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Properties

Label 1872.4.a.p.1.1
Level $1872$
Weight $4$
Character 1872.1
Self dual yes
Analytic conductor $110.452$
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] = [1872,4,Mod(1,1872)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1872, 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("1872.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1872 = 2^{4} \cdot 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1872.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: \(110.451575531\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 78)
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1872.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+16.0000 q^{5} +8.00000 q^{7} +O(q^{10})\) \(q+16.0000 q^{5} +8.00000 q^{7} -38.0000 q^{11} -13.0000 q^{13} +78.0000 q^{17} +72.0000 q^{19} -52.0000 q^{23} +131.000 q^{25} -242.000 q^{29} -76.0000 q^{31} +128.000 q^{35} +342.000 q^{37} +336.000 q^{41} -76.0000 q^{43} +94.0000 q^{47} -279.000 q^{49} +450.000 q^{53} -608.000 q^{55} +854.000 q^{59} -110.000 q^{61} -208.000 q^{65} +908.000 q^{67} +838.000 q^{71} -970.000 q^{73} -304.000 q^{77} +352.000 q^{79} +474.000 q^{83} +1248.00 q^{85} +1452.00 q^{89} -104.000 q^{91} +1152.00 q^{95} -562.000 q^{97} +O(q^{100})\)

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
\(5\) 16.0000 1.43108 0.715542 − 0.698570i \(-0.246180\pi\)
0.715542 + 0.698570i \(0.246180\pi\)
\(6\) 0 0
\(7\) 8.00000 0.431959 0.215980 − 0.976398i \(-0.430705\pi\)
0.215980 + 0.976398i \(0.430705\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −38.0000 −1.04158 −0.520792 − 0.853683i \(-0.674363\pi\)
−0.520792 + 0.853683i \(0.674363\pi\)
\(12\) 0 0
\(13\) −13.0000 −0.277350
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 78.0000 1.11281 0.556405 − 0.830911i \(-0.312180\pi\)
0.556405 + 0.830911i \(0.312180\pi\)
\(18\) 0 0
\(19\) 72.0000 0.869365 0.434682 − 0.900584i \(-0.356861\pi\)
0.434682 + 0.900584i \(0.356861\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −52.0000 −0.471424 −0.235712 − 0.971823i \(-0.575742\pi\)
−0.235712 + 0.971823i \(0.575742\pi\)
\(24\) 0 0
\(25\) 131.000 1.04800
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −242.000 −1.54960 −0.774798 − 0.632209i \(-0.782148\pi\)
−0.774798 + 0.632209i \(0.782148\pi\)
\(30\) 0 0
\(31\) −76.0000 −0.440323 −0.220161 − 0.975463i \(-0.570658\pi\)
−0.220161 + 0.975463i \(0.570658\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 128.000 0.618170
\(36\) 0 0
\(37\) 342.000 1.51958 0.759790 − 0.650169i \(-0.225302\pi\)
0.759790 + 0.650169i \(0.225302\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 336.000 1.27986 0.639932 − 0.768432i \(-0.278963\pi\)
0.639932 + 0.768432i \(0.278963\pi\)
\(42\) 0 0
\(43\) −76.0000 −0.269532 −0.134766 − 0.990877i \(-0.543028\pi\)
−0.134766 + 0.990877i \(0.543028\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 94.0000 0.291730 0.145865 − 0.989305i \(-0.453403\pi\)
0.145865 + 0.989305i \(0.453403\pi\)
\(48\) 0 0
\(49\) −279.000 −0.813411
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 450.000 1.16627 0.583134 − 0.812376i \(-0.301826\pi\)
0.583134 + 0.812376i \(0.301826\pi\)
\(54\) 0 0
\(55\) −608.000 −1.49059
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 854.000 1.88443 0.942215 − 0.335010i \(-0.108740\pi\)
0.942215 + 0.335010i \(0.108740\pi\)
\(60\) 0 0
\(61\) −110.000 −0.230886 −0.115443 − 0.993314i \(-0.536829\pi\)
−0.115443 + 0.993314i \(0.536829\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −208.000 −0.396911
\(66\) 0 0
\(67\) 908.000 1.65567 0.827835 − 0.560972i \(-0.189572\pi\)
0.827835 + 0.560972i \(0.189572\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 838.000 1.40074 0.700368 − 0.713782i \(-0.253019\pi\)
0.700368 + 0.713782i \(0.253019\pi\)
\(72\) 0 0
\(73\) −970.000 −1.55520 −0.777602 − 0.628757i \(-0.783564\pi\)
−0.777602 + 0.628757i \(0.783564\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −304.000 −0.449922
\(78\) 0 0
\(79\) 352.000 0.501305 0.250652 − 0.968077i \(-0.419355\pi\)
