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Properties

Label 720.4.a.r.1.1
Level $720$
Weight $4$
Character 720.1
Self dual yes
Analytic conductor $42.481$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [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: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 15)
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)
 
\(f(q)\) \(=\) \(q+5.00000 q^{5} -20.0000 q^{7} +O(q^{10})\) \(q+5.00000 q^{5} -20.0000 q^{7} -24.0000 q^{11} +74.0000 q^{13} -54.0000 q^{17} +124.000 q^{19} -120.000 q^{23} +25.0000 q^{25} +78.0000 q^{29} -200.000 q^{31} -100.000 q^{35} -70.0000 q^{37} -330.000 q^{41} -92.0000 q^{43} -24.0000 q^{47} +57.0000 q^{49} -450.000 q^{53} -120.000 q^{55} +24.0000 q^{59} -322.000 q^{61} +370.000 q^{65} +196.000 q^{67} -288.000 q^{71} -430.000 q^{73} +480.000 q^{77} +520.000 q^{79} +156.000 q^{83} -270.000 q^{85} -1026.00 q^{89} -1480.00 q^{91} +620.000 q^{95} -286.000 q^{97} +O(q^{100})\)

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
\(5\) 5.00000 0.447214
\(6\) 0 0
\(7\) −20.0000 −1.07990 −0.539949 − 0.841698i \(-0.681557\pi\)
−0.539949 + 0.841698i \(0.681557\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −24.0000 −0.657843 −0.328921 − 0.944357i \(-0.606685\pi\)
−0.328921 + 0.944357i \(0.606685\pi\)
\(12\) 0 0
\(13\) 74.0000 1.57876 0.789381 − 0.613904i \(-0.210402\pi\)
0.789381 + 0.613904i \(0.210402\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −54.0000 −0.770407 −0.385204 − 0.922832i \(-0.625869\pi\)
−0.385204 + 0.922832i \(0.625869\pi\)
\(18\) 0 0
\(19\) 124.000 1.49724 0.748620 − 0.663000i \(-0.230717\pi\)
0.748620 + 0.663000i \(0.230717\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −120.000 −1.08790 −0.543951 − 0.839117i \(-0.683072\pi\)
−0.543951 + 0.839117i \(0.683072\pi\)
\(24\) 0 0
\(25\) 25.0000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 78.0000 0.499456 0.249728 − 0.968316i \(-0.419659\pi\)
0.249728 + 0.968316i \(0.419659\pi\)
\(30\) 0 0
\(31\) −200.000 −1.15874 −0.579372 − 0.815063i \(-0.696702\pi\)
−0.579372 + 0.815063i \(0.696702\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −100.000 −0.482945
\(36\) 0 0
\(37\) −70.0000 −0.311025 −0.155513 − 0.987834i \(-0.549703\pi\)
−0.155513 + 0.987834i \(0.549703\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −330.000 −1.25701 −0.628504 − 0.777806i \(-0.716332\pi\)
−0.628504 + 0.777806i \(0.716332\pi\)
\(42\) 0 0
\(43\) −92.0000 −0.326276 −0.163138 − 0.986603i \(-0.552162\pi\)
−0.163138 + 0.986603i \(0.552162\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −24.0000 −0.0744843 −0.0372421 − 0.999306i \(-0.511857\pi\)
−0.0372421 + 0.999306i \(0.511857\pi\)
\(48\) 0 0
\(49\) 57.0000 0.166181
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −450.000 −1.16627 −0.583134 − 0.812376i \(-0.698174\pi\)
−0.583134 + 0.812376i \(0.698174\pi\)
\(54\) 0 0
\(55\) −120.000 −0.294196
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 24.0000 0.0529582 0.0264791 − 0.999649i \(-0.491570\pi\)
0.0264791 + 0.999649i \(0.491570\pi\)
\(60\) 0 0
\(61\) −322.000 −0.675867 −0.337933 − 0.941170i \(-0.609728\pi\)
−0.337933 + 0.941170i \(0.609728\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 370.000 0.706044
\(66\) 0 0
\(67\) 196.000 0.357391 0.178696 − 0.983904i \(-0.442812\pi\)
0.178696 + 0.983904i \(0.442812\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −288.000 −0.481399 −0.240699 − 0.970600i \(-0.577377\pi\)
−0.240699 + 0.970600i \(0.577377\pi\)
\(72\) 0 0
\(73\) −430.000 −0.689420 −0.344710 − 0.938709i \(-0.612023\pi\)
−0.344710 + 0.938709i \(0.612023\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 480.000 0.710404
\(78\) 0 0
\(79\) 520.000 0.740564 0.370282 − 0.928919i \(-0.379261\pi\)
0.370282 + 0.928919i \(0.379261\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 156.000 0.206304 0.103152 − 0.994666i \(-0.467107\pi\)
0.103152 + 0.994666i \(0.467107\pi\)
\(84\) 0 0
\(85\) −270.000 −0.344537
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −1026.00 −1.22198 −0.610988 − 0.791640i \(-0.709227\pi\)
