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Properties

Label 1584.4.a.v.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 22)
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)
 
\(f(q)\) \(=\) \(q+19.0000 q^{5} -14.0000 q^{7} +O(q^{10})\) \(q+19.0000 q^{5} -14.0000 q^{7} +11.0000 q^{11} -72.0000 q^{13} +46.0000 q^{17} +20.0000 q^{19} -107.000 q^{23} +236.000 q^{25} -120.000 q^{29} -117.000 q^{31} -266.000 q^{35} -201.000 q^{37} +228.000 q^{41} +242.000 q^{43} -96.0000 q^{47} -147.000 q^{49} -458.000 q^{53} +209.000 q^{55} +435.000 q^{59} -668.000 q^{61} -1368.00 q^{65} -439.000 q^{67} -1113.00 q^{71} -72.0000 q^{73} -154.000 q^{77} +70.0000 q^{79} +358.000 q^{83} +874.000 q^{85} -895.000 q^{89} +1008.00 q^{91} +380.000 q^{95} +409.000 q^{97} +O(q^{100})\)

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
\(5\) 19.0000 1.69941 0.849706 − 0.527257i \(-0.176780\pi\)
0.849706 + 0.527257i \(0.176780\pi\)
\(6\) 0 0
\(7\) −14.0000 −0.755929 −0.377964 − 0.925820i \(-0.623376\pi\)
−0.377964 + 0.925820i \(0.623376\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 11.0000 0.301511
\(12\) 0 0
\(13\) −72.0000 −1.53609 −0.768046 − 0.640394i \(-0.778771\pi\)
−0.768046 + 0.640394i \(0.778771\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 46.0000 0.656273 0.328136 − 0.944630i \(-0.393579\pi\)
0.328136 + 0.944630i \(0.393579\pi\)
\(18\) 0 0
\(19\) 20.0000 0.241490 0.120745 − 0.992684i \(-0.461472\pi\)
0.120745 + 0.992684i \(0.461472\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −107.000 −0.970045 −0.485023 − 0.874502i \(-0.661189\pi\)
−0.485023 + 0.874502i \(0.661189\pi\)
\(24\) 0 0
\(25\) 236.000 1.88800
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −120.000 −0.768395 −0.384197 − 0.923251i \(-0.625522\pi\)
−0.384197 + 0.923251i \(0.625522\pi\)
\(30\) 0 0
\(31\) −117.000 −0.677865 −0.338933 − 0.940811i \(-0.610066\pi\)
−0.338933 + 0.940811i \(0.610066\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −266.000 −1.28463
\(36\) 0 0
\(37\) −201.000 −0.893086 −0.446543 − 0.894762i \(-0.647345\pi\)
−0.446543 + 0.894762i \(0.647345\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 228.000 0.868478 0.434239 − 0.900798i \(-0.357017\pi\)
0.434239 + 0.900798i \(0.357017\pi\)
\(42\) 0 0
\(43\) 242.000 0.858248 0.429124 − 0.903246i \(-0.358822\pi\)
0.429124 + 0.903246i \(0.358822\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −96.0000 −0.297937 −0.148969 − 0.988842i \(-0.547595\pi\)
−0.148969 + 0.988842i \(0.547595\pi\)
\(48\) 0 0
\(49\) −147.000 −0.428571
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −458.000 −1.18700 −0.593501 − 0.804833i \(-0.702255\pi\)
−0.593501 + 0.804833i \(0.702255\pi\)
\(54\) 0 0
\(55\) 209.000 0.512392
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 435.000 0.959867 0.479934 − 0.877305i \(-0.340661\pi\)
0.479934 + 0.877305i \(0.340661\pi\)
\(60\) 0 0
\(61\) −668.000 −1.40211 −0.701054 − 0.713108i \(-0.747287\pi\)
−0.701054 + 0.713108i \(0.747287\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −1368.00 −2.61045
\(66\) 0 0
\(67\) −439.000 −0.800483 −0.400242 − 0.916410i \(-0.631074\pi\)
−0.400242 + 0.916410i \(0.631074\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −1113.00 −1.86041 −0.930203 − 0.367046i \(-0.880369\pi\)
−0.930203 + 0.367046i \(0.880369\pi\)
\(72\) 0 0
\(73\) −72.0000 −0.115438 −0.0577189 − 0.998333i \(-0.518383\pi\)
−0.0577189 + 0.998333i \(0.518383\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −154.000 −0.227921
\(78\) 0 0
\(79\) 70.0000 0.0996913 0.0498457 − 0.998757i \(-0.484127\pi\)
0.0498457 + 0.998757i \(0.484127\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 358.000 0.473441 0.236721 − 0.971578i \(-0.423927\pi\)
0.236721 + 0.971578i \(0.423927\pi\)
\(84\) 0 0
\(85\) 874.000 1.11528
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −895.000 −1.06595 −0.532976 − 0.846130i \(-0.678927\pi\)
−0.532976 + 0.846130i \(0.678927\pi\)
\(90\) 0 0
\(91\) 1008.00 1.16118
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 380.000 0.410391
\(96\) 0 0
