Properties

Label 1078.4.a.g.1.1
Level $1078$
Weight $4$
Character 1078.1
Self dual yes
Analytic conductor $63.604$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1078.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(63.6040589862\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 154)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1078.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.00000 q^{2} +2.00000 q^{3} +4.00000 q^{4} -18.0000 q^{5} +4.00000 q^{6} +8.00000 q^{8} -23.0000 q^{9} +O(q^{10})\) \(q+2.00000 q^{2} +2.00000 q^{3} +4.00000 q^{4} -18.0000 q^{5} +4.00000 q^{6} +8.00000 q^{8} -23.0000 q^{9} -36.0000 q^{10} -11.0000 q^{11} +8.00000 q^{12} -56.0000 q^{13} -36.0000 q^{15} +16.0000 q^{16} -36.0000 q^{17} -46.0000 q^{18} +28.0000 q^{19} -72.0000 q^{20} -22.0000 q^{22} +180.000 q^{23} +16.0000 q^{24} +199.000 q^{25} -112.000 q^{26} -100.000 q^{27} -54.0000 q^{29} -72.0000 q^{30} +334.000 q^{31} +32.0000 q^{32} -22.0000 q^{33} -72.0000 q^{34} -92.0000 q^{36} +386.000 q^{37} +56.0000 q^{38} -112.000 q^{39} -144.000 q^{40} +444.000 q^{41} -316.000 q^{43} -44.0000 q^{44} +414.000 q^{45} +360.000 q^{46} +402.000 q^{47} +32.0000 q^{48} +398.000 q^{50} -72.0000 q^{51} -224.000 q^{52} -486.000 q^{53} -200.000 q^{54} +198.000 q^{55} +56.0000 q^{57} -108.000 q^{58} +282.000 q^{59} -144.000 q^{60} -380.000 q^{61} +668.000 q^{62} +64.0000 q^{64} +1008.00 q^{65} -44.0000 q^{66} +176.000 q^{67} -144.000 q^{68} +360.000 q^{69} -324.000 q^{71} -184.000 q^{72} -800.000 q^{73} +772.000 q^{74} +398.000 q^{75} +112.000 q^{76} -224.000 q^{78} -1144.00 q^{79} -288.000 q^{80} +421.000 q^{81} +888.000 q^{82} -468.000 q^{83} +648.000 q^{85} -632.000 q^{86} -108.000 q^{87} -88.0000 q^{88} +870.000 q^{89} +828.000 q^{90} +720.000 q^{92} +668.000 q^{93} +804.000 q^{94} -504.000 q^{95} +64.0000 q^{96} +1330.00 q^{97} +253.000 q^{99} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.00000 0.707107
\(3\) 2.00000 0.384900 0.192450 0.981307i \(-0.438357\pi\)
0.192450 + 0.981307i \(0.438357\pi\)
\(4\) 4.00000 0.500000
\(5\) −18.0000 −1.60997 −0.804984 0.593296i \(-0.797826\pi\)
−0.804984 + 0.593296i \(0.797826\pi\)
\(6\) 4.00000 0.272166
\(7\) 0 0
\(8\) 8.00000 0.353553
\(9\) −23.0000 −0.851852
\(10\) −36.0000 −1.13842
\(11\) −11.0000 −0.301511
\(12\) 8.00000 0.192450
\(13\) −56.0000 −1.19474 −0.597369 0.801966i \(-0.703787\pi\)
−0.597369 + 0.801966i \(0.703787\pi\)
\(14\) 0 0
\(15\) −36.0000 −0.619677
\(16\) 16.0000 0.250000
\(17\) −36.0000 −0.513605 −0.256802 0.966464i \(-0.582669\pi\)
−0.256802 + 0.966464i \(0.582669\pi\)
\(18\) −46.0000 −0.602350
\(19\) 28.0000 0.338086 0.169043 0.985609i \(-0.445932\pi\)
0.169043 + 0.985609i \(0.445932\pi\)
\(20\) −72.0000 −0.804984
\(21\) 0 0
\(22\) −22.0000 −0.213201
\(23\) 180.000 1.63185 0.815926 0.578156i \(-0.196228\pi\)
0.815926 + 0.578156i \(0.196228\pi\)
\(24\) 16.0000 0.136083
\(25\) 199.000 1.59200
\(26\) −112.000 −0.844808
\(27\) −100.000 −0.712778
\(28\) 0 0
\(29\) −54.0000 −0.345778 −0.172889 0.984941i \(-0.555310\pi\)
−0.172889 + 0.984941i \(0.555310\pi\)
\(30\) −72.0000 −0.438178
\(31\) 334.000 1.93510 0.967551 0.252675i \(-0.0813104\pi\)
0.967551 + 0.252675i \(0.0813104\pi\)
\(32\) 32.0000 0.176777
\(33\) −22.0000 −0.116052
\(34\) −72.0000 −0.363173
\(35\) 0 0
\(36\) −92.0000 −0.425926
\(37\) 386.000 1.71508 0.857541 0.514416i \(-0.171991\pi\)
0.857541 + 0.514416i \(0.171991\pi\)
\(38\) 56.0000 0.239063
\(39\) −112.000 −0.459855
\(40\) −144.000 −0.569210
\(41\) 444.000 1.69125 0.845624 0.533779i \(-0.179229\pi\)
0.845624 + 0.533779i \(0.179229\pi\)
\(42\) 0 0
\(43\) −316.000 −1.12069 −0.560344 0.828260i \(-0.689331\pi\)
−0.560344 + 0.828260i \(0.689331\pi\)
\(44\) −44.0000 −0.150756
\(45\) 414.000 1.37146
\(46\) 360.000 1.15389
\(47\) 402.000 1.24761 0.623806 0.781580i \(-0.285586\pi\)
0.623806 + 0.781580i \(0.285586\pi\)
\(48\) 32.0000 0.0962250
\(49\) 0 0
\(50\) 398.000 1.12571
\(51\) −72.0000 −0.197687
\(52\) −224.000 −0.597369
\(53\) −486.000 −1.25957 −0.629785 0.776769i \(-0.716857\pi\)
−0.629785 + 0.776769i \(0.716857\pi\)
\(54\) −200.000 −0.504010
\(55\) 198.000 0.485424
\(56\) 0 0
\(57\) 56.0000 0.130129
\(58\) −108.000 −0.244502
\(59\) 282.000 0.622259 0.311129 0.950368i \(-0.399293\pi\)
0.311129 + 0.950368i \(0.399293\pi\)
\(60\) −144.000 −0.309839
\(61\) −380.000 −0.797607 −0.398803 0.917036i \(-0.630574\pi\)
−0.398803 + 0.917036i \(0.630574\pi\)
\(62\) 668.000 1.36832
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) 1008.00 1.92349
\(66\) −44.0000 −0.0820610
\(67\) 176.000 0.320923 0.160461 0.987042i \(-0.448702\pi\)
0.160461 + 0.987042i \(0.448702\pi\)
\(68\) −144.000 −0.256802
\(69\) 360.000 0.628100
\(70\) 0 0
\(71\) −324.000 −0.541574 −0.270787 0.962639i \(-0.587284\pi\)
−0.270787 + 0.962639i \(0.587284\pi\)