0.250652 + 0.968077i \(0.419355\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 474.000 0.626846 0.313423 − 0.949614i \(-0.398524\pi\)
0.313423 + 0.949614i \(0.398524\pi\)
\(84\) 0 0
\(85\) 1248.00 1.59252
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 1452.00 1.72934 0.864672 − 0.502336i \(-0.167526\pi\)
0.864672 + 0.502336i \(0.167526\pi\)
\(90\) 0 0
\(91\) −104.000 −0.119804
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 1152.00 1.24413
\(96\) 0 0
\(97\) −562.000 −0.588273 −0.294136 − 0.955763i \(-0.595032\pi\)
−0.294136 + 0.955763i \(0.595032\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −466.000 −0.459096 −0.229548 − 0.973297i \(-0.573725\pi\)
−0.229548 + 0.973297i \(0.573725\pi\)
\(102\) 0 0
\(103\) 1448.00 1.38520 0.692600 − 0.721321i \(-0.256465\pi\)
0.692600 + 0.721321i \(0.256465\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −424.000 −0.383081 −0.191540 − 0.981485i \(-0.561348\pi\)
−0.191540 + 0.981485i \(0.561348\pi\)
\(108\) 0 0
\(109\) −782.000 −0.687174 −0.343587 − 0.939121i \(-0.611642\pi\)
−0.343587 + 0.939121i \(0.611642\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 634.000 0.527803 0.263901 − 0.964550i \(-0.414991\pi\)
0.263901 + 0.964550i \(0.414991\pi\)
\(114\) 0 0
\(115\) −832.000 −0.674647
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 624.000 0.480689
\(120\) 0 0
\(121\) 113.000 0.0848986
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 96.0000 0.0686920
\(126\) 0 0
\(127\) −256.000 −0.178869 −0.0894344 − 0.995993i \(-0.528506\pi\)
−0.0894344 + 0.995993i \(0.528506\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −1360.00 −0.907052 −0.453526 − 0.891243i \(-0.649834\pi\)
−0.453526 + 0.891243i \(0.649834\pi\)
\(132\) 0 0
\(133\) 576.000 0.375530
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −2976.00 −1.85589 −0.927945 − 0.372718i \(-0.878426\pi\)
−0.927945 + 0.372718i \(0.878426\pi\)
\(138\) 0 0
\(139\) −2764.00 −1.68661 −0.843307 − 0.537432i \(-0.819395\pi\)
−0.843307 + 0.537432i \(0.819395\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 494.000 0.288884
\(144\) 0 0
\(145\) −3872.00 −2.21760
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 2940.00 1.61647 0.808236 − 0.588859i \(-0.200423\pi\)
0.808236 + 0.588859i \(0.200423\pi\)
\(150\) 0 0
\(151\) −1188.00 −0.640252 −0.320126 − 0.947375i \(-0.603725\pi\)
−0.320126 + 0.947375i \(0.603725\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −1216.00 −0.630139
\(156\) 0 0
\(157\) −2410.00 −1.22509 −0.612544 − 0.790436i \(-0.709854\pi\)
−0.612544 + 0.790436i \(0.709854\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −416.000 −0.203636
\(162\) 0 0
\(163\) 2248.00 1.08023 0.540113 − 0.841592i \(-0.318381\pi\)
0.540113 + 0.841592i \(0.318381\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −1530.00 −0.708952 −0.354476 − 0.935065i \(-0.615341\pi\)
−0.354476 + 0.935065i \(0.615341\pi\)
\(168\) 0 0
\(169\) 169.000 0.0769231
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 1030.00 0.452656 0.226328 − 0.974051i \(-0.427328\pi\)
0.226328 + 0.974051i \(0.427328\pi\)
\(174\) 0 0
\(175\) 1048.00 0.452693
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 1380.00 0.576235 0.288117 − 0.957595i \(-0.406971\pi\)
0.288117 + 0.957595i \(0.406971\pi\)
\(180\) 0 0
\(181\) 2286.00 0.938768 0.469384 − 0.882994i \(-0.344476\pi\)
0.469384 + 0.882994i \(0.344476\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 5472.00 2.17465
\(186\) 0 0
\(187\) −2964.00 −1.15909
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 4720.00 1.78810 0.894050 − 0.447967i \(-0.147852\pi\)
0.894050 + 0.447967i \(0.147852\pi\)
\(192\) 0 0
\(193\) 2042.00 0.761587 0.380794 − 0.924660i \(-0.375651\pi\)
0.380794 + 0.924660i \(0.375651\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 1512.00 0.546830 0.273415 − 0.961896i \(-0.411847\pi\)
0.273415 + 0.961896i \(0.411847\pi\)
\(198\) 0 0
\(199\) 2224.00 0.792237 0.396119 − 0.918199i \(-0.370357\pi\)
0.396119 + 0.918199i \(0.370357\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −1936.00 −0.669362