\(97\) 409.000 0.428120 0.214060 − 0.976820i \(-0.431331\pi\)
0.214060 + 0.976820i \(0.431331\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 898.000 0.884696 0.442348 − 0.896843i \(-0.354146\pi\)
0.442348 + 0.896843i \(0.354146\pi\)
\(102\) 0 0
\(103\) 312.000 0.298469 0.149234 − 0.988802i \(-0.452319\pi\)
0.149234 + 0.988802i \(0.452319\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 274.000 0.247557 0.123778 − 0.992310i \(-0.460499\pi\)
0.123778 + 0.992310i \(0.460499\pi\)
\(108\) 0 0
\(109\) −1470.00 −1.29175 −0.645874 − 0.763444i \(-0.723507\pi\)
−0.645874 + 0.763444i \(0.723507\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −113.000 −0.0940721 −0.0470360 − 0.998893i \(-0.514978\pi\)
−0.0470360 + 0.998893i \(0.514978\pi\)
\(114\) 0 0
\(115\) −2033.00 −1.64851
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −644.000 −0.496096
\(120\) 0 0
\(121\) 121.000 0.0909091
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 2109.00 1.50908
\(126\) 0 0
\(127\) 1476.00 1.03129 0.515645 − 0.856802i \(-0.327552\pi\)
0.515645 + 0.856802i \(0.327552\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 1342.00 0.895046 0.447523 − 0.894272i \(-0.352306\pi\)
0.447523 + 0.894272i \(0.352306\pi\)
\(132\) 0 0
\(133\) −280.000 −0.182549
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −1769.00 −1.10318 −0.551591 − 0.834115i \(-0.685979\pi\)
−0.551591 + 0.834115i \(0.685979\pi\)
\(138\) 0 0
\(139\) 550.000 0.335614 0.167807 − 0.985820i \(-0.446331\pi\)
0.167807 + 0.985820i \(0.446331\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −792.000 −0.463149
\(144\) 0 0
\(145\) −2280.00 −1.30582
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 790.000 0.434358 0.217179 − 0.976132i \(-0.430314\pi\)
0.217179 + 0.976132i \(0.430314\pi\)
\(150\) 0 0
\(151\) −2902.00 −1.56398 −0.781991 − 0.623289i \(-0.785796\pi\)
−0.781991 + 0.623289i \(0.785796\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −2223.00 −1.15197
\(156\) 0 0
\(157\) 749.000 0.380743 0.190372 − 0.981712i \(-0.439031\pi\)
0.190372 + 0.981712i \(0.439031\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 1498.00 0.733285
\(162\) 0 0
\(163\) −1228.00 −0.590088 −0.295044 − 0.955484i \(-0.595334\pi\)
−0.295044 + 0.955484i \(0.595334\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 2424.00 1.12320 0.561601 − 0.827408i \(-0.310186\pi\)
0.561601 + 0.827408i \(0.310186\pi\)
\(168\) 0 0
\(169\) 2987.00 1.35958
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 3742.00 1.64450 0.822251 − 0.569124i \(-0.192718\pi\)
0.822251 + 0.569124i \(0.192718\pi\)
\(174\) 0 0
\(175\) −3304.00 −1.42719
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −265.000 −0.110654 −0.0553269 − 0.998468i \(-0.517620\pi\)
−0.0553269 + 0.998468i \(0.517620\pi\)
\(180\) 0 0
\(181\) 67.0000 0.0275142 0.0137571 − 0.999905i \(-0.495621\pi\)
0.0137571 + 0.999905i \(0.495621\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −3819.00 −1.51772
\(186\) 0 0
\(187\) 506.000 0.197874
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −3453.00 −1.30812 −0.654058 − 0.756444i \(-0.726935\pi\)
−0.654058 + 0.756444i \(0.726935\pi\)
\(192\) 0 0
\(193\) −4172.00 −1.55600 −0.777998 − 0.628267i \(-0.783765\pi\)
−0.777998 + 0.628267i \(0.783765\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 2426.00 0.877388 0.438694 − 0.898637i \(-0.355441\pi\)
0.438694 + 0.898637i \(0.355441\pi\)
\(198\) 0 0
\(199\) 400.000 0.142489 0.0712443 − 0.997459i \(-0.477303\pi\)
0.0712443 + 0.997459i \(0.477303\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 1680.00 0.580852
\(204\) 0 0
\(205\) 4332.00 1.47590
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 220.000 0.0728120
\(210\) 0 0
\(211\) −3332.00 −1.08713 −0.543565 − 0.839367i \(-0.682926\pi\)
−0.543565 + 0.839367i \(0.682926\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 4598.00 1.45852
\(216\) 0 0
\(217\) 1638.00 0.512418
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −3312.00 −1.00810
\(222\) 0 0
\(223\) −6033.00 −1.81166 −0.905829 − 0.423644i \(-0.860751\pi\)
