Properties

Label 140.4.a.d.1.1
Level $140$
Weight $4$
Character 140.1
Self dual yes
Analytic conductor $8.260$
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] = [140,4,Mod(1,140)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(140, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("140.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 140.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: \(8.26026740080\)
Analytic rank: \(1\)
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 \(\chi\) \(=\) 140.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{3} -5.00000 q^{5} -7.00000 q^{7} -26.0000 q^{9} +O(q^{10})\) \(q+1.00000 q^{3} -5.00000 q^{5} -7.00000 q^{7} -26.0000 q^{9} -7.00000 q^{11} -23.0000 q^{13} -5.00000 q^{15} -25.0000 q^{17} -62.0000 q^{19} -7.00000 q^{21} -86.0000 q^{23} +25.0000 q^{25} -53.0000 q^{27} -29.0000 q^{29} -12.0000 q^{31} -7.00000 q^{33} +35.0000 q^{35} -150.000 q^{37} -23.0000 q^{39} +204.000 q^{41} -178.000 q^{43} +130.000 q^{45} +33.0000 q^{47} +49.0000 q^{49} -25.0000 q^{51} +452.000 q^{53} +35.0000 q^{55} -62.0000 q^{57} +120.000 q^{59} +920.000 q^{61} +182.000 q^{63} +115.000 q^{65} -300.000 q^{67} -86.0000 q^{69} +520.000 q^{71} +370.000 q^{73} +25.0000 q^{75} +49.0000 q^{77} -1013.00 q^{79} +649.000 q^{81} -636.000 q^{83} +125.000 q^{85} -29.0000 q^{87} +292.000 q^{89} +161.000 q^{91} -12.0000 q^{93} +310.000 q^{95} -1381.00 q^{97} +182.000 q^{99} +O(q^{100})\)

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
\(3\) 1.00000 0.192450 0.0962250 0.995360i \(-0.469323\pi\)
0.0962250 + 0.995360i \(0.469323\pi\)
\(4\) 0 0
\(5\) −5.00000 −0.447214
\(6\) 0 0
\(7\) −7.00000 −0.377964
\(8\) 0 0
\(9\) −26.0000 −0.962963
\(10\) 0 0
\(11\) −7.00000 −0.191871 −0.0959354 0.995388i \(-0.530584\pi\)
−0.0959354 + 0.995388i \(0.530584\pi\)
\(12\) 0 0
\(13\) −23.0000 −0.490696 −0.245348 0.969435i \(-0.578902\pi\)
−0.245348 + 0.969435i \(0.578902\pi\)
\(14\) 0 0
\(15\) −5.00000 −0.0860663
\(16\) 0 0
\(17\) −25.0000 −0.356670 −0.178335 0.983970i \(-0.557071\pi\)
−0.178335 + 0.983970i \(0.557071\pi\)
\(18\) 0 0
\(19\) −62.0000 −0.748620 −0.374310 0.927304i \(-0.622120\pi\)
−0.374310 + 0.927304i \(0.622120\pi\)
\(20\) 0 0
\(21\) −7.00000 −0.0727393
\(22\) 0 0
\(23\) −86.0000 −0.779663 −0.389831 0.920886i \(-0.627467\pi\)
−0.389831 + 0.920886i \(0.627467\pi\)
\(24\) 0 0
\(25\) 25.0000 0.200000
\(26\) 0 0
\(27\) −53.0000 −0.377772
\(28\) 0 0
\(29\) −29.0000 −0.185695 −0.0928477 0.995680i \(-0.529597\pi\)
−0.0928477 + 0.995680i \(0.529597\pi\)
\(30\) 0 0
\(31\) −12.0000 −0.0695246 −0.0347623 0.999396i \(-0.511067\pi\)
−0.0347623 + 0.999396i \(0.511067\pi\)
\(32\) 0 0
\(33\) −7.00000 −0.0369256
\(34\) 0 0
\(35\) 35.0000 0.169031
\(36\) 0 0
\(37\) −150.000 −0.666482 −0.333241 0.942842i \(-0.608142\pi\)
−0.333241 + 0.942842i \(0.608142\pi\)
\(38\) 0 0
\(39\) −23.0000 −0.0944346
\(40\) 0 0
\(41\) 204.000 0.777060 0.388530 0.921436i \(-0.372983\pi\)
0.388530 + 0.921436i \(0.372983\pi\)
\(42\) 0 0
\(43\) −178.000 −0.631273 −0.315637 0.948880i \(-0.602218\pi\)
−0.315637 + 0.948880i \(0.602218\pi\)
\(44\) 0 0
\(45\) 130.000 0.430650
\(46\) 0 0
\(47\) 33.0000 0.102416 0.0512079 0.998688i \(-0.483693\pi\)
0.0512079 + 0.998688i \(0.483693\pi\)
\(48\) 0 0
\(49\) 49.0000 0.142857
\(50\) 0 0
\(51\) −25.0000 −0.0686412
\(52\) 0 0
\(53\) 452.000 1.17145 0.585726 0.810509i \(-0.300809\pi\)
0.585726 + 0.810509i \(0.300809\pi\)
\(54\) 0 0
\(55\) 35.0000 0.0858073
\(56\) 0 0
\(57\) −62.0000 −0.144072
\(58\) 0 0
\(59\) 120.000 0.264791 0.132396 0.991197i \(-0.457733\pi\)
0.132396 + 0.991197i \(0.457733\pi\)
\(60\) 0 0
\(61\) 920.000 1.93105 0.965524 0.260314i \(-0.0838261\pi\)
0.965524 + 0.260314i \(0.0838261\pi\)
\(62\) 0 0
\(63\) 182.000 0.363966
\(64\) 0 0
\(65\) 115.000 0.219446
\(66\) 0 0
\(67\) −300.000 −0.547027 −0.273514 0.961868i \(-0.588186\pi\)
−0.273514 + 0.961868i \(0.588186\pi\)
\(68\) 0 0
\(69\) −86.0000 −0.150046
\(70\) 0 0
\(71\) 520.000 0.869192 0.434596 0.900625i \(-0.356891\pi\)
0.434596 + 0.900625i \(0.356891\pi\)
\(72\) 0 0
\(73\) 370.000 0.593222 0.296611 0.954998i \(-0.404143\pi\)
0.296611 + 0.954998i \(0.404143\pi\)
\(74\) 0 0
\(75\) 25.0000 0.0384900
\(76\) 0 0
