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Properties

Label 2400.4.a.m.1.1
Level $2400$
Weight $4$
Character 2400.1
Self dual yes
Analytic conductor $141.605$
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] = [2400,4,Mod(1,2400)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2400, 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("2400.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2400 = 2^{5} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2400.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: \(141.604584014\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 480)
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 2400.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+3.00000 q^{3} -18.0000 q^{7} +9.00000 q^{9} -30.0000 q^{11} -38.0000 q^{13} +70.0000 q^{17} -12.0000 q^{19} -54.0000 q^{21} +72.0000 q^{23} +27.0000 q^{27} -64.0000 q^{29} +312.000 q^{31} -90.0000 q^{33} -138.000 q^{37} -114.000 q^{39} -374.000 q^{41} -468.000 q^{43} +132.000 q^{47} -19.0000 q^{49} +210.000 q^{51} -446.000 q^{53} -36.0000 q^{57} -510.000 q^{59} +754.000 q^{61} -162.000 q^{63} +384.000 q^{67} +216.000 q^{69} +924.000 q^{71} +340.000 q^{73} +540.000 q^{77} -72.0000 q^{79} +81.0000 q^{81} -156.000 q^{83} -192.000 q^{87} -290.000 q^{89} +684.000 q^{91} +936.000 q^{93} +376.000 q^{97} -270.000 q^{99} +O(q^{100})\)

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
\(7\) −18.0000 −0.971909 −0.485954 − 0.873984i \(-0.661528\pi\)
−0.485954 + 0.873984i \(0.661528\pi\)
\(8\) 0 0
\(9\) 9.00000 0.333333
\(10\) 0 0
\(11\) −30.0000 −0.822304 −0.411152 − 0.911567i \(-0.634873\pi\)
−0.411152 + 0.911567i \(0.634873\pi\)
\(12\) 0 0
\(13\) −38.0000 −0.810716 −0.405358 − 0.914158i \(-0.632853\pi\)
−0.405358 + 0.914158i \(0.632853\pi\)
\(14\) 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
\(19\) −12.0000 −0.144894 −0.0724471 − 0.997372i \(-0.523081\pi\)
−0.0724471 + 0.997372i \(0.523081\pi\)
\(20\) 0 0
\(21\) −54.0000 −0.561132
\(22\) 0 0
\(23\) 72.0000 0.652741 0.326370 − 0.945242i \(-0.394174\pi\)
0.326370 + 0.945242i \(0.394174\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 27.0000 0.192450
\(28\) 0 0
\(29\) −64.0000 −0.409810 −0.204905 − 0.978782i \(-0.565689\pi\)
−0.204905 + 0.978782i \(0.565689\pi\)
\(30\) 0 0
\(31\) 312.000 1.80764 0.903820 − 0.427912i \(-0.140751\pi\)
0.903820 + 0.427912i \(0.140751\pi\)
\(32\) 0 0
\(33\) −90.0000 −0.474757
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −138.000 −0.613164 −0.306582 − 0.951844i \(-0.599185\pi\)
−0.306582 + 0.951844i \(0.599185\pi\)
\(38\) 0 0
\(39\) −114.000 −0.468067
\(40\) 0 0
\(41\) −374.000 −1.42461 −0.712305 − 0.701870i \(-0.752349\pi\)
−0.712305 + 0.701870i \(0.752349\pi\)
\(42\) 0 0
\(43\) −468.000 −1.65975 −0.829876 − 0.557948i \(-0.811589\pi\)
−0.829876 + 0.557948i \(0.811589\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 132.000 0.409663 0.204832 − 0.978797i \(-0.434335\pi\)
0.204832 + 0.978797i \(0.434335\pi\)
\(48\) 0 0
\(49\) −19.0000 −0.0553936
\(50\) 0 0
\(51\) 210.000 0.576586
\(52\) 0 0
\(53\) −446.000 −1.15590 −0.577951 − 0.816071i \(-0.696148\pi\)
−0.577951 + 0.816071i \(0.696148\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −36.0000 −0.0836547
\(58\) 0 0
\(59\) −510.000 −1.12536 −0.562681 − 0.826674i \(-0.690230\pi\)
−0.562681 + 0.826674i \(0.690230\pi\)
\(60\) 0 0
\(61\) 754.000 1.58262 0.791310 − 0.611415i \(-0.209399\pi\)
0.791310 + 0.611415i \(0.209399\pi\)
\(62\) 0 0
\(63\) −162.000 −0.323970
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 384.000 0.700195 0.350098 − 0.936713i \(-0.386148\pi\)
0.350098 + 0.936713i \(0.386148\pi\)
\(68\) 0 0
\(69\) 216.000 0.376860
\(70\) 0 0
\(71\) 924.000 1.54449 0.772244 − 0.635326i \(-0.219134\pi\)
0.772244 + 0.635326i \(0.219134\pi\)
\(72\) 0 0
\(73\) 340.000 0.545123 0.272562 − 0.962138i \(-0.412129\pi\)
0.272562 + 0.962138i \(0.412129\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 540.000 0.799204
\(78\) 0 0
\(79\) −72.0000 −0.102540 −0.0512698 − 0.998685i \(-0.516327\pi\)
−0.0512698 + 0.998685i \(0.516327\pi\)
\(80\) 0 0
\(81\) 81.0000 0.111111
\(82\) 0 0
