Properties

Label 7350.2.a.bs.1.1
Level 7350
Weight 2
Character 7350.1
Self dual yes
Analytic conductor 58.690
Analytic rank 1
Dimension 1
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 7350 = 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7350.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(58.6900454856\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1050)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 7350.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -4.00000 q^{11} -1.00000 q^{12} +4.00000 q^{13} +1.00000 q^{16} +3.00000 q^{17} +1.00000 q^{18} -6.00000 q^{19} -4.00000 q^{22} -7.00000 q^{23} -1.00000 q^{24} +4.00000 q^{26} -1.00000 q^{27} +4.00000 q^{29} +5.00000 q^{31} +1.00000 q^{32} +4.00000 q^{33} +3.00000 q^{34} +1.00000 q^{36} -2.00000 q^{37} -6.00000 q^{38} -4.00000 q^{39} -7.00000 q^{41} -2.00000 q^{43} -4.00000 q^{44} -7.00000 q^{46} +1.00000 q^{47} -1.00000 q^{48} -3.00000 q^{51} +4.00000 q^{52} +2.00000 q^{53} -1.00000 q^{54} +6.00000 q^{57} +4.00000 q^{58} +14.0000 q^{59} -12.0000 q^{61} +5.00000 q^{62} +1.00000 q^{64} +4.00000 q^{66} -12.0000 q^{67} +3.00000 q^{68} +7.00000 q^{69} -9.00000 q^{71} +1.00000 q^{72} +6.00000 q^{73} -2.00000 q^{74} -6.00000 q^{76} -4.00000 q^{78} -17.0000 q^{79} +1.00000 q^{81} -7.00000 q^{82} -4.00000 q^{83} -2.00000 q^{86} -4.00000 q^{87} -4.00000 q^{88} +7.00000 q^{89} -7.00000 q^{92} -5.00000 q^{93} +1.00000 q^{94} -1.00000 q^{96} -7.00000 q^{97} -4.00000 q^{99} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −1.00000 −0.577350
\(4\) 1.00000 0.500000
\(5\) 0 0
\(6\) −1.00000 −0.408248
\(7\) 0 0
\(8\) 1.00000 0.353553
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −4.00000 −1.20605 −0.603023 0.797724i \(-0.706037\pi\)
−0.603023 + 0.797724i \(0.706037\pi\)
\(12\) −1.00000 −0.288675
\(13\) 4.00000 1.10940 0.554700 0.832050i \(-0.312833\pi\)
0.554700 + 0.832050i \(0.312833\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 3.00000 0.727607 0.363803 0.931476i \(-0.381478\pi\)
0.363803 + 0.931476i \(0.381478\pi\)
\(18\) 1.00000 0.235702
\(19\) −6.00000 −1.37649 −0.688247 0.725476i \(-0.741620\pi\)
−0.688247 + 0.725476i \(0.741620\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −4.00000 −0.852803
\(23\) −7.00000 −1.45960 −0.729800 0.683660i \(-0.760387\pi\)
−0.729800 + 0.683660i \(0.760387\pi\)
\(24\) −1.00000 −0.204124
\(25\) 0 0
\(26\) 4.00000 0.784465
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 4.00000 0.742781 0.371391 0.928477i \(-0.378881\pi\)
0.371391 + 0.928477i \(0.378881\pi\)
\(30\) 0 0
\(31\) 5.00000 0.898027 0.449013 0.893525i \(-0.351776\pi\)
0.449013 + 0.893525i \(0.351776\pi\)
\(32\) 1.00000 0.176777
\(33\) 4.00000 0.696311
\(34\) 3.00000 0.514496
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) −2.00000 −0.328798 −0.164399 0.986394i \(-0.552568\pi\)
−0.164399 + 0.986394i \(0.552568\pi\)
\(38\) −6.00000 −0.973329
\(39\) −4.00000 −0.640513
\(40\) 0 0
\(41\) −7.00000 −1.09322 −0.546608 0.837389i \(-0.684081\pi\)
−0.546608 + 0.837389i \(0.684081\pi\)
\(42\) 0 0
\(43\) −2.00000 −0.304997 −0.152499 0.988304i \(-0.548732\pi\)
−0.152499 + 0.988304i \(0.548732\pi\)
\(44\) −4.00000 −0.603023
\(45\) 0 0
\(46\) −7.00000 −1.03209
\(47\) 1.00000 0.145865 0.0729325 0.997337i \(-0.476764\pi\)
0.0729325 + 0.997337i \(0.476764\pi\)
\(48\) −1.00000 −0.144338
\(49\) 0 0
\(50\) 0 0
\(51\) −3.00000 −0.420084
\(52\) 4.00000 0.554700
\(53\) 2.00000 0.274721 0.137361 0.990521i \(-0.456138\pi\)
0.137361 + 0.990521i \(0.456138\pi\)
\(54\) −1.00000 −0.136083
\(55\) 0 0
\(56\) 0 0
\(57\) 6.00000 0.794719
\(58\) 4.00000 0.525226
\(59\) 14.0000 1.82264 0.911322 0.411693i \(-0.135063\pi\)
0.911322 + 0.411693i \(0.135063\pi\)
\(60\) 0 0
\(61\) −12.0000 −1.53644 −0.768221 0.640184i \(-0.778858\pi\)
−0.768221 + 0.640184i \(0.778858\pi\)
\(62\) 5.00000 0.635001
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 4.00000 0.492366
\(67\) −12.0000 −1.46603 −0.733017 0.680211i \(-0.761888\pi\)
−0.733017 + 0.680211i \(0.761888\pi\)
\(68\) 3.00000 0.363803
\(69\) 7.00000 0.842701
\(70\) 0 0
\(71\) −9.00000 −1.06810 −0.534052 0.845452i \(-0.679331\pi\)
−0.534052 + 0.845452i \(0.679331\pi\)
\(72\) 1.00000 0.117851
\(73\) 6.00000 0.702247 0.351123 0.936329i \(-0.385800\pi\)