\(77\) 49.0000 0.0725204
\(78\) 0 0
\(79\) −1013.00 −1.44268 −0.721338 0.692583i \(-0.756473\pi\)
−0.721338 + 0.692583i \(0.756473\pi\)
\(80\) 0 0
\(81\) 649.000 0.890261
\(82\) 0 0
\(83\) −636.000 −0.841085 −0.420543 0.907273i \(-0.638160\pi\)
−0.420543 + 0.907273i \(0.638160\pi\)
\(84\) 0 0
\(85\) 125.000 0.159508
\(86\) 0 0
\(87\) −29.0000 −0.0357371
\(88\) 0 0
\(89\) 292.000 0.347775 0.173887 0.984766i \(-0.444367\pi\)
0.173887 + 0.984766i \(0.444367\pi\)
\(90\) 0 0
\(91\) 161.000 0.185466
\(92\) 0 0
\(93\) −12.0000 −0.0133800
\(94\) 0 0
\(95\) 310.000 0.334793
\(96\) 0 0
\(97\) −1381.00 −1.44556 −0.722780 0.691078i \(-0.757136\pi\)
−0.722780 + 0.691078i \(0.757136\pi\)
\(98\) 0 0
\(99\) 182.000 0.184765
\(100\) 0 0
\(101\) 1278.00 1.25907 0.629533 0.776973i \(-0.283246\pi\)
0.629533 + 0.776973i \(0.283246\pi\)
\(102\) 0 0
\(103\) −875.000 −0.837052 −0.418526 0.908205i \(-0.637453\pi\)
−0.418526 + 0.908205i \(0.637453\pi\)
\(104\) 0 0
\(105\) 35.0000 0.0325300
\(106\) 0 0
\(107\) −1986.00 −1.79434 −0.897168 0.441690i \(-0.854379\pi\)
−0.897168 + 0.441690i \(0.854379\pi\)
\(108\) 0 0
\(109\) −223.000 −0.195959 −0.0979795 0.995188i \(-0.531238\pi\)
−0.0979795 + 0.995188i \(0.531238\pi\)
\(110\) 0 0
\(111\) −150.000 −0.128265
\(112\) 0 0
\(113\) −930.000 −0.774222 −0.387111 0.922033i \(-0.626527\pi\)
−0.387111 + 0.922033i \(0.626527\pi\)
\(114\) 0 0
\(115\) 430.000 0.348676
\(116\) 0 0
\(117\) 598.000 0.472522
\(118\) 0 0
\(119\) 175.000 0.134809
\(120\) 0 0
\(121\) −1282.00 −0.963186
\(122\) 0 0
\(123\) 204.000 0.149545
\(124\) 0 0
\(125\) −125.000 −0.0894427
\(126\) 0 0
\(127\) −2056.00 −1.43654 −0.718270 0.695765i \(-0.755066\pi\)
−0.718270 + 0.695765i \(0.755066\pi\)
\(128\) 0 0
\(129\) −178.000 −0.121489
\(130\) 0 0
\(131\) 1442.00 0.961741 0.480871 0.876792i \(-0.340321\pi\)
0.480871 + 0.876792i \(0.340321\pi\)
\(132\) 0 0
\(133\) 434.000 0.282952
\(134\) 0 0
\(135\) 265.000 0.168945
\(136\) 0 0
\(137\) −908.000 −0.566246 −0.283123 0.959084i \(-0.591370\pi\)
−0.283123 + 0.959084i \(0.591370\pi\)
\(138\) 0 0
\(139\) −1690.00 −1.03125 −0.515626 0.856814i \(-0.672440\pi\)
−0.515626 + 0.856814i \(0.672440\pi\)
\(140\) 0 0
\(141\) 33.0000 0.0197099
\(142\) 0 0
\(143\) 161.000 0.0941503
\(144\) 0 0
\(145\) 145.000 0.0830455
\(146\) 0 0
\(147\) 49.0000 0.0274929
\(148\) 0 0
\(149\) −2014.00 −1.10734 −0.553669 0.832737i \(-0.686773\pi\)
−0.553669 + 0.832737i \(0.686773\pi\)
\(150\) 0 0
\(151\) 619.000 0.333599 0.166800 0.985991i \(-0.446657\pi\)
0.166800 + 0.985991i \(0.446657\pi\)
\(152\) 0 0
\(153\) 650.000 0.343460
\(154\) 0 0
\(155\) 60.0000 0.0310924
\(156\) 0 0
\(157\) 1446.00 0.735053 0.367527 0.930013i \(-0.380205\pi\)
0.367527 + 0.930013i \(0.380205\pi\)
\(158\) 0 0
\(159\) 452.000 0.225446
\(160\) 0 0
\(161\) 602.000 0.294685
\(162\) 0 0
\(163\) −2638.00 −1.26763 −0.633816 0.773484i \(-0.718512\pi\)
−0.633816 + 0.773484i \(0.718512\pi\)
\(164\) 0 0
\(165\) 35.0000 0.0165136
\(166\) 0 0
\(167\) −11.0000 −0.00509704 −0.00254852 0.999997i \(-0.500811\pi\)
−0.00254852 + 0.999997i \(0.500811\pi\)
\(168\) 0 0
\(169\) −1668.00 −0.759217
\(170\) 0 0
\(171\) 1612.00 0.720893
\(172\) 0 0
\(173\) 3267.00 1.43575 0.717877 0.696170i \(-0.245114\pi\)
0.717877 + 0.696170i \(0.245114\pi\)
\(174\) 0 0
\(175\) −175.000 −0.0755929
\(176\) 0 0
\(177\) 120.000 0.0509591
\(178\) 0 0
\(179\) 3676.00 1.53496 0.767478 0.641075i \(-0.221511\pi\)
0.767478 + 0.641075i \(0.221511\pi\)
\(180\) 0 0
\(181\) 780.000 0.320315 0.160157 0.987092i \(-0.448800\pi\)
0.160157 + 0.987092i \(0.448800\pi\)
\(182\) 0 0
\(183\) 920.000 0.371630
\(184\) 0 0
\(185\) 750.000 0.298060
\(186\) 0 0
\(187\) 175.000 0.0684346
\(188\) 0 0
\(189\) 371.000 0.142785
\(190\) 0 0
\(191\) −283.000 −0.107210 −0.0536051 0.998562i \(-0.517071\pi\)
−0.0536051 + 0.998562i \(0.517071\pi\)
\(192\) 0 0
\(193\) −484.000 −0.180513 −0.0902567 0.995919i \(-0.528769\pi\)
−0.0902567 + 0.995919i \(0.528769\pi\)
\(194\) 0 0
\(195\) 115.000 0.0422324
\(196\) 0 0
\(197\) −360.000 −0.130198 −0.0650988 0.997879i \(-0.520736\pi\)
−0.0650988 + 0.997879i \(0.520736\pi\)
\(198\) 0 0
\(199\) 1032.00 0.367621 0.183810 0.982962i \(-0.441157\pi\)
0.183810 + 0.982962i \(0.441157\pi\)
\(200\) 0 0