\(72\) −184.000 −0.301175
\(73\) −800.000 −1.28264 −0.641321 0.767272i \(-0.721613\pi\)
−0.641321 + 0.767272i \(0.721613\pi\)
\(74\) 772.000 1.21275
\(75\) 398.000 0.612761
\(76\) 112.000 0.169043
\(77\) 0 0
\(78\) −224.000 −0.325167
\(79\) −1144.00 −1.62924 −0.814621 0.579994i \(-0.803055\pi\)
−0.814621 + 0.579994i \(0.803055\pi\)
\(80\) −288.000 −0.402492
\(81\) 421.000 0.577503
\(82\) 888.000 1.19589
\(83\) −468.000 −0.618912 −0.309456 0.950914i \(-0.600147\pi\)
−0.309456 + 0.950914i \(0.600147\pi\)
\(84\) 0 0
\(85\) 648.000 0.826888
\(86\) −632.000 −0.792445
\(87\) −108.000 −0.133090
\(88\) −88.0000 −0.106600
\(89\) 870.000 1.03618 0.518089 0.855327i \(-0.326644\pi\)
0.518089 + 0.855327i \(0.326644\pi\)
\(90\) 828.000 0.969765
\(91\) 0 0
\(92\) 720.000 0.815926
\(93\) 668.000 0.744821
\(94\) 804.000 0.882194
\(95\) −504.000 −0.544309
\(96\) 64.0000 0.0680414
\(97\) 1330.00 1.39218 0.696088 0.717957i \(-0.254922\pi\)
0.696088 + 0.717957i \(0.254922\pi\)
\(98\) 0 0
\(99\) 253.000 0.256843
\(100\) 796.000 0.796000
\(101\) 120.000 0.118222 0.0591111 0.998251i \(-0.481173\pi\)
0.0591111 + 0.998251i \(0.481173\pi\)
\(102\) −144.000 −0.139786
\(103\) 1210.00 1.15752 0.578761 0.815497i \(-0.303536\pi\)
0.578761 + 0.815497i \(0.303536\pi\)
\(104\) −448.000 −0.422404
\(105\) 0 0
\(106\) −972.000 −0.890651
\(107\) 1236.00 1.11672 0.558358 0.829600i \(-0.311432\pi\)
0.558358 + 0.829600i \(0.311432\pi\)
\(108\) −400.000 −0.356389
\(109\) −694.000 −0.609845 −0.304923 0.952377i \(-0.598631\pi\)
−0.304923 + 0.952377i \(0.598631\pi\)
\(110\) 396.000 0.343247
\(111\) 772.000 0.660135
\(112\) 0 0
\(113\) 978.000 0.814181 0.407091 0.913388i \(-0.366543\pi\)
0.407091 + 0.913388i \(0.366543\pi\)
\(114\) 112.000 0.0920154
\(115\) −3240.00 −2.62723
\(116\) −216.000 −0.172889
\(117\) 1288.00 1.01774
\(118\) 564.000 0.440003
\(119\) 0 0
\(120\) −288.000 −0.219089
\(121\) 121.000 0.0909091
\(122\) −760.000 −0.563993
\(123\) 888.000 0.650961
\(124\) 1336.00 0.967551
\(125\) −1332.00 −0.953102
\(126\) 0 0
\(127\) −1216.00 −0.849626 −0.424813 0.905281i \(-0.639660\pi\)
−0.424813 + 0.905281i \(0.639660\pi\)
\(128\) 128.000 0.0883883
\(129\) −632.000 −0.431353
\(130\) 2016.00 1.36011
\(131\) −1680.00 −1.12048 −0.560238 0.828332i \(-0.689290\pi\)
−0.560238 + 0.828332i \(0.689290\pi\)
\(132\) −88.0000 −0.0580259
\(133\) 0 0
\(134\) 352.000 0.226927
\(135\) 1800.00 1.14755
\(136\) −288.000 −0.181587
\(137\) 1062.00 0.662283 0.331142 0.943581i \(-0.392566\pi\)
0.331142 + 0.943581i \(0.392566\pi\)
\(138\) 720.000 0.444134
\(139\) 508.000 0.309986 0.154993 0.987916i \(-0.450465\pi\)
0.154993 + 0.987916i \(0.450465\pi\)
\(140\) 0 0
\(141\) 804.000 0.480206
\(142\) −648.000 −0.382950
\(143\) 616.000 0.360227
\(144\) −368.000 −0.212963
\(145\) 972.000 0.556691
\(146\) −1600.00 −0.906965
\(147\) 0 0
\(148\) 1544.00 0.857541
\(149\) 2598.00 1.42843 0.714216 0.699925i \(-0.246783\pi\)
0.714216 + 0.699925i \(0.246783\pi\)
\(150\) 796.000 0.433288
\(151\) 2648.00 1.42709 0.713547 0.700607i \(-0.247088\pi\)
0.713547 + 0.700607i \(0.247088\pi\)
\(152\) 224.000 0.119532
\(153\) 828.000 0.437515
\(154\) 0 0
\(155\) −6012.00 −3.11545
\(156\) −448.000 −0.229928
\(157\) 790.000 0.401585 0.200793 0.979634i \(-0.435648\pi\)
0.200793 + 0.979634i \(0.435648\pi\)
\(158\) −2288.00 −1.15205
\(159\) −972.000 −0.484809
\(160\) −576.000 −0.284605
\(161\) 0 0
\(162\) 842.000 0.408357
\(163\) −160.000 −0.0768845 −0.0384422 0.999261i \(-0.512240\pi\)
−0.0384422 + 0.999261i \(0.512240\pi\)
\(164\) 1776.00 0.845624
\(165\) 396.000 0.186840
\(166\) −936.000 −0.437637
\(167\) −264.000 −0.122329 −0.0611645 0.998128i \(-0.519481\pi\)
−0.0611645 + 0.998128i \(0.519481\pi\)
\(168\) 0 0
\(169\) 939.000 0.427401
\(170\) 1296.00 0.584698
\(171\) −644.000 −0.287999
\(172\) −1264.00 −0.560344
\(173\) −1632.00 −0.717218 −0.358609 0.933488i \(-0.616749\pi\)
−0.358609 + 0.933488i \(0.616749\pi\)
\(174\) −216.000 −0.0941087
\(175\) 0 0
\(176\) −176.000 −0.0753778
\(177\) 564.000 0.239508
\(178\) 1740.00 0.732688
\(179\) −708.000 −0.295634 −0.147817 0.989015i \(-0.547225\pi\)
−0.147817 + 0.989015i \(0.547225\pi\)
\(180\) 1656.00 0.685728
\(181\) −902.000 −0.370415 −0.185208 0.982699i \(-0.559296\pi\)
−0.185208 + 0.982699i \(0.559296\pi\)
\(182\) 0 0
\(183\) −760.000 −0.306999
\(184\) 1440.00 0.576947
\(185\) −6948.00 −2.76123
\(186\) 1336.00 0.526668
\(187\) 396.000 0.154858
\(188\) 1608.00 0.623806
\(189\) 0 0
\(190\) −1008.00 −0.384884
\(191\) 1824.00 0.690995 0.345497 0.938420i \(-0.387710\pi\)
0.345497 + 0.938420i \(0.387710\pi\)
\(192\) 128.000 0.0481125
\(193\) 2090.00 0.779490 0.389745 0.920923i \(-0.372563\pi\)
0.389745 + 0.920923i \(0.372563\pi\)
\(194\) 2660.00 0.984417
\(195\) 2016.00 0.740353
\(196\) 0 0
\(197\) −1602.00 −0.579380 −0.289690 0.957121i \(-0.593552\pi\)