−0.610988 + 0.791640i \(0.709227\pi\)
\(90\) 0 0
\(91\) −1480.00 −1.70490
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 620.000 0.669586
\(96\) 0 0
\(97\) −286.000 −0.299370 −0.149685 − 0.988734i \(-0.547826\pi\)
−0.149685 + 0.988734i \(0.547826\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 1734.00 1.70831 0.854156 − 0.520017i \(-0.174075\pi\)
0.854156 + 0.520017i \(0.174075\pi\)
\(102\) 0 0
\(103\) −452.000 −0.432397 −0.216198 − 0.976349i \(-0.569366\pi\)
−0.216198 + 0.976349i \(0.569366\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1404.00 −1.26850 −0.634251 − 0.773127i \(-0.718692\pi\)
−0.634251 + 0.773127i \(0.718692\pi\)
\(108\) 0 0
\(109\) −1474.00 −1.29526 −0.647631 − 0.761954i \(-0.724240\pi\)
−0.647631 + 0.761954i \(0.724240\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −1086.00 −0.904091 −0.452046 − 0.891995i \(-0.649306\pi\)
−0.452046 + 0.891995i \(0.649306\pi\)
\(114\) 0 0
\(115\) −600.000 −0.486524
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 1080.00 0.831962
\(120\) 0 0
\(121\) −755.000 −0.567243
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 125.000 0.0894427
\(126\) 0 0
\(127\) −1244.00 −0.869190 −0.434595 − 0.900626i \(-0.643109\pi\)
−0.434595 + 0.900626i \(0.643109\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 2328.00 1.55266 0.776329 − 0.630327i \(-0.217079\pi\)
0.776329 + 0.630327i \(0.217079\pi\)
\(132\) 0 0
\(133\) −2480.00 −1.61687
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −2118.00 −1.32082 −0.660412 − 0.750903i \(-0.729618\pi\)
−0.660412 + 0.750903i \(0.729618\pi\)
\(138\) 0 0
\(139\) −2324.00 −1.41812 −0.709062 − 0.705147i \(-0.750881\pi\)
−0.709062 + 0.705147i \(0.750881\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −1776.00 −1.03858
\(144\) 0 0
\(145\) 390.000 0.223364
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −258.000 −0.141854 −0.0709268 − 0.997482i \(-0.522596\pi\)
−0.0709268 + 0.997482i \(0.522596\pi\)
\(150\) 0 0
\(151\) 808.000 0.435458 0.217729 − 0.976009i \(-0.430135\pi\)
0.217729 + 0.976009i \(0.430135\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −1000.00 −0.518206
\(156\) 0 0
\(157\) 2378.00 1.20882 0.604411 − 0.796673i \(-0.293408\pi\)
0.604411 + 0.796673i \(0.293408\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 2400.00 1.17482
\(162\) 0 0
\(163\) 52.0000 0.0249874 0.0124937 − 0.999922i \(-0.496023\pi\)
0.0124937 + 0.999922i \(0.496023\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −3720.00 −1.72373 −0.861863 − 0.507141i \(-0.830702\pi\)
−0.861863 + 0.507141i \(0.830702\pi\)
\(168\) 0 0
\(169\) 3279.00 1.49249
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −426.000 −0.187215 −0.0936075 − 0.995609i \(-0.529840\pi\)
−0.0936075 + 0.995609i \(0.529840\pi\)
\(174\) 0 0
\(175\) −500.000 −0.215980
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −1440.00 −0.601289 −0.300644 − 0.953736i \(-0.597202\pi\)
−0.300644 + 0.953736i \(0.597202\pi\)
\(180\) 0 0
\(181\) −3130.00 −1.28537 −0.642683 − 0.766133i \(-0.722179\pi\)
−0.642683 + 0.766133i \(0.722179\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −350.000 −0.139095
\(186\) 0 0
\(187\) 1296.00 0.506807
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 3576.00 1.35471 0.677357 − 0.735655i \(-0.263125\pi\)
0.677357 + 0.735655i \(0.263125\pi\)
\(192\) 0 0
\(193\) 2666.00 0.994315 0.497158 − 0.867660i \(-0.334377\pi\)
0.497158 + 0.867660i \(0.334377\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 2718.00 0.982992 0.491496 − 0.870880i \(-0.336450\pi\)
0.491496 + 0.870880i \(0.336450\pi\)
\(198\) 0 0
\(199\) 3832.00 1.36504 0.682521 − 0.730866i \(-0.260884\pi\)
0.682521 + 0.730866i \(0.260884\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −1560.00 −0.539362
\(204\) 0 0
\(205\) −1650.00 −0.562151
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −2976.00 −0.984948
\(210\) 0 0
\(211\) −1100.00 −0.358896 −0.179448 − 0.983767i \(-0.557431\pi\)
−0.179448 + 0.983767i \(0.557431\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −460.000 −0.145915
\(216\) 0 0
\(217\) 4000.00 1.25133