\(204\) 0 0
\(205\) 5376.00 1.83159
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −2736.00 −0.905517
\(210\) 0 0
\(211\) −4652.00 −1.51781 −0.758903 − 0.651204i \(-0.774264\pi\)
−0.758903 + 0.651204i \(0.774264\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −1216.00 −0.385723
\(216\) 0 0
\(217\) −608.000 −0.190202
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −1014.00 −0.308638
\(222\) 0 0
\(223\) 1812.00 0.544128 0.272064 − 0.962279i \(-0.412294\pi\)
0.272064 + 0.962279i \(0.412294\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 126.000 0.0368410 0.0184205 − 0.999830i \(-0.494136\pi\)
0.0184205 + 0.999830i \(0.494136\pi\)
\(228\) 0 0
\(229\) 3186.00 0.919375 0.459687 − 0.888081i \(-0.347961\pi\)
0.459687 + 0.888081i \(0.347961\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 2378.00 0.668618 0.334309 − 0.942464i \(-0.391497\pi\)
0.334309 + 0.942464i \(0.391497\pi\)
\(234\) 0 0
\(235\) 1504.00 0.417490
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −1338.00 −0.362126 −0.181063 − 0.983472i \(-0.557954\pi\)
−0.181063 + 0.983472i \(0.557954\pi\)
\(240\) 0 0
\(241\) 6870.00 1.83625 0.918124 − 0.396294i \(-0.129704\pi\)
0.918124 + 0.396294i \(0.129704\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −4464.00 −1.16406
\(246\) 0 0
\(247\) −936.000 −0.241118
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 6768.00 1.70196 0.850981 − 0.525197i \(-0.176008\pi\)
0.850981 + 0.525197i \(0.176008\pi\)
\(252\) 0 0
\(253\) 1976.00 0.491028
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 3546.00 0.860675 0.430337 − 0.902668i \(-0.358395\pi\)
0.430337 + 0.902668i \(0.358395\pi\)
\(258\) 0 0
\(259\) 2736.00 0.656397
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −5340.00 −1.25201 −0.626005 − 0.779819i \(-0.715311\pi\)
−0.626005 + 0.779819i \(0.715311\pi\)
\(264\) 0 0
\(265\) 7200.00 1.66903
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 3486.00 0.790131 0.395065 − 0.918653i \(-0.370722\pi\)
0.395065 + 0.918653i \(0.370722\pi\)
\(270\) 0 0
\(271\) −256.000 −0.0573834 −0.0286917 − 0.999588i \(-0.509134\pi\)
−0.0286917 + 0.999588i \(0.509134\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −4978.00 −1.09158
\(276\) 0 0
\(277\) −3354.00 −0.727517 −0.363759 − 0.931493i \(-0.618507\pi\)
−0.363759 + 0.931493i \(0.618507\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 6608.00 1.40285 0.701424 − 0.712744i \(-0.252548\pi\)
0.701424 + 0.712744i \(0.252548\pi\)
\(282\) 0 0
\(283\) 1148.00 0.241136 0.120568 − 0.992705i \(-0.461528\pi\)
0.120568 + 0.992705i \(0.461528\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 2688.00 0.552849
\(288\) 0 0
\(289\) 1171.00 0.238347
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −1972.00 −0.393193 −0.196596 − 0.980485i \(-0.562989\pi\)
−0.196596 + 0.980485i \(0.562989\pi\)
\(294\) 0 0
\(295\) 13664.0 2.69678
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 676.000 0.130749
\(300\) 0 0
\(301\) −608.000 −0.116427
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −1760.00 −0.330417
\(306\) 0 0
\(307\) 7876.00 1.46419 0.732096 − 0.681201i \(-0.238542\pi\)
0.732096 + 0.681201i \(0.238542\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −6852.00 −1.24933 −0.624664 − 0.780893i \(-0.714764\pi\)
−0.624664 + 0.780893i \(0.714764\pi\)
\(312\) 0 0
\(313\) −4714.00 −0.851281 −0.425641 − 0.904892i \(-0.639951\pi\)
−0.425641 + 0.904892i \(0.639951\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 480.000 0.0850457 0.0425228 − 0.999095i \(-0.486460\pi\)
0.0425228 + 0.999095i \(0.486460\pi\)
\(318\) 0 0
\(319\) 9196.00 1.61403
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 5616.00 0.967438
\(324\) 0 0
\(325\) −1703.00 −0.290663
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 752.000 0.126016
\(330\) 0 0
\(331\) −7628.00 −1.26669 −0.633343 − 0.773872i \(-0.718318\pi\)
−0.633343 + 0.773872i \(0.718318\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 14528.0 2.36940
\(336\) 0 0
\(337\) −9346.00 −1.51071 −0.755355 − 0.655316i \(-0.772535\pi\)
