Properties

Label 600.4.a.n.1.1
Level $600$
Weight $4$
Character 600.1
Self dual yes
Analytic conductor $35.401$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [600,4,Mod(1,600)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(600, 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("600.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 600.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: \(35.4011460034\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 600.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+3.00000 q^{3} +5.00000 q^{7} +9.00000 q^{9} +O(q^{10})\) \(q+3.00000 q^{3} +5.00000 q^{7} +9.00000 q^{9} +14.0000 q^{11} +1.00000 q^{13} +46.0000 q^{17} +19.0000 q^{19} +15.0000 q^{21} -46.0000 q^{23} +27.0000 q^{27} +14.0000 q^{29} +133.000 q^{31} +42.0000 q^{33} +258.000 q^{37} +3.00000 q^{39} +84.0000 q^{41} -167.000 q^{43} +410.000 q^{47} -318.000 q^{49} +138.000 q^{51} +456.000 q^{53} +57.0000 q^{57} -194.000 q^{59} -17.0000 q^{61} +45.0000 q^{63} +653.000 q^{67} -138.000 q^{69} +828.000 q^{71} +570.000 q^{73} +70.0000 q^{77} -552.000 q^{79} +81.0000 q^{81} +142.000 q^{83} +42.0000 q^{87} -1104.00 q^{89} +5.00000 q^{91} +399.000 q^{93} +841.000 q^{97} +126.000 q^{99} +O(q^{100})\)

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
\(3\) 3.00000 0.577350
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 5.00000 0.269975 0.134987 0.990847i \(-0.456901\pi\)
0.134987 + 0.990847i \(0.456901\pi\)
\(8\) 0 0
\(9\) 9.00000 0.333333
\(10\) 0 0
\(11\) 14.0000 0.383742 0.191871 0.981420i \(-0.438545\pi\)
0.191871 + 0.981420i \(0.438545\pi\)
\(12\) 0 0
\(13\) 1.00000 0.0213346 0.0106673 0.999943i \(-0.496604\pi\)
0.0106673 + 0.999943i \(0.496604\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 46.0000 0.656273 0.328136 0.944630i \(-0.393579\pi\)
0.328136 + 0.944630i \(0.393579\pi\)
\(18\) 0 0
\(19\) 19.0000 0.229416 0.114708 0.993399i \(-0.463407\pi\)
0.114708 + 0.993399i \(0.463407\pi\)
\(20\) 0 0
\(21\) 15.0000 0.155870
\(22\) 0 0
\(23\) −46.0000 −0.417029 −0.208514 0.978019i \(-0.566863\pi\)
−0.208514 + 0.978019i \(0.566863\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 27.0000 0.192450
\(28\) 0 0
\(29\) 14.0000 0.0896460 0.0448230 0.998995i \(-0.485728\pi\)
0.0448230 + 0.998995i \(0.485728\pi\)
\(30\) 0 0
\(31\) 133.000 0.770565 0.385282 0.922799i \(-0.374104\pi\)
0.385282 + 0.922799i \(0.374104\pi\)
\(32\) 0 0
\(33\) 42.0000 0.221553
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 258.000 1.14635 0.573175 0.819433i \(-0.305712\pi\)
0.573175 + 0.819433i \(0.305712\pi\)
\(38\) 0 0
\(39\) 3.00000 0.0123176
\(40\) 0 0
\(41\) 84.0000 0.319966 0.159983 0.987120i \(-0.448856\pi\)
0.159983 + 0.987120i \(0.448856\pi\)
\(42\) 0 0
\(43\) −167.000 −0.592262 −0.296131 0.955147i \(-0.595696\pi\)
−0.296131 + 0.955147i \(0.595696\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 410.000 1.27244 0.636220 0.771508i \(-0.280497\pi\)
0.636220 + 0.771508i \(0.280497\pi\)
\(48\) 0 0
\(49\) −318.000 −0.927114
\(50\) 0 0
\(51\) 138.000 0.378899
\(52\) 0 0
\(53\) 456.000 1.18182 0.590910 0.806738i \(-0.298769\pi\)
0.590910 + 0.806738i \(0.298769\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 57.0000 0.132453
\(58\) 0 0
\(59\) −194.000 −0.428079 −0.214039 0.976825i \(-0.568662\pi\)
−0.214039 + 0.976825i \(0.568662\pi\)
\(60\) 0 0
\(61\) −17.0000 −0.0356824 −0.0178412 0.999841i \(-0.505679\pi\)
−0.0178412 + 0.999841i \(0.505679\pi\)
\(62\) 0 0
\(63\) 45.0000 0.0899915
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 653.000 1.19070 0.595348 0.803468i \(-0.297014\pi\)
0.595348 + 0.803468i \(0.297014\pi\)
\(68\) 0 0
\(69\) −138.000 −0.240772
\(70\) 0 0
\(71\) 828.000 1.38402 0.692011 0.721887i \(-0.256725\pi\)
0.692011 + 0.721887i \(0.256725\pi\)
\(72\) 0 0
\(73\) 570.000 0.913883 0.456941 0.889497i \(-0.348945\pi\)
0.456941 + 0.889497i \(0.348945\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 70.0000 0.103601
\(78\) 0 0
\(79\) −552.000 −0.786137 −0.393069 0.919509i \(-0.628587\pi\)
−0.393069 + 0.919509i \(0.628587\pi\)
\(80\) 0 0
\(81\) 81.0000 0.111111