\(83\) −156.000 −0.206304 −0.103152 − 0.994666i \(-0.532893\pi\)
−0.103152 + 0.994666i \(0.532893\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −192.000 −0.236604
\(88\) 0 0
\(89\) −290.000 −0.345393 −0.172696 − 0.984975i \(-0.555248\pi\)
−0.172696 + 0.984975i \(0.555248\pi\)
\(90\) 0 0
\(91\) 684.000 0.787942
\(92\) 0 0
\(93\) 936.000 1.04364
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 376.000 0.393577 0.196789 − 0.980446i \(-0.436949\pi\)
0.196789 + 0.980446i \(0.436949\pi\)
\(98\) 0 0
\(99\) −270.000 −0.274101
\(100\) 0 0
\(101\) 104.000 0.102459 0.0512296 − 0.998687i \(-0.483686\pi\)
0.0512296 + 0.998687i \(0.483686\pi\)
\(102\) 0 0
\(103\) 1014.00 0.970023 0.485012 − 0.874508i \(-0.338815\pi\)
0.485012 + 0.874508i \(0.338815\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1284.00 1.16008 0.580042 − 0.814587i \(-0.303036\pi\)
0.580042 + 0.814587i \(0.303036\pi\)
\(108\) 0 0
\(109\) 570.000 0.500882 0.250441 − 0.968132i \(-0.419424\pi\)
0.250441 + 0.968132i \(0.419424\pi\)
\(110\) 0 0
\(111\) −414.000 −0.354010
\(112\) 0 0
\(113\) −254.000 −0.211454 −0.105727 − 0.994395i \(-0.533717\pi\)
−0.105727 + 0.994395i \(0.533717\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −342.000 −0.270239
\(118\) 0 0
\(119\) −1260.00 −0.970622
\(120\) 0 0
\(121\) −431.000 −0.323817
\(122\) 0 0
\(123\) −1122.00 −0.822499
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −138.000 −0.0964214 −0.0482107 − 0.998837i \(-0.515352\pi\)
−0.0482107 + 0.998837i \(0.515352\pi\)
\(128\) 0 0
\(129\) −1404.00 −0.958258
\(130\) 0 0
\(131\) 894.000 0.596253 0.298126 − 0.954526i \(-0.403638\pi\)
0.298126 + 0.954526i \(0.403638\pi\)
\(132\) 0 0
\(133\) 216.000 0.140824
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 3050.00 1.90204 0.951019 − 0.309134i \(-0.100039\pi\)
0.951019 + 0.309134i \(0.100039\pi\)
\(138\) 0 0
\(139\) 2352.00 1.43521 0.717604 − 0.696451i \(-0.245239\pi\)
0.717604 + 0.696451i \(0.245239\pi\)
\(140\) 0 0
\(141\) 396.000 0.236519
\(142\) 0 0
\(143\) 1140.00 0.666654
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −57.0000 −0.0319815
\(148\) 0 0
\(149\) 2476.00 1.36135 0.680677 − 0.732583i \(-0.261686\pi\)
0.680677 + 0.732583i \(0.261686\pi\)
\(150\) 0 0
\(151\) 3192.00 1.72027 0.860137 − 0.510064i \(-0.170378\pi\)
0.860137 + 0.510064i \(0.170378\pi\)
\(152\) 0 0
\(153\) 630.000 0.332892
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 1218.00 0.619153 0.309576 − 0.950875i \(-0.399813\pi\)
0.309576 + 0.950875i \(0.399813\pi\)
\(158\) 0 0
\(159\) −1338.00 −0.667360
\(160\) 0 0
\(161\) −1296.00 −0.634404
\(162\) 0 0
\(163\) −2328.00 −1.11867 −0.559334 − 0.828942i \(-0.688943\pi\)
−0.559334 + 0.828942i \(0.688943\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −2928.00 −1.35674 −0.678370 − 0.734721i \(-0.737313\pi\)
−0.678370 + 0.734721i \(0.737313\pi\)
\(168\) 0 0
\(169\) −753.000 −0.342740
\(170\) 0 0
\(171\) −108.000 −0.0482980
\(172\) 0 0
\(173\) 502.000 0.220615 0.110307 − 0.993898i \(-0.464816\pi\)
0.110307 + 0.993898i \(0.464816\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −1530.00 −0.649728
\(178\) 0 0
\(179\) 4026.00 1.68110 0.840551 − 0.541732i \(-0.182231\pi\)
0.840551 + 0.541732i \(0.182231\pi\)
\(180\) 0 0
\(181\) 594.000 0.243932 0.121966 − 0.992534i \(-0.461080\pi\)
0.121966 + 0.992534i \(0.461080\pi\)
\(182\) 0 0
\(183\) 2262.00 0.913726
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −2100.00 −0.821215
\(188\) 0 0
\(189\) −486.000 −0.187044
\(190\) 0 0
\(191\) −1044.00 −0.395504 −0.197752 − 0.980252i \(-0.563364\pi\)
−0.197752 + 0.980252i \(0.563364\pi\)
\(192\) 0 0
\(193\) 3252.00 1.21287 0.606435 − 0.795133i \(-0.292599\pi\)
0.606435 + 0.795133i \(0.292599\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 2914.00 1.05388 0.526939 − 0.849903i \(-0.323340\pi\)
0.526939 + 0.849903i \(0.323340\pi\)
\(198\) 0 0
\(199\) 4872.00 1.73551 0.867756 − 0.496990i \(-0.165562\pi\)
0.867756 + 0.496990i \(0.165562\pi\)
\(200\) 0 0
\(201\) 1152.00 0.404258
\(202\) 0 0
\(203\) 1152.00 0.398298
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 648.000 0.217580
\(208\) 0 0
\(209\) 360.000 0.119147
\(210\) 0 0
