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Properties

Label 1584.4.a.t.1.1
Level $1584$
Weight $4$
Character 1584.1
Self dual yes
Analytic conductor $93.459$
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] = [1584,4,Mod(1,1584)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1584, 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("1584.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1584 = 2^{4} \cdot 3^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1584.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: \(93.4590254491\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 33)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1584.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+14.0000 q^{5} +32.0000 q^{7} +O(q^{10})\) \(q+14.0000 q^{5} +32.0000 q^{7} -11.0000 q^{11} -38.0000 q^{13} +2.00000 q^{17} -72.0000 q^{19} +68.0000 q^{23} +71.0000 q^{25} +54.0000 q^{29} +152.000 q^{31} +448.000 q^{35} +174.000 q^{37} -94.0000 q^{41} +528.000 q^{43} -340.000 q^{47} +681.000 q^{49} +438.000 q^{53} -154.000 q^{55} +20.0000 q^{59} +570.000 q^{61} -532.000 q^{65} +460.000 q^{67} -1092.00 q^{71} +562.000 q^{73} -352.000 q^{77} +16.0000 q^{79} +372.000 q^{83} +28.0000 q^{85} +966.000 q^{89} -1216.00 q^{91} -1008.00 q^{95} -526.000 q^{97} +O(q^{100})\)

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
\(5\) 14.0000 1.25220 0.626099 − 0.779744i \(-0.284651\pi\)
0.626099 + 0.779744i \(0.284651\pi\)
\(6\) 0 0
\(7\) 32.0000 1.72784 0.863919 − 0.503631i \(-0.168003\pi\)
0.863919 + 0.503631i \(0.168003\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −11.0000 −0.301511
\(12\) 0 0
\(13\) −38.0000 −0.810716 −0.405358 − 0.914158i \(-0.632853\pi\)
−0.405358 + 0.914158i \(0.632853\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2.00000 0.0285336 0.0142668 − 0.999898i \(-0.495459\pi\)
0.0142668 + 0.999898i \(0.495459\pi\)
\(18\) 0 0
\(19\) −72.0000 −0.869365 −0.434682 − 0.900584i \(-0.643139\pi\)
−0.434682 + 0.900584i \(0.643139\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 68.0000 0.616477 0.308239 − 0.951309i \(-0.400260\pi\)
0.308239 + 0.951309i \(0.400260\pi\)
\(24\) 0 0
\(25\) 71.0000 0.568000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 54.0000 0.345778 0.172889 − 0.984941i \(-0.444690\pi\)
0.172889 + 0.984941i \(0.444690\pi\)
\(30\) 0 0
\(31\) 152.000 0.880645 0.440323 − 0.897840i \(-0.354864\pi\)
0.440323 + 0.897840i \(0.354864\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 448.000 2.16359
\(36\) 0 0
\(37\) 174.000 0.773120 0.386560 − 0.922264i \(-0.373663\pi\)
0.386560 + 0.922264i \(0.373663\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −94.0000 −0.358057 −0.179028 − 0.983844i \(-0.557295\pi\)
−0.179028 + 0.983844i \(0.557295\pi\)
\(42\) 0 0
\(43\) 528.000 1.87254 0.936270 − 0.351280i \(-0.114254\pi\)
0.936270 + 0.351280i \(0.114254\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −340.000 −1.05519 −0.527597 − 0.849495i \(-0.676907\pi\)
−0.527597 + 0.849495i \(0.676907\pi\)
\(48\) 0 0
\(49\) 681.000 1.98542
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 438.000 1.13517 0.567584 − 0.823315i \(-0.307878\pi\)
0.567584 + 0.823315i \(0.307878\pi\)
\(54\) 0 0
\(55\) −154.000 −0.377552
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 20.0000 0.0441318 0.0220659 − 0.999757i \(-0.492976\pi\)
0.0220659 + 0.999757i \(0.492976\pi\)
\(60\) 0 0
\(61\) 570.000 1.19641 0.598205 − 0.801343i \(-0.295881\pi\)
0.598205 + 0.801343i \(0.295881\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −532.000 −1.01518
\(66\) 0 0
\(67\) 460.000 0.838775 0.419388 − 0.907807i \(-0.362245\pi\)
0.419388 + 0.907807i \(0.362245\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −1092.00 −1.82530 −0.912652 − 0.408738i \(-0.865969\pi\)
−0.912652 + 0.408738i \(0.865969\pi\)
\(72\) 0 0
\(73\) 562.000 0.901057 0.450528 − 0.892762i \(-0.351236\pi\)
0.450528 + 0.892762i \(0.351236\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −352.000 −0.520963
\(78\) 0 0
\(79\) 16.0000 0.0227866 0.0113933 − 0.999935i \(-0.496373\pi\)