\(82\) 0 0
\(83\) 142.000 0.187789 0.0938947 0.995582i \(-0.470068\pi\)
0.0938947 + 0.995582i \(0.470068\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 42.0000 0.0517572
\(88\) 0 0
\(89\) −1104.00 −1.31487 −0.657437 0.753510i \(-0.728359\pi\)
−0.657437 + 0.753510i \(0.728359\pi\)
\(90\) 0 0
\(91\) 5.00000 0.00575981
\(92\) 0 0
\(93\) 399.000 0.444886
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 841.000 0.880316 0.440158 0.897920i \(-0.354923\pi\)
0.440158 + 0.897920i \(0.354923\pi\)
\(98\) 0 0
\(99\) 126.000 0.127914
\(100\) 0 0
\(101\) 552.000 0.543822 0.271911 0.962322i \(-0.412344\pi\)
0.271911 + 0.962322i \(0.412344\pi\)
\(102\) 0 0
\(103\) −308.000 −0.294642 −0.147321 0.989089i \(-0.547065\pi\)
−0.147321 + 0.989089i \(0.547065\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 984.000 0.889036 0.444518 0.895770i \(-0.353375\pi\)
0.444518 + 0.895770i \(0.353375\pi\)
\(108\) 0 0
\(109\) −1843.00 −1.61952 −0.809759 0.586763i \(-0.800402\pi\)
−0.809759 + 0.586763i \(0.800402\pi\)
\(110\) 0 0
\(111\) 774.000 0.661845
\(112\) 0 0
\(113\) 876.000 0.729267 0.364633 0.931151i \(-0.381194\pi\)
0.364633 + 0.931151i \(0.381194\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 9.00000 0.00711154
\(118\) 0 0
\(119\) 230.000 0.177177
\(120\) 0 0
\(121\) −1135.00 −0.852742
\(122\) 0 0
\(123\) 252.000 0.184732
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 2376.00 1.66013 0.830063 0.557670i \(-0.188305\pi\)
0.830063 + 0.557670i \(0.188305\pi\)
\(128\) 0 0
\(129\) −501.000 −0.341943
\(130\) 0 0
\(131\) 1056.00 0.704299 0.352149 0.935944i \(-0.385451\pi\)
0.352149 + 0.935944i \(0.385451\pi\)
\(132\) 0 0
\(133\) 95.0000 0.0619364
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −778.000 −0.485175 −0.242588 0.970129i \(-0.577996\pi\)
−0.242588 + 0.970129i \(0.577996\pi\)
\(138\) 0 0
\(139\) 1692.00 1.03247 0.516236 0.856446i \(-0.327333\pi\)
0.516236 + 0.856446i \(0.327333\pi\)
\(140\) 0 0
\(141\) 1230.00 0.734643
\(142\) 0 0
\(143\) 14.0000 0.00818698
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −954.000 −0.535269
\(148\) 0 0
\(149\) −494.000 −0.271611 −0.135806 0.990736i \(-0.543362\pi\)
−0.135806 + 0.990736i \(0.543362\pi\)
\(150\) 0 0
\(151\) −841.000 −0.453242 −0.226621 0.973983i \(-0.572768\pi\)
−0.226621 + 0.973983i \(0.572768\pi\)
\(152\) 0 0
\(153\) 414.000 0.218758
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 19.0000 0.00965838 0.00482919 0.999988i \(-0.498463\pi\)
0.00482919 + 0.999988i \(0.498463\pi\)
\(158\) 0 0
\(159\) 1368.00 0.682324
\(160\) 0 0
\(161\) −230.000 −0.112587
\(162\) 0 0
\(163\) −2261.00 −1.08647 −0.543237 0.839580i \(-0.682801\pi\)
−0.543237 + 0.839580i \(0.682801\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 2112.00 0.978632 0.489316 0.872107i \(-0.337247\pi\)
0.489316 + 0.872107i \(0.337247\pi\)
\(168\) 0 0
\(169\) −2196.00 −0.999545
\(170\) 0 0
\(171\) 171.000 0.0764719
\(172\) 0 0
\(173\) 562.000 0.246983 0.123492 0.992346i \(-0.460591\pi\)
0.123492 + 0.992346i \(0.460591\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −582.000 −0.247151
\(178\) 0 0
\(179\) 3718.00 1.55249 0.776247 0.630429i \(-0.217121\pi\)
0.776247 + 0.630429i \(0.217121\pi\)
\(180\) 0 0
\(181\) −1639.00 −0.673071 −0.336536 0.941671i \(-0.609255\pi\)
−0.336536 + 0.941671i \(0.609255\pi\)
\(182\) 0 0
\(183\) −51.0000 −0.0206012
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 644.000 0.251839
\(188\) 0 0
\(189\) 135.000 0.0519566
\(190\) 0 0
\(191\) 2410.00 0.912992 0.456496 0.889725i \(-0.349104\pi\)
0.456496 + 0.889725i \(0.349104\pi\)
\(192\) 0 0
\(193\) −2621.00 −0.977532 −0.488766 0.872415i \(-0.662553\pi\)
−0.488766 + 0.872415i \(0.662553\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −4954.00 −1.79166 −0.895832 0.444392i \(-0.853420\pi\)
−0.895832 + 0.444392i \(0.853420\pi\)
\(198\) 0 0
\(199\) 1739.00 0.619470 0.309735 0.950823i \(-0.399760\pi\)
0.309735 + 0.950823i \(0.399760\pi\)
\(200\) 0 0
\(201\) 1959.00 0.687449
\(202\) 0 0
\(203\) 70.0000 0.0242022
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −414.000 −0.139010