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −3996.00 −1.21629
\(222\) 0 0
\(223\) −1964.00 −0.589772 −0.294886 − 0.955532i \(-0.595282\pi\)
−0.294886 + 0.955532i \(0.595282\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 660.000 0.192977 0.0964884 − 0.995334i \(-0.469239\pi\)
0.0964884 + 0.995334i \(0.469239\pi\)
\(228\) 0 0
\(229\) −1906.00 −0.550009 −0.275004 − 0.961443i \(-0.588679\pi\)
−0.275004 + 0.961443i \(0.588679\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 1458.00 0.409943 0.204972 − 0.978768i \(-0.434290\pi\)
0.204972 + 0.978768i \(0.434290\pi\)
\(234\) 0 0
\(235\) −120.000 −0.0333104
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 1176.00 0.318281 0.159140 − 0.987256i \(-0.449128\pi\)
0.159140 + 0.987256i \(0.449128\pi\)
\(240\) 0 0
\(241\) 866.000 0.231469 0.115734 − 0.993280i \(-0.463078\pi\)
0.115734 + 0.993280i \(0.463078\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 285.000 0.0743183
\(246\) 0 0
\(247\) 9176.00 2.36379
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 432.000 0.108636 0.0543179 − 0.998524i \(-0.482702\pi\)
0.0543179 + 0.998524i \(0.482702\pi\)
\(252\) 0 0
\(253\) 2880.00 0.715668
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −2526.00 −0.613103 −0.306552 − 0.951854i \(-0.599175\pi\)
−0.306552 + 0.951854i \(0.599175\pi\)
\(258\) 0 0
\(259\) 1400.00 0.335876
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 5448.00 1.27733 0.638666 − 0.769484i \(-0.279487\pi\)
0.638666 + 0.769484i \(0.279487\pi\)
\(264\) 0 0
\(265\) −2250.00 −0.521571
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 2574.00 0.583418 0.291709 − 0.956507i \(-0.405776\pi\)
0.291709 + 0.956507i \(0.405776\pi\)
\(270\) 0 0
\(271\) 3184.00 0.713706 0.356853 − 0.934161i \(-0.383850\pi\)
0.356853 + 0.934161i \(0.383850\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −600.000 −0.131569
\(276\) 0 0
\(277\) 3962.00 0.859399 0.429699 − 0.902972i \(-0.358620\pi\)
0.429699 + 0.902972i \(0.358620\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 8286.00 1.75908 0.879540 − 0.475825i \(-0.157851\pi\)
0.879540 + 0.475825i \(0.157851\pi\)
\(282\) 0 0
\(283\) 2716.00 0.570493 0.285246 − 0.958454i \(-0.407925\pi\)
0.285246 + 0.958454i \(0.407925\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 6600.00 1.35744
\(288\) 0 0
\(289\) −1997.00 −0.406473
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −6018.00 −1.19992 −0.599958 − 0.800032i \(-0.704816\pi\)
−0.599958 + 0.800032i \(0.704816\pi\)
\(294\) 0 0
\(295\) 120.000 0.0236836
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −8880.00 −1.71754
\(300\) 0 0
\(301\) 1840.00 0.352345
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −1610.00 −0.302257
\(306\) 0 0
\(307\) −9236.00 −1.71702 −0.858512 − 0.512793i \(-0.828611\pi\)
−0.858512 + 0.512793i \(0.828611\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 1536.00 0.280060 0.140030 − 0.990147i \(-0.455280\pi\)
0.140030 + 0.990147i \(0.455280\pi\)
\(312\) 0 0
\(313\) −7342.00 −1.32586 −0.662930 − 0.748681i \(-0.730687\pi\)
−0.662930 + 0.748681i \(0.730687\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 3894.00 0.689933 0.344967 − 0.938615i \(-0.387890\pi\)
0.344967 + 0.938615i \(0.387890\pi\)
\(318\) 0 0
\(319\) −1872.00 −0.328564
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −6696.00 −1.15348
\(324\) 0 0
\(325\) 1850.00 0.315752
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 480.000 0.0804354
\(330\) 0 0
\(331\) −3692.00 −0.613084 −0.306542 − 0.951857i \(-0.599172\pi\)
−0.306542 + 0.951857i \(0.599172\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 980.000 0.159830
\(336\) 0 0
\(337\) −8998.00 −1.45446 −0.727229 − 0.686395i \(-0.759192\pi\)
−0.727229 + 0.686395i \(0.759192\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 4800.00 0.762271
\(342\) 0 0
\(343\) 5720.00 0.900440
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 5244.00 0.811276 0.405638 − 0.914034i \(-0.367049\pi\)
0.405638 + 0.914034i \(0.367049\pi\)
\(348\) 0 0
\(349\) 6302.00 0.966585 0.483293 − 0.875459i \(-0.339441\pi\)