0.351123 + 0.936329i \(0.385800\pi\)
\(74\) −2.00000 −0.232495
\(75\) 0 0
\(76\) −6.00000 −0.688247
\(77\) 0 0
\(78\) −4.00000 −0.452911
\(79\) −17.0000 −1.91265 −0.956325 0.292306i \(-0.905577\pi\)
−0.956325 + 0.292306i \(0.905577\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) −7.00000 −0.773021
\(83\) −4.00000 −0.439057 −0.219529 0.975606i \(-0.570452\pi\)
−0.219529 + 0.975606i \(0.570452\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −2.00000 −0.215666
\(87\) −4.00000 −0.428845
\(88\) −4.00000 −0.426401
\(89\) 7.00000 0.741999 0.370999 0.928633i \(-0.379015\pi\)
0.370999 + 0.928633i \(0.379015\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −7.00000 −0.729800
\(93\) −5.00000 −0.518476
\(94\) 1.00000 0.103142
\(95\) 0 0
\(96\) −1.00000 −0.102062
\(97\) −7.00000 −0.710742 −0.355371 0.934725i \(-0.615646\pi\)
−0.355371 + 0.934725i \(0.615646\pi\)
\(98\) 0 0
\(99\) −4.00000 −0.402015
\(100\) 0 0
\(101\) 18.0000 1.79107 0.895533 0.444994i \(-0.146794\pi\)
0.895533 + 0.444994i \(0.146794\pi\)
\(102\) −3.00000 −0.297044
\(103\) −7.00000 −0.689730 −0.344865 0.938652i \(-0.612075\pi\)
−0.344865 + 0.938652i \(0.612075\pi\)
\(104\) 4.00000 0.392232
\(105\) 0 0
\(106\) 2.00000 0.194257
\(107\) −14.0000 −1.35343 −0.676716 0.736245i \(-0.736597\pi\)
−0.676716 + 0.736245i \(0.736597\pi\)
\(108\) −1.00000 −0.0962250
\(109\) 6.00000 0.574696 0.287348 0.957826i \(-0.407226\pi\)
0.287348 + 0.957826i \(0.407226\pi\)
\(110\) 0 0
\(111\) 2.00000 0.189832
\(112\) 0 0
\(113\) 3.00000 0.282216 0.141108 0.989994i \(-0.454933\pi\)
0.141108 + 0.989994i \(0.454933\pi\)
\(114\) 6.00000 0.561951
\(115\) 0 0
\(116\) 4.00000 0.371391
\(117\) 4.00000 0.369800
\(118\) 14.0000 1.28880
\(119\) 0 0
\(120\) 0 0
\(121\) 5.00000 0.454545
\(122\) −12.0000 −1.08643
\(123\) 7.00000 0.631169
\(124\) 5.00000 0.449013
\(125\) 0 0
\(126\) 0 0
\(127\) −16.0000 −1.41977 −0.709885 0.704317i \(-0.751253\pi\)
−0.709885 + 0.704317i \(0.751253\pi\)
\(128\) 1.00000 0.0883883
\(129\) 2.00000 0.176090
\(130\) 0 0
\(131\) 8.00000 0.698963 0.349482 0.936943i \(-0.386358\pi\)
0.349482 + 0.936943i \(0.386358\pi\)
\(132\) 4.00000 0.348155
\(133\) 0 0
\(134\) −12.0000 −1.03664
\(135\) 0 0
\(136\) 3.00000 0.257248
\(137\) −15.0000 −1.28154 −0.640768 0.767734i \(-0.721384\pi\)
−0.640768 + 0.767734i \(0.721384\pi\)
\(138\) 7.00000 0.595880
\(139\) −2.00000 −0.169638 −0.0848189 0.996396i \(-0.527031\pi\)
−0.0848189 + 0.996396i \(0.527031\pi\)
\(140\) 0 0
\(141\) −1.00000 −0.0842152
\(142\) −9.00000 −0.755263
\(143\) −16.0000 −1.33799
\(144\) 1.00000 0.0833333
\(145\) 0 0
\(146\) 6.00000 0.496564
\(147\) 0 0
\(148\) −2.00000 −0.164399
\(149\) −6.00000 −0.491539 −0.245770 0.969328i \(-0.579041\pi\)
−0.245770 + 0.969328i \(0.579041\pi\)
\(150\) 0 0
\(151\) 24.0000 1.95309 0.976546 0.215308i \(-0.0690756\pi\)
0.976546 + 0.215308i \(0.0690756\pi\)
\(152\) −6.00000 −0.486664
\(153\) 3.00000 0.242536
\(154\) 0 0
\(155\) 0 0
\(156\) −4.00000 −0.320256
\(157\) −4.00000 −0.319235 −0.159617 0.987179i \(-0.551026\pi\)
−0.159617 + 0.987179i \(0.551026\pi\)
\(158\) −17.0000 −1.35245
\(159\) −2.00000 −0.158610
\(160\) 0 0
\(161\) 0 0
\(162\) 1.00000 0.0785674
\(163\) 8.00000 0.626608 0.313304 0.949653i \(-0.398564\pi\)
0.313304 + 0.949653i \(0.398564\pi\)
\(164\) −7.00000 −0.546608
\(165\) 0 0
\(166\) −4.00000 −0.310460
\(167\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(168\) 0 0
\(169\) 3.00000 0.230769
\(170\) 0 0
\(171\) −6.00000 −0.458831
\(172\) −2.00000 −0.152499
\(173\) 6.00000 0.456172 0.228086 0.973641i \(-0.426753\pi\)
0.228086 + 0.973641i \(0.426753\pi\)
\(174\) −4.00000 −0.303239
\(175\) 0 0
\(176\) −4.00000 −0.301511
\(177\) −14.0000 −1.05230
\(178\) 7.00000 0.524672
\(179\) 2.00000 0.149487 0.0747435 0.997203i \(-0.476186\pi\)
0.0747435 + 0.997203i \(0.476186\pi\)
\(180\) 0 0
\(181\) −12.0000 −0.891953 −0.445976 0.895045i \(-0.647144\pi\)
−0.445976 + 0.895045i \(0.647144\pi\)
\(182\) 0 0
\(183\) 12.0000 0.887066
\(184\) −7.00000 −0.516047
\(185\) 0 0
\(186\) −5.00000 −0.366618
\(187\) −12.0000 −0.877527
\(188\) 1.00000 0.0729325
\(189\) 0 0
\(190\) 0 0
\(191\) 15.0000 1.08536 0.542681 0.839939i \(-0.317409\pi\)
0.542681 + 0.839939i \(0.317409\pi\)