−0.289690 + 0.957121i \(0.593552\pi\)
\(198\) 506.000 0.181615
\(199\) 3274.00 1.16627 0.583135 0.812375i \(-0.301826\pi\)
0.583135 + 0.812375i \(0.301826\pi\)
\(200\) 1592.00 0.562857
\(201\) 352.000 0.123523
\(202\) 240.000 0.0835957
\(203\) 0 0
\(204\) −288.000 −0.0988433
\(205\) −7992.00 −2.72286
\(206\) 2420.00 0.818492
\(207\) −4140.00 −1.39010
\(208\) −896.000 −0.298685
\(209\) −308.000 −0.101937
\(210\) 0 0
\(211\) −4948.00 −1.61438 −0.807190 0.590291i \(-0.799013\pi\)
−0.807190 + 0.590291i \(0.799013\pi\)
\(212\) −1944.00 −0.629785
\(213\) −648.000 −0.208452
\(214\) 2472.00 0.789638
\(215\) 5688.00 1.80427
\(216\) −800.000 −0.252005
\(217\) 0 0
\(218\) −1388.00 −0.431226
\(219\) −1600.00 −0.493689
\(220\) 792.000 0.242712
\(221\) 2016.00 0.613624
\(222\) 1544.00 0.466786
\(223\) −2342.00 −0.703282 −0.351641 0.936135i \(-0.614376\pi\)
−0.351641 + 0.936135i \(0.614376\pi\)
\(224\) 0 0
\(225\) −4577.00 −1.35615
\(226\) 1956.00 0.575713
\(227\) −2064.00 −0.603491 −0.301746 0.953388i \(-0.597569\pi\)
−0.301746 + 0.953388i \(0.597569\pi\)
\(228\) 224.000 0.0650647
\(229\) 1666.00 0.480753 0.240376 0.970680i \(-0.422729\pi\)
0.240376 + 0.970680i \(0.422729\pi\)
\(230\) −6480.00 −1.85773
\(231\) 0 0
\(232\) −432.000 −0.122251
\(233\) 4158.00 1.16910 0.584549 0.811359i \(-0.301272\pi\)
0.584549 + 0.811359i \(0.301272\pi\)
\(234\) 2576.00 0.719651
\(235\) −7236.00 −2.00862
\(236\) 1128.00 0.311129
\(237\) −2288.00 −0.627095
\(238\) 0 0
\(239\) 72.0000 0.0194866 0.00974329 0.999953i \(-0.496899\pi\)
0.00974329 + 0.999953i \(0.496899\pi\)
\(240\) −576.000 −0.154919
\(241\) −6860.00 −1.83357 −0.916787 0.399376i \(-0.869227\pi\)
−0.916787 + 0.399376i \(0.869227\pi\)
\(242\) 242.000 0.0642824
\(243\) 3542.00 0.935059
\(244\) −1520.00 −0.398803
\(245\) 0 0
\(246\) 1776.00 0.460299
\(247\) −1568.00 −0.403925
\(248\) 2672.00 0.684162
\(249\) −936.000 −0.238219
\(250\) −2664.00 −0.673945
\(251\) 150.000 0.0377208 0.0188604 0.999822i \(-0.493996\pi\)
0.0188604 + 0.999822i \(0.493996\pi\)
\(252\) 0 0
\(253\) −1980.00 −0.492022
\(254\) −2432.00 −0.600777
\(255\) 1296.00 0.318269
\(256\) 256.000 0.0625000
\(257\) 2430.00 0.589802 0.294901 0.955528i \(-0.404713\pi\)
0.294901 + 0.955528i \(0.404713\pi\)
\(258\) −1264.00 −0.305012
\(259\) 0 0
\(260\) 4032.00 0.961746
\(261\) 1242.00 0.294551
\(262\) −3360.00 −0.792296
\(263\) 3048.00 0.714630 0.357315 0.933984i \(-0.383692\pi\)
0.357315 + 0.933984i \(0.383692\pi\)
\(264\) −176.000 −0.0410305
\(265\) 8748.00 2.02787
\(266\) 0 0
\(267\) 1740.00 0.398825
\(268\) 704.000 0.160461
\(269\) 3834.00 0.869008 0.434504 0.900670i \(-0.356924\pi\)
0.434504 + 0.900670i \(0.356924\pi\)
\(270\) 3600.00 0.811441
\(271\) 3508.00 0.786331 0.393166 0.919468i \(-0.371380\pi\)
0.393166 + 0.919468i \(0.371380\pi\)
\(272\) −576.000 −0.128401
\(273\) 0 0
\(274\) 2124.00 0.468305
\(275\) −2189.00 −0.480006
\(276\) 1440.00 0.314050
\(277\) 8294.00 1.79905 0.899527 0.436864i \(-0.143911\pi\)
0.899527 + 0.436864i \(0.143911\pi\)
\(278\) 1016.00 0.219193
\(279\) −7682.00 −1.64842
\(280\) 0 0
\(281\) 8022.00 1.70303 0.851517 0.524327i \(-0.175683\pi\)
0.851517 + 0.524327i \(0.175683\pi\)
\(282\) 1608.00 0.339557
\(283\) −392.000 −0.0823392 −0.0411696 0.999152i \(-0.513108\pi\)
−0.0411696 + 0.999152i \(0.513108\pi\)
\(284\) −1296.00 −0.270787
\(285\) −1008.00 −0.209504
\(286\) 1232.00 0.254719
\(287\) 0 0
\(288\) −736.000 −0.150588
\(289\) −3617.00 −0.736210
\(290\) 1944.00 0.393640
\(291\) 2660.00 0.535849
\(292\) −3200.00 −0.641321
\(293\) 2748.00 0.547918 0.273959 0.961741i \(-0.411667\pi\)
0.273959 + 0.961741i \(0.411667\pi\)
\(294\) 0 0
\(295\) −5076.00 −1.00182
\(296\) 3088.00 0.606373
\(297\) 1100.00 0.214911
\(298\) 5196.00 1.01005
\(299\) −10080.0 −1.94964
\(300\) 1592.00 0.306381
\(301\) 0 0
\(302\) 5296.00 1.00911
\(303\) 240.000 0.0455038
\(304\) 448.000 0.0845216
\(305\) 6840.00 1.28412
\(306\) 1656.00 0.309370
\(307\) 3064.00 0.569615 0.284807 0.958585i \(-0.408070\pi\)
0.284807 + 0.958585i \(0.408070\pi\)
\(308\) 0 0
\(309\) 2420.00 0.445531
\(310\) −12024.0 −2.20296
\(311\) −4062.00 −0.740627 −0.370313 0.928907i \(-0.620750\pi\)
−0.370313 + 0.928907i \(0.620750\pi\)
\(312\) −896.000 −0.162583
\(313\) 4870.00 0.879453 0.439726 0.898132i \(-0.355075\pi\)
0.439726 + 0.898132i \(0.355075\pi\)
\(314\) 1580.00 0.283964
\(315\) 0 0
\(316\) −4576.00 −0.814621
\(317\) 4806.00 0.851520 0.425760 0.904836i \(-0.360007\pi\)
0.425760 + 0.904836i \(0.360007\pi\)
\(318\) −1944.00 −0.342812
\(319\) 594.000 0.104256
\(320\) −1152.00 −0.201246
\(321\) 2472.00 0.429824
\(322\) 0 0
\(323\) −1008.00 −0.173643
\(324\) 1684.00 0.288752
\(325\) −11144.0 −1.90202
\(326\) −320.000 −0.0543655
\(327\) −1388.00 −0.234730
\(328\) 3552.00 0.597946
\(329\) 0 0
\(330\) 792.000 0.132116
