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Properties

Label 1584.4.a.l.1.1
Level $1584$
Weight $4$
Character 1584.1
Self dual yes
Analytic conductor $93.459$
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] = [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: \(1\)
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)
 
\(f(q)\) \(=\) \(q+4.00000 q^{5} +26.0000 q^{7} +O(q^{10})\) \(q+4.00000 q^{5} +26.0000 q^{7} +11.0000 q^{11} -32.0000 q^{13} -74.0000 q^{17} +60.0000 q^{19} -182.000 q^{23} -109.000 q^{25} +90.0000 q^{29} +8.00000 q^{31} +104.000 q^{35} -66.0000 q^{37} -422.000 q^{41} -408.000 q^{43} -506.000 q^{47} +333.000 q^{49} -348.000 q^{53} +44.0000 q^{55} -200.000 q^{59} +132.000 q^{61} -128.000 q^{65} +1036.00 q^{67} +762.000 q^{71} -542.000 q^{73} +286.000 q^{77} +550.000 q^{79} -132.000 q^{83} -296.000 q^{85} -570.000 q^{89} -832.000 q^{91} +240.000 q^{95} +14.0000 q^{97} +O(q^{100})\)

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
\(5\) 4.00000 0.357771 0.178885 − 0.983870i \(-0.442751\pi\)
0.178885 + 0.983870i \(0.442751\pi\)
\(6\) 0 0
\(7\) 26.0000 1.40387 0.701934 − 0.712242i \(-0.252320\pi\)
0.701934 + 0.712242i \(0.252320\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 11.0000 0.301511
\(12\) 0 0
\(13\) −32.0000 −0.682708 −0.341354 − 0.939935i \(-0.610885\pi\)
−0.341354 + 0.939935i \(0.610885\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −74.0000 −1.05574 −0.527872 − 0.849324i \(-0.677010\pi\)
−0.527872 + 0.849324i \(0.677010\pi\)
\(18\) 0 0
\(19\) 60.0000 0.724471 0.362235 − 0.932087i \(-0.382014\pi\)
0.362235 + 0.932087i \(0.382014\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −182.000 −1.64998 −0.824992 − 0.565145i \(-0.808820\pi\)
−0.824992 + 0.565145i \(0.808820\pi\)
\(24\) 0 0
\(25\) −109.000 −0.872000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 90.0000 0.576296 0.288148 − 0.957586i \(-0.406961\pi\)
0.288148 + 0.957586i \(0.406961\pi\)
\(30\) 0 0
\(31\) 8.00000 0.0463498 0.0231749 − 0.999731i \(-0.492623\pi\)
0.0231749 + 0.999731i \(0.492623\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 104.000 0.502263
\(36\) 0 0
\(37\) −66.0000 −0.293252 −0.146626 − 0.989192i \(-0.546841\pi\)
−0.146626 + 0.989192i \(0.546841\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −422.000 −1.60745 −0.803724 − 0.595003i \(-0.797151\pi\)
−0.803724 + 0.595003i \(0.797151\pi\)
\(42\) 0 0
\(43\) −408.000 −1.44696 −0.723482 − 0.690344i \(-0.757459\pi\)
−0.723482 + 0.690344i \(0.757459\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −506.000 −1.57038 −0.785188 − 0.619257i \(-0.787434\pi\)
−0.785188 + 0.619257i \(0.787434\pi\)
\(48\) 0 0
\(49\) 333.000 0.970845
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −348.000 −0.901915 −0.450957 − 0.892546i \(-0.648917\pi\)
−0.450957 + 0.892546i \(0.648917\pi\)
\(54\) 0 0
\(55\) 44.0000 0.107872
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −200.000 −0.441318 −0.220659 − 0.975351i \(-0.570821\pi\)
−0.220659 + 0.975351i \(0.570821\pi\)
\(60\) 0 0
\(61\) 132.000 0.277063 0.138532 − 0.990358i \(-0.455762\pi\)
0.138532 + 0.990358i \(0.455762\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −128.000 −0.244253
\(66\) 0 0
\(67\) 1036.00 1.88907 0.944534 − 0.328414i \(-0.106514\pi\)
0.944534 + 0.328414i \(0.106514\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 762.000 1.27370 0.636850 − 0.770987i \(-0.280237\pi\)
0.636850 + 0.770987i \(0.280237\pi\)
\(72\) 0 0
\(73\) −542.000 −0.868990 −0.434495 − 0.900674i \(-0.643073\pi\)
−0.434495 + 0.900674i \(0.643073\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 286.000 0.423282
\(78\) 0 0
\(79\) 550.000 0.783289 0.391645 − 0.920117i \(-0.371906\pi\)
0.391645 + 0.920117i \(0.371906\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −132.000 −0.174565 −0.0872824 − 0.996184i \(-0.527818\pi\)
−0.0872824 + 0.996184i \(0.527818\pi\)
\(84\) 0 0
\(85\) −296.000 −0.377714
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −570.000 −0.678875 −0.339438 − 0.940629i \(-0.610237\pi\)
