Properties

Label 1710.2.a.n.1.1
Level $1710$
Weight $2$
Character 1710.1
Self dual yes
Analytic conductor $13.654$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1710.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(13.6544187456\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 570)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1710.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{5} -2.00000 q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{5} -2.00000 q^{7} +1.00000 q^{8} -1.00000 q^{10} +2.00000 q^{11} -2.00000 q^{14} +1.00000 q^{16} +2.00000 q^{17} +1.00000 q^{19} -1.00000 q^{20} +2.00000 q^{22} +8.00000 q^{23} +1.00000 q^{25} -2.00000 q^{28} +1.00000 q^{32} +2.00000 q^{34} +2.00000 q^{35} +4.00000 q^{37} +1.00000 q^{38} -1.00000 q^{40} +8.00000 q^{41} -6.00000 q^{43} +2.00000 q^{44} +8.00000 q^{46} +8.00000 q^{47} -3.00000 q^{49} +1.00000 q^{50} +10.0000 q^{53} -2.00000 q^{55} -2.00000 q^{56} +8.00000 q^{59} +2.00000 q^{61} +1.00000 q^{64} +2.00000 q^{68} +2.00000 q^{70} -8.00000 q^{71} -2.00000 q^{73} +4.00000 q^{74} +1.00000 q^{76} -4.00000 q^{77} -8.00000 q^{79} -1.00000 q^{80} +8.00000 q^{82} +16.0000 q^{83} -2.00000 q^{85} -6.00000 q^{86} +2.00000 q^{88} -16.0000 q^{89} +8.00000 q^{92} +8.00000 q^{94} -1.00000 q^{95} +8.00000 q^{97} -3.00000 q^{98} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 0 0
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) −2.00000 −0.755929 −0.377964 0.925820i \(-0.623376\pi\)
−0.377964 + 0.925820i \(0.623376\pi\)
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) −1.00000 −0.316228
\(11\) 2.00000 0.603023 0.301511 0.953463i \(-0.402509\pi\)
0.301511 + 0.953463i \(0.402509\pi\)
\(12\) 0 0
\(13\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) −2.00000 −0.534522
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 2.00000 0.485071 0.242536 0.970143i \(-0.422021\pi\)
0.242536 + 0.970143i \(0.422021\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) −1.00000 −0.223607
\(21\) 0 0
\(22\) 2.00000 0.426401
\(23\) 8.00000 1.66812 0.834058 0.551677i \(-0.186012\pi\)
0.834058 + 0.551677i \(0.186012\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) −2.00000 −0.377964
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) 2.00000 0.342997
\(35\) 2.00000 0.338062
\(36\) 0 0
\(37\) 4.00000 0.657596 0.328798 0.944400i \(-0.393356\pi\)
0.328798 + 0.944400i \(0.393356\pi\)
\(38\) 1.00000 0.162221
\(39\) 0 0
\(40\) −1.00000 −0.158114
\(41\) 8.00000 1.24939 0.624695 0.780869i \(-0.285223\pi\)
0.624695 + 0.780869i \(0.285223\pi\)
\(42\) 0 0
\(43\) −6.00000 −0.914991 −0.457496 0.889212i \(-0.651253\pi\)
−0.457496 + 0.889212i \(0.651253\pi\)
\(44\) 2.00000 0.301511
\(45\) 0 0
\(46\) 8.00000 1.17954
\(47\) 8.00000 1.16692 0.583460 0.812142i \(-0.301699\pi\)
0.583460 + 0.812142i \(0.301699\pi\)
\(48\) 0 0
\(49\) −3.00000 −0.428571
\(50\) 1.00000 0.141421
\(51\) 0 0
\(52\) 0 0
\(53\) 10.0000 1.37361 0.686803 0.726844i \(-0.259014\pi\)
0.686803 + 0.726844i \(0.259014\pi\)
\(54\) 0 0
\(55\) −2.00000 −0.269680
\(56\) −2.00000 −0.267261
\(57\) 0 0
\(58\) 0 0
\(59\) 8.00000 1.04151 0.520756 0.853706i \(-0.325650\pi\)
0.520756 + 0.853706i \(0.325650\pi\)
\(60\) 0 0
\(61\) 2.00000 0.256074 0.128037 0.991769i \(-0.459132\pi\)
0.128037 + 0.991769i \(0.459132\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(68\) 2.00000 0.242536
\(69\) 0 0
\(70\) 2.00000 0.239046
\(71\) −8.00000 −0.949425 −0.474713 0.880141i \(-0.657448\pi\)
−0.474713 + 0.880141i \(0.657448\pi\)
\(72\) 0 0
\(73\) −2.00000 −0.234082 −0.117041 0.993127i \(-0.537341\pi\)
−0.117041 + 0.993127i \(0.537341\pi\)
\(74\) 4.00000 0.464991
\(75\) 0 0
\(76\) 1.00000 0.114708
\(77\) −4.00000 −0.455842
\(78\) 0 0
\(79\) −8.00000 −0.900070 −0.450035 0.893011i \(-0.648589\pi\)
−0.450035 + 0.893011i \(0.648589\pi\)
\(80\) −1.00000 −0.111803
\(81\) 0 0
\(82\) 8.00000 0.883452
\(83\) 16.0000 1.75623 0.878114 0.478451i \(-0.158802\pi\)
0.878114 + 0.478451i \(0.158802\pi\)
\(84\) 0 0
\(85\) −2.00000 −0.216930
\(86\) −6.00000 −0.646997
\(87\) 0 0
\(88\) 2.00000 0.213201
\(89\) −16.0000 −1.69600 −0.847998 0.529999i \(-0.822192\pi\)
−0.847998 + 0.529999i \(0.822192\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 8.00000 0.834058