\(211\) −1872.00 −0.610776 −0.305388 − 0.952228i \(-0.598786\pi\)
−0.305388 + 0.952228i \(0.598786\pi\)
\(212\) 0 0
\(213\) 2772.00 0.891710
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −5616.00 −1.75686
\(218\) 0 0
\(219\) 1020.00 0.314727
\(220\) 0 0
\(221\) −2660.00 −0.809642
\(222\) 0 0
\(223\) 1302.00 0.390979 0.195490 − 0.980706i \(-0.437370\pi\)
0.195490 + 0.980706i \(0.437370\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −708.000 −0.207011 −0.103506 − 0.994629i \(-0.533006\pi\)
−0.103506 + 0.994629i \(0.533006\pi\)
\(228\) 0 0
\(229\) −5082.00 −1.46650 −0.733249 − 0.679960i \(-0.761997\pi\)
−0.733249 + 0.679960i \(0.761997\pi\)
\(230\) 0 0
\(231\) 1620.00 0.461421
\(232\) 0 0
\(233\) −5786.00 −1.62684 −0.813419 − 0.581678i \(-0.802397\pi\)
−0.813419 + 0.581678i \(0.802397\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −216.000 −0.0592013
\(238\) 0 0
\(239\) 3156.00 0.854162 0.427081 − 0.904213i \(-0.359542\pi\)
0.427081 + 0.904213i \(0.359542\pi\)
\(240\) 0 0
\(241\) −3306.00 −0.883644 −0.441822 − 0.897103i \(-0.645668\pi\)
−0.441822 + 0.897103i \(0.645668\pi\)
\(242\) 0 0
\(243\) 243.000 0.0641500
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 456.000 0.117468
\(248\) 0 0
\(249\) −468.000 −0.119110
\(250\) 0 0
\(251\) 4134.00 1.03958 0.519792 − 0.854293i \(-0.326009\pi\)
0.519792 + 0.854293i \(0.326009\pi\)
\(252\) 0 0
\(253\) −2160.00 −0.536751
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 3482.00 0.845141 0.422570 − 0.906330i \(-0.361128\pi\)
0.422570 + 0.906330i \(0.361128\pi\)
\(258\) 0 0
\(259\) 2484.00 0.595939
\(260\) 0 0
\(261\) −576.000 −0.136603
\(262\) 0 0
\(263\) −2856.00 −0.669614 −0.334807 − 0.942287i \(-0.608671\pi\)
−0.334807 + 0.942287i \(0.608671\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −870.000 −0.199412
\(268\) 0 0
\(269\) 6464.00 1.46512 0.732560 − 0.680703i \(-0.238326\pi\)
0.732560 + 0.680703i \(0.238326\pi\)
\(270\) 0 0
\(271\) 5184.00 1.16201 0.581007 − 0.813899i \(-0.302659\pi\)
0.581007 + 0.813899i \(0.302659\pi\)
\(272\) 0 0
\(273\) 2052.00 0.454918
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −3818.00 −0.828164 −0.414082 − 0.910240i \(-0.635897\pi\)
−0.414082 + 0.910240i \(0.635897\pi\)
\(278\) 0 0
\(279\) 2808.00 0.602547
\(280\) 0 0
\(281\) 6094.00 1.29373 0.646864 − 0.762605i \(-0.276080\pi\)
0.646864 + 0.762605i \(0.276080\pi\)
\(282\) 0 0
\(283\) 4440.00 0.932617 0.466308 − 0.884622i \(-0.345584\pi\)
0.466308 + 0.884622i \(0.345584\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 6732.00 1.38459
\(288\) 0 0
\(289\) −13.0000 −0.00264604
\(290\) 0 0
\(291\) 1128.00 0.227232
\(292\) 0 0
\(293\) −5950.00 −1.18636 −0.593179 − 0.805071i \(-0.702127\pi\)
−0.593179 + 0.805071i \(0.702127\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −810.000 −0.158252
\(298\) 0 0
\(299\) −2736.00 −0.529187
\(300\) 0 0
\(301\) 8424.00 1.61313
\(302\) 0 0
\(303\) 312.000 0.0591549
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 924.000 0.171777 0.0858884 − 0.996305i \(-0.472627\pi\)
0.0858884 + 0.996305i \(0.472627\pi\)
\(308\) 0 0
\(309\) 3042.00 0.560043
\(310\) 0 0
\(311\) 7020.00 1.27996 0.639980 − 0.768391i \(-0.278943\pi\)
0.639980 + 0.768391i \(0.278943\pi\)
\(312\) 0 0
\(313\) −5244.00 −0.946992 −0.473496 − 0.880796i \(-0.657008\pi\)
−0.473496 + 0.880796i \(0.657008\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −5194.00 −0.920265 −0.460133 − 0.887850i \(-0.652198\pi\)
−0.460133 + 0.887850i \(0.652198\pi\)
\(318\) 0 0
\(319\) 1920.00 0.336989
\(320\) 0 0
\(321\) 3852.00 0.669775
\(322\) 0 0
\(323\) −840.000 −0.144702
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 1710.00 0.289184
\(328\) 0 0
\(329\) −2376.00 −0.398155
\(330\) 0 0
\(331\) 11628.0 1.93091 0.965457 − 0.260562i \(-0.0839077\pi\)
0.965457 + 0.260562i \(0.0839077\pi\)
\(332\) 0 0
\(333\) −1242.00 −0.204388
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −4372.00 −0.706700 −0.353350 − 0.935491i \(-0.614958\pi\)
−0.353350 + 0.935491i \(0.614958\pi\)
\(338\) 0 0
\(339\) −762.000 −0.122083
\(340\) 0 0
\(341\) −9360.00 −1.48643
\(342\) 0 0
\(343\) 6516.00 1.02575
