Properties

Label 1840.4.a.b.1.1
Level $1840$
Weight $4$
Character 1840.1
Self dual yes
Analytic conductor $108.564$
Analytic rank $1$
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] = [1840,4,Mod(1,1840)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1840, 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("1840.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1840 = 2^{4} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1840.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: \(108.563514411\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 230)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1840.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-4.00000 q^{3} -5.00000 q^{5} -3.00000 q^{7} -11.0000 q^{9} +O(q^{10})\) \(q-4.00000 q^{3} -5.00000 q^{5} -3.00000 q^{7} -11.0000 q^{9} +2.00000 q^{11} -38.0000 q^{13} +20.0000 q^{15} -45.0000 q^{17} +74.0000 q^{19} +12.0000 q^{21} -23.0000 q^{23} +25.0000 q^{25} +152.000 q^{27} +283.000 q^{29} +303.000 q^{31} -8.00000 q^{33} +15.0000 q^{35} +79.0000 q^{37} +152.000 q^{39} -407.000 q^{41} +328.000 q^{43} +55.0000 q^{45} -360.000 q^{47} -334.000 q^{49} +180.000 q^{51} -561.000 q^{53} -10.0000 q^{55} -296.000 q^{57} -101.000 q^{59} -268.000 q^{61} +33.0000 q^{63} +190.000 q^{65} +69.0000 q^{67} +92.0000 q^{69} +641.000 q^{71} +994.000 q^{73} -100.000 q^{75} -6.00000 q^{77} +884.000 q^{79} -311.000 q^{81} -503.000 q^{83} +225.000 q^{85} -1132.00 q^{87} +1608.00 q^{89} +114.000 q^{91} -1212.00 q^{93} -370.000 q^{95} +1082.00 q^{97} -22.0000 q^{99} +O(q^{100})\)

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
\(3\) −4.00000 −0.769800 −0.384900 0.922958i \(-0.625764\pi\)
−0.384900 + 0.922958i \(0.625764\pi\)
\(4\) 0 0
\(5\) −5.00000 −0.447214
\(6\) 0 0
\(7\) −3.00000 −0.161985 −0.0809924 0.996715i \(-0.525809\pi\)
−0.0809924 + 0.996715i \(0.525809\pi\)
\(8\) 0 0
\(9\) −11.0000 −0.407407
\(10\) 0 0
\(11\) 2.00000 0.0548202 0.0274101 0.999624i \(-0.491274\pi\)
0.0274101 + 0.999624i \(0.491274\pi\)
\(12\) 0 0
\(13\) −38.0000 −0.810716 −0.405358 0.914158i \(-0.632853\pi\)
−0.405358 + 0.914158i \(0.632853\pi\)
\(14\) 0 0
\(15\) 20.0000 0.344265
\(16\) 0 0
\(17\) −45.0000 −0.642006 −0.321003 0.947078i \(-0.604020\pi\)
−0.321003 + 0.947078i \(0.604020\pi\)
\(18\) 0 0
\(19\) 74.0000 0.893514 0.446757 0.894655i \(-0.352579\pi\)
0.446757 + 0.894655i \(0.352579\pi\)
\(20\) 0 0
\(21\) 12.0000 0.124696
\(22\) 0 0
\(23\) −23.0000 −0.208514
\(24\) 0 0
\(25\) 25.0000 0.200000
\(26\) 0 0
\(27\) 152.000 1.08342
\(28\) 0 0
\(29\) 283.000 1.81213 0.906065 0.423138i \(-0.139072\pi\)
0.906065 + 0.423138i \(0.139072\pi\)
\(30\) 0 0
\(31\) 303.000 1.75550 0.877748 0.479122i \(-0.159045\pi\)
0.877748 + 0.479122i \(0.159045\pi\)
\(32\) 0 0
\(33\) −8.00000 −0.0422006
\(34\) 0 0
\(35\) 15.0000 0.0724418
\(36\) 0 0
\(37\) 79.0000 0.351014 0.175507 0.984478i \(-0.443844\pi\)
0.175507 + 0.984478i \(0.443844\pi\)
\(38\) 0 0
\(39\) 152.000 0.624089
\(40\) 0 0
\(41\) −407.000 −1.55031 −0.775155 0.631771i \(-0.782328\pi\)
−0.775155 + 0.631771i \(0.782328\pi\)
\(42\) 0 0
\(43\) 328.000 1.16324 0.581622 0.813459i \(-0.302418\pi\)
0.581622 + 0.813459i \(0.302418\pi\)
\(44\) 0 0
\(45\) 55.0000 0.182198
\(46\) 0 0
\(47\) −360.000 −1.11726 −0.558632 0.829416i \(-0.688674\pi\)
−0.558632 + 0.829416i \(0.688674\pi\)
\(48\) 0 0
\(49\) −334.000 −0.973761
\(50\) 0 0
\(51\) 180.000 0.494217
\(52\) 0 0
\(53\) −561.000 −1.45395 −0.726974 0.686665i \(-0.759074\pi\)
−0.726974 + 0.686665i \(0.759074\pi\)
\(54\) 0 0
\(55\) −10.0000 −0.0245164
\(56\) 0 0
\(57\) −296.000 −0.687827
\(58\) 0 0
\(59\) −101.000 −0.222866 −0.111433 0.993772i \(-0.535544\pi\)
−0.111433 + 0.993772i \(0.535544\pi\)
\(60\) 0 0
\(61\) −268.000 −0.562523 −0.281261 0.959631i \(-0.590753\pi\)
−0.281261 + 0.959631i \(0.590753\pi\)
\(62\) 0 0
\(63\) 33.0000 0.0659938
\(64\) 0 0
\(65\) 190.000 0.362563
\(66\) 0 0
\(67\) 69.0000 0.125816 0.0629081 0.998019i \(-0.479962\pi\)
0.0629081 + 0.998019i \(0.479962\pi\)
\(68\) 0 0
\(69\) 92.0000 0.160514
\(70\) 0 0
\(71\) 641.000 1.07145 0.535723 0.844394i \(-0.320039\pi\)
0.535723 + 0.844394i \(0.320039\pi\)
\(72\) 0 0