\(93\) 0 0
\(94\) 8.00000 0.825137
\(95\) −1.00000 −0.102598
\(96\) 0 0
\(97\) 8.00000 0.812277 0.406138 0.913812i \(-0.366875\pi\)
0.406138 + 0.913812i \(0.366875\pi\)
\(98\) −3.00000 −0.303046
\(99\) 0 0
\(100\) 1.00000 0.100000
\(101\) −2.00000 −0.199007 −0.0995037 0.995037i \(-0.531726\pi\)
−0.0995037 + 0.995037i \(0.531726\pi\)
\(102\) 0 0
\(103\) 12.0000 1.18240 0.591198 0.806527i \(-0.298655\pi\)
0.591198 + 0.806527i \(0.298655\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 10.0000 0.971286
\(107\) −20.0000 −1.93347 −0.966736 0.255774i \(-0.917670\pi\)
−0.966736 + 0.255774i \(0.917670\pi\)
\(108\) 0 0
\(109\) 2.00000 0.191565 0.0957826 0.995402i \(-0.469465\pi\)
0.0957826 + 0.995402i \(0.469465\pi\)
\(110\) −2.00000 −0.190693
\(111\) 0 0
\(112\) −2.00000 −0.188982
\(113\) 2.00000 0.188144 0.0940721 0.995565i \(-0.470012\pi\)
0.0940721 + 0.995565i \(0.470012\pi\)
\(114\) 0 0
\(115\) −8.00000 −0.746004
\(116\) 0 0
\(117\) 0 0
\(118\) 8.00000 0.736460
\(119\) −4.00000 −0.366679
\(120\) 0 0
\(121\) −7.00000 −0.636364
\(122\) 2.00000 0.181071
\(123\) 0 0
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 16.0000 1.41977 0.709885 0.704317i \(-0.248747\pi\)
0.709885 + 0.704317i \(0.248747\pi\)
\(128\) 1.00000 0.0883883
\(129\) 0 0
\(130\) 0 0
\(131\) 6.00000 0.524222 0.262111 0.965038i \(-0.415581\pi\)
0.262111 + 0.965038i \(0.415581\pi\)
\(132\) 0 0
\(133\) −2.00000 −0.173422
\(134\) 0 0
\(135\) 0 0
\(136\) 2.00000 0.171499
\(137\) −18.0000 −1.53784 −0.768922 0.639343i \(-0.779207\pi\)
−0.768922 + 0.639343i \(0.779207\pi\)
\(138\) 0 0
\(139\) 8.00000 0.678551 0.339276 0.940687i \(-0.389818\pi\)
0.339276 + 0.940687i \(0.389818\pi\)
\(140\) 2.00000 0.169031
\(141\) 0 0
\(142\) −8.00000 −0.671345
\(143\) 0 0
\(144\) 0 0
\(145\) 0 0
\(146\) −2.00000 −0.165521
\(147\) 0 0
\(148\) 4.00000 0.328798
\(149\) −2.00000 −0.163846 −0.0819232 0.996639i \(-0.526106\pi\)
−0.0819232 + 0.996639i \(0.526106\pi\)
\(150\) 0 0
\(151\) −8.00000 −0.651031 −0.325515 0.945537i \(-0.605538\pi\)
−0.325515 + 0.945537i \(0.605538\pi\)
\(152\) 1.00000 0.0811107
\(153\) 0 0
\(154\) −4.00000 −0.322329
\(155\) 0 0
\(156\) 0 0
\(157\) −6.00000 −0.478852 −0.239426 0.970915i \(-0.576959\pi\)
−0.239426 + 0.970915i \(0.576959\pi\)
\(158\) −8.00000 −0.636446
\(159\) 0 0
\(160\) −1.00000 −0.0790569
\(161\) −16.0000 −1.26098
\(162\) 0 0
\(163\) −10.0000 −0.783260 −0.391630 0.920123i \(-0.628089\pi\)
−0.391630 + 0.920123i \(0.628089\pi\)
\(164\) 8.00000 0.624695
\(165\) 0 0
\(166\) 16.0000 1.24184
\(167\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(168\) 0 0
\(169\) −13.0000 −1.00000
\(170\) −2.00000 −0.153393
\(171\) 0 0
\(172\) −6.00000 −0.457496
\(173\) 6.00000 0.456172 0.228086 0.973641i \(-0.426753\pi\)
0.228086 + 0.973641i \(0.426753\pi\)
\(174\) 0 0
\(175\) −2.00000 −0.151186
\(176\) 2.00000 0.150756
\(177\) 0 0
\(178\) −16.0000 −1.19925
\(179\) 8.00000 0.597948 0.298974 0.954261i \(-0.403356\pi\)
0.298974 + 0.954261i \(0.403356\pi\)
\(180\) 0 0
\(181\) −6.00000 −0.445976 −0.222988 0.974821i \(-0.571581\pi\)
−0.222988 + 0.974821i \(0.571581\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 8.00000 0.589768
\(185\) −4.00000 −0.294086
\(186\) 0 0
\(187\) 4.00000 0.292509
\(188\) 8.00000 0.583460
\(189\) 0 0
\(190\) −1.00000 −0.0725476
\(191\) −10.0000 −0.723575 −0.361787 0.932261i \(-0.617833\pi\)
−0.361787 + 0.932261i \(0.617833\pi\)
\(192\) 0 0
\(193\) −4.00000 −0.287926 −0.143963 0.989583i \(-0.545985\pi\)
−0.143963 + 0.989583i \(0.545985\pi\)
\(194\) 8.00000 0.574367
\(195\) 0 0
\(196\) −3.00000 −0.214286
\(197\) −10.0000 −0.712470 −0.356235 0.934396i \(-0.615940\pi\)
−0.356235 + 0.934396i \(0.615940\pi\)
\(198\) 0 0
\(199\) −4.00000 −0.283552 −0.141776 0.989899i \(-0.545281\pi\)
−0.141776 + 0.989899i \(0.545281\pi\)
\(200\) 1.00000 0.0707107
\(201\) 0 0
\(202\) −2.00000 −0.140720
\(203\) 0 0
\(204\) 0 0
\(205\) −8.00000 −0.558744
\(206\) 12.0000 0.836080
\(207\) 0 0
\(208\) 0 0
\(209\) 2.00000 0.138343
\(210\) 0 0
\(211\) 4.00000 0.275371 0.137686 0.990476i \(-0.456034\pi\)
0.137686 + 0.990476i \(0.456034\pi\)
\(212\) 10.0000 0.686803
\(213\) 0 0
\(214\) −20.0000 −1.36717
\(215\) 6.00000 0.409197
\(216\) 0 0
\(217\) 0 0
\(218\) 2.00000 0.135457
