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Properties

Label 720.4.a.bd.1.1
Level $720$
Weight $4$
Character 720.1
Self dual yes
Analytic conductor $42.481$
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] = [720,4,Mod(1,720)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(720, 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("720.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 720.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: \(42.4813752041\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 40)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 720.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+5.00000 q^{5} +34.0000 q^{7} +O(q^{10})\) \(q+5.00000 q^{5} +34.0000 q^{7} +16.0000 q^{11} +58.0000 q^{13} +70.0000 q^{17} -4.00000 q^{19} -134.000 q^{23} +25.0000 q^{25} +242.000 q^{29} -100.000 q^{31} +170.000 q^{35} -438.000 q^{37} +138.000 q^{41} -178.000 q^{43} +22.0000 q^{47} +813.000 q^{49} -162.000 q^{53} +80.0000 q^{55} -268.000 q^{59} +250.000 q^{61} +290.000 q^{65} -422.000 q^{67} -852.000 q^{71} +306.000 q^{73} +544.000 q^{77} +456.000 q^{79} +434.000 q^{83} +350.000 q^{85} +726.000 q^{89} +1972.00 q^{91} -20.0000 q^{95} +1378.00 q^{97} +O(q^{100})\)

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
\(5\) 5.00000 0.447214
\(6\) 0 0
\(7\) 34.0000 1.83583 0.917914 − 0.396780i \(-0.129872\pi\)
0.917914 + 0.396780i \(0.129872\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 16.0000 0.438562 0.219281 − 0.975662i \(-0.429629\pi\)
0.219281 + 0.975662i \(0.429629\pi\)
\(12\) 0 0
\(13\) 58.0000 1.23741 0.618704 − 0.785624i \(-0.287658\pi\)
0.618704 + 0.785624i \(0.287658\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 70.0000 0.998676 0.499338 − 0.866407i \(-0.333577\pi\)
0.499338 + 0.866407i \(0.333577\pi\)
\(18\) 0 0
\(19\) −4.00000 −0.0482980 −0.0241490 − 0.999708i \(-0.507688\pi\)
−0.0241490 + 0.999708i \(0.507688\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −134.000 −1.21482 −0.607412 − 0.794387i \(-0.707792\pi\)
−0.607412 + 0.794387i \(0.707792\pi\)
\(24\) 0 0
\(25\) 25.0000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 242.000 1.54960 0.774798 − 0.632209i \(-0.217852\pi\)
0.774798 + 0.632209i \(0.217852\pi\)
\(30\) 0 0
\(31\) −100.000 −0.579372 −0.289686 − 0.957122i \(-0.593551\pi\)
−0.289686 + 0.957122i \(0.593551\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 170.000 0.821007
\(36\) 0 0
\(37\) −438.000 −1.94613 −0.973064 − 0.230534i \(-0.925953\pi\)
−0.973064 + 0.230534i \(0.925953\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 138.000 0.525658 0.262829 − 0.964842i \(-0.415344\pi\)
0.262829 + 0.964842i \(0.415344\pi\)
\(42\) 0 0
\(43\) −178.000 −0.631273 −0.315637 − 0.948880i \(-0.602218\pi\)
−0.315637 + 0.948880i \(0.602218\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 22.0000 0.0682772 0.0341386 − 0.999417i \(-0.489131\pi\)
0.0341386 + 0.999417i \(0.489131\pi\)
\(48\) 0 0
\(49\) 813.000 2.37026
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −162.000 −0.419857 −0.209928 − 0.977717i \(-0.567323\pi\)
−0.209928 + 0.977717i \(0.567323\pi\)
\(54\) 0 0
\(55\) 80.0000 0.196131
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −268.000 −0.591367 −0.295683 − 0.955286i \(-0.595547\pi\)
−0.295683 + 0.955286i \(0.595547\pi\)
\(60\) 0 0
\(61\) 250.000 0.524741 0.262371 − 0.964967i \(-0.415496\pi\)
0.262371 + 0.964967i \(0.415496\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 290.000 0.553386
\(66\) 0 0
\(67\) −422.000 −0.769485 −0.384743 − 0.923024i \(-0.625710\pi\)
−0.384743 + 0.923024i \(0.625710\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −852.000 −1.42414 −0.712069 − 0.702109i \(-0.752242\pi\)
−0.712069 + 0.702109i \(0.752242\pi\)
\(72\) 0 0
\(73\) 306.000 0.490611 0.245305 − 0.969446i \(-0.421112\pi\)
0.245305 + 0.969446i \(0.421112\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 544.000 0.805124
\(78\) 0 0
\(79\) 456.000 0.649418 0.324709 − 0.945814i \(-0.394734\pi\)
0.324709 + 0.945814i \(0.394734\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 434.000 0.573948 0.286974 − 0.957938i \(-0.407351\pi\)