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −12564.0 −1.94372 −0.971860 − 0.235559i \(-0.924308\pi\)
−0.971860 + 0.235559i \(0.924308\pi\)
\(348\) 0 0
\(349\) 970.000 0.148776 0.0743881 − 0.997229i \(-0.476300\pi\)
0.0743881 + 0.997229i \(0.476300\pi\)
\(350\) 0 0
\(351\) −1026.00 −0.156022
\(352\) 0 0
\(353\) 1958.00 0.295223 0.147612 − 0.989045i \(-0.452841\pi\)
0.147612 + 0.989045i \(0.452841\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −3780.00 −0.560389
\(358\) 0 0
\(359\) 1920.00 0.282267 0.141133 − 0.989991i \(-0.454925\pi\)
0.141133 + 0.989991i \(0.454925\pi\)
\(360\) 0 0
\(361\) −6715.00 −0.979006
\(362\) 0 0
\(363\) −1293.00 −0.186956
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 8886.00 1.26388 0.631942 − 0.775016i \(-0.282258\pi\)
0.631942 + 0.775016i \(0.282258\pi\)
\(368\) 0 0
\(369\) −3366.00 −0.474870
\(370\) 0 0
\(371\) 8028.00 1.12343
\(372\) 0 0
\(373\) −7470.00 −1.03695 −0.518474 − 0.855093i \(-0.673500\pi\)
−0.518474 + 0.855093i \(0.673500\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 2432.00 0.332240
\(378\) 0 0
\(379\) −6312.00 −0.855477 −0.427738 − 0.903903i \(-0.640690\pi\)
−0.427738 + 0.903903i \(0.640690\pi\)
\(380\) 0 0
\(381\) −414.000 −0.0556689
\(382\) 0 0
\(383\) −12876.0 −1.71784 −0.858920 − 0.512109i \(-0.828864\pi\)
−0.858920 + 0.512109i \(0.828864\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −4212.00 −0.553251
\(388\) 0 0
\(389\) −8780.00 −1.14438 −0.572190 − 0.820121i \(-0.693906\pi\)
−0.572190 + 0.820121i \(0.693906\pi\)
\(390\) 0 0
\(391\) 5040.00 0.651877
\(392\) 0 0
\(393\) 2682.00 0.344247
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 3246.00 0.410358 0.205179 − 0.978724i \(-0.434222\pi\)
0.205179 + 0.978724i \(0.434222\pi\)
\(398\) 0 0
\(399\) 648.000 0.0813047
\(400\) 0 0
\(401\) 1870.00 0.232876 0.116438 − 0.993198i \(-0.462852\pi\)
0.116438 + 0.993198i \(0.462852\pi\)
\(402\) 0 0
\(403\) −11856.0 −1.46548
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 4140.00 0.504207
\(408\) 0 0
\(409\) 15990.0 1.93314 0.966570 − 0.256401i \(-0.0825368\pi\)
0.966570 + 0.256401i \(0.0825368\pi\)
\(410\) 0 0
\(411\) 9150.00 1.09814
\(412\) 0 0
\(413\) 9180.00 1.09375
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 7056.00 0.828618
\(418\) 0 0
\(419\) 3054.00 0.356080 0.178040 − 0.984023i \(-0.443024\pi\)
0.178040 + 0.984023i \(0.443024\pi\)
\(420\) 0 0
\(421\) −1194.00 −0.138223 −0.0691116 − 0.997609i \(-0.522016\pi\)
−0.0691116 + 0.997609i \(0.522016\pi\)
\(422\) 0 0
\(423\) 1188.00 0.136554
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −13572.0 −1.53816
\(428\) 0 0
\(429\) 3420.00 0.384893
\(430\) 0 0
\(431\) 15264.0 1.70590 0.852948 − 0.521996i \(-0.174812\pi\)
0.852948 + 0.521996i \(0.174812\pi\)
\(432\) 0 0
\(433\) −8220.00 −0.912305 −0.456152 − 0.889902i \(-0.650773\pi\)
−0.456152 + 0.889902i \(0.650773\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −864.000 −0.0945783
\(438\) 0 0
\(439\) −16248.0 −1.76646 −0.883229 − 0.468943i \(-0.844635\pi\)
−0.883229 + 0.468943i \(0.844635\pi\)
\(440\) 0 0
\(441\) −171.000 −0.0184645
\(442\) 0 0
\(443\) 8220.00 0.881589 0.440795 − 0.897608i \(-0.354697\pi\)
0.440795 + 0.897608i \(0.354697\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 7428.00 0.785978
\(448\) 0 0
\(449\) −9490.00 −0.997463 −0.498731 − 0.866757i \(-0.666201\pi\)
−0.498731 + 0.866757i \(0.666201\pi\)
\(450\) 0 0
\(451\) 11220.0 1.17146
\(452\) 0 0
\(453\) 9576.00 0.993200
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −5776.00 −0.591225 −0.295613 − 0.955308i \(-0.595524\pi\)
−0.295613 + 0.955308i \(0.595524\pi\)
\(458\) 0 0
\(459\) 1890.00 0.192195
\(460\) 0 0
\(461\) 2812.00 0.284095 0.142048 − 0.989860i \(-0.454631\pi\)
0.142048 + 0.989860i \(0.454631\pi\)
\(462\) 0 0
\(463\) −13710.0 −1.37615 −0.688075 − 0.725639i \(-0.741544\pi\)
−0.688075 + 0.725639i \(0.741544\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 6252.00 0.619503 0.309752 − 0.950817i \(-0.399754\pi\)
0.309752 + 0.950817i \(0.399754\pi\)
\(468\) 0 0
\(469\) −6912.00 −0.680526
\(470\) 0 0
\(471\) 3654.00 0.357468
\(472\) 0 0
\(473\) 14040.0 1.36482
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −4014.00 −0.385301