\(208\) 0 0
\(209\) 266.000 0.0880364
\(210\) 0 0
\(211\) −4525.00 −1.47637 −0.738184 0.674599i \(-0.764317\pi\)
−0.738184 + 0.674599i \(0.764317\pi\)
\(212\) 0 0
\(213\) 2484.00 0.799065
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 665.000 0.208033
\(218\) 0 0
\(219\) 1710.00 0.527631
\(220\) 0 0
\(221\) 46.0000 0.0140013
\(222\) 0 0
\(223\) −3211.00 −0.964235 −0.482118 0.876106i \(-0.660132\pi\)
−0.482118 + 0.876106i \(0.660132\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −2484.00 −0.726295 −0.363147 0.931732i \(-0.618298\pi\)
−0.363147 + 0.931732i \(0.618298\pi\)
\(228\) 0 0
\(229\) −1847.00 −0.532983 −0.266492 0.963837i \(-0.585864\pi\)
−0.266492 + 0.963837i \(0.585864\pi\)
\(230\) 0 0
\(231\) 210.000 0.0598138
\(232\) 0 0
\(233\) −1020.00 −0.286792 −0.143396 0.989665i \(-0.545802\pi\)
−0.143396 + 0.989665i \(0.545802\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −1656.00 −0.453877
\(238\) 0 0
\(239\) 1176.00 0.318281 0.159140 0.987256i \(-0.449128\pi\)
0.159140 + 0.987256i \(0.449128\pi\)
\(240\) 0 0
\(241\) −6967.00 −1.86217 −0.931087 0.364797i \(-0.881138\pi\)
−0.931087 + 0.364797i \(0.881138\pi\)
\(242\) 0 0
\(243\) 243.000 0.0641500
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 19.0000 0.00489450
\(248\) 0 0
\(249\) 426.000 0.108420
\(250\) 0 0
\(251\) 1380.00 0.347031 0.173516 0.984831i \(-0.444487\pi\)
0.173516 + 0.984831i \(0.444487\pi\)
\(252\) 0 0
\(253\) −644.000 −0.160031
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −6924.00 −1.68057 −0.840286 0.542143i \(-0.817613\pi\)
−0.840286 + 0.542143i \(0.817613\pi\)
\(258\) 0 0
\(259\) 1290.00 0.309485
\(260\) 0 0
\(261\) 126.000 0.0298820
\(262\) 0 0
\(263\) 1884.00 0.441720 0.220860 0.975305i \(-0.429114\pi\)
0.220860 + 0.975305i \(0.429114\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −3312.00 −0.759143
\(268\) 0 0
\(269\) 3610.00 0.818236 0.409118 0.912481i \(-0.365836\pi\)
0.409118 + 0.912481i \(0.365836\pi\)
\(270\) 0 0
\(271\) −6072.00 −1.36106 −0.680531 0.732719i \(-0.738251\pi\)
−0.680531 + 0.732719i \(0.738251\pi\)
\(272\) 0 0
\(273\) 15.0000 0.00332543
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −2803.00 −0.608000 −0.304000 0.952672i \(-0.598322\pi\)
−0.304000 + 0.952672i \(0.598322\pi\)
\(278\) 0 0
\(279\) 1197.00 0.256855
\(280\) 0 0
\(281\) −6694.00 −1.42111 −0.710553 0.703644i \(-0.751555\pi\)
−0.710553 + 0.703644i \(0.751555\pi\)
\(282\) 0 0
\(283\) −6481.00 −1.36133 −0.680663 0.732596i \(-0.738308\pi\)
−0.680663 + 0.732596i \(0.738308\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 420.000 0.0863826
\(288\) 0 0
\(289\) −2797.00 −0.569306
\(290\) 0 0
\(291\) 2523.00 0.508250
\(292\) 0 0
\(293\) 3014.00 0.600955 0.300477 0.953789i \(-0.402854\pi\)
0.300477 + 0.953789i \(0.402854\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 378.000 0.0738511
\(298\) 0 0
\(299\) −46.0000 −0.00889715
\(300\) 0 0
\(301\) −835.000 −0.159896
\(302\) 0 0
\(303\) 1656.00 0.313976
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −5369.00 −0.998127 −0.499064 0.866565i \(-0.666323\pi\)
−0.499064 + 0.866565i \(0.666323\pi\)
\(308\) 0 0
\(309\) −924.000 −0.170112
\(310\) 0 0
\(311\) 4846.00 0.883574 0.441787 0.897120i \(-0.354345\pi\)
0.441787 + 0.897120i \(0.354345\pi\)
\(312\) 0 0
\(313\) −757.000 −0.136703 −0.0683517 0.997661i \(-0.521774\pi\)
−0.0683517 + 0.997661i \(0.521774\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −7632.00 −1.35223 −0.676113 0.736798i \(-0.736337\pi\)
−0.676113 + 0.736798i \(0.736337\pi\)
\(318\) 0 0
\(319\) 196.000 0.0344009
\(320\) 0 0
\(321\) 2952.00 0.513285
\(322\) 0 0
\(323\) 874.000 0.150559
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −5529.00 −0.935029
\(328\) 0 0
\(329\) 2050.00 0.343526
\(330\) 0 0
\(331\) −6780.00 −1.12587 −0.562934 0.826502i \(-0.690328\pi\)
−0.562934 + 0.826502i \(0.690328\pi\)
\(332\) 0 0
\(333\) 2322.00 0.382117
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 7849.00 1.26873 0.634365 0.773033i \(-0.281261\pi\)
0.634365 + 0.773033i \(0.281261\pi\)
\(338\) 0 0
\(339\) 2628.00 0.421042
\(340\) 0 0