0.286974 + 0.957938i \(0.407351\pi\)
\(84\) 0 0
\(85\) 350.000 0.446622
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 726.000 0.864672 0.432336 − 0.901712i \(-0.357689\pi\)
0.432336 + 0.901712i \(0.357689\pi\)
\(90\) 0 0
\(91\) 1972.00 2.27167
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −20.0000 −0.0215995
\(96\) 0 0
\(97\) 1378.00 1.44242 0.721210 − 0.692717i \(-0.243586\pi\)
0.721210 + 0.692717i \(0.243586\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −126.000 −0.124133 −0.0620667 − 0.998072i \(-0.519769\pi\)
−0.0620667 + 0.998072i \(0.519769\pi\)
\(102\) 0 0
\(103\) 1262.00 1.20727 0.603634 − 0.797262i \(-0.293719\pi\)
0.603634 + 0.797262i \(0.293719\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 510.000 0.460781 0.230390 − 0.973098i \(-0.426000\pi\)
0.230390 + 0.973098i \(0.426000\pi\)
\(108\) 0 0
\(109\) 26.0000 0.0228472 0.0114236 − 0.999935i \(-0.496364\pi\)
0.0114236 + 0.999935i \(0.496364\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −1242.00 −1.03396 −0.516980 − 0.855997i \(-0.672944\pi\)
−0.516980 + 0.855997i \(0.672944\pi\)
\(114\) 0 0
\(115\) −670.000 −0.543285
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 2380.00 1.83340
\(120\) 0 0
\(121\) −1075.00 −0.807663
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 125.000 0.0894427
\(126\) 0 0
\(127\) 978.000 0.683334 0.341667 − 0.939821i \(-0.389008\pi\)
0.341667 + 0.939821i \(0.389008\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −912.000 −0.608258 −0.304129 − 0.952631i \(-0.598365\pi\)
−0.304129 + 0.952631i \(0.598365\pi\)
\(132\) 0 0
\(133\) −136.000 −0.0886669
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 926.000 0.577471 0.288735 − 0.957409i \(-0.406765\pi\)
0.288735 + 0.957409i \(0.406765\pi\)
\(138\) 0 0
\(139\) −516.000 −0.314867 −0.157434 − 0.987530i \(-0.550322\pi\)
−0.157434 + 0.987530i \(0.550322\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 928.000 0.542680
\(144\) 0 0
\(145\) 1210.00 0.693000
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 958.000 0.526728 0.263364 − 0.964697i \(-0.415168\pi\)
0.263364 + 0.964697i \(0.415168\pi\)
\(150\) 0 0
\(151\) −332.000 −0.178926 −0.0894628 − 0.995990i \(-0.528515\pi\)
−0.0894628 + 0.995990i \(0.528515\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −500.000 −0.259103
\(156\) 0 0
\(157\) −1022.00 −0.519519 −0.259759 − 0.965673i \(-0.583643\pi\)
−0.259759 + 0.965673i \(0.583643\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −4556.00 −2.23021
\(162\) 0 0
\(163\) 926.000 0.444969 0.222484 − 0.974936i \(-0.428583\pi\)
0.222484 + 0.974936i \(0.428583\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 654.000 0.303042 0.151521 − 0.988454i \(-0.451583\pi\)
0.151521 + 0.988454i \(0.451583\pi\)
\(168\) 0 0
\(169\) 1167.00 0.531179
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 1294.00 0.568676 0.284338 − 0.958724i \(-0.408226\pi\)
0.284338 + 0.958724i \(0.408226\pi\)
\(174\) 0 0
\(175\) 850.000 0.367165
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −2836.00 −1.18420 −0.592102 − 0.805863i \(-0.701702\pi\)
−0.592102 + 0.805863i \(0.701702\pi\)
\(180\) 0 0
\(181\) 1742.00 0.715369 0.357685 − 0.933842i \(-0.383566\pi\)
0.357685 + 0.933842i \(0.383566\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −2190.00 −0.870335
\(186\) 0 0
\(187\) 1120.00 0.437981
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 4460.00 1.68960 0.844802 − 0.535079i \(-0.179718\pi\)
0.844802 + 0.535079i \(0.179718\pi\)
\(192\) 0 0
\(193\) −3782.00 −1.41054 −0.705270 − 0.708939i \(-0.749174\pi\)
−0.705270 + 0.708939i \(0.749174\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −4474.00 −1.61807 −0.809034 − 0.587762i \(-0.800009\pi\)
−0.809034 + 0.587762i \(0.800009\pi\)
\(198\) 0 0
\(199\) −3608.00 −1.28525 −0.642624 − 0.766182i \(-0.722154\pi\)
−0.642624 + 0.766182i \(0.722154\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 8228.00 2.84479
\(204\) 0 0
\(205\) 690.000 0.235081
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −64.0000 −0.0211817
\(210\) 0 0
\(211\) 256.000 0.0835250 0.0417625 − 0.999128i \(-0.486703\pi\)
