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Properties

Label 1872.4.a.l.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 104)
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)
 
\(f(q)\) \(=\) \(q+7.00000 q^{5} +21.0000 q^{7} +O(q^{10})\) \(q+7.00000 q^{5} +21.0000 q^{7} +6.00000 q^{11} +13.0000 q^{13} +115.000 q^{17} +46.0000 q^{19} +144.000 q^{23} -76.0000 q^{25} +162.000 q^{29} -180.000 q^{31} +147.000 q^{35} +13.0000 q^{37} -192.000 q^{41} +33.0000 q^{43} +383.000 q^{47} +98.0000 q^{49} -288.000 q^{53} +42.0000 q^{55} +442.000 q^{59} -680.000 q^{61} +91.0000 q^{65} +722.000 q^{67} -207.000 q^{71} +274.000 q^{73} +126.000 q^{77} +936.000 q^{79} -1204.00 q^{83} +805.000 q^{85} +966.000 q^{89} +273.000 q^{91} +322.000 q^{95} -138.000 q^{97} +O(q^{100})\)

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
\(5\) 7.00000 0.626099 0.313050 − 0.949737i \(-0.398649\pi\)
0.313050 + 0.949737i \(0.398649\pi\)
\(6\) 0 0
\(7\) 21.0000 1.13389 0.566947 − 0.823754i \(-0.308125\pi\)
0.566947 + 0.823754i \(0.308125\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 6.00000 0.164461 0.0822304 − 0.996613i \(-0.473796\pi\)
0.0822304 + 0.996613i \(0.473796\pi\)
\(12\) 0 0
\(13\) 13.0000 0.277350
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 115.000 1.64068 0.820341 − 0.571875i \(-0.193784\pi\)
0.820341 + 0.571875i \(0.193784\pi\)
\(18\) 0 0
\(19\) 46.0000 0.555428 0.277714 − 0.960664i \(-0.410423\pi\)
0.277714 + 0.960664i \(0.410423\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 144.000 1.30548 0.652741 − 0.757581i \(-0.273619\pi\)
0.652741 + 0.757581i \(0.273619\pi\)
\(24\) 0 0
\(25\) −76.0000 −0.608000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 162.000 1.03733 0.518666 − 0.854977i \(-0.326429\pi\)
0.518666 + 0.854977i \(0.326429\pi\)
\(30\) 0 0
\(31\) −180.000 −1.04287 −0.521435 − 0.853291i \(-0.674603\pi\)
−0.521435 + 0.853291i \(0.674603\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 147.000 0.709930
\(36\) 0 0
\(37\) 13.0000 0.0577618 0.0288809 − 0.999583i \(-0.490806\pi\)
0.0288809 + 0.999583i \(0.490806\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −192.000 −0.731350 −0.365675 − 0.930743i \(-0.619162\pi\)
−0.365675 + 0.930743i \(0.619162\pi\)
\(42\) 0 0
\(43\) 33.0000 0.117034 0.0585169 − 0.998286i \(-0.481363\pi\)
0.0585169 + 0.998286i \(0.481363\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 383.000 1.18864 0.594322 − 0.804227i \(-0.297420\pi\)
0.594322 + 0.804227i \(0.297420\pi\)
\(48\) 0 0
\(49\) 98.0000 0.285714
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −288.000 −0.746412 −0.373206 − 0.927748i \(-0.621742\pi\)
−0.373206 + 0.927748i \(0.621742\pi\)
\(54\) 0 0
\(55\) 42.0000 0.102969
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 442.000 0.975314 0.487657 − 0.873035i \(-0.337852\pi\)
0.487657 + 0.873035i \(0.337852\pi\)
\(60\) 0 0
\(61\) −680.000 −1.42730 −0.713648 − 0.700504i \(-0.752958\pi\)
−0.713648 + 0.700504i \(0.752958\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 91.0000 0.173649
\(66\) 0 0
\(67\) 722.000 1.31651 0.658256 − 0.752794i \(-0.271294\pi\)
0.658256 + 0.752794i \(0.271294\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −207.000 −0.346005 −0.173003 − 0.984921i \(-0.555347\pi\)
−0.173003 + 0.984921i \(0.555347\pi\)
\(72\) 0 0
\(73\) 274.000 0.439305 0.219653 − 0.975578i \(-0.429508\pi\)
0.219653 + 0.975578i \(0.429508\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 126.000 0.186481
\(78\) 0 0
\(79\) 936.000 1.33302 0.666508 − 0.745498i \(-0.267788\pi\)
0.666508 + 0.745498i \(0.267788\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −1204.00 −1.59224 −0.796122 − 0.605137i \(-0.793118\pi\)
−0.796122 + 0.605137i \(0.793118\pi\)
\(84\) 0 0
\(85\) 805.000 1.02723
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 966.000 1.15051 0.575257 − 0.817973i \(-0.304902\pi\)
0.575257 + 0.817973i \(0.304902\pi\)
\(90\) 0 0
\(91\) 273.000 0.314485