0.0113933 + 0.999935i \(0.496373\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 372.000 0.491955 0.245978 − 0.969275i \(-0.420891\pi\)
0.245978 + 0.969275i \(0.420891\pi\)
\(84\) 0 0
\(85\) 28.0000 0.0357297
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 966.000 1.15051 0.575257 − 0.817973i \(-0.304902\pi\)
0.575257 + 0.817973i \(0.304902\pi\)
\(90\) 0 0
\(91\) −1216.00 −1.40079
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −1008.00 −1.08862
\(96\) 0 0
\(97\) −526.000 −0.550590 −0.275295 − 0.961360i \(-0.588775\pi\)
−0.275295 + 0.961360i \(0.588775\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −50.0000 −0.0492593 −0.0246296 − 0.999697i \(-0.507841\pi\)
−0.0246296 + 0.999697i \(0.507841\pi\)
\(102\) 0 0
\(103\) −944.000 −0.903059 −0.451530 − 0.892256i \(-0.649121\pi\)
−0.451530 + 0.892256i \(0.649121\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 468.000 0.422834 0.211417 − 0.977396i \(-0.432192\pi\)
0.211417 + 0.977396i \(0.432192\pi\)
\(108\) 0 0
\(109\) 154.000 0.135326 0.0676630 − 0.997708i \(-0.478446\pi\)
0.0676630 + 0.997708i \(0.478446\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 54.0000 0.0449548 0.0224774 − 0.999747i \(-0.492845\pi\)
0.0224774 + 0.999747i \(0.492845\pi\)
\(114\) 0 0
\(115\) 952.000 0.771952
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 64.0000 0.0493014
\(120\) 0 0
\(121\) 121.000 0.0909091
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −756.000 −0.540950
\(126\) 0 0
\(127\) 2224.00 1.55392 0.776961 − 0.629549i \(-0.216760\pi\)
0.776961 + 0.629549i \(0.216760\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −2772.00 −1.84878 −0.924392 − 0.381443i \(-0.875427\pi\)
−0.924392 + 0.381443i \(0.875427\pi\)
\(132\) 0 0
\(133\) −2304.00 −1.50212
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −1130.00 −0.704689 −0.352345 − 0.935870i \(-0.614615\pi\)
−0.352345 + 0.935870i \(0.614615\pi\)
\(138\) 0 0
\(139\) 1616.00 0.986096 0.493048 − 0.870002i \(-0.335883\pi\)
0.493048 + 0.870002i \(0.335883\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 418.000 0.244440
\(144\) 0 0
\(145\) 756.000 0.432982
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −2066.00 −1.13593 −0.567964 − 0.823053i \(-0.692269\pi\)
−0.567964 + 0.823053i \(0.692269\pi\)
\(150\) 0 0
\(151\) −248.000 −0.133655 −0.0668277 − 0.997765i \(-0.521288\pi\)
−0.0668277 + 0.997765i \(0.521288\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 2128.00 1.10274
\(156\) 0 0
\(157\) 2366.00 1.20272 0.601361 − 0.798977i \(-0.294625\pi\)
0.601361 + 0.798977i \(0.294625\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 2176.00 1.06517
\(162\) 0 0
\(163\) 284.000 0.136470 0.0682350 − 0.997669i \(-0.478263\pi\)
0.0682350 + 0.997669i \(0.478263\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 600.000 0.278020 0.139010 − 0.990291i \(-0.455608\pi\)
0.139010 + 0.990291i \(0.455608\pi\)
\(168\) 0 0
\(169\) −753.000 −0.342740
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −138.000 −0.0606471 −0.0303235 − 0.999540i \(-0.509654\pi\)
−0.0303235 + 0.999540i \(0.509654\pi\)
\(174\) 0 0
\(175\) 2272.00 0.981412
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 3972.00 1.65855 0.829277 − 0.558838i \(-0.188752\pi\)
0.829277 + 0.558838i \(0.188752\pi\)
\(180\) 0 0
\(181\) 2230.00 0.915771 0.457886 − 0.889011i \(-0.348607\pi\)
0.457886 + 0.889011i \(0.348607\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 2436.00 0.968099
\(186\) 0 0
\(187\) −22.0000 −0.00860320
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −772.000 −0.292461 −0.146230 − 0.989251i \(-0.546714\pi\)
−0.146230 + 0.989251i \(0.546714\pi\)
\(192\) 0 0
\(193\) 394.000 0.146947 0.0734734 − 0.997297i \(-0.476592\pi\)
0.0734734 + 0.997297i \(0.476592\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −3058.00 −1.10596 −0.552978 − 0.833196i \(-0.686509\pi\)
−0.552978 + 0.833196i \(0.686509\pi\)
\(198\) 0 0
\(199\) −2664.00 −0.948975 −0.474487 − 0.880262i \(-0.657367\pi\)
−0.474487 + 0.880262i \(0.657367\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 1728.00 0.597447