\(192\) −1.00000 −0.0721688
\(193\) −25.0000 −1.79954 −0.899770 0.436365i \(-0.856266\pi\)
−0.899770 + 0.436365i \(0.856266\pi\)
\(194\) −7.00000 −0.502571
\(195\) 0 0
\(196\) 0 0
\(197\) −20.0000 −1.42494 −0.712470 0.701702i \(-0.752424\pi\)
−0.712470 + 0.701702i \(0.752424\pi\)
\(198\) −4.00000 −0.284268
\(199\) −15.0000 −1.06332 −0.531661 0.846957i \(-0.678432\pi\)
−0.531661 + 0.846957i \(0.678432\pi\)
\(200\) 0 0
\(201\) 12.0000 0.846415
\(202\) 18.0000 1.26648
\(203\) 0 0
\(204\) −3.00000 −0.210042
\(205\) 0 0
\(206\) −7.00000 −0.487713
\(207\) −7.00000 −0.486534
\(208\) 4.00000 0.277350
\(209\) 24.0000 1.66011
\(210\) 0 0
\(211\) −22.0000 −1.51454 −0.757271 0.653101i \(-0.773468\pi\)
−0.757271 + 0.653101i \(0.773468\pi\)
\(212\) 2.00000 0.137361
\(213\) 9.00000 0.616670
\(214\) −14.0000 −0.957020
\(215\) 0 0
\(216\) −1.00000 −0.0680414
\(217\) 0 0
\(218\) 6.00000 0.406371
\(219\) −6.00000 −0.405442
\(220\) 0 0
\(221\) 12.0000 0.807207
\(222\) 2.00000 0.134231
\(223\) 9.00000 0.602685 0.301342 0.953516i \(-0.402565\pi\)
0.301342 + 0.953516i \(0.402565\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 3.00000 0.199557
\(227\) −22.0000 −1.46019 −0.730096 0.683345i \(-0.760525\pi\)
−0.730096 + 0.683345i \(0.760525\pi\)
\(228\) 6.00000 0.397360
\(229\) −8.00000 −0.528655 −0.264327 0.964433i \(-0.585150\pi\)
−0.264327 + 0.964433i \(0.585150\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 4.00000 0.262613
\(233\) 6.00000 0.393073 0.196537 0.980497i \(-0.437031\pi\)
0.196537 + 0.980497i \(0.437031\pi\)
\(234\) 4.00000 0.261488
\(235\) 0 0
\(236\) 14.0000 0.911322
\(237\) 17.0000 1.10427
\(238\) 0 0
\(239\) 3.00000 0.194054 0.0970269 0.995282i \(-0.469067\pi\)
0.0970269 + 0.995282i \(0.469067\pi\)
\(240\) 0 0
\(241\) 2.00000 0.128831 0.0644157 0.997923i \(-0.479482\pi\)
0.0644157 + 0.997923i \(0.479482\pi\)
\(242\) 5.00000 0.321412
\(243\) −1.00000 −0.0641500
\(244\) −12.0000 −0.768221
\(245\) 0 0
\(246\) 7.00000 0.446304
\(247\) −24.0000 −1.52708
\(248\) 5.00000 0.317500
\(249\) 4.00000 0.253490
\(250\) 0 0
\(251\) −4.00000 −0.252478 −0.126239 0.992000i \(-0.540291\pi\)
−0.126239 + 0.992000i \(0.540291\pi\)
\(252\) 0 0
\(253\) 28.0000 1.76034
\(254\) −16.0000 −1.00393
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −2.00000 −0.124757 −0.0623783 0.998053i \(-0.519869\pi\)
−0.0623783 + 0.998053i \(0.519869\pi\)
\(258\) 2.00000 0.124515
\(259\) 0 0
\(260\) 0 0
\(261\) 4.00000 0.247594
\(262\) 8.00000 0.494242
\(263\) 27.0000 1.66489 0.832446 0.554107i \(-0.186940\pi\)
0.832446 + 0.554107i \(0.186940\pi\)
\(264\) 4.00000 0.246183
\(265\) 0 0
\(266\) 0 0
\(267\) −7.00000 −0.428393
\(268\) −12.0000 −0.733017
\(269\) 10.0000 0.609711 0.304855 0.952399i \(-0.401392\pi\)
0.304855 + 0.952399i \(0.401392\pi\)
\(270\) 0 0
\(271\) −5.00000 −0.303728 −0.151864 0.988401i \(-0.548528\pi\)
−0.151864 + 0.988401i \(0.548528\pi\)
\(272\) 3.00000 0.181902
\(273\) 0 0
\(274\) −15.0000 −0.906183
\(275\) 0 0
\(276\) 7.00000 0.421350
\(277\) 16.0000 0.961347 0.480673 0.876900i \(-0.340392\pi\)
0.480673 + 0.876900i \(0.340392\pi\)
\(278\) −2.00000 −0.119952
\(279\) 5.00000 0.299342
\(280\) 0 0
\(281\) 17.0000 1.01413 0.507067 0.861906i \(-0.330729\pi\)
0.507067 + 0.861906i \(0.330729\pi\)
\(282\) −1.00000 −0.0595491
\(283\) −8.00000 −0.475551 −0.237775 0.971320i \(-0.576418\pi\)
−0.237775 + 0.971320i \(0.576418\pi\)
\(284\) −9.00000 −0.534052
\(285\) 0 0
\(286\) −16.0000 −0.946100
\(287\) 0 0
\(288\) 1.00000 0.0589256
\(289\) −8.00000 −0.470588
\(290\) 0 0
\(291\) 7.00000 0.410347
\(292\) 6.00000 0.351123
\(293\) −12.0000 −0.701047 −0.350524 0.936554i \(-0.613996\pi\)
−0.350524 + 0.936554i \(0.613996\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −2.00000 −0.116248
\(297\) 4.00000 0.232104
\(298\) −6.00000 −0.347571
\(299\) −28.0000 −1.61928
\(300\) 0 0
\(301\) 0 0
\(302\) 24.0000 1.38104
\(303\) −18.0000 −1.03407
\(304\) −6.00000 −0.344124
\(305\) 0 0
\(306\) 3.00000 0.171499
\(307\) 20.0000 1.14146 0.570730 0.821138i \(-0.306660\pi\)
0.570730 + 0.821138i \(0.306660\pi\)
\(308\) 0 0
\(309\) 7.00000 0.398216
\(310\) 0 0
\(311\) −21.0000 −1.19080 −0.595400 0.803429i \(-0.703007\pi\)
−0.595400 + 0.803429i \(0.703007\pi\)
\(312\) −4.00000 −0.226455