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 322.000 0.347753
\(96\) 0 0
\(97\) −138.000 −0.144451 −0.0722257 − 0.997388i \(-0.523010\pi\)
−0.0722257 + 0.997388i \(0.523010\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −356.000 −0.350726 −0.175363 − 0.984504i \(-0.556110\pi\)
−0.175363 + 0.984504i \(0.556110\pi\)
\(102\) 0 0
\(103\) 788.000 0.753825 0.376912 − 0.926249i \(-0.376986\pi\)
0.376912 + 0.926249i \(0.376986\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −860.000 −0.777003 −0.388502 − 0.921448i \(-0.627007\pi\)
−0.388502 + 0.921448i \(0.627007\pi\)
\(108\) 0 0
\(109\) −1019.00 −0.895436 −0.447718 − 0.894175i \(-0.647763\pi\)
−0.447718 + 0.894175i \(0.647763\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −378.000 −0.314684 −0.157342 − 0.987544i \(-0.550292\pi\)
−0.157342 + 0.987544i \(0.550292\pi\)
\(114\) 0 0
\(115\) 1008.00 0.817361
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 2415.00 1.86036
\(120\) 0 0
\(121\) −1295.00 −0.972953
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −1407.00 −1.00677
\(126\) 0 0
\(127\) −2068.00 −1.44492 −0.722462 − 0.691411i \(-0.756990\pi\)
−0.722462 + 0.691411i \(0.756990\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 3.00000 0.00200085 0.00100042 − 0.999999i \(-0.499682\pi\)
0.00100042 + 0.999999i \(0.499682\pi\)
\(132\) 0 0
\(133\) 966.000 0.629796
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −1536.00 −0.957878 −0.478939 − 0.877848i \(-0.658979\pi\)
−0.478939 + 0.877848i \(0.658979\pi\)
\(138\) 0 0
\(139\) 2069.00 1.26252 0.631260 − 0.775571i \(-0.282538\pi\)
0.631260 + 0.775571i \(0.282538\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 78.0000 0.0456132
\(144\) 0 0
\(145\) 1134.00 0.649473
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 158.000 0.0868716 0.0434358 − 0.999056i \(-0.486170\pi\)
0.0434358 + 0.999056i \(0.486170\pi\)
\(150\) 0 0
\(151\) −1757.00 −0.946905 −0.473452 − 0.880819i \(-0.656992\pi\)
−0.473452 + 0.880819i \(0.656992\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −1260.00 −0.652940
\(156\) 0 0
\(157\) −3418.00 −1.73749 −0.868746 − 0.495259i \(-0.835073\pi\)
−0.868746 + 0.495259i \(0.835073\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 3024.00 1.48028
\(162\) 0 0
\(163\) 1104.00 0.530503 0.265251 − 0.964179i \(-0.414545\pi\)
0.265251 + 0.964179i \(0.414545\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 3816.00 1.76821 0.884105 − 0.467289i \(-0.154769\pi\)
0.884105 + 0.467289i \(0.154769\pi\)
\(168\) 0 0
\(169\) 169.000 0.0769231
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −1584.00 −0.696123 −0.348062 − 0.937472i \(-0.613160\pi\)
−0.348062 + 0.937472i \(0.613160\pi\)
\(174\) 0 0
\(175\) −1596.00 −0.689407
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 4739.00 1.97882 0.989412 − 0.145134i \(-0.0463614\pi\)
0.989412 + 0.145134i \(0.0463614\pi\)
\(180\) 0 0
\(181\) −2108.00 −0.865671 −0.432835 − 0.901473i \(-0.642487\pi\)
−0.432835 + 0.901473i \(0.642487\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 91.0000 0.0361646
\(186\) 0 0
\(187\) 690.000 0.269828
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −890.000 −0.337163 −0.168582 − 0.985688i \(-0.553919\pi\)
−0.168582 + 0.985688i \(0.553919\pi\)
\(192\) 0 0
\(193\) −3028.00 −1.12933 −0.564664 − 0.825321i \(-0.690994\pi\)
−0.564664 + 0.825321i \(0.690994\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 3649.00 1.31970 0.659849 − 0.751398i \(-0.270620\pi\)
0.659849 + 0.751398i \(0.270620\pi\)
\(198\) 0 0
\(199\) 2742.00 0.976760 0.488380 − 0.872631i \(-0.337588\pi\)
0.488380 + 0.872631i \(0.337588\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 3402.00 1.17622
\(204\) 0 0
\(205\) −1344.00 −0.457898
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 276.000 0.0913460
\(210\) 0 0
\(211\) 5621.00 1.83396 0.916980 − 0.398933i \(-0.130619\pi\)
0.916980 + 0.398933i \(0.130619\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 231.000 0.0732747