\(201\) −300.000 −0.105275
\(202\) 0 0
\(203\) 203.000 0.0701862
\(204\) 0 0
\(205\) −1020.00 −0.347512
\(206\) 0 0
\(207\) 2236.00 0.750786
\(208\) 0 0
\(209\) 434.000 0.143638
\(210\) 0 0
\(211\) −513.000 −0.167376 −0.0836881 0.996492i \(-0.526670\pi\)
−0.0836881 + 0.996492i \(0.526670\pi\)
\(212\) 0 0
\(213\) 520.000 0.167276
\(214\) 0 0
\(215\) 890.000 0.282314
\(216\) 0 0
\(217\) 84.0000 0.0262778
\(218\) 0 0
\(219\) 370.000 0.114166
\(220\) 0 0
\(221\) 575.000 0.175017
\(222\) 0 0
\(223\) −907.000 −0.272364 −0.136182 0.990684i \(-0.543483\pi\)
−0.136182 + 0.990684i \(0.543483\pi\)
\(224\) 0 0
\(225\) −650.000 −0.192593
\(226\) 0 0
\(227\) 5701.00 1.66691 0.833455 0.552587i \(-0.186359\pi\)
0.833455 + 0.552587i \(0.186359\pi\)
\(228\) 0 0
\(229\) −2044.00 −0.589831 −0.294916 0.955523i \(-0.595292\pi\)
−0.294916 + 0.955523i \(0.595292\pi\)
\(230\) 0 0
\(231\) 49.0000 0.0139566
\(232\) 0 0
\(233\) −2728.00 −0.767027 −0.383513 0.923535i \(-0.625286\pi\)
−0.383513 + 0.923535i \(0.625286\pi\)
\(234\) 0 0
\(235\) −165.000 −0.0458018
\(236\) 0 0
\(237\) −1013.00 −0.277643
\(238\) 0 0
\(239\) 7095.00 1.92024 0.960120 0.279588i \(-0.0901979\pi\)
0.960120 + 0.279588i \(0.0901979\pi\)
\(240\) 0 0
\(241\) −2618.00 −0.699752 −0.349876 0.936796i \(-0.613776\pi\)
−0.349876 + 0.936796i \(0.613776\pi\)
\(242\) 0 0
\(243\) 2080.00 0.549103
\(244\) 0 0
\(245\) −245.000 −0.0638877
\(246\) 0 0
\(247\) 1426.00 0.367345
\(248\) 0 0
\(249\) −636.000 −0.161867
\(250\) 0 0
\(251\) −3318.00 −0.834384 −0.417192 0.908818i \(-0.636986\pi\)
−0.417192 + 0.908818i \(0.636986\pi\)
\(252\) 0 0
\(253\) 602.000 0.149595
\(254\) 0 0
\(255\) 125.000 0.0306973
\(256\) 0 0
\(257\) 1678.00 0.407279 0.203640 0.979046i \(-0.434723\pi\)
0.203640 + 0.979046i \(0.434723\pi\)
\(258\) 0 0
\(259\) 1050.00 0.251907
\(260\) 0 0
\(261\) 754.000 0.178818
\(262\) 0 0
\(263\) −898.000 −0.210544 −0.105272 0.994443i \(-0.533571\pi\)
−0.105272 + 0.994443i \(0.533571\pi\)
\(264\) 0 0
\(265\) −2260.00 −0.523889
\(266\) 0 0
\(267\) 292.000 0.0669293
\(268\) 0 0
\(269\) −4902.00 −1.11108 −0.555539 0.831490i \(-0.687488\pi\)
−0.555539 + 0.831490i \(0.687488\pi\)
\(270\) 0 0
\(271\) −7040.00 −1.57804 −0.789021 0.614366i \(-0.789412\pi\)
−0.789021 + 0.614366i \(0.789412\pi\)
\(272\) 0 0
\(273\) 161.000 0.0356929
\(274\) 0 0
\(275\) −175.000 −0.0383742
\(276\) 0 0
\(277\) −2402.00 −0.521019 −0.260509 0.965471i \(-0.583890\pi\)
−0.260509 + 0.965471i \(0.583890\pi\)
\(278\) 0 0
\(279\) 312.000 0.0669496
\(280\) 0 0
\(281\) −6525.00 −1.38523 −0.692614 0.721309i \(-0.743541\pi\)
−0.692614 + 0.721309i \(0.743541\pi\)
\(282\) 0 0
\(283\) −4109.00 −0.863091 −0.431545 0.902091i \(-0.642032\pi\)
−0.431545 + 0.902091i \(0.642032\pi\)
\(284\) 0 0
\(285\) 310.000 0.0644309
\(286\) 0 0
\(287\) −1428.00 −0.293701
\(288\) 0 0
\(289\) −4288.00 −0.872786
\(290\) 0 0
\(291\) −1381.00 −0.278198
\(292\) 0 0
\(293\) 3495.00 0.696860 0.348430 0.937335i \(-0.386715\pi\)
0.348430 + 0.937335i \(0.386715\pi\)
\(294\) 0 0
\(295\) −600.000 −0.118418
\(296\) 0 0
\(297\) 371.000 0.0724835
\(298\) 0 0
\(299\) 1978.00 0.382578
\(300\) 0 0
\(301\) 1246.00 0.238599
\(302\) 0 0
\(303\) 1278.00 0.242308
\(304\) 0 0
\(305\) −4600.00 −0.863591
\(306\) 0 0
\(307\) 803.000 0.149282 0.0746411 0.997210i \(-0.476219\pi\)
0.0746411 + 0.997210i \(0.476219\pi\)
\(308\) 0 0
\(309\) −875.000 −0.161091
\(310\) 0 0
\(311\) −5438.00 −0.991513 −0.495757 0.868461i \(-0.665109\pi\)
−0.495757 + 0.868461i \(0.665109\pi\)
\(312\) 0 0
\(313\) 681.000 0.122979 0.0614895 0.998108i \(-0.480415\pi\)
0.0614895 + 0.998108i \(0.480415\pi\)
\(314\) 0 0
\(315\) −910.000 −0.162770
\(316\) 0 0
\(317\) 9214.00 1.63252 0.816262 0.577683i \(-0.196043\pi\)
0.816262 + 0.577683i \(0.196043\pi\)
\(318\) 0 0
\(319\) 203.000 0.0356295
\(320\) 0 0
\(321\) −1986.00 −0.345320
\(322\) 0 0
\(323\) 1550.00 0.267010
\(324\) 0 0
\(325\) −575.000 −0.0981393
\(326\) 0 0
\(327\) −223.000 −0.0377123
\(328\) 0 0
\(329\) −231.000 −0.0387096
\(330\) 0 0
\(331\) −2700.00 −0.448355 −0.224177 0.974548i \(-0.571969\pi\)
−0.224177 + 0.974548i \(0.571969\pi\)
\(332\) 0 0
\(333\) 3900.00 0.641798
\(334\) 0 0
\(335\) 1500.00 0.244638
\(336\) 0 0
\(337\) −3834.00 −0.619737 −0.309868 0.950779i \(-0.600285\pi\)