\(313\) −27.0000 −1.52613 −0.763065 0.646322i \(-0.776306\pi\)
−0.763065 + 0.646322i \(0.776306\pi\)
\(314\) −4.00000 −0.225733
\(315\) 0 0
\(316\) −17.0000 −0.956325
\(317\) −18.0000 −1.01098 −0.505490 0.862832i \(-0.668688\pi\)
−0.505490 + 0.862832i \(0.668688\pi\)
\(318\) −2.00000 −0.112154
\(319\) −16.0000 −0.895828
\(320\) 0 0
\(321\) 14.0000 0.781404
\(322\) 0 0
\(323\) −18.0000 −1.00155
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) 8.00000 0.443079
\(327\) −6.00000 −0.331801
\(328\) −7.00000 −0.386510
\(329\) 0 0
\(330\) 0 0
\(331\) −34.0000 −1.86881 −0.934405 0.356214i \(-0.884068\pi\)
−0.934405 + 0.356214i \(0.884068\pi\)
\(332\) −4.00000 −0.219529
\(333\) −2.00000 −0.109599
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −3.00000 −0.163420 −0.0817102 0.996656i \(-0.526038\pi\)
−0.0817102 + 0.996656i \(0.526038\pi\)
\(338\) 3.00000 0.163178
\(339\) −3.00000 −0.162938
\(340\) 0 0
\(341\) −20.0000 −1.08306
\(342\) −6.00000 −0.324443
\(343\) 0 0
\(344\) −2.00000 −0.107833
\(345\) 0 0
\(346\) 6.00000 0.322562
\(347\) −32.0000 −1.71785 −0.858925 0.512101i \(-0.828867\pi\)
−0.858925 + 0.512101i \(0.828867\pi\)
\(348\) −4.00000 −0.214423
\(349\) 18.0000 0.963518 0.481759 0.876304i \(-0.339998\pi\)
0.481759 + 0.876304i \(0.339998\pi\)
\(350\) 0 0
\(351\) −4.00000 −0.213504
\(352\) −4.00000 −0.213201
\(353\) −15.0000 −0.798369 −0.399185 0.916871i \(-0.630707\pi\)
−0.399185 + 0.916871i \(0.630707\pi\)
\(354\) −14.0000 −0.744092
\(355\) 0 0
\(356\) 7.00000 0.370999
\(357\) 0 0
\(358\) 2.00000 0.105703
\(359\) 4.00000 0.211112 0.105556 0.994413i \(-0.466338\pi\)
0.105556 + 0.994413i \(0.466338\pi\)
\(360\) 0 0
\(361\) 17.0000 0.894737
\(362\) −12.0000 −0.630706
\(363\) −5.00000 −0.262432
\(364\) 0 0
\(365\) 0 0
\(366\) 12.0000 0.627250
\(367\) −32.0000 −1.67039 −0.835193 0.549957i \(-0.814644\pi\)
−0.835193 + 0.549957i \(0.814644\pi\)
\(368\) −7.00000 −0.364900
\(369\) −7.00000 −0.364405
\(370\) 0 0
\(371\) 0 0
\(372\) −5.00000 −0.259238
\(373\) −12.0000 −0.621336 −0.310668 0.950518i \(-0.600553\pi\)
−0.310668 + 0.950518i \(0.600553\pi\)
\(374\) −12.0000 −0.620505
\(375\) 0 0
\(376\) 1.00000 0.0515711
\(377\) 16.0000 0.824042
\(378\) 0 0
\(379\) 20.0000 1.02733 0.513665 0.857991i \(-0.328287\pi\)
0.513665 + 0.857991i \(0.328287\pi\)
\(380\) 0 0
\(381\) 16.0000 0.819705
\(382\) 15.0000 0.767467
\(383\) −31.0000 −1.58403 −0.792013 0.610504i \(-0.790967\pi\)
−0.792013 + 0.610504i \(0.790967\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) −25.0000 −1.27247
\(387\) −2.00000 −0.101666
\(388\) −7.00000 −0.355371
\(389\) 10.0000 0.507020 0.253510 0.967333i \(-0.418415\pi\)
0.253510 + 0.967333i \(0.418415\pi\)
\(390\) 0 0
\(391\) −21.0000 −1.06202
\(392\) 0 0
\(393\) −8.00000 −0.403547
\(394\) −20.0000 −1.00759
\(395\) 0 0
\(396\) −4.00000 −0.201008
\(397\) −22.0000 −1.10415 −0.552074 0.833795i \(-0.686163\pi\)
−0.552074 + 0.833795i \(0.686163\pi\)
\(398\) −15.0000 −0.751882
\(399\) 0 0
\(400\) 0 0
\(401\) 34.0000 1.69788 0.848939 0.528490i \(-0.177242\pi\)
0.848939 + 0.528490i \(0.177242\pi\)
\(402\) 12.0000 0.598506
\(403\) 20.0000 0.996271
\(404\) 18.0000 0.895533
\(405\) 0 0
\(406\) 0 0
\(407\) 8.00000 0.396545
\(408\) −3.00000 −0.148522
\(409\) −29.0000 −1.43396 −0.716979 0.697095i \(-0.754476\pi\)
−0.716979 + 0.697095i \(0.754476\pi\)
\(410\) 0 0
\(411\) 15.0000 0.739895
\(412\) −7.00000 −0.344865
\(413\) 0 0
\(414\) −7.00000 −0.344031
\(415\) 0 0
\(416\) 4.00000 0.196116
\(417\) 2.00000 0.0979404
\(418\) 24.0000 1.17388
\(419\) 26.0000 1.27018 0.635092 0.772437i \(-0.280962\pi\)
0.635092 + 0.772437i \(0.280962\pi\)
\(420\) 0 0
\(421\) 16.0000 0.779792 0.389896 0.920859i \(-0.372511\pi\)
0.389896 + 0.920859i \(0.372511\pi\)
\(422\) −22.0000 −1.07094
\(423\) 1.00000 0.0486217
\(424\) 2.00000 0.0971286
\(425\) 0 0
\(426\) 9.00000 0.436051
\(427\) 0 0
\(428\) −14.0000 −0.676716
\(429\) 16.0000 0.772487
\(430\) 0 0
\(431\) −39.0000 −1.87856 −0.939282 0.343146i \(-0.888507\pi\)
−0.939282 + 0.343146i \(0.888507\pi\)
\(432\) −1.00000 −0.0481125
\(433\) 37.0000 1.77811 0.889053 0.457804i \(-0.151364\pi\)
0.889053 + 0.457804i \(0.151364\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 6.00000 0.287348
\(437\) 42.0000 2.00913