−0.905829 + 0.423644i \(0.860751\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −5646.00 −1.65083 −0.825414 − 0.564527i \(-0.809059\pi\)
−0.825414 + 0.564527i \(0.809059\pi\)
\(228\) 0 0
\(229\) −4645.00 −1.34039 −0.670197 − 0.742183i \(-0.733790\pi\)
−0.670197 + 0.742183i \(0.733790\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 2432.00 0.683801 0.341900 − 0.939736i \(-0.388929\pi\)
0.341900 + 0.939736i \(0.388929\pi\)
\(234\) 0 0
\(235\) −1824.00 −0.506318
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −6010.00 −1.62659 −0.813294 − 0.581853i \(-0.802328\pi\)
−0.813294 + 0.581853i \(0.802328\pi\)
\(240\) 0 0
\(241\) −3728.00 −0.996438 −0.498219 − 0.867051i \(-0.666012\pi\)
−0.498219 + 0.867051i \(0.666012\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −2793.00 −0.728319
\(246\) 0 0
\(247\) −1440.00 −0.370951
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 527.000 0.132526 0.0662628 − 0.997802i \(-0.478892\pi\)
0.0662628 + 0.997802i \(0.478892\pi\)
\(252\) 0 0
\(253\) −1177.00 −0.292480
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 1786.00 0.433493 0.216746 − 0.976228i \(-0.430456\pi\)
0.216746 + 0.976228i \(0.430456\pi\)
\(258\) 0 0
\(259\) 2814.00 0.675110
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 3198.00 0.749799 0.374899 − 0.927065i \(-0.377677\pi\)
0.374899 + 0.927065i \(0.377677\pi\)
\(264\) 0 0
\(265\) −8702.00 −2.01721
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 1630.00 0.369453 0.184726 − 0.982790i \(-0.440860\pi\)
0.184726 + 0.982790i \(0.440860\pi\)
\(270\) 0 0
\(271\) 3688.00 0.826679 0.413340 − 0.910577i \(-0.364362\pi\)
0.413340 + 0.910577i \(0.364362\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 2596.00 0.569253
\(276\) 0 0
\(277\) 5294.00 1.14832 0.574162 − 0.818742i \(-0.305328\pi\)
0.574162 + 0.818742i \(0.305328\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −5942.00 −1.26146 −0.630730 − 0.776003i \(-0.717244\pi\)
−0.630730 + 0.776003i \(0.717244\pi\)
\(282\) 0 0
\(283\) 6572.00 1.38044 0.690221 − 0.723599i \(-0.257513\pi\)
0.690221 + 0.723599i \(0.257513\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −3192.00 −0.656508
\(288\) 0 0
\(289\) −2797.00 −0.569306
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −5668.00 −1.13013 −0.565065 − 0.825046i \(-0.691149\pi\)
−0.565065 + 0.825046i \(0.691149\pi\)
\(294\) 0 0
\(295\) 8265.00 1.63121
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 7704.00 1.49008
\(300\) 0 0
\(301\) −3388.00 −0.648774
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −12692.0 −2.38276
\(306\) 0 0
\(307\) −9844.00 −1.83005 −0.915027 − 0.403392i \(-0.867831\pi\)
−0.915027 + 0.403392i \(0.867831\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −6068.00 −1.10638 −0.553191 − 0.833055i \(-0.686590\pi\)
−0.553191 + 0.833055i \(0.686590\pi\)
\(312\) 0 0
\(313\) 3743.00 0.675932 0.337966 − 0.941158i \(-0.390261\pi\)
0.337966 + 0.941158i \(0.390261\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −6849.00 −1.21350 −0.606748 − 0.794894i \(-0.707526\pi\)
−0.606748 + 0.794894i \(0.707526\pi\)
\(318\) 0 0
\(319\) −1320.00 −0.231680
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 920.000 0.158483
\(324\) 0 0
\(325\) −16992.0 −2.90014
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 1344.00 0.225219
\(330\) 0 0
\(331\) −9617.00 −1.59697 −0.798487 − 0.602013i \(-0.794366\pi\)
−0.798487 + 0.602013i \(0.794366\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −8341.00 −1.36035
\(336\) 0 0
\(337\) −1026.00 −0.165845 −0.0829225 − 0.996556i \(-0.526425\pi\)
−0.0829225 + 0.996556i \(0.526425\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −1287.00 −0.204384
\(342\) 0 0
\(343\) 6860.00 1.07990
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −2536.00 −0.392333 −0.196167 − 0.980571i \(-0.562849\pi\)
−0.196167 + 0.980571i \(0.562849\pi\)
\(348\) 0 0
\(349\) 7770.00 1.19174 0.595872 − 0.803080i \(-0.296807\pi\)
0.595872 + 0.803080i \(0.296807\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 9597.00 1.44702 0.723508 − 0.690316i \(-0.242528\pi\)
0.723508 + 0.690316i \(0.242528\pi\)