0.0417625 + 0.999128i \(0.486703\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −890.000 −0.282314
\(216\) 0 0
\(217\) −3400.00 −1.06363
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 4060.00 1.23577
\(222\) 0 0
\(223\) 5158.00 1.54890 0.774451 − 0.632634i \(-0.218026\pi\)
0.774451 + 0.632634i \(0.218026\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −2226.00 −0.650858 −0.325429 − 0.945566i \(-0.605509\pi\)
−0.325429 + 0.945566i \(0.605509\pi\)
\(228\) 0 0
\(229\) 2086.00 0.601951 0.300975 − 0.953632i \(-0.402688\pi\)
0.300975 + 0.953632i \(0.402688\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 5718.00 1.60772 0.803860 − 0.594819i \(-0.202776\pi\)
0.803860 + 0.594819i \(0.202776\pi\)
\(234\) 0 0
\(235\) 110.000 0.0305345
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −3624.00 −0.980825 −0.490412 − 0.871491i \(-0.663154\pi\)
−0.490412 + 0.871491i \(0.663154\pi\)
\(240\) 0 0
\(241\) −82.0000 −0.0219174 −0.0109587 − 0.999940i \(-0.503488\pi\)
−0.0109587 + 0.999940i \(0.503488\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 4065.00 1.06001
\(246\) 0 0
\(247\) −232.000 −0.0597644
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −5040.00 −1.26742 −0.633709 − 0.773571i \(-0.718468\pi\)
−0.633709 + 0.773571i \(0.718468\pi\)
\(252\) 0 0
\(253\) −2144.00 −0.532775
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 2310.00 0.560676 0.280338 − 0.959901i \(-0.409553\pi\)
0.280338 + 0.959901i \(0.409553\pi\)
\(258\) 0 0
\(259\) −14892.0 −3.57276
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −4110.00 −0.963625 −0.481813 − 0.876274i \(-0.660021\pi\)
−0.481813 + 0.876274i \(0.660021\pi\)
\(264\) 0 0
\(265\) −810.000 −0.187766
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −746.000 −0.169087 −0.0845435 − 0.996420i \(-0.526943\pi\)
−0.0845435 + 0.996420i \(0.526943\pi\)
\(270\) 0 0
\(271\) 4596.00 1.03021 0.515105 − 0.857127i \(-0.327753\pi\)
0.515105 + 0.857127i \(0.327753\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 400.000 0.0877124
\(276\) 0 0
\(277\) −2206.00 −0.478504 −0.239252 − 0.970957i \(-0.576902\pi\)
−0.239252 + 0.970957i \(0.576902\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −8278.00 −1.75738 −0.878691 − 0.477392i \(-0.841582\pi\)
−0.878691 + 0.477392i \(0.841582\pi\)
\(282\) 0 0
\(283\) −1178.00 −0.247438 −0.123719 − 0.992317i \(-0.539482\pi\)
−0.123719 + 0.992317i \(0.539482\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 4692.00 0.965017
\(288\) 0 0
\(289\) −13.0000 −0.00264604
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −106.000 −0.0211351 −0.0105676 − 0.999944i \(-0.503364\pi\)
−0.0105676 + 0.999944i \(0.503364\pi\)
\(294\) 0 0
\(295\) −1340.00 −0.264467
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −7772.00 −1.50323
\(300\) 0 0
\(301\) −6052.00 −1.15891
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 1250.00 0.234671
\(306\) 0 0
\(307\) −8134.00 −1.51216 −0.756078 − 0.654482i \(-0.772887\pi\)
−0.756078 + 0.654482i \(0.772887\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −4396.00 −0.801525 −0.400763 − 0.916182i \(-0.631255\pi\)
−0.400763 + 0.916182i \(0.631255\pi\)
\(312\) 0 0
\(313\) 4826.00 0.871507 0.435753 − 0.900066i \(-0.356482\pi\)
0.435753 + 0.900066i \(0.356482\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −7026.00 −1.24486 −0.622428 − 0.782677i \(-0.713854\pi\)
−0.622428 + 0.782677i \(0.713854\pi\)
\(318\) 0 0
\(319\) 3872.00 0.679594
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −280.000 −0.0482341
\(324\) 0 0
\(325\) 1450.00 0.247482
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 748.000 0.125345
\(330\) 0 0
\(331\) −8808.00 −1.46263 −0.731316 − 0.682038i \(-0.761094\pi\)
−0.731316 + 0.682038i \(0.761094\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −2110.00 −0.344124
\(336\) 0 0
\(337\) 5602.00 0.905520 0.452760 − 0.891632i \(-0.350439\pi\)
0.452760 + 0.891632i \(0.350439\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −1600.00 −0.254090
\(342\) 0 0
\(343\) 15980.0 2.51557
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −6634.00 −1.02632 −0.513158 − 0.858294i \(-0.671525\pi\)