0.483293 + 0.875459i \(0.339441\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −3414.00 −0.514756 −0.257378 − 0.966311i \(-0.582859\pi\)
−0.257378 + 0.966311i \(0.582859\pi\)
\(354\) 0 0
\(355\) −1440.00 −0.215288
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 4824.00 0.709195 0.354597 − 0.935019i \(-0.384618\pi\)
0.354597 + 0.935019i \(0.384618\pi\)
\(360\) 0 0
\(361\) 8517.00 1.24173
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −2150.00 −0.308318
\(366\) 0 0
\(367\) 3508.00 0.498954 0.249477 − 0.968381i \(-0.419741\pi\)
0.249477 + 0.968381i \(0.419741\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 9000.00 1.25945
\(372\) 0 0
\(373\) 10802.0 1.49948 0.749740 − 0.661732i \(-0.230178\pi\)
0.749740 + 0.661732i \(0.230178\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 5772.00 0.788523
\(378\) 0 0
\(379\) −1460.00 −0.197876 −0.0989382 − 0.995094i \(-0.531545\pi\)
−0.0989382 + 0.995094i \(0.531545\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −4872.00 −0.649994 −0.324997 − 0.945715i \(-0.605363\pi\)
−0.324997 + 0.945715i \(0.605363\pi\)
\(384\) 0 0
\(385\) 2400.00 0.317702
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 14046.0 1.83075 0.915373 − 0.402606i \(-0.131896\pi\)
0.915373 + 0.402606i \(0.131896\pi\)
\(390\) 0 0
\(391\) 6480.00 0.838127
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 2600.00 0.331190
\(396\) 0 0
\(397\) −2734.00 −0.345631 −0.172816 − 0.984954i \(-0.555286\pi\)
−0.172816 + 0.984954i \(0.555286\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 15942.0 1.98530 0.992650 − 0.121019i \(-0.0386161\pi\)
0.992650 + 0.121019i \(0.0386161\pi\)
\(402\) 0 0
\(403\) −14800.0 −1.82938
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 1680.00 0.204606
\(408\) 0 0
\(409\) 8714.00 1.05350 0.526748 − 0.850022i \(-0.323411\pi\)
0.526748 + 0.850022i \(0.323411\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −480.000 −0.0571895
\(414\) 0 0
\(415\) 780.000 0.0922619
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 11976.0 1.39634 0.698169 − 0.715933i \(-0.253998\pi\)
0.698169 + 0.715933i \(0.253998\pi\)
\(420\) 0 0
\(421\) 11054.0 1.27967 0.639833 − 0.768514i \(-0.279004\pi\)
0.639833 + 0.768514i \(0.279004\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −1350.00 −0.154081
\(426\) 0 0
\(427\) 6440.00 0.729868
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 720.000 0.0804668 0.0402334 − 0.999190i \(-0.487190\pi\)
0.0402334 + 0.999190i \(0.487190\pi\)
\(432\) 0 0
\(433\) −15622.0 −1.73382 −0.866912 − 0.498462i \(-0.833898\pi\)
−0.866912 + 0.498462i \(0.833898\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −14880.0 −1.62885
\(438\) 0 0
\(439\) 9880.00 1.07414 0.537069 − 0.843538i \(-0.319531\pi\)
0.537069 + 0.843538i \(0.319531\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −16116.0 −1.72843 −0.864215 − 0.503123i \(-0.832184\pi\)
−0.864215 + 0.503123i \(0.832184\pi\)
\(444\) 0 0
\(445\) −5130.00 −0.546484
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −9018.00 −0.947852 −0.473926 − 0.880565i \(-0.657164\pi\)
−0.473926 + 0.880565i \(0.657164\pi\)
\(450\) 0 0
\(451\) 7920.00 0.826914
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −7400.00 −0.762456
\(456\) 0 0
\(457\) −3670.00 −0.375657 −0.187829 − 0.982202i \(-0.560145\pi\)
−0.187829 + 0.982202i \(0.560145\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −17562.0 −1.77428 −0.887141 − 0.461499i \(-0.847312\pi\)
−0.887141 + 0.461499i \(0.847312\pi\)
\(462\) 0 0
\(463\) −1172.00 −0.117640 −0.0588202 − 0.998269i \(-0.518734\pi\)
−0.0588202 + 0.998269i \(0.518734\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 6876.00 0.681335 0.340667 − 0.940184i \(-0.389347\pi\)
0.340667 + 0.940184i \(0.389347\pi\)
\(468\) 0 0
\(469\) −3920.00 −0.385946
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 2208.00 0.214638
\(474\) 0 0
\(475\) 3100.00 0.299448
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 2280.00 0.217486 0.108743 − 0.994070i \(-0.465317\pi\)
0.108743 + 0.994070i \(0.465317\pi\)
\(480\) 0 0
\(481\) −5180.00 −0.491035
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −1430.00 −0.133882