\(216\) 0 0
\(217\) −3780.00 −1.18250
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 1495.00 0.455043
\(222\) 0 0
\(223\) −2353.00 −0.706585 −0.353293 − 0.935513i \(-0.614938\pi\)
−0.353293 + 0.935513i \(0.614938\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 2016.00 0.589456 0.294728 − 0.955581i \(-0.404771\pi\)
0.294728 + 0.955581i \(0.404771\pi\)
\(228\) 0 0
\(229\) 5191.00 1.49795 0.748976 − 0.662597i \(-0.230546\pi\)
0.748976 + 0.662597i \(0.230546\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 5627.00 1.58213 0.791067 − 0.611730i \(-0.209526\pi\)
0.791067 + 0.611730i \(0.209526\pi\)
\(234\) 0 0
\(235\) 2681.00 0.744209
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −2429.00 −0.657401 −0.328701 − 0.944434i \(-0.606611\pi\)
−0.328701 + 0.944434i \(0.606611\pi\)
\(240\) 0 0
\(241\) 6998.00 1.87046 0.935230 − 0.354041i \(-0.115193\pi\)
0.935230 + 0.354041i \(0.115193\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 686.000 0.178885
\(246\) 0 0
\(247\) 598.000 0.154048
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −4320.00 −1.08636 −0.543179 − 0.839617i \(-0.682780\pi\)
−0.543179 + 0.839617i \(0.682780\pi\)
\(252\) 0 0
\(253\) 864.000 0.214700
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 135.000 0.0327668 0.0163834 − 0.999866i \(-0.494785\pi\)
0.0163834 + 0.999866i \(0.494785\pi\)
\(258\) 0 0
\(259\) 273.000 0.0654957
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 6100.00 1.43020 0.715099 − 0.699023i \(-0.246382\pi\)
0.715099 + 0.699023i \(0.246382\pi\)
\(264\) 0 0
\(265\) −2016.00 −0.467328
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 1304.00 0.295562 0.147781 − 0.989020i \(-0.452787\pi\)
0.147781 + 0.989020i \(0.452787\pi\)
\(270\) 0 0
\(271\) 4361.00 0.977535 0.488767 − 0.872414i \(-0.337447\pi\)
0.488767 + 0.872414i \(0.337447\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −456.000 −0.0999921
\(276\) 0 0
\(277\) 5156.00 1.11839 0.559195 − 0.829036i \(-0.311110\pi\)
0.559195 + 0.829036i \(0.311110\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 2022.00 0.429261 0.214631 − 0.976695i \(-0.431145\pi\)
0.214631 + 0.976695i \(0.431145\pi\)
\(282\) 0 0
\(283\) −8772.00 −1.84255 −0.921274 − 0.388913i \(-0.872851\pi\)
−0.921274 + 0.388913i \(0.872851\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −4032.00 −0.829273
\(288\) 0 0
\(289\) 8312.00 1.69184
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −8329.00 −1.66070 −0.830350 − 0.557242i \(-0.811860\pi\)
−0.830350 + 0.557242i \(0.811860\pi\)
\(294\) 0 0
\(295\) 3094.00 0.610643
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 1872.00 0.362075
\(300\) 0 0
\(301\) 693.000 0.132704
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −4760.00 −0.893629
\(306\) 0 0
\(307\) −4706.00 −0.874872 −0.437436 − 0.899250i \(-0.644113\pi\)
−0.437436 + 0.899250i \(0.644113\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −1606.00 −0.292823 −0.146411 − 0.989224i \(-0.546772\pi\)
−0.146411 + 0.989224i \(0.546772\pi\)
\(312\) 0 0
\(313\) 6799.00 1.22780 0.613901 − 0.789383i \(-0.289599\pi\)
0.613901 + 0.789383i \(0.289599\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 7086.00 1.25549 0.627744 − 0.778420i \(-0.283979\pi\)
0.627744 + 0.778420i \(0.283979\pi\)
\(318\) 0 0
\(319\) 972.000 0.170600
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 5290.00 0.911280
\(324\) 0 0
\(325\) −988.000 −0.168629
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 8043.00 1.34780
\(330\) 0 0
\(331\) 3672.00 0.609762 0.304881 − 0.952390i \(-0.401383\pi\)
0.304881 + 0.952390i \(0.401383\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 5054.00 0.824267
\(336\) 0 0
\(337\) 9023.00 1.45850 0.729249 − 0.684248i \(-0.239869\pi\)
0.729249 + 0.684248i \(0.239869\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −1080.00 −0.171511
\(342\) 0 0
\(343\) −5145.00 −0.809924
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 1579.00 0.244280 0.122140 − 0.992513i \(-0.461024\pi\)