\(478\) 0 0
\(479\) 7908.00 0.754333 0.377167 − 0.926145i \(-0.376898\pi\)
0.377167 + 0.926145i \(0.376898\pi\)
\(480\) 0 0
\(481\) 5244.00 0.497101
\(482\) 0 0
\(483\) −3888.00 −0.366274
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 17562.0 1.63411 0.817054 − 0.576562i \(-0.195606\pi\)
0.817054 + 0.576562i \(0.195606\pi\)
\(488\) 0 0
\(489\) −6984.00 −0.645864
\(490\) 0 0
\(491\) 13062.0 1.20057 0.600285 − 0.799786i \(-0.295054\pi\)
0.600285 + 0.799786i \(0.295054\pi\)
\(492\) 0 0
\(493\) −4480.00 −0.409268
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −16632.0 −1.50110
\(498\) 0 0
\(499\) −8556.00 −0.767573 −0.383787 − 0.923422i \(-0.625380\pi\)
−0.383787 + 0.923422i \(0.625380\pi\)
\(500\) 0 0
\(501\) −8784.00 −0.783314
\(502\) 0 0
\(503\) 14436.0 1.27966 0.639830 − 0.768516i \(-0.279005\pi\)
0.639830 + 0.768516i \(0.279005\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −2259.00 −0.197881
\(508\) 0 0
\(509\) 9536.00 0.830404 0.415202 − 0.909729i \(-0.363711\pi\)
0.415202 + 0.909729i \(0.363711\pi\)
\(510\) 0 0
\(511\) −6120.00 −0.529810
\(512\) 0 0
\(513\) −324.000 −0.0278849
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −3960.00 −0.336868
\(518\) 0 0
\(519\) 1506.00 0.127372
\(520\) 0 0
\(521\) −1130.00 −0.0950215 −0.0475107 − 0.998871i \(-0.515129\pi\)
−0.0475107 + 0.998871i \(0.515129\pi\)
\(522\) 0 0
\(523\) 4104.00 0.343127 0.171563 − 0.985173i \(-0.445118\pi\)
0.171563 + 0.985173i \(0.445118\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 21840.0 1.80525
\(528\) 0 0
\(529\) −6983.00 −0.573929
\(530\) 0 0
\(531\) −4590.00 −0.375121
\(532\) 0 0
\(533\) 14212.0 1.15495
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 12078.0 0.970585
\(538\) 0 0
\(539\) 570.000 0.0455503
\(540\) 0 0
\(541\) 6810.00 0.541192 0.270596 − 0.962693i \(-0.412779\pi\)
0.270596 + 0.962693i \(0.412779\pi\)
\(542\) 0 0
\(543\) 1782.00 0.140834
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −23772.0 −1.85817 −0.929083 − 0.369870i \(-0.879402\pi\)
−0.929083 + 0.369870i \(0.879402\pi\)
\(548\) 0 0
\(549\) 6786.00 0.527540
\(550\) 0 0
\(551\) 768.000 0.0593791
\(552\) 0 0
\(553\) 1296.00 0.0996592
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 10762.0 0.818672 0.409336 − 0.912384i \(-0.365760\pi\)
0.409336 + 0.912384i \(0.365760\pi\)
\(558\) 0 0
\(559\) 17784.0 1.34559
\(560\) 0 0
\(561\) −6300.00 −0.474129
\(562\) 0 0
\(563\) 1716.00 0.128456 0.0642280 − 0.997935i \(-0.479541\pi\)
0.0642280 + 0.997935i \(0.479541\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −1458.00 −0.107990
\(568\) 0 0
\(569\) 6670.00 0.491425 0.245713 − 0.969343i \(-0.420978\pi\)
0.245713 + 0.969343i \(0.420978\pi\)
\(570\) 0 0
\(571\) 5580.00 0.408959 0.204480 − 0.978871i \(-0.434450\pi\)
0.204480 + 0.978871i \(0.434450\pi\)
\(572\) 0 0
\(573\) −3132.00 −0.228344
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 17808.0 1.28485 0.642424 − 0.766350i \(-0.277929\pi\)
0.642424 + 0.766350i \(0.277929\pi\)
\(578\) 0 0
\(579\) 9756.00 0.700251
\(580\) 0 0
\(581\) 2808.00 0.200509
\(582\) 0 0
\(583\) 13380.0 0.950503
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −23004.0 −1.61751 −0.808754 − 0.588148i \(-0.799857\pi\)
−0.808754 + 0.588148i \(0.799857\pi\)
\(588\) 0 0
\(589\) −3744.00 −0.261917
\(590\) 0 0
\(591\) 8742.00 0.608457
\(592\) 0 0
\(593\) 3266.00 0.226170 0.113085 − 0.993585i \(-0.463927\pi\)
0.113085 + 0.993585i \(0.463927\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 14616.0 1.00200
\(598\) 0 0
\(599\) 2208.00 0.150612 0.0753059 − 0.997160i \(-0.476007\pi\)
0.0753059 + 0.997160i \(0.476007\pi\)
\(600\) 0 0
\(601\) −21166.0 −1.43657 −0.718285 − 0.695748i \(-0.755073\pi\)
−0.718285 + 0.695748i \(0.755073\pi\)
\(602\) 0 0
\(603\) 3456.00 0.233398
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 17610.0 1.17754 0.588771 − 0.808300i \(-0.299612\pi\)
0.588771 + 0.808300i \(0.299612\pi\)
\(608\) 0 0
\(609\) 3456.00 0.229958
\(610\) 0 0
\(611\) −5016.00 −0.332121
\(612\) 0 0
\(613\) −29610.0 −1.95096 −0.975478 − 0.220095i \(-0.929363\pi\)
−0.975478 + 0.220095i \(0.929363\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 2294.00 0.149681 0.0748403 − 0.997196i \(-0.476155\pi\)