\(354\) 0 0
\(355\) −21147.0 −3.16159
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 5760.00 0.846800 0.423400 − 0.905943i \(-0.360837\pi\)
0.423400 + 0.905943i \(0.360837\pi\)
\(360\) 0 0
\(361\) −6459.00 −0.941682
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −1368.00 −0.196176
\(366\) 0 0
\(367\) 1891.00 0.268963 0.134481 − 0.990916i \(-0.457063\pi\)
0.134481 + 0.990916i \(0.457063\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 6412.00 0.897290
\(372\) 0 0
\(373\) −11582.0 −1.60776 −0.803878 − 0.594794i \(-0.797234\pi\)
−0.803878 + 0.594794i \(0.797234\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 8640.00 1.18033
\(378\) 0 0
\(379\) −1925.00 −0.260899 −0.130449 − 0.991455i \(-0.541642\pi\)
−0.130449 + 0.991455i \(0.541642\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −3307.00 −0.441201 −0.220600 − 0.975364i \(-0.570802\pi\)
−0.220600 + 0.975364i \(0.570802\pi\)
\(384\) 0 0
\(385\) −2926.00 −0.387332
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 7275.00 0.948219 0.474109 − 0.880466i \(-0.342770\pi\)
0.474109 + 0.880466i \(0.342770\pi\)
\(390\) 0 0
\(391\) −4922.00 −0.636614
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 1330.00 0.169417
\(396\) 0 0
\(397\) 11374.0 1.43790 0.718948 − 0.695064i \(-0.244624\pi\)
0.718948 + 0.695064i \(0.244624\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 4598.00 0.572601 0.286301 − 0.958140i \(-0.407574\pi\)
0.286301 + 0.958140i \(0.407574\pi\)
\(402\) 0 0
\(403\) 8424.00 1.04126
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −2211.00 −0.269276
\(408\) 0 0
\(409\) 9970.00 1.20534 0.602671 − 0.797990i \(-0.294103\pi\)
0.602671 + 0.797990i \(0.294103\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −6090.00 −0.725592
\(414\) 0 0
\(415\) 6802.00 0.804571
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −8940.00 −1.04236 −0.521178 − 0.853448i \(-0.674507\pi\)
−0.521178 + 0.853448i \(0.674507\pi\)
\(420\) 0 0
\(421\) 5462.00 0.632308 0.316154 − 0.948708i \(-0.397608\pi\)
0.316154 + 0.948708i \(0.397608\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 10856.0 1.23904
\(426\) 0 0
\(427\) 9352.00 1.05989
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 3942.00 0.440556 0.220278 − 0.975437i \(-0.429304\pi\)
0.220278 + 0.975437i \(0.429304\pi\)
\(432\) 0 0
\(433\) 12773.0 1.41762 0.708812 − 0.705397i \(-0.249231\pi\)
0.708812 + 0.705397i \(0.249231\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −2140.00 −0.234256
\(438\) 0 0
\(439\) 4880.00 0.530546 0.265273 − 0.964173i \(-0.414538\pi\)
0.265273 + 0.964173i \(0.414538\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −13277.0 −1.42395 −0.711974 − 0.702205i \(-0.752199\pi\)
−0.711974 + 0.702205i \(0.752199\pi\)
\(444\) 0 0
\(445\) −17005.0 −1.81149
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 4885.00 0.513446 0.256723 − 0.966485i \(-0.417357\pi\)
0.256723 + 0.966485i \(0.417357\pi\)
\(450\) 0 0
\(451\) 2508.00 0.261856
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 19152.0 1.97332
\(456\) 0 0
\(457\) 17884.0 1.83059 0.915293 − 0.402788i \(-0.131959\pi\)
0.915293 + 0.402788i \(0.131959\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −4532.00 −0.457866 −0.228933 − 0.973442i \(-0.573524\pi\)
−0.228933 + 0.973442i \(0.573524\pi\)
\(462\) 0 0
\(463\) 1977.00 0.198443 0.0992214 − 0.995065i \(-0.468365\pi\)
0.0992214 + 0.995065i \(0.468365\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 7179.00 0.711359 0.355679 − 0.934608i \(-0.384250\pi\)
0.355679 + 0.934608i \(0.384250\pi\)
\(468\) 0 0
\(469\) 6146.00 0.605109
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 2662.00 0.258771
\(474\) 0 0
\(475\) 4720.00 0.455934
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −3600.00 −0.343399 −0.171700 − 0.985149i \(-0.554926\pi\)
−0.171700 + 0.985149i \(0.554926\pi\)
\(480\) 0 0
\(481\) 14472.0 1.37186
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 7771.00 0.727552
\(486\) 0 0
\(487\) 9691.00 0.901727 0.450864 − 0.892593i \(-0.351116\pi\)