−0.309868 + 0.950779i \(0.600285\pi\)
\(338\) 0 0
\(339\) −930.000 −0.148999
\(340\) 0 0
\(341\) 84.0000 0.0133398
\(342\) 0 0
\(343\) −343.000 −0.0539949
\(344\) 0 0
\(345\) 430.000 0.0671027
\(346\) 0 0
\(347\) −2626.00 −0.406257 −0.203128 0.979152i \(-0.565111\pi\)
−0.203128 + 0.979152i \(0.565111\pi\)
\(348\) 0 0
\(349\) 8354.00 1.28132 0.640658 0.767826i \(-0.278662\pi\)
0.640658 + 0.767826i \(0.278662\pi\)
\(350\) 0 0
\(351\) 1219.00 0.185372
\(352\) 0 0
\(353\) −8213.00 −1.23834 −0.619170 0.785257i \(-0.712531\pi\)
−0.619170 + 0.785257i \(0.712531\pi\)
\(354\) 0 0
\(355\) −2600.00 −0.388715
\(356\) 0 0
\(357\) 175.000 0.0259439
\(358\) 0 0
\(359\) 6432.00 0.945593 0.472797 0.881172i \(-0.343245\pi\)
0.472797 + 0.881172i \(0.343245\pi\)
\(360\) 0 0
\(361\) −3015.00 −0.439568
\(362\) 0 0
\(363\) −1282.00 −0.185365
\(364\) 0 0
\(365\) −1850.00 −0.265297
\(366\) 0 0
\(367\) 11617.0 1.65232 0.826161 0.563434i \(-0.190520\pi\)
0.826161 + 0.563434i \(0.190520\pi\)
\(368\) 0 0
\(369\) −5304.00 −0.748280
\(370\) 0 0
\(371\) −3164.00 −0.442767
\(372\) 0 0
\(373\) 11084.0 1.53863 0.769313 0.638872i \(-0.220599\pi\)
0.769313 + 0.638872i \(0.220599\pi\)
\(374\) 0 0
\(375\) −125.000 −0.0172133
\(376\) 0 0
\(377\) 667.000 0.0911200
\(378\) 0 0
\(379\) 12292.0 1.66596 0.832978 0.553306i \(-0.186634\pi\)
0.832978 + 0.553306i \(0.186634\pi\)
\(380\) 0 0
\(381\) −2056.00 −0.276462
\(382\) 0 0
\(383\) −10820.0 −1.44354 −0.721770 0.692133i \(-0.756671\pi\)
−0.721770 + 0.692133i \(0.756671\pi\)
\(384\) 0 0
\(385\) −245.000 −0.0324321
\(386\) 0 0
\(387\) 4628.00 0.607893
\(388\) 0 0
\(389\) 7501.00 0.977676 0.488838 0.872375i \(-0.337421\pi\)
0.488838 + 0.872375i \(0.337421\pi\)
\(390\) 0 0
\(391\) 2150.00 0.278082
\(392\) 0 0
\(393\) 1442.00 0.185087
\(394\) 0 0
\(395\) 5065.00 0.645184
\(396\) 0 0
\(397\) 7899.00 0.998588 0.499294 0.866433i \(-0.333593\pi\)
0.499294 + 0.866433i \(0.333593\pi\)
\(398\) 0 0
\(399\) 434.000 0.0544541
\(400\) 0 0
\(401\) 1753.00 0.218306 0.109153 0.994025i \(-0.465186\pi\)
0.109153 + 0.994025i \(0.465186\pi\)
\(402\) 0 0
\(403\) 276.000 0.0341155
\(404\) 0 0
\(405\) −3245.00 −0.398137
\(406\) 0 0
\(407\) 1050.00 0.127879
\(408\) 0 0
\(409\) −11834.0 −1.43069 −0.715347 0.698770i \(-0.753731\pi\)
−0.715347 + 0.698770i \(0.753731\pi\)
\(410\) 0 0
\(411\) −908.000 −0.108974
\(412\) 0 0
\(413\) −840.000 −0.100082
\(414\) 0 0
\(415\) 3180.00 0.376145
\(416\) 0 0
\(417\) −1690.00 −0.198464
\(418\) 0 0
\(419\) 6908.00 0.805436 0.402718 0.915324i \(-0.368065\pi\)
0.402718 + 0.915324i \(0.368065\pi\)
\(420\) 0 0
\(421\) 8377.00 0.969762 0.484881 0.874580i \(-0.338863\pi\)
0.484881 + 0.874580i \(0.338863\pi\)
\(422\) 0 0
\(423\) −858.000 −0.0986227
\(424\) 0 0
\(425\) −625.000 −0.0713340
\(426\) 0 0
\(427\) −6440.00 −0.729868
\(428\) 0 0
\(429\) 161.000 0.0181192
\(430\) 0 0
\(431\) −4287.00 −0.479113 −0.239556 0.970882i \(-0.577002\pi\)
−0.239556 + 0.970882i \(0.577002\pi\)
\(432\) 0 0
\(433\) 15874.0 1.76179 0.880896 0.473310i \(-0.156941\pi\)
0.880896 + 0.473310i \(0.156941\pi\)
\(434\) 0 0
\(435\) 145.000 0.0159821
\(436\) 0 0
\(437\) 5332.00 0.583671
\(438\) 0 0
\(439\) −7646.00 −0.831261 −0.415631 0.909534i \(-0.636439\pi\)
−0.415631 + 0.909534i \(0.636439\pi\)
\(440\) 0 0
\(441\) −1274.00 −0.137566
\(442\) 0 0
\(443\) −1626.00 −0.174387 −0.0871937 0.996191i \(-0.527790\pi\)
−0.0871937 + 0.996191i \(0.527790\pi\)
\(444\) 0 0
\(445\) −1460.00 −0.155530
\(446\) 0 0
\(447\) −2014.00 −0.213107
\(448\) 0 0
\(449\) −841.000 −0.0883948 −0.0441974 0.999023i \(-0.514073\pi\)
−0.0441974 + 0.999023i \(0.514073\pi\)
\(450\) 0 0
\(451\) −1428.00 −0.149095
\(452\) 0 0
\(453\) 619.000 0.0642012
\(454\) 0 0
\(455\) −805.000 −0.0829428
\(456\) 0 0
\(457\) 15424.0 1.57878 0.789392 0.613889i \(-0.210396\pi\)
0.789392 + 0.613889i \(0.210396\pi\)
\(458\) 0 0
\(459\) 1325.00 0.134740
\(460\) 0 0
\(461\) 10568.0 1.06768 0.533840 0.845585i \(-0.320748\pi\)
0.533840 + 0.845585i \(0.320748\pi\)
\(462\) 0 0
\(463\) 4368.00 0.438441 0.219220 0.975675i \(-0.429649\pi\)
0.219220 + 0.975675i \(0.429649\pi\)
\(464\) 0 0
\(465\) 60.0000 0.00598373
\(466\) 0 0
\(467\) −4329.00 −0.428956 −0.214478 0.976729i \(-0.568805\pi\)