0.0748403 + 0.997196i \(0.476155\pi\)
\(618\) 0 0
\(619\) 19704.0 1.27944 0.639718 − 0.768610i \(-0.279051\pi\)
0.639718 + 0.768610i \(0.279051\pi\)
\(620\) 0 0
\(621\) 1944.00 0.125620
\(622\) 0 0
\(623\) 5220.00 0.335690
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 1080.00 0.0687895
\(628\) 0 0
\(629\) −9660.00 −0.612352
\(630\) 0 0
\(631\) −4392.00 −0.277088 −0.138544 − 0.990356i \(-0.544242\pi\)
−0.138544 + 0.990356i \(0.544242\pi\)
\(632\) 0 0
\(633\) −5616.00 −0.352632
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 722.000 0.0449084
\(638\) 0 0
\(639\) 8316.00 0.514829
\(640\) 0 0
\(641\) 19586.0 1.20687 0.603433 − 0.797414i \(-0.293799\pi\)
0.603433 + 0.797414i \(0.293799\pi\)
\(642\) 0 0
\(643\) 624.000 0.0382709 0.0191354 − 0.999817i \(-0.493909\pi\)
0.0191354 + 0.999817i \(0.493909\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −8556.00 −0.519893 −0.259947 − 0.965623i \(-0.583705\pi\)
−0.259947 + 0.965623i \(0.583705\pi\)
\(648\) 0 0
\(649\) 15300.0 0.925389
\(650\) 0 0
\(651\) −16848.0 −1.01432
\(652\) 0 0
\(653\) 22910.0 1.37295 0.686476 − 0.727153i \(-0.259157\pi\)
0.686476 + 0.727153i \(0.259157\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 3060.00 0.181708
\(658\) 0 0
\(659\) 7590.00 0.448656 0.224328 − 0.974514i \(-0.427981\pi\)
0.224328 + 0.974514i \(0.427981\pi\)
\(660\) 0 0
\(661\) 31970.0 1.88122 0.940612 − 0.339484i \(-0.110252\pi\)
0.940612 + 0.339484i \(0.110252\pi\)
\(662\) 0 0
\(663\) −7980.00 −0.467447
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −4608.00 −0.267500
\(668\) 0 0
\(669\) 3906.00 0.225732
\(670\) 0 0
\(671\) −22620.0 −1.30139
\(672\) 0 0
\(673\) −24996.0 −1.43169 −0.715843 − 0.698261i \(-0.753957\pi\)
−0.715843 + 0.698261i \(0.753957\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −3226.00 −0.183139 −0.0915696 − 0.995799i \(-0.529188\pi\)
−0.0915696 + 0.995799i \(0.529188\pi\)
\(678\) 0 0
\(679\) −6768.00 −0.382521
\(680\) 0 0
\(681\) −2124.00 −0.119518
\(682\) 0 0
\(683\) −23412.0 −1.31162 −0.655809 − 0.754927i \(-0.727672\pi\)
−0.655809 + 0.754927i \(0.727672\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −15246.0 −0.846683
\(688\) 0 0
\(689\) 16948.0 0.937108
\(690\) 0 0
\(691\) −16572.0 −0.912342 −0.456171 − 0.889892i \(-0.650780\pi\)
−0.456171 + 0.889892i \(0.650780\pi\)
\(692\) 0 0
\(693\) 4860.00 0.266401
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −26180.0 −1.42272
\(698\) 0 0
\(699\) −17358.0 −0.939256
\(700\) 0 0
\(701\) −448.000 −0.0241380 −0.0120690 − 0.999927i \(-0.503842\pi\)
−0.0120690 + 0.999927i \(0.503842\pi\)
\(702\) 0 0
\(703\) 1656.00 0.0888438
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −1872.00 −0.0995811
\(708\) 0 0
\(709\) −11922.0 −0.631509 −0.315755 − 0.948841i \(-0.602258\pi\)
−0.315755 + 0.948841i \(0.602258\pi\)
\(710\) 0 0
\(711\) −648.000 −0.0341799
\(712\) 0 0
\(713\) 22464.0 1.17992
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 9468.00 0.493151
\(718\) 0 0
\(719\) −4344.00 −0.225318 −0.112659 − 0.993634i \(-0.535937\pi\)
−0.112659 + 0.993634i \(0.535937\pi\)
\(720\) 0 0
\(721\) −18252.0 −0.942774
\(722\) 0 0
\(723\) −9918.00 −0.510172
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −26934.0 −1.37404 −0.687020 − 0.726639i \(-0.741081\pi\)
−0.687020 + 0.726639i \(0.741081\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) 0 0
\(731\) −32760.0 −1.65755
\(732\) 0 0
\(733\) −35962.0 −1.81212 −0.906062 − 0.423145i \(-0.860926\pi\)
−0.906062 + 0.423145i \(0.860926\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −11520.0 −0.575773
\(738\) 0 0
\(739\) 4860.00 0.241919 0.120959 − 0.992657i \(-0.461403\pi\)
0.120959 + 0.992657i \(0.461403\pi\)
\(740\) 0 0
\(741\) 1368.00 0.0678202
\(742\) 0 0
\(743\) 29844.0 1.47358 0.736790 − 0.676121i \(-0.236341\pi\)
0.736790 + 0.676121i \(0.236341\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −1404.00 −0.0687680
\(748\) 0 0
\(749\) −23112.0 −1.12750
\(750\) 0 0
\(751\) −1248.00 −0.0606394 −0.0303197 − 0.999540i \(-0.509653\pi\)
−0.0303197 + 0.999540i \(0.509653\pi\)
\(752\) 0 0
\(753\) 12402.0 0.600205