\(438\) −6.00000 −0.286691
\(439\) −17.0000 −0.811366 −0.405683 0.914014i \(-0.632966\pi\)
−0.405683 + 0.914014i \(0.632966\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 12.0000 0.570782
\(443\) 26.0000 1.23530 0.617649 0.786454i \(-0.288085\pi\)
0.617649 + 0.786454i \(0.288085\pi\)
\(444\) 2.00000 0.0949158
\(445\) 0 0
\(446\) 9.00000 0.426162
\(447\) 6.00000 0.283790
\(448\) 0 0
\(449\) −13.0000 −0.613508 −0.306754 0.951789i \(-0.599243\pi\)
−0.306754 + 0.951789i \(0.599243\pi\)
\(450\) 0 0
\(451\) 28.0000 1.31847
\(452\) 3.00000 0.141108
\(453\) −24.0000 −1.12762
\(454\) −22.0000 −1.03251
\(455\) 0 0
\(456\) 6.00000 0.280976
\(457\) −18.0000 −0.842004 −0.421002 0.907060i \(-0.638322\pi\)
−0.421002 + 0.907060i \(0.638322\pi\)
\(458\) −8.00000 −0.373815
\(459\) −3.00000 −0.140028
\(460\) 0 0
\(461\) −36.0000 −1.67669 −0.838344 0.545142i \(-0.816476\pi\)
−0.838344 + 0.545142i \(0.816476\pi\)
\(462\) 0 0
\(463\) 7.00000 0.325318 0.162659 0.986682i \(-0.447993\pi\)
0.162659 + 0.986682i \(0.447993\pi\)
\(464\) 4.00000 0.185695
\(465\) 0 0
\(466\) 6.00000 0.277945
\(467\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(468\) 4.00000 0.184900
\(469\) 0 0
\(470\) 0 0
\(471\) 4.00000 0.184310
\(472\) 14.0000 0.644402
\(473\) 8.00000 0.367840
\(474\) 17.0000 0.780836
\(475\) 0 0
\(476\) 0 0
\(477\) 2.00000 0.0915737
\(478\) 3.00000 0.137217
\(479\) −1.00000 −0.0456912 −0.0228456 0.999739i \(-0.507273\pi\)
−0.0228456 + 0.999739i \(0.507273\pi\)
\(480\) 0 0
\(481\) −8.00000 −0.364769
\(482\) 2.00000 0.0910975
\(483\) 0 0
\(484\) 5.00000 0.227273
\(485\) 0 0
\(486\) −1.00000 −0.0453609
\(487\) −5.00000 −0.226572 −0.113286 0.993562i \(-0.536138\pi\)
−0.113286 + 0.993562i \(0.536138\pi\)
\(488\) −12.0000 −0.543214
\(489\) −8.00000 −0.361773
\(490\) 0 0
\(491\) 38.0000 1.71492 0.857458 0.514554i \(-0.172042\pi\)
0.857458 + 0.514554i \(0.172042\pi\)
\(492\) 7.00000 0.315584
\(493\) 12.0000 0.540453
\(494\) −24.0000 −1.07981
\(495\) 0 0
\(496\) 5.00000 0.224507
\(497\) 0 0
\(498\) 4.00000 0.179244
\(499\) 28.0000 1.25345 0.626726 0.779240i \(-0.284395\pi\)
0.626726 + 0.779240i \(0.284395\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −4.00000 −0.178529
\(503\) 36.0000 1.60516 0.802580 0.596544i \(-0.203460\pi\)
0.802580 + 0.596544i \(0.203460\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 28.0000 1.24475
\(507\) −3.00000 −0.133235
\(508\) −16.0000 −0.709885
\(509\) 16.0000 0.709188 0.354594 0.935020i \(-0.384619\pi\)
0.354594 + 0.935020i \(0.384619\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) 6.00000 0.264906
\(514\) −2.00000 −0.0882162
\(515\) 0 0
\(516\) 2.00000 0.0880451
\(517\) −4.00000 −0.175920
\(518\) 0 0
\(519\) −6.00000 −0.263371
\(520\) 0 0
\(521\) 9.00000 0.394297 0.197149 0.980374i \(-0.436832\pi\)
0.197149 + 0.980374i \(0.436832\pi\)
\(522\) 4.00000 0.175075
\(523\) 44.0000 1.92399 0.961993 0.273075i \(-0.0880406\pi\)
0.961993 + 0.273075i \(0.0880406\pi\)
\(524\) 8.00000 0.349482
\(525\) 0 0
\(526\) 27.0000 1.17726
\(527\) 15.0000 0.653410
\(528\) 4.00000 0.174078
\(529\) 26.0000 1.13043
\(530\) 0 0
\(531\) 14.0000 0.607548
\(532\) 0 0
\(533\) −28.0000 −1.21281
\(534\) −7.00000 −0.302920
\(535\) 0 0
\(536\) −12.0000 −0.518321
\(537\) −2.00000 −0.0863064
\(538\) 10.0000 0.431131
\(539\) 0 0
\(540\) 0 0
\(541\) 32.0000 1.37579 0.687894 0.725811i \(-0.258536\pi\)
0.687894 + 0.725811i \(0.258536\pi\)
\(542\) −5.00000 −0.214768
\(543\) 12.0000 0.514969
\(544\) 3.00000 0.128624
\(545\) 0 0
\(546\) 0 0
\(547\) −22.0000 −0.940652 −0.470326 0.882493i \(-0.655864\pi\)
−0.470326 + 0.882493i \(0.655864\pi\)
\(548\) −15.0000 −0.640768
\(549\) −12.0000 −0.512148
\(550\) 0 0
\(551\) −24.0000 −1.02243
\(552\) 7.00000 0.297940
\(553\) 0 0
\(554\) 16.0000 0.679775
\(555\) 0 0
\(556\) −2.00000 −0.0848189
\(557\) −30.0000 −1.27114 −0.635570 0.772043i \(-0.719235\pi\)
−0.635570 + 0.772043i \(0.719235\pi\)
\(558\) 5.00000 0.211667
\(559\) −8.00000 −0.338364
\(560\) 0 0
\(561\) 12.0000 0.506640
\(562\) 17.0000 0.717102
\(563\) −2.00000 −0.0842900 −0.0421450 0.999112i \(-0.513419\pi\)
−0.0421450 + 0.999112i \(0.513419\pi\)
\(564\) −1.00000 −0.0421076
\(565\) 0 0
\(566\) −8.00000 −0.336265
\(567\) 0 0
\(568\) −9.00000 −0.377632