\(486\) 0 0
\(487\) 3076.00 0.286215 0.143108 − 0.989707i \(-0.454290\pi\)
0.143108 + 0.989707i \(0.454290\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −18912.0 −1.73826 −0.869131 − 0.494582i \(-0.835321\pi\)
−0.869131 + 0.494582i \(0.835321\pi\)
\(492\) 0 0
\(493\) −4212.00 −0.384785
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 5760.00 0.519862
\(498\) 0 0
\(499\) −9956.00 −0.893170 −0.446585 − 0.894741i \(-0.647360\pi\)
−0.446585 + 0.894741i \(0.647360\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −10656.0 −0.944588 −0.472294 − 0.881441i \(-0.656574\pi\)
−0.472294 + 0.881441i \(0.656574\pi\)
\(504\) 0 0
\(505\) 8670.00 0.763980
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 2766.00 0.240866 0.120433 − 0.992721i \(-0.461572\pi\)
0.120433 + 0.992721i \(0.461572\pi\)
\(510\) 0 0
\(511\) 8600.00 0.744504
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −2260.00 −0.193374
\(516\) 0 0
\(517\) 576.000 0.0489989
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −10530.0 −0.885466 −0.442733 − 0.896654i \(-0.645991\pi\)
−0.442733 + 0.896654i \(0.645991\pi\)
\(522\) 0 0
\(523\) −12692.0 −1.06115 −0.530576 − 0.847637i \(-0.678024\pi\)
−0.530576 + 0.847637i \(0.678024\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 10800.0 0.892705
\(528\) 0 0
\(529\) 2233.00 0.183529
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −24420.0 −1.98452
\(534\) 0 0
\(535\) −7020.00 −0.567292
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −1368.00 −0.109321
\(540\) 0 0
\(541\) 18110.0 1.43920 0.719602 − 0.694386i \(-0.244324\pi\)
0.719602 + 0.694386i \(0.244324\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −7370.00 −0.579259
\(546\) 0 0
\(547\) −3620.00 −0.282962 −0.141481 − 0.989941i \(-0.545186\pi\)
−0.141481 + 0.989941i \(0.545186\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 9672.00 0.747806
\(552\) 0 0
\(553\) −10400.0 −0.799734
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 14166.0 1.07762 0.538809 − 0.842428i \(-0.318875\pi\)
0.538809 + 0.842428i \(0.318875\pi\)
\(558\) 0 0
\(559\) −6808.00 −0.515112
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −13404.0 −1.00339 −0.501697 − 0.865043i \(-0.667291\pi\)
−0.501697 + 0.865043i \(0.667291\pi\)
\(564\) 0 0
\(565\) −5430.00 −0.404322
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 18654.0 1.37437 0.687185 − 0.726483i \(-0.258846\pi\)
0.687185 + 0.726483i \(0.258846\pi\)
\(570\) 0 0
\(571\) 7684.00 0.563162 0.281581 − 0.959537i \(-0.409141\pi\)
0.281581 + 0.959537i \(0.409141\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −3000.00 −0.217580
\(576\) 0 0
\(577\) −1726.00 −0.124531 −0.0622654 − 0.998060i \(-0.519833\pi\)
−0.0622654 + 0.998060i \(0.519833\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −3120.00 −0.222787
\(582\) 0 0
\(583\) 10800.0 0.767222
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 10596.0 0.745049 0.372524 − 0.928022i \(-0.378492\pi\)
0.372524 + 0.928022i \(0.378492\pi\)
\(588\) 0 0
\(589\) −24800.0 −1.73492
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −2862.00 −0.198193 −0.0990963 − 0.995078i \(-0.531595\pi\)
−0.0990963 + 0.995078i \(0.531595\pi\)
\(594\) 0 0
\(595\) 5400.00 0.372065
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −23592.0 −1.60925 −0.804627 − 0.593781i \(-0.797635\pi\)
−0.804627 + 0.593781i \(0.797635\pi\)
\(600\) 0 0
\(601\) −9574.00 −0.649803 −0.324902 − 0.945748i \(-0.605331\pi\)
−0.324902 + 0.945748i \(0.605331\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −3775.00 −0.253679
\(606\) 0 0
\(607\) −17444.0 −1.16644 −0.583221 − 0.812314i \(-0.698208\pi\)
−0.583221 + 0.812314i \(0.698208\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −1776.00 −0.117593
\(612\) 0 0
\(613\) −2374.00 −0.156419 −0.0782096 − 0.996937i \(-0.524920\pi\)
−0.0782096 + 0.996937i \(0.524920\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 12162.0 0.793555 0.396778 − 0.917915i \(-0.370128\pi\)
0.396778 + 0.917915i \(0.370128\pi\)
\(618\) 0 0
\(619\) −8804.00 −0.571668 −0.285834 − 0.958279i \(-0.592271\pi\)