0.450864 + 0.892593i \(0.351116\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 14072.0 1.29340 0.646701 − 0.762744i \(-0.276148\pi\)
0.646701 + 0.762744i \(0.276148\pi\)
\(492\) 0 0
\(493\) −5520.00 −0.504276
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 15582.0 1.40633
\(498\) 0 0
\(499\) −3980.00 −0.357053 −0.178526 − 0.983935i \(-0.557133\pi\)
−0.178526 + 0.983935i \(0.557133\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −2182.00 −0.193421 −0.0967103 − 0.995313i \(-0.530832\pi\)
−0.0967103 + 0.995313i \(0.530832\pi\)
\(504\) 0 0
\(505\) 17062.0 1.50346
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −15875.0 −1.38241 −0.691205 − 0.722658i \(-0.742920\pi\)
−0.691205 + 0.722658i \(0.742920\pi\)
\(510\) 0 0
\(511\) 1008.00 0.0872628
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 5928.00 0.507221
\(516\) 0 0
\(517\) −1056.00 −0.0898314
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −6837.00 −0.574922 −0.287461 − 0.957792i \(-0.592811\pi\)
−0.287461 + 0.957792i \(0.592811\pi\)
\(522\) 0 0
\(523\) 17212.0 1.43906 0.719530 − 0.694462i \(-0.244357\pi\)
0.719530 + 0.694462i \(0.244357\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −5382.00 −0.444865
\(528\) 0 0
\(529\) −718.000 −0.0590121
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −16416.0 −1.33406
\(534\) 0 0
\(535\) 5206.00 0.420701
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −1617.00 −0.129219
\(540\) 0 0
\(541\) −22028.0 −1.75057 −0.875284 − 0.483609i \(-0.839326\pi\)
−0.875284 + 0.483609i \(0.839326\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −27930.0 −2.19521
\(546\) 0 0
\(547\) 19696.0 1.53956 0.769781 − 0.638308i \(-0.220366\pi\)
0.769781 + 0.638308i \(0.220366\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −2400.00 −0.185560
\(552\) 0 0
\(553\) −980.000 −0.0753596
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 11886.0 0.904176 0.452088 − 0.891973i \(-0.350679\pi\)
0.452088 + 0.891973i \(0.350679\pi\)
\(558\) 0 0
\(559\) −17424.0 −1.31835
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −12572.0 −0.941113 −0.470557 − 0.882370i \(-0.655947\pi\)
−0.470557 + 0.882370i \(0.655947\pi\)
\(564\) 0 0
\(565\) −2147.00 −0.159867
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 12920.0 0.951906 0.475953 − 0.879471i \(-0.342103\pi\)
0.475953 + 0.879471i \(0.342103\pi\)
\(570\) 0 0
\(571\) −412.000 −0.0301956 −0.0150978 − 0.999886i \(-0.504806\pi\)
−0.0150978 + 0.999886i \(0.504806\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −25252.0 −1.83145
\(576\) 0 0
\(577\) 22649.0 1.63413 0.817063 − 0.576549i \(-0.195601\pi\)
0.817063 + 0.576549i \(0.195601\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −5012.00 −0.357888
\(582\) 0 0
\(583\) −5038.00 −0.357895
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −24276.0 −1.70695 −0.853473 − 0.521136i \(-0.825508\pi\)
−0.853473 + 0.521136i \(0.825508\pi\)
\(588\) 0 0
\(589\) −2340.00 −0.163698
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 14292.0 0.989717 0.494858 − 0.868974i \(-0.335220\pi\)
0.494858 + 0.868974i \(0.335220\pi\)
\(594\) 0 0
\(595\) −12236.0 −0.843071
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 18360.0 1.25237 0.626185 − 0.779675i \(-0.284616\pi\)
0.626185 + 0.779675i \(0.284616\pi\)
\(600\) 0 0
\(601\) −98.0000 −0.00665142 −0.00332571 − 0.999994i \(-0.501059\pi\)
−0.00332571 + 0.999994i \(0.501059\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 2299.00 0.154492
\(606\) 0 0
\(607\) −22054.0 −1.47470 −0.737351 − 0.675510i \(-0.763924\pi\)
−0.737351 + 0.675510i \(0.763924\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 6912.00 0.457659
\(612\) 0 0
\(613\) 288.000 0.0189759 0.00948794 − 0.999955i \(-0.496980\pi\)
0.00948794 + 0.999955i \(0.496980\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 5086.00 0.331855 0.165928 − 0.986138i \(-0.446938\pi\)
0.165928 + 0.986138i \(0.446938\pi\)
\(618\) 0 0
\(619\) −27305.0 −1.77299 −0.886495 − 0.462738i \(-0.846867\pi\)
−0.886495 + 0.462738i \(0.846867\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 12530.0 0.805785
\(624\) 0 0