0.122140 + 0.992513i \(0.461024\pi\)
\(348\) 0 0
\(349\) −3167.00 −0.485747 −0.242873 − 0.970058i \(-0.578090\pi\)
−0.242873 + 0.970058i \(0.578090\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −7560.00 −1.13988 −0.569941 − 0.821686i \(-0.693034\pi\)
−0.569941 + 0.821686i \(0.693034\pi\)
\(354\) 0 0
\(355\) −1449.00 −0.216634
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −7512.00 −1.10437 −0.552184 − 0.833722i \(-0.686205\pi\)
−0.552184 + 0.833722i \(0.686205\pi\)
\(360\) 0 0
\(361\) −4743.00 −0.691500
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 1918.00 0.275049
\(366\) 0 0
\(367\) 10270.0 1.46073 0.730367 − 0.683055i \(-0.239349\pi\)
0.730367 + 0.683055i \(0.239349\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −6048.00 −0.846352
\(372\) 0 0
\(373\) −1700.00 −0.235986 −0.117993 − 0.993014i \(-0.537646\pi\)
−0.117993 + 0.993014i \(0.537646\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 2106.00 0.287704
\(378\) 0 0
\(379\) −8420.00 −1.14118 −0.570589 − 0.821236i \(-0.693285\pi\)
−0.570589 + 0.821236i \(0.693285\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 2473.00 0.329933 0.164967 − 0.986299i \(-0.447248\pi\)
0.164967 + 0.986299i \(0.447248\pi\)
\(384\) 0 0
\(385\) 882.000 0.116756
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 6750.00 0.879791 0.439895 − 0.898049i \(-0.355016\pi\)
0.439895 + 0.898049i \(0.355016\pi\)
\(390\) 0 0
\(391\) 16560.0 2.14188
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 6552.00 0.834600
\(396\) 0 0
\(397\) −3962.00 −0.500874 −0.250437 − 0.968133i \(-0.580574\pi\)
−0.250437 + 0.968133i \(0.580574\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 6444.00 0.802489 0.401244 − 0.915971i \(-0.368578\pi\)
0.401244 + 0.915971i \(0.368578\pi\)
\(402\) 0 0
\(403\) −2340.00 −0.289240
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 78.0000 0.00949955
\(408\) 0 0
\(409\) −9264.00 −1.11999 −0.559994 − 0.828496i \(-0.689197\pi\)
−0.559994 + 0.828496i \(0.689197\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 9282.00 1.10590
\(414\) 0 0
\(415\) −8428.00 −0.996902
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −7847.00 −0.914919 −0.457459 − 0.889230i \(-0.651241\pi\)
−0.457459 + 0.889230i \(0.651241\pi\)
\(420\) 0 0
\(421\) 6813.00 0.788706 0.394353 − 0.918959i \(-0.370969\pi\)
0.394353 + 0.918959i \(0.370969\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −8740.00 −0.997535
\(426\) 0 0
\(427\) −14280.0 −1.61840
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 2371.00 0.264982 0.132491 − 0.991184i \(-0.457703\pi\)
0.132491 + 0.991184i \(0.457703\pi\)
\(432\) 0 0
\(433\) 2495.00 0.276910 0.138455 − 0.990369i \(-0.455786\pi\)
0.138455 + 0.990369i \(0.455786\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 6624.00 0.725100
\(438\) 0 0
\(439\) 926.000 0.100673 0.0503366 − 0.998732i \(-0.483971\pi\)
0.0503366 + 0.998732i \(0.483971\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −363.000 −0.0389315 −0.0194657 − 0.999811i \(-0.506197\pi\)
−0.0194657 + 0.999811i \(0.506197\pi\)
\(444\) 0 0
\(445\) 6762.00 0.720336
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 1626.00 0.170904 0.0854518 − 0.996342i \(-0.472767\pi\)
0.0854518 + 0.996342i \(0.472767\pi\)
\(450\) 0 0
\(451\) −1152.00 −0.120278
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 1911.00 0.196899
\(456\) 0 0
\(457\) −17978.0 −1.84021 −0.920104 − 0.391673i \(-0.871896\pi\)
−0.920104 + 0.391673i \(0.871896\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 8043.00 0.812581 0.406291 − 0.913744i \(-0.366822\pi\)
0.406291 + 0.913744i \(0.366822\pi\)
\(462\) 0 0
\(463\) 1008.00 0.101179 0.0505893 − 0.998720i \(-0.483890\pi\)
0.0505893 + 0.998720i \(0.483890\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 7804.00 0.773289 0.386645 − 0.922229i \(-0.373634\pi\)
0.386645 + 0.922229i \(0.373634\pi\)
\(468\) 0 0
\(469\) 15162.0 1.49278
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 198.000 0.0192475