−0.339438 + 0.940629i \(0.610237\pi\)
\(90\) 0 0
\(91\) −832.000 −0.958432
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 240.000 0.259195
\(96\) 0 0
\(97\) 14.0000 0.0146545 0.00732724 − 0.999973i \(-0.497668\pi\)
0.00732724 + 0.999973i \(0.497668\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −1702.00 −1.67679 −0.838393 − 0.545067i \(-0.816504\pi\)
−0.838393 + 0.545067i \(0.816504\pi\)
\(102\) 0 0
\(103\) 1132.00 1.08291 0.541453 − 0.840731i \(-0.317874\pi\)
0.541453 + 0.840731i \(0.317874\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 564.000 0.509570 0.254785 − 0.966998i \(-0.417995\pi\)
0.254785 + 0.966998i \(0.417995\pi\)
\(108\) 0 0
\(109\) −320.000 −0.281197 −0.140598 − 0.990067i \(-0.544903\pi\)
−0.140598 + 0.990067i \(0.544903\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 2142.00 1.78321 0.891604 − 0.452817i \(-0.149581\pi\)
0.891604 + 0.452817i \(0.149581\pi\)
\(114\) 0 0
\(115\) −728.000 −0.590316
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −1924.00 −1.48212
\(120\) 0 0
\(121\) 121.000 0.0909091
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −936.000 −0.669747
\(126\) 0 0
\(127\) 1606.00 1.12212 0.561061 − 0.827775i \(-0.310393\pi\)
0.561061 + 0.827775i \(0.310393\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −1908.00 −1.27254 −0.636270 − 0.771466i \(-0.719524\pi\)
−0.636270 + 0.771466i \(0.719524\pi\)
\(132\) 0 0
\(133\) 1560.00 1.01706
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 2186.00 1.36323 0.681615 − 0.731711i \(-0.261278\pi\)
0.681615 + 0.731711i \(0.261278\pi\)
\(138\) 0 0
\(139\) −2740.00 −1.67197 −0.835985 − 0.548753i \(-0.815103\pi\)
−0.835985 + 0.548753i \(0.815103\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −352.000 −0.205844
\(144\) 0 0
\(145\) 360.000 0.206182
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 1310.00 0.720264 0.360132 − 0.932901i \(-0.382732\pi\)
0.360132 + 0.932901i \(0.382732\pi\)
\(150\) 0 0
\(151\) 1198.00 0.645641 0.322821 − 0.946460i \(-0.395369\pi\)
0.322821 + 0.946460i \(0.395369\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 32.0000 0.0165826
\(156\) 0 0
\(157\) 2114.00 1.07462 0.537311 − 0.843384i \(-0.319440\pi\)
0.537311 + 0.843384i \(0.319440\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −4732.00 −2.31636
\(162\) 0 0
\(163\) −3868.00 −1.85868 −0.929341 − 0.369223i \(-0.879624\pi\)
−0.929341 + 0.369223i \(0.879624\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 2004.00 0.928588 0.464294 − 0.885681i \(-0.346308\pi\)
0.464294 + 0.885681i \(0.346308\pi\)
\(168\) 0 0
\(169\) −1173.00 −0.533910
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −678.000 −0.297962 −0.148981 − 0.988840i \(-0.547599\pi\)
−0.148981 + 0.988840i \(0.547599\pi\)
\(174\) 0 0
\(175\) −2834.00 −1.22417
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −1680.00 −0.701503 −0.350752 − 0.936469i \(-0.614074\pi\)
−0.350752 + 0.936469i \(0.614074\pi\)
\(180\) 0 0
\(181\) −4358.00 −1.78966 −0.894828 − 0.446412i \(-0.852702\pi\)
−0.894828 + 0.446412i \(0.852702\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −264.000 −0.104917
\(186\) 0 0
\(187\) −814.000 −0.318319
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −1778.00 −0.673568 −0.336784 − 0.941582i \(-0.609339\pi\)
−0.336784 + 0.941582i \(0.609339\pi\)
\(192\) 0 0
\(193\) −3962.00 −1.47767 −0.738837 − 0.673884i \(-0.764625\pi\)
−0.738837 + 0.673884i \(0.764625\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −374.000 −0.135261 −0.0676304 − 0.997710i \(-0.521544\pi\)
−0.0676304 + 0.997710i \(0.521544\pi\)
\(198\) 0 0
\(199\) −2100.00 −0.748066 −0.374033 − 0.927415i \(-0.622025\pi\)
−0.374033 + 0.927415i \(0.622025\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 2340.00 0.809043
\(204\) 0 0
\(205\) −1688.00 −0.575098
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 660.000 0.218436
\(210\) 0 0
\(211\) −2232.00 −0.728233 −0.364117 − 0.931353i \(-0.618629\pi\)
−0.364117 + 0.931353i \(0.618629\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −1632.00 −0.517681