−0.755355 + 0.655316i \(0.772535\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 2888.00 0.458633
\(342\) 0 0
\(343\) −4976.00 −0.783320
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −492.000 −0.0761151 −0.0380576 − 0.999276i \(-0.512117\pi\)
−0.0380576 + 0.999276i \(0.512117\pi\)
\(348\) 0 0
\(349\) 358.000 0.0549092 0.0274546 − 0.999623i \(-0.491260\pi\)
0.0274546 + 0.999623i \(0.491260\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −1648.00 −0.248482 −0.124241 − 0.992252i \(-0.539650\pi\)
−0.124241 + 0.992252i \(0.539650\pi\)
\(354\) 0 0
\(355\) 13408.0 2.00457
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 9750.00 1.43339 0.716693 − 0.697389i \(-0.245655\pi\)
0.716693 + 0.697389i \(0.245655\pi\)
\(360\) 0 0
\(361\) −1675.00 −0.244205
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −15520.0 −2.22563
\(366\) 0 0
\(367\) −10856.0 −1.54408 −0.772042 − 0.635572i \(-0.780764\pi\)
−0.772042 + 0.635572i \(0.780764\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 3600.00 0.503781
\(372\) 0 0
\(373\) 1826.00 0.253476 0.126738 − 0.991936i \(-0.459549\pi\)
0.126738 + 0.991936i \(0.459549\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 3146.00 0.429780
\(378\) 0 0
\(379\) 896.000 0.121436 0.0607182 − 0.998155i \(-0.480661\pi\)
0.0607182 + 0.998155i \(0.480661\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 2826.00 0.377028 0.188514 − 0.982070i \(-0.439633\pi\)
0.188514 + 0.982070i \(0.439633\pi\)
\(384\) 0 0
\(385\) −4864.00 −0.643876
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −9846.00 −1.28332 −0.641661 − 0.766989i \(-0.721754\pi\)
−0.641661 + 0.766989i \(0.721754\pi\)
\(390\) 0 0
\(391\) −4056.00 −0.524605
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 5632.00 0.717409
\(396\) 0 0
\(397\) 8678.00 1.09707 0.548534 − 0.836128i \(-0.315186\pi\)
0.548534 + 0.836128i \(0.315186\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 9948.00 1.23885 0.619426 − 0.785055i \(-0.287366\pi\)
0.619426 + 0.785055i \(0.287366\pi\)
\(402\) 0 0
\(403\) 988.000 0.122124
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −12996.0 −1.58277
\(408\) 0 0
\(409\) −98.0000 −0.0118479 −0.00592395 − 0.999982i \(-0.501886\pi\)
−0.00592395 + 0.999982i \(0.501886\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 6832.00 0.813997
\(414\) 0 0
\(415\) 7584.00 0.897070
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −3216.00 −0.374969 −0.187484 − 0.982268i \(-0.560033\pi\)
−0.187484 + 0.982268i \(0.560033\pi\)
\(420\) 0 0
\(421\) 4738.00 0.548494 0.274247 − 0.961659i \(-0.411571\pi\)
0.274247 + 0.961659i \(0.411571\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 10218.0 1.16623
\(426\) 0 0
\(427\) −880.000 −0.0997335
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −2598.00 −0.290351 −0.145175 − 0.989406i \(-0.546375\pi\)
−0.145175 + 0.989406i \(0.546375\pi\)
\(432\) 0 0
\(433\) −7490.00 −0.831285 −0.415643 − 0.909528i \(-0.636443\pi\)
−0.415643 + 0.909528i \(0.636443\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −3744.00 −0.409839
\(438\) 0 0
\(439\) 17632.0 1.91692 0.958462 − 0.285221i \(-0.0920670\pi\)
0.958462 + 0.285221i \(0.0920670\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 9696.00 1.03989 0.519945 − 0.854200i \(-0.325953\pi\)
0.519945 + 0.854200i \(0.325953\pi\)
\(444\) 0 0
\(445\) 23232.0 2.47484
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 4436.00 0.466253 0.233127 − 0.972446i \(-0.425104\pi\)
0.233127 + 0.972446i \(0.425104\pi\)
\(450\) 0 0
\(451\) −12768.0 −1.33309
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −1664.00 −0.171450
\(456\) 0 0
\(457\) 12862.0 1.31654 0.658270 − 0.752782i \(-0.271288\pi\)
0.658270 + 0.752782i \(0.271288\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −9816.00 −0.991707 −0.495853 − 0.868406i \(-0.665145\pi\)
−0.495853 + 0.868406i \(0.665145\pi\)
\(462\) 0 0
\(463\) −10408.0 −1.04471 −0.522355 − 0.852728i \(-0.674946\pi\)
−0.522355 + 0.852728i \(0.674946\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 10472.0 1.03766 0.518829 − 0.854878i \(-0.326368\pi\)