\(73\) 994.000 1.59368 0.796842 0.604188i \(-0.206502\pi\)
0.796842 + 0.604188i \(0.206502\pi\)
\(74\) 0 0
\(75\) −100.000 −0.153960
\(76\) 0 0
\(77\) −6.00000 −0.00888004
\(78\) 0 0
\(79\) 884.000 1.25896 0.629480 0.777017i \(-0.283268\pi\)
0.629480 + 0.777017i \(0.283268\pi\)
\(80\) 0 0
\(81\) −311.000 −0.426612
\(82\) 0 0
\(83\) −503.000 −0.665198 −0.332599 0.943068i \(-0.607926\pi\)
−0.332599 + 0.943068i \(0.607926\pi\)
\(84\) 0 0
\(85\) 225.000 0.287114
\(86\) 0 0
\(87\) −1132.00 −1.39498
\(88\) 0 0
\(89\) 1608.00 1.91514 0.957571 0.288197i \(-0.0930558\pi\)
0.957571 + 0.288197i \(0.0930558\pi\)
\(90\) 0 0
\(91\) 114.000 0.131324
\(92\) 0 0
\(93\) −1212.00 −1.35138
\(94\) 0 0
\(95\) −370.000 −0.399592
\(96\) 0 0
\(97\) 1082.00 1.13258 0.566291 0.824205i \(-0.308378\pi\)
0.566291 + 0.824205i \(0.308378\pi\)
\(98\) 0 0
\(99\) −22.0000 −0.0223342
\(100\) 0 0
\(101\) 879.000 0.865978 0.432989 0.901399i \(-0.357459\pi\)
0.432989 + 0.901399i \(0.357459\pi\)
\(102\) 0 0
\(103\) −360.000 −0.344387 −0.172193 0.985063i \(-0.555085\pi\)
−0.172193 + 0.985063i \(0.555085\pi\)
\(104\) 0 0
\(105\) −60.0000 −0.0557657
\(106\) 0 0
\(107\) −1815.00 −1.63984 −0.819919 0.572480i \(-0.805982\pi\)
−0.819919 + 0.572480i \(0.805982\pi\)
\(108\) 0 0
\(109\) −430.000 −0.377858 −0.188929 0.981991i \(-0.560502\pi\)
−0.188929 + 0.981991i \(0.560502\pi\)
\(110\) 0 0
\(111\) −316.000 −0.270211
\(112\) 0 0
\(113\) 255.000 0.212287 0.106143 0.994351i \(-0.466150\pi\)
0.106143 + 0.994351i \(0.466150\pi\)
\(114\) 0 0
\(115\) 115.000 0.0932505
\(116\) 0 0
\(117\) 418.000 0.330292
\(118\) 0 0
\(119\) 135.000 0.103995
\(120\) 0 0
\(121\) −1327.00 −0.996995
\(122\) 0 0
\(123\) 1628.00 1.19343
\(124\) 0 0
\(125\) −125.000 −0.0894427
\(126\) 0 0
\(127\) −344.000 −0.240355 −0.120177 0.992752i \(-0.538346\pi\)
−0.120177 + 0.992752i \(0.538346\pi\)
\(128\) 0 0
\(129\) −1312.00 −0.895466
\(130\) 0 0
\(131\) 1348.00 0.899048 0.449524 0.893268i \(-0.351594\pi\)
0.449524 + 0.893268i \(0.351594\pi\)
\(132\) 0 0
\(133\) −222.000 −0.144736
\(134\) 0 0
\(135\) −760.000 −0.484521
\(136\) 0 0
\(137\) 734.000 0.457736 0.228868 0.973457i \(-0.426498\pi\)
0.228868 + 0.973457i \(0.426498\pi\)
\(138\) 0 0
\(139\) −2659.00 −1.62254 −0.811271 0.584670i \(-0.801224\pi\)
−0.811271 + 0.584670i \(0.801224\pi\)
\(140\) 0 0
\(141\) 1440.00 0.860070
\(142\) 0 0
\(143\) −76.0000 −0.0444436
\(144\) 0 0
\(145\) −1415.00 −0.810409
\(146\) 0 0
\(147\) 1336.00 0.749602
\(148\) 0 0
\(149\) −3196.00 −1.75722 −0.878612 0.477535i \(-0.841530\pi\)
−0.878612 + 0.477535i \(0.841530\pi\)
\(150\) 0 0
\(151\) 100.000 0.0538933 0.0269466 0.999637i \(-0.491422\pi\)
0.0269466 + 0.999637i \(0.491422\pi\)
\(152\) 0 0
\(153\) 495.000 0.261558
\(154\) 0 0
\(155\) −1515.00 −0.785082
\(156\) 0 0
\(157\) −787.000 −0.400060 −0.200030 0.979790i \(-0.564104\pi\)
−0.200030 + 0.979790i \(0.564104\pi\)
\(158\) 0 0
\(159\) 2244.00 1.11925
\(160\) 0 0
\(161\) 69.0000 0.0337762
\(162\) 0 0
\(163\) 70.0000 0.0336370 0.0168185 0.999859i \(-0.494646\pi\)
0.0168185 + 0.999859i \(0.494646\pi\)
\(164\) 0 0
\(165\) 40.0000 0.0188727
\(166\) 0 0
\(167\) −1784.00 −0.826647 −0.413324 0.910584i \(-0.635632\pi\)
−0.413324 + 0.910584i \(0.635632\pi\)
\(168\) 0 0
\(169\) −753.000 −0.342740
\(170\) 0 0
\(171\) −814.000 −0.364024
\(172\) 0 0
\(173\) −28.0000 −0.0123052 −0.00615260 0.999981i \(-0.501958\pi\)
−0.00615260 + 0.999981i \(0.501958\pi\)
\(174\) 0 0
\(175\) −75.0000 −0.0323970
\(176\) 0 0
\(177\) 404.000 0.171562
\(178\) 0 0
\(179\) 32.0000 0.0133620 0.00668098 0.999978i \(-0.497873\pi\)
0.00668098 + 0.999978i \(0.497873\pi\)
\(180\) 0 0
\(181\) −1172.00 −0.481293 −0.240647 0.970613i \(-0.577359\pi\)
−0.240647 + 0.970613i \(0.577359\pi\)
\(182\) 0 0
\(183\) 1072.00 0.433030
\(184\) 0 0
\(185\) −395.000 −0.156978
\(186\) 0 0
\(187\) −90.0000 −0.0351949
\(188\) 0 0
\(189\) −456.000 −0.175498
\(190\) 0 0
\(191\) 648.000 0.245485 0.122742 0.992439i \(-0.460831\pi\)
0.122742 + 0.992439i \(0.460831\pi\)
\(192\) 0 0
\(193\) −772.000 −0.287926 −0.143963 0.989583i \(-0.545985\pi\)
−0.143963 + 0.989583i \(0.545985\pi\)
\(194\) 0 0
\(195\) −760.000 −0.279101
\(196\) 0 0
\(197\) −66.0000 −0.0238696 −0.0119348 0.999929i \(-0.503799\pi\)