\(569\) −45.0000 −1.88650 −0.943249 0.332086i \(-0.892248\pi\)
−0.943249 + 0.332086i \(0.892248\pi\)
\(570\) 0 0
\(571\) 40.0000 1.67395 0.836974 0.547243i \(-0.184323\pi\)
0.836974 + 0.547243i \(0.184323\pi\)
\(572\) −16.0000 −0.668994
\(573\) −15.0000 −0.626634
\(574\) 0 0
\(575\) 0 0
\(576\) 1.00000 0.0416667
\(577\) −2.00000 −0.0832611 −0.0416305 0.999133i \(-0.513255\pi\)
−0.0416305 + 0.999133i \(0.513255\pi\)
\(578\) −8.00000 −0.332756
\(579\) 25.0000 1.03896
\(580\) 0 0
\(581\) 0 0
\(582\) 7.00000 0.290159
\(583\) −8.00000 −0.331326
\(584\) 6.00000 0.248282
\(585\) 0 0
\(586\) −12.0000 −0.495715
\(587\) 42.0000 1.73353 0.866763 0.498721i \(-0.166197\pi\)
0.866763 + 0.498721i \(0.166197\pi\)
\(588\) 0 0
\(589\) −30.0000 −1.23613
\(590\) 0 0
\(591\) 20.0000 0.822690
\(592\) −2.00000 −0.0821995
\(593\) 13.0000 0.533846 0.266923 0.963718i \(-0.413993\pi\)
0.266923 + 0.963718i \(0.413993\pi\)
\(594\) 4.00000 0.164122
\(595\) 0 0
\(596\) −6.00000 −0.245770
\(597\) 15.0000 0.613909
\(598\) −28.0000 −1.14501
\(599\) −31.0000 −1.26663 −0.633313 0.773896i \(-0.718305\pi\)
−0.633313 + 0.773896i \(0.718305\pi\)
\(600\) 0 0
\(601\) −46.0000 −1.87638 −0.938190 0.346122i \(-0.887498\pi\)
−0.938190 + 0.346122i \(0.887498\pi\)
\(602\) 0 0
\(603\) −12.0000 −0.488678
\(604\) 24.0000 0.976546
\(605\) 0 0
\(606\) −18.0000 −0.731200
\(607\) 29.0000 1.17707 0.588537 0.808470i \(-0.299704\pi\)
0.588537 + 0.808470i \(0.299704\pi\)
\(608\) −6.00000 −0.243332
\(609\) 0 0
\(610\) 0 0
\(611\) 4.00000 0.161823
\(612\) 3.00000 0.121268
\(613\) −4.00000 −0.161558 −0.0807792 0.996732i \(-0.525741\pi\)
−0.0807792 + 0.996732i \(0.525741\pi\)
\(614\) 20.0000 0.807134
\(615\) 0 0
\(616\) 0 0
\(617\) −1.00000 −0.0402585 −0.0201292 0.999797i \(-0.506408\pi\)
−0.0201292 + 0.999797i \(0.506408\pi\)
\(618\) 7.00000 0.281581
\(619\) 16.0000 0.643094 0.321547 0.946894i \(-0.395797\pi\)
0.321547 + 0.946894i \(0.395797\pi\)
\(620\) 0 0
\(621\) 7.00000 0.280900
\(622\) −21.0000 −0.842023
\(623\) 0 0
\(624\) −4.00000 −0.160128
\(625\) 0 0
\(626\) −27.0000 −1.07914
\(627\) −24.0000 −0.958468
\(628\) −4.00000 −0.159617
\(629\) −6.00000 −0.239236
\(630\) 0 0
\(631\) 7.00000 0.278666 0.139333 0.990246i \(-0.455504\pi\)
0.139333 + 0.990246i \(0.455504\pi\)
\(632\) −17.0000 −0.676224
\(633\) 22.0000 0.874421
\(634\) −18.0000 −0.714871
\(635\) 0 0
\(636\) −2.00000 −0.0793052
\(637\) 0 0
\(638\) −16.0000 −0.633446
\(639\) −9.00000 −0.356034
\(640\) 0 0
\(641\) −9.00000 −0.355479 −0.177739 0.984078i \(-0.556878\pi\)
−0.177739 + 0.984078i \(0.556878\pi\)
\(642\) 14.0000 0.552536
\(643\) 14.0000 0.552106 0.276053 0.961142i \(-0.410973\pi\)
0.276053 + 0.961142i \(0.410973\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −18.0000 −0.708201
\(647\) −32.0000 −1.25805 −0.629025 0.777385i \(-0.716546\pi\)
−0.629025 + 0.777385i \(0.716546\pi\)
\(648\) 1.00000 0.0392837
\(649\) −56.0000 −2.19819
\(650\) 0 0
\(651\) 0 0
\(652\) 8.00000 0.313304
\(653\) −16.0000 −0.626128 −0.313064 0.949732i \(-0.601356\pi\)
−0.313064 + 0.949732i \(0.601356\pi\)
\(654\) −6.00000 −0.234619
\(655\) 0 0
\(656\) −7.00000 −0.273304
\(657\) 6.00000 0.234082
\(658\) 0 0
\(659\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(660\) 0 0
\(661\) −30.0000 −1.16686 −0.583432 0.812162i \(-0.698291\pi\)
−0.583432 + 0.812162i \(0.698291\pi\)
\(662\) −34.0000 −1.32145
\(663\) −12.0000 −0.466041
\(664\) −4.00000 −0.155230
\(665\) 0 0
\(666\) −2.00000 −0.0774984
\(667\) −28.0000 −1.08416
\(668\) 0 0
\(669\) −9.00000 −0.347960
\(670\) 0 0
\(671\) 48.0000 1.85302
\(672\) 0 0
\(673\) 11.0000 0.424019 0.212009 0.977268i \(-0.431999\pi\)
0.212009 + 0.977268i \(0.431999\pi\)
\(674\) −3.00000 −0.115556
\(675\) 0 0
\(676\) 3.00000 0.115385
\(677\) 32.0000 1.22986 0.614930 0.788582i \(-0.289184\pi\)
0.614930 + 0.788582i \(0.289184\pi\)
\(678\) −3.00000 −0.115214
\(679\) 0 0
\(680\) 0 0
\(681\) 22.0000 0.843042
\(682\) −20.0000 −0.765840
\(683\) −22.0000 −0.841807 −0.420903 0.907106i \(-0.638287\pi\)
−0.420903 + 0.907106i \(0.638287\pi\)
\(684\) −6.00000 −0.229416
\(685\) 0 0
\(686\) 0 0
\(687\) 8.00000 0.305219
\(688\) −2.00000 −0.0762493
\(689\) 8.00000 0.304776
\(690\) 0 0
\(691\) 24.0000 0.913003 0.456502 0.889723i \(-0.349102\pi\)