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 25094.0 1.20483 0.602415 − 0.798183i \(-0.294205\pi\)
0.602415 + 0.798183i \(0.294205\pi\)
\(758\) 0 0
\(759\) −6480.00 −0.309893
\(760\) 0 0
\(761\) 23294.0 1.10960 0.554801 − 0.831983i \(-0.312794\pi\)
0.554801 + 0.831983i \(0.312794\pi\)
\(762\) 0 0
\(763\) −10260.0 −0.486811
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 19380.0 0.912348
\(768\) 0 0
\(769\) −254.000 −0.0119109 −0.00595544 − 0.999982i \(-0.501896\pi\)
−0.00595544 + 0.999982i \(0.501896\pi\)
\(770\) 0 0
\(771\) 10446.0 0.487942
\(772\) 0 0
\(773\) 21886.0 1.01835 0.509175 − 0.860663i \(-0.329951\pi\)
0.509175 + 0.860663i \(0.329951\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 7452.00 0.344066
\(778\) 0 0
\(779\) 4488.00 0.206418
\(780\) 0 0
\(781\) −27720.0 −1.27004
\(782\) 0 0
\(783\) −1728.00 −0.0788680
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 14904.0 0.675057 0.337529 − 0.941315i \(-0.390409\pi\)
0.337529 + 0.941315i \(0.390409\pi\)
\(788\) 0 0
\(789\) −8568.00 −0.386602
\(790\) 0 0
\(791\) 4572.00 0.205514
\(792\) 0 0
\(793\) −28652.0 −1.28305
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −23834.0 −1.05928 −0.529638 − 0.848224i \(-0.677672\pi\)
−0.529638 + 0.848224i \(0.677672\pi\)
\(798\) 0 0
\(799\) 9240.00 0.409121
\(800\) 0 0
\(801\) −2610.00 −0.115131
\(802\) 0 0
\(803\) −10200.0 −0.448257
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 19392.0 0.845887
\(808\) 0 0
\(809\) −31502.0 −1.36904 −0.684519 − 0.728995i \(-0.739988\pi\)
−0.684519 + 0.728995i \(0.739988\pi\)
\(810\) 0 0
\(811\) −21072.0 −0.912377 −0.456189 − 0.889883i \(-0.650786\pi\)
−0.456189 + 0.889883i \(0.650786\pi\)
\(812\) 0 0
\(813\) 15552.0 0.670889
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 5616.00 0.240488
\(818\) 0 0
\(819\) 6156.00 0.262647
\(820\) 0 0
\(821\) −38072.0 −1.61842 −0.809209 − 0.587520i \(-0.800104\pi\)
−0.809209 + 0.587520i \(0.800104\pi\)
\(822\) 0 0
\(823\) 31578.0 1.33747 0.668736 − 0.743500i \(-0.266836\pi\)
0.668736 + 0.743500i \(0.266836\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −41532.0 −1.74632 −0.873162 − 0.487431i \(-0.837934\pi\)
−0.873162 + 0.487431i \(0.837934\pi\)
\(828\) 0 0
\(829\) 24786.0 1.03842 0.519212 − 0.854646i \(-0.326226\pi\)
0.519212 + 0.854646i \(0.326226\pi\)
\(830\) 0 0
\(831\) −11454.0 −0.478141
\(832\) 0 0
\(833\) −1330.00 −0.0553203
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 8424.00 0.347881
\(838\) 0 0
\(839\) −1608.00 −0.0661673 −0.0330836 − 0.999453i \(-0.510533\pi\)
−0.0330836 + 0.999453i \(0.510533\pi\)
\(840\) 0 0
\(841\) −20293.0 −0.832055
\(842\) 0 0
\(843\) 18282.0 0.746934
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 7758.00 0.314720
\(848\) 0 0
\(849\) 13320.0 0.538447
\(850\) 0 0
\(851\) −9936.00 −0.400237
\(852\) 0 0
\(853\) −8514.00 −0.341751 −0.170876 − 0.985293i \(-0.554660\pi\)
−0.170876 + 0.985293i \(0.554660\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 29726.0 1.18486 0.592428 − 0.805624i \(-0.298170\pi\)
0.592428 + 0.805624i \(0.298170\pi\)
\(858\) 0 0
\(859\) −2136.00 −0.0848421 −0.0424211 − 0.999100i \(-0.513507\pi\)
−0.0424211 + 0.999100i \(0.513507\pi\)
\(860\) 0 0
\(861\) 20196.0 0.799394
\(862\) 0 0
\(863\) 11928.0 0.470491 0.235246 − 0.971936i \(-0.424411\pi\)
0.235246 + 0.971936i \(0.424411\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −39.0000 −0.00152769
\(868\) 0 0
\(869\) 2160.00 0.0843187
\(870\) 0 0
\(871\) −14592.0 −0.567659
\(872\) 0 0
\(873\) 3384.00 0.131192
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −27006.0 −1.03983 −0.519913 − 0.854219i \(-0.674036\pi\)
−0.519913 + 0.854219i \(0.674036\pi\)
\(878\) 0 0
\(879\) −17850.0 −0.684944
\(880\) 0 0
\(881\) 29318.0 1.12117 0.560584 − 0.828098i \(-0.310577\pi\)
0.560584 + 0.828098i \(0.310577\pi\)
\(882\) 0 0
\(883\) −7008.00 −0.267087 −0.133544 − 0.991043i \(-0.542636\pi\)
−0.133544 + 0.991043i \(0.542636\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 15024.0 0.568722 0.284361 − 0.958717i \(-0.408219\pi\)
0.284361 + 0.958717i \(0.408219\pi\)
\(888\) 0 0
\(889\) 2484.00 0.0937128
\(890\) 0 0
\(891\) −2430.00 −0.0913671