−0.0119348 + 0.999929i \(0.503799\pi\)
\(198\) 0 0
\(199\) 3358.00 1.19619 0.598096 0.801424i \(-0.295924\pi\)
0.598096 + 0.801424i \(0.295924\pi\)
\(200\) 0 0
\(201\) −276.000 −0.0968534
\(202\) 0 0
\(203\) −849.000 −0.293538
\(204\) 0 0
\(205\) 2035.00 0.693320
\(206\) 0 0
\(207\) 253.000 0.0849503
\(208\) 0 0
\(209\) 148.000 0.0489827
\(210\) 0 0
\(211\) −4489.00 −1.46462 −0.732312 0.680970i \(-0.761559\pi\)
−0.732312 + 0.680970i \(0.761559\pi\)
\(212\) 0 0
\(213\) −2564.00 −0.824800
\(214\) 0 0
\(215\) −1640.00 −0.520219
\(216\) 0 0
\(217\) −909.000 −0.284364
\(218\) 0 0
\(219\) −3976.00 −1.22682
\(220\) 0 0
\(221\) 1710.00 0.520484
\(222\) 0 0
\(223\) −1990.00 −0.597580 −0.298790 0.954319i \(-0.596583\pi\)
−0.298790 + 0.954319i \(0.596583\pi\)
\(224\) 0 0
\(225\) −275.000 −0.0814815
\(226\) 0 0
\(227\) −5524.00 −1.61516 −0.807579 0.589760i \(-0.799222\pi\)
−0.807579 + 0.589760i \(0.799222\pi\)
\(228\) 0 0
\(229\) −1300.00 −0.375137 −0.187569 0.982252i \(-0.560061\pi\)
−0.187569 + 0.982252i \(0.560061\pi\)
\(230\) 0 0
\(231\) 24.0000 0.00683586
\(232\) 0 0
\(233\) −1212.00 −0.340776 −0.170388 0.985377i \(-0.554502\pi\)
−0.170388 + 0.985377i \(0.554502\pi\)
\(234\) 0 0
\(235\) 1800.00 0.499656
\(236\) 0 0
\(237\) −3536.00 −0.969147
\(238\) 0 0
\(239\) −2761.00 −0.747256 −0.373628 0.927579i \(-0.621886\pi\)
−0.373628 + 0.927579i \(0.621886\pi\)
\(240\) 0 0
\(241\) −5742.00 −1.53475 −0.767375 0.641199i \(-0.778437\pi\)
−0.767375 + 0.641199i \(0.778437\pi\)
\(242\) 0 0
\(243\) −2860.00 −0.755017
\(244\) 0 0
\(245\) 1670.00 0.435479
\(246\) 0 0
\(247\) −2812.00 −0.724386
\(248\) 0 0
\(249\) 2012.00 0.512070
\(250\) 0 0
\(251\) 4162.00 1.04663 0.523313 0.852141i \(-0.324696\pi\)
0.523313 + 0.852141i \(0.324696\pi\)
\(252\) 0 0
\(253\) −46.0000 −0.0114308
\(254\) 0 0
\(255\) −900.000 −0.221020
\(256\) 0 0
\(257\) 2464.00 0.598055 0.299027 0.954245i \(-0.403338\pi\)
0.299027 + 0.954245i \(0.403338\pi\)
\(258\) 0 0
\(259\) −237.000 −0.0568589
\(260\) 0 0
\(261\) −3113.00 −0.738275
\(262\) 0 0
\(263\) 4167.00 0.976989 0.488495 0.872567i \(-0.337546\pi\)
0.488495 + 0.872567i \(0.337546\pi\)
\(264\) 0 0
\(265\) 2805.00 0.650226
\(266\) 0 0
\(267\) −6432.00 −1.47428
\(268\) 0 0
\(269\) −1639.00 −0.371493 −0.185746 0.982598i \(-0.559470\pi\)
−0.185746 + 0.982598i \(0.559470\pi\)
\(270\) 0 0
\(271\) −2655.00 −0.595128 −0.297564 0.954702i \(-0.596174\pi\)
−0.297564 + 0.954702i \(0.596174\pi\)
\(272\) 0 0
\(273\) −456.000 −0.101093
\(274\) 0 0
\(275\) 50.0000 0.0109640
\(276\) 0 0
\(277\) −826.000 −0.179168 −0.0895840 0.995979i \(-0.528554\pi\)
−0.0895840 + 0.995979i \(0.528554\pi\)
\(278\) 0 0
\(279\) −3333.00 −0.715202
\(280\) 0 0
\(281\) 3930.00 0.834321 0.417160 0.908833i \(-0.363025\pi\)
0.417160 + 0.908833i \(0.363025\pi\)
\(282\) 0 0
\(283\) 7339.00 1.54155 0.770774 0.637108i \(-0.219870\pi\)
0.770774 + 0.637108i \(0.219870\pi\)
\(284\) 0 0
\(285\) 1480.00 0.307606
\(286\) 0 0
\(287\) 1221.00 0.251127
\(288\) 0 0
\(289\) −2888.00 −0.587828
\(290\) 0 0
\(291\) −4328.00 −0.871862
\(292\) 0 0
\(293\) −4763.00 −0.949684 −0.474842 0.880071i \(-0.657495\pi\)
−0.474842 + 0.880071i \(0.657495\pi\)
\(294\) 0 0
\(295\) 505.000 0.0996686
\(296\) 0 0
\(297\) 304.000 0.0593935
\(298\) 0 0
\(299\) 874.000 0.169046
\(300\) 0 0
\(301\) −984.000 −0.188428
\(302\) 0 0
\(303\) −3516.00 −0.666630
\(304\) 0 0
\(305\) 1340.00 0.251568
\(306\) 0 0
\(307\) 4238.00 0.787868 0.393934 0.919139i \(-0.371114\pi\)
0.393934 + 0.919139i \(0.371114\pi\)
\(308\) 0 0
\(309\) 1440.00 0.265109
\(310\) 0 0
\(311\) −4352.00 −0.793503 −0.396751 0.917926i \(-0.629862\pi\)
−0.396751 + 0.917926i \(0.629862\pi\)
\(312\) 0 0
\(313\) −515.000 −0.0930017 −0.0465008 0.998918i \(-0.514807\pi\)
−0.0465008 + 0.998918i \(0.514807\pi\)
\(314\) 0 0
\(315\) −165.000 −0.0295133
\(316\) 0 0
\(317\) −6816.00 −1.20765 −0.603824 0.797117i \(-0.706357\pi\)
−0.603824 + 0.797117i \(0.706357\pi\)
\(318\) 0 0
\(319\) 566.000 0.0993414
\(320\) 0 0
\(321\) 7260.00 1.26235
\(322\) 0 0
\(323\) −3330.00 −0.573641
\(324\) 0 0
\(325\) −950.000 −0.162143
\(326\) 0 0
\(327\) 1720.00 0.290875
\(328\) 0 0
\(329\) 1080.00 0.180980