\(204\) 0 0
\(205\) −1316.00 −0.448358
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 792.000 0.262123
\(210\) 0 0
\(211\) 6000.00 1.95762 0.978808 − 0.204779i \(-0.0656477\pi\)
0.978808 + 0.204779i \(0.0656477\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 7392.00 2.34479
\(216\) 0 0
\(217\) 4864.00 1.52161
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −76.0000 −0.0231326
\(222\) 0 0
\(223\) 560.000 0.168163 0.0840816 − 0.996459i \(-0.473204\pi\)
0.0840816 + 0.996459i \(0.473204\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 5292.00 1.54732 0.773662 − 0.633599i \(-0.218423\pi\)
0.773662 + 0.633599i \(0.218423\pi\)
\(228\) 0 0
\(229\) −5322.00 −1.53575 −0.767877 − 0.640597i \(-0.778687\pi\)
−0.767877 + 0.640597i \(0.778687\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 3954.00 1.11174 0.555869 − 0.831270i \(-0.312385\pi\)
0.555869 + 0.831270i \(0.312385\pi\)
\(234\) 0 0
\(235\) −4760.00 −1.32131
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −3360.00 −0.909374 −0.454687 − 0.890651i \(-0.650249\pi\)
−0.454687 + 0.890651i \(0.650249\pi\)
\(240\) 0 0
\(241\) −3278.00 −0.876160 −0.438080 − 0.898936i \(-0.644341\pi\)
−0.438080 + 0.898936i \(0.644341\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 9534.00 2.48614
\(246\) 0 0
\(247\) 2736.00 0.704808
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 2092.00 0.526079 0.263040 − 0.964785i \(-0.415275\pi\)
0.263040 + 0.964785i \(0.415275\pi\)
\(252\) 0 0
\(253\) −748.000 −0.185875
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −658.000 −0.159708 −0.0798539 − 0.996807i \(-0.525445\pi\)
−0.0798539 + 0.996807i \(0.525445\pi\)
\(258\) 0 0
\(259\) 5568.00 1.33583
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −5104.00 −1.19668 −0.598339 − 0.801243i \(-0.704172\pi\)
−0.598339 + 0.801243i \(0.704172\pi\)
\(264\) 0 0
\(265\) 6132.00 1.42146
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 4238.00 0.960578 0.480289 − 0.877110i \(-0.340532\pi\)
0.480289 + 0.877110i \(0.340532\pi\)
\(270\) 0 0
\(271\) 3376.00 0.756743 0.378372 − 0.925654i \(-0.376484\pi\)
0.378372 + 0.925654i \(0.376484\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −781.000 −0.171258
\(276\) 0 0
\(277\) 2074.00 0.449872 0.224936 − 0.974374i \(-0.427783\pi\)
0.224936 + 0.974374i \(0.427783\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −702.000 −0.149031 −0.0745157 − 0.997220i \(-0.523741\pi\)
−0.0745157 + 0.997220i \(0.523741\pi\)
\(282\) 0 0
\(283\) −4912.00 −1.03176 −0.515880 − 0.856661i \(-0.672535\pi\)
−0.515880 + 0.856661i \(0.672535\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −3008.00 −0.618664
\(288\) 0 0
\(289\) −4909.00 −0.999186
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 3486.00 0.695066 0.347533 − 0.937668i \(-0.387019\pi\)
0.347533 + 0.937668i \(0.387019\pi\)
\(294\) 0 0
\(295\) 280.000 0.0552618
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −2584.00 −0.499788
\(300\) 0 0
\(301\) 16896.0 3.23545
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 7980.00 1.49814
\(306\) 0 0
\(307\) −8360.00 −1.55417 −0.777085 − 0.629395i \(-0.783303\pi\)
−0.777085 + 0.629395i \(0.783303\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −5532.00 −1.00865 −0.504326 − 0.863513i \(-0.668259\pi\)
−0.504326 + 0.863513i \(0.668259\pi\)
\(312\) 0 0
\(313\) 4826.00 0.871507 0.435753 − 0.900066i \(-0.356482\pi\)
0.435753 + 0.900066i \(0.356482\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −7570.00 −1.34124 −0.670621 − 0.741800i \(-0.733972\pi\)
−0.670621 + 0.741800i \(0.733972\pi\)
\(318\) 0 0
\(319\) −594.000 −0.104256
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −144.000 −0.0248061
\(324\) 0 0
\(325\) −2698.00 −0.460487
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −10880.0 −1.82320
\(330\) 0 0
\(331\) −3676.00 −0.610427 −0.305213 − 0.952284i \(-0.598728\pi\)
−0.305213 + 0.952284i \(0.598728\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 6440.00 1.05031
\(336\) 0 0
\(337\) −5686.00 −0.919098 −0.459549 − 0.888152i \(-0.651989\pi\)