\(216\) 0 0
\(217\) 208.000 0.0650689
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 2368.00 0.720764
\(222\) 0 0
\(223\) −2128.00 −0.639020 −0.319510 − 0.947583i \(-0.603518\pi\)
−0.319510 + 0.947583i \(0.603518\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 2964.00 0.866641 0.433321 − 0.901240i \(-0.357342\pi\)
0.433321 + 0.901240i \(0.357342\pi\)
\(228\) 0 0
\(229\) −2550.00 −0.735846 −0.367923 − 0.929856i \(-0.619931\pi\)
−0.367923 + 0.929856i \(0.619931\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 3042.00 0.855314 0.427657 − 0.903941i \(-0.359339\pi\)
0.427657 + 0.903941i \(0.359339\pi\)
\(234\) 0 0
\(235\) −2024.00 −0.561835
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 2700.00 0.730747 0.365373 − 0.930861i \(-0.380941\pi\)
0.365373 + 0.930861i \(0.380941\pi\)
\(240\) 0 0
\(241\) −578.000 −0.154491 −0.0772453 − 0.997012i \(-0.524612\pi\)
−0.0772453 + 0.997012i \(0.524612\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 1332.00 0.347340
\(246\) 0 0
\(247\) −1920.00 −0.494602
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 3752.00 0.943522 0.471761 − 0.881726i \(-0.343618\pi\)
0.471761 + 0.881726i \(0.343618\pi\)
\(252\) 0 0
\(253\) −2002.00 −0.497489
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −674.000 −0.163591 −0.0817957 − 0.996649i \(-0.526065\pi\)
−0.0817957 + 0.996649i \(0.526065\pi\)
\(258\) 0 0
\(259\) −1716.00 −0.411687
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −4352.00 −1.02036 −0.510182 − 0.860066i \(-0.670422\pi\)
−0.510182 + 0.860066i \(0.670422\pi\)
\(264\) 0 0
\(265\) −1392.00 −0.322679
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −500.000 −0.113329 −0.0566646 − 0.998393i \(-0.518047\pi\)
−0.0566646 + 0.998393i \(0.518047\pi\)
\(270\) 0 0
\(271\) 6538.00 1.46552 0.732759 − 0.680489i \(-0.238232\pi\)
0.732759 + 0.680489i \(0.238232\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −1199.00 −0.262918
\(276\) 0 0
\(277\) 124.000 0.0268969 0.0134484 − 0.999910i \(-0.495719\pi\)
0.0134484 + 0.999910i \(0.495719\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −3642.00 −0.773180 −0.386590 − 0.922252i \(-0.626347\pi\)
−0.386590 + 0.922252i \(0.626347\pi\)
\(282\) 0 0
\(283\) −4648.00 −0.976307 −0.488154 − 0.872758i \(-0.662329\pi\)
−0.488154 + 0.872758i \(0.662329\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −10972.0 −2.25664
\(288\) 0 0
\(289\) 563.000 0.114594
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 3102.00 0.618501 0.309250 − 0.950981i \(-0.399922\pi\)
0.309250 + 0.950981i \(0.399922\pi\)
\(294\) 0 0
\(295\) −800.000 −0.157891
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 5824.00 1.12646
\(300\) 0 0
\(301\) −10608.0 −2.03135
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 528.000 0.0991252
\(306\) 0 0
\(307\) −1244.00 −0.231267 −0.115633 − 0.993292i \(-0.536890\pi\)
−0.115633 + 0.993292i \(0.536890\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 2082.00 0.379612 0.189806 − 0.981822i \(-0.439214\pi\)
0.189806 + 0.981822i \(0.439214\pi\)
\(312\) 0 0
\(313\) 2378.00 0.429433 0.214716 − 0.976676i \(-0.431117\pi\)
0.214716 + 0.976676i \(0.431117\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 496.000 0.0878806 0.0439403 − 0.999034i \(-0.486009\pi\)
0.0439403 + 0.999034i \(0.486009\pi\)
\(318\) 0 0
\(319\) 990.000 0.173760
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −4440.00 −0.764855
\(324\) 0 0
\(325\) 3488.00 0.595321
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −13156.0 −2.20460
\(330\) 0 0
\(331\) 2708.00 0.449683 0.224842 − 0.974395i \(-0.427814\pi\)
0.224842 + 0.974395i \(0.427814\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 4144.00 0.675853
\(336\) 0 0
\(337\) 4034.00 0.652065 0.326033 − 0.945359i \(-0.394288\pi\)
0.326033 + 0.945359i \(0.394288\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 88.0000 0.0139750
\(342\) 0 0
\(343\) −260.000 −0.0409291
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 11084.0 1.71476 0.857378 − 0.514687i \(-0.172092\pi\)