0.456502 + 0.889723i \(0.349102\pi\)
\(692\) 6.00000 0.228086
\(693\) 0 0
\(694\) −32.0000 −1.21470
\(695\) 0 0
\(696\) −4.00000 −0.151620
\(697\) −21.0000 −0.795432
\(698\) 18.0000 0.681310
\(699\) −6.00000 −0.226941
\(700\) 0 0
\(701\) 12.0000 0.453234 0.226617 0.973984i \(-0.427233\pi\)
0.226617 + 0.973984i \(0.427233\pi\)
\(702\) −4.00000 −0.150970
\(703\) 12.0000 0.452589
\(704\) −4.00000 −0.150756
\(705\) 0 0
\(706\) −15.0000 −0.564532
\(707\) 0 0
\(708\) −14.0000 −0.526152
\(709\) 14.0000 0.525781 0.262891 0.964826i \(-0.415324\pi\)
0.262891 + 0.964826i \(0.415324\pi\)
\(710\) 0 0
\(711\) −17.0000 −0.637550
\(712\) 7.00000 0.262336
\(713\) −35.0000 −1.31076
\(714\) 0 0
\(715\) 0 0
\(716\) 2.00000 0.0747435
\(717\) −3.00000 −0.112037
\(718\) 4.00000 0.149279
\(719\) 7.00000 0.261056 0.130528 0.991445i \(-0.458333\pi\)
0.130528 + 0.991445i \(0.458333\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 17.0000 0.632674
\(723\) −2.00000 −0.0743808
\(724\) −12.0000 −0.445976
\(725\) 0 0
\(726\) −5.00000 −0.185567
\(727\) −49.0000 −1.81731 −0.908655 0.417548i \(-0.862889\pi\)
−0.908655 + 0.417548i \(0.862889\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −6.00000 −0.221918
\(732\) 12.0000 0.443533
\(733\) −10.0000 −0.369358 −0.184679 0.982799i \(-0.559125\pi\)
−0.184679 + 0.982799i \(0.559125\pi\)
\(734\) −32.0000 −1.18114
\(735\) 0 0
\(736\) −7.00000 −0.258023
\(737\) 48.0000 1.76810
\(738\) −7.00000 −0.257674
\(739\) 14.0000 0.514998 0.257499 0.966279i \(-0.417102\pi\)
0.257499 + 0.966279i \(0.417102\pi\)
\(740\) 0 0
\(741\) 24.0000 0.881662
\(742\) 0 0
\(743\) −1.00000 −0.0366864 −0.0183432 0.999832i \(-0.505839\pi\)
−0.0183432 + 0.999832i \(0.505839\pi\)
\(744\) −5.00000 −0.183309
\(745\) 0 0
\(746\) −12.0000 −0.439351
\(747\) −4.00000 −0.146352
\(748\) −12.0000 −0.438763
\(749\) 0 0
\(750\) 0 0
\(751\) −16.0000 −0.583848 −0.291924 0.956441i \(-0.594295\pi\)
−0.291924 + 0.956441i \(0.594295\pi\)
\(752\) 1.00000 0.0364662
\(753\) 4.00000 0.145768
\(754\) 16.0000 0.582686
\(755\) 0 0
\(756\) 0 0
\(757\) 16.0000 0.581530 0.290765 0.956795i \(-0.406090\pi\)
0.290765 + 0.956795i \(0.406090\pi\)
\(758\) 20.0000 0.726433
\(759\) −28.0000 −1.01634
\(760\) 0 0
\(761\) 21.0000 0.761249 0.380625 0.924730i \(-0.375709\pi\)
0.380625 + 0.924730i \(0.375709\pi\)
\(762\) 16.0000 0.579619
\(763\) 0 0
\(764\) 15.0000 0.542681
\(765\) 0 0
\(766\) −31.0000 −1.12008
\(767\) 56.0000 2.02204
\(768\) −1.00000 −0.0360844
\(769\) −10.0000 −0.360609 −0.180305 0.983611i \(-0.557708\pi\)
−0.180305 + 0.983611i \(0.557708\pi\)
\(770\) 0 0
\(771\) 2.00000 0.0720282
\(772\) −25.0000 −0.899770
\(773\) −18.0000 −0.647415 −0.323708 0.946157i \(-0.604929\pi\)
−0.323708 + 0.946157i \(0.604929\pi\)
\(774\) −2.00000 −0.0718885
\(775\) 0 0
\(776\) −7.00000 −0.251285
\(777\) 0 0
\(778\) 10.0000 0.358517
\(779\) 42.0000 1.50481
\(780\) 0 0
\(781\) 36.0000 1.28818
\(782\) −21.0000 −0.750958
\(783\) −4.00000 −0.142948
\(784\) 0 0
\(785\) 0 0
\(786\) −8.00000 −0.285351
\(787\) 22.0000 0.784215 0.392108 0.919919i \(-0.371746\pi\)
0.392108 + 0.919919i \(0.371746\pi\)
\(788\) −20.0000 −0.712470
\(789\) −27.0000 −0.961225
\(790\) 0 0
\(791\) 0 0
\(792\) −4.00000 −0.142134
\(793\) −48.0000 −1.70453
\(794\) −22.0000 −0.780751
\(795\) 0 0
\(796\) −15.0000 −0.531661
\(797\) −12.0000 −0.425062 −0.212531 0.977154i \(-0.568171\pi\)
−0.212531 + 0.977154i \(0.568171\pi\)
\(798\) 0 0
\(799\) 3.00000 0.106132
\(800\) 0 0
\(801\) 7.00000 0.247333
\(802\) 34.0000 1.20058
\(803\) −24.0000 −0.846942
\(804\) 12.0000 0.423207
\(805\) 0 0
\(806\) 20.0000 0.704470
\(807\) −10.0000 −0.352017
\(808\) 18.0000 0.633238
\(809\) 54.0000 1.89854 0.949269 0.314464i \(-0.101825\pi\)
0.949269 + 0.314464i \(0.101825\pi\)
\(810\) 0 0
\(811\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(812\) 0 0
\(813\) 5.00000 0.175358
\(814\) 8.00000 0.280400
\(815\) 0 0
\(816\) −3.00000 −0.105021
\(817\) 12.0000 0.419827
\(818\) −29.0000 −1.01396
\(819\) 0 0
\(820\) 0 0
\(821\) 6.00000 0.209401 0.104701 0.994504i \(-0.466612\pi\)
0.104701 + 0.994504i \(0.466612\pi\)
\(822\) 15.0000 0.523185
\(823\) 24.0000 0.836587 0.418294 0.908312i \(-0.362628\pi\)
0.418294 + 0.908312i \(0.362628\pi\)
\(824\) −7.00000 −0.243857