−0.459549 + 0.888152i \(0.651989\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −1672.00 −0.265525
\(342\) 0 0
\(343\) 10816.0 1.70265
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −1652.00 −0.255574 −0.127787 − 0.991802i \(-0.540787\pi\)
−0.127787 + 0.991802i \(0.540787\pi\)
\(348\) 0 0
\(349\) −6990.00 −1.07211 −0.536055 − 0.844183i \(-0.680086\pi\)
−0.536055 + 0.844183i \(0.680086\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 8094.00 1.22040 0.610199 − 0.792249i \(-0.291090\pi\)
0.610199 + 0.792249i \(0.291090\pi\)
\(354\) 0 0
\(355\) −15288.0 −2.28564
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 1024.00 0.150542 0.0752711 − 0.997163i \(-0.476018\pi\)
0.0752711 + 0.997163i \(0.476018\pi\)
\(360\) 0 0
\(361\) −1675.00 −0.244205
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 7868.00 1.12830
\(366\) 0 0
\(367\) 13664.0 1.94347 0.971737 − 0.236066i \(-0.0758581\pi\)
0.971737 + 0.236066i \(0.0758581\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 14016.0 1.96139
\(372\) 0 0
\(373\) −1958.00 −0.271800 −0.135900 − 0.990723i \(-0.543393\pi\)
−0.135900 + 0.990723i \(0.543393\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −2052.00 −0.280327
\(378\) 0 0
\(379\) −6124.00 −0.829997 −0.414998 − 0.909822i \(-0.636218\pi\)
−0.414998 + 0.909822i \(0.636218\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 5612.00 0.748720 0.374360 − 0.927283i \(-0.377862\pi\)
0.374360 + 0.927283i \(0.377862\pi\)
\(384\) 0 0
\(385\) −4928.00 −0.652348
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −12450.0 −1.62273 −0.811363 − 0.584543i \(-0.801274\pi\)
−0.811363 + 0.584543i \(0.801274\pi\)
\(390\) 0 0
\(391\) 136.000 0.0175903
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 224.000 0.0285333
\(396\) 0 0
\(397\) 14830.0 1.87480 0.937401 − 0.348252i \(-0.113225\pi\)
0.937401 + 0.348252i \(0.113225\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 3358.00 0.418181 0.209090 − 0.977896i \(-0.432950\pi\)
0.209090 + 0.977896i \(0.432950\pi\)
\(402\) 0 0
\(403\) −5776.00 −0.713953
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −1914.00 −0.233104
\(408\) 0 0
\(409\) 10698.0 1.29335 0.646677 − 0.762764i \(-0.276158\pi\)
0.646677 + 0.762764i \(0.276158\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 640.000 0.0762526
\(414\) 0 0
\(415\) 5208.00 0.616026
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −2044.00 −0.238320 −0.119160 − 0.992875i \(-0.538020\pi\)
−0.119160 + 0.992875i \(0.538020\pi\)
\(420\) 0 0
\(421\) 3070.00 0.355398 0.177699 − 0.984085i \(-0.443135\pi\)
0.177699 + 0.984085i \(0.443135\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 142.000 0.0162071
\(426\) 0 0
\(427\) 18240.0 2.06720
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −12600.0 −1.40817 −0.704084 − 0.710116i \(-0.748642\pi\)
−0.704084 + 0.710116i \(0.748642\pi\)
\(432\) 0 0
\(433\) −9902.00 −1.09898 −0.549492 − 0.835499i \(-0.685179\pi\)
−0.549492 + 0.835499i \(0.685179\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −4896.00 −0.535944
\(438\) 0 0
\(439\) −11440.0 −1.24374 −0.621869 − 0.783121i \(-0.713627\pi\)
−0.621869 + 0.783121i \(0.713627\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −5180.00 −0.555551 −0.277776 − 0.960646i \(-0.589597\pi\)
−0.277776 + 0.960646i \(0.589597\pi\)
\(444\) 0 0
\(445\) 13524.0 1.44067
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −10826.0 −1.13789 −0.568943 − 0.822377i \(-0.692647\pi\)
−0.568943 + 0.822377i \(0.692647\pi\)
\(450\) 0 0
\(451\) 1034.00 0.107958
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −17024.0 −1.75406
\(456\) 0 0
\(457\) −15798.0 −1.61707 −0.808533 − 0.588451i \(-0.799738\pi\)
−0.808533 + 0.588451i \(0.799738\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 3894.00 0.393409 0.196705 − 0.980463i \(-0.436976\pi\)
0.196705 + 0.980463i \(0.436976\pi\)
\(462\) 0 0
\(463\) 15992.0 1.60521 0.802604 − 0.596512i \(-0.203447\pi\)
0.802604 + 0.596512i \(0.203447\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 11844.0 1.17361 0.586804 − 0.809729i \(-0.300386\pi\)
0.586804 + 0.809729i \(0.300386\pi\)