0.857378 + 0.514687i \(0.172092\pi\)
\(348\) 0 0
\(349\) −3120.00 −0.478538 −0.239269 − 0.970953i \(-0.576908\pi\)
−0.239269 + 0.970953i \(0.576908\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 5622.00 0.847674 0.423837 − 0.905739i \(-0.360683\pi\)
0.423837 + 0.905739i \(0.360683\pi\)
\(354\) 0 0
\(355\) 3048.00 0.455693
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −8500.00 −1.24962 −0.624809 − 0.780778i \(-0.714823\pi\)
−0.624809 + 0.780778i \(0.714823\pi\)
\(360\) 0 0
\(361\) −3259.00 −0.475142
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −2168.00 −0.310899
\(366\) 0 0
\(367\) −7144.00 −1.01611 −0.508057 − 0.861324i \(-0.669636\pi\)
−0.508057 + 0.861324i \(0.669636\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −9048.00 −1.26617
\(372\) 0 0
\(373\) −632.000 −0.0877312 −0.0438656 − 0.999037i \(-0.513967\pi\)
−0.0438656 + 0.999037i \(0.513967\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −2880.00 −0.393442
\(378\) 0 0
\(379\) 4220.00 0.571944 0.285972 − 0.958238i \(-0.407684\pi\)
0.285972 + 0.958238i \(0.407684\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 8458.00 1.12842 0.564208 − 0.825632i \(-0.309181\pi\)
0.564208 + 0.825632i \(0.309181\pi\)
\(384\) 0 0
\(385\) 1144.00 0.151438
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −1740.00 −0.226790 −0.113395 − 0.993550i \(-0.536173\pi\)
−0.113395 + 0.993550i \(0.536173\pi\)
\(390\) 0 0
\(391\) 13468.0 1.74196
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 2200.00 0.280238
\(396\) 0 0
\(397\) −5126.00 −0.648027 −0.324013 − 0.946053i \(-0.605032\pi\)
−0.324013 + 0.946053i \(0.605032\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 3098.00 0.385802 0.192901 − 0.981218i \(-0.438210\pi\)
0.192901 + 0.981218i \(0.438210\pi\)
\(402\) 0 0
\(403\) −256.000 −0.0316433
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −726.000 −0.0884189
\(408\) 0 0
\(409\) 6390.00 0.772531 0.386265 − 0.922388i \(-0.373765\pi\)
0.386265 + 0.922388i \(0.373765\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −5200.00 −0.619553
\(414\) 0 0
\(415\) −528.000 −0.0624542
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 9760.00 1.13796 0.568982 − 0.822350i \(-0.307337\pi\)
0.568982 + 0.822350i \(0.307337\pi\)
\(420\) 0 0
\(421\) −5138.00 −0.594800 −0.297400 − 0.954753i \(-0.596119\pi\)
−0.297400 + 0.954753i \(0.596119\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 8066.00 0.920608
\(426\) 0 0
\(427\) 3432.00 0.388960
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −7008.00 −0.783210 −0.391605 − 0.920133i \(-0.628080\pi\)
−0.391605 + 0.920133i \(0.628080\pi\)
\(432\) 0 0
\(433\) 5578.00 0.619080 0.309540 − 0.950886i \(-0.399825\pi\)
0.309540 + 0.950886i \(0.399825\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −10920.0 −1.19536
\(438\) 0 0
\(439\) 10430.0 1.13393 0.566967 − 0.823741i \(-0.308117\pi\)
0.566967 + 0.823741i \(0.308117\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −4432.00 −0.475329 −0.237664 − 0.971347i \(-0.576382\pi\)
−0.237664 + 0.971347i \(0.576382\pi\)
\(444\) 0 0
\(445\) −2280.00 −0.242882
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 6290.00 0.661121 0.330561 − 0.943785i \(-0.392762\pi\)
0.330561 + 0.943785i \(0.392762\pi\)
\(450\) 0 0
\(451\) −4642.00 −0.484664
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −3328.00 −0.342899
\(456\) 0 0
\(457\) 3054.00 0.312604 0.156302 − 0.987709i \(-0.450043\pi\)
0.156302 + 0.987709i \(0.450043\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −12882.0 −1.30146 −0.650732 − 0.759308i \(-0.725538\pi\)
−0.650732 + 0.759308i \(0.725538\pi\)
\(462\) 0 0
\(463\) −6148.00 −0.617110 −0.308555 − 0.951207i \(-0.599845\pi\)
−0.308555 + 0.951207i \(0.599845\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 5124.00 0.507731 0.253866 − 0.967240i \(-0.418298\pi\)
0.253866 + 0.967240i \(0.418298\pi\)
\(468\) 0 0
\(469\) 26936.0 2.65200
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −4488.00 −0.436276
\(474\) 0 0
\(475\) −6540.00 −0.631738