\(341\) 1862.00 0.295698
\(342\) 0 0
\(343\) −3305.00 −0.520272
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 634.000 0.0980833 0.0490416 0.998797i \(-0.484383\pi\)
0.0490416 + 0.998797i \(0.484383\pi\)
\(348\) 0 0
\(349\) 930.000 0.142641 0.0713206 0.997453i \(-0.477279\pi\)
0.0713206 + 0.997453i \(0.477279\pi\)
\(350\) 0 0
\(351\) 27.0000 0.00410585
\(352\) 0 0
\(353\) −4286.00 −0.646234 −0.323117 0.946359i \(-0.604731\pi\)
−0.323117 + 0.946359i \(0.604731\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 690.000 0.102293
\(358\) 0 0
\(359\) −4236.00 −0.622751 −0.311375 0.950287i \(-0.600790\pi\)
−0.311375 + 0.950287i \(0.600790\pi\)
\(360\) 0 0
\(361\) −6498.00 −0.947368
\(362\) 0 0
\(363\) −3405.00 −0.492331
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 1451.00 0.206380 0.103190 0.994662i \(-0.467095\pi\)
0.103190 + 0.994662i \(0.467095\pi\)
\(368\) 0 0
\(369\) 756.000 0.106655
\(370\) 0 0
\(371\) 2280.00 0.319061
\(372\) 0 0
\(373\) 3115.00 0.432409 0.216205 0.976348i \(-0.430632\pi\)
0.216205 + 0.976348i \(0.430632\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 14.0000 0.00191256
\(378\) 0 0
\(379\) −1415.00 −0.191777 −0.0958887 0.995392i \(-0.530569\pi\)
−0.0958887 + 0.995392i \(0.530569\pi\)
\(380\) 0 0
\(381\) 7128.00 0.958474
\(382\) 0 0
\(383\) −180.000 −0.0240145 −0.0120073 0.999928i \(-0.503822\pi\)
−0.0120073 + 0.999928i \(0.503822\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −1503.00 −0.197421
\(388\) 0 0
\(389\) 12372.0 1.61256 0.806279 0.591535i \(-0.201478\pi\)
0.806279 + 0.591535i \(0.201478\pi\)
\(390\) 0 0
\(391\) −2116.00 −0.273685
\(392\) 0 0
\(393\) 3168.00 0.406627
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 5767.00 0.729062 0.364531 0.931191i \(-0.381229\pi\)
0.364531 + 0.931191i \(0.381229\pi\)
\(398\) 0 0
\(399\) 285.000 0.0357590
\(400\) 0 0
\(401\) −3120.00 −0.388542 −0.194271 0.980948i \(-0.562234\pi\)
−0.194271 + 0.980948i \(0.562234\pi\)
\(402\) 0 0
\(403\) 133.000 0.0164397
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 3612.00 0.439902
\(408\) 0 0
\(409\) 1501.00 0.181466 0.0907331 0.995875i \(-0.471079\pi\)
0.0907331 + 0.995875i \(0.471079\pi\)
\(410\) 0 0
\(411\) −2334.00 −0.280116
\(412\) 0 0
\(413\) −970.000 −0.115570
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 5076.00 0.596098
\(418\) 0 0
\(419\) −9072.00 −1.05775 −0.528874 0.848701i \(-0.677386\pi\)
−0.528874 + 0.848701i \(0.677386\pi\)
\(420\) 0 0
\(421\) 7350.00 0.850872 0.425436 0.904989i \(-0.360121\pi\)
0.425436 + 0.904989i \(0.360121\pi\)
\(422\) 0 0
\(423\) 3690.00 0.424146
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −85.0000 −0.00963334
\(428\) 0 0
\(429\) 42.0000 0.00472676
\(430\) 0 0
\(431\) 5962.00 0.666310 0.333155 0.942872i \(-0.391887\pi\)
0.333155 + 0.942872i \(0.391887\pi\)
\(432\) 0 0
\(433\) −10093.0 −1.12018 −0.560091 0.828431i \(-0.689234\pi\)
−0.560091 + 0.828431i \(0.689234\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −874.000 −0.0956730
\(438\) 0 0
\(439\) −2555.00 −0.277776 −0.138888 0.990308i \(-0.544353\pi\)
−0.138888 + 0.990308i \(0.544353\pi\)
\(440\) 0 0
\(441\) −2862.00 −0.309038
\(442\) 0 0
\(443\) 6240.00 0.669236 0.334618 0.942354i \(-0.391393\pi\)
0.334618 + 0.942354i \(0.391393\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −1482.00 −0.156815
\(448\) 0 0
\(449\) 3324.00 0.349375 0.174687 0.984624i \(-0.444109\pi\)
0.174687 + 0.984624i \(0.444109\pi\)
\(450\) 0 0
\(451\) 1176.00 0.122784
\(452\) 0 0
\(453\) −2523.00 −0.261680
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 16774.0 1.71697 0.858484 0.512840i \(-0.171407\pi\)
0.858484 + 0.512840i \(0.171407\pi\)
\(458\) 0 0
\(459\) 1242.00 0.126300
\(460\) 0 0
\(461\) 14304.0 1.44513 0.722564 0.691304i \(-0.242964\pi\)
0.722564 + 0.691304i \(0.242964\pi\)
\(462\) 0 0
\(463\) 6936.00 0.696206 0.348103 0.937456i \(-0.386826\pi\)
0.348103 + 0.937456i \(0.386826\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 15622.0 1.54797 0.773983 0.633207i \(-0.218262\pi\)
0.773983 + 0.633207i \(0.218262\pi\)
\(468\) 0 0
\(469\) 3265.00 0.321458