\(468\) 0 0
\(469\) 14720.0 1.44927
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −5808.00 −0.564592
\(474\) 0 0
\(475\) −5112.00 −0.493799
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 14936.0 1.42472 0.712362 − 0.701812i \(-0.247625\pi\)
0.712362 + 0.701812i \(0.247625\pi\)
\(480\) 0 0
\(481\) −6612.00 −0.626780
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −7364.00 −0.689447
\(486\) 0 0
\(487\) 2056.00 0.191306 0.0956532 − 0.995415i \(-0.469506\pi\)
0.0956532 + 0.995415i \(0.469506\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −17852.0 −1.64083 −0.820417 − 0.571766i \(-0.806259\pi\)
−0.820417 + 0.571766i \(0.806259\pi\)
\(492\) 0 0
\(493\) 108.000 0.00986628
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −34944.0 −3.15383
\(498\) 0 0
\(499\) −4508.00 −0.404420 −0.202210 − 0.979342i \(-0.564812\pi\)
−0.202210 + 0.979342i \(0.564812\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −5912.00 −0.524062 −0.262031 − 0.965059i \(-0.584392\pi\)
−0.262031 + 0.965059i \(0.584392\pi\)
\(504\) 0 0
\(505\) −700.000 −0.0616824
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 11406.0 0.993246 0.496623 − 0.867966i \(-0.334573\pi\)
0.496623 + 0.867966i \(0.334573\pi\)
\(510\) 0 0
\(511\) 17984.0 1.55688
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −13216.0 −1.13081
\(516\) 0 0
\(517\) 3740.00 0.318153
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 1542.00 0.129667 0.0648333 − 0.997896i \(-0.479348\pi\)
0.0648333 + 0.997896i \(0.479348\pi\)
\(522\) 0 0
\(523\) 7504.00 0.627394 0.313697 − 0.949523i \(-0.398432\pi\)
0.313697 + 0.949523i \(0.398432\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 304.000 0.0251280
\(528\) 0 0
\(529\) −7543.00 −0.619956
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 3572.00 0.290282
\(534\) 0 0
\(535\) 6552.00 0.529472
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −7491.00 −0.598627
\(540\) 0 0
\(541\) 1018.00 0.0809006 0.0404503 − 0.999182i \(-0.487121\pi\)
0.0404503 + 0.999182i \(0.487121\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 2156.00 0.169455
\(546\) 0 0
\(547\) −7904.00 −0.617826 −0.308913 − 0.951090i \(-0.599965\pi\)
−0.308913 + 0.951090i \(0.599965\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −3888.00 −0.300607
\(552\) 0 0
\(553\) 512.000 0.0393715
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 22934.0 1.74460 0.872302 − 0.488967i \(-0.162626\pi\)
0.872302 + 0.488967i \(0.162626\pi\)
\(558\) 0 0
\(559\) −20064.0 −1.51810
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 14020.0 1.04951 0.524754 − 0.851254i \(-0.324157\pi\)
0.524754 + 0.851254i \(0.324157\pi\)
\(564\) 0 0
\(565\) 756.000 0.0562923
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −4230.00 −0.311653 −0.155827 − 0.987784i \(-0.549804\pi\)
−0.155827 + 0.987784i \(0.549804\pi\)
\(570\) 0 0
\(571\) 8536.00 0.625605 0.312803 − 0.949818i \(-0.398732\pi\)
0.312803 + 0.949818i \(0.398732\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 4828.00 0.350159
\(576\) 0 0
\(577\) −11982.0 −0.864501 −0.432251 − 0.901754i \(-0.642280\pi\)
−0.432251 + 0.901754i \(0.642280\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 11904.0 0.850019
\(582\) 0 0
\(583\) −4818.00 −0.342266
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −20396.0 −1.43413 −0.717064 − 0.697007i \(-0.754514\pi\)
−0.717064 + 0.697007i \(0.754514\pi\)
\(588\) 0 0
\(589\) −10944.0 −0.765602
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −12518.0 −0.866868 −0.433434 − 0.901185i \(-0.642698\pi\)
−0.433434 + 0.901185i \(0.642698\pi\)
\(594\) 0 0
\(595\) 896.000 0.0617352
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −25292.0 −1.72521 −0.862607 − 0.505875i \(-0.831170\pi\)
−0.862607 + 0.505875i \(0.831170\pi\)
\(600\) 0 0
\(601\) 15962.0 1.08337 0.541683 − 0.840583i \(-0.317787\pi\)
0.541683 + 0.840583i \(0.317787\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 1694.00 0.113836
\(606\) 0 0
\(607\) 1600.00 0.106988 0.0534942 − 0.998568i \(-0.482964\pi\)