\(219\) 0 0
\(220\) −2.00000 −0.134840
\(221\) 0 0
\(222\) 0 0
\(223\) 12.0000 0.803579 0.401790 0.915732i \(-0.368388\pi\)
0.401790 + 0.915732i \(0.368388\pi\)
\(224\) −2.00000 −0.133631
\(225\) 0 0
\(226\) 2.00000 0.133038
\(227\) 4.00000 0.265489 0.132745 0.991150i \(-0.457621\pi\)
0.132745 + 0.991150i \(0.457621\pi\)
\(228\) 0 0
\(229\) 10.0000 0.660819 0.330409 0.943838i \(-0.392813\pi\)
0.330409 + 0.943838i \(0.392813\pi\)
\(230\) −8.00000 −0.527504
\(231\) 0 0
\(232\) 0 0
\(233\) 6.00000 0.393073 0.196537 0.980497i \(-0.437031\pi\)
0.196537 + 0.980497i \(0.437031\pi\)
\(234\) 0 0
\(235\) −8.00000 −0.521862
\(236\) 8.00000 0.520756
\(237\) 0 0
\(238\) −4.00000 −0.259281
\(239\) −6.00000 −0.388108 −0.194054 0.980991i \(-0.562164\pi\)
−0.194054 + 0.980991i \(0.562164\pi\)
\(240\) 0 0
\(241\) 10.0000 0.644157 0.322078 0.946713i \(-0.395619\pi\)
0.322078 + 0.946713i \(0.395619\pi\)
\(242\) −7.00000 −0.449977
\(243\) 0 0
\(244\) 2.00000 0.128037
\(245\) 3.00000 0.191663
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) −1.00000 −0.0632456
\(251\) −6.00000 −0.378717 −0.189358 0.981908i \(-0.560641\pi\)
−0.189358 + 0.981908i \(0.560641\pi\)
\(252\) 0 0
\(253\) 16.0000 1.00591
\(254\) 16.0000 1.00393
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −30.0000 −1.87135 −0.935674 0.352865i \(-0.885208\pi\)
−0.935674 + 0.352865i \(0.885208\pi\)
\(258\) 0 0
\(259\) −8.00000 −0.497096
\(260\) 0 0
\(261\) 0 0
\(262\) 6.00000 0.370681
\(263\) 12.0000 0.739952 0.369976 0.929041i \(-0.379366\pi\)
0.369976 + 0.929041i \(0.379366\pi\)
\(264\) 0 0
\(265\) −10.0000 −0.614295
\(266\) −2.00000 −0.122628
\(267\) 0 0
\(268\) 0 0
\(269\) −8.00000 −0.487769 −0.243884 0.969804i \(-0.578422\pi\)
−0.243884 + 0.969804i \(0.578422\pi\)
\(270\) 0 0
\(271\) −4.00000 −0.242983 −0.121491 0.992592i \(-0.538768\pi\)
−0.121491 + 0.992592i \(0.538768\pi\)
\(272\) 2.00000 0.121268
\(273\) 0 0
\(274\) −18.0000 −1.08742
\(275\) 2.00000 0.120605
\(276\) 0 0
\(277\) −14.0000 −0.841178 −0.420589 0.907251i \(-0.638177\pi\)
−0.420589 + 0.907251i \(0.638177\pi\)
\(278\) 8.00000 0.479808
\(279\) 0 0
\(280\) 2.00000 0.119523
\(281\) 20.0000 1.19310 0.596550 0.802576i \(-0.296538\pi\)
0.596550 + 0.802576i \(0.296538\pi\)
\(282\) 0 0
\(283\) −2.00000 −0.118888 −0.0594438 0.998232i \(-0.518933\pi\)
−0.0594438 + 0.998232i \(0.518933\pi\)
\(284\) −8.00000 −0.474713
\(285\) 0 0
\(286\) 0 0
\(287\) −16.0000 −0.944450
\(288\) 0 0
\(289\) −13.0000 −0.764706
\(290\) 0 0
\(291\) 0 0
\(292\) −2.00000 −0.117041
\(293\) 22.0000 1.28525 0.642627 0.766179i \(-0.277845\pi\)
0.642627 + 0.766179i \(0.277845\pi\)
\(294\) 0 0
\(295\) −8.00000 −0.465778
\(296\) 4.00000 0.232495
\(297\) 0 0
\(298\) −2.00000 −0.115857
\(299\) 0 0
\(300\) 0 0
\(301\) 12.0000 0.691669
\(302\) −8.00000 −0.460348
\(303\) 0 0
\(304\) 1.00000 0.0573539
\(305\) −2.00000 −0.114520
\(306\) 0 0
\(307\) −24.0000 −1.36975 −0.684876 0.728659i \(-0.740144\pi\)
−0.684876 + 0.728659i \(0.740144\pi\)
\(308\) −4.00000 −0.227921
\(309\) 0 0
\(310\) 0 0
\(311\) 14.0000 0.793867 0.396934 0.917847i \(-0.370074\pi\)
0.396934 + 0.917847i \(0.370074\pi\)
\(312\) 0 0
\(313\) 18.0000 1.01742 0.508710 0.860938i \(-0.330123\pi\)
0.508710 + 0.860938i \(0.330123\pi\)
\(314\) −6.00000 −0.338600
\(315\) 0 0
\(316\) −8.00000 −0.450035
\(317\) −6.00000 −0.336994 −0.168497 0.985702i \(-0.553891\pi\)
−0.168497 + 0.985702i \(0.553891\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −1.00000 −0.0559017
\(321\) 0 0
\(322\) −16.0000 −0.891645
\(323\) 2.00000 0.111283
\(324\) 0 0
\(325\) 0 0
\(326\) −10.0000 −0.553849
\(327\) 0 0
\(328\) 8.00000 0.441726
\(329\) −16.0000 −0.882109
\(330\) 0 0
\(331\) −12.0000 −0.659580 −0.329790 0.944054i \(-0.606978\pi\)
−0.329790 + 0.944054i \(0.606978\pi\)
\(332\) 16.0000 0.878114
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −16.0000 −0.871576 −0.435788 0.900049i \(-0.643530\pi\)
−0.435788 + 0.900049i \(0.643530\pi\)
\(338\) −13.0000 −0.707107
\(339\) 0 0
\(340\) −2.00000 −0.108465
\(341\) 0 0
\(342\) 0 0
\(343\) 20.0000 1.07990
\(344\) −6.00000 −0.323498
\(345\) 0 0
\(346\) 6.00000 0.322562
\(347\) 8.00000 0.429463 0.214731 0.976673i \(-0.431112\pi\)
0.214731 + 0.976673i \(0.431112\pi\)
\(348\) 0 0