\(331\) 6620.00 1.09930 0.549650 0.835395i \(-0.314761\pi\)
0.549650 + 0.835395i \(0.314761\pi\)
\(332\) −1872.00 −0.309456
\(333\) −8878.00 −1.46100
\(334\) −528.000 −0.0864996
\(335\) −3168.00 −0.516676
\(336\) 0 0
\(337\) 1094.00 0.176837 0.0884184 0.996083i \(-0.471819\pi\)
0.0884184 + 0.996083i \(0.471819\pi\)
\(338\) 1878.00 0.302218
\(339\) 1956.00 0.313379
\(340\) 2592.00 0.413444
\(341\) −3674.00 −0.583455
\(342\) −1288.00 −0.203646
\(343\) 0 0
\(344\) −2528.00 −0.396223
\(345\) −6480.00 −1.01122
\(346\) −3264.00 −0.507150
\(347\) 3468.00 0.536519 0.268259 0.963347i \(-0.413552\pi\)
0.268259 + 0.963347i \(0.413552\pi\)
\(348\) −432.000 −0.0665449
\(349\) 8188.00 1.25586 0.627928 0.778272i \(-0.283903\pi\)
0.627928 + 0.778272i \(0.283903\pi\)
\(350\) 0 0
\(351\) 5600.00 0.851584
\(352\) −352.000 −0.0533002
\(353\) 5070.00 0.764444 0.382222 0.924070i \(-0.375159\pi\)
0.382222 + 0.924070i \(0.375159\pi\)
\(354\) 1128.00 0.169357
\(355\) 5832.00 0.871917
\(356\) 3480.00 0.518089
\(357\) 0 0
\(358\) −1416.00 −0.209044
\(359\) 1656.00 0.243455 0.121727 0.992564i \(-0.461157\pi\)
0.121727 + 0.992564i \(0.461157\pi\)
\(360\) 3312.00 0.484883
\(361\) −6075.00 −0.885698
\(362\) −1804.00 −0.261923
\(363\) 242.000 0.0349909
\(364\) 0 0
\(365\) 14400.0 2.06501
\(366\) −1520.00 −0.217081
\(367\) −10166.0 −1.44594 −0.722971 0.690878i \(-0.757224\pi\)
−0.722971 + 0.690878i \(0.757224\pi\)
\(368\) 2880.00 0.407963
\(369\) −10212.0 −1.44069
\(370\) −13896.0 −1.95248
\(371\) 0 0
\(372\) 2672.00 0.372411
\(373\) −2722.00 −0.377855 −0.188927 0.981991i \(-0.560501\pi\)
−0.188927 + 0.981991i \(0.560501\pi\)
\(374\) 792.000 0.109501
\(375\) −2664.00 −0.366849
\(376\) 3216.00 0.441097
\(377\) 3024.00 0.413114
\(378\) 0 0
\(379\) −5872.00 −0.795843 −0.397921 0.917420i \(-0.630268\pi\)
−0.397921 + 0.917420i \(0.630268\pi\)
\(380\) −2016.00 −0.272154
\(381\) −2432.00 −0.327021
\(382\) 3648.00 0.488607
\(383\) −12330.0 −1.64500 −0.822498 0.568768i \(-0.807420\pi\)
−0.822498 + 0.568768i \(0.807420\pi\)
\(384\) 256.000 0.0340207
\(385\) 0 0
\(386\) 4180.00 0.551182
\(387\) 7268.00 0.954659
\(388\) 5320.00 0.696088
\(389\) −14586.0 −1.90113 −0.950565 0.310526i \(-0.899495\pi\)
−0.950565 + 0.310526i \(0.899495\pi\)
\(390\) 4032.00 0.523508
\(391\) −6480.00 −0.838127
\(392\) 0 0
\(393\) −3360.00 −0.431271
\(394\) −3204.00 −0.409683
\(395\) 20592.0 2.62303
\(396\) 1012.00 0.128421
\(397\) −1874.00 −0.236910 −0.118455 0.992959i \(-0.537794\pi\)
−0.118455 + 0.992959i \(0.537794\pi\)
\(398\) 6548.00 0.824677
\(399\) 0 0
\(400\) 3184.00 0.398000
\(401\) 13338.0 1.66102 0.830509 0.557006i \(-0.188050\pi\)
0.830509 + 0.557006i \(0.188050\pi\)
\(402\) 704.000 0.0873441
\(403\) −18704.0 −2.31194
\(404\) 480.000 0.0591111
\(405\) −7578.00 −0.929763
\(406\) 0 0
\(407\) −4246.00 −0.517116
\(408\) −576.000 −0.0698928
\(409\) 8200.00 0.991354 0.495677 0.868507i \(-0.334920\pi\)
0.495677 + 0.868507i \(0.334920\pi\)
\(410\) −15984.0 −1.92535
\(411\) 2124.00 0.254913
\(412\) 4840.00 0.578761
\(413\) 0 0
\(414\) −8280.00 −0.982946
\(415\) 8424.00 0.996429
\(416\) −1792.00 −0.211202
\(417\) 1016.00 0.119314
\(418\) −616.000 −0.0720803
\(419\) 7362.00 0.858370 0.429185 0.903216i \(-0.358801\pi\)
0.429185 + 0.903216i \(0.358801\pi\)
\(420\) 0 0
\(421\) −11710.0 −1.35561 −0.677803 0.735243i \(-0.737068\pi\)
−0.677803 + 0.735243i \(0.737068\pi\)
\(422\) −9896.00 −1.14154
\(423\) −9246.00 −1.06278
\(424\) −3888.00 −0.445325
\(425\) −7164.00 −0.817659
\(426\) −1296.00 −0.147398
\(427\) 0 0
\(428\) 4944.00 0.558358
\(429\) 1232.00 0.138652
\(430\) 11376.0 1.27581
\(431\) −936.000 −0.104607 −0.0523034 0.998631i \(-0.516656\pi\)
−0.0523034 + 0.998631i \(0.516656\pi\)
\(432\) −1600.00 −0.178195
\(433\) −9038.00 −1.00309 −0.501546 0.865131i \(-0.667235\pi\)
−0.501546 + 0.865131i \(0.667235\pi\)
\(434\) 0 0
\(435\) 1944.00 0.214270
\(436\) −2776.00 −0.304923
\(437\) 5040.00 0.551707
\(438\) −3200.00 −0.349091
\(439\) −1964.00 −0.213523 −0.106762 0.994285i \(-0.534048\pi\)
−0.106762 + 0.994285i \(0.534048\pi\)
\(440\) 1584.00 0.171623
\(441\) 0 0
\(442\) 4032.00 0.433897
\(443\) 10068.0 1.07979 0.539893 0.841734i \(-0.318465\pi\)
0.539893 + 0.841734i \(0.318465\pi\)
\(444\) 3088.00 0.330068
\(445\) −15660.0 −1.66821
\(446\) −4684.00 −0.497296
\(447\) 5196.00 0.549804
\(448\) 0 0
\(449\) 3270.00 0.343699 0.171849 0.985123i \(-0.445026\pi\)
0.171849 + 0.985123i \(0.445026\pi\)
\(450\) −9154.00 −0.958942
\(451\) −4884.00 −0.509930
\(452\) 3912.00 0.407091
\(453\) 5296.00 0.549289
\(454\) −4128.00 −0.426733
\(455\) 0 0
\(456\) 448.000 0.0460077
\(457\) −15526.0 −1.58922 −0.794612 0.607117i \(-0.792326\pi\)
−0.794612 + 0.607117i \(0.792326\pi\)
\(458\) 3332.00 0.339944
\(459\) 3600.00 0.366086
\(460\) −12960.0 −1.31362
\(461\) −10548.0 −1.06566 −0.532830 0.846222i \(-0.678872\pi\)