\(330\) 0 0
\(331\) 8795.00 1.46047 0.730237 0.683194i \(-0.239410\pi\)
0.730237 + 0.683194i \(0.239410\pi\)
\(332\) 0 0
\(333\) −869.000 −0.143006
\(334\) 0 0
\(335\) −345.000 −0.0562668
\(336\) 0 0
\(337\) −10654.0 −1.72214 −0.861069 0.508488i \(-0.830204\pi\)
−0.861069 + 0.508488i \(0.830204\pi\)
\(338\) 0 0
\(339\) −1020.00 −0.163418
\(340\) 0 0
\(341\) 606.000 0.0962368
\(342\) 0 0
\(343\) 2031.00 0.319719
\(344\) 0 0
\(345\) −460.000 −0.0717843
\(346\) 0 0
\(347\) −6624.00 −1.02477 −0.512385 0.858756i \(-0.671238\pi\)
−0.512385 + 0.858756i \(0.671238\pi\)
\(348\) 0 0
\(349\) 9719.00 1.49068 0.745338 0.666686i \(-0.232288\pi\)
0.745338 + 0.666686i \(0.232288\pi\)
\(350\) 0 0
\(351\) −5776.00 −0.878348
\(352\) 0 0
\(353\) 664.000 0.100117 0.0500583 0.998746i \(-0.484059\pi\)
0.0500583 + 0.998746i \(0.484059\pi\)
\(354\) 0 0
\(355\) −3205.00 −0.479165
\(356\) 0 0
\(357\) −540.000 −0.0800555
\(358\) 0 0
\(359\) −5600.00 −0.823278 −0.411639 0.911347i \(-0.635043\pi\)
−0.411639 + 0.911347i \(0.635043\pi\)
\(360\) 0 0
\(361\) −1383.00 −0.201633
\(362\) 0 0
\(363\) 5308.00 0.767487
\(364\) 0 0
\(365\) −4970.00 −0.712717
\(366\) 0 0
\(367\) −5689.00 −0.809165 −0.404582 0.914502i \(-0.632583\pi\)
−0.404582 + 0.914502i \(0.632583\pi\)
\(368\) 0 0
\(369\) 4477.00 0.631608
\(370\) 0 0
\(371\) 1683.00 0.235518
\(372\) 0 0
\(373\) −10626.0 −1.47505 −0.737525 0.675320i \(-0.764005\pi\)
−0.737525 + 0.675320i \(0.764005\pi\)
\(374\) 0 0
\(375\) 500.000 0.0688530
\(376\) 0 0
\(377\) −10754.0 −1.46912
\(378\) 0 0
\(379\) −5160.00 −0.699344 −0.349672 0.936872i \(-0.613707\pi\)
−0.349672 + 0.936872i \(0.613707\pi\)
\(380\) 0 0
\(381\) 1376.00 0.185025
\(382\) 0 0
\(383\) 11063.0 1.47596 0.737980 0.674822i \(-0.235780\pi\)
0.737980 + 0.674822i \(0.235780\pi\)
\(384\) 0 0
\(385\) 30.0000 0.00397128
\(386\) 0 0
\(387\) −3608.00 −0.473915
\(388\) 0 0
\(389\) −5374.00 −0.700444 −0.350222 0.936667i \(-0.613894\pi\)
−0.350222 + 0.936667i \(0.613894\pi\)
\(390\) 0 0
\(391\) 1035.00 0.133868
\(392\) 0 0
\(393\) −5392.00 −0.692088
\(394\) 0 0
\(395\) −4420.00 −0.563024
\(396\) 0 0
\(397\) 376.000 0.0475338 0.0237669 0.999718i \(-0.492434\pi\)
0.0237669 + 0.999718i \(0.492434\pi\)
\(398\) 0 0
\(399\) 888.000 0.111418
\(400\) 0 0
\(401\) −7790.00 −0.970110 −0.485055 0.874484i \(-0.661200\pi\)
−0.485055 + 0.874484i \(0.661200\pi\)
\(402\) 0 0
\(403\) −11514.0 −1.42321
\(404\) 0 0
\(405\) 1555.00 0.190787
\(406\) 0 0
\(407\) 158.000 0.0192427
\(408\) 0 0
\(409\) 11909.0 1.43976 0.719880 0.694098i \(-0.244197\pi\)
0.719880 + 0.694098i \(0.244197\pi\)
\(410\) 0 0
\(411\) −2936.00 −0.352365
\(412\) 0 0
\(413\) 303.000 0.0361009
\(414\) 0 0
\(415\) 2515.00 0.297486
\(416\) 0 0
\(417\) 10636.0 1.24903
\(418\) 0 0
\(419\) −9162.00 −1.06824 −0.534121 0.845408i \(-0.679357\pi\)
−0.534121 + 0.845408i \(0.679357\pi\)
\(420\) 0 0
\(421\) 2086.00 0.241486 0.120743 0.992684i \(-0.461472\pi\)
0.120743 + 0.992684i \(0.461472\pi\)
\(422\) 0 0
\(423\) 3960.00 0.455182
\(424\) 0 0
\(425\) −1125.00 −0.128401
\(426\) 0 0
\(427\) 804.000 0.0911201
\(428\) 0 0
\(429\) 304.000 0.0342127
\(430\) 0 0
\(431\) 9824.00 1.09792 0.548962 0.835847i \(-0.315023\pi\)
0.548962 + 0.835847i \(0.315023\pi\)
\(432\) 0 0
\(433\) −1793.00 −0.198998 −0.0994989 0.995038i \(-0.531724\pi\)
−0.0994989 + 0.995038i \(0.531724\pi\)
\(434\) 0 0
\(435\) 5660.00 0.623853
\(436\) 0 0
\(437\) −1702.00 −0.186311
\(438\) 0 0
\(439\) 7544.00 0.820172 0.410086 0.912047i \(-0.365499\pi\)
0.410086 + 0.912047i \(0.365499\pi\)
\(440\) 0 0
\(441\) 3674.00 0.396717
\(442\) 0 0
\(443\) −6548.00 −0.702268 −0.351134 0.936325i \(-0.614204\pi\)
−0.351134 + 0.936325i \(0.614204\pi\)
\(444\) 0 0
\(445\) −8040.00 −0.856478
\(446\) 0 0
\(447\) 12784.0 1.35271
\(448\) 0 0
\(449\) 14235.0 1.49619 0.748097 0.663589i \(-0.230968\pi\)
0.748097 + 0.663589i \(0.230968\pi\)
\(450\) 0 0
\(451\) −814.000 −0.0849884
\(452\) 0 0
\(453\) −400.000 −0.0414871
\(454\) 0 0
\(455\) −570.000 −0.0587297
\(456\) 0 0
\(457\) −8039.00 −0.822863 −0.411432 0.911441i \(-0.634971\pi\)
−0.411432 + 0.911441i \(0.634971\pi\)
\(458\) 0 0
\(459\) −6840.00 −0.695564
\(460\) 0 0