\(349\) −26.0000 −1.39175 −0.695874 0.718164i \(-0.744983\pi\)
−0.695874 + 0.718164i \(0.744983\pi\)
\(350\) −2.00000 −0.106904
\(351\) 0 0
\(352\) 2.00000 0.106600
\(353\) −18.0000 −0.958043 −0.479022 0.877803i \(-0.659008\pi\)
−0.479022 + 0.877803i \(0.659008\pi\)
\(354\) 0 0
\(355\) 8.00000 0.424596
\(356\) −16.0000 −0.847998
\(357\) 0 0
\(358\) 8.00000 0.422813
\(359\) 30.0000 1.58334 0.791670 0.610949i \(-0.209212\pi\)
0.791670 + 0.610949i \(0.209212\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) −6.00000 −0.315353
\(363\) 0 0
\(364\) 0 0
\(365\) 2.00000 0.104685
\(366\) 0 0
\(367\) 26.0000 1.35719 0.678594 0.734513i \(-0.262589\pi\)
0.678594 + 0.734513i \(0.262589\pi\)
\(368\) 8.00000 0.417029
\(369\) 0 0
\(370\) −4.00000 −0.207950
\(371\) −20.0000 −1.03835
\(372\) 0 0
\(373\) 32.0000 1.65690 0.828449 0.560065i \(-0.189224\pi\)
0.828449 + 0.560065i \(0.189224\pi\)
\(374\) 4.00000 0.206835
\(375\) 0 0
\(376\) 8.00000 0.412568
\(377\) 0 0
\(378\) 0 0
\(379\) −28.0000 −1.43826 −0.719132 0.694874i \(-0.755460\pi\)
−0.719132 + 0.694874i \(0.755460\pi\)
\(380\) −1.00000 −0.0512989
\(381\) 0 0
\(382\) −10.0000 −0.511645
\(383\) −8.00000 −0.408781 −0.204390 0.978889i \(-0.565521\pi\)
−0.204390 + 0.978889i \(0.565521\pi\)
\(384\) 0 0
\(385\) 4.00000 0.203859
\(386\) −4.00000 −0.203595
\(387\) 0 0
\(388\) 8.00000 0.406138
\(389\) −14.0000 −0.709828 −0.354914 0.934899i \(-0.615490\pi\)
−0.354914 + 0.934899i \(0.615490\pi\)
\(390\) 0 0
\(391\) 16.0000 0.809155
\(392\) −3.00000 −0.151523
\(393\) 0 0
\(394\) −10.0000 −0.503793
\(395\) 8.00000 0.402524
\(396\) 0 0
\(397\) −6.00000 −0.301131 −0.150566 0.988600i \(-0.548110\pi\)
−0.150566 + 0.988600i \(0.548110\pi\)
\(398\) −4.00000 −0.200502
\(399\) 0 0
\(400\) 1.00000 0.0500000
\(401\) 12.0000 0.599251 0.299626 0.954057i \(-0.403138\pi\)
0.299626 + 0.954057i \(0.403138\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) −2.00000 −0.0995037
\(405\) 0 0
\(406\) 0 0
\(407\) 8.00000 0.396545
\(408\) 0 0
\(409\) −18.0000 −0.890043 −0.445021 0.895520i \(-0.646804\pi\)
−0.445021 + 0.895520i \(0.646804\pi\)
\(410\) −8.00000 −0.395092
\(411\) 0 0
\(412\) 12.0000 0.591198
\(413\) −16.0000 −0.787309
\(414\) 0 0
\(415\) −16.0000 −0.785409
\(416\) 0 0
\(417\) 0 0
\(418\) 2.00000 0.0978232
\(419\) −30.0000 −1.46560 −0.732798 0.680446i \(-0.761786\pi\)
−0.732798 + 0.680446i \(0.761786\pi\)
\(420\) 0 0
\(421\) −26.0000 −1.26716 −0.633581 0.773676i \(-0.718416\pi\)
−0.633581 + 0.773676i \(0.718416\pi\)
\(422\) 4.00000 0.194717
\(423\) 0 0
\(424\) 10.0000 0.485643
\(425\) 2.00000 0.0970143
\(426\) 0 0
\(427\) −4.00000 −0.193574
\(428\) −20.0000 −0.966736
\(429\) 0 0
\(430\) 6.00000 0.289346
\(431\) −20.0000 −0.963366 −0.481683 0.876346i \(-0.659974\pi\)
−0.481683 + 0.876346i \(0.659974\pi\)
\(432\) 0 0
\(433\) −12.0000 −0.576683 −0.288342 0.957528i \(-0.593104\pi\)
−0.288342 + 0.957528i \(0.593104\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 2.00000 0.0957826
\(437\) 8.00000 0.382692
\(438\) 0 0
\(439\) 16.0000 0.763638 0.381819 0.924237i \(-0.375298\pi\)
0.381819 + 0.924237i \(0.375298\pi\)
\(440\) −2.00000 −0.0953463
\(441\) 0 0
\(442\) 0 0
\(443\) −12.0000 −0.570137 −0.285069 0.958507i \(-0.592016\pi\)
−0.285069 + 0.958507i \(0.592016\pi\)
\(444\) 0 0
\(445\) 16.0000 0.758473
\(446\) 12.0000 0.568216
\(447\) 0 0
\(448\) −2.00000 −0.0944911
\(449\) −24.0000 −1.13263 −0.566315 0.824189i \(-0.691631\pi\)
−0.566315 + 0.824189i \(0.691631\pi\)
\(450\) 0 0
\(451\) 16.0000 0.753411
\(452\) 2.00000 0.0940721
\(453\) 0 0
\(454\) 4.00000 0.187729
\(455\) 0 0
\(456\) 0 0
\(457\) −22.0000 −1.02912 −0.514558 0.857455i \(-0.672044\pi\)
−0.514558 + 0.857455i \(0.672044\pi\)
\(458\) 10.0000 0.467269
\(459\) 0 0
\(460\) −8.00000 −0.373002
\(461\) 6.00000 0.279448 0.139724 0.990190i \(-0.455378\pi\)
0.139724 + 0.990190i \(0.455378\pi\)
\(462\) 0 0
\(463\) 18.0000 0.836531 0.418265 0.908325i \(-0.362638\pi\)
0.418265 + 0.908325i \(0.362638\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 6.00000 0.277945
\(467\) −20.0000 −0.925490 −0.462745 0.886492i \(-0.653135\pi\)
−0.462745 + 0.886492i \(0.653135\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −8.00000 −0.369012
\(471\) 0 0
\(472\) 8.00000 0.368230