−0.285834 + 0.958279i \(0.592271\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 20520.0 1.31961
\(624\) 0 0
\(625\) 625.000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 3780.00 0.239616
\(630\) 0 0
\(631\) 12688.0 0.800478 0.400239 − 0.916411i \(-0.368927\pi\)
0.400239 + 0.916411i \(0.368927\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −6220.00 −0.388714
\(636\) 0 0
\(637\) 4218.00 0.262360
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 9150.00 0.563812 0.281906 − 0.959442i \(-0.409033\pi\)
0.281906 + 0.959442i \(0.409033\pi\)
\(642\) 0 0
\(643\) −25292.0 −1.55120 −0.775598 − 0.631227i \(-0.782552\pi\)
−0.775598 + 0.631227i \(0.782552\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −2736.00 −0.166249 −0.0831246 − 0.996539i \(-0.526490\pi\)
−0.0831246 + 0.996539i \(0.526490\pi\)
\(648\) 0 0
\(649\) −576.000 −0.0348382
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −22218.0 −1.33148 −0.665741 − 0.746183i \(-0.731884\pi\)
−0.665741 + 0.746183i \(0.731884\pi\)
\(654\) 0 0
\(655\) 11640.0 0.694370
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 14520.0 0.858299 0.429149 − 0.903234i \(-0.358813\pi\)
0.429149 + 0.903234i \(0.358813\pi\)
\(660\) 0 0
\(661\) −10618.0 −0.624799 −0.312400 − 0.949951i \(-0.601133\pi\)
−0.312400 + 0.949951i \(0.601133\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −12400.0 −0.723085
\(666\) 0 0
\(667\) −9360.00 −0.543359
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 7728.00 0.444614
\(672\) 0 0
\(673\) 1370.00 0.0784690 0.0392345 − 0.999230i \(-0.487508\pi\)
0.0392345 + 0.999230i \(0.487508\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 13758.0 0.781038 0.390519 − 0.920595i \(-0.372296\pi\)
0.390519 + 0.920595i \(0.372296\pi\)
\(678\) 0 0
\(679\) 5720.00 0.323289
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 11988.0 0.671608 0.335804 − 0.941932i \(-0.390992\pi\)
0.335804 + 0.941932i \(0.390992\pi\)
\(684\) 0 0
\(685\) −10590.0 −0.590691
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −33300.0 −1.84126
\(690\) 0 0
\(691\) −32996.0 −1.81654 −0.908268 − 0.418388i \(-0.862595\pi\)
−0.908268 + 0.418388i \(0.862595\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −11620.0 −0.634204
\(696\) 0 0
\(697\) 17820.0 0.968408
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 25902.0 1.39558 0.697792 − 0.716300i \(-0.254166\pi\)
0.697792 + 0.716300i \(0.254166\pi\)
\(702\) 0 0
\(703\) −8680.00 −0.465679
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −34680.0 −1.84480
\(708\) 0 0
\(709\) −27394.0 −1.45106 −0.725531 − 0.688189i \(-0.758406\pi\)
−0.725531 + 0.688189i \(0.758406\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 24000.0 1.26060
\(714\) 0 0
\(715\) −8880.00 −0.464466
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 34848.0 1.80753 0.903763 − 0.428033i \(-0.140793\pi\)
0.903763 + 0.428033i \(0.140793\pi\)
\(720\) 0 0
\(721\) 9040.00 0.466945
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 1950.00 0.0998913
\(726\) 0 0
\(727\) −28028.0 −1.42985 −0.714925 − 0.699201i \(-0.753539\pi\)
−0.714925 + 0.699201i \(0.753539\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 4968.00 0.251365
\(732\) 0 0
\(733\) 18002.0 0.907120 0.453560 − 0.891226i \(-0.350154\pi\)
0.453560 + 0.891226i \(0.350154\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −4704.00 −0.235107
\(738\) 0 0
\(739\) −15284.0 −0.760800 −0.380400 − 0.924822i \(-0.624214\pi\)
−0.380400 + 0.924822i \(0.624214\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −18768.0 −0.926691 −0.463345 − 0.886178i \(-0.653351\pi\)
−0.463345 + 0.886178i \(0.653351\pi\)
\(744\) 0 0
\(745\) −1290.00 −0.0634388
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 28080.0 1.36985
\(750\) 0 0
\(751\) −8696.00 −0.422532 −0.211266 − 0.977429i \(-0.567759\pi\)
−0.211266 + 0.977429i \(0.567759\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 4040.00 0.194743
\(756\) 0 0
\(757\) −38662.0 −1.85627 −0.928134 − 0.372247i \(-0.878587\pi\)
−0.928134 + 0.372247i \(0.878587\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −23874.0 −1.13723 −0.568615 − 0.822604i \(-0.692521\pi\)