\(461\) −9354.00 −0.945031 −0.472515 0.881322i \(-0.656654\pi\)
−0.472515 + 0.881322i \(0.656654\pi\)
\(462\) 0 0
\(463\) 2402.00 0.241102 0.120551 0.992707i \(-0.461534\pi\)
0.120551 + 0.992707i \(0.461534\pi\)
\(464\) 0 0
\(465\) 6060.00 0.604356
\(466\) 0 0
\(467\) 14529.0 1.43966 0.719831 0.694150i \(-0.244219\pi\)
0.719831 + 0.694150i \(0.244219\pi\)
\(468\) 0 0
\(469\) −207.000 −0.0203803
\(470\) 0 0
\(471\) 3148.00 0.307966
\(472\) 0 0
\(473\) 656.000 0.0637694
\(474\) 0 0
\(475\) 1850.00 0.178703
\(476\) 0 0
\(477\) 6171.00 0.592349
\(478\) 0 0
\(479\) −1724.00 −0.164450 −0.0822250 0.996614i \(-0.526203\pi\)
−0.0822250 + 0.996614i \(0.526203\pi\)
\(480\) 0 0
\(481\) −3002.00 −0.284573
\(482\) 0 0
\(483\) −276.000 −0.0260009
\(484\) 0 0
\(485\) −5410.00 −0.506506
\(486\) 0 0
\(487\) 9920.00 0.923035 0.461518 0.887131i \(-0.347305\pi\)
0.461518 + 0.887131i \(0.347305\pi\)
\(488\) 0 0
\(489\) −280.000 −0.0258937
\(490\) 0 0
\(491\) 8665.00 0.796428 0.398214 0.917293i \(-0.369630\pi\)
0.398214 + 0.917293i \(0.369630\pi\)
\(492\) 0 0
\(493\) −12735.0 −1.16340
\(494\) 0 0
\(495\) 110.000 0.00998815
\(496\) 0 0
\(497\) −1923.00 −0.173558
\(498\) 0 0
\(499\) 12673.0 1.13692 0.568458 0.822712i \(-0.307540\pi\)
0.568458 + 0.822712i \(0.307540\pi\)
\(500\) 0 0
\(501\) 7136.00 0.636353
\(502\) 0 0
\(503\) 3667.00 0.325057 0.162528 0.986704i \(-0.448035\pi\)
0.162528 + 0.986704i \(0.448035\pi\)
\(504\) 0 0
\(505\) −4395.00 −0.387277
\(506\) 0 0
\(507\) 3012.00 0.263841
\(508\) 0 0
\(509\) −13246.0 −1.15347 −0.576737 0.816930i \(-0.695674\pi\)
−0.576737 + 0.816930i \(0.695674\pi\)
\(510\) 0 0
\(511\) −2982.00 −0.258152
\(512\) 0 0
\(513\) 11248.0 0.968053
\(514\) 0 0
\(515\) 1800.00 0.154015
\(516\) 0 0
\(517\) −720.000 −0.0612487
\(518\) 0 0
\(519\) 112.000 0.00947255
\(520\) 0 0
\(521\) −4934.00 −0.414899 −0.207450 0.978246i \(-0.566516\pi\)
−0.207450 + 0.978246i \(0.566516\pi\)
\(522\) 0 0
\(523\) −17436.0 −1.45779 −0.728894 0.684627i \(-0.759965\pi\)
−0.728894 + 0.684627i \(0.759965\pi\)
\(524\) 0 0
\(525\) 300.000 0.0249392
\(526\) 0 0
\(527\) −13635.0 −1.12704
\(528\) 0 0
\(529\) 529.000 0.0434783
\(530\) 0 0
\(531\) 1111.00 0.0907972
\(532\) 0 0
\(533\) 15466.0 1.25686
\(534\) 0 0
\(535\) 9075.00 0.733358
\(536\) 0 0
\(537\) −128.000 −0.0102860
\(538\) 0 0
\(539\) −668.000 −0.0533818
\(540\) 0 0
\(541\) −1714.00 −0.136212 −0.0681059 0.997678i \(-0.521696\pi\)
−0.0681059 + 0.997678i \(0.521696\pi\)
\(542\) 0 0
\(543\) 4688.00 0.370500
\(544\) 0 0
\(545\) 2150.00 0.168983
\(546\) 0 0
\(547\) −9616.00 −0.751646 −0.375823 0.926691i \(-0.622640\pi\)
−0.375823 + 0.926691i \(0.622640\pi\)
\(548\) 0 0
\(549\) 2948.00 0.229176
\(550\) 0 0
\(551\) 20942.0 1.61916
\(552\) 0 0
\(553\) −2652.00 −0.203932
\(554\) 0 0
\(555\) 1580.00 0.120842
\(556\) 0 0
\(557\) −21385.0 −1.62677 −0.813386 0.581725i \(-0.802378\pi\)
−0.813386 + 0.581725i \(0.802378\pi\)
\(558\) 0 0
\(559\) −12464.0 −0.943061
\(560\) 0 0
\(561\) 360.000 0.0270931
\(562\) 0 0
\(563\) 5967.00 0.446677 0.223338 0.974741i \(-0.428304\pi\)
0.223338 + 0.974741i \(0.428304\pi\)
\(564\) 0 0
\(565\) −1275.00 −0.0949374
\(566\) 0 0
\(567\) 933.000 0.0691046
\(568\) 0 0
\(569\) 9714.00 0.715698 0.357849 0.933779i \(-0.383510\pi\)
0.357849 + 0.933779i \(0.383510\pi\)
\(570\) 0 0
\(571\) −4244.00 −0.311044 −0.155522 0.987832i \(-0.549706\pi\)
−0.155522 + 0.987832i \(0.549706\pi\)
\(572\) 0 0
\(573\) −2592.00 −0.188974
\(574\) 0 0
\(575\) −575.000 −0.0417029
\(576\) 0 0
\(577\) −15136.0 −1.09206 −0.546031 0.837765i \(-0.683862\pi\)
−0.546031 + 0.837765i \(0.683862\pi\)
\(578\) 0 0
\(579\) 3088.00 0.221646
\(580\) 0 0
\(581\) 1509.00 0.107752
\(582\) 0 0
\(583\) −1122.00 −0.0797058
\(584\) 0 0
\(585\) −2090.00 −0.147711
\(586\) 0 0
\(587\) −22414.0 −1.57602 −0.788011 0.615661i \(-0.788889\pi\)
−0.788011 + 0.615661i \(0.788889\pi\)
\(588\) 0 0
\(589\) 22422.0 1.56856
\(590\) 0 0
\(591\) 264.000 0.0183748
\(592\) 0 0
\(593\) 22560.0 1.56227 0.781137 0.624360i \(-0.214640\pi\)
0.781137 + 0.624360i \(0.214640\pi\)
\(594\) 0 0
\(595\) −675.000 −0.0465081
\(596\) 0 0
\(597\) −13432.0 −0.920829
\(598\) 0 0
\(599\) 1240.00 0.0845827 0.0422913 0.999105i \(-0.486534\pi\)