\(473\) −12.0000 −0.551761
\(474\) 0 0
\(475\) 1.00000 0.0458831
\(476\) −4.00000 −0.183340
\(477\) 0 0
\(478\) −6.00000 −0.274434
\(479\) 30.0000 1.37073 0.685367 0.728197i \(-0.259642\pi\)
0.685367 + 0.728197i \(0.259642\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 10.0000 0.455488
\(483\) 0 0
\(484\) −7.00000 −0.318182
\(485\) −8.00000 −0.363261
\(486\) 0 0
\(487\) 20.0000 0.906287 0.453143 0.891438i \(-0.350303\pi\)
0.453143 + 0.891438i \(0.350303\pi\)
\(488\) 2.00000 0.0905357
\(489\) 0 0
\(490\) 3.00000 0.135526
\(491\) 30.0000 1.35388 0.676941 0.736038i \(-0.263305\pi\)
0.676941 + 0.736038i \(0.263305\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 16.0000 0.717698
\(498\) 0 0
\(499\) −16.0000 −0.716258 −0.358129 0.933672i \(-0.616585\pi\)
−0.358129 + 0.933672i \(0.616585\pi\)
\(500\) −1.00000 −0.0447214
\(501\) 0 0
\(502\) −6.00000 −0.267793
\(503\) −28.0000 −1.24846 −0.624229 0.781241i \(-0.714587\pi\)
−0.624229 + 0.781241i \(0.714587\pi\)
\(504\) 0 0
\(505\) 2.00000 0.0889988
\(506\) 16.0000 0.711287
\(507\) 0 0
\(508\) 16.0000 0.709885
\(509\) −20.0000 −0.886484 −0.443242 0.896402i \(-0.646172\pi\)
−0.443242 + 0.896402i \(0.646172\pi\)
\(510\) 0 0
\(511\) 4.00000 0.176950
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) −30.0000 −1.32324
\(515\) −12.0000 −0.528783
\(516\) 0 0
\(517\) 16.0000 0.703679
\(518\) −8.00000 −0.351500
\(519\) 0 0
\(520\) 0 0
\(521\) 20.0000 0.876216 0.438108 0.898922i \(-0.355649\pi\)
0.438108 + 0.898922i \(0.355649\pi\)
\(522\) 0 0
\(523\) 28.0000 1.22435 0.612177 0.790721i \(-0.290294\pi\)
0.612177 + 0.790721i \(0.290294\pi\)
\(524\) 6.00000 0.262111
\(525\) 0 0
\(526\) 12.0000 0.523225
\(527\) 0 0
\(528\) 0 0
\(529\) 41.0000 1.78261
\(530\) −10.0000 −0.434372
\(531\) 0 0
\(532\) −2.00000 −0.0867110
\(533\) 0 0
\(534\) 0 0
\(535\) 20.0000 0.864675
\(536\) 0 0
\(537\) 0 0
\(538\) −8.00000 −0.344904
\(539\) −6.00000 −0.258438
\(540\) 0 0
\(541\) 14.0000 0.601907 0.300954 0.953639i \(-0.402695\pi\)
0.300954 + 0.953639i \(0.402695\pi\)
\(542\) −4.00000 −0.171815
\(543\) 0 0
\(544\) 2.00000 0.0857493
\(545\) −2.00000 −0.0856706
\(546\) 0 0
\(547\) −40.0000 −1.71028 −0.855138 0.518400i \(-0.826528\pi\)
−0.855138 + 0.518400i \(0.826528\pi\)
\(548\) −18.0000 −0.768922
\(549\) 0 0
\(550\) 2.00000 0.0852803
\(551\) 0 0
\(552\) 0 0
\(553\) 16.0000 0.680389
\(554\) −14.0000 −0.594803
\(555\) 0 0
\(556\) 8.00000 0.339276
\(557\) 2.00000 0.0847427 0.0423714 0.999102i \(-0.486509\pi\)
0.0423714 + 0.999102i \(0.486509\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 2.00000 0.0845154
\(561\) 0 0
\(562\) 20.0000 0.843649
\(563\) 36.0000 1.51722 0.758610 0.651546i \(-0.225879\pi\)
0.758610 + 0.651546i \(0.225879\pi\)
\(564\) 0 0
\(565\) −2.00000 −0.0841406
\(566\) −2.00000 −0.0840663
\(567\) 0 0
\(568\) −8.00000 −0.335673
\(569\) −24.0000 −1.00613 −0.503066 0.864248i \(-0.667795\pi\)
−0.503066 + 0.864248i \(0.667795\pi\)
\(570\) 0 0
\(571\) 32.0000 1.33916 0.669579 0.742741i \(-0.266474\pi\)
0.669579 + 0.742741i \(0.266474\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) −16.0000 −0.667827
\(575\) 8.00000 0.333623
\(576\) 0 0
\(577\) −14.0000 −0.582828 −0.291414 0.956597i \(-0.594126\pi\)
−0.291414 + 0.956597i \(0.594126\pi\)
\(578\) −13.0000 −0.540729
\(579\) 0 0
\(580\) 0 0
\(581\) −32.0000 −1.32758
\(582\) 0 0
\(583\) 20.0000 0.828315
\(584\) −2.00000 −0.0827606
\(585\) 0 0
\(586\) 22.0000 0.908812
\(587\) 44.0000 1.81607 0.908037 0.418890i \(-0.137581\pi\)
0.908037 + 0.418890i \(0.137581\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) −8.00000 −0.329355
\(591\) 0 0
\(592\) 4.00000 0.164399
\(593\) −34.0000 −1.39621 −0.698106 0.715994i \(-0.745974\pi\)
−0.698106 + 0.715994i \(0.745974\pi\)
\(594\) 0 0
\(595\) 4.00000 0.163984
\(596\) −2.00000 −0.0819232
\(597\) 0 0
\(598\) 0 0
\(599\) 4.00000 0.163436 0.0817178 0.996656i \(-0.473959\pi\)
0.0817178 + 0.996656i \(0.473959\pi\)
\(600\) 0 0
\(601\) −42.0000 −1.71322 −0.856608 0.515968i \(-0.827432\pi\)
−0.856608 + 0.515968i \(0.827432\pi\)
\(602\) 12.0000 0.489083
\(603\) 0 0
\(604\) −8.00000 −0.325515
\(605\) 7.00000 0.284590
\(606\) 0 0
\(607\) 44.0000 1.78590 0.892952 0.450151i \(-0.148630\pi\)
0.892952 + 0.450151i \(0.148630\pi\)