\(470\) 0 0
\(471\) 57.0000 0.00557627
\(472\) 0 0
\(473\) −2338.00 −0.227276
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 4104.00 0.393940
\(478\) 0 0
\(479\) −13354.0 −1.27382 −0.636910 0.770938i \(-0.719788\pi\)
−0.636910 + 0.770938i \(0.719788\pi\)
\(480\) 0 0
\(481\) 258.000 0.0244569
\(482\) 0 0
\(483\) −690.000 −0.0650023
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −461.000 −0.0428951 −0.0214475 0.999770i \(-0.506827\pi\)
−0.0214475 + 0.999770i \(0.506827\pi\)
\(488\) 0 0
\(489\) −6783.00 −0.627276
\(490\) 0 0
\(491\) 3768.00 0.346329 0.173164 0.984893i \(-0.444601\pi\)
0.173164 + 0.984893i \(0.444601\pi\)
\(492\) 0 0
\(493\) 644.000 0.0588323
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 4140.00 0.373651
\(498\) 0 0
\(499\) −14317.0 −1.28440 −0.642201 0.766536i \(-0.721979\pi\)
−0.642201 + 0.766536i \(0.721979\pi\)
\(500\) 0 0
\(501\) 6336.00 0.565013
\(502\) 0 0
\(503\) 9228.00 0.818004 0.409002 0.912533i \(-0.365877\pi\)
0.409002 + 0.912533i \(0.365877\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −6588.00 −0.577087
\(508\) 0 0
\(509\) 4574.00 0.398308 0.199154 0.979968i \(-0.436181\pi\)
0.199154 + 0.979968i \(0.436181\pi\)
\(510\) 0 0
\(511\) 2850.00 0.246725
\(512\) 0 0
\(513\) 513.000 0.0441511
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 5740.00 0.488288
\(518\) 0 0
\(519\) 1686.00 0.142596
\(520\) 0 0
\(521\) −8494.00 −0.714259 −0.357129 0.934055i \(-0.616245\pi\)
−0.357129 + 0.934055i \(0.616245\pi\)
\(522\) 0 0
\(523\) 8263.00 0.690852 0.345426 0.938446i \(-0.387734\pi\)
0.345426 + 0.938446i \(0.387734\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 6118.00 0.505701
\(528\) 0 0
\(529\) −10051.0 −0.826087
\(530\) 0 0
\(531\) −1746.00 −0.142693
\(532\) 0 0
\(533\) 84.0000 0.00682635
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 11154.0 0.896333
\(538\) 0 0
\(539\) −4452.00 −0.355772
\(540\) 0 0
\(541\) 21157.0 1.68135 0.840675 0.541540i \(-0.182158\pi\)
0.840675 + 0.541540i \(0.182158\pi\)
\(542\) 0 0
\(543\) −4917.00 −0.388598
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −4048.00 −0.316417 −0.158208 0.987406i \(-0.550572\pi\)
−0.158208 + 0.987406i \(0.550572\pi\)
\(548\) 0 0
\(549\) −153.000 −0.0118941
\(550\) 0 0
\(551\) 266.000 0.0205662
\(552\) 0 0
\(553\) −2760.00 −0.212237
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −6758.00 −0.514086 −0.257043 0.966400i \(-0.582748\pi\)
−0.257043 + 0.966400i \(0.582748\pi\)
\(558\) 0 0
\(559\) −167.000 −0.0126357
\(560\) 0 0
\(561\) 1932.00 0.145399
\(562\) 0 0
\(563\) 24506.0 1.83447 0.917233 0.398350i \(-0.130417\pi\)
0.917233 + 0.398350i \(0.130417\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 405.000 0.0299972
\(568\) 0 0
\(569\) −1430.00 −0.105358 −0.0526790 0.998611i \(-0.516776\pi\)
−0.0526790 + 0.998611i \(0.516776\pi\)
\(570\) 0 0
\(571\) 3691.00 0.270514 0.135257 0.990811i \(-0.456814\pi\)
0.135257 + 0.990811i \(0.456814\pi\)
\(572\) 0 0
\(573\) 7230.00 0.527116
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 4571.00 0.329798 0.164899 0.986310i \(-0.447270\pi\)
0.164899 + 0.986310i \(0.447270\pi\)
\(578\) 0 0
\(579\) −7863.00 −0.564378
\(580\) 0 0
\(581\) 710.000 0.0506984
\(582\) 0 0
\(583\) 6384.00 0.453513
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 14808.0 1.04121 0.520606 0.853797i \(-0.325706\pi\)
0.520606 + 0.853797i \(0.325706\pi\)
\(588\) 0 0
\(589\) 2527.00 0.176780
\(590\) 0 0
\(591\) −14862.0 −1.03442
\(592\) 0 0
\(593\) −24588.0 −1.70271 −0.851356 0.524588i \(-0.824219\pi\)
−0.851356 + 0.524588i \(0.824219\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 5217.00 0.357651
\(598\) 0 0
\(599\) −27564.0 −1.88019 −0.940096 0.340911i \(-0.889265\pi\)
−0.940096 + 0.340911i \(0.889265\pi\)
\(600\) 0 0
\(601\) 10987.0 0.745706 0.372853 0.927891i \(-0.378380\pi\)
0.372853 + 0.927891i \(0.378380\pi\)
\(602\) 0 0
\(603\) 5877.00 0.396899
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −13200.0 −0.882655 −0.441327 0.897346i \(-0.645492\pi\)
−0.441327 + 0.897346i \(0.645492\pi\)
\(608\) 0 0
\(609\) 210.000 0.0139731
\(610\) 0 0