0.0534942 + 0.998568i \(0.482964\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 12920.0 0.855462
\(612\) 0 0
\(613\) 2162.00 0.142451 0.0712254 − 0.997460i \(-0.477309\pi\)
0.0712254 + 0.997460i \(0.477309\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 18126.0 1.18270 0.591350 − 0.806415i \(-0.298595\pi\)
0.591350 + 0.806415i \(0.298595\pi\)
\(618\) 0 0
\(619\) −17348.0 −1.12645 −0.563227 − 0.826302i \(-0.690440\pi\)
−0.563227 + 0.826302i \(0.690440\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 30912.0 1.98790
\(624\) 0 0
\(625\) −19459.0 −1.24538
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 348.000 0.0220599
\(630\) 0 0
\(631\) −10096.0 −0.636950 −0.318475 − 0.947931i \(-0.603171\pi\)
−0.318475 + 0.947931i \(0.603171\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 31136.0 1.94582
\(636\) 0 0
\(637\) −25878.0 −1.60961
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −8922.00 −0.549763 −0.274881 − 0.961478i \(-0.588639\pi\)
−0.274881 + 0.961478i \(0.588639\pi\)
\(642\) 0 0
\(643\) 14644.0 0.898138 0.449069 − 0.893497i \(-0.351756\pi\)
0.449069 + 0.893497i \(0.351756\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 6932.00 0.421213 0.210607 − 0.977571i \(-0.432456\pi\)
0.210607 + 0.977571i \(0.432456\pi\)
\(648\) 0 0
\(649\) −220.000 −0.0133062
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 5942.00 0.356093 0.178046 − 0.984022i \(-0.443022\pi\)
0.178046 + 0.984022i \(0.443022\pi\)
\(654\) 0 0
\(655\) −38808.0 −2.31504
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 484.000 0.0286100 0.0143050 − 0.999898i \(-0.495446\pi\)
0.0143050 + 0.999898i \(0.495446\pi\)
\(660\) 0 0
\(661\) −17114.0 −1.00705 −0.503523 − 0.863982i \(-0.667963\pi\)
−0.503523 + 0.863982i \(0.667963\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −32256.0 −1.88095
\(666\) 0 0
\(667\) 3672.00 0.213164
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −6270.00 −0.360731
\(672\) 0 0
\(673\) 16154.0 0.925247 0.462623 − 0.886555i \(-0.346908\pi\)
0.462623 + 0.886555i \(0.346908\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 3390.00 0.192449 0.0962247 − 0.995360i \(-0.469323\pi\)
0.0962247 + 0.995360i \(0.469323\pi\)
\(678\) 0 0
\(679\) −16832.0 −0.951330
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −25540.0 −1.43084 −0.715418 − 0.698697i \(-0.753764\pi\)
−0.715418 + 0.698697i \(0.753764\pi\)
\(684\) 0 0
\(685\) −15820.0 −0.882410
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −16644.0 −0.920299
\(690\) 0 0
\(691\) −12476.0 −0.686844 −0.343422 − 0.939181i \(-0.611586\pi\)
−0.343422 + 0.939181i \(0.611586\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 22624.0 1.23479
\(696\) 0 0
\(697\) −188.000 −0.0102167
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 20806.0 1.12102 0.560508 − 0.828149i \(-0.310606\pi\)
0.560508 + 0.828149i \(0.310606\pi\)
\(702\) 0 0
\(703\) −12528.0 −0.672123
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −1600.00 −0.0851120
\(708\) 0 0
\(709\) 14198.0 0.752069 0.376035 − 0.926606i \(-0.377287\pi\)
0.376035 + 0.926606i \(0.377287\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 10336.0 0.542898
\(714\) 0 0
\(715\) 5852.00 0.306087
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 4596.00 0.238389 0.119195 − 0.992871i \(-0.461969\pi\)
0.119195 + 0.992871i \(0.461969\pi\)
\(720\) 0 0
\(721\) −30208.0 −1.56034
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 3834.00 0.196402
\(726\) 0 0
\(727\) −19560.0 −0.997855 −0.498927 − 0.866644i \(-0.666273\pi\)
−0.498927 + 0.866644i \(0.666273\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 1056.00 0.0534303
\(732\) 0 0
\(733\) −1638.00 −0.0825388 −0.0412694 − 0.999148i \(-0.513140\pi\)
−0.0412694 + 0.999148i \(0.513140\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −5060.00 −0.252900
\(738\) 0 0
\(739\) 15592.0 0.776131 0.388066 − 0.921632i \(-0.373143\pi\)
0.388066 + 0.921632i \(0.373143\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 592.000 0.0292307 0.0146153 − 0.999893i \(-0.495348\pi\)
0.0146153 + 0.999893i \(0.495348\pi\)
\(744\) 0 0
\(745\) −28924.0 −1.42241