\(608\) 1.00000 0.0405554
\(609\) 0 0
\(610\) −2.00000 −0.0809776
\(611\) 0 0
\(612\) 0 0
\(613\) −46.0000 −1.85792 −0.928961 0.370177i \(-0.879297\pi\)
−0.928961 + 0.370177i \(0.879297\pi\)
\(614\) −24.0000 −0.968561
\(615\) 0 0
\(616\) −4.00000 −0.161165
\(617\) 42.0000 1.69086 0.845428 0.534089i \(-0.179345\pi\)
0.845428 + 0.534089i \(0.179345\pi\)
\(618\) 0 0
\(619\) −32.0000 −1.28619 −0.643094 0.765787i \(-0.722350\pi\)
−0.643094 + 0.765787i \(0.722350\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 14.0000 0.561349
\(623\) 32.0000 1.28205
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 18.0000 0.719425
\(627\) 0 0
\(628\) −6.00000 −0.239426
\(629\) 8.00000 0.318981
\(630\) 0 0
\(631\) −40.0000 −1.59237 −0.796187 0.605050i \(-0.793153\pi\)
−0.796187 + 0.605050i \(0.793153\pi\)
\(632\) −8.00000 −0.318223
\(633\) 0 0
\(634\) −6.00000 −0.238290
\(635\) −16.0000 −0.634941
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) −1.00000 −0.0395285
\(641\) −16.0000 −0.631962 −0.315981 0.948766i \(-0.602334\pi\)
−0.315981 + 0.948766i \(0.602334\pi\)
\(642\) 0 0
\(643\) 46.0000 1.81406 0.907031 0.421063i \(-0.138343\pi\)
0.907031 + 0.421063i \(0.138343\pi\)
\(644\) −16.0000 −0.630488
\(645\) 0 0
\(646\) 2.00000 0.0786889
\(647\) −36.0000 −1.41531 −0.707653 0.706560i \(-0.750246\pi\)
−0.707653 + 0.706560i \(0.750246\pi\)
\(648\) 0 0
\(649\) 16.0000 0.628055
\(650\) 0 0
\(651\) 0 0
\(652\) −10.0000 −0.391630
\(653\) 30.0000 1.17399 0.586995 0.809590i \(-0.300311\pi\)
0.586995 + 0.809590i \(0.300311\pi\)
\(654\) 0 0
\(655\) −6.00000 −0.234439
\(656\) 8.00000 0.312348
\(657\) 0 0
\(658\) −16.0000 −0.623745
\(659\) 44.0000 1.71400 0.856998 0.515319i \(-0.172327\pi\)
0.856998 + 0.515319i \(0.172327\pi\)
\(660\) 0 0
\(661\) −38.0000 −1.47803 −0.739014 0.673690i \(-0.764708\pi\)
−0.739014 + 0.673690i \(0.764708\pi\)
\(662\) −12.0000 −0.466393
\(663\) 0 0
\(664\) 16.0000 0.620920
\(665\) 2.00000 0.0775567
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 4.00000 0.154418
\(672\) 0 0
\(673\) −16.0000 −0.616755 −0.308377 0.951264i \(-0.599786\pi\)
−0.308377 + 0.951264i \(0.599786\pi\)
\(674\) −16.0000 −0.616297
\(675\) 0 0
\(676\) −13.0000 −0.500000
\(677\) 18.0000 0.691796 0.345898 0.938272i \(-0.387574\pi\)
0.345898 + 0.938272i \(0.387574\pi\)
\(678\) 0 0
\(679\) −16.0000 −0.614024
\(680\) −2.00000 −0.0766965
\(681\) 0 0
\(682\) 0 0
\(683\) 36.0000 1.37750 0.688751 0.724998i \(-0.258159\pi\)
0.688751 + 0.724998i \(0.258159\pi\)
\(684\) 0 0
\(685\) 18.0000 0.687745
\(686\) 20.0000 0.763604
\(687\) 0 0
\(688\) −6.00000 −0.228748
\(689\) 0 0
\(690\) 0 0
\(691\) 40.0000 1.52167 0.760836 0.648944i \(-0.224789\pi\)
0.760836 + 0.648944i \(0.224789\pi\)
\(692\) 6.00000 0.228086
\(693\) 0 0
\(694\) 8.00000 0.303676
\(695\) −8.00000 −0.303457
\(696\) 0 0
\(697\) 16.0000 0.606043
\(698\) −26.0000 −0.984115
\(699\) 0 0
\(700\) −2.00000 −0.0755929
\(701\) 38.0000 1.43524 0.717620 0.696435i \(-0.245231\pi\)
0.717620 + 0.696435i \(0.245231\pi\)
\(702\) 0 0
\(703\) 4.00000 0.150863
\(704\) 2.00000 0.0753778
\(705\) 0 0
\(706\) −18.0000 −0.677439
\(707\) 4.00000 0.150435
\(708\) 0 0
\(709\) 26.0000 0.976450 0.488225 0.872718i \(-0.337644\pi\)
0.488225 + 0.872718i \(0.337644\pi\)
\(710\) 8.00000 0.300235
\(711\) 0 0
\(712\) −16.0000 −0.599625
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 8.00000 0.298974
\(717\) 0 0
\(718\) 30.0000 1.11959
\(719\) −22.0000 −0.820462 −0.410231 0.911982i \(-0.634552\pi\)
−0.410231 + 0.911982i \(0.634552\pi\)
\(720\) 0 0
\(721\) −24.0000 −0.893807
\(722\) 1.00000 0.0372161
\(723\) 0 0
\(724\) −6.00000 −0.222988
\(725\) 0 0
\(726\) 0 0
\(727\) −22.0000 −0.815935 −0.407967 0.912996i \(-0.633762\pi\)
−0.407967 + 0.912996i \(0.633762\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 2.00000 0.0740233
\(731\) −12.0000 −0.443836
\(732\) 0 0
\(733\) −26.0000 −0.960332 −0.480166 0.877178i \(-0.659424\pi\)
−0.480166 + 0.877178i \(0.659424\pi\)
\(734\) 26.0000 0.959678
\(735\) 0 0
\(736\) 8.00000 0.294884
\(737\) 0 0
\(738\) 0 0
\(739\) −20.0000 −0.735712 −0.367856 0.929883i \(-0.619908\pi\)
−0.367856 + 0.929883i \(0.619908\pi\)
\(740\) −4.00000 −0.147043
\(741\) 0 0
\(742\) −20.0000 −0.734223
\(743\) −24.0000 −0.880475 −0.440237 0.897881i \(-0.645106\pi\)