0.518829 + 0.854878i \(0.326368\pi\)
\(468\) 0 0
\(469\) 7264.00 0.715182
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 2888.00 0.280741
\(474\) 0 0
\(475\) 9432.00 0.911094
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −13398.0 −1.27802 −0.639009 − 0.769200i \(-0.720655\pi\)
−0.639009 + 0.769200i \(0.720655\pi\)
\(480\) 0 0
\(481\) −4446.00 −0.421456
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −8992.00 −0.841867
\(486\) 0 0
\(487\) −14780.0 −1.37525 −0.687624 − 0.726067i \(-0.741346\pi\)
−0.687624 + 0.726067i \(0.741346\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −12632.0 −1.16105 −0.580524 − 0.814243i \(-0.697152\pi\)
−0.580524 + 0.814243i \(0.697152\pi\)
\(492\) 0 0
\(493\) −18876.0 −1.72441
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 6704.00 0.605061
\(498\) 0 0
\(499\) −17260.0 −1.54842 −0.774212 − 0.632926i \(-0.781854\pi\)
−0.774212 + 0.632926i \(0.781854\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 76.0000 0.00673692 0.00336846 − 0.999994i \(-0.498928\pi\)
0.00336846 + 0.999994i \(0.498928\pi\)
\(504\) 0 0
\(505\) −7456.00 −0.657005
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 11144.0 0.970430 0.485215 − 0.874395i \(-0.338741\pi\)
0.485215 + 0.874395i \(0.338741\pi\)
\(510\) 0 0
\(511\) −7760.00 −0.671785
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 23168.0 1.98234
\(516\) 0 0
\(517\) −3572.00 −0.303861
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 4242.00 0.356709 0.178355 − 0.983966i \(-0.442923\pi\)
0.178355 + 0.983966i \(0.442923\pi\)
\(522\) 0 0
\(523\) 9564.00 0.799626 0.399813 − 0.916597i \(-0.369075\pi\)
0.399813 + 0.916597i \(0.369075\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −5928.00 −0.489996
\(528\) 0 0
\(529\) −9463.00 −0.777760
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −4368.00 −0.354970
\(534\) 0 0
\(535\) −6784.00 −0.548220
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 10602.0 0.847236
\(540\) 0 0
\(541\) −16078.0 −1.27772 −0.638861 − 0.769322i \(-0.720594\pi\)
−0.638861 + 0.769322i \(0.720594\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −12512.0 −0.983404
\(546\) 0 0
\(547\) −6292.00 −0.491822 −0.245911 − 0.969292i \(-0.579087\pi\)
−0.245911 + 0.969292i \(0.579087\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −17424.0 −1.34716
\(552\) 0 0
\(553\) 2816.00 0.216543
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 3588.00 0.272942 0.136471 − 0.990644i \(-0.456424\pi\)
0.136471 + 0.990644i \(0.456424\pi\)
\(558\) 0 0
\(559\) 988.000 0.0747548
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −5932.00 −0.444057 −0.222028 − 0.975040i \(-0.571268\pi\)
−0.222028 + 0.975040i \(0.571268\pi\)
\(564\) 0 0
\(565\) 10144.0 0.755330
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 1178.00 0.0867914 0.0433957 − 0.999058i \(-0.486182\pi\)
0.0433957 + 0.999058i \(0.486182\pi\)
\(570\) 0 0
\(571\) −18444.0 −1.35176 −0.675882 − 0.737010i \(-0.736237\pi\)
−0.675882 + 0.737010i \(0.736237\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −6812.00 −0.494052
\(576\) 0 0
\(577\) −2382.00 −0.171861 −0.0859306 − 0.996301i \(-0.527386\pi\)
−0.0859306 + 0.996301i \(0.527386\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 3792.00 0.270772
\(582\) 0 0
\(583\) −17100.0 −1.21477
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 15698.0 1.10379 0.551896 − 0.833913i \(-0.313905\pi\)
0.551896 + 0.833913i \(0.313905\pi\)
\(588\) 0 0
\(589\) −5472.00 −0.382801
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 8452.00 0.585299 0.292649 − 0.956220i \(-0.405463\pi\)
0.292649 + 0.956220i \(0.405463\pi\)
\(594\) 0 0
\(595\) 9984.00 0.687906
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 5836.00 0.398084 0.199042 − 0.979991i \(-0.436217\pi\)
0.199042 + 0.979991i \(0.436217\pi\)
\(600\) 0 0
\(601\) −25850.0 −1.75448 −0.877241 − 0.480051i \(-0.840618\pi\)
−0.877241 + 0.480051i \(0.840618\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 1808.00 0.121497
\(606\) 0 0