−0.532830 + 0.846222i \(0.678872\pi\)
\(462\) 0 0
\(463\) −3796.00 −0.381026 −0.190513 0.981685i \(-0.561015\pi\)
−0.190513 + 0.981685i \(0.561015\pi\)
\(464\) −864.000 −0.0864444
\(465\) −12024.0 −1.19914
\(466\) 8316.00 0.826677
\(467\) −7122.00 −0.705711 −0.352855 0.935678i \(-0.614789\pi\)
−0.352855 + 0.935678i \(0.614789\pi\)
\(468\) 5152.00 0.508870
\(469\) 0 0
\(470\) −14472.0 −1.42031
\(471\) 1580.00 0.154570
\(472\) 2256.00 0.220002
\(473\) 3476.00 0.337900
\(474\) −4576.00 −0.443423
\(475\) 5572.00 0.538233
\(476\) 0 0
\(477\) 11178.0 1.07297
\(478\) 144.000 0.0137791
\(479\) −2292.00 −0.218631 −0.109315 0.994007i \(-0.534866\pi\)
−0.109315 + 0.994007i \(0.534866\pi\)
\(480\) −1152.00 −0.109545
\(481\) −21616.0 −2.04907
\(482\) −13720.0 −1.29653
\(483\) 0 0
\(484\) 484.000 0.0454545
\(485\) −23940.0 −2.24136
\(486\) 7084.00 0.661187
\(487\) 5132.00 0.477522 0.238761 0.971078i \(-0.423259\pi\)
0.238761 + 0.971078i \(0.423259\pi\)
\(488\) −3040.00 −0.281997
\(489\) −320.000 −0.0295928
\(490\) 0 0
\(491\) 4188.00 0.384932 0.192466 0.981304i \(-0.438351\pi\)
0.192466 + 0.981304i \(0.438351\pi\)
\(492\) 3552.00 0.325481
\(493\) 1944.00 0.177593
\(494\) −3136.00 −0.285618
\(495\) −4554.00 −0.413509
\(496\) 5344.00 0.483776
\(497\) 0 0
\(498\) −1872.00 −0.168446
\(499\) 3848.00 0.345211 0.172605 0.984991i \(-0.444781\pi\)
0.172605 + 0.984991i \(0.444781\pi\)
\(500\) −5328.00 −0.476551
\(501\) −528.000 −0.0470844
\(502\) 300.000 0.0266726
\(503\) 1068.00 0.0946715 0.0473358 0.998879i \(-0.484927\pi\)
0.0473358 + 0.998879i \(0.484927\pi\)
\(504\) 0 0
\(505\) −2160.00 −0.190334
\(506\) −3960.00 −0.347912
\(507\) 1878.00 0.164507
\(508\) −4864.00 −0.424813
\(509\) 6162.00 0.536593 0.268297 0.963336i \(-0.413539\pi\)
0.268297 + 0.963336i \(0.413539\pi\)
\(510\) 2592.00 0.225050
\(511\) 0 0
\(512\) 512.000 0.0441942
\(513\) −2800.00 −0.240981
\(514\) 4860.00 0.417053
\(515\) −21780.0 −1.86358
\(516\) −2528.00 −0.215676
\(517\) −4422.00 −0.376169
\(518\) 0 0
\(519\) −3264.00 −0.276057
\(520\) 8064.00 0.680057
\(521\) 20946.0 1.76135 0.880673 0.473725i \(-0.157091\pi\)
0.880673 + 0.473725i \(0.157091\pi\)
\(522\) 2484.00 0.208279
\(523\) 4696.00 0.392623 0.196311 0.980542i \(-0.437104\pi\)
0.196311 + 0.980542i \(0.437104\pi\)
\(524\) −6720.00 −0.560238
\(525\) 0 0
\(526\) 6096.00 0.505320
\(527\) −12024.0 −0.993878
\(528\) −352.000 −0.0290129
\(529\) 20233.0 1.66294
\(530\) 17496.0 1.43392
\(531\) −6486.00 −0.530072
\(532\) 0 0
\(533\) −24864.0 −2.02060
\(534\) 3480.00 0.282012
\(535\) −22248.0 −1.79788
\(536\) 1408.00 0.113463
\(537\) −1416.00 −0.113789
\(538\) 7668.00 0.614481
\(539\) 0 0
\(540\) 7200.00 0.573775
\(541\) 19358.0 1.53838 0.769192 0.639018i \(-0.220659\pi\)
0.769192 + 0.639018i \(0.220659\pi\)
\(542\) 7016.00 0.556020
\(543\) −1804.00 −0.142573
\(544\) −1152.00 −0.0907934
\(545\) 12492.0 0.981832
\(546\) 0 0
\(547\) 18020.0 1.40855 0.704277 0.709925i \(-0.251271\pi\)
0.704277 + 0.709925i \(0.251271\pi\)
\(548\) 4248.00 0.331142
\(549\) 8740.00 0.679443
\(550\) −4378.00 −0.339416
\(551\) −1512.00 −0.116903
\(552\) 2880.00 0.222067
\(553\) 0 0
\(554\) 16588.0 1.27212
\(555\) −13896.0 −1.06280
\(556\) 2032.00 0.154993
\(557\) 14622.0 1.11231 0.556153 0.831080i \(-0.312277\pi\)
0.556153 + 0.831080i \(0.312277\pi\)
\(558\) −15364.0 −1.16561
\(559\) 17696.0 1.33893
\(560\) 0 0
\(561\) 792.000 0.0596048
\(562\) 16044.0 1.20423
\(563\) 2244.00 0.167981 0.0839905 0.996467i \(-0.473233\pi\)
0.0839905 + 0.996467i \(0.473233\pi\)
\(564\) 3216.00 0.240103
\(565\) −17604.0 −1.31081
\(566\) −784.000 −0.0582226
\(567\) 0 0
\(568\) −2592.00 −0.191475
\(569\) −3258.00 −0.240039 −0.120020 0.992772i \(-0.538296\pi\)
−0.120020 + 0.992772i \(0.538296\pi\)
\(570\) −2016.00 −0.148142
\(571\) −6604.00 −0.484008 −0.242004 0.970275i \(-0.577805\pi\)
−0.242004 + 0.970275i \(0.577805\pi\)
\(572\) 2464.00 0.180114
\(573\) 3648.00 0.265964
\(574\) 0 0
\(575\) 35820.0 2.59791
\(576\) −1472.00 −0.106481
\(577\) 16594.0 1.19726 0.598628 0.801027i \(-0.295713\pi\)
0.598628 + 0.801027i \(0.295713\pi\)
\(578\) −7234.00 −0.520579
\(579\) 4180.00 0.300026
\(580\) 3888.00 0.278346
\(581\) 0 0
\(582\) 5320.00 0.378902
\(583\) 5346.00 0.379775
\(584\) −6400.00 −0.453483
\(585\) −23184.0 −1.63853
\(586\) 5496.00 0.387436
\(587\) 19062.0 1.34033 0.670164 0.742213i \(-0.266224\pi\)
0.670164 + 0.742213i \(0.266224\pi\)
\(588\) 0 0
\(589\) 9352.00 0.654232
\(590\) −10152.0 −0.708392
\(591\) −3204.00 −0.223003
\(592\) 6176.00 0.428770
\(593\) 4776.00 0.330737 0.165368 0.986232i \(-0.447119\pi\)
0.165368 + 0.986232i \(0.447119\pi\)
\(594\) 2200.00 0.151965
\(595\) 0 0
\(596\) 10392.0 0.714216
\(597\) 6548.00 0.448897
\(598\) −20160.0 −1.37860
\(599\) 7956.00 0.542693 0.271347 0.962482i \(-0.412531\pi\)
0.271347 + 0.962482i \(0.412531\pi\)