−0.440237 + 0.897881i \(0.645106\pi\)
\(744\) 0 0
\(745\) 2.00000 0.0732743
\(746\) 32.0000 1.17160
\(747\) 0 0
\(748\) 4.00000 0.146254
\(749\) 40.0000 1.46157
\(750\) 0 0
\(751\) −8.00000 −0.291924 −0.145962 0.989290i \(-0.546628\pi\)
−0.145962 + 0.989290i \(0.546628\pi\)
\(752\) 8.00000 0.291730
\(753\) 0 0
\(754\) 0 0
\(755\) 8.00000 0.291150
\(756\) 0 0
\(757\) 38.0000 1.38113 0.690567 0.723269i \(-0.257361\pi\)
0.690567 + 0.723269i \(0.257361\pi\)
\(758\) −28.0000 −1.01701
\(759\) 0 0
\(760\) −1.00000 −0.0362738
\(761\) 10.0000 0.362500 0.181250 0.983437i \(-0.441986\pi\)
0.181250 + 0.983437i \(0.441986\pi\)
\(762\) 0 0
\(763\) −4.00000 −0.144810
\(764\) −10.0000 −0.361787
\(765\) 0 0
\(766\) −8.00000 −0.289052
\(767\) 0 0
\(768\) 0 0
\(769\) 18.0000 0.649097 0.324548 0.945869i \(-0.394788\pi\)
0.324548 + 0.945869i \(0.394788\pi\)
\(770\) 4.00000 0.144150
\(771\) 0 0
\(772\) −4.00000 −0.143963
\(773\) 42.0000 1.51064 0.755318 0.655359i \(-0.227483\pi\)
0.755318 + 0.655359i \(0.227483\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 8.00000 0.287183
\(777\) 0 0
\(778\) −14.0000 −0.501924
\(779\) 8.00000 0.286630
\(780\) 0 0
\(781\) −16.0000 −0.572525
\(782\) 16.0000 0.572159
\(783\) 0 0
\(784\) −3.00000 −0.107143
\(785\) 6.00000 0.214149
\(786\) 0 0
\(787\) 52.0000 1.85360 0.926800 0.375555i \(-0.122548\pi\)
0.926800 + 0.375555i \(0.122548\pi\)
\(788\) −10.0000 −0.356235
\(789\) 0 0
\(790\) 8.00000 0.284627
\(791\) −4.00000 −0.142224
\(792\) 0 0
\(793\) 0 0
\(794\) −6.00000 −0.212932
\(795\) 0 0
\(796\) −4.00000 −0.141776
\(797\) 22.0000 0.779280 0.389640 0.920967i \(-0.372599\pi\)
0.389640 + 0.920967i \(0.372599\pi\)
\(798\) 0 0
\(799\) 16.0000 0.566039
\(800\) 1.00000 0.0353553
\(801\) 0 0
\(802\) 12.0000 0.423735
\(803\) −4.00000 −0.141157
\(804\) 0 0
\(805\) 16.0000 0.563926
\(806\) 0 0
\(807\) 0 0
\(808\) −2.00000 −0.0703598
\(809\) −18.0000 −0.632846 −0.316423 0.948618i \(-0.602482\pi\)
−0.316423 + 0.948618i \(0.602482\pi\)
\(810\) 0 0
\(811\) 28.0000 0.983213 0.491606 0.870817i \(-0.336410\pi\)
0.491606 + 0.870817i \(0.336410\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 8.00000 0.280400
\(815\) 10.0000 0.350285
\(816\) 0 0
\(817\) −6.00000 −0.209913
\(818\) −18.0000 −0.629355
\(819\) 0 0
\(820\) −8.00000 −0.279372
\(821\) 6.00000 0.209401 0.104701 0.994504i \(-0.466612\pi\)
0.104701 + 0.994504i \(0.466612\pi\)
\(822\) 0 0
\(823\) 34.0000 1.18517 0.592583 0.805510i \(-0.298108\pi\)
0.592583 + 0.805510i \(0.298108\pi\)
\(824\) 12.0000 0.418040
\(825\) 0 0
\(826\) −16.0000 −0.556711
\(827\) −12.0000 −0.417281 −0.208640 0.977992i \(-0.566904\pi\)
−0.208640 + 0.977992i \(0.566904\pi\)
\(828\) 0 0
\(829\) −46.0000 −1.59765 −0.798823 0.601566i \(-0.794544\pi\)
−0.798823 + 0.601566i \(0.794544\pi\)
\(830\) −16.0000 −0.555368
\(831\) 0 0
\(832\) 0 0
\(833\) −6.00000 −0.207888
\(834\) 0 0
\(835\) 0 0
\(836\) 2.00000 0.0691714
\(837\) 0 0
\(838\) −30.0000 −1.03633
\(839\) −24.0000 −0.828572 −0.414286 0.910147i \(-0.635969\pi\)
−0.414286 + 0.910147i \(0.635969\pi\)
\(840\) 0 0
\(841\) −29.0000 −1.00000
\(842\) −26.0000 −0.896019
\(843\) 0 0
\(844\) 4.00000 0.137686
\(845\) 13.0000 0.447214
\(846\) 0 0
\(847\) 14.0000 0.481046
\(848\) 10.0000 0.343401
\(849\) 0 0
\(850\) 2.00000 0.0685994
\(851\) 32.0000 1.09695
\(852\) 0 0
\(853\) 6.00000 0.205436 0.102718 0.994711i \(-0.467246\pi\)
0.102718 + 0.994711i \(0.467246\pi\)
\(854\) −4.00000 −0.136877
\(855\) 0 0
\(856\) −20.0000 −0.683586
\(857\) 30.0000 1.02478 0.512390 0.858753i \(-0.328760\pi\)
0.512390 + 0.858753i \(0.328760\pi\)
\(858\) 0 0
\(859\) −20.0000 −0.682391 −0.341196 0.939992i \(-0.610832\pi\)
−0.341196 + 0.939992i \(0.610832\pi\)
\(860\) 6.00000 0.204598
\(861\) 0 0
\(862\) −20.0000 −0.681203
\(863\) 16.0000 0.544646 0.272323 0.962206i \(-0.412208\pi\)
0.272323 + 0.962206i \(0.412208\pi\)
\(864\) 0 0
\(865\) −6.00000 −0.204006
\(866\) −12.0000 −0.407777
\(867\) 0 0
\(868\) 0 0
\(869\) −16.0000 −0.542763
\(870\) 0 0
\(871\) 0 0
\(872\) 2.00000 0.0677285
\(873\) 0 0
\(874\) 8.00000 0.270604
\(875\) 2.00000 0.0676123
\(876\) 0 0
\(877\) 8.00000 0.270141 0.135070 0.990836i \(-0.456874\pi\)
0.135070 + 0.990836i \(0.456874\pi\)
\(878\) 16.0000 0.539974
