pi\)
−0.650969 + 0.759105i \(0.725637\pi\)
\(588\) 0 0
\(589\) −6624.00 −0.463391
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −20038.0 −1.38763 −0.693813 0.720155i \(-0.744071\pi\)
−0.693813 + 0.720155i \(0.744071\pi\)
\(594\) 0 0
\(595\) −16380.0 −1.12860
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −2596.00 −0.177078 −0.0885390 0.996073i \(-0.528220\pi\)
−0.0885390 + 0.996073i \(0.528220\pi\)
\(600\) 0 0
\(601\) −5190.00 −0.352254 −0.176127 0.984367i \(-0.556357\pi\)
−0.176127 + 0.984367i \(0.556357\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 10890.0 0.731804
\(606\) 0 0
\(607\) 6536.00 0.437048 0.218524 0.975832i \(-0.429876\pi\)
0.218524 + 0.975832i \(0.429876\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 26912.0 1.78190
\(612\) 0 0
\(613\) 4702.00 0.309807 0.154904 0.987930i \(-0.450493\pi\)
0.154904 + 0.987930i \(0.450493\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 8638.00 0.563619 0.281809 0.959470i \(-0.409065\pi\)
0.281809 + 0.959470i \(0.409065\pi\)
\(618\) 0 0
\(619\) −19676.0 −1.27762 −0.638809 0.769366i \(-0.720572\pi\)
−0.638809 + 0.769366i \(0.720572\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 8778.00 0.564499
\(624\) 0 0
\(625\) −899.000 −0.0575360
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −46020.0 −2.91723
\(630\) 0 0
\(631\) 26720.0 1.68575 0.842874 0.538112i \(-0.180862\pi\)
0.842874 + 0.538112i \(0.180862\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 14256.0 0.890917
\(636\) 0 0
\(637\) 2842.00 0.176773
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 1990.00 0.122621 0.0613107 0.998119i \(-0.480472\pi\)
0.0613107 + 0.998119i \(0.480472\pi\)
\(642\) 0 0
\(643\) −6956.00 −0.426622 −0.213311 0.976984i \(-0.568425\pi\)
−0.213311 + 0.976984i \(0.568425\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 15984.0 0.971246 0.485623 0.874168i \(-0.338593\pi\)
0.485623 + 0.874168i \(0.338593\pi\)
\(648\) 0 0
\(649\) −22704.0 −1.37320
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −6614.00 −0.396364 −0.198182 0.980165i \(-0.563504\pi\)
−0.198182 + 0.980165i \(0.563504\pi\)
\(654\) 0 0
\(655\) 7704.00 0.459573
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 29364.0 1.73575 0.867875 0.496783i \(-0.165485\pi\)
0.867875 + 0.496783i \(0.165485\pi\)
\(660\) 0 0
\(661\) −3150.00 −0.185357 −0.0926784 0.995696i \(-0.529543\pi\)
−0.0926784 + 0.995696i \(0.529543\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −11592.0 −0.675968
\(666\) 0 0
\(667\) −21000.0 −1.21908
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −2552.00 −0.146824
\(672\) 0 0
\(673\) 8402.00 0.481238 0.240619 0.970620i \(-0.422650\pi\)
0.240619 + 0.970620i \(0.422650\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −7854.00 −0.445870 −0.222935 0.974833i \(-0.571564\pi\)
−0.222935 + 0.974833i \(0.571564\pi\)
\(678\) 0 0
\(679\) −1470.00 −0.0830831
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 14244.0 0.797996 0.398998 0.916952i \(-0.369358\pi\)
0.398998 + 0.916952i \(0.369358\pi\)
\(684\) 0 0
\(685\) 40284.0 2.24697
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 26100.0 1.44315
\(690\) 0 0
\(691\) 22420.0 1.23429 0.617147 0.786848i \(-0.288288\pi\)
0.617147 + 0.786848i \(0.288288\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 5400.00 0.294725
\(696\) 0 0
\(697\) −43420.0 −2.35961
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −19814.0 −1.06757 −0.533783 0.845621i \(-0.679230\pi\)
−0.533783 + 0.845621i \(0.679230\pi\)
\(702\) 0 0
\(703\) −32568.0 −1.74726
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −1302.00 −0.0692599
\(708\) 0 0
\(709\) −15986.0 −0.846780 −0.423390 0.905948i \(-0.639160\pi\)
−0.423390 + 0.905948i \(0.639160\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 6048.00 0.317671
\(714\) 0 0
\(715\) −45936.0 −2.40267
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −22440.0 −1.16394 −0.581969 0.813211i \(-0.697717\pi\)
−0.581969 + 0.813211i \(0.697717\pi\)
\(720\) 0 0
\(721\) −3304.00 −0.170662
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 49750.0 2.54851
\(726\) 0 0