\(474\) 0 0
\(475\) −3496.00 −0.337700
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 13383.0 1.27659 0.638293 − 0.769793i \(-0.279641\pi\)
0.638293 + 0.769793i \(0.279641\pi\)
\(480\) 0 0
\(481\) 169.000 0.0160202
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −966.000 −0.0904408
\(486\) 0 0
\(487\) −13384.0 −1.24535 −0.622677 − 0.782479i \(-0.713955\pi\)
−0.622677 + 0.782479i \(0.713955\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −12729.0 −1.16996 −0.584981 − 0.811047i \(-0.698898\pi\)
−0.584981 + 0.811047i \(0.698898\pi\)
\(492\) 0 0
\(493\) 18630.0 1.70193
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −4347.00 −0.392333
\(498\) 0 0
\(499\) −9304.00 −0.834678 −0.417339 − 0.908751i \(-0.637037\pi\)
−0.417339 + 0.908751i \(0.637037\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 2618.00 0.232069 0.116035 − 0.993245i \(-0.462982\pi\)
0.116035 + 0.993245i \(0.462982\pi\)
\(504\) 0 0
\(505\) −2492.00 −0.219589
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −86.0000 −0.00748896 −0.00374448 − 0.999993i \(-0.501192\pi\)
−0.00374448 + 0.999993i \(0.501192\pi\)
\(510\) 0 0
\(511\) 5754.00 0.498125
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 5516.00 0.471969
\(516\) 0 0
\(517\) 2298.00 0.195485
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −11335.0 −0.953158 −0.476579 − 0.879132i \(-0.658123\pi\)
−0.476579 + 0.879132i \(0.658123\pi\)
\(522\) 0 0
\(523\) −7500.00 −0.627059 −0.313530 − 0.949578i \(-0.601512\pi\)
−0.313530 + 0.949578i \(0.601512\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −20700.0 −1.71102
\(528\) 0 0
\(529\) 8569.00 0.704282
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −2496.00 −0.202840
\(534\) 0 0
\(535\) −6020.00 −0.486481
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 588.000 0.0469888
\(540\) 0 0
\(541\) −21457.0 −1.70519 −0.852596 − 0.522571i \(-0.824973\pi\)
−0.852596 + 0.522571i \(0.824973\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −7133.00 −0.560631
\(546\) 0 0
\(547\) −23617.0 −1.84605 −0.923026 − 0.384739i \(-0.874292\pi\)
−0.923026 + 0.384739i \(0.874292\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 7452.00 0.576163
\(552\) 0 0
\(553\) 19656.0 1.51150
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 24921.0 1.89576 0.947879 − 0.318632i \(-0.103223\pi\)
0.947879 + 0.318632i \(0.103223\pi\)
\(558\) 0 0
\(559\) 429.000 0.0324593
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −4521.00 −0.338432 −0.169216 − 0.985579i \(-0.554124\pi\)
−0.169216 + 0.985579i \(0.554124\pi\)
\(564\) 0 0
\(565\) −2646.00 −0.197023
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 25497.0 1.87854 0.939271 − 0.343178i \(-0.111503\pi\)
0.939271 + 0.343178i \(0.111503\pi\)
\(570\) 0 0
\(571\) 18995.0 1.39215 0.696074 − 0.717970i \(-0.254929\pi\)
0.696074 + 0.717970i \(0.254929\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −10944.0 −0.793733
\(576\) 0 0
\(577\) 7254.00 0.523376 0.261688 − 0.965153i \(-0.415721\pi\)
0.261688 + 0.965153i \(0.415721\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −25284.0 −1.80543
\(582\) 0 0
\(583\) −1728.00 −0.122755
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −22744.0 −1.59923 −0.799613 − 0.600516i \(-0.794962\pi\)
−0.799613 + 0.600516i \(0.794962\pi\)
\(588\) 0 0
\(589\) −8280.00 −0.579238
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 5358.00 0.371040 0.185520 − 0.982640i \(-0.440603\pi\)
0.185520 + 0.982640i \(0.440603\pi\)
\(594\) 0 0
\(595\) 16905.0 1.16477
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 2510.00 0.171212 0.0856059 − 0.996329i \(-0.472717\pi\)
0.0856059 + 0.996329i \(0.472717\pi\)
\(600\) 0 0
\(601\) −6827.00 −0.463360 −0.231680 − 0.972792i \(-0.574422\pi\)
−0.231680 + 0.972792i \(0.574422\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −9065.00 −0.609165
\(606\) 0 0
\(607\) −9190.00 −0.614515 −0.307257 − 0.951626i \(-0.599411\pi\)