\(600\) 3184.00 0.216644
\(601\) −14348.0 −0.973822 −0.486911 0.873452i \(-0.661876\pi\)
−0.486911 + 0.873452i \(0.661876\pi\)
\(602\) 0 0
\(603\) −4048.00 −0.273379
\(604\) 10592.0 0.713547
\(605\) −2178.00 −0.146361
\(606\) 480.000 0.0321760
\(607\) −24488.0 −1.63746 −0.818729 0.574180i \(-0.805321\pi\)
−0.818729 + 0.574180i \(0.805321\pi\)
\(608\) 896.000 0.0597658
\(609\) 0 0
\(610\) 13680.0 0.908011
\(611\) −22512.0 −1.49057
\(612\) 3312.00 0.218758
\(613\) −19654.0 −1.29497 −0.647486 0.762078i \(-0.724179\pi\)
−0.647486 + 0.762078i \(0.724179\pi\)
\(614\) 6128.00 0.402778
\(615\) −15984.0 −1.04803
\(616\) 0 0
\(617\) 2694.00 0.175780 0.0878901 0.996130i \(-0.471988\pi\)
0.0878901 + 0.996130i \(0.471988\pi\)
\(618\) 4840.00 0.315038
\(619\) −10178.0 −0.660886 −0.330443 0.943826i \(-0.607198\pi\)
−0.330443 + 0.943826i \(0.607198\pi\)
\(620\) −24048.0 −1.55773
\(621\) −18000.0 −1.16315
\(622\) −8124.00 −0.523702
\(623\) 0 0
\(624\) −1792.00 −0.114964
\(625\) −899.000 −0.0575360
\(626\) 9740.00 0.621867
\(627\) −616.000 −0.0392355
\(628\) 3160.00 0.200793
\(629\) −13896.0 −0.880874
\(630\) 0 0
\(631\) −7648.00 −0.482507 −0.241254 0.970462i \(-0.577559\pi\)
−0.241254 + 0.970462i \(0.577559\pi\)
\(632\) −9152.00 −0.576024
\(633\) −9896.00 −0.621375
\(634\) 9612.00 0.602116
\(635\) 21888.0 1.36787
\(636\) −3888.00 −0.242404
\(637\) 0 0
\(638\) 1188.00 0.0737200
\(639\) 7452.00 0.461340
\(640\) −2304.00 −0.142302
\(641\) 270.000 0.0166371 0.00831853 0.999965i \(-0.497352\pi\)
0.00831853 + 0.999965i \(0.497352\pi\)
\(642\) 4944.00 0.303932
\(643\) −16250.0 −0.996637 −0.498318 0.866994i \(-0.666049\pi\)
−0.498318 + 0.866994i \(0.666049\pi\)
\(644\) 0 0
\(645\) 11376.0 0.694464
\(646\) −2016.00 −0.122784
\(647\) −10242.0 −0.622341 −0.311170 0.950354i \(-0.600721\pi\)
−0.311170 + 0.950354i \(0.600721\pi\)
\(648\) 3368.00 0.204178
\(649\) −3102.00 −0.187618
\(650\) −22288.0 −1.34493
\(651\) 0 0
\(652\) −640.000 −0.0384422
\(653\) −17322.0 −1.03807 −0.519037 0.854752i \(-0.673709\pi\)
−0.519037 + 0.854752i \(0.673709\pi\)
\(654\) −2776.00 −0.165979
\(655\) 30240.0 1.80393
\(656\) 7104.00 0.422812
\(657\) 18400.0 1.09262
\(658\) 0 0
\(659\) 11676.0 0.690186 0.345093 0.938569i \(-0.387847\pi\)
0.345093 + 0.938569i \(0.387847\pi\)
\(660\) 1584.00 0.0934199
\(661\) 20710.0 1.21865 0.609323 0.792922i \(-0.291441\pi\)
0.609323 + 0.792922i \(0.291441\pi\)
\(662\) 13240.0 0.777322
\(663\) 4032.00 0.236184
\(664\) −3744.00 −0.218818
\(665\) 0 0
\(666\) −17756.0 −1.03308
\(667\) −9720.00 −0.564258
\(668\) −1056.00 −0.0611645
\(669\) −4684.00 −0.270693
\(670\) −6336.00 −0.365345
\(671\) 4180.00 0.240487
\(672\) 0 0
\(673\) −10354.0 −0.593042 −0.296521 0.955026i \(-0.595827\pi\)
−0.296521 + 0.955026i \(0.595827\pi\)
\(674\) 2188.00 0.125042
\(675\) −19900.0 −1.13474
\(676\) 3756.00 0.213701
\(677\) 10920.0 0.619926 0.309963 0.950749i \(-0.399683\pi\)
0.309963 + 0.950749i \(0.399683\pi\)
\(678\) 3912.00 0.221592
\(679\) 0 0
\(680\) 5184.00 0.292349
\(681\) −4128.00 −0.232284
\(682\) −7348.00 −0.412565
\(683\) 27804.0 1.55767 0.778836 0.627227i \(-0.215810\pi\)
0.778836 + 0.627227i \(0.215810\pi\)
\(684\) −2576.00 −0.144000
\(685\) −19116.0 −1.06626
\(686\) 0 0
\(687\) 3332.00 0.185042
\(688\) −5056.00 −0.280172
\(689\) 27216.0 1.50486
\(690\) −12960.0 −0.715042
\(691\) 25834.0 1.42225 0.711123 0.703068i \(-0.248187\pi\)
0.711123 + 0.703068i \(0.248187\pi\)
\(692\) −6528.00 −0.358609
\(693\) 0 0
\(694\) 6936.00 0.379376
\(695\) −9144.00 −0.499067
\(696\) −864.000 −0.0470544
\(697\) −15984.0 −0.868633
\(698\) 16376.0 0.888024
\(699\) 8316.00 0.449986
\(700\) 0 0
\(701\) −10590.0 −0.570583 −0.285292 0.958441i \(-0.592090\pi\)
−0.285292 + 0.958441i \(0.592090\pi\)
\(702\) 11200.0 0.602161
\(703\) 10808.0 0.579846
\(704\) −704.000 −0.0376889
\(705\) −14472.0 −0.773116
\(706\) 10140.0 0.540544
\(707\) 0 0
\(708\) 2256.00 0.119754
\(709\) −6802.00 −0.360302 −0.180151 0.983639i \(-0.557659\pi\)
−0.180151 + 0.983639i \(0.557659\pi\)
\(710\) 11664.0 0.616538
\(711\) 26312.0 1.38787
\(712\) 6960.00 0.366344
\(713\) 60120.0 3.15780
\(714\) 0 0
\(715\) −11088.0 −0.579955
\(716\) −2832.00 −0.147817
\(717\) 144.000 0.00750039
\(718\) 3312.00 0.172149
\(719\) −23010.0 −1.19350 −0.596751 0.802426i \(-0.703542\pi\)
−0.596751 + 0.802426i \(0.703542\pi\)
\(720\) 6624.00 0.342864
\(721\) 0 0
\(722\) −12150.0 −0.626283
\(723\) −13720.0 −0.705743
\(724\) −3608.00 −0.185208
\(725\) −10746.0 −0.550478
\(726\) 484.000 0.0247423
\(727\) −4682.00 −0.238853 −0.119426 0.992843i \(-0.538106\pi\)
−0.119426 + 0.992843i \(0.538106\pi\)
\(728\) 0 0
\(729\) −4283.00 −0.217599
\(730\) 28800.0 1.46019
\(731\) 11376.0 0.575590
\(732\) −3040.00 −0.153499
\(733\) 17860.0 0.899965 0.449982 0.893037i \(-0.351430\pi\)
0.449982 + 0.893037i \(0.351430\pi\)