\(727\) 10264.0 0.523619 0.261809 0.965120i \(-0.415681\pi\)
0.261809 + 0.965120i \(0.415681\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −54080.0 −2.73628
\(732\) 0 0
\(733\) 9282.00 0.467720 0.233860 0.972270i \(-0.424864\pi\)
0.233860 + 0.972270i \(0.424864\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 28864.0 1.44263
\(738\) 0 0
\(739\) 12792.0 0.636754 0.318377 0.947964i \(-0.396862\pi\)
0.318377 + 0.947964i \(0.396862\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −25644.0 −1.26620 −0.633100 0.774070i \(-0.718218\pi\)
−0.633100 + 0.774070i \(0.718218\pi\)
\(744\) 0 0
\(745\) −29628.0 −1.45703
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −8484.00 −0.413883
\(750\) 0 0
\(751\) −4528.00 −0.220012 −0.110006 0.993931i \(-0.535087\pi\)
−0.110006 + 0.993931i \(0.535087\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −21312.0 −1.02732
\(756\) 0 0
\(757\) 31310.0 1.50328 0.751639 0.659575i \(-0.229264\pi\)
0.751639 + 0.659575i \(0.229264\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −16622.0 −0.791783 −0.395892 0.918297i \(-0.629564\pi\)
−0.395892 + 0.918297i \(0.629564\pi\)
\(762\) 0 0
\(763\) 9702.00 0.460335
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 29928.0 1.40891
\(768\) 0 0
\(769\) −9814.00 −0.460211 −0.230105 0.973166i \(-0.573907\pi\)
−0.230105 + 0.973166i \(0.573907\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −7686.00 −0.357628 −0.178814 0.983883i \(-0.557226\pi\)
−0.178814 + 0.983883i \(0.557226\pi\)
\(774\) 0 0
\(775\) −14328.0 −0.664099
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −30728.0 −1.41328
\(780\) 0 0
\(781\) −41360.0 −1.89498
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −20700.0 −0.941165
\(786\) 0 0
\(787\) 5860.00 0.265421 0.132711 0.991155i \(-0.457632\pi\)
0.132711 + 0.991155i \(0.457632\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 798.000 0.0358706
\(792\) 0 0
\(793\) 3364.00 0.150642
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 15450.0 0.686659 0.343329 0.939215i \(-0.388445\pi\)
0.343329 + 0.939215i \(0.388445\pi\)
\(798\) 0 0
\(799\) 60320.0 2.67080
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −7832.00 −0.344191
\(804\) 0 0
\(805\) 10584.0 0.463400
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 26726.0 1.16148 0.580739 0.814090i \(-0.302764\pi\)
0.580739 + 0.814090i \(0.302764\pi\)
\(810\) 0 0
\(811\) −3052.00 −0.132146 −0.0660729 0.997815i \(-0.521047\pi\)
−0.0660729 + 0.997815i \(0.521047\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −6192.00 −0.266130
\(816\) 0 0
\(817\) −38272.0 −1.63888
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −23838.0 −1.01334 −0.506670 0.862140i \(-0.669124\pi\)
−0.506670 + 0.862140i \(0.669124\pi\)
\(822\) 0 0
\(823\) 19136.0 0.810497 0.405248 0.914207i \(-0.367185\pi\)
0.405248 + 0.914207i \(0.367185\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 32556.0 1.36890 0.684452 0.729058i \(-0.260042\pi\)
0.684452 + 0.729058i \(0.260042\pi\)
\(828\) 0 0
\(829\) −33086.0 −1.38616 −0.693079 0.720862i \(-0.743746\pi\)
−0.693079 + 0.720862i \(0.743746\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 6370.00 0.264955
\(834\) 0 0
\(835\) 41472.0 1.71880
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −35248.0 −1.45041 −0.725206 0.688532i \(-0.758256\pi\)
−0.725206 + 0.688532i \(0.758256\pi\)
\(840\) 0 0
\(841\) 38111.0 1.56263
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 21006.0 0.855182
\(846\) 0 0
\(847\) −4235.00 −0.171802
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 29736.0 1.19781
\(852\) 0 0
\(853\) 8922.00 0.358128 0.179064 0.983837i \(-0.442693\pi\)
0.179064 + 0.983837i \(0.442693\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −28126.0 −1.12108 −0.560540 0.828127i \(-0.689406\pi\)
−0.560540 + 0.828127i \(0.689406\pi\)
\(858\) 0 0
\(859\) 28916.0 1.14855 0.574273 0.818664i \(-0.305285\pi\)
0.574273 + 0.818664i \(0.305285\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 22308.0 0.879923 0.439961 0.898017i \(-0.354992\pi\)
0.439961 + 0.898017i \(0.354992\pi\)
\(864\) 0 0
\(865\) −49356.0 −1.94006
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −47168.0 −1.84127