−0.214478 + 0.976729i \(0.568805\pi\)
\(468\) 0 0
\(469\) 2100.00 0.206757
\(470\) 0 0
\(471\) 1446.00 0.141461
\(472\) 0 0
\(473\) 1246.00 0.121123
\(474\) 0 0
\(475\) −1550.00 −0.149724
\(476\) 0 0
\(477\) −11752.0 −1.12807
\(478\) 0 0
\(479\) −11062.0 −1.05519 −0.527595 0.849496i \(-0.676906\pi\)
−0.527595 + 0.849496i \(0.676906\pi\)
\(480\) 0 0
\(481\) 3450.00 0.327040
\(482\) 0 0
\(483\) 602.000 0.0567121
\(484\) 0 0
\(485\) 6905.00 0.646474
\(486\) 0 0
\(487\) −18698.0 −1.73981 −0.869905 0.493220i \(-0.835820\pi\)
−0.869905 + 0.493220i \(0.835820\pi\)
\(488\) 0 0
\(489\) −2638.00 −0.243956
\(490\) 0 0
\(491\) 3003.00 0.276015 0.138008 0.990431i \(-0.455930\pi\)
0.138008 + 0.990431i \(0.455930\pi\)
\(492\) 0 0
\(493\) 725.000 0.0662320
\(494\) 0 0
\(495\) −910.000 −0.0826292
\(496\) 0 0
\(497\) −3640.00 −0.328524
\(498\) 0 0
\(499\) −3291.00 −0.295241 −0.147621 0.989044i \(-0.547161\pi\)
−0.147621 + 0.989044i \(0.547161\pi\)
\(500\) 0 0
\(501\) −11.0000 −0.000980926 0
\(502\) 0 0
\(503\) −12533.0 −1.11097 −0.555486 0.831526i \(-0.687468\pi\)
−0.555486 + 0.831526i \(0.687468\pi\)
\(504\) 0 0
\(505\) −6390.00 −0.563072
\(506\) 0 0
\(507\) −1668.00 −0.146111
\(508\) 0 0
\(509\) −2406.00 −0.209517 −0.104758 0.994498i \(-0.533407\pi\)
−0.104758 + 0.994498i \(0.533407\pi\)
\(510\) 0 0
\(511\) −2590.00 −0.224217
\(512\) 0 0
\(513\) 3286.00 0.282808
\(514\) 0 0
\(515\) 4375.00 0.374341
\(516\) 0 0
\(517\) −231.000 −0.0196506
\(518\) 0 0
\(519\) 3267.00 0.276311
\(520\) 0 0
\(521\) −10098.0 −0.849139 −0.424569 0.905395i \(-0.639575\pi\)
−0.424569 + 0.905395i \(0.639575\pi\)
\(522\) 0 0
\(523\) −16100.0 −1.34609 −0.673044 0.739603i \(-0.735013\pi\)
−0.673044 + 0.739603i \(0.735013\pi\)
\(524\) 0 0
\(525\) −175.000 −0.0145479
\(526\) 0 0
\(527\) 300.000 0.0247974
\(528\) 0 0
\(529\) −4771.00 −0.392126
\(530\) 0 0
\(531\) −3120.00 −0.254984
\(532\) 0 0
\(533\) −4692.00 −0.381300
\(534\) 0 0
\(535\) 9930.00 0.802451
\(536\) 0 0
\(537\) 3676.00 0.295402
\(538\) 0 0
\(539\) −343.000 −0.0274101
\(540\) 0 0
\(541\) 16835.0 1.33788 0.668940 0.743316i \(-0.266748\pi\)
0.668940 + 0.743316i \(0.266748\pi\)
\(542\) 0 0
\(543\) 780.000 0.0616446
\(544\) 0 0
\(545\) 1115.00 0.0876355
\(546\) 0 0
\(547\) −4104.00 −0.320794 −0.160397 0.987053i \(-0.551277\pi\)
−0.160397 + 0.987053i \(0.551277\pi\)
\(548\) 0 0
\(549\) −23920.0 −1.85953
\(550\) 0 0
\(551\) 1798.00 0.139015
\(552\) 0 0
\(553\) 7091.00 0.545280
\(554\) 0 0
\(555\) 750.000 0.0573617
\(556\) 0 0
\(557\) −20280.0 −1.54271 −0.771357 0.636403i \(-0.780421\pi\)
−0.771357 + 0.636403i \(0.780421\pi\)
\(558\) 0 0
\(559\) 4094.00 0.309763
\(560\) 0 0
\(561\) 175.000 0.0131702
\(562\) 0 0
\(563\) −17092.0 −1.27947 −0.639735 0.768595i \(-0.720956\pi\)
−0.639735 + 0.768595i \(0.720956\pi\)
\(564\) 0 0
\(565\) 4650.00 0.346242
\(566\) 0 0
\(567\) −4543.00 −0.336487
\(568\) 0 0
\(569\) 242.000 0.0178298 0.00891491 0.999960i \(-0.497162\pi\)
0.00891491 + 0.999960i \(0.497162\pi\)
\(570\) 0 0
\(571\) 1180.00 0.0864824 0.0432412 0.999065i \(-0.486232\pi\)
0.0432412 + 0.999065i \(0.486232\pi\)
\(572\) 0 0
\(573\) −283.000 −0.0206326
\(574\) 0 0
\(575\) −2150.00 −0.155933
\(576\) 0 0
\(577\) 18421.0 1.32907 0.664537 0.747255i \(-0.268629\pi\)
0.664537 + 0.747255i \(0.268629\pi\)
\(578\) 0 0
\(579\) −484.000 −0.0347398
\(580\) 0 0
\(581\) 4452.00 0.317900
\(582\) 0 0
\(583\) −3164.00 −0.224768
\(584\) 0 0
\(585\) −2990.00 −0.211318
\(586\) 0 0
\(587\) −19776.0 −1.39053 −0.695267 0.718752i \(-0.744714\pi\)
−0.695267 + 0.718752i \(0.744714\pi\)
\(588\) 0 0
\(589\) 744.000 0.0520475
\(590\) 0 0
\(591\) −360.000 −0.0250566
\(592\) 0 0
\(593\) −2451.00 −0.169731 −0.0848655 0.996392i \(-0.527046\pi\)
−0.0848655 + 0.996392i \(0.527046\pi\)
\(594\) 0 0
\(595\) −875.000 −0.0602882
\(596\) 0 0
\(597\) 1032.00 0.0707487
\(598\) 0 0
\(599\) 18081.0 1.23334 0.616669 0.787222i \(-0.288482\pi\)
0.616669 + 0.787222i \(0.288482\pi\)
\(600\) 0 0
\(601\) 18238.0 1.23784 0.618921 0.785453i \(-0.287570\pi\)
0.618921 + 0.785453i \(0.287570\pi\)
\(602\) 0 0
\(603\) 7800.00 0.526767
\(604\) 0 0
\(605\) 6410.00 0.430750
\(606\) 0 0
\(607\) −10925.0 −0.730531 −0.365265 0.930903i \(-0.619022\pi\)