\(611\) 410.000 0.0271470
\(612\) 0 0
\(613\) 21066.0 1.38801 0.694003 0.719972i \(-0.255845\pi\)
0.694003 + 0.719972i \(0.255845\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 12336.0 0.804909 0.402454 0.915440i \(-0.368157\pi\)
0.402454 + 0.915440i \(0.368157\pi\)
\(618\) 0 0
\(619\) −1441.00 −0.0935681 −0.0467841 0.998905i \(-0.514897\pi\)
−0.0467841 + 0.998905i \(0.514897\pi\)
\(620\) 0 0
\(621\) −1242.00 −0.0802572
\(622\) 0 0
\(623\) −5520.00 −0.354983
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 798.000 0.0508278
\(628\) 0 0
\(629\) 11868.0 0.752318
\(630\) 0 0
\(631\) −9839.00 −0.620736 −0.310368 0.950616i \(-0.600452\pi\)
−0.310368 + 0.950616i \(0.600452\pi\)
\(632\) 0 0
\(633\) −13575.0 −0.852382
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −318.000 −0.0197796
\(638\) 0 0
\(639\) 7452.00 0.461340
\(640\) 0 0
\(641\) −21564.0 −1.32875 −0.664373 0.747401i \(-0.731302\pi\)
−0.664373 + 0.747401i \(0.731302\pi\)
\(642\) 0 0
\(643\) 8604.00 0.527696 0.263848 0.964564i \(-0.415008\pi\)
0.263848 + 0.964564i \(0.415008\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 3444.00 0.209270 0.104635 0.994511i \(-0.466633\pi\)
0.104635 + 0.994511i \(0.466633\pi\)
\(648\) 0 0
\(649\) −2716.00 −0.164272
\(650\) 0 0
\(651\) 1995.00 0.120108
\(652\) 0 0
\(653\) −3518.00 −0.210827 −0.105413 0.994428i \(-0.533617\pi\)
−0.105413 + 0.994428i \(0.533617\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 5130.00 0.304628
\(658\) 0 0
\(659\) −12612.0 −0.745514 −0.372757 0.927929i \(-0.621588\pi\)
−0.372757 + 0.927929i \(0.621588\pi\)
\(660\) 0 0
\(661\) 27090.0 1.59407 0.797034 0.603935i \(-0.206401\pi\)
0.797034 + 0.603935i \(0.206401\pi\)
\(662\) 0 0
\(663\) 138.000 0.00808367
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −644.000 −0.0373850
\(668\) 0 0
\(669\) −9633.00 −0.556701
\(670\) 0 0
\(671\) −238.000 −0.0136928
\(672\) 0 0
\(673\) −5442.00 −0.311699 −0.155850 0.987781i \(-0.549812\pi\)
−0.155850 + 0.987781i \(0.549812\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −15226.0 −0.864376 −0.432188 0.901783i \(-0.642258\pi\)
−0.432188 + 0.901783i \(0.642258\pi\)
\(678\) 0 0
\(679\) 4205.00 0.237663
\(680\) 0 0
\(681\) −7452.00 −0.419326
\(682\) 0 0
\(683\) −552.000 −0.0309249 −0.0154624 0.999880i \(-0.504922\pi\)
−0.0154624 + 0.999880i \(0.504922\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −5541.00 −0.307718
\(688\) 0 0
\(689\) 456.000 0.0252137
\(690\) 0 0
\(691\) 9776.00 0.538201 0.269100 0.963112i \(-0.413274\pi\)
0.269100 + 0.963112i \(0.413274\pi\)
\(692\) 0 0
\(693\) 630.000 0.0345335
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 3864.00 0.209985
\(698\) 0 0
\(699\) −3060.00 −0.165579
\(700\) 0 0
\(701\) 13066.0 0.703989 0.351994 0.936002i \(-0.385504\pi\)
0.351994 + 0.936002i \(0.385504\pi\)
\(702\) 0 0
\(703\) 4902.00 0.262991
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 2760.00 0.146818
\(708\) 0 0
\(709\) 28985.0 1.53534 0.767669 0.640847i \(-0.221417\pi\)
0.767669 + 0.640847i \(0.221417\pi\)
\(710\) 0 0
\(711\) −4968.00 −0.262046
\(712\) 0 0
\(713\) −6118.00 −0.321348
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 3528.00 0.183760
\(718\) 0 0
\(719\) 15722.0 0.815482 0.407741 0.913098i \(-0.366317\pi\)
0.407741 + 0.913098i \(0.366317\pi\)
\(720\) 0 0
\(721\) −1540.00 −0.0795459
\(722\) 0 0
\(723\) −20901.0 −1.07513
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −32611.0 −1.66365 −0.831826 0.555036i \(-0.812704\pi\)
−0.831826 + 0.555036i \(0.812704\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) 0 0
\(731\) −7682.00 −0.388685
\(732\) 0 0
\(733\) 8358.00 0.421159 0.210580 0.977577i \(-0.432465\pi\)
0.210580 + 0.977577i \(0.432465\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 9142.00 0.456920
\(738\) 0 0
\(739\) 20604.0 1.02562 0.512808 0.858503i \(-0.328605\pi\)
0.512808 + 0.858503i \(0.328605\pi\)
\(740\) 0 0
\(741\) 57.0000 0.00282584
\(742\) 0 0
\(743\) −19476.0 −0.961649 −0.480824 0.876817i \(-0.659663\pi\)
−0.480824 + 0.876817i \(0.659663\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 1278.00 0.0625965