−0.513158 + 0.858294i \(0.671525\pi\)
\(348\) 0 0
\(349\) 3198.00 0.490501 0.245251 − 0.969460i \(-0.421130\pi\)
0.245251 + 0.969460i \(0.421130\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 5230.00 0.788569 0.394284 − 0.918988i \(-0.370992\pi\)
0.394284 + 0.918988i \(0.370992\pi\)
\(354\) 0 0
\(355\) −4260.00 −0.636894
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −312.000 −0.0458683 −0.0229342 − 0.999737i \(-0.507301\pi\)
−0.0229342 + 0.999737i \(0.507301\pi\)
\(360\) 0 0
\(361\) −6843.00 −0.997667
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 1530.00 0.219408
\(366\) 0 0
\(367\) −10790.0 −1.53470 −0.767348 − 0.641231i \(-0.778424\pi\)
−0.767348 + 0.641231i \(0.778424\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −5508.00 −0.770785
\(372\) 0 0
\(373\) −4190.00 −0.581635 −0.290818 − 0.956778i \(-0.593927\pi\)
−0.290818 + 0.956778i \(0.593927\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 14036.0 1.91748
\(378\) 0 0
\(379\) 6980.00 0.946012 0.473006 − 0.881059i \(-0.343169\pi\)
0.473006 + 0.881059i \(0.343169\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 13962.0 1.86273 0.931364 − 0.364089i \(-0.118620\pi\)
0.931364 + 0.364089i \(0.118620\pi\)
\(384\) 0 0
\(385\) 2720.00 0.360062
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −3810.00 −0.496593 −0.248296 − 0.968684i \(-0.579871\pi\)
−0.248296 + 0.968684i \(0.579871\pi\)
\(390\) 0 0
\(391\) −9380.00 −1.21321
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 2280.00 0.290428
\(396\) 0 0
\(397\) −9158.00 −1.15775 −0.578875 − 0.815416i \(-0.696508\pi\)
−0.578875 + 0.815416i \(0.696508\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −4866.00 −0.605976 −0.302988 − 0.952994i \(-0.597984\pi\)
−0.302988 + 0.952994i \(0.597984\pi\)
\(402\) 0 0
\(403\) −5800.00 −0.716920
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −7008.00 −0.853498
\(408\) 0 0
\(409\) 13486.0 1.63042 0.815208 − 0.579169i \(-0.196623\pi\)
0.815208 + 0.579169i \(0.196623\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −9112.00 −1.08565
\(414\) 0 0
\(415\) 2170.00 0.256677
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 5628.00 0.656195 0.328098 − 0.944644i \(-0.393593\pi\)
0.328098 + 0.944644i \(0.393593\pi\)
\(420\) 0 0
\(421\) 7938.00 0.918942 0.459471 − 0.888193i \(-0.348039\pi\)
0.459471 + 0.888193i \(0.348039\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 1750.00 0.199735
\(426\) 0 0
\(427\) 8500.00 0.963334
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 1916.00 0.214131 0.107066 − 0.994252i \(-0.465855\pi\)
0.107066 + 0.994252i \(0.465855\pi\)
\(432\) 0 0
\(433\) −16510.0 −1.83238 −0.916189 − 0.400746i \(-0.868751\pi\)
−0.916189 + 0.400746i \(0.868751\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 536.000 0.0586736
\(438\) 0 0
\(439\) 1256.00 0.136550 0.0682752 − 0.997667i \(-0.478250\pi\)
0.0682752 + 0.997667i \(0.478250\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −12222.0 −1.31080 −0.655400 − 0.755282i \(-0.727500\pi\)
−0.655400 + 0.755282i \(0.727500\pi\)
\(444\) 0 0
\(445\) 3630.00 0.386693
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 5946.00 0.624965 0.312482 − 0.949924i \(-0.398840\pi\)
0.312482 + 0.949924i \(0.398840\pi\)
\(450\) 0 0
\(451\) 2208.00 0.230534
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 9860.00 1.01592
\(456\) 0 0
\(457\) 1258.00 0.128768 0.0643838 − 0.997925i \(-0.479492\pi\)
0.0643838 + 0.997925i \(0.479492\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −16422.0 −1.65911 −0.829554 − 0.558426i \(-0.811405\pi\)
−0.829554 + 0.558426i \(0.811405\pi\)
\(462\) 0 0
\(463\) −2658.00 −0.266799 −0.133399 − 0.991062i \(-0.542589\pi\)
−0.133399 + 0.991062i \(0.542589\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 3686.00 0.365241 0.182621 − 0.983183i \(-0.441542\pi\)
0.182621 + 0.983183i \(0.441542\pi\)
\(468\) 0 0
\(469\) −14348.0 −1.41264
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −2848.00 −0.276852
\(474\) 0 0
\(475\) −100.000 −0.00965961
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 88.0000 0.00839420 0.00419710 − 0.999991i \(-0.498664\pi\)
0.00419710 + 0.999991i \(0.498664\pi\)