\(892\) 0 0
\(893\) −1584.00 −0.0593578
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −8208.00 −0.305526
\(898\) 0 0
\(899\) −19968.0 −0.740790
\(900\) 0 0
\(901\) −31220.0 −1.15437
\(902\) 0 0
\(903\) 25272.0 0.931339
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −1380.00 −0.0505206 −0.0252603 − 0.999681i \(-0.508041\pi\)
−0.0252603 + 0.999681i \(0.508041\pi\)
\(908\) 0 0
\(909\) 936.000 0.0341531
\(910\) 0 0
\(911\) −17952.0 −0.652883 −0.326441 − 0.945217i \(-0.605850\pi\)
−0.326441 + 0.945217i \(0.605850\pi\)
\(912\) 0 0
\(913\) 4680.00 0.169644
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −16092.0 −0.579503
\(918\) 0 0
\(919\) −19056.0 −0.684004 −0.342002 − 0.939699i \(-0.611105\pi\)
−0.342002 + 0.939699i \(0.611105\pi\)
\(920\) 0 0
\(921\) 2772.00 0.0991754
\(922\) 0 0
\(923\) −35112.0 −1.25214
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 9126.00 0.323341
\(928\) 0 0
\(929\) 26398.0 0.932282 0.466141 − 0.884710i \(-0.345644\pi\)
0.466141 + 0.884710i \(0.345644\pi\)
\(930\) 0 0
\(931\) 228.000 0.00802621
\(932\) 0 0
\(933\) 21060.0 0.738985
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 21192.0 0.738861 0.369430 − 0.929258i \(-0.379553\pi\)
0.369430 + 0.929258i \(0.379553\pi\)
\(938\) 0 0
\(939\) −15732.0 −0.546746
\(940\) 0 0
\(941\) 7300.00 0.252894 0.126447 − 0.991973i \(-0.459643\pi\)
0.126447 + 0.991973i \(0.459643\pi\)
\(942\) 0 0
\(943\) −26928.0 −0.929901
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 33540.0 1.15090 0.575451 − 0.817836i \(-0.304827\pi\)
0.575451 + 0.817836i \(0.304827\pi\)
\(948\) 0 0
\(949\) −12920.0 −0.441940
\(950\) 0 0
\(951\) −15582.0 −0.531315
\(952\) 0 0
\(953\) 32714.0 1.11197 0.555987 − 0.831191i \(-0.312341\pi\)
0.555987 + 0.831191i \(0.312341\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 5760.00 0.194560
\(958\) 0 0
\(959\) −54900.0 −1.84861
\(960\) 0 0
\(961\) 67553.0 2.26756
\(962\) 0 0
\(963\) 11556.0 0.386695
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 35334.0 1.17504 0.587521 − 0.809209i \(-0.300104\pi\)
0.587521 + 0.809209i \(0.300104\pi\)
\(968\) 0 0
\(969\) −2520.00 −0.0835439
\(970\) 0 0
\(971\) 17094.0 0.564956 0.282478 − 0.959274i \(-0.408844\pi\)
0.282478 + 0.959274i \(0.408844\pi\)
\(972\) 0 0
\(973\) −42336.0 −1.39489
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 46814.0 1.53297 0.766485 − 0.642262i \(-0.222004\pi\)
0.766485 + 0.642262i \(0.222004\pi\)
\(978\) 0 0
\(979\) 8700.00 0.284018
\(980\) 0 0
\(981\) 5130.00 0.166961
\(982\) 0 0
\(983\) −5076.00 −0.164699 −0.0823496 − 0.996604i \(-0.526242\pi\)
−0.0823496 + 0.996604i \(0.526242\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) −7128.00 −0.229875
\(988\) 0 0
\(989\) −33696.0 −1.08339
\(990\) 0 0
\(991\) 9456.00 0.303108 0.151554 − 0.988449i \(-0.451572\pi\)
0.151554 + 0.988449i \(0.451572\pi\)
\(992\) 0 0
\(993\) 34884.0 1.11481
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −33486.0 −1.06370 −0.531852 − 0.846838i \(-0.678504\pi\)
−0.531852 + 0.846838i \(0.678504\pi\)
\(998\) 0 0
\(999\) −3726.00 −0.118003
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 2400.4.a.m.1.1 1
4.3 odd 2 2400.4.a.j.1.1 1
5.2 odd 4 480.4.f.a.289.1 ✓ 2
5.3 odd 4 480.4.f.a.289.2 yes 2
5.4 even 2 2400.4.a.i.1.1 1
15.2 even 4 1440.4.f.d.289.1 2
15.8 even 4 1440.4.f.d.289.2 2
20.3 even 4 480.4.f.b.289.1 yes 2
20.7 even 4 480.4.f.b.289.2 yes 2
20.19 odd 2 2400.4.a.n.1.1 1
40.3 even 4 960.4.f.h.769.2 2
40.13 odd 4 960.4.f.k.769.1 2
40.27 even 4 960.4.f.h.769.1 2
40.37 odd 4 960.4.f.k.769.2 2
60.23 odd 4 1440.4.f.c.289.2 2
60.47 odd 4 1440.4.f.c.289.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
480.4.f.a.289.1 ✓ 2 5.2 odd 4
480.4.f.a.289.2 yes 2 5.3 odd 4
480.4.f.b.289.1 yes 2 20.3 even 4
480.4.f.b.289.2 yes 2 20.7 even 4
960.4.f.h.769.1 2 40.27 even 4
960.4.f.h.769.2 2 40.3 even 4
960.4.f.k.769.1 2 40.13 odd 4
960.4.f.k.769.2 2 40.37 odd 4
1440.4.f.c.289.1 2 60.47 odd 4
1440.4.f.c.289.2 2 60.23 odd 4
1440.4.f.d.289.1 2 15.2 even 4
1440.4.f.d.289.2 2 15.8 even 4
2400.4.a.i.1.1 1 5.4 even 2
2400.4.a.j.1.1 1 4.3 odd 2
2400.4.a.m.1.1 1 1.1 even 1 trivial
2400.4.a.n.1.1 1 20.19 odd 2