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 14976.0 0.730589
\(750\) 0 0
\(751\) −39832.0 −1.93541 −0.967703 − 0.252092i \(-0.918881\pi\)
−0.967703 + 0.252092i \(0.918881\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −3472.00 −0.167363
\(756\) 0 0
\(757\) 10958.0 0.526123 0.263062 − 0.964779i \(-0.415268\pi\)
0.263062 + 0.964779i \(0.415268\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 8970.00 0.427283 0.213641 − 0.976912i \(-0.431468\pi\)
0.213641 + 0.976912i \(0.431468\pi\)
\(762\) 0 0
\(763\) 4928.00 0.233821
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −760.000 −0.0357784
\(768\) 0 0
\(769\) −10054.0 −0.471465 −0.235732 − 0.971818i \(-0.575749\pi\)
−0.235732 + 0.971818i \(0.575749\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −26346.0 −1.22587 −0.612936 − 0.790132i \(-0.710012\pi\)
−0.612936 + 0.790132i \(0.710012\pi\)
\(774\) 0 0
\(775\) 10792.0 0.500207
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 6768.00 0.311282
\(780\) 0 0
\(781\) 12012.0 0.550350
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 33124.0 1.50605
\(786\) 0 0
\(787\) 16040.0 0.726511 0.363256 − 0.931690i \(-0.381665\pi\)
0.363256 + 0.931690i \(0.381665\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 1728.00 0.0776746
\(792\) 0 0
\(793\) −21660.0 −0.969948
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −32810.0 −1.45821 −0.729103 − 0.684404i \(-0.760062\pi\)
−0.729103 + 0.684404i \(0.760062\pi\)
\(798\) 0 0
\(799\) −680.000 −0.0301085
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −6182.00 −0.271679
\(804\) 0 0
\(805\) 30464.0 1.33381
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −18918.0 −0.822153 −0.411076 − 0.911601i \(-0.634847\pi\)
−0.411076 + 0.911601i \(0.634847\pi\)
\(810\) 0 0
\(811\) 8552.00 0.370285 0.185143 − 0.982712i \(-0.440725\pi\)
0.185143 + 0.982712i \(0.440725\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 3976.00 0.170887
\(816\) 0 0
\(817\) −38016.0 −1.62792
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 46430.0 1.97371 0.986856 − 0.161600i \(-0.0516654\pi\)
0.986856 + 0.161600i \(0.0516654\pi\)
\(822\) 0 0
\(823\) −16392.0 −0.694276 −0.347138 − 0.937814i \(-0.612846\pi\)
−0.347138 + 0.937814i \(0.612846\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −13876.0 −0.583453 −0.291727 − 0.956502i \(-0.594230\pi\)
−0.291727 + 0.956502i \(0.594230\pi\)
\(828\) 0 0
\(829\) −24554.0 −1.02870 −0.514352 − 0.857579i \(-0.671968\pi\)
−0.514352 + 0.857579i \(0.671968\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 1362.00 0.0566513
\(834\) 0 0
\(835\) 8400.00 0.348137
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 19900.0 0.818861 0.409430 − 0.912341i \(-0.365727\pi\)
0.409430 + 0.912341i \(0.365727\pi\)
\(840\) 0 0
\(841\) −21473.0 −0.880438
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −10542.0 −0.429178
\(846\) 0 0
\(847\) 3872.00 0.157076
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 11832.0 0.476611
\(852\) 0 0
\(853\) 41138.0 1.65128 0.825638 − 0.564200i \(-0.190815\pi\)
0.825638 + 0.564200i \(0.190815\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −19910.0 −0.793597 −0.396799 − 0.917906i \(-0.629879\pi\)
−0.396799 + 0.917906i \(0.629879\pi\)
\(858\) 0 0
\(859\) −42924.0 −1.70495 −0.852473 − 0.522772i \(-0.824898\pi\)
−0.852473 + 0.522772i \(0.824898\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −46236.0 −1.82374 −0.911872 − 0.410474i \(-0.865363\pi\)
−0.911872 + 0.410474i \(0.865363\pi\)
\(864\) 0 0
\(865\) −1932.00 −0.0759422
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −176.000 −0.00687042
\(870\) 0 0
\(871\) −17480.0 −0.680008
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −24192.0 −0.934673
\(876\) 0 0
\(877\) 25746.0 0.991312 0.495656 − 0.868519i \(-0.334928\pi\)
0.495656 + 0.868519i \(0.334928\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 24550.0 0.938831 0.469416 − 0.882977i \(-0.344465\pi\)
0.469416 + 0.882977i \(0.344465\pi\)
\(882\) 0 0
\(883\) 19436.0 0.740740 0.370370 − 0.928884i \(-0.379231\pi\)