−0.365265 + 0.930903i \(0.619022\pi\)
\(608\) 0 0
\(609\) 203.000 0.0135073
\(610\) 0 0
\(611\) −759.000 −0.0502551
\(612\) 0 0
\(613\) 1506.00 0.0992280 0.0496140 0.998768i \(-0.484201\pi\)
0.0496140 + 0.998768i \(0.484201\pi\)
\(614\) 0 0
\(615\) −1020.00 −0.0668787
\(616\) 0 0
\(617\) −24142.0 −1.57524 −0.787618 0.616164i \(-0.788686\pi\)
−0.787618 + 0.616164i \(0.788686\pi\)
\(618\) 0 0
\(619\) −16558.0 −1.07516 −0.537579 0.843214i \(-0.680661\pi\)
−0.537579 + 0.843214i \(0.680661\pi\)
\(620\) 0 0
\(621\) 4558.00 0.294535
\(622\) 0 0
\(623\) −2044.00 −0.131446
\(624\) 0 0
\(625\) 625.000 0.0400000
\(626\) 0 0
\(627\) 434.000 0.0276432
\(628\) 0 0
\(629\) 3750.00 0.237714
\(630\) 0 0
\(631\) 25025.0 1.57881 0.789405 0.613872i \(-0.210389\pi\)
0.789405 + 0.613872i \(0.210389\pi\)
\(632\) 0 0
\(633\) −513.000 −0.0322116
\(634\) 0 0
\(635\) 10280.0 0.642440
\(636\) 0 0
\(637\) −1127.00 −0.0700995
\(638\) 0 0
\(639\) −13520.0 −0.837000
\(640\) 0 0
\(641\) 9154.00 0.564058 0.282029 0.959406i \(-0.408993\pi\)
0.282029 + 0.959406i \(0.408993\pi\)
\(642\) 0 0
\(643\) 8225.00 0.504452 0.252226 0.967668i \(-0.418837\pi\)
0.252226 + 0.967668i \(0.418837\pi\)
\(644\) 0 0
\(645\) 890.000 0.0543313
\(646\) 0 0
\(647\) 23688.0 1.43937 0.719684 0.694302i \(-0.244287\pi\)
0.719684 + 0.694302i \(0.244287\pi\)
\(648\) 0 0
\(649\) −840.000 −0.0508057
\(650\) 0 0
\(651\) 84.0000 0.00505717
\(652\) 0 0
\(653\) −14518.0 −0.870036 −0.435018 0.900422i \(-0.643258\pi\)
−0.435018 + 0.900422i \(0.643258\pi\)
\(654\) 0 0
\(655\) −7210.00 −0.430104
\(656\) 0 0
\(657\) −9620.00 −0.571251
\(658\) 0 0
\(659\) 30381.0 1.79587 0.897933 0.440132i \(-0.145068\pi\)
0.897933 + 0.440132i \(0.145068\pi\)
\(660\) 0 0
\(661\) 25568.0 1.50451 0.752254 0.658873i \(-0.228967\pi\)
0.752254 + 0.658873i \(0.228967\pi\)
\(662\) 0 0
\(663\) 575.000 0.0336820
\(664\) 0 0
\(665\) −2170.00 −0.126540
\(666\) 0 0
\(667\) 2494.00 0.144780
\(668\) 0 0
\(669\) −907.000 −0.0524165
\(670\) 0 0
\(671\) −6440.00 −0.370512
\(672\) 0 0
\(673\) 19428.0 1.11277 0.556385 0.830925i \(-0.312188\pi\)
0.556385 + 0.830925i \(0.312188\pi\)
\(674\) 0 0
\(675\) −1325.00 −0.0755545
\(676\) 0 0
\(677\) 937.000 0.0531933 0.0265966 0.999646i \(-0.491533\pi\)
0.0265966 + 0.999646i \(0.491533\pi\)
\(678\) 0 0
\(679\) 9667.00 0.546370
\(680\) 0 0
\(681\) 5701.00 0.320797
\(682\) 0 0
\(683\) 15960.0 0.894132 0.447066 0.894501i \(-0.352469\pi\)
0.447066 + 0.894501i \(0.352469\pi\)
\(684\) 0 0
\(685\) 4540.00 0.253233
\(686\) 0 0
\(687\) −2044.00 −0.113513
\(688\) 0 0
\(689\) −10396.0 −0.574827
\(690\) 0 0
\(691\) 10260.0 0.564846 0.282423 0.959290i \(-0.408862\pi\)
0.282423 + 0.959290i \(0.408862\pi\)
\(692\) 0 0
\(693\) −1274.00 −0.0698344
\(694\) 0 0
\(695\) 8450.00 0.461190
\(696\) 0 0
\(697\) −5100.00 −0.277154
\(698\) 0 0
\(699\) −2728.00 −0.147614
\(700\) 0 0
\(701\) −15465.0 −0.833245 −0.416623 0.909080i \(-0.636786\pi\)
−0.416623 + 0.909080i \(0.636786\pi\)
\(702\) 0 0
\(703\) 9300.00 0.498942
\(704\) 0 0
\(705\) −165.000 −0.00881455
\(706\) 0 0
\(707\) −8946.00 −0.475883
\(708\) 0 0
\(709\) −21005.0 −1.11264 −0.556318 0.830969i \(-0.687786\pi\)
−0.556318 + 0.830969i \(0.687786\pi\)
\(710\) 0 0
\(711\) 26338.0 1.38924
\(712\) 0 0
\(713\) 1032.00 0.0542058
\(714\) 0 0
\(715\) −805.000 −0.0421053
\(716\) 0 0
\(717\) 7095.00 0.369550
\(718\) 0 0
\(719\) −22.0000 −0.00114111 −0.000570557 1.00000i \(-0.500182\pi\)
−0.000570557 1.00000i \(0.500182\pi\)
\(720\) 0 0
\(721\) 6125.00 0.316376
\(722\) 0 0
\(723\) −2618.00 −0.134667
\(724\) 0 0
\(725\) −725.000 −0.0371391
\(726\) 0 0
\(727\) −1816.00 −0.0926433 −0.0463217 0.998927i \(-0.514750\pi\)
−0.0463217 + 0.998927i \(0.514750\pi\)
\(728\) 0 0
\(729\) −15443.0 −0.784586
\(730\) 0 0
\(731\) 4450.00 0.225156
\(732\) 0 0
\(733\) 24397.0 1.22936 0.614682 0.788775i \(-0.289284\pi\)
0.614682 + 0.788775i \(0.289284\pi\)
\(734\) 0 0
\(735\) −245.000 −0.0122952
\(736\) 0 0
\(737\) 2100.00 0.104959
\(738\) 0 0
\(739\) 6065.00 0.301901 0.150950 0.988541i \(-0.451767\pi\)
0.150950 + 0.988541i \(0.451767\pi\)
\(740\) 0 0
\(741\) 1426.00 0.0706956
\(742\) 0 0
\(743\) 3660.00 0.180717 0.0903583 0.995909i \(-0.471199\pi\)
0.0903583 + 0.995909i \(0.471199\pi\)