−0.307257 + 0.951626i \(0.599411\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 4979.00 0.329671
\(612\) 0 0
\(613\) −4930.00 −0.324830 −0.162415 − 0.986723i \(-0.551928\pi\)
−0.162415 + 0.986723i \(0.551928\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −3384.00 −0.220802 −0.110401 − 0.993887i \(-0.535213\pi\)
−0.110401 + 0.993887i \(0.535213\pi\)
\(618\) 0 0
\(619\) 9644.00 0.626212 0.313106 − 0.949718i \(-0.398631\pi\)
0.313106 + 0.949718i \(0.398631\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 20286.0 1.30456
\(624\) 0 0
\(625\) −349.000 −0.0223360
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 1495.00 0.0947688
\(630\) 0 0
\(631\) 18935.0 1.19460 0.597298 − 0.802019i \(-0.296241\pi\)
0.597298 + 0.802019i \(0.296241\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −14476.0 −0.904665
\(636\) 0 0
\(637\) 1274.00 0.0792429
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −22894.0 −1.41070 −0.705350 − 0.708859i \(-0.749210\pi\)
−0.705350 + 0.708859i \(0.749210\pi\)
\(642\) 0 0
\(643\) 29426.0 1.80474 0.902370 − 0.430962i \(-0.141826\pi\)
0.902370 + 0.430962i \(0.141826\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 9474.00 0.575674 0.287837 − 0.957679i \(-0.407064\pi\)
0.287837 + 0.957679i \(0.407064\pi\)
\(648\) 0 0
\(649\) 2652.00 0.160401
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −768.000 −0.0460248 −0.0230124 − 0.999735i \(-0.507326\pi\)
−0.0230124 + 0.999735i \(0.507326\pi\)
\(654\) 0 0
\(655\) 21.0000 0.00125273
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −13724.0 −0.811246 −0.405623 − 0.914040i \(-0.632945\pi\)
−0.405623 + 0.914040i \(0.632945\pi\)
\(660\) 0 0
\(661\) 12434.0 0.731659 0.365829 − 0.930682i \(-0.380785\pi\)
0.365829 + 0.930682i \(0.380785\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 6762.00 0.394314
\(666\) 0 0
\(667\) 23328.0 1.35422
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −4080.00 −0.234734
\(672\) 0 0
\(673\) −21123.0 −1.20985 −0.604927 − 0.796281i \(-0.706798\pi\)
−0.604927 + 0.796281i \(0.706798\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −17456.0 −0.990973 −0.495486 − 0.868616i \(-0.665010\pi\)
−0.495486 + 0.868616i \(0.665010\pi\)
\(678\) 0 0
\(679\) −2898.00 −0.163792
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −21784.0 −1.22041 −0.610206 − 0.792243i \(-0.708913\pi\)
−0.610206 + 0.792243i \(0.708913\pi\)
\(684\) 0 0
\(685\) −10752.0 −0.599727
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −3744.00 −0.207017
\(690\) 0 0
\(691\) 2104.00 0.115832 0.0579160 − 0.998321i \(-0.481554\pi\)
0.0579160 + 0.998321i \(0.481554\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 14483.0 0.790463
\(696\) 0 0
\(697\) −22080.0 −1.19991
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −4832.00 −0.260345 −0.130173 − 0.991491i \(-0.541553\pi\)
−0.130173 + 0.991491i \(0.541553\pi\)
\(702\) 0 0
\(703\) 598.000 0.0320825
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −7476.00 −0.397686
\(708\) 0 0
\(709\) −31102.0 −1.64748 −0.823738 − 0.566971i \(-0.808115\pi\)
−0.823738 + 0.566971i \(0.808115\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −25920.0 −1.36145
\(714\) 0 0
\(715\) 546.000 0.0285584
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 32734.0 1.69788 0.848938 − 0.528493i \(-0.177243\pi\)
0.848938 + 0.528493i \(0.177243\pi\)
\(720\) 0 0
\(721\) 16548.0 0.854757
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −12312.0 −0.630698
\(726\) 0 0
\(727\) −27886.0 −1.42261 −0.711303 − 0.702886i \(-0.751895\pi\)
−0.711303 + 0.702886i \(0.751895\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 3795.00 0.192015
\(732\) 0 0
\(733\) 16803.0 0.846703 0.423351 − 0.905966i \(-0.360854\pi\)
0.423351 + 0.905966i \(0.360854\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 4332.00 0.216515
\(738\) 0 0
\(739\) −33748.0 −1.67989 −0.839946 − 0.542670i \(-0.817413\pi\)
−0.839946 + 0.542670i \(0.817413\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 10795.0 0.533015 0.266507 − 0.963833i \(-0.414130\pi\)