\(480\) 0 0
\(481\) −25404.0 −2.40816
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 6890.00 0.645070
\(486\) 0 0
\(487\) 14714.0 1.36911 0.684553 − 0.728963i \(-0.259997\pi\)
0.684553 + 0.728963i \(0.259997\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −7344.00 −0.675010 −0.337505 − 0.941324i \(-0.609583\pi\)
−0.337505 + 0.941324i \(0.609583\pi\)
\(492\) 0 0
\(493\) 16940.0 1.54754
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −28968.0 −2.61447
\(498\) 0 0
\(499\) −1604.00 −0.143898 −0.0719488 − 0.997408i \(-0.522922\pi\)
−0.0719488 + 0.997408i \(0.522922\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 14802.0 1.31210 0.656052 − 0.754715i \(-0.272225\pi\)
0.656052 + 0.754715i \(0.272225\pi\)
\(504\) 0 0
\(505\) −630.000 −0.0555141
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 22514.0 1.96054 0.980271 − 0.197660i \(-0.0633342\pi\)
0.980271 + 0.197660i \(0.0633342\pi\)
\(510\) 0 0
\(511\) 10404.0 0.900677
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 6310.00 0.539906
\(516\) 0 0
\(517\) 352.000 0.0299438
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 6710.00 0.564243 0.282121 − 0.959379i \(-0.408962\pi\)
0.282121 + 0.959379i \(0.408962\pi\)
\(522\) 0 0
\(523\) −7930.00 −0.663011 −0.331505 − 0.943453i \(-0.607557\pi\)
−0.331505 + 0.943453i \(0.607557\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −7000.00 −0.578605
\(528\) 0 0
\(529\) 5789.00 0.475795
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 8004.00 0.650454
\(534\) 0 0
\(535\) 2550.00 0.206068
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 13008.0 1.03951
\(540\) 0 0
\(541\) 4918.00 0.390834 0.195417 − 0.980720i \(-0.437394\pi\)
0.195417 + 0.980720i \(0.437394\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 130.000 0.0102176
\(546\) 0 0
\(547\) 3922.00 0.306568 0.153284 − 0.988182i \(-0.451015\pi\)
0.153284 + 0.988182i \(0.451015\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −968.000 −0.0748424
\(552\) 0 0
\(553\) 15504.0 1.19222
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −17786.0 −1.35299 −0.676496 − 0.736446i \(-0.736503\pi\)
−0.676496 + 0.736446i \(0.736503\pi\)
\(558\) 0 0
\(559\) −10324.0 −0.781143
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 20266.0 1.51707 0.758535 − 0.651633i \(-0.225916\pi\)
0.758535 + 0.651633i \(0.225916\pi\)
\(564\) 0 0
\(565\) −6210.00 −0.462401
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −13358.0 −0.984177 −0.492088 − 0.870545i \(-0.663766\pi\)
−0.492088 + 0.870545i \(0.663766\pi\)
\(570\) 0 0
\(571\) −16360.0 −1.19903 −0.599514 − 0.800364i \(-0.704639\pi\)
−0.599514 + 0.800364i \(0.704639\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −3350.00 −0.242965
\(576\) 0 0
\(577\) −15574.0 −1.12366 −0.561832 − 0.827251i \(-0.689903\pi\)
−0.561832 + 0.827251i \(0.689903\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 14756.0 1.05367
\(582\) 0 0
\(583\) −2592.00 −0.184133
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 6654.00 0.467870 0.233935 − 0.972252i \(-0.424840\pi\)
0.233935 + 0.972252i \(0.424840\pi\)
\(588\) 0 0
\(589\) 400.000 0.0279825
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 17742.0 1.22863 0.614314 − 0.789062i \(-0.289433\pi\)
0.614314 + 0.789062i \(0.289433\pi\)
\(594\) 0 0
\(595\) 11900.0 0.819920
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 15840.0 1.08048 0.540238 − 0.841512i \(-0.318334\pi\)
0.540238 + 0.841512i \(0.318334\pi\)
\(600\) 0 0
\(601\) −3002.00 −0.203751 −0.101875 − 0.994797i \(-0.532484\pi\)
−0.101875 + 0.994797i \(0.532484\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −5375.00 −0.361198
\(606\) 0 0
\(607\) 23610.0 1.57875 0.789374 − 0.613912i \(-0.210405\pi\)
0.789374 + 0.613912i \(0.210405\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 1276.00 0.0844868
\(612\) 0 0
\(613\) 23850.0 1.57144 0.785720 − 0.618583i \(-0.212293\pi\)
0.785720 + 0.618583i \(0.212293\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 5334.00 0.348037 0.174018 − 0.984742i \(-0.444325\pi\)
0.174018 + 0.984742i \(0.444325\pi\)
\(618\) 0 0
\(619\) 2164.00 0.140515 0.0702573 − 0.997529i \(-0.477618\pi\)