\(744\) 0 0
\(745\) 10070.0 0.495216
\(746\) 0 0
\(747\) 16536.0 0.809934
\(748\) 0 0
\(749\) 13902.0 0.678195
\(750\) 0 0
\(751\) −27077.0 −1.31565 −0.657825 0.753170i \(-0.728524\pi\)
−0.657825 + 0.753170i \(0.728524\pi\)
\(752\) 0 0
\(753\) −3318.00 −0.160577
\(754\) 0 0
\(755\) −3095.00 −0.149190
\(756\) 0 0
\(757\) −31424.0 −1.50875 −0.754376 0.656443i \(-0.772060\pi\)
−0.754376 + 0.656443i \(0.772060\pi\)
\(758\) 0 0
\(759\) 602.000 0.0287895
\(760\) 0 0
\(761\) −16898.0 −0.804930 −0.402465 0.915435i \(-0.631847\pi\)
−0.402465 + 0.915435i \(0.631847\pi\)
\(762\) 0 0
\(763\) 1561.00 0.0740655
\(764\) 0 0
\(765\) −3250.00 −0.153600
\(766\) 0 0
\(767\) −2760.00 −0.129932
\(768\) 0 0
\(769\) 16294.0 0.764079 0.382039 0.924146i \(-0.375222\pi\)
0.382039 + 0.924146i \(0.375222\pi\)
\(770\) 0 0
\(771\) 1678.00 0.0783809
\(772\) 0 0
\(773\) −35279.0 −1.64152 −0.820762 0.571271i \(-0.806451\pi\)
−0.820762 + 0.571271i \(0.806451\pi\)
\(774\) 0 0
\(775\) −300.000 −0.0139049
\(776\) 0 0
\(777\) 1050.00 0.0484795
\(778\) 0 0
\(779\) −12648.0 −0.581722
\(780\) 0 0
\(781\) −3640.00 −0.166773
\(782\) 0 0
\(783\) 1537.00 0.0701506
\(784\) 0 0
\(785\) −7230.00 −0.328726
\(786\) 0 0
\(787\) 37829.0 1.71342 0.856708 0.515802i \(-0.172506\pi\)
0.856708 + 0.515802i \(0.172506\pi\)
\(788\) 0 0
\(789\) −898.000 −0.0405192
\(790\) 0 0
\(791\) 6510.00 0.292628
\(792\) 0 0
\(793\) −21160.0 −0.947558
\(794\) 0 0
\(795\) −2260.00 −0.100823
\(796\) 0 0
\(797\) −27741.0 −1.23292 −0.616460 0.787387i \(-0.711434\pi\)
−0.616460 + 0.787387i \(0.711434\pi\)
\(798\) 0 0
\(799\) −825.000 −0.0365287
\(800\) 0 0
\(801\) −7592.00 −0.334894
\(802\) 0 0
\(803\) −2590.00 −0.113822
\(804\) 0 0
\(805\) −3010.00 −0.131787
\(806\) 0 0
\(807\) −4902.00 −0.213827
\(808\) 0 0
\(809\) 27521.0 1.19603 0.598014 0.801486i \(-0.295957\pi\)
0.598014 + 0.801486i \(0.295957\pi\)
\(810\) 0 0
\(811\) −10694.0 −0.463030 −0.231515 0.972831i \(-0.574368\pi\)
−0.231515 + 0.972831i \(0.574368\pi\)
\(812\) 0 0
\(813\) −7040.00 −0.303694
\(814\) 0 0
\(815\) 13190.0 0.566903
\(816\) 0 0
\(817\) 11036.0 0.472584
\(818\) 0 0
\(819\) −4186.00 −0.178597
\(820\) 0 0
\(821\) −13835.0 −0.588118 −0.294059 0.955787i \(-0.595006\pi\)
−0.294059 + 0.955787i \(0.595006\pi\)
\(822\) 0 0
\(823\) −5196.00 −0.220074 −0.110037 0.993927i \(-0.535097\pi\)
−0.110037 + 0.993927i \(0.535097\pi\)
\(824\) 0 0
\(825\) −175.000 −0.00738511
\(826\) 0 0
\(827\) −22346.0 −0.939597 −0.469798 0.882774i \(-0.655673\pi\)
−0.469798 + 0.882774i \(0.655673\pi\)
\(828\) 0 0
\(829\) −22044.0 −0.923546 −0.461773 0.886998i \(-0.652787\pi\)
−0.461773 + 0.886998i \(0.652787\pi\)
\(830\) 0 0
\(831\) −2402.00 −0.100270
\(832\) 0 0
\(833\) −1225.00 −0.0509529
\(834\) 0 0
\(835\) 55.0000 0.00227947
\(836\) 0 0
\(837\) 636.000 0.0262645
\(838\) 0 0
\(839\) 21566.0 0.887415 0.443707 0.896172i \(-0.353663\pi\)
0.443707 + 0.896172i \(0.353663\pi\)
\(840\) 0 0
\(841\) −23548.0 −0.965517
\(842\) 0 0
\(843\) −6525.00 −0.266587
\(844\) 0 0
\(845\) 8340.00 0.339532
\(846\) 0 0
\(847\) 8974.00 0.364050
\(848\) 0 0
\(849\) −4109.00 −0.166102
\(850\) 0 0
\(851\) 12900.0 0.519631
\(852\) 0 0
\(853\) −6098.00 −0.244773 −0.122387 0.992483i \(-0.539055\pi\)
−0.122387 + 0.992483i \(0.539055\pi\)
\(854\) 0 0
\(855\) −8060.00 −0.322393
\(856\) 0 0
\(857\) 40514.0 1.61486 0.807428 0.589966i \(-0.200859\pi\)
0.807428 + 0.589966i \(0.200859\pi\)
\(858\) 0 0
\(859\) −24884.0 −0.988395 −0.494197 0.869350i \(-0.664538\pi\)
−0.494197 + 0.869350i \(0.664538\pi\)
\(860\) 0 0
\(861\) −1428.00 −0.0565228
\(862\) 0 0
\(863\) −35968.0 −1.41873 −0.709366 0.704841i \(-0.751018\pi\)
−0.709366 + 0.704841i \(0.751018\pi\)
\(864\) 0 0
\(865\) −16335.0 −0.642089
\(866\) 0 0
\(867\) −4288.00 −0.167968
\(868\) 0 0
\(869\) 7091.00 0.276807
\(870\) 0 0
\(871\) 6900.00 0.268424
\(872\) 0 0
\(873\) 35906.0 1.39202
\(874\) 0 0
\(875\) 875.000 0.0338062
\(876\) 0 0
\(877\) −9790.00 −0.376950 −0.188475 0.982078i \(-0.560354\pi\)
−0.188475 + 0.982078i \(0.560354\pi\)
\(878\) 0 0
\(879\) 3495.00 0.134111
\(880\) 0 0
\(881\) −47008.0 −1.79766 −0.898831 0.438296i \(-0.855582\pi\)
−0.898831 + 0.438296i \(0.855582\pi\)
\(882\) 0 0
\(883\) 23828.0 0.908127 0.454063 0.890969i \(-0.349974\pi\)