0.0422913 + 0.999105i \(0.486534\pi\)
\(600\) 0 0
\(601\) 27931.0 1.89572 0.947861 0.318683i \(-0.103241\pi\)
0.947861 + 0.318683i \(0.103241\pi\)
\(602\) 0 0
\(603\) −759.000 −0.0512585
\(604\) 0 0
\(605\) 6635.00 0.445870
\(606\) 0 0
\(607\) −8660.00 −0.579075 −0.289538 0.957167i \(-0.593502\pi\)
−0.289538 + 0.957167i \(0.593502\pi\)
\(608\) 0 0
\(609\) 3396.00 0.225965
\(610\) 0 0
\(611\) 13680.0 0.905783
\(612\) 0 0
\(613\) 22326.0 1.47103 0.735513 0.677511i \(-0.236941\pi\)
0.735513 + 0.677511i \(0.236941\pi\)
\(614\) 0 0
\(615\) −8140.00 −0.533718
\(616\) 0 0
\(617\) −7035.00 −0.459025 −0.229513 0.973306i \(-0.573713\pi\)
−0.229513 + 0.973306i \(0.573713\pi\)
\(618\) 0 0
\(619\) 15808.0 1.02646 0.513229 0.858252i \(-0.328449\pi\)
0.513229 + 0.858252i \(0.328449\pi\)
\(620\) 0 0
\(621\) −3496.00 −0.225909
\(622\) 0 0
\(623\) −4824.00 −0.310224
\(624\) 0 0
\(625\) 625.000 0.0400000
\(626\) 0 0
\(627\) −592.000 −0.0377069
\(628\) 0 0
\(629\) −3555.00 −0.225353
\(630\) 0 0
\(631\) 9740.00 0.614490 0.307245 0.951630i \(-0.400593\pi\)
0.307245 + 0.951630i \(0.400593\pi\)
\(632\) 0 0
\(633\) 17956.0 1.12747
\(634\) 0 0
\(635\) 1720.00 0.107490
\(636\) 0 0
\(637\) 12692.0 0.789443
\(638\) 0 0
\(639\) −7051.00 −0.436515
\(640\) 0 0
\(641\) −18730.0 −1.15412 −0.577060 0.816702i \(-0.695800\pi\)
−0.577060 + 0.816702i \(0.695800\pi\)
\(642\) 0 0
\(643\) −18191.0 −1.11568 −0.557841 0.829948i \(-0.688370\pi\)
−0.557841 + 0.829948i \(0.688370\pi\)
\(644\) 0 0
\(645\) 6560.00 0.400465
\(646\) 0 0
\(647\) −2126.00 −0.129183 −0.0645917 0.997912i \(-0.520575\pi\)
−0.0645917 + 0.997912i \(0.520575\pi\)
\(648\) 0 0
\(649\) −202.000 −0.0122176
\(650\) 0 0
\(651\) 3636.00 0.218903
\(652\) 0 0
\(653\) −27478.0 −1.64670 −0.823352 0.567532i \(-0.807898\pi\)
−0.823352 + 0.567532i \(0.807898\pi\)
\(654\) 0 0
\(655\) −6740.00 −0.402067
\(656\) 0 0
\(657\) −10934.0 −0.649278
\(658\) 0 0
\(659\) 25430.0 1.50321 0.751603 0.659616i \(-0.229281\pi\)
0.751603 + 0.659616i \(0.229281\pi\)
\(660\) 0 0
\(661\) 33610.0 1.97773 0.988863 0.148826i \(-0.0475493\pi\)
0.988863 + 0.148826i \(0.0475493\pi\)
\(662\) 0 0
\(663\) −6840.00 −0.400669
\(664\) 0 0
\(665\) 1110.00 0.0647278
\(666\) 0 0
\(667\) −6509.00 −0.377855
\(668\) 0 0
\(669\) 7960.00 0.460017
\(670\) 0 0
\(671\) −536.000 −0.0308376
\(672\) 0 0
\(673\) 20732.0 1.18746 0.593729 0.804665i \(-0.297655\pi\)
0.593729 + 0.804665i \(0.297655\pi\)
\(674\) 0 0
\(675\) 3800.00 0.216685
\(676\) 0 0
\(677\) −24271.0 −1.37786 −0.688929 0.724829i \(-0.741919\pi\)
−0.688929 + 0.724829i \(0.741919\pi\)
\(678\) 0 0
\(679\) −3246.00 −0.183461
\(680\) 0 0
\(681\) 22096.0 1.24335
\(682\) 0 0
\(683\) 14280.0 0.800013 0.400007 0.916512i \(-0.369008\pi\)
0.400007 + 0.916512i \(0.369008\pi\)
\(684\) 0 0
\(685\) −3670.00 −0.204706
\(686\) 0 0
\(687\) 5200.00 0.288781
\(688\) 0 0
\(689\) 21318.0 1.17874
\(690\) 0 0
\(691\) 4756.00 0.261833 0.130917 0.991393i \(-0.458208\pi\)
0.130917 + 0.991393i \(0.458208\pi\)
\(692\) 0 0
\(693\) 66.0000 0.00361780
\(694\) 0 0
\(695\) 13295.0 0.725623
\(696\) 0 0
\(697\) 18315.0 0.995309
\(698\) 0 0
\(699\) 4848.00 0.262329
\(700\) 0 0
\(701\) 5632.00 0.303449 0.151724 0.988423i \(-0.451517\pi\)
0.151724 + 0.988423i \(0.451517\pi\)
\(702\) 0 0
\(703\) 5846.00 0.313636
\(704\) 0 0
\(705\) −7200.00 −0.384635
\(706\) 0 0
\(707\) −2637.00 −0.140275
\(708\) 0 0
\(709\) −8536.00 −0.452153 −0.226076 0.974110i \(-0.572590\pi\)
−0.226076 + 0.974110i \(0.572590\pi\)
\(710\) 0 0
\(711\) −9724.00 −0.512909
\(712\) 0 0
\(713\) −6969.00 −0.366046
\(714\) 0 0
\(715\) 380.000 0.0198758
\(716\) 0 0
\(717\) 11044.0 0.575238
\(718\) 0 0
\(719\) −32137.0 −1.66691 −0.833455 0.552588i \(-0.813640\pi\)
−0.833455 + 0.552588i \(0.813640\pi\)
\(720\) 0 0
\(721\) 1080.00 0.0557854
\(722\) 0 0
\(723\) 22968.0 1.18145
\(724\) 0 0
\(725\) 7075.00 0.362426
\(726\) 0 0
\(727\) −20329.0 −1.03709 −0.518543 0.855052i \(-0.673525\pi\)
−0.518543 + 0.855052i \(0.673525\pi\)
\(728\) 0 0
\(729\) 19837.0 1.00782
\(730\) 0 0
\(731\) −14760.0 −0.746810
\(732\) 0 0
\(733\) 12879.0 0.648972 0.324486 0.945890i \(-0.394809\pi\)
0.324486 + 0.945890i \(0.394809\pi\)
\(734\) 0 0
\(735\) −6680.00 −0.335232