\(748\) 0 0
\(749\) 4920.00 0.240017
\(750\) 0 0
\(751\) 3864.00 0.187749 0.0938744 0.995584i \(-0.470075\pi\)
0.0938744 + 0.995584i \(0.470075\pi\)
\(752\) 0 0
\(753\) 4140.00 0.200359
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −18871.0 −0.906048 −0.453024 0.891498i \(-0.649655\pi\)
−0.453024 + 0.891498i \(0.649655\pi\)
\(758\) 0 0
\(759\) −1932.00 −0.0923941
\(760\) 0 0
\(761\) −36372.0 −1.73257 −0.866284 0.499552i \(-0.833498\pi\)
−0.866284 + 0.499552i \(0.833498\pi\)
\(762\) 0 0
\(763\) −9215.00 −0.437229
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −194.000 −0.00913290
\(768\) 0 0
\(769\) 4603.00 0.215850 0.107925 0.994159i \(-0.465579\pi\)
0.107925 + 0.994159i \(0.465579\pi\)
\(770\) 0 0
\(771\) −20772.0 −0.970279
\(772\) 0 0
\(773\) −36.0000 −0.00167507 −0.000837536 1.00000i \(-0.500267\pi\)
−0.000837536 1.00000i \(0.500267\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 3870.00 0.178681
\(778\) 0 0
\(779\) 1596.00 0.0734052
\(780\) 0 0
\(781\) 11592.0 0.531107
\(782\) 0 0
\(783\) 378.000 0.0172524
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −20281.0 −0.918602 −0.459301 0.888281i \(-0.651900\pi\)
−0.459301 + 0.888281i \(0.651900\pi\)
\(788\) 0 0
\(789\) 5652.00 0.255027
\(790\) 0 0
\(791\) 4380.00 0.196884
\(792\) 0 0
\(793\) −17.0000 −0.000761271 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −37524.0 −1.66771 −0.833857 0.551980i \(-0.813872\pi\)
−0.833857 + 0.551980i \(0.813872\pi\)
\(798\) 0 0
\(799\) 18860.0 0.835067
\(800\) 0 0
\(801\) −9936.00 −0.438291
\(802\) 0 0
\(803\) 7980.00 0.350695
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 10830.0 0.472409
\(808\) 0 0
\(809\) 31224.0 1.35696 0.678478 0.734621i \(-0.262640\pi\)
0.678478 + 0.734621i \(0.262640\pi\)
\(810\) 0 0
\(811\) 32579.0 1.41061 0.705304 0.708905i \(-0.250810\pi\)
0.705304 + 0.708905i \(0.250810\pi\)
\(812\) 0 0
\(813\) −18216.0 −0.785809
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −3173.00 −0.135874
\(818\) 0 0
\(819\) 45.0000 0.00191994
\(820\) 0 0
\(821\) −19810.0 −0.842112 −0.421056 0.907035i \(-0.638340\pi\)
−0.421056 + 0.907035i \(0.638340\pi\)
\(822\) 0 0
\(823\) 10273.0 0.435108 0.217554 0.976048i \(-0.430192\pi\)
0.217554 + 0.976048i \(0.430192\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 16656.0 0.700346 0.350173 0.936685i \(-0.386123\pi\)
0.350173 + 0.936685i \(0.386123\pi\)
\(828\) 0 0
\(829\) −4790.00 −0.200680 −0.100340 0.994953i \(-0.531993\pi\)
−0.100340 + 0.994953i \(0.531993\pi\)
\(830\) 0 0
\(831\) −8409.00 −0.351029
\(832\) 0 0
\(833\) −14628.0 −0.608440
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 3591.00 0.148295
\(838\) 0 0
\(839\) 7414.00 0.305077 0.152539 0.988298i \(-0.451255\pi\)
0.152539 + 0.988298i \(0.451255\pi\)
\(840\) 0 0
\(841\) −24193.0 −0.991964
\(842\) 0 0
\(843\) −20082.0 −0.820475
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −5675.00 −0.230219
\(848\) 0 0
\(849\) −19443.0 −0.785962
\(850\) 0 0
\(851\) −11868.0 −0.478061
\(852\) 0 0
\(853\) 30155.0 1.21042 0.605210 0.796066i \(-0.293089\pi\)
0.605210 + 0.796066i \(0.293089\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −8244.00 −0.328599 −0.164300 0.986410i \(-0.552536\pi\)
−0.164300 + 0.986410i \(0.552536\pi\)
\(858\) 0 0
\(859\) 17552.0 0.697167 0.348584 0.937278i \(-0.386663\pi\)
0.348584 + 0.937278i \(0.386663\pi\)
\(860\) 0 0
\(861\) 1260.00 0.0498730
\(862\) 0 0
\(863\) −34104.0 −1.34521 −0.672604 0.740003i \(-0.734824\pi\)
−0.672604 + 0.740003i \(0.734824\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −8391.00 −0.328689
\(868\) 0 0
\(869\) −7728.00 −0.301674
\(870\) 0 0
\(871\) 653.000 0.0254031
\(872\) 0 0
\(873\) 7569.00 0.293439
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −46229.0 −1.77998 −0.889990 0.455980i \(-0.849289\pi\)
−0.889990 + 0.455980i \(0.849289\pi\)
\(878\) 0 0
\(879\) 9042.00 0.346961
\(880\) 0 0
\(881\) −22440.0 −0.858142 −0.429071 0.903271i \(-0.641159\pi\)
−0.429071 + 0.903271i \(0.641159\pi\)
\(882\) 0 0
\(883\) −17143.0 −0.653350 −0.326675 0.945137i \(-0.605928\pi\)