−0.568615 + 0.822604i \(0.692521\pi\)
\(762\) 0 0
\(763\) 29480.0 1.39875
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 1776.00 0.0836084
\(768\) 0 0
\(769\) 23618.0 1.10753 0.553763 − 0.832675i \(-0.313192\pi\)
0.553763 + 0.832675i \(0.313192\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −11538.0 −0.536860 −0.268430 − 0.963299i \(-0.586505\pi\)
−0.268430 + 0.963299i \(0.586505\pi\)
\(774\) 0 0
\(775\) −5000.00 −0.231749
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −40920.0 −1.88204
\(780\) 0 0
\(781\) 6912.00 0.316685
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 11890.0 0.540602
\(786\) 0 0
\(787\) 14884.0 0.674152 0.337076 − 0.941478i \(-0.390562\pi\)
0.337076 + 0.941478i \(0.390562\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 21720.0 0.976327
\(792\) 0 0
\(793\) −23828.0 −1.06703
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 11334.0 0.503728 0.251864 − 0.967763i \(-0.418957\pi\)
0.251864 + 0.967763i \(0.418957\pi\)
\(798\) 0 0
\(799\) 1296.00 0.0573832
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 10320.0 0.453530
\(804\) 0 0
\(805\) 12000.0 0.525397
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −44730.0 −1.94391 −0.971955 − 0.235167i \(-0.924436\pi\)
−0.971955 + 0.235167i \(0.924436\pi\)
\(810\) 0 0
\(811\) 42748.0 1.85091 0.925453 − 0.378862i \(-0.123684\pi\)
0.925453 + 0.378862i \(0.123684\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 260.000 0.0111747
\(816\) 0 0
\(817\) −11408.0 −0.488513
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 31686.0 1.34695 0.673477 − 0.739208i \(-0.264800\pi\)
0.673477 + 0.739208i \(0.264800\pi\)
\(822\) 0 0
\(823\) −11036.0 −0.467425 −0.233713 − 0.972306i \(-0.575087\pi\)
−0.233713 + 0.972306i \(0.575087\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 25884.0 1.08836 0.544181 − 0.838968i \(-0.316841\pi\)
0.544181 + 0.838968i \(0.316841\pi\)
\(828\) 0 0
\(829\) 15950.0 0.668234 0.334117 − 0.942532i \(-0.391562\pi\)
0.334117 + 0.942532i \(0.391562\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −3078.00 −0.128027
\(834\) 0 0
\(835\) −18600.0 −0.770874
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 13800.0 0.567853 0.283927 − 0.958846i \(-0.408363\pi\)
0.283927 + 0.958846i \(0.408363\pi\)
\(840\) 0 0
\(841\) −18305.0 −0.750543
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 16395.0 0.667462
\(846\) 0 0
\(847\) 15100.0 0.612565
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 8400.00 0.338365
\(852\) 0 0
\(853\) −27862.0 −1.11838 −0.559189 − 0.829040i \(-0.688887\pi\)
−0.559189 + 0.829040i \(0.688887\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 7314.00 0.291530 0.145765 − 0.989319i \(-0.453436\pi\)
0.145765 + 0.989319i \(0.453436\pi\)
\(858\) 0 0
\(859\) 28780.0 1.14314 0.571572 − 0.820552i \(-0.306334\pi\)
0.571572 + 0.820552i \(0.306334\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −32688.0 −1.28935 −0.644677 − 0.764455i \(-0.723008\pi\)
−0.644677 + 0.764455i \(0.723008\pi\)
\(864\) 0 0
\(865\) −2130.00 −0.0837251
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −12480.0 −0.487175
\(870\) 0 0
\(871\) 14504.0 0.564236
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −2500.00 −0.0965891
\(876\) 0 0
\(877\) 36650.0 1.41115 0.705577 − 0.708633i \(-0.250688\pi\)
0.705577 + 0.708633i \(0.250688\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 2646.00 0.101187 0.0505936 − 0.998719i \(-0.483889\pi\)
0.0505936 + 0.998719i \(0.483889\pi\)
\(882\) 0 0
\(883\) −10892.0 −0.415113 −0.207557 − 0.978223i \(-0.566551\pi\)
−0.207557 + 0.978223i \(0.566551\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −43464.0 −1.64530 −0.822648 − 0.568550i \(-0.807504\pi\)
−0.822648 + 0.568550i \(0.807504\pi\)
\(888\) 0 0
\(889\) 24880.0 0.938637
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −2976.00 −0.111521
\(894\) 0 0
\(895\) −7200.00 −0.268904
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −15600.0 −0.578742
\(900\) 0 0
\(901\) 24300.0 0.898502
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −15650.0 −0.574833