\(607\) −21624.0 −1.44595 −0.722975 − 0.690875i \(-0.757226\pi\)
−0.722975 + 0.690875i \(0.757226\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −1222.00 −0.0809113
\(612\) 0 0
\(613\) 3902.00 0.257097 0.128548 − 0.991703i \(-0.458968\pi\)
0.128548 + 0.991703i \(0.458968\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −16888.0 −1.10192 −0.550961 − 0.834531i \(-0.685739\pi\)
−0.550961 + 0.834531i \(0.685739\pi\)
\(618\) 0 0
\(619\) 27452.0 1.78253 0.891267 − 0.453478i \(-0.149817\pi\)
0.891267 + 0.453478i \(0.149817\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 11616.0 0.747007
\(624\) 0 0
\(625\) −14839.0 −0.949696
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 26676.0 1.69100
\(630\) 0 0
\(631\) −5548.00 −0.350020 −0.175010 − 0.984567i \(-0.555996\pi\)
−0.175010 + 0.984567i \(0.555996\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −4096.00 −0.255976
\(636\) 0 0
\(637\) 3627.00 0.225600
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −1618.00 −0.0996992 −0.0498496 − 0.998757i \(-0.515874\pi\)
−0.0498496 + 0.998757i \(0.515874\pi\)
\(642\) 0 0
\(643\) 19900.0 1.22050 0.610248 − 0.792210i \(-0.291070\pi\)
0.610248 + 0.792210i \(0.291070\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 18832.0 1.14430 0.572150 − 0.820149i \(-0.306109\pi\)
0.572150 + 0.820149i \(0.306109\pi\)
\(648\) 0 0
\(649\) −32452.0 −1.96279
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 4542.00 0.272193 0.136097 − 0.990696i \(-0.456544\pi\)
0.136097 + 0.990696i \(0.456544\pi\)
\(654\) 0 0
\(655\) −21760.0 −1.29807
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 8820.00 0.521363 0.260682 − 0.965425i \(-0.416053\pi\)
0.260682 + 0.965425i \(0.416053\pi\)
\(660\) 0 0
\(661\) 21014.0 1.23654 0.618268 − 0.785968i \(-0.287835\pi\)
0.618268 + 0.785968i \(0.287835\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 9216.00 0.537415
\(666\) 0 0
\(667\) 12584.0 0.730516
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 4180.00 0.240487
\(672\) 0 0
\(673\) 1714.00 0.0981721 0.0490861 − 0.998795i \(-0.484369\pi\)
0.0490861 + 0.998795i \(0.484369\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 15114.0 0.858018 0.429009 − 0.903300i \(-0.358863\pi\)
0.429009 + 0.903300i \(0.358863\pi\)
\(678\) 0 0
\(679\) −4496.00 −0.254110
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −20486.0 −1.14769 −0.573847 − 0.818963i \(-0.694550\pi\)
−0.573847 + 0.818963i \(0.694550\pi\)
\(684\) 0 0
\(685\) −47616.0 −2.65593
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −5850.00 −0.323465
\(690\) 0 0
\(691\) 8948.00 0.492616 0.246308 − 0.969192i \(-0.420782\pi\)
0.246308 + 0.969192i \(0.420782\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −44224.0 −2.41369
\(696\) 0 0
\(697\) 26208.0 1.42425
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −1350.00 −0.0727372 −0.0363686 − 0.999338i \(-0.511579\pi\)
−0.0363686 + 0.999338i \(0.511579\pi\)
\(702\) 0 0
\(703\) 24624.0 1.32107
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −3728.00 −0.198311
\(708\) 0 0
\(709\) 19802.0 1.04891 0.524457 − 0.851437i \(-0.324268\pi\)
0.524457 + 0.851437i \(0.324268\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 3952.00 0.207579
\(714\) 0 0
\(715\) 7904.00 0.413417
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −28204.0 −1.46291 −0.731455 − 0.681890i \(-0.761158\pi\)
−0.731455 + 0.681890i \(0.761158\pi\)
\(720\) 0 0
\(721\) 11584.0 0.598350
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −31702.0 −1.62398
\(726\) 0 0
\(727\) −20992.0 −1.07091 −0.535454 − 0.844564i \(-0.679859\pi\)
−0.535454 + 0.844564i \(0.679859\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −5928.00 −0.299938
\(732\) 0 0
\(733\) −19894.0 −1.00246 −0.501229 − 0.865315i \(-0.667119\pi\)
−0.501229 + 0.865315i \(0.667119\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −34504.0 −1.72452
\(738\) 0 0
\(739\) −6252.00 −0.311209 −0.155605 − 0.987819i \(-0.549733\pi\)
−0.155605 + 0.987819i \(0.549733\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −30938.0 −1.52760 −0.763799 − 0.645454i \(-0.776668\pi\)