0.0702573 + 0.997529i \(0.477618\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 24684.0 1.58739
\(624\) 0 0
\(625\) 625.000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −30660.0 −1.94355
\(630\) 0 0
\(631\) 25220.0 1.59111 0.795557 − 0.605879i \(-0.207179\pi\)
0.795557 + 0.605879i \(0.207179\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 4890.00 0.305596
\(636\) 0 0
\(637\) 47154.0 2.93298
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 12306.0 0.758280 0.379140 − 0.925339i \(-0.376220\pi\)
0.379140 + 0.925339i \(0.376220\pi\)
\(642\) 0 0
\(643\) 27414.0 1.68134 0.840671 − 0.541547i \(-0.182161\pi\)
0.840671 + 0.541547i \(0.182161\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −21834.0 −1.32671 −0.663356 − 0.748304i \(-0.730869\pi\)
−0.663356 + 0.748304i \(0.730869\pi\)
\(648\) 0 0
\(649\) −4288.00 −0.259351
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 23998.0 1.43815 0.719077 − 0.694931i \(-0.244565\pi\)
0.719077 + 0.694931i \(0.244565\pi\)
\(654\) 0 0
\(655\) −4560.00 −0.272021
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −32004.0 −1.89180 −0.945902 − 0.324452i \(-0.894820\pi\)
−0.945902 + 0.324452i \(0.894820\pi\)
\(660\) 0 0
\(661\) −8526.00 −0.501699 −0.250849 − 0.968026i \(-0.580710\pi\)
−0.250849 + 0.968026i \(0.580710\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −680.000 −0.0396530
\(666\) 0 0
\(667\) −32428.0 −1.88248
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 4000.00 0.230132
\(672\) 0 0
\(673\) 8178.00 0.468408 0.234204 − 0.972187i \(-0.424752\pi\)
0.234204 + 0.972187i \(0.424752\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 16646.0 0.944989 0.472495 − 0.881334i \(-0.343354\pi\)
0.472495 + 0.881334i \(0.343354\pi\)
\(678\) 0 0
\(679\) 46852.0 2.64803
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −22446.0 −1.25750 −0.628750 − 0.777608i \(-0.716433\pi\)
−0.628750 + 0.777608i \(0.716433\pi\)
\(684\) 0 0
\(685\) 4630.00 0.258253
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −9396.00 −0.519534
\(690\) 0 0
\(691\) −35336.0 −1.94536 −0.972681 − 0.232147i \(-0.925425\pi\)
−0.972681 + 0.232147i \(0.925425\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −2580.00 −0.140813
\(696\) 0 0
\(697\) 9660.00 0.524962
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −3482.00 −0.187608 −0.0938041 − 0.995591i \(-0.529903\pi\)
−0.0938041 + 0.995591i \(0.529903\pi\)
\(702\) 0 0
\(703\) 1752.00 0.0939942
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −4284.00 −0.227887
\(708\) 0 0
\(709\) −19402.0 −1.02773 −0.513863 − 0.857872i \(-0.671786\pi\)
−0.513863 + 0.857872i \(0.671786\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 13400.0 0.703834
\(714\) 0 0
\(715\) 4640.00 0.242694
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −9896.00 −0.513294 −0.256647 − 0.966505i \(-0.582618\pi\)
−0.256647 + 0.966505i \(0.582618\pi\)
\(720\) 0 0
\(721\) 42908.0 2.21633
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 6050.00 0.309919
\(726\) 0 0
\(727\) −494.000 −0.0252014 −0.0126007 − 0.999921i \(-0.504011\pi\)
−0.0126007 + 0.999921i \(0.504011\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −12460.0 −0.630437
\(732\) 0 0
\(733\) 9282.00 0.467720 0.233860 − 0.972270i \(-0.424864\pi\)
0.233860 + 0.972270i \(0.424864\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −6752.00 −0.337467
\(738\) 0 0
\(739\) 3252.00 0.161877 0.0809383 − 0.996719i \(-0.474208\pi\)
0.0809383 + 0.996719i \(0.474208\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −4710.00 −0.232561 −0.116281 − 0.993216i \(-0.537097\pi\)
−0.116281 + 0.993216i \(0.537097\pi\)
\(744\) 0 0
\(745\) 4790.00 0.235560
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 17340.0 0.845914
\(750\) 0 0
\(751\) −25764.0 −1.25185 −0.625927 − 0.779882i \(-0.715279\pi\)
−0.625927 + 0.779882i \(0.715279\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −1660.00 −0.0800180
\(756\) 0 0
\(757\) −30094.0 −1.44489 −0.722447 − 0.691426i \(-0.756983\pi\)
−0.722447 + 0.691426i \(0.756983\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −22362.0 −1.06521 −0.532603 − 0.846365i \(-0.678786\pi\)