\(879\) 0 0
\(880\) −2.00000 −0.0674200
\(881\) −30.0000 −1.01073 −0.505363 0.862907i \(-0.668641\pi\)
−0.505363 + 0.862907i \(0.668641\pi\)
\(882\) 0 0
\(883\) −18.0000 −0.605748 −0.302874 0.953031i \(-0.597946\pi\)
−0.302874 + 0.953031i \(0.597946\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) −12.0000 −0.403148
\(887\) −24.0000 −0.805841 −0.402921 0.915235i \(-0.632005\pi\)
−0.402921 + 0.915235i \(0.632005\pi\)
\(888\) 0 0
\(889\) −32.0000 −1.07325
\(890\) 16.0000 0.536321
\(891\) 0 0
\(892\) 12.0000 0.401790
\(893\) 8.00000 0.267710
\(894\) 0 0
\(895\) −8.00000 −0.267411
\(896\) −2.00000 −0.0668153
\(897\) 0 0
\(898\) −24.0000 −0.800890
\(899\) 0 0
\(900\) 0 0
\(901\) 20.0000 0.666297
\(902\) 16.0000 0.532742
\(903\) 0 0
\(904\) 2.00000 0.0665190
\(905\) 6.00000 0.199447
\(906\) 0 0
\(907\) −44.0000 −1.46100 −0.730498 0.682915i \(-0.760712\pi\)
−0.730498 + 0.682915i \(0.760712\pi\)
\(908\) 4.00000 0.132745
\(909\) 0 0
\(910\) 0 0
\(911\) −48.0000 −1.59031 −0.795155 0.606406i \(-0.792611\pi\)
−0.795155 + 0.606406i \(0.792611\pi\)
\(912\) 0 0
\(913\) 32.0000 1.05905
\(914\) −22.0000 −0.727695
\(915\) 0 0
\(916\) 10.0000 0.330409
\(917\) −12.0000 −0.396275
\(918\) 0 0
\(919\) 40.0000 1.31948 0.659739 0.751495i \(-0.270667\pi\)
0.659739 + 0.751495i \(0.270667\pi\)
\(920\) −8.00000 −0.263752
\(921\) 0 0
\(922\) 6.00000 0.197599
\(923\) 0 0
\(924\) 0 0
\(925\) 4.00000 0.131519
\(926\) 18.0000 0.591517
\(927\) 0 0
\(928\) 0 0
\(929\) 6.00000 0.196854 0.0984268 0.995144i \(-0.468619\pi\)
0.0984268 + 0.995144i \(0.468619\pi\)
\(930\) 0 0
\(931\) −3.00000 −0.0983210
\(932\) 6.00000 0.196537
\(933\) 0 0
\(934\) −20.0000 −0.654420
\(935\) −4.00000 −0.130814
\(936\) 0 0
\(937\) −58.0000 −1.89478 −0.947389 0.320085i \(-0.896288\pi\)
−0.947389 + 0.320085i \(0.896288\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) −8.00000 −0.260931
\(941\) −16.0000 −0.521585 −0.260793 0.965395i \(-0.583984\pi\)
−0.260793 + 0.965395i \(0.583984\pi\)
\(942\) 0 0
\(943\) 64.0000 2.08413
\(944\) 8.00000 0.260378
\(945\) 0 0
\(946\) −12.0000 −0.390154
\(947\) 32.0000 1.03986 0.519930 0.854209i \(-0.325958\pi\)
0.519930 + 0.854209i \(0.325958\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 1.00000 0.0324443
\(951\) 0 0
\(952\) −4.00000 −0.129641
\(953\) 18.0000 0.583077 0.291539 0.956559i \(-0.405833\pi\)
0.291539 + 0.956559i \(0.405833\pi\)
\(954\) 0 0
\(955\) 10.0000 0.323592
\(956\) −6.00000 −0.194054
\(957\) 0 0
\(958\) 30.0000 0.969256
\(959\) 36.0000 1.16250
\(960\) 0 0
\(961\) −31.0000 −1.00000
\(962\) 0 0
\(963\) 0 0
\(964\) 10.0000 0.322078
\(965\) 4.00000 0.128765
\(966\) 0 0
\(967\) −6.00000 −0.192947 −0.0964735 0.995336i \(-0.530756\pi\)
−0.0964735 + 0.995336i \(0.530756\pi\)
\(968\) −7.00000 −0.224989
\(969\) 0 0
\(970\) −8.00000 −0.256865
\(971\) 36.0000 1.15529 0.577647 0.816286i \(-0.303971\pi\)
0.577647 + 0.816286i \(0.303971\pi\)
\(972\) 0 0
\(973\) −16.0000 −0.512936
\(974\) 20.0000 0.640841
\(975\) 0 0
\(976\) 2.00000 0.0640184
\(977\) −18.0000 −0.575871 −0.287936 0.957650i \(-0.592969\pi\)
−0.287936 + 0.957650i \(0.592969\pi\)
\(978\) 0 0
\(979\) −32.0000 −1.02272
\(980\) 3.00000 0.0958315
\(981\) 0 0
\(982\) 30.0000 0.957338
\(983\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(984\) 0 0
\(985\) 10.0000 0.318626
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −48.0000 −1.52631
\(990\) 0 0
\(991\) 40.0000 1.27064 0.635321 0.772248i \(-0.280868\pi\)
0.635321 + 0.772248i \(0.280868\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 16.0000 0.507489
\(995\) 4.00000 0.126809
\(996\) 0 0
\(997\) −22.0000 −0.696747 −0.348373 0.937356i \(-0.613266\pi\)
−0.348373 + 0.937356i \(0.613266\pi\)
\(998\) −16.0000 −0.506471
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1710.2.a.n.1.1 1
3.2 odd 2 570.2.a.c.1.1 1
5.4 even 2 8550.2.a.o.1.1 1
12.11 even 2 4560.2.a.bd.1.1 1
15.2 even 4 2850.2.d.n.799.1 2
15.8 even 4 2850.2.d.n.799.2 2
15.14 odd 2 2850.2.a.ba.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
570.2.a.c.1.1 1 3.2 odd 2
1710.2.a.n.1.1 1 1.1 even 1 trivial
2850.2.a.ba.1.1 1 15.14 odd 2
2850.2.d.n.799.1 2 15.2 even 4
2850.2.d.n.799.2 2 15.8 even 4
4560.2.a.bd.1.1 1 12.11 even 2
8550.2.a.o.1.1 1 5.4 even 2