0.454063 + 0.890969i \(0.349974\pi\)
\(884\) 0 0
\(885\) −600.000 −0.0227896
\(886\) 0 0
\(887\) 22616.0 0.856112 0.428056 0.903752i \(-0.359199\pi\)
0.428056 + 0.903752i \(0.359199\pi\)
\(888\) 0 0
\(889\) 14392.0 0.542961
\(890\) 0 0
\(891\) −4543.00 −0.170815
\(892\) 0 0
\(893\) −2046.00 −0.0766705
\(894\) 0 0
\(895\) −18380.0 −0.686453
\(896\) 0 0
\(897\) 1978.00 0.0736271
\(898\) 0 0
\(899\) 348.000 0.0129104
\(900\) 0 0
\(901\) −11300.0 −0.417822
\(902\) 0 0
\(903\) 1246.00 0.0459184
\(904\) 0 0
\(905\) −3900.00 −0.143249
\(906\) 0 0
\(907\) −40406.0 −1.47923 −0.739614 0.673032i \(-0.764992\pi\)
−0.739614 + 0.673032i \(0.764992\pi\)
\(908\) 0 0
\(909\) −33228.0 −1.21243
\(910\) 0 0
\(911\) 6368.00 0.231593 0.115797 0.993273i \(-0.463058\pi\)
0.115797 + 0.993273i \(0.463058\pi\)
\(912\) 0 0
\(913\) 4452.00 0.161380
\(914\) 0 0
\(915\) −4600.00 −0.166198
\(916\) 0 0
\(917\) −10094.0 −0.363504
\(918\) 0 0
\(919\) −42305.0 −1.51851 −0.759256 0.650792i \(-0.774437\pi\)
−0.759256 + 0.650792i \(0.774437\pi\)
\(920\) 0 0
\(921\) 803.000 0.0287294
\(922\) 0 0
\(923\) −11960.0 −0.426509
\(924\) 0 0
\(925\) −3750.00 −0.133296
\(926\) 0 0
\(927\) 22750.0 0.806050
\(928\) 0 0
\(929\) 38668.0 1.36561 0.682807 0.730599i \(-0.260759\pi\)
0.682807 + 0.730599i \(0.260759\pi\)
\(930\) 0 0
\(931\) −3038.00 −0.106946
\(932\) 0 0
\(933\) −5438.00 −0.190817
\(934\) 0 0
\(935\) −875.000 −0.0306049
\(936\) 0 0
\(937\) 16171.0 0.563803 0.281902 0.959443i \(-0.409035\pi\)
0.281902 + 0.959443i \(0.409035\pi\)
\(938\) 0 0
\(939\) 681.000 0.0236673
\(940\) 0 0
\(941\) −18240.0 −0.631888 −0.315944 0.948778i \(-0.602321\pi\)
−0.315944 + 0.948778i \(0.602321\pi\)
\(942\) 0 0
\(943\) −17544.0 −0.605844
\(944\) 0 0
\(945\) −1855.00 −0.0638552
\(946\) 0 0
\(947\) 45928.0 1.57599 0.787993 0.615684i \(-0.211120\pi\)
0.787993 + 0.615684i \(0.211120\pi\)
\(948\) 0 0
\(949\) −8510.00 −0.291092
\(950\) 0 0
\(951\) 9214.00 0.314179
\(952\) 0 0
\(953\) −14104.0 −0.479405 −0.239703 0.970846i \(-0.577050\pi\)
−0.239703 + 0.970846i \(0.577050\pi\)
\(954\) 0 0
\(955\) 1415.00 0.0479459
\(956\) 0 0
\(957\) 203.000 0.00685690
\(958\) 0 0
\(959\) 6356.00 0.214021
\(960\) 0 0
\(961\) −29647.0 −0.995166
\(962\) 0 0
\(963\) 51636.0 1.72788
\(964\) 0 0
\(965\) 2420.00 0.0807280
\(966\) 0 0
\(967\) 26914.0 0.895032 0.447516 0.894276i \(-0.352309\pi\)
0.447516 + 0.894276i \(0.352309\pi\)
\(968\) 0 0
\(969\) 1550.00 0.0513861
\(970\) 0 0
\(971\) 10408.0 0.343984 0.171992 0.985098i \(-0.444980\pi\)
0.171992 + 0.985098i \(0.444980\pi\)
\(972\) 0 0
\(973\) 11830.0 0.389776
\(974\) 0 0
\(975\) −575.000 −0.0188869
\(976\) 0 0
\(977\) 39510.0 1.29379 0.646897 0.762577i \(-0.276066\pi\)
0.646897 + 0.762577i \(0.276066\pi\)
\(978\) 0 0
\(979\) −2044.00 −0.0667278
\(980\) 0 0
\(981\) 5798.00 0.188701
\(982\) 0 0
\(983\) 52131.0 1.69148 0.845738 0.533599i \(-0.179161\pi\)
0.845738 + 0.533599i \(0.179161\pi\)
\(984\) 0 0
\(985\) 1800.00 0.0582262
\(986\) 0 0
\(987\) −231.000 −0.00744966
\(988\) 0 0
\(989\) 15308.0 0.492180
\(990\) 0 0
\(991\) −48512.0 −1.55503 −0.777515 0.628865i \(-0.783520\pi\)
−0.777515 + 0.628865i \(0.783520\pi\)
\(992\) 0 0
\(993\) −2700.00 −0.0862859
\(994\) 0 0
\(995\) −5160.00 −0.164405
\(996\) 0 0
\(997\) 40951.0 1.30083 0.650417 0.759577i \(-0.274594\pi\)
0.650417 + 0.759577i \(0.274594\pi\)
\(998\) 0 0
\(999\) 7950.00 0.251779
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 140.4.a.d.1.1 1
3.2 odd 2 1260.4.a.i.1.1 1
4.3 odd 2 560.4.a.h.1.1 1
5.2 odd 4 700.4.e.i.449.1 2
5.3 odd 4 700.4.e.i.449.2 2
5.4 even 2 700.4.a.g.1.1 1
7.2 even 3 980.4.i.i.361.1 2
7.3 odd 6 980.4.i.k.961.1 2
7.4 even 3 980.4.i.i.961.1 2
7.5 odd 6 980.4.i.k.361.1 2
7.6 odd 2 980.4.a.g.1.1 1
8.3 odd 2 2240.4.a.u.1.1 1
8.5 even 2 2240.4.a.s.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
140.4.a.d.1.1 1 1.1 even 1 trivial
560.4.a.h.1.1 1 4.3 odd 2
700.4.a.g.1.1 1 5.4 even 2
700.4.e.i.449.1 2 5.2 odd 4
700.4.e.i.449.2 2 5.3 odd 4
980.4.a.g.1.1 1 7.6 odd 2
980.4.i.i.361.1 2 7.2 even 3
980.4.i.i.961.1 2 7.4 even 3
980.4.i.k.361.1 2 7.5 odd 6
980.4.i.k.961.1 2 7.3 odd 6
1260.4.a.i.1.1 1 3.2 odd 2
2240.4.a.s.1.1 1 8.5 even 2
2240.4.a.u.1.1 1 8.3 odd 2