\(870\) 0 0
\(871\) −38048.0 −1.48015
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −9324.00 −0.360239
\(876\) 0 0
\(877\) −34970.0 −1.34647 −0.673234 0.739429i \(-0.735095\pi\)
−0.673234 + 0.739429i \(0.735095\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 858.000 0.0328113 0.0164056 0.999865i \(-0.494778\pi\)
0.0164056 + 0.999865i \(0.494778\pi\)
\(882\) 0 0
\(883\) 24088.0 0.918036 0.459018 0.888427i \(-0.348201\pi\)
0.459018 + 0.888427i \(0.348201\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 30960.0 1.17197 0.585984 0.810323i \(-0.300708\pi\)
0.585984 + 0.810323i \(0.300708\pi\)
\(888\) 0 0
\(889\) −5544.00 −0.209156
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 42688.0 1.59966
\(894\) 0 0
\(895\) 70920.0 2.64871
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −18000.0 −0.667779
\(900\) 0 0
\(901\) 58500.0 2.16306
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 35460.0 1.30246
\(906\) 0 0
\(907\) −37048.0 −1.35629 −0.678147 0.734926i \(-0.737217\pi\)
−0.678147 + 0.734926i \(0.737217\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −25228.0 −0.917498 −0.458749 0.888566i \(-0.651702\pi\)
−0.458749 + 0.888566i \(0.651702\pi\)
\(912\) 0 0
\(913\) 29040.0 1.05267
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −2996.00 −0.107892
\(918\) 0 0
\(919\) −19336.0 −0.694054 −0.347027 0.937855i \(-0.612809\pi\)
−0.347027 + 0.937855i \(0.612809\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 54520.0 1.94426
\(924\) 0 0
\(925\) −70446.0 −2.50405
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −11926.0 −0.421183 −0.210592 0.977574i \(-0.567539\pi\)
−0.210592 + 0.977574i \(0.567539\pi\)
\(930\) 0 0
\(931\) 4508.00 0.158694
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −102960. −3.60123
\(936\) 0 0
\(937\) 4698.00 0.163796 0.0818981 0.996641i \(-0.473902\pi\)
0.0818981 + 0.996641i \(0.473902\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 12986.0 0.449874 0.224937 0.974373i \(-0.427782\pi\)
0.224937 + 0.974373i \(0.427782\pi\)
\(942\) 0 0
\(943\) 28056.0 0.968854
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 17972.0 0.616696 0.308348 0.951274i \(-0.400224\pi\)
0.308348 + 0.951274i \(0.400224\pi\)
\(948\) 0 0
\(949\) 10324.0 0.353141
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 5414.00 0.184026 0.0920129 0.995758i \(-0.470670\pi\)
0.0920129 + 0.995758i \(0.470670\pi\)
\(954\) 0 0
\(955\) 8568.00 0.290318
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −15666.0 −0.527509
\(960\) 0 0
\(961\) −24607.0 −0.825988
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −14076.0 −0.469557
\(966\) 0 0
\(967\) −57496.0 −1.91204 −0.956022 0.293295i \(-0.905248\pi\)
−0.956022 + 0.293295i \(0.905248\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 36812.0 1.21664 0.608318 0.793693i \(-0.291845\pi\)
0.608318 + 0.793693i \(0.291845\pi\)
\(972\) 0 0
\(973\) −2100.00 −0.0691911
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −26442.0 −0.865870 −0.432935 0.901425i \(-0.642522\pi\)
−0.432935 + 0.901425i \(0.642522\pi\)
\(978\) 0 0
\(979\) 55176.0 1.80126
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −35240.0 −1.14342 −0.571710 0.820456i \(-0.693720\pi\)
−0.571710 + 0.820456i \(0.693720\pi\)
\(984\) 0 0
\(985\) 37188.0 1.20295
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 34944.0 1.12351
\(990\) 0 0
\(991\) −36472.0 −1.16909 −0.584547 0.811360i \(-0.698728\pi\)
−0.584547 + 0.811360i \(0.698728\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 13824.0 0.440453
\(996\) 0 0
\(997\) 25090.0 0.796999 0.398500 0.917168i \(-0.369531\pi\)
0.398500 + 0.917168i \(0.369531\pi\)
\(998\) 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 2016.4.a.e.1.1 1
3.2 odd 2 672.4.a.c.1.1 yes 1
4.3 odd 2 2016.4.a.f.1.1 1
12.11 even 2 672.4.a.a.1.1 1
24.5 odd 2 1344.4.a.m.1.1 1
24.11 even 2 1344.4.a.bb.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
672.4.a.a.1.1 1 12.11 even 2
672.4.a.c.1.1 yes 1 3.2 odd 2
1344.4.a.m.1.1 1 24.5 odd 2
1344.4.a.bb.1.1 1 24.11 even 2
2016.4.a.e.1.1 1 1.1 even 1 trivial
2016.4.a.f.1.1 1 4.3 odd 2