\(625\) 10571.0 0.676544
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −9246.00 −0.586108
\(630\) 0 0
\(631\) −1117.00 −0.0704708 −0.0352354 − 0.999379i \(-0.511218\pi\)
−0.0352354 + 0.999379i \(0.511218\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 28044.0 1.75259
\(636\) 0 0
\(637\) 10584.0 0.658326
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −10047.0 −0.619084 −0.309542 − 0.950886i \(-0.600176\pi\)
−0.309542 + 0.950886i \(0.600176\pi\)
\(642\) 0 0
\(643\) 4597.00 0.281941 0.140970 − 0.990014i \(-0.454978\pi\)
0.140970 + 0.990014i \(0.454978\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 1859.00 0.112960 0.0564798 − 0.998404i \(-0.482012\pi\)
0.0564798 + 0.998404i \(0.482012\pi\)
\(648\) 0 0
\(649\) 4785.00 0.289411
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 837.000 0.0501598 0.0250799 − 0.999685i \(-0.492016\pi\)
0.0250799 + 0.999685i \(0.492016\pi\)
\(654\) 0 0
\(655\) 25498.0 1.52105
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −4770.00 −0.281962 −0.140981 − 0.990012i \(-0.545026\pi\)
−0.140981 + 0.990012i \(0.545026\pi\)
\(660\) 0 0
\(661\) −2343.00 −0.137870 −0.0689351 − 0.997621i \(-0.521960\pi\)
−0.0689351 + 0.997621i \(0.521960\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −5320.00 −0.310227
\(666\) 0 0
\(667\) 12840.0 0.745377
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −7348.00 −0.422752
\(672\) 0 0
\(673\) −18802.0 −1.07692 −0.538458 − 0.842653i \(-0.680993\pi\)
−0.538458 + 0.842653i \(0.680993\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −874.000 −0.0496168 −0.0248084 − 0.999692i \(-0.507898\pi\)
−0.0248084 + 0.999692i \(0.507898\pi\)
\(678\) 0 0
\(679\) −5726.00 −0.323628
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 30888.0 1.73045 0.865224 − 0.501385i \(-0.167176\pi\)
0.865224 + 0.501385i \(0.167176\pi\)
\(684\) 0 0
\(685\) −33611.0 −1.87476
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 32976.0 1.82335
\(690\) 0 0
\(691\) −4647.00 −0.255832 −0.127916 − 0.991785i \(-0.540829\pi\)
−0.127916 + 0.991785i \(0.540829\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 10450.0 0.570347
\(696\) 0 0
\(697\) 10488.0 0.569959
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 7698.00 0.414764 0.207382 − 0.978260i \(-0.433506\pi\)
0.207382 + 0.978260i \(0.433506\pi\)
\(702\) 0 0
\(703\) −4020.00 −0.215672
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −12572.0 −0.668768
\(708\) 0 0
\(709\) −18285.0 −0.968558 −0.484279 − 0.874914i \(-0.660918\pi\)
−0.484279 + 0.874914i \(0.660918\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 12519.0 0.657560
\(714\) 0 0
\(715\) −15048.0 −0.787082
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 19365.0 1.00444 0.502220 − 0.864740i \(-0.332517\pi\)
0.502220 + 0.864740i \(0.332517\pi\)
\(720\) 0 0
\(721\) −4368.00 −0.225621
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −28320.0 −1.45073
\(726\) 0 0
\(727\) −9.00000 −0.000459136 0 −0.000229568 − 1.00000i \(-0.500073\pi\)
−0.000229568 1.00000i \(0.500073\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 11132.0 0.563245
\(732\) 0 0
\(733\) 25748.0 1.29744 0.648720 − 0.761027i \(-0.275304\pi\)
0.648720 + 0.761027i \(0.275304\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −4829.00 −0.241355
\(738\) 0 0
\(739\) 22690.0 1.12945 0.564726 − 0.825278i \(-0.308982\pi\)
0.564726 + 0.825278i \(0.308982\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 3628.00 0.179136 0.0895682 − 0.995981i \(-0.471451\pi\)
0.0895682 + 0.995981i \(0.471451\pi\)
\(744\) 0 0
\(745\) 15010.0 0.738153
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −3836.00 −0.187135
\(750\) 0 0
\(751\) 33373.0 1.62157 0.810784 − 0.585345i \(-0.199041\pi\)
0.810784 + 0.585345i \(0.199041\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −55138.0 −2.65785
\(756\) 0 0
\(757\) 11954.0 0.573944 0.286972 − 0.957939i \(-0.407351\pi\)
0.286972 + 0.957939i \(0.407351\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 13368.0 0.636780 0.318390 − 0.947960i \(-0.396858\pi\)
0.318390 + 0.947960i \(0.396858\pi\)