\(734\) −20332.0 −1.02244
\(735\) 0 0
\(736\) 5760.00 0.288473
\(737\) −1936.00 −0.0967618
\(738\) −20424.0 −1.01872
\(739\) 6860.00 0.341474 0.170737 0.985317i \(-0.445385\pi\)
0.170737 + 0.985317i \(0.445385\pi\)
\(740\) −27792.0 −1.38061
\(741\) −3136.00 −0.155471
\(742\) 0 0
\(743\) −22752.0 −1.12341 −0.561703 0.827339i \(-0.689853\pi\)
−0.561703 + 0.827339i \(0.689853\pi\)
\(744\) 5344.00 0.263334
\(745\) −46764.0 −2.29973
\(746\) −5444.00 −0.267184
\(747\) 10764.0 0.527221
\(748\) 1584.00 0.0774288
\(749\) 0 0
\(750\) −5328.00 −0.259401
\(751\) 7364.00 0.357811 0.178906 0.983866i \(-0.442744\pi\)
0.178906 + 0.983866i \(0.442744\pi\)
\(752\) 6432.00 0.311903
\(753\) 300.000 0.0145187
\(754\) 6048.00 0.292116
\(755\) −47664.0 −2.29758
\(756\) 0 0
\(757\) −34378.0 −1.65058 −0.825290 0.564709i \(-0.808989\pi\)
−0.825290 + 0.564709i \(0.808989\pi\)
\(758\) −11744.0 −0.562746
\(759\) −3960.00 −0.189379
\(760\) −4032.00 −0.192442
\(761\) −27456.0 −1.30786 −0.653929 0.756556i \(-0.726880\pi\)
−0.653929 + 0.756556i \(0.726880\pi\)
\(762\) −4864.00 −0.231239
\(763\) 0 0
\(764\) 7296.00 0.345497
\(765\) −14904.0 −0.704386
\(766\) −24660.0 −1.16319
\(767\) −15792.0 −0.743437
\(768\) 512.000 0.0240563
\(769\) −7952.00 −0.372895 −0.186448 0.982465i \(-0.559697\pi\)
−0.186448 + 0.982465i \(0.559697\pi\)
\(770\) 0 0
\(771\) 4860.00 0.227015
\(772\) 8360.00 0.389745
\(773\) 4986.00 0.231997 0.115999 0.993249i \(-0.462993\pi\)
0.115999 + 0.993249i \(0.462993\pi\)
\(774\) 14536.0 0.675046
\(775\) 66466.0 3.08068
\(776\) 10640.0 0.492208
\(777\) 0 0
\(778\) −29172.0 −1.34430
\(779\) 12432.0 0.571788
\(780\) 8064.00 0.370176
\(781\) 3564.00 0.163291
\(782\) −12960.0 −0.592645
\(783\) 5400.00 0.246463
\(784\) 0 0
\(785\) −14220.0 −0.646540
\(786\) −6720.00 −0.304955
\(787\) 42748.0 1.93622 0.968108 0.250534i \(-0.0806062\pi\)
0.968108 + 0.250534i \(0.0806062\pi\)
\(788\) −6408.00 −0.289690
\(789\) 6096.00 0.275061
\(790\) 41184.0 1.85476
\(791\) 0 0
\(792\) 2024.00 0.0908077
\(793\) 21280.0 0.952932
\(794\) −3748.00 −0.167521
\(795\) 17496.0 0.780527
\(796\) 13096.0 0.583135
\(797\) −35610.0 −1.58265 −0.791324 0.611397i \(-0.790608\pi\)
−0.791324 + 0.611397i \(0.790608\pi\)
\(798\) 0 0
\(799\) −14472.0 −0.640779
\(800\) 6368.00 0.281428
\(801\) −20010.0 −0.882670
\(802\) 26676.0 1.17452
\(803\) 8800.00 0.386731
\(804\) 1408.00 0.0617616
\(805\) 0 0
\(806\) −37408.0 −1.63479
\(807\) 7668.00 0.334481
\(808\) 960.000 0.0417979
\(809\) −17046.0 −0.740798 −0.370399 0.928873i \(-0.620779\pi\)
−0.370399 + 0.928873i \(0.620779\pi\)
\(810\) −15156.0 −0.657441
\(811\) 2176.00 0.0942166 0.0471083 0.998890i \(-0.484999\pi\)
0.0471083 + 0.998890i \(0.484999\pi\)
\(812\) 0 0
\(813\) 7016.00 0.302659
\(814\) −8492.00 −0.365657
\(815\) 2880.00 0.123782
\(816\) −1152.00 −0.0494217
\(817\) −8848.00 −0.378889
\(818\) 16400.0 0.700993
\(819\) 0 0
\(820\) −31968.0 −1.36143
\(821\) 2094.00 0.0890147 0.0445074 0.999009i \(-0.485828\pi\)
0.0445074 + 0.999009i \(0.485828\pi\)
\(822\) 4248.00 0.180251
\(823\) 7328.00 0.310374 0.155187 0.987885i \(-0.450402\pi\)
0.155187 + 0.987885i \(0.450402\pi\)
\(824\) 9680.00 0.409246
\(825\) −4378.00 −0.184754
\(826\) 0 0
\(827\) −12492.0 −0.525259 −0.262630 0.964897i \(-0.584590\pi\)
−0.262630 + 0.964897i \(0.584590\pi\)
\(828\) −16560.0 −0.695048
\(829\) 37486.0 1.57050 0.785249 0.619180i \(-0.212535\pi\)
0.785249 + 0.619180i \(0.212535\pi\)
\(830\) 16848.0 0.704581
\(831\) 16588.0 0.692456
\(832\) −3584.00 −0.149342
\(833\) 0 0
\(834\) 2032.00 0.0843674
\(835\) 4752.00 0.196946
\(836\) −1232.00 −0.0509684
\(837\) −33400.0 −1.37930
\(838\) 14724.0 0.606960
\(839\) 17574.0 0.723149 0.361574 0.932343i \(-0.382239\pi\)
0.361574 + 0.932343i \(0.382239\pi\)
\(840\) 0 0
\(841\) −21473.0 −0.880438
\(842\) −23420.0 −0.958559
\(843\) 16044.0 0.655498
\(844\) −19792.0 −0.807190
\(845\) −16902.0 −0.688102
\(846\) −18492.0 −0.751499
\(847\) 0 0
\(848\) −7776.00 −0.314893
\(849\) −784.000 −0.0316924
\(850\) −14328.0 −0.578172
\(851\) 69480.0 2.79876
\(852\) −2592.00 −0.104226
\(853\) −9440.00 −0.378921 −0.189460 0.981888i \(-0.560674\pi\)
−0.189460 + 0.981888i \(0.560674\pi\)
\(854\) 0 0
\(855\) 11592.0 0.463670
\(856\) 9888.00 0.394819
\(857\) 28440.0 1.13360 0.566798 0.823857i \(-0.308182\pi\)
0.566798 + 0.823857i \(0.308182\pi\)
\(858\) 2464.00 0.0980415
\(859\) 24334.0 0.966549 0.483274 0.875469i \(-0.339447\pi\)
0.483274 + 0.875469i \(0.339447\pi\)
\(860\) 22752.0 0.902136
\(861\) 0 0
\(862\) −1872.00 −0.0739682
\(863\) 39264.0 1.54874 0.774370 0.632733i \(-0.218067\pi\)
0.774370 + 0.632733i \(0.218067\pi\)
\(864\) −3200.00 −0.126003
\(865\) 29376.0 1.15470
\(866\) −18076.0 −0.709293
\(867\) −7234.00 −0.283367
\(868\) 0 0
\(869\) 12584.0 0.491235
\(870\) 3888.00 0.151512
\(871\) −9856.00 −0.383419