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −16520.0 −1.57582 −0.787910 − 0.615790i \(-0.788837\pi\)
−0.787910 + 0.615790i \(0.788837\pi\)
\(480\) 0 0
\(481\) 2112.00 0.200206
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 56.0000 0.00524295
\(486\) 0 0
\(487\) −524.000 −0.0487571 −0.0243785 − 0.999703i \(-0.507761\pi\)
−0.0243785 + 0.999703i \(0.507761\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −15028.0 −1.38127 −0.690636 − 0.723203i \(-0.742669\pi\)
−0.690636 + 0.723203i \(0.742669\pi\)
\(492\) 0 0
\(493\) −6660.00 −0.608421
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 19812.0 1.78811
\(498\) 0 0
\(499\) −9020.00 −0.809200 −0.404600 − 0.914494i \(-0.632589\pi\)
−0.404600 + 0.914494i \(0.632589\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −14812.0 −1.31299 −0.656495 − 0.754330i \(-0.727962\pi\)
−0.656495 + 0.754330i \(0.727962\pi\)
\(504\) 0 0
\(505\) −6808.00 −0.599905
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −12660.0 −1.10245 −0.551223 − 0.834358i \(-0.685839\pi\)
−0.551223 + 0.834358i \(0.685839\pi\)
\(510\) 0 0
\(511\) −14092.0 −1.21995
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 4528.00 0.387432
\(516\) 0 0
\(517\) −5566.00 −0.473486
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 3738.00 0.314328 0.157164 − 0.987573i \(-0.449765\pi\)
0.157164 + 0.987573i \(0.449765\pi\)
\(522\) 0 0
\(523\) 6352.00 0.531078 0.265539 − 0.964100i \(-0.414450\pi\)
0.265539 + 0.964100i \(0.414450\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −592.000 −0.0489334
\(528\) 0 0
\(529\) 20957.0 1.72245
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 13504.0 1.09742
\(534\) 0 0
\(535\) 2256.00 0.182309
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 3663.00 0.292721
\(540\) 0 0
\(541\) −24728.0 −1.96514 −0.982569 − 0.185898i \(-0.940481\pi\)
−0.982569 + 0.185898i \(0.940481\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −1280.00 −0.100604
\(546\) 0 0
\(547\) 22756.0 1.77875 0.889375 − 0.457178i \(-0.151140\pi\)
0.889375 + 0.457178i \(0.151140\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 5400.00 0.417509
\(552\) 0 0
\(553\) 14300.0 1.09963
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 9526.00 0.724649 0.362325 − 0.932052i \(-0.381983\pi\)
0.362325 + 0.932052i \(0.381983\pi\)
\(558\) 0 0
\(559\) 13056.0 0.987853
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 12068.0 0.903385 0.451692 − 0.892174i \(-0.350820\pi\)
0.451692 + 0.892174i \(0.350820\pi\)
\(564\) 0 0
\(565\) 8568.00 0.637980
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −15090.0 −1.11179 −0.555893 − 0.831254i \(-0.687623\pi\)
−0.555893 + 0.831254i \(0.687623\pi\)
\(570\) 0 0
\(571\) −4412.00 −0.323356 −0.161678 − 0.986844i \(-0.551691\pi\)
−0.161678 + 0.986844i \(0.551691\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 19838.0 1.43879
\(576\) 0 0
\(577\) −3906.00 −0.281818 −0.140909 − 0.990023i \(-0.545002\pi\)
−0.140909 + 0.990023i \(0.545002\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −3432.00 −0.245066
\(582\) 0 0
\(583\) −3828.00 −0.271937
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −12016.0 −0.844895 −0.422448 − 0.906387i \(-0.638829\pi\)
−0.422448 + 0.906387i \(0.638829\pi\)
\(588\) 0 0
\(589\) 480.000 0.0335790
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 11342.0 0.785430 0.392715 − 0.919660i \(-0.371536\pi\)
0.392715 + 0.919660i \(0.371536\pi\)
\(594\) 0 0
\(595\) −7696.00 −0.530261
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 20690.0 1.41130 0.705651 − 0.708559i \(-0.250654\pi\)
0.705651 + 0.708559i \(0.250654\pi\)
\(600\) 0 0
\(601\) −598.000 −0.0405872 −0.0202936 − 0.999794i \(-0.506460\pi\)
−0.0202936 + 0.999794i \(0.506460\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 484.000 0.0325246
\(606\) 0 0
\(607\) 166.000 0.0111001 0.00555003 − 0.999985i \(-0.498233\pi\)
0.00555003 + 0.999985i \(0.498233\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 16192.0 1.07211
\(612\) 0 0
\(613\) 20108.0 1.32488 0.662442 − 0.749113i \(-0.269520\pi\)