\(762\) 0 0
\(763\) 20580.0 0.976469
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −31320.0 −1.47445
\(768\) 0 0
\(769\) −37640.0 −1.76506 −0.882531 − 0.470254i \(-0.844162\pi\)
−0.882531 + 0.470254i \(0.844162\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 17742.0 0.825531 0.412765 − 0.910837i \(-0.364563\pi\)
0.412765 + 0.910837i \(0.364563\pi\)
\(774\) 0 0
\(775\) −27612.0 −1.27981
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 4560.00 0.209729
\(780\) 0 0
\(781\) −12243.0 −0.560933
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 14231.0 0.647040
\(786\) 0 0
\(787\) −22744.0 −1.03016 −0.515080 − 0.857142i \(-0.672238\pi\)
−0.515080 + 0.857142i \(0.672238\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 1582.00 0.0711118
\(792\) 0 0
\(793\) 48096.0 2.15377
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 31311.0 1.39158 0.695792 − 0.718243i \(-0.255054\pi\)
0.695792 + 0.718243i \(0.255054\pi\)
\(798\) 0 0
\(799\) −4416.00 −0.195528
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −792.000 −0.0348058
\(804\) 0 0
\(805\) 28462.0 1.24615
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −3940.00 −0.171227 −0.0856137 − 0.996328i \(-0.527285\pi\)
−0.0856137 + 0.996328i \(0.527285\pi\)
\(810\) 0 0
\(811\) 19618.0 0.849422 0.424711 − 0.905329i \(-0.360376\pi\)
0.424711 + 0.905329i \(0.360376\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −23332.0 −1.00280
\(816\) 0 0
\(817\) 4840.00 0.207258
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −32062.0 −1.36294 −0.681469 − 0.731847i \(-0.738658\pi\)
−0.681469 + 0.731847i \(0.738658\pi\)
\(822\) 0 0
\(823\) 427.000 0.0180854 0.00904270 − 0.999959i \(-0.497122\pi\)
0.00904270 + 0.999959i \(0.497122\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −3256.00 −0.136907 −0.0684536 − 0.997654i \(-0.521807\pi\)
−0.0684536 + 0.997654i \(0.521807\pi\)
\(828\) 0 0
\(829\) −9155.00 −0.383554 −0.191777 − 0.981439i \(-0.561425\pi\)
−0.191777 + 0.981439i \(0.561425\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −6762.00 −0.281260
\(834\) 0 0
\(835\) 46056.0 1.90878
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 29265.0 1.20422 0.602110 − 0.798413i \(-0.294327\pi\)
0.602110 + 0.798413i \(0.294327\pi\)
\(840\) 0 0
\(841\) −9989.00 −0.409570
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 56753.0 2.31049
\(846\) 0 0
\(847\) −1694.00 −0.0687208
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 21507.0 0.866334
\(852\) 0 0
\(853\) 20598.0 0.826802 0.413401 − 0.910549i \(-0.364341\pi\)
0.413401 + 0.910549i \(0.364341\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −9944.00 −0.396360 −0.198180 − 0.980166i \(-0.563503\pi\)
−0.198180 + 0.980166i \(0.563503\pi\)
\(858\) 0 0
\(859\) 31745.0 1.26091 0.630457 − 0.776224i \(-0.282867\pi\)
0.630457 + 0.776224i \(0.282867\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 28568.0 1.12684 0.563422 − 0.826169i \(-0.309485\pi\)
0.563422 + 0.826169i \(0.309485\pi\)
\(864\) 0 0
\(865\) 71098.0 2.79469
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 770.000 0.0300581
\(870\) 0 0
\(871\) 31608.0 1.22962
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −29526.0 −1.14076
\(876\) 0 0
\(877\) −33936.0 −1.30666 −0.653328 − 0.757075i \(-0.726628\pi\)
−0.653328 + 0.757075i \(0.726628\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −7117.00 −0.272166 −0.136083 − 0.990697i \(-0.543451\pi\)
−0.136083 + 0.990697i \(0.543451\pi\)
\(882\) 0 0
\(883\) 4172.00 0.159002 0.0795011 − 0.996835i \(-0.474667\pi\)
0.0795011 + 0.996835i \(0.474667\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 9174.00 0.347275 0.173637 − 0.984810i \(-0.444448\pi\)
0.173637 + 0.984810i \(0.444448\pi\)
\(888\) 0 0
\(889\) −20664.0 −0.779582
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −1920.00 −0.0719489
\(894\) 0 0
\(895\) −5035.00 −0.188046
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 14040.0 0.520868
\(900\) 0 0
\(901\) −21068.0 −0.778998
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 1273.00 0.0467580
\(906\) 0 0