−0.326675 + 0.945137i \(0.605928\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −23626.0 −0.894344 −0.447172 0.894448i \(-0.647569\pi\)
−0.447172 + 0.894448i \(0.647569\pi\)
\(888\) 0 0
\(889\) 11880.0 0.448192
\(890\) 0 0
\(891\) 1134.00 0.0426380
\(892\) 0 0
\(893\) 7790.00 0.291918
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −138.000 −0.00513677
\(898\) 0 0
\(899\) 1862.00 0.0690781
\(900\) 0 0
\(901\) 20976.0 0.775596
\(902\) 0 0
\(903\) −2505.00 −0.0923158
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −11268.0 −0.412511 −0.206256 0.978498i \(-0.566128\pi\)
−0.206256 + 0.978498i \(0.566128\pi\)
\(908\) 0 0
\(909\) 4968.00 0.181274
\(910\) 0 0
\(911\) 10046.0 0.365355 0.182678 0.983173i \(-0.441524\pi\)
0.182678 + 0.983173i \(0.441524\pi\)
\(912\) 0 0
\(913\) 1988.00 0.0720626
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 5280.00 0.190143
\(918\) 0 0
\(919\) 15359.0 0.551302 0.275651 0.961258i \(-0.411107\pi\)
0.275651 + 0.961258i \(0.411107\pi\)
\(920\) 0 0
\(921\) −16107.0 −0.576269
\(922\) 0 0
\(923\) 828.000 0.0295276
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −2772.00 −0.0982141
\(928\) 0 0
\(929\) −39790.0 −1.40524 −0.702620 0.711565i \(-0.747986\pi\)
−0.702620 + 0.711565i \(0.747986\pi\)
\(930\) 0 0
\(931\) −6042.00 −0.212694
\(932\) 0 0
\(933\) 14538.0 0.510132
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −17009.0 −0.593020 −0.296510 0.955030i \(-0.595823\pi\)
−0.296510 + 0.955030i \(0.595823\pi\)
\(938\) 0 0
\(939\) −2271.00 −0.0789258
\(940\) 0 0
\(941\) −11674.0 −0.404422 −0.202211 0.979342i \(-0.564813\pi\)
−0.202211 + 0.979342i \(0.564813\pi\)
\(942\) 0 0
\(943\) −3864.00 −0.133435
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 6026.00 0.206778 0.103389 0.994641i \(-0.467031\pi\)
0.103389 + 0.994641i \(0.467031\pi\)
\(948\) 0 0
\(949\) 570.000 0.0194973
\(950\) 0 0
\(951\) −22896.0 −0.780708
\(952\) 0 0
\(953\) −14088.0 −0.478862 −0.239431 0.970913i \(-0.576961\pi\)
−0.239431 + 0.970913i \(0.576961\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 588.000 0.0198614
\(958\) 0 0
\(959\) −3890.00 −0.130985
\(960\) 0 0
\(961\) −12102.0 −0.406230
\(962\) 0 0
\(963\) 8856.00 0.296345
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −11208.0 −0.372725 −0.186362 0.982481i \(-0.559670\pi\)
−0.186362 + 0.982481i \(0.559670\pi\)
\(968\) 0 0
\(969\) 2622.00 0.0869255
\(970\) 0 0
\(971\) −26054.0 −0.861084 −0.430542 0.902571i \(-0.641678\pi\)
−0.430542 + 0.902571i \(0.641678\pi\)
\(972\) 0 0
\(973\) 8460.00 0.278741
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −26870.0 −0.879885 −0.439942 0.898026i \(-0.645001\pi\)
−0.439942 + 0.898026i \(0.645001\pi\)
\(978\) 0 0
\(979\) −15456.0 −0.504572
\(980\) 0 0
\(981\) −16587.0 −0.539839
\(982\) 0 0
\(983\) −23388.0 −0.758862 −0.379431 0.925220i \(-0.623880\pi\)
−0.379431 + 0.925220i \(0.623880\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 6150.00 0.198335
\(988\) 0 0
\(989\) 7682.00 0.246990
\(990\) 0 0
\(991\) 17345.0 0.555986 0.277993 0.960583i \(-0.410331\pi\)
0.277993 + 0.960583i \(0.410331\pi\)
\(992\) 0 0
\(993\) −20340.0 −0.650021
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −25998.0 −0.825842 −0.412921 0.910767i \(-0.635492\pi\)
−0.412921 + 0.910767i \(0.635492\pi\)
\(998\) 0 0
\(999\) 6966.00 0.220615
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 600.4.a.n.1.1 yes 1
3.2 odd 2 1800.4.a.v.1.1 1
4.3 odd 2 1200.4.a.g.1.1 1
5.2 odd 4 600.4.f.e.49.1 2
5.3 odd 4 600.4.f.e.49.2 2
5.4 even 2 600.4.a.e.1.1 1
15.2 even 4 1800.4.f.l.649.2 2
15.8 even 4 1800.4.f.l.649.1 2
15.14 odd 2 1800.4.a.m.1.1 1
20.3 even 4 1200.4.f.i.49.1 2
20.7 even 4 1200.4.f.i.49.2 2
20.19 odd 2 1200.4.a.bd.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
600.4.a.e.1.1 1 5.4 even 2
600.4.a.n.1.1 yes 1 1.1 even 1 trivial
600.4.f.e.49.1 2 5.2 odd 4
600.4.f.e.49.2 2 5.3 odd 4
1200.4.a.g.1.1 1 4.3 odd 2
1200.4.a.bd.1.1 1 20.19 odd 2
1200.4.f.i.49.1 2 20.3 even 4
1200.4.f.i.49.2 2 20.7 even 4
1800.4.a.m.1.1 1 15.14 odd 2
1800.4.a.v.1.1 1 3.2 odd 2
1800.4.f.l.649.1 2 15.8 even 4
1800.4.f.l.649.2 2 15.2 even 4