0.662442 + 0.749113i \(0.269520\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 2286.00 0.149159 0.0745793 − 0.997215i \(-0.476239\pi\)
0.0745793 + 0.997215i \(0.476239\pi\)
\(618\) 0 0
\(619\) 25660.0 1.66618 0.833088 − 0.553141i \(-0.186571\pi\)
0.833088 + 0.553141i \(0.186571\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −14820.0 −0.953051
\(624\) 0 0
\(625\) 9881.00 0.632384
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 4884.00 0.309599
\(630\) 0 0
\(631\) 11408.0 0.719723 0.359862 − 0.933006i \(-0.382824\pi\)
0.359862 + 0.933006i \(0.382824\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 6424.00 0.401462
\(636\) 0 0
\(637\) −10656.0 −0.662804
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 3378.00 0.208148 0.104074 − 0.994570i \(-0.466812\pi\)
0.104074 + 0.994570i \(0.466812\pi\)
\(642\) 0 0
\(643\) 11212.0 0.687649 0.343824 − 0.939034i \(-0.388278\pi\)
0.343824 + 0.939034i \(0.388278\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −86.0000 −0.00522567 −0.00261284 − 0.999997i \(-0.500832\pi\)
−0.00261284 + 0.999997i \(0.500832\pi\)
\(648\) 0 0
\(649\) −2200.00 −0.133062
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 4432.00 0.265601 0.132801 − 0.991143i \(-0.457603\pi\)
0.132801 + 0.991143i \(0.457603\pi\)
\(654\) 0 0
\(655\) −7632.00 −0.455278
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 4580.00 0.270731 0.135365 − 0.990796i \(-0.456779\pi\)
0.135365 + 0.990796i \(0.456779\pi\)
\(660\) 0 0
\(661\) 4282.00 0.251967 0.125984 − 0.992032i \(-0.459791\pi\)
0.125984 + 0.992032i \(0.459791\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 6240.00 0.363875
\(666\) 0 0
\(667\) −16380.0 −0.950879
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 1452.00 0.0835378
\(672\) 0 0
\(673\) 8438.00 0.483300 0.241650 − 0.970363i \(-0.422311\pi\)
0.241650 + 0.970363i \(0.422311\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −34494.0 −1.95822 −0.979108 − 0.203341i \(-0.934820\pi\)
−0.979108 + 0.203341i \(0.934820\pi\)
\(678\) 0 0
\(679\) 364.000 0.0205730
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −13712.0 −0.768192 −0.384096 − 0.923293i \(-0.625487\pi\)
−0.384096 + 0.923293i \(0.625487\pi\)
\(684\) 0 0
\(685\) 8744.00 0.487724
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 11136.0 0.615744
\(690\) 0 0
\(691\) −11372.0 −0.626066 −0.313033 − 0.949742i \(-0.601345\pi\)
−0.313033 + 0.949742i \(0.601345\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −10960.0 −0.598182
\(696\) 0 0
\(697\) 31228.0 1.69705
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 6398.00 0.344721 0.172360 − 0.985034i \(-0.444861\pi\)
0.172360 + 0.985034i \(0.444861\pi\)
\(702\) 0 0
\(703\) −3960.00 −0.212453
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −44252.0 −2.35399
\(708\) 0 0
\(709\) −5830.00 −0.308816 −0.154408 − 0.988007i \(-0.549347\pi\)
−0.154408 + 0.988007i \(0.549347\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −1456.00 −0.0764763
\(714\) 0 0
\(715\) −1408.00 −0.0736451
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 34530.0 1.79103 0.895516 − 0.445030i \(-0.146807\pi\)
0.895516 + 0.445030i \(0.146807\pi\)
\(720\) 0 0
\(721\) 29432.0 1.52026
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −9810.00 −0.502530
\(726\) 0 0
\(727\) 17316.0 0.883377 0.441688 − 0.897169i \(-0.354380\pi\)
0.441688 + 0.897169i \(0.354380\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 30192.0 1.52762
\(732\) 0 0
\(733\) −27072.0 −1.36416 −0.682079 − 0.731279i \(-0.738924\pi\)
−0.682079 + 0.731279i \(0.738924\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 11396.0 0.569575
\(738\) 0 0
\(739\) 17320.0 0.862147 0.431073 − 0.902317i \(-0.358135\pi\)
0.431073 + 0.902317i \(0.358135\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 14588.0 0.720299 0.360149 − 0.932895i \(-0.382726\pi\)
0.360149 + 0.932895i \(0.382726\pi\)
\(744\) 0 0
\(745\) 5240.00 0.257690
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 14664.0 0.715368
\(750\) 0 0