\(736\) 0 0
\(737\) 138.000 0.00689728
\(738\) 0 0
\(739\) −16689.0 −0.830737 −0.415369 0.909653i \(-0.636347\pi\)
−0.415369 + 0.909653i \(0.636347\pi\)
\(740\) 0 0
\(741\) 11248.0 0.557632
\(742\) 0 0
\(743\) −32328.0 −1.59623 −0.798115 0.602505i \(-0.794169\pi\)
−0.798115 + 0.602505i \(0.794169\pi\)
\(744\) 0 0
\(745\) 15980.0 0.785855
\(746\) 0 0
\(747\) 5533.00 0.271007
\(748\) 0 0
\(749\) 5445.00 0.265629
\(750\) 0 0
\(751\) 13966.0 0.678597 0.339299 0.940679i \(-0.389810\pi\)
0.339299 + 0.940679i \(0.389810\pi\)
\(752\) 0 0
\(753\) −16648.0 −0.805693
\(754\) 0 0
\(755\) −500.000 −0.0241018
\(756\) 0 0
\(757\) −14103.0 −0.677123 −0.338562 0.940944i \(-0.609940\pi\)
−0.338562 + 0.940944i \(0.609940\pi\)
\(758\) 0 0
\(759\) 184.000 0.00879944
\(760\) 0 0
\(761\) 28805.0 1.37212 0.686058 0.727547i \(-0.259340\pi\)
0.686058 + 0.727547i \(0.259340\pi\)
\(762\) 0 0
\(763\) 1290.00 0.0612073
\(764\) 0 0
\(765\) −2475.00 −0.116972
\(766\) 0 0
\(767\) 3838.00 0.180681
\(768\) 0 0
\(769\) −26264.0 −1.23160 −0.615802 0.787901i \(-0.711168\pi\)
−0.615802 + 0.787901i \(0.711168\pi\)
\(770\) 0 0
\(771\) −9856.00 −0.460383
\(772\) 0 0
\(773\) 29622.0 1.37830 0.689152 0.724617i \(-0.257983\pi\)
0.689152 + 0.724617i \(0.257983\pi\)
\(774\) 0 0
\(775\) 7575.00 0.351099
\(776\) 0 0
\(777\) 948.000 0.0437700
\(778\) 0 0
\(779\) −30118.0 −1.38522
\(780\) 0 0
\(781\) 1282.00 0.0587370
\(782\) 0 0
\(783\) 43016.0 1.96330
\(784\) 0 0
\(785\) 3935.00 0.178912
\(786\) 0 0
\(787\) 8129.00 0.368193 0.184096 0.982908i \(-0.441064\pi\)
0.184096 + 0.982908i \(0.441064\pi\)
\(788\) 0 0
\(789\) −16668.0 −0.752087
\(790\) 0 0
\(791\) −765.000 −0.0343872
\(792\) 0 0
\(793\) 10184.0 0.456046
\(794\) 0 0
\(795\) −11220.0 −0.500544
\(796\) 0 0
\(797\) −35431.0 −1.57469 −0.787347 0.616511i \(-0.788546\pi\)
−0.787347 + 0.616511i \(0.788546\pi\)
\(798\) 0 0
\(799\) 16200.0 0.717290
\(800\) 0 0
\(801\) −17688.0 −0.780243
\(802\) 0 0
\(803\) 1988.00 0.0873661
\(804\) 0 0
\(805\) −345.000 −0.0151052
\(806\) 0 0
\(807\) 6556.00 0.285975
\(808\) 0 0
\(809\) −36025.0 −1.56560 −0.782801 0.622272i \(-0.786210\pi\)
−0.782801 + 0.622272i \(0.786210\pi\)
\(810\) 0 0
\(811\) 35351.0 1.53063 0.765315 0.643656i \(-0.222583\pi\)
0.765315 + 0.643656i \(0.222583\pi\)
\(812\) 0 0
\(813\) 10620.0 0.458130
\(814\) 0 0
\(815\) −350.000 −0.0150429
\(816\) 0 0
\(817\) 24272.0 1.03938
\(818\) 0 0
\(819\) −1254.00 −0.0535022
\(820\) 0 0
\(821\) −33534.0 −1.42551 −0.712756 0.701412i \(-0.752553\pi\)
−0.712756 + 0.701412i \(0.752553\pi\)
\(822\) 0 0
\(823\) −452.000 −0.0191443 −0.00957213 0.999954i \(-0.503047\pi\)
−0.00957213 + 0.999954i \(0.503047\pi\)
\(824\) 0 0
\(825\) −200.000 −0.00844013
\(826\) 0 0
\(827\) 2379.00 0.100031 0.0500157 0.998748i \(-0.484073\pi\)
0.0500157 + 0.998748i \(0.484073\pi\)
\(828\) 0 0
\(829\) −599.000 −0.0250955 −0.0125477 0.999921i \(-0.503994\pi\)
−0.0125477 + 0.999921i \(0.503994\pi\)
\(830\) 0 0
\(831\) 3304.00 0.137924
\(832\) 0 0
\(833\) 15030.0 0.625160
\(834\) 0 0
\(835\) 8920.00 0.369688
\(836\) 0 0
\(837\) 46056.0 1.90195
\(838\) 0 0
\(839\) 16746.0 0.689078 0.344539 0.938772i \(-0.388035\pi\)
0.344539 + 0.938772i \(0.388035\pi\)
\(840\) 0 0
\(841\) 55700.0 2.28382
\(842\) 0 0
\(843\) −15720.0 −0.642260
\(844\) 0 0
\(845\) 3765.00 0.153278
\(846\) 0 0
\(847\) 3981.00 0.161498
\(848\) 0 0
\(849\) −29356.0 −1.18668
\(850\) 0 0
\(851\) −1817.00 −0.0731915
\(852\) 0 0
\(853\) −41754.0 −1.67600 −0.838001 0.545669i \(-0.816276\pi\)
−0.838001 + 0.545669i \(0.816276\pi\)
\(854\) 0 0
\(855\) 4070.00 0.162797
\(856\) 0 0
\(857\) −8802.00 −0.350841 −0.175420 0.984494i \(-0.556128\pi\)
−0.175420 + 0.984494i \(0.556128\pi\)
\(858\) 0 0
\(859\) −7901.00 −0.313828 −0.156914 0.987612i \(-0.550155\pi\)
−0.156914 + 0.987612i \(0.550155\pi\)
\(860\) 0 0
\(861\) −4884.00 −0.193317
\(862\) 0 0
\(863\) 43358.0 1.71022 0.855112 0.518443i \(-0.173488\pi\)
0.855112 + 0.518443i \(0.173488\pi\)
\(864\) 0 0
\(865\) 140.000 0.00550306
\(866\) 0 0
\(867\) 11552.0 0.452510
\(868\) 0 0
\(869\) 1768.00 0.0690164
\(870\) 0 0
\(871\) −2622.00 −0.102001
\(872\) 0 0
\(873\) −11902.0 −0.461422
\(874\) 0 0
\(875\) 375.000 0.0144884