−0.532603 + 0.846365i \(0.678786\pi\)
\(762\) 0 0
\(763\) 884.000 0.0419436
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −15544.0 −0.731762
\(768\) 0 0
\(769\) −30398.0 −1.42546 −0.712731 − 0.701438i \(-0.752542\pi\)
−0.712731 + 0.701438i \(0.752542\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −1290.00 −0.0600234 −0.0300117 − 0.999550i \(-0.509554\pi\)
−0.0300117 + 0.999550i \(0.509554\pi\)
\(774\) 0 0
\(775\) −2500.00 −0.115874
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −552.000 −0.0253883
\(780\) 0 0
\(781\) −13632.0 −0.624573
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −5110.00 −0.232336
\(786\) 0 0
\(787\) −14.0000 −0.000634112 0 −0.000317056 − 1.00000i \(-0.500101\pi\)
−0.000317056 1.00000i \(0.500101\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −42228.0 −1.89817
\(792\) 0 0
\(793\) 14500.0 0.649319
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 38814.0 1.72505 0.862523 − 0.506017i \(-0.168883\pi\)
0.862523 + 0.506017i \(0.168883\pi\)
\(798\) 0 0
\(799\) 1540.00 0.0681868
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 4896.00 0.215163
\(804\) 0 0
\(805\) −22780.0 −0.997378
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −27402.0 −1.19086 −0.595428 − 0.803408i \(-0.703018\pi\)
−0.595428 + 0.803408i \(0.703018\pi\)
\(810\) 0 0
\(811\) 28576.0 1.23729 0.618643 − 0.785672i \(-0.287683\pi\)
0.618643 + 0.785672i \(0.287683\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 4630.00 0.198996
\(816\) 0 0
\(817\) 712.000 0.0304893
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −31762.0 −1.35018 −0.675092 − 0.737733i \(-0.735896\pi\)
−0.675092 + 0.737733i \(0.735896\pi\)
\(822\) 0 0
\(823\) −20506.0 −0.868523 −0.434261 − 0.900787i \(-0.642991\pi\)
−0.434261 + 0.900787i \(0.642991\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 13014.0 0.547208 0.273604 − 0.961842i \(-0.411784\pi\)
0.273604 + 0.961842i \(0.411784\pi\)
\(828\) 0 0
\(829\) −22790.0 −0.954800 −0.477400 − 0.878686i \(-0.658421\pi\)
−0.477400 + 0.878686i \(0.658421\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 56910.0 2.36712
\(834\) 0 0
\(835\) 3270.00 0.135525
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 23696.0 0.975062 0.487531 − 0.873106i \(-0.337898\pi\)
0.487531 + 0.873106i \(0.337898\pi\)
\(840\) 0 0
\(841\) 34175.0 1.40125
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 5835.00 0.237550
\(846\) 0 0
\(847\) −36550.0 −1.48273
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 58692.0 2.36420
\(852\) 0 0
\(853\) 5306.00 0.212982 0.106491 − 0.994314i \(-0.466038\pi\)
0.106491 + 0.994314i \(0.466038\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 21054.0 0.839196 0.419598 − 0.907710i \(-0.362171\pi\)
0.419598 + 0.907710i \(0.362171\pi\)
\(858\) 0 0
\(859\) −7364.00 −0.292499 −0.146249 − 0.989248i \(-0.546720\pi\)
−0.146249 + 0.989248i \(0.546720\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 17226.0 0.679467 0.339733 − 0.940522i \(-0.389663\pi\)
0.339733 + 0.940522i \(0.389663\pi\)
\(864\) 0 0
\(865\) 6470.00 0.254320
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 7296.00 0.284810
\(870\) 0 0
\(871\) −24476.0 −0.952167
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 4250.00 0.164201
\(876\) 0 0
\(877\) 21202.0 0.816352 0.408176 − 0.912903i \(-0.366165\pi\)
0.408176 + 0.912903i \(0.366165\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 29490.0 1.12774 0.563872 − 0.825862i \(-0.309311\pi\)
0.563872 + 0.825862i \(0.309311\pi\)
\(882\) 0 0
\(883\) −2570.00 −0.0979472 −0.0489736 − 0.998800i \(-0.515595\pi\)
−0.0489736 + 0.998800i \(0.515595\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 36334.0 1.37540 0.687698 − 0.725997i \(-0.258621\pi\)
0.687698 + 0.725997i \(0.258621\pi\)
\(888\) 0 0
\(889\) 33252.0 1.25448
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −88.0000 −0.00329766
\(894\) 0 0
\(895\) −14180.0 −0.529592
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −24200.0 −0.897792
\(900\) 0 0
\(901\) −11340.0 −0.419301
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 8710.00 0.319923
\(906\) 0 0