\(751\) −26152.0 −1.27071 −0.635353 − 0.772222i \(-0.719145\pi\)
−0.635353 + 0.772222i \(0.719145\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 4792.00 0.230992
\(756\) 0 0
\(757\) −1066.00 −0.0511815 −0.0255908 − 0.999673i \(-0.508147\pi\)
−0.0255908 + 0.999673i \(0.508147\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 37518.0 1.78716 0.893578 − 0.448907i \(-0.148187\pi\)
0.893578 + 0.448907i \(0.148187\pi\)
\(762\) 0 0
\(763\) −8320.00 −0.394763
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 6400.00 0.301292
\(768\) 0 0
\(769\) −17290.0 −0.810785 −0.405392 − 0.914143i \(-0.632865\pi\)
−0.405392 + 0.914143i \(0.632865\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 17172.0 0.799009 0.399504 − 0.916731i \(-0.369182\pi\)
0.399504 + 0.916731i \(0.369182\pi\)
\(774\) 0 0
\(775\) −872.000 −0.0404170
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −25320.0 −1.16455
\(780\) 0 0
\(781\) 8382.00 0.384035
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 8456.00 0.384468
\(786\) 0 0
\(787\) 9536.00 0.431921 0.215960 − 0.976402i \(-0.430712\pi\)
0.215960 + 0.976402i \(0.430712\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 55692.0 2.50339
\(792\) 0 0
\(793\) −4224.00 −0.189153
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 20516.0 0.911812 0.455906 − 0.890028i \(-0.349315\pi\)
0.455906 + 0.890028i \(0.349315\pi\)
\(798\) 0 0
\(799\) 37444.0 1.65791
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −5962.00 −0.262010
\(804\) 0 0
\(805\) −18928.0 −0.828726
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −22470.0 −0.976518 −0.488259 − 0.872699i \(-0.662368\pi\)
−0.488259 + 0.872699i \(0.662368\pi\)
\(810\) 0 0
\(811\) 3368.00 0.145828 0.0729140 − 0.997338i \(-0.476770\pi\)
0.0729140 + 0.997338i \(0.476770\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −15472.0 −0.664982
\(816\) 0 0
\(817\) −24480.0 −1.04828
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 10738.0 0.456466 0.228233 − 0.973607i \(-0.426705\pi\)
0.228233 + 0.973607i \(0.426705\pi\)
\(822\) 0 0
\(823\) 15912.0 0.673946 0.336973 − 0.941514i \(-0.390597\pi\)
0.336973 + 0.941514i \(0.390597\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 22924.0 0.963900 0.481950 − 0.876199i \(-0.339929\pi\)
0.481950 + 0.876199i \(0.339929\pi\)
\(828\) 0 0
\(829\) −41690.0 −1.74663 −0.873313 − 0.487159i \(-0.838033\pi\)
−0.873313 + 0.487159i \(0.838033\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −24642.0 −1.02496
\(834\) 0 0
\(835\) 8016.00 0.332222
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −16450.0 −0.676898 −0.338449 − 0.940985i \(-0.609902\pi\)
−0.338449 + 0.940985i \(0.609902\pi\)
\(840\) 0 0
\(841\) −16289.0 −0.667883
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −4692.00 −0.191017
\(846\) 0 0
\(847\) 3146.00 0.127624
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 12012.0 0.483861
\(852\) 0 0
\(853\) −30892.0 −1.24000 −0.620001 − 0.784601i \(-0.712868\pi\)
−0.620001 + 0.784601i \(0.712868\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 38906.0 1.55076 0.775381 − 0.631493i \(-0.217558\pi\)
0.775381 + 0.631493i \(0.217558\pi\)
\(858\) 0 0
\(859\) 1020.00 0.0405145 0.0202572 − 0.999795i \(-0.493551\pi\)
0.0202572 + 0.999795i \(0.493551\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 15078.0 0.594741 0.297370 − 0.954762i \(-0.403890\pi\)
0.297370 + 0.954762i \(0.403890\pi\)
\(864\) 0 0
\(865\) −2712.00 −0.106602
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 6050.00 0.236171
\(870\) 0 0
\(871\) −33152.0 −1.28968
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −24336.0 −0.940237
\(876\) 0 0
\(877\) 22704.0 0.874184 0.437092 − 0.899417i \(-0.356008\pi\)
0.437092 + 0.899417i \(0.356008\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 19358.0 0.740281 0.370141 − 0.928976i \(-0.379310\pi\)
0.370141 + 0.928976i \(0.379310\pi\)
\(882\) 0 0
\(883\) 11252.0 0.428833 0.214417 − 0.976742i \(-0.431215\pi\)
0.214417 + 0.976742i \(0.431215\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 43684.0 1.65362 0.826812 − 0.562478i \(-0.190152\pi\)