\(876\) 0 0
\(877\) −5834.00 −0.224630 −0.112315 0.993673i \(-0.535827\pi\)
−0.112315 + 0.993673i \(0.535827\pi\)
\(878\) 0 0
\(879\) 19052.0 0.731067
\(880\) 0 0
\(881\) −40940.0 −1.56561 −0.782806 0.622266i \(-0.786212\pi\)
−0.782806 + 0.622266i \(0.786212\pi\)
\(882\) 0 0
\(883\) 22756.0 0.867271 0.433636 0.901088i \(-0.357231\pi\)
0.433636 + 0.901088i \(0.357231\pi\)
\(884\) 0 0
\(885\) −2020.00 −0.0767249
\(886\) 0 0
\(887\) −20814.0 −0.787898 −0.393949 0.919132i \(-0.628891\pi\)
−0.393949 + 0.919132i \(0.628891\pi\)
\(888\) 0 0
\(889\) 1032.00 0.0389338
\(890\) 0 0
\(891\) −622.000 −0.0233870
\(892\) 0 0
\(893\) −26640.0 −0.998291
\(894\) 0 0
\(895\) −160.000 −0.00597565
\(896\) 0 0
\(897\) −3496.00 −0.130132
\(898\) 0 0
\(899\) 85749.0 3.18119
\(900\) 0 0
\(901\) 25245.0 0.933444
\(902\) 0 0
\(903\) 3936.00 0.145052
\(904\) 0 0
\(905\) 5860.00 0.215241
\(906\) 0 0
\(907\) 36661.0 1.34213 0.671063 0.741400i \(-0.265838\pi\)
0.671063 + 0.741400i \(0.265838\pi\)
\(908\) 0 0
\(909\) −9669.00 −0.352806
\(910\) 0 0
\(911\) −22340.0 −0.812467 −0.406233 0.913769i \(-0.633158\pi\)
−0.406233 + 0.913769i \(0.633158\pi\)
\(912\) 0 0
\(913\) −1006.00 −0.0364663
\(914\) 0 0
\(915\) −5360.00 −0.193657
\(916\) 0 0
\(917\) −4044.00 −0.145632
\(918\) 0 0
\(919\) 34112.0 1.22443 0.612215 0.790691i \(-0.290279\pi\)
0.612215 + 0.790691i \(0.290279\pi\)
\(920\) 0 0
\(921\) −16952.0 −0.606501
\(922\) 0 0
\(923\) −24358.0 −0.868639
\(924\) 0 0
\(925\) 1975.00 0.0702028
\(926\) 0 0
\(927\) 3960.00 0.140306
\(928\) 0 0
\(929\) −14133.0 −0.499127 −0.249563 0.968358i \(-0.580287\pi\)
−0.249563 + 0.968358i \(0.580287\pi\)
\(930\) 0 0
\(931\) −24716.0 −0.870069
\(932\) 0 0
\(933\) 17408.0 0.610839
\(934\) 0 0
\(935\) 450.000 0.0157397
\(936\) 0 0
\(937\) 22442.0 0.782442 0.391221 0.920297i \(-0.372053\pi\)
0.391221 + 0.920297i \(0.372053\pi\)
\(938\) 0 0
\(939\) 2060.00 0.0715927
\(940\) 0 0
\(941\) −36076.0 −1.24978 −0.624891 0.780712i \(-0.714856\pi\)
−0.624891 + 0.780712i \(0.714856\pi\)
\(942\) 0 0
\(943\) 9361.00 0.323262
\(944\) 0 0
\(945\) 2280.00 0.0784851
\(946\) 0 0
\(947\) 43316.0 1.48636 0.743179 0.669093i \(-0.233317\pi\)
0.743179 + 0.669093i \(0.233317\pi\)
\(948\) 0 0
\(949\) −37772.0 −1.29202
\(950\) 0 0
\(951\) 27264.0 0.929649
\(952\) 0 0
\(953\) −8326.00 −0.283007 −0.141503 0.989938i \(-0.545194\pi\)
−0.141503 + 0.989938i \(0.545194\pi\)
\(954\) 0 0
\(955\) −3240.00 −0.109784
\(956\) 0 0
\(957\) −2264.00 −0.0764731
\(958\) 0 0
\(959\) −2202.00 −0.0741463
\(960\) 0 0
\(961\) 62018.0 2.08177
\(962\) 0 0
\(963\) 19965.0 0.668082
\(964\) 0 0
\(965\) 3860.00 0.128765
\(966\) 0 0
\(967\) −47244.0 −1.57111 −0.785556 0.618791i \(-0.787623\pi\)
−0.785556 + 0.618791i \(0.787623\pi\)
\(968\) 0 0
\(969\) 13320.0 0.441589
\(970\) 0 0
\(971\) 40460.0 1.33720 0.668601 0.743621i \(-0.266893\pi\)
0.668601 + 0.743621i \(0.266893\pi\)
\(972\) 0 0
\(973\) 7977.00 0.262827
\(974\) 0 0
\(975\) 3800.00 0.124818
\(976\) 0 0
\(977\) 42369.0 1.38741 0.693707 0.720257i \(-0.255976\pi\)
0.693707 + 0.720257i \(0.255976\pi\)
\(978\) 0 0
\(979\) 3216.00 0.104989
\(980\) 0 0
\(981\) 4730.00 0.153942
\(982\) 0 0
\(983\) −56331.0 −1.82775 −0.913876 0.405994i \(-0.866925\pi\)
−0.913876 + 0.405994i \(0.866925\pi\)
\(984\) 0 0
\(985\) 330.000 0.0106748
\(986\) 0 0
\(987\) −4320.00 −0.139318
\(988\) 0 0
\(989\) −7544.00 −0.242553
\(990\) 0 0
\(991\) −237.000 −0.00759693 −0.00379846 0.999993i \(-0.501209\pi\)
−0.00379846 + 0.999993i \(0.501209\pi\)
\(992\) 0 0
\(993\) −35180.0 −1.12427
\(994\) 0 0
\(995\) −16790.0 −0.534954
\(996\) 0 0
\(997\) −36856.0 −1.17075 −0.585377 0.810761i \(-0.699053\pi\)
−0.585377 + 0.810761i \(0.699053\pi\)
\(998\) 0 0
\(999\) 12008.0 0.380297
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 1840.4.a.b.1.1 1
4.3 odd 2 230.4.a.b.1.1 1
12.11 even 2 2070.4.a.n.1.1 1
20.3 even 4 1150.4.b.c.599.2 2
20.7 even 4 1150.4.b.c.599.1 2
20.19 odd 2 1150.4.a.f.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
230.4.a.b.1.1 1 4.3 odd 2
1150.4.a.f.1.1 1 20.19 odd 2
1150.4.b.c.599.1 2 20.7 even 4
1150.4.b.c.599.2 2 20.3 even 4
1840.4.a.b.1.1 1 1.1 even 1 trivial
2070.4.a.n.1.1 1 12.11 even 2