−0.763799 + 0.645454i \(0.776668\pi\)
\(744\) 0 0
\(745\) 47040.0 2.31331
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −3392.00 −0.165475
\(750\) 0 0
\(751\) −11328.0 −0.550419 −0.275209 − 0.961384i \(-0.588747\pi\)
−0.275209 + 0.961384i \(0.588747\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −19008.0 −0.916254
\(756\) 0 0
\(757\) 32754.0 1.57261 0.786304 − 0.617840i \(-0.211992\pi\)
0.786304 + 0.617840i \(0.211992\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 19776.0 0.942023 0.471011 − 0.882127i \(-0.343889\pi\)
0.471011 + 0.882127i \(0.343889\pi\)
\(762\) 0 0
\(763\) −6256.00 −0.296831
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −11102.0 −0.522647
\(768\) 0 0
\(769\) 28362.0 1.32999 0.664993 − 0.746849i \(-0.268434\pi\)
0.664993 + 0.746849i \(0.268434\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −17108.0 −0.796031 −0.398016 − 0.917379i \(-0.630301\pi\)
−0.398016 + 0.917379i \(0.630301\pi\)
\(774\) 0 0
\(775\) −9956.00 −0.461458
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 24192.0 1.11267
\(780\) 0 0
\(781\) −31844.0 −1.45899
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −38560.0 −1.75320
\(786\) 0 0
\(787\) 21364.0 0.967655 0.483827 − 0.875163i \(-0.339246\pi\)
0.483827 + 0.875163i \(0.339246\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 5072.00 0.227989
\(792\) 0 0
\(793\) 1430.00 0.0640363
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −28542.0 −1.26852 −0.634259 − 0.773120i \(-0.718695\pi\)
−0.634259 + 0.773120i \(0.718695\pi\)
\(798\) 0 0
\(799\) 7332.00 0.324640
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 36860.0 1.61988
\(804\) 0 0
\(805\) −6656.00 −0.291420
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −26046.0 −1.13193 −0.565963 − 0.824430i \(-0.691496\pi\)
−0.565963 + 0.824430i \(0.691496\pi\)
\(810\) 0 0
\(811\) 15352.0 0.664712 0.332356 − 0.943154i \(-0.392156\pi\)
0.332356 + 0.943154i \(0.392156\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 35968.0 1.54589
\(816\) 0 0
\(817\) −5472.00 −0.234322
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 31972.0 1.35911 0.679556 − 0.733624i \(-0.262173\pi\)
0.679556 + 0.733624i \(0.262173\pi\)
\(822\) 0 0
\(823\) 32208.0 1.36416 0.682078 − 0.731279i \(-0.261076\pi\)
0.682078 + 0.731279i \(0.261076\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −27006.0 −1.13554 −0.567769 − 0.823188i \(-0.692193\pi\)
−0.567769 + 0.823188i \(0.692193\pi\)
\(828\) 0 0
\(829\) 5818.00 0.243748 0.121874 − 0.992546i \(-0.461110\pi\)
0.121874 + 0.992546i \(0.461110\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −21762.0 −0.905172
\(834\) 0 0
\(835\) −24480.0 −1.01457
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −5926.00 −0.243848 −0.121924 − 0.992539i \(-0.538906\pi\)
−0.121924 + 0.992539i \(0.538906\pi\)
\(840\) 0 0
\(841\) 34175.0 1.40125
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 2704.00 0.110083
\(846\) 0 0
\(847\) 904.000 0.0366727
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −17784.0 −0.716366
\(852\) 0 0
\(853\) −40874.0 −1.64068 −0.820339 − 0.571877i \(-0.806215\pi\)
−0.820339 + 0.571877i \(0.806215\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 3530.00 0.140703 0.0703515 − 0.997522i \(-0.477588\pi\)
0.0703515 + 0.997522i \(0.477588\pi\)
\(858\) 0 0
\(859\) 34756.0 1.38051 0.690256 − 0.723565i \(-0.257498\pi\)
0.690256 + 0.723565i \(0.257498\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −9878.00 −0.389630 −0.194815 − 0.980840i \(-0.562411\pi\)
−0.194815 + 0.980840i \(0.562411\pi\)
\(864\) 0 0
\(865\) 16480.0 0.647788
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −13376.0 −0.522152
\(870\) 0 0
\(871\) −11804.0 −0.459200
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 768.000 0.0296722
\(876\) 0 0
\(877\) 150.000 0.00577553 0.00288777 − 0.999996i \(-0.499081\pi\)
0.00288777 + 0.999996i \(0.499081\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 3666.00 0.140194 0.0700969 − 0.997540i \(-0.477669\pi\)