0.826812 + 0.562478i \(0.190152\pi\)
\(888\) 0 0
\(889\) 41756.0 1.57531
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −30360.0 −1.13769
\(894\) 0 0
\(895\) −6720.00 −0.250977
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 720.000 0.0267112
\(900\) 0 0
\(901\) 25752.0 0.952190
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −17432.0 −0.640287
\(906\) 0 0
\(907\) −45804.0 −1.67684 −0.838422 − 0.545022i \(-0.816521\pi\)
−0.838422 + 0.545022i \(0.816521\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −15318.0 −0.557089 −0.278544 − 0.960423i \(-0.589852\pi\)
−0.278544 + 0.960423i \(0.589852\pi\)
\(912\) 0 0
\(913\) −1452.00 −0.0526333
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −49608.0 −1.78648
\(918\) 0 0
\(919\) −11350.0 −0.407401 −0.203701 − 0.979033i \(-0.565297\pi\)
−0.203701 + 0.979033i \(0.565297\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −24384.0 −0.869566
\(924\) 0 0
\(925\) 7194.00 0.255716
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −33030.0 −1.16650 −0.583250 − 0.812292i \(-0.698219\pi\)
−0.583250 + 0.812292i \(0.698219\pi\)
\(930\) 0 0
\(931\) 19980.0 0.703349
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −3256.00 −0.113885
\(936\) 0 0
\(937\) −10006.0 −0.348860 −0.174430 − 0.984670i \(-0.555808\pi\)
−0.174430 + 0.984670i \(0.555808\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −2622.00 −0.0908340 −0.0454170 − 0.998968i \(-0.514462\pi\)
−0.0454170 + 0.998968i \(0.514462\pi\)
\(942\) 0 0
\(943\) 76804.0 2.65226
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −39876.0 −1.36832 −0.684158 − 0.729334i \(-0.739830\pi\)
−0.684158 + 0.729334i \(0.739830\pi\)
\(948\) 0 0
\(949\) 17344.0 0.593267
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −38918.0 −1.32285 −0.661426 − 0.750011i \(-0.730048\pi\)
−0.661426 + 0.750011i \(0.730048\pi\)
\(954\) 0 0
\(955\) −7112.00 −0.240983
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 56836.0 1.91380
\(960\) 0 0
\(961\) −29727.0 −0.997852
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −15848.0 −0.528669
\(966\) 0 0
\(967\) −1114.00 −0.0370464 −0.0185232 − 0.999828i \(-0.505896\pi\)
−0.0185232 + 0.999828i \(0.505896\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −1688.00 −0.0557884 −0.0278942 − 0.999611i \(-0.508880\pi\)
−0.0278942 + 0.999611i \(0.508880\pi\)
\(972\) 0 0
\(973\) −71240.0 −2.34722
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 41826.0 1.36963 0.684817 − 0.728715i \(-0.259882\pi\)
0.684817 + 0.728715i \(0.259882\pi\)
\(978\) 0 0
\(979\) −6270.00 −0.204689
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 978.000 0.0317328 0.0158664 − 0.999874i \(-0.494949\pi\)
0.0158664 + 0.999874i \(0.494949\pi\)
\(984\) 0 0
\(985\) −1496.00 −0.0483924
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 74256.0 2.38747
\(990\) 0 0
\(991\) −47272.0 −1.51528 −0.757641 − 0.652671i \(-0.773648\pi\)
−0.757641 + 0.652671i \(0.773648\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −8400.00 −0.267636
\(996\) 0 0
\(997\) 51104.0 1.62335 0.811675 − 0.584109i \(-0.198556\pi\)
0.811675 + 0.584109i \(0.198556\pi\)
\(998\) 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.l.1.1 1
3.2 odd 2 528.4.a.h.1.1 1
4.3 odd 2 99.4.a.a.1.1 1
12.11 even 2 33.4.a.b.1.1 ✓ 1
20.19 odd 2 2475.4.a.e.1.1 1
24.5 odd 2 2112.4.a.h.1.1 1
24.11 even 2 2112.4.a.u.1.1 1
44.43 even 2 1089.4.a.e.1.1 1
60.23 odd 4 825.4.c.f.199.2 2
60.47 odd 4 825.4.c.f.199.1 2
60.59 even 2 825.4.a.f.1.1 1
84.83 odd 2 1617.4.a.d.1.1 1
132.131 odd 2 363.4.a.d.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
33.4.a.b.1.1 ✓ 1 12.11 even 2
99.4.a.a.1.1 1 4.3 odd 2
363.4.a.d.1.1 1 132.131 odd 2
528.4.a.h.1.1 1 3.2 odd 2
825.4.a.f.1.1 1 60.59 even 2
825.4.c.f.199.1 2 60.47 odd 4
825.4.c.f.199.2 2 60.23 odd 4
1089.4.a.e.1.1 1 44.43 even 2
1584.4.a.l.1.1 1 1.1 even 1 trivial
1617.4.a.d.1.1 1 84.83 odd 2
2112.4.a.h.1.1 1 24.5 odd 2
2112.4.a.u.1.1 1 24.11 even 2
2475.4.a.e.1.1 1 20.19 odd 2