\(907\) 12474.0 0.456662 0.228331 − 0.973584i \(-0.426673\pi\)
0.228331 + 0.973584i \(0.426673\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −41132.0 −1.49590 −0.747949 − 0.663756i \(-0.768961\pi\)
−0.747949 + 0.663756i \(0.768961\pi\)
\(912\) 0 0
\(913\) 6944.00 0.251712
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −31008.0 −1.11666
\(918\) 0 0
\(919\) 38416.0 1.37892 0.689460 − 0.724324i \(-0.257848\pi\)
0.689460 + 0.724324i \(0.257848\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −49416.0 −1.76224
\(924\) 0 0
\(925\) −10950.0 −0.389226
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −41302.0 −1.45864 −0.729319 − 0.684174i \(-0.760163\pi\)
−0.729319 + 0.684174i \(0.760163\pi\)
\(930\) 0 0
\(931\) −3252.00 −0.114479
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 5600.00 0.195871
\(936\) 0 0
\(937\) −26150.0 −0.911722 −0.455861 − 0.890051i \(-0.650669\pi\)
−0.455861 + 0.890051i \(0.650669\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −35254.0 −1.22130 −0.610652 − 0.791899i \(-0.709093\pi\)
−0.610652 + 0.791899i \(0.709093\pi\)
\(942\) 0 0
\(943\) −18492.0 −0.638582
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 18550.0 0.636530 0.318265 − 0.948002i \(-0.396900\pi\)
0.318265 + 0.948002i \(0.396900\pi\)
\(948\) 0 0
\(949\) 17748.0 0.607086
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −17322.0 −0.588788 −0.294394 − 0.955684i \(-0.595118\pi\)
−0.294394 + 0.955684i \(0.595118\pi\)
\(954\) 0 0
\(955\) 22300.0 0.755614
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 31484.0 1.06014
\(960\) 0 0
\(961\) −19791.0 −0.664328
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −18910.0 −0.630813
\(966\) 0 0
\(967\) −35190.0 −1.17025 −0.585126 − 0.810942i \(-0.698955\pi\)
−0.585126 + 0.810942i \(0.698955\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −40696.0 −1.34500 −0.672501 − 0.740096i \(-0.734780\pi\)
−0.672501 + 0.740096i \(0.734780\pi\)
\(972\) 0 0
\(973\) −17544.0 −0.578042
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −44306.0 −1.45084 −0.725422 − 0.688304i \(-0.758355\pi\)
−0.725422 + 0.688304i \(0.758355\pi\)
\(978\) 0 0
\(979\) 11616.0 0.379212
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −18798.0 −0.609932 −0.304966 − 0.952363i \(-0.598645\pi\)
−0.304966 + 0.952363i \(0.598645\pi\)
\(984\) 0 0
\(985\) −22370.0 −0.723622
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 23852.0 0.766885
\(990\) 0 0
\(991\) −2468.00 −0.0791106 −0.0395553 − 0.999217i \(-0.512594\pi\)
−0.0395553 + 0.999217i \(0.512594\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −18040.0 −0.574780
\(996\) 0 0
\(997\) −61086.0 −1.94043 −0.970217 − 0.242237i \(-0.922119\pi\)
−0.970217 + 0.242237i \(0.922119\pi\)
\(998\) 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 720.4.a.bd.1.1 1
3.2 odd 2 80.4.a.e.1.1 1
4.3 odd 2 360.4.a.h.1.1 1
12.11 even 2 40.4.a.a.1.1 ✓ 1
15.2 even 4 400.4.c.f.49.1 2
15.8 even 4 400.4.c.f.49.2 2
15.14 odd 2 400.4.a.e.1.1 1
20.3 even 4 1800.4.f.j.649.2 2
20.7 even 4 1800.4.f.j.649.1 2
20.19 odd 2 1800.4.a.bi.1.1 1
24.5 odd 2 320.4.a.c.1.1 1
24.11 even 2 320.4.a.l.1.1 1
48.5 odd 4 1280.4.d.a.641.1 2
48.11 even 4 1280.4.d.p.641.2 2
48.29 odd 4 1280.4.d.a.641.2 2
48.35 even 4 1280.4.d.p.641.1 2
60.23 odd 4 200.4.c.c.49.1 2
60.47 odd 4 200.4.c.c.49.2 2
60.59 even 2 200.4.a.i.1.1 1
84.83 odd 2 1960.4.a.h.1.1 1
120.29 odd 2 1600.4.a.br.1.1 1
120.59 even 2 1600.4.a.j.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
40.4.a.a.1.1 ✓ 1 12.11 even 2
80.4.a.e.1.1 1 3.2 odd 2
200.4.a.i.1.1 1 60.59 even 2
200.4.c.c.49.1 2 60.23 odd 4
200.4.c.c.49.2 2 60.47 odd 4
320.4.a.c.1.1 1 24.5 odd 2
320.4.a.l.1.1 1 24.11 even 2
360.4.a.h.1.1 1 4.3 odd 2
400.4.a.e.1.1 1 15.14 odd 2
400.4.c.f.49.1 2 15.2 even 4
400.4.c.f.49.2 2 15.8 even 4
720.4.a.bd.1.1 1 1.1 even 1 trivial
1280.4.d.a.641.1 2 48.5 odd 4
1280.4.d.a.641.2 2 48.29 odd 4
1280.4.d.p.641.1 2 48.35 even 4
1280.4.d.p.641.2 2 48.11 even 4
1600.4.a.j.1.1 1 120.59 even 2
1600.4.a.br.1.1 1 120.29 odd 2
1800.4.a.bi.1.1 1 20.19 odd 2
1800.4.f.j.649.1 2 20.7 even 4
1800.4.f.j.649.2 2 20.3 even 4
1960.4.a.h.1.1 1 84.83 odd 2