\(907\) 37316.0 1.36611 0.683053 − 0.730369i \(-0.260652\pi\)
0.683053 + 0.730369i \(0.260652\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 34332.0 1.24859 0.624297 − 0.781187i \(-0.285385\pi\)
0.624297 + 0.781187i \(0.285385\pi\)
\(912\) 0 0
\(913\) 3938.00 0.142748
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −18788.0 −0.676592
\(918\) 0 0
\(919\) −37670.0 −1.35214 −0.676071 − 0.736836i \(-0.736319\pi\)
−0.676071 + 0.736836i \(0.736319\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 80136.0 2.85776
\(924\) 0 0
\(925\) −47436.0 −1.68615
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 34950.0 1.23431 0.617154 − 0.786842i \(-0.288286\pi\)
0.617154 + 0.786842i \(0.288286\pi\)
\(930\) 0 0
\(931\) −2940.00 −0.103496
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 9614.00 0.336269
\(936\) 0 0
\(937\) 17164.0 0.598424 0.299212 − 0.954187i \(-0.403276\pi\)
0.299212 + 0.954187i \(0.403276\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −6522.00 −0.225942 −0.112971 − 0.993598i \(-0.536037\pi\)
−0.112971 + 0.993598i \(0.536037\pi\)
\(942\) 0 0
\(943\) −24396.0 −0.842463
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −53901.0 −1.84957 −0.924787 − 0.380484i \(-0.875757\pi\)
−0.924787 + 0.380484i \(0.875757\pi\)
\(948\) 0 0
\(949\) 5184.00 0.177323
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 15162.0 0.515368 0.257684 − 0.966229i \(-0.417041\pi\)
0.257684 + 0.966229i \(0.417041\pi\)
\(954\) 0 0
\(955\) −65607.0 −2.22303
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 24766.0 0.833927
\(960\) 0 0
\(961\) −16102.0 −0.540499
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −79268.0 −2.64428
\(966\) 0 0
\(967\) −1864.00 −0.0619878 −0.0309939 − 0.999520i \(-0.509867\pi\)
−0.0309939 + 0.999520i \(0.509867\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 56937.0 1.88177 0.940883 − 0.338731i \(-0.109998\pi\)
0.940883 + 0.338731i \(0.109998\pi\)
\(972\) 0 0
\(973\) −7700.00 −0.253701
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −12269.0 −0.401761 −0.200880 − 0.979616i \(-0.564380\pi\)
−0.200880 + 0.979616i \(0.564380\pi\)
\(978\) 0 0
\(979\) −9845.00 −0.321397
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −9627.00 −0.312364 −0.156182 − 0.987728i \(-0.549919\pi\)
−0.156182 + 0.987728i \(0.549919\pi\)
\(984\) 0 0
\(985\) 46094.0 1.49104
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −25894.0 −0.832539
\(990\) 0 0
\(991\) 26728.0 0.856754 0.428377 − 0.903600i \(-0.359086\pi\)
0.428377 + 0.903600i \(0.359086\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 7600.00 0.242147
\(996\) 0 0
\(997\) −15206.0 −0.483028 −0.241514 − 0.970397i \(-0.577644\pi\)
−0.241514 + 0.970397i \(0.577644\pi\)
\(998\) 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.v.1.1 1
3.2 odd 2 176.4.a.f.1.1 1
4.3 odd 2 198.4.a.g.1.1 1
12.11 even 2 22.4.a.a.1.1 ✓ 1
24.5 odd 2 704.4.a.b.1.1 1
24.11 even 2 704.4.a.l.1.1 1
33.32 even 2 1936.4.a.n.1.1 1
44.43 even 2 2178.4.a.l.1.1 1
60.23 odd 4 550.4.b.k.199.2 2
60.47 odd 4 550.4.b.k.199.1 2
60.59 even 2 550.4.a.n.1.1 1
84.83 odd 2 1078.4.a.d.1.1 1
132.35 odd 10 242.4.c.e.81.1 4
132.47 even 10 242.4.c.l.9.1 4
132.59 even 10 242.4.c.l.27.1 4
132.71 even 10 242.4.c.l.3.1 4
132.83 odd 10 242.4.c.e.3.1 4
132.95 odd 10 242.4.c.e.27.1 4
132.107 odd 10 242.4.c.e.9.1 4
132.119 even 10 242.4.c.l.81.1 4
132.131 odd 2 242.4.a.d.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
22.4.a.a.1.1 ✓ 1 12.11 even 2
176.4.a.f.1.1 1 3.2 odd 2
198.4.a.g.1.1 1 4.3 odd 2
242.4.a.d.1.1 1 132.131 odd 2
242.4.c.e.3.1 4 132.83 odd 10
242.4.c.e.9.1 4 132.107 odd 10
242.4.c.e.27.1 4 132.95 odd 10
242.4.c.e.81.1 4 132.35 odd 10
242.4.c.l.3.1 4 132.71 even 10
242.4.c.l.9.1 4 132.47 even 10
242.4.c.l.27.1 4 132.59 even 10
242.4.c.l.81.1 4 132.119 even 10
550.4.a.n.1.1 1 60.59 even 2
550.4.b.k.199.1 2 60.47 odd 4
550.4.b.k.199.2 2 60.23 odd 4
704.4.a.b.1.1 1 24.5 odd 2
704.4.a.l.1.1 1 24.11 even 2
1078.4.a.d.1.1 1 84.83 odd 2
1584.4.a.v.1.1 1 1.1 even 1 trivial
1936.4.a.n.1.1 1 33.32 even 2
2178.4.a.l.1.1 1 44.43 even 2