0.266507 + 0.963833i \(0.414130\pi\)
\(744\) 0 0
\(745\) 1106.00 0.0543902
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −18060.0 −0.881039
\(750\) 0 0
\(751\) 1976.00 0.0960123 0.0480062 − 0.998847i \(-0.484713\pi\)
0.0480062 + 0.998847i \(0.484713\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −12299.0 −0.592856
\(756\) 0 0
\(757\) −16896.0 −0.811223 −0.405611 − 0.914046i \(-0.632941\pi\)
−0.405611 + 0.914046i \(0.632941\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 22198.0 1.05739 0.528697 − 0.848811i \(-0.322681\pi\)
0.528697 + 0.848811i \(0.322681\pi\)
\(762\) 0 0
\(763\) −21399.0 −1.01533
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 5746.00 0.270503
\(768\) 0 0
\(769\) −8288.00 −0.388651 −0.194326 − 0.980937i \(-0.562252\pi\)
−0.194326 + 0.980937i \(0.562252\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 5835.00 0.271501 0.135751 − 0.990743i \(-0.456655\pi\)
0.135751 + 0.990743i \(0.456655\pi\)
\(774\) 0 0
\(775\) 13680.0 0.634065
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −8832.00 −0.406212
\(780\) 0 0
\(781\) −1242.00 −0.0569043
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −23926.0 −1.08784
\(786\) 0 0
\(787\) −28216.0 −1.27801 −0.639004 − 0.769204i \(-0.720653\pi\)
−0.639004 + 0.769204i \(0.720653\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −7938.00 −0.356818
\(792\) 0 0
\(793\) −8840.00 −0.395861
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 5826.00 0.258930 0.129465 − 0.991584i \(-0.458674\pi\)
0.129465 + 0.991584i \(0.458674\pi\)
\(798\) 0 0
\(799\) 44045.0 1.95019
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 1644.00 0.0722484
\(804\) 0 0
\(805\) 21168.0 0.926800
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −1807.00 −0.0785300 −0.0392650 − 0.999229i \(-0.512502\pi\)
−0.0392650 + 0.999229i \(0.512502\pi\)
\(810\) 0 0
\(811\) −16724.0 −0.724117 −0.362059 − 0.932155i \(-0.617926\pi\)
−0.362059 + 0.932155i \(0.617926\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 7728.00 0.332147
\(816\) 0 0
\(817\) 1518.00 0.0650038
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −30617.0 −1.30151 −0.650756 − 0.759287i \(-0.725548\pi\)
−0.650756 + 0.759287i \(0.725548\pi\)
\(822\) 0 0
\(823\) −14854.0 −0.629135 −0.314567 − 0.949235i \(-0.601859\pi\)
−0.314567 + 0.949235i \(0.601859\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −28334.0 −1.19138 −0.595689 − 0.803215i \(-0.703121\pi\)
−0.595689 + 0.803215i \(0.703121\pi\)
\(828\) 0 0
\(829\) −19170.0 −0.803138 −0.401569 − 0.915829i \(-0.631535\pi\)
−0.401569 + 0.915829i \(0.631535\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 11270.0 0.468766
\(834\) 0 0
\(835\) 26712.0 1.10707
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 26376.0 1.08534 0.542670 − 0.839946i \(-0.317413\pi\)
0.542670 + 0.839946i \(0.317413\pi\)
\(840\) 0 0
\(841\) 1855.00 0.0760589
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 1183.00 0.0481615
\(846\) 0 0
\(847\) −27195.0 −1.10322
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 1872.00 0.0754070
\(852\) 0 0
\(853\) −22961.0 −0.921653 −0.460826 − 0.887490i \(-0.652447\pi\)
−0.460826 + 0.887490i \(0.652447\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −6694.00 −0.266818 −0.133409 − 0.991061i \(-0.542592\pi\)
−0.133409 + 0.991061i \(0.542592\pi\)
\(858\) 0 0
\(859\) −12404.0 −0.492688 −0.246344 − 0.969182i \(-0.579229\pi\)
−0.246344 + 0.969182i \(0.579229\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −28361.0 −1.11868 −0.559339 − 0.828939i \(-0.688945\pi\)
−0.559339 + 0.828939i \(0.688945\pi\)
\(864\) 0 0
\(865\) −11088.0 −0.435842
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 5616.00 0.219229
\(870\) 0 0
\(871\) 9386.00 0.365135
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −29547.0 −1.14157
\(876\) 0 0
\(877\) −20257.0 −0.779966 −0.389983 − 0.920822i \(-0.627519\pi\)