\(872\) −5552.00 −0.215613
\(873\) −30590.0 −1.18593
\(874\) 10080.0 0.390116
\(875\) 0 0
\(876\) −6400.00 −0.246845
\(877\) 32114.0 1.23650 0.618251 0.785981i \(-0.287841\pi\)
0.618251 + 0.785981i \(0.287841\pi\)
\(878\) −3928.00 −0.150984
\(879\) 5496.00 0.210894
\(880\) 3168.00 0.121356
\(881\) −41454.0 −1.58527 −0.792634 0.609698i \(-0.791291\pi\)
−0.792634 + 0.609698i \(0.791291\pi\)
\(882\) 0 0
\(883\) 2876.00 0.109609 0.0548047 0.998497i \(-0.482546\pi\)
0.0548047 + 0.998497i \(0.482546\pi\)
\(884\) 8064.00 0.306812
\(885\) −10152.0 −0.385600
\(886\) 20136.0 0.763524
\(887\) −13932.0 −0.527385 −0.263693 0.964607i \(-0.584940\pi\)
−0.263693 + 0.964607i \(0.584940\pi\)
\(888\) 6176.00 0.233393
\(889\) 0 0
\(890\) −31320.0 −1.17961
\(891\) −4631.00 −0.174124
\(892\) −9368.00 −0.351641
\(893\) 11256.0 0.421800
\(894\) 10392.0 0.388770
\(895\) 12744.0 0.475961
\(896\) 0 0
\(897\) −20160.0 −0.750416
\(898\) 6540.00 0.243032
\(899\) −18036.0 −0.669115
\(900\) −18308.0 −0.678074
\(901\) 17496.0 0.646921
\(902\) −9768.00 −0.360575
\(903\) 0 0
\(904\) 7824.00 0.287857
\(905\) 16236.0 0.596357
\(906\) 10592.0 0.388406
\(907\) −19768.0 −0.723689 −0.361844 0.932239i \(-0.617853\pi\)
−0.361844 + 0.932239i \(0.617853\pi\)
\(908\) −8256.00 −0.301746
\(909\) −2760.00 −0.100708
\(910\) 0 0
\(911\) 43836.0 1.59424 0.797119 0.603822i \(-0.206356\pi\)
0.797119 + 0.603822i \(0.206356\pi\)
\(912\) 896.000 0.0325324
\(913\) 5148.00 0.186609
\(914\) −31052.0 −1.12375
\(915\) 13680.0 0.494259
\(916\) 6664.00 0.240376
\(917\) 0 0
\(918\) 7200.00 0.258862
\(919\) 31544.0 1.13225 0.566127 0.824318i \(-0.308441\pi\)
0.566127 + 0.824318i \(0.308441\pi\)
\(920\) −25920.0 −0.928866
\(921\) 6128.00 0.219245
\(922\) −21096.0 −0.753536
\(923\) 18144.0 0.647039
\(924\) 0 0
\(925\) 76814.0 2.73041
\(926\) −7592.00 −0.269426
\(927\) −27830.0 −0.986038
\(928\) −1728.00 −0.0611254
\(929\) −11118.0 −0.392648 −0.196324 0.980539i \(-0.562900\pi\)
−0.196324 + 0.980539i \(0.562900\pi\)
\(930\) −24048.0 −0.847919
\(931\) 0 0
\(932\) 16632.0 0.584549
\(933\) −8124.00 −0.285067
\(934\) −14244.0 −0.499013
\(935\) −7128.00 −0.249316
\(936\) 10304.0 0.359826
\(937\) −10568.0 −0.368454 −0.184227 0.982884i \(-0.558978\pi\)
−0.184227 + 0.982884i \(0.558978\pi\)
\(938\) 0 0
\(939\) 9740.00 0.338501
\(940\) −28944.0 −1.00431
\(941\) −14964.0 −0.518398 −0.259199 0.965824i \(-0.583459\pi\)
−0.259199 + 0.965824i \(0.583459\pi\)
\(942\) 3160.00 0.109298
\(943\) 79920.0 2.75987
\(944\) 4512.00 0.155565
\(945\) 0 0
\(946\) 6952.00 0.238931
\(947\) 3324.00 0.114061 0.0570304 0.998372i \(-0.481837\pi\)
0.0570304 + 0.998372i \(0.481837\pi\)
\(948\) −9152.00 −0.313548
\(949\) 44800.0 1.53242
\(950\) 11144.0 0.380589
\(951\) 9612.00 0.327750
\(952\) 0 0
\(953\) 3906.00 0.132768 0.0663839 0.997794i \(-0.478854\pi\)
0.0663839 + 0.997794i \(0.478854\pi\)
\(954\) 22356.0 0.758703
\(955\) −32832.0 −1.11248
\(956\) 288.000 0.00974329
\(957\) 1188.00 0.0401281
\(958\) −4584.00 −0.154595
\(959\) 0 0
\(960\) −2304.00 −0.0774597
\(961\) 81765.0 2.74462
\(962\) −43232.0 −1.44891
\(963\) −28428.0 −0.951277
\(964\) −27440.0 −0.916787
\(965\) −37620.0 −1.25495
\(966\) 0 0
\(967\) −36448.0 −1.21209 −0.606044 0.795431i \(-0.707244\pi\)
−0.606044 + 0.795431i \(0.707244\pi\)
\(968\) 968.000 0.0321412
\(969\) −2016.00 −0.0668351
\(970\) −47880.0 −1.58488
\(971\) 20526.0 0.678384 0.339192 0.940717i \(-0.389846\pi\)
0.339192 + 0.940717i \(0.389846\pi\)
\(972\) 14168.0 0.467530
\(973\) 0 0
\(974\) 10264.0 0.337659
\(975\) −22288.0 −0.732089
\(976\) −6080.00 −0.199402
\(977\) 37434.0 1.22581 0.612907 0.790155i \(-0.290000\pi\)
0.612907 + 0.790155i \(0.290000\pi\)
\(978\) −640.000 −0.0209253
\(979\) −9570.00 −0.312419
\(980\) 0 0
\(981\) 15962.0 0.519498
\(982\) 8376.00 0.272188
\(983\) 52194.0 1.69352 0.846760 0.531975i \(-0.178550\pi\)
0.846760 + 0.531975i \(0.178550\pi\)
\(984\) 7104.00 0.230150
\(985\) 28836.0 0.932783
\(986\) 3888.00 0.125577
\(987\) 0 0
\(988\) −6272.00 −0.201962
\(989\) −56880.0 −1.82880
\(990\) −9108.00 −0.292395
\(991\) −15220.0 −0.487870 −0.243935 0.969792i \(-0.578438\pi\)
−0.243935 + 0.969792i \(0.578438\pi\)
\(992\) 10688.0 0.342081
\(993\) 13240.0 0.423121
\(994\) 0 0
\(995\) −58932.0 −1.87766
\(996\) −3744.00 −0.119110
\(997\) −37664.0 −1.19642 −0.598210 0.801339i \(-0.704121\pi\)
−0.598210 + 0.801339i \(0.704121\pi\)
\(998\) 7696.00 0.244101
\(999\) −38600.0 −1.22247
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 1078.4.a.g.1.1 1
7.6 odd 2 154.4.a.d.1.1 1
21.20 even 2 1386.4.a.a.1.1 1
28.27 even 2 1232.4.a.f.1.1 1
77.76 even 2 1694.4.a.c.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
154.4.a.d.1.1 1 7.6 odd 2
1078.4.a.g.1.1 1 1.1 even 1 trivial
1232.4.a.f.1.1 1 28.27 even 2
1386.4.a.a.1.1 1 21.20 even 2
1694.4.a.c.1.1 1 77.76 even 2