0.0700969 + 0.997540i \(0.477669\pi\)
\(882\) 0 0
\(883\) −24316.0 −0.926725 −0.463363 − 0.886169i \(-0.653357\pi\)
−0.463363 + 0.886169i \(0.653357\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 2992.00 0.113260 0.0566299 − 0.998395i \(-0.481964\pi\)
0.0566299 + 0.998395i \(0.481964\pi\)
\(888\) 0 0
\(889\) −2048.00 −0.0772640
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 6768.00 0.253620
\(894\) 0 0
\(895\) 22080.0 0.824640
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 18392.0 0.682322
\(900\) 0 0
\(901\) 35100.0 1.29784
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 36576.0 1.34346
\(906\) 0 0
\(907\) 1956.00 0.0716074 0.0358037 − 0.999359i \(-0.488601\pi\)
0.0358037 + 0.999359i \(0.488601\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −38832.0 −1.41225 −0.706126 − 0.708086i \(-0.749559\pi\)
−0.706126 + 0.708086i \(0.749559\pi\)
\(912\) 0 0
\(913\) −18012.0 −0.652914
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −10880.0 −0.391809
\(918\) 0 0
\(919\) −504.000 −0.0180908 −0.00904539 − 0.999959i \(-0.502879\pi\)
−0.00904539 + 0.999959i \(0.502879\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −10894.0 −0.388494
\(924\) 0 0
\(925\) 44802.0 1.59252
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 2976.00 0.105102 0.0525508 − 0.998618i \(-0.483265\pi\)
0.0525508 + 0.998618i \(0.483265\pi\)
\(930\) 0 0
\(931\) −20088.0 −0.707151
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −47424.0 −1.65875
\(936\) 0 0
\(937\) −14082.0 −0.490970 −0.245485 − 0.969400i \(-0.578947\pi\)
−0.245485 + 0.969400i \(0.578947\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 3260.00 0.112936 0.0564681 − 0.998404i \(-0.482016\pi\)
0.0564681 + 0.998404i \(0.482016\pi\)
\(942\) 0 0
\(943\) −17472.0 −0.603358
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 5886.00 0.201974 0.100987 − 0.994888i \(-0.467800\pi\)
0.100987 + 0.994888i \(0.467800\pi\)
\(948\) 0 0
\(949\) 12610.0 0.431336
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −22574.0 −0.767307 −0.383654 − 0.923477i \(-0.625334\pi\)
−0.383654 + 0.923477i \(0.625334\pi\)
\(954\) 0 0
\(955\) 75520.0 2.55892
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −23808.0 −0.801669
\(960\) 0 0
\(961\) −24015.0 −0.806116
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 32672.0 1.08990
\(966\) 0 0
\(967\) −32996.0 −1.09729 −0.548645 − 0.836055i \(-0.684856\pi\)
−0.548645 + 0.836055i \(0.684856\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 14292.0 0.472350 0.236175 − 0.971711i \(-0.424106\pi\)
0.236175 + 0.971711i \(0.424106\pi\)
\(972\) 0 0
\(973\) −22112.0 −0.728549
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −48756.0 −1.59656 −0.798282 − 0.602284i \(-0.794257\pi\)
−0.798282 + 0.602284i \(0.794257\pi\)
\(978\) 0 0
\(979\) −55176.0 −1.80126
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −42022.0 −1.36347 −0.681736 − 0.731598i \(-0.738775\pi\)
−0.681736 + 0.731598i \(0.738775\pi\)
\(984\) 0 0
\(985\) 24192.0 0.782560
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 3952.00 0.127064
\(990\) 0 0
\(991\) −46752.0 −1.49861 −0.749307 − 0.662223i \(-0.769613\pi\)
−0.749307 + 0.662223i \(0.769613\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 35584.0 1.13376
\(996\) 0 0
\(997\) −37666.0 −1.19648 −0.598242 − 0.801316i \(-0.704134\pi\)
−0.598242 + 0.801316i \(0.704134\pi\)
\(998\) 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 1872.4.a.p.1.1 1
3.2 odd 2 624.4.a.a.1.1 1
4.3 odd 2 234.4.a.j.1.1 1
12.11 even 2 78.4.a.b.1.1 ✓ 1
24.5 odd 2 2496.4.a.p.1.1 1
24.11 even 2 2496.4.a.h.1.1 1
60.59 even 2 1950.4.a.k.1.1 1
156.47 odd 4 1014.4.b.f.337.1 2
156.83 odd 4 1014.4.b.f.337.2 2
156.155 even 2 1014.4.a.k.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
78.4.a.b.1.1 ✓ 1 12.11 even 2
234.4.a.j.1.1 1 4.3 odd 2
624.4.a.a.1.1 1 3.2 odd 2
1014.4.a.k.1.1 1 156.155 even 2
1014.4.b.f.337.1 2 156.47 odd 4
1014.4.b.f.337.2 2 156.83 odd 4
1872.4.a.p.1.1 1 1.1 even 1 trivial
1950.4.a.k.1.1 1 60.59 even 2
2496.4.a.h.1.1 1 24.11 even 2
2496.4.a.p.1.1 1 24.5 odd 2