0.370370 + 0.928884i \(0.379231\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −22912.0 −0.867316 −0.433658 − 0.901077i \(-0.642777\pi\)
−0.433658 + 0.901077i \(0.642777\pi\)
\(888\) 0 0
\(889\) 71168.0 2.68492
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 24480.0 0.917348
\(894\) 0 0
\(895\) 55608.0 2.07684
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 8208.00 0.304507
\(900\) 0 0
\(901\) 876.000 0.0323904
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 31220.0 1.14673
\(906\) 0 0
\(907\) 39900.0 1.46070 0.730352 − 0.683071i \(-0.239356\pi\)
0.730352 + 0.683071i \(0.239356\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 29460.0 1.07141 0.535704 − 0.844406i \(-0.320046\pi\)
0.535704 + 0.844406i \(0.320046\pi\)
\(912\) 0 0
\(913\) −4092.00 −0.148330
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −88704.0 −3.19440
\(918\) 0 0
\(919\) −29368.0 −1.05415 −0.527073 − 0.849820i \(-0.676711\pi\)
−0.527073 + 0.849820i \(0.676711\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 41496.0 1.47980
\(924\) 0 0
\(925\) 12354.0 0.439132
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −33954.0 −1.19913 −0.599567 − 0.800325i \(-0.704660\pi\)
−0.599567 + 0.800325i \(0.704660\pi\)
\(930\) 0 0
\(931\) −49032.0 −1.72606
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −308.000 −0.0107729
\(936\) 0 0
\(937\) −2854.00 −0.0995049 −0.0497525 − 0.998762i \(-0.515843\pi\)
−0.0497525 + 0.998762i \(0.515843\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 6294.00 0.218043 0.109022 − 0.994039i \(-0.465228\pi\)
0.109022 + 0.994039i \(0.465228\pi\)
\(942\) 0 0
\(943\) −6392.00 −0.220734
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 2268.00 0.0778248 0.0389124 − 0.999243i \(-0.487611\pi\)
0.0389124 + 0.999243i \(0.487611\pi\)
\(948\) 0 0
\(949\) −21356.0 −0.730501
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −26566.0 −0.902998 −0.451499 − 0.892272i \(-0.649111\pi\)
−0.451499 + 0.892272i \(0.649111\pi\)
\(954\) 0 0
\(955\) −10808.0 −0.366218
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −36160.0 −1.21759
\(960\) 0 0
\(961\) −6687.00 −0.224464
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 5516.00 0.184007
\(966\) 0 0
\(967\) −11176.0 −0.371661 −0.185830 − 0.982582i \(-0.559497\pi\)
−0.185830 + 0.982582i \(0.559497\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −42316.0 −1.39854 −0.699271 − 0.714856i \(-0.746492\pi\)
−0.699271 + 0.714856i \(0.746492\pi\)
\(972\) 0 0
\(973\) 51712.0 1.70381
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 45054.0 1.47534 0.737669 − 0.675163i \(-0.235927\pi\)
0.737669 + 0.675163i \(0.235927\pi\)
\(978\) 0 0
\(979\) −10626.0 −0.346893
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −12300.0 −0.399094 −0.199547 − 0.979888i \(-0.563947\pi\)
−0.199547 + 0.979888i \(0.563947\pi\)
\(984\) 0 0
\(985\) −42812.0 −1.38488
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 35904.0 1.15438
\(990\) 0 0
\(991\) −36280.0 −1.16294 −0.581469 − 0.813568i \(-0.697522\pi\)
−0.581469 + 0.813568i \(0.697522\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −37296.0 −1.18830
\(996\) 0 0
\(997\) 3290.00 0.104509 0.0522544 − 0.998634i \(-0.483359\pi\)
0.0522544 + 0.998634i \(0.483359\pi\)
\(998\) 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 1584.4.a.t.1.1 1
3.2 odd 2 528.4.a.a.1.1 1
4.3 odd 2 99.4.a.b.1.1 1
12.11 even 2 33.4.a.a.1.1 ✓ 1
20.19 odd 2 2475.4.a.b.1.1 1
24.5 odd 2 2112.4.a.y.1.1 1
24.11 even 2 2112.4.a.l.1.1 1
44.43 even 2 1089.4.a.a.1.1 1
60.23 odd 4 825.4.c.a.199.2 2
60.47 odd 4 825.4.c.a.199.1 2
60.59 even 2 825.4.a.i.1.1 1
84.83 odd 2 1617.4.a.a.1.1 1
132.131 odd 2 363.4.a.h.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
33.4.a.a.1.1 ✓ 1 12.11 even 2
99.4.a.b.1.1 1 4.3 odd 2
363.4.a.h.1.1 1 132.131 odd 2
528.4.a.a.1.1 1 3.2 odd 2
825.4.a.i.1.1 1 60.59 even 2
825.4.c.a.199.1 2 60.47 odd 4
825.4.c.a.199.2 2 60.23 odd 4
1089.4.a.a.1.1 1 44.43 even 2
1584.4.a.t.1.1 1 1.1 even 1 trivial
1617.4.a.a.1.1 1 84.83 odd 2
2112.4.a.l.1.1 1 24.11 even 2
2112.4.a.y.1.1 1 24.5 odd 2
2475.4.a.b.1.1 1 20.19 odd 2