\(906\) 0 0
\(907\) 14884.0 0.544890 0.272445 − 0.962171i \(-0.412168\pi\)
0.272445 + 0.962171i \(0.412168\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −1248.00 −0.0453876 −0.0226938 − 0.999742i \(-0.507224\pi\)
−0.0226938 + 0.999742i \(0.507224\pi\)
\(912\) 0 0
\(913\) −3744.00 −0.135716
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −46560.0 −1.67671
\(918\) 0 0
\(919\) 6640.00 0.238339 0.119169 − 0.992874i \(-0.461977\pi\)
0.119169 + 0.992874i \(0.461977\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −21312.0 −0.760014
\(924\) 0 0
\(925\) −1750.00 −0.0622050
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −29946.0 −1.05758 −0.528792 − 0.848751i \(-0.677355\pi\)
−0.528792 + 0.848751i \(0.677355\pi\)
\(930\) 0 0
\(931\) 7068.00 0.248812
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 6480.00 0.226651
\(936\) 0 0
\(937\) 45002.0 1.56900 0.784499 − 0.620130i \(-0.212920\pi\)
0.784499 + 0.620130i \(0.212920\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −6090.00 −0.210976 −0.105488 − 0.994421i \(-0.533640\pi\)
−0.105488 + 0.994421i \(0.533640\pi\)
\(942\) 0 0
\(943\) 39600.0 1.36750
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 56388.0 1.93491 0.967457 − 0.253035i \(-0.0814288\pi\)
0.967457 + 0.253035i \(0.0814288\pi\)
\(948\) 0 0
\(949\) −31820.0 −1.08843
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −10854.0 −0.368936 −0.184468 − 0.982839i \(-0.559056\pi\)
−0.184468 + 0.982839i \(0.559056\pi\)
\(954\) 0 0
\(955\) 17880.0 0.605846
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 42360.0 1.42636
\(960\) 0 0
\(961\) 10209.0 0.342687
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 13330.0 0.444671
\(966\) 0 0
\(967\) 42316.0 1.40723 0.703615 − 0.710582i \(-0.251568\pi\)
0.703615 + 0.710582i \(0.251568\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 24480.0 0.809063 0.404532 − 0.914524i \(-0.367435\pi\)
0.404532 + 0.914524i \(0.367435\pi\)
\(972\) 0 0
\(973\) 46480.0 1.53143
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 6906.00 0.226144 0.113072 − 0.993587i \(-0.463931\pi\)
0.113072 + 0.993587i \(0.463931\pi\)
\(978\) 0 0
\(979\) 24624.0 0.803868
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 6960.00 0.225829 0.112914 − 0.993605i \(-0.463981\pi\)
0.112914 + 0.993605i \(0.463981\pi\)
\(984\) 0 0
\(985\) 13590.0 0.439608
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 11040.0 0.354956
\(990\) 0 0
\(991\) −47792.0 −1.53195 −0.765975 − 0.642870i \(-0.777744\pi\)
−0.765975 + 0.642870i \(0.777744\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 19160.0 0.610465
\(996\) 0 0
\(997\) 9938.00 0.315687 0.157843 − 0.987464i \(-0.449546\pi\)
0.157843 + 0.987464i \(0.449546\pi\)
\(998\) 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.r.1.1 1
3.2 odd 2 240.4.a.f.1.1 1
4.3 odd 2 45.4.a.b.1.1 1
12.11 even 2 15.4.a.b.1.1 ✓ 1
15.2 even 4 1200.4.f.m.49.1 2
15.8 even 4 1200.4.f.m.49.2 2
15.14 odd 2 1200.4.a.o.1.1 1
20.3 even 4 225.4.b.d.199.2 2
20.7 even 4 225.4.b.d.199.1 2
20.19 odd 2 225.4.a.g.1.1 1
24.5 odd 2 960.4.a.l.1.1 1
24.11 even 2 960.4.a.bi.1.1 1
28.27 even 2 2205.4.a.c.1.1 1
36.7 odd 6 405.4.e.k.271.1 2
36.11 even 6 405.4.e.d.271.1 2
36.23 even 6 405.4.e.d.136.1 2
36.31 odd 6 405.4.e.k.136.1 2
60.23 odd 4 75.4.b.a.49.1 2
60.47 odd 4 75.4.b.a.49.2 2
60.59 even 2 75.4.a.a.1.1 1
84.83 odd 2 735.4.a.i.1.1 1
132.131 odd 2 1815.4.a.a.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
15.4.a.b.1.1 ✓ 1 12.11 even 2
45.4.a.b.1.1 1 4.3 odd 2
75.4.a.a.1.1 1 60.59 even 2
75.4.b.a.49.1 2 60.23 odd 4
75.4.b.a.49.2 2 60.47 odd 4
225.4.a.g.1.1 1 20.19 odd 2
225.4.b.d.199.1 2 20.7 even 4
225.4.b.d.199.2 2 20.3 even 4
240.4.a.f.1.1 1 3.2 odd 2
405.4.e.d.136.1 2 36.23 even 6
405.4.e.d.271.1 2 36.11 even 6
405.4.e.k.136.1 2 36.31 odd 6
405.4.e.k.271.1 2 36.7 odd 6
720.4.a.r.1.1 1 1.1 even 1 trivial
735.4.a.i.1.1 1 84.83 odd 2
960.4.a.l.1.1 1 24.5 odd 2
960.4.a.bi.1.1 1 24.11 even 2
1200.4.a.o.1.1 1 15.14 odd 2
1200.4.f.m.49.1 2 15.2 even 4
1200.4.f.m.49.2 2 15.8 even 4
1815.4.a.a.1.1 1 132.131 odd 2
2205.4.a.c.1.1 1 28.27 even 2