−0.389983 + 0.920822i \(0.627519\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −7845.00 −0.300005 −0.150003 − 0.988686i \(-0.547928\pi\)
−0.150003 + 0.988686i \(0.547928\pi\)
\(882\) 0 0
\(883\) 33275.0 1.26817 0.634084 − 0.773264i \(-0.281377\pi\)
0.634084 + 0.773264i \(0.281377\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 48096.0 1.82064 0.910319 − 0.413908i \(-0.135836\pi\)
0.910319 + 0.413908i \(0.135836\pi\)
\(888\) 0 0
\(889\) −43428.0 −1.63839
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 17618.0 0.660206
\(894\) 0 0
\(895\) 33173.0 1.23894
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −29160.0 −1.08180
\(900\) 0 0
\(901\) −33120.0 −1.22463
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −14756.0 −0.541996
\(906\) 0 0
\(907\) −38459.0 −1.40795 −0.703975 − 0.710225i \(-0.748593\pi\)
−0.703975 + 0.710225i \(0.748593\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 15638.0 0.568727 0.284363 − 0.958717i \(-0.408218\pi\)
0.284363 + 0.958717i \(0.408218\pi\)
\(912\) 0 0
\(913\) −7224.00 −0.261861
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 63.0000 0.00226875
\(918\) 0 0
\(919\) 50976.0 1.82975 0.914877 − 0.403734i \(-0.132288\pi\)
0.914877 + 0.403734i \(0.132288\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −2691.00 −0.0959646
\(924\) 0 0
\(925\) −988.000 −0.0351192
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −15572.0 −0.549947 −0.274973 − 0.961452i \(-0.588669\pi\)
−0.274973 + 0.961452i \(0.588669\pi\)
\(930\) 0 0
\(931\) 4508.00 0.158694
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 4830.00 0.168939
\(936\) 0 0
\(937\) 8750.00 0.305069 0.152535 − 0.988298i \(-0.451256\pi\)
0.152535 + 0.988298i \(0.451256\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −16599.0 −0.575039 −0.287520 − 0.957775i \(-0.592831\pi\)
−0.287520 + 0.957775i \(0.592831\pi\)
\(942\) 0 0
\(943\) −27648.0 −0.954764
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −44010.0 −1.51017 −0.755086 − 0.655626i \(-0.772405\pi\)
−0.755086 + 0.655626i \(0.772405\pi\)
\(948\) 0 0
\(949\) 3562.00 0.121841
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 19657.0 0.668156 0.334078 − 0.942545i \(-0.391575\pi\)
0.334078 + 0.942545i \(0.391575\pi\)
\(954\) 0 0
\(955\) −6230.00 −0.211097
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −32256.0 −1.08613
\(960\) 0 0
\(961\) 2609.00 0.0875768
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −21196.0 −0.707071
\(966\) 0 0
\(967\) 50555.0 1.68122 0.840610 − 0.541641i \(-0.182197\pi\)
0.840610 + 0.541641i \(0.182197\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −36771.0 −1.21528 −0.607640 − 0.794212i \(-0.707884\pi\)
−0.607640 + 0.794212i \(0.707884\pi\)
\(972\) 0 0
\(973\) 43449.0 1.43156
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 14886.0 0.487457 0.243728 − 0.969844i \(-0.421629\pi\)
0.243728 + 0.969844i \(0.421629\pi\)
\(978\) 0 0
\(979\) 5796.00 0.189214
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −4637.00 −0.150455 −0.0752275 − 0.997166i \(-0.523968\pi\)
−0.0752275 + 0.997166i \(0.523968\pi\)
\(984\) 0 0
\(985\) 25543.0 0.826262
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 4752.00 0.152785
\(990\) 0 0
\(991\) 342.000 0.0109627 0.00548133 − 0.999985i \(-0.498255\pi\)
0.00548133 + 0.999985i \(0.498255\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 19194.0 0.611548
\(996\) 0 0
\(997\) 10586.0 0.336271 0.168135 − 0.985764i \(-0.446225\pi\)
0.168135 + 0.985764i \(0.446225\pi\)
\(998\) 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.l.1.1 1
3.2 odd 2 208.4.a.d.1.1 1
4.3 odd 2 936.4.a.b.1.1 1
12.11 even 2 104.4.a.a.1.1 ✓ 1
24.5 odd 2 832.4.a.l.1.1 1
24.11 even 2 832.4.a.i.1.1 1
156.155 even 2 1352.4.a.b.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
104.4.a.a.1.1 ✓ 1 12.11 even 2
208.4.a.d.1.1 1 3.2 odd 2
832.4.a.i.1.1 1 24.11 even 2
832.4.a.l.1.1 1 24.5 odd 2
936.4.a.b.1.1 1 4.3 odd 2
1352.4.a.b.1.1 1 156.155 even 2
1872.4.a.l.1.1 1 1.1 even 1 trivial