\(825\) 0 0
\(826\) 0 0
\(827\) −20.0000 −0.695468 −0.347734 0.937593i \(-0.613049\pi\)
−0.347734 + 0.937593i \(0.613049\pi\)
\(828\) −7.00000 −0.243267
\(829\) 38.0000 1.31979 0.659897 0.751356i \(-0.270600\pi\)
0.659897 + 0.751356i \(0.270600\pi\)
\(830\) 0 0
\(831\) −16.0000 −0.555034
\(832\) 4.00000 0.138675
\(833\) 0 0
\(834\) 2.00000 0.0692543
\(835\) 0 0
\(836\) 24.0000 0.830057
\(837\) −5.00000 −0.172825
\(838\) 26.0000 0.898155
\(839\) 25.0000 0.863096 0.431548 0.902090i \(-0.357968\pi\)
0.431548 + 0.902090i \(0.357968\pi\)
\(840\) 0 0
\(841\) −13.0000 −0.448276
\(842\) 16.0000 0.551396
\(843\) −17.0000 −0.585511
\(844\) −22.0000 −0.757271
\(845\) 0 0
\(846\) 1.00000 0.0343807
\(847\) 0 0
\(848\) 2.00000 0.0686803
\(849\) 8.00000 0.274559
\(850\) 0 0
\(851\) 14.0000 0.479914
\(852\) 9.00000 0.308335
\(853\) −2.00000 −0.0684787 −0.0342393 0.999414i \(-0.510901\pi\)
−0.0342393 + 0.999414i \(0.510901\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) −14.0000 −0.478510
\(857\) −26.0000 −0.888143 −0.444072 0.895991i \(-0.646466\pi\)
−0.444072 + 0.895991i \(0.646466\pi\)
\(858\) 16.0000 0.546231
\(859\) −24.0000 −0.818869 −0.409435 0.912339i \(-0.634274\pi\)
−0.409435 + 0.912339i \(0.634274\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) −39.0000 −1.32835
\(863\) 11.0000 0.374444 0.187222 0.982318i \(-0.440052\pi\)
0.187222 + 0.982318i \(0.440052\pi\)
\(864\) −1.00000 −0.0340207
\(865\) 0 0
\(866\) 37.0000 1.25731
\(867\) 8.00000 0.271694
\(868\) 0 0
\(869\) 68.0000 2.30674
\(870\) 0 0
\(871\) −48.0000 −1.62642
\(872\) 6.00000 0.203186
\(873\) −7.00000 −0.236914
\(874\) 42.0000 1.42067
\(875\) 0 0
\(876\) −6.00000 −0.202721
\(877\) −38.0000 −1.28317 −0.641584 0.767052i \(-0.721723\pi\)
−0.641584 + 0.767052i \(0.721723\pi\)
\(878\) −17.0000 −0.573722
\(879\) 12.0000 0.404750
\(880\) 0 0
\(881\) 35.0000 1.17918 0.589590 0.807703i \(-0.299289\pi\)
0.589590 + 0.807703i \(0.299289\pi\)
\(882\) 0 0
\(883\) −6.00000 −0.201916 −0.100958 0.994891i \(-0.532191\pi\)
−0.100958 + 0.994891i \(0.532191\pi\)
\(884\) 12.0000 0.403604
\(885\) 0 0
\(886\) 26.0000 0.873487
\(887\) 56.0000 1.88030 0.940148 0.340766i \(-0.110687\pi\)
0.940148 + 0.340766i \(0.110687\pi\)
\(888\) 2.00000 0.0671156
\(889\) 0 0
\(890\) 0 0
\(891\) −4.00000 −0.134005
\(892\) 9.00000 0.301342
\(893\) −6.00000 −0.200782
\(894\) 6.00000 0.200670
\(895\) 0 0
\(896\) 0 0
\(897\) 28.0000 0.934893
\(898\) −13.0000 −0.433816
\(899\) 20.0000 0.667037
\(900\) 0 0
\(901\) 6.00000 0.199889
\(902\) 28.0000 0.932298
\(903\) 0 0
\(904\) 3.00000 0.0997785
\(905\) 0 0
\(906\) −24.0000 −0.797347
\(907\) 28.0000 0.929725 0.464862 0.885383i \(-0.346104\pi\)
0.464862 + 0.885383i \(0.346104\pi\)
\(908\) −22.0000 −0.730096
\(909\) 18.0000 0.597022
\(910\) 0 0
\(911\) 19.0000 0.629498 0.314749 0.949175i \(-0.398080\pi\)
0.314749 + 0.949175i \(0.398080\pi\)
\(912\) 6.00000 0.198680
\(913\) 16.0000 0.529523
\(914\) −18.0000 −0.595387
\(915\) 0 0
\(916\) −8.00000 −0.264327
\(917\) 0 0
\(918\) −3.00000 −0.0990148
\(919\) −39.0000 −1.28649 −0.643246 0.765660i \(-0.722413\pi\)
−0.643246 + 0.765660i \(0.722413\pi\)
\(920\) 0 0
\(921\) −20.0000 −0.659022
\(922\) −36.0000 −1.18560
\(923\) −36.0000 −1.18495
\(924\) 0 0
\(925\) 0 0
\(926\) 7.00000 0.230034
\(927\) −7.00000 −0.229910
\(928\) 4.00000 0.131306
\(929\) 30.0000 0.984268 0.492134 0.870519i \(-0.336217\pi\)
0.492134 + 0.870519i \(0.336217\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 6.00000 0.196537
\(933\) 21.0000 0.687509
\(934\) 0 0
\(935\) 0 0
\(936\) 4.00000 0.130744
\(937\) −6.00000 −0.196011 −0.0980057 0.995186i \(-0.531246\pi\)
−0.0980057 + 0.995186i \(0.531246\pi\)
\(938\) 0 0
\(939\) 27.0000 0.881112
\(940\) 0 0
\(941\) −42.0000 −1.36916 −0.684580 0.728937i \(-0.740015\pi\)
−0.684580 + 0.728937i \(0.740015\pi\)
\(942\) 4.00000 0.130327
\(943\) 49.0000 1.59566
\(944\) 14.0000 0.455661
\(945\) 0 0
\(946\) 8.00000 0.260102
\(947\) 32.0000 1.03986 0.519930 0.854209i \(-0.325958\pi\)
0.519930 + 0.854209i \(0.325958\pi\)
\(948\) 17.0000 0.552134
\(949\) 24.0000 0.779073
\(950\) 0 0
\(951\) 18.0000 0.583690
\(952\) 0 0
\(953\) 26.0000 0.842223 0.421111 0.907009i \(-0.361640\pi\)
0.421111 + 0.907009i \(0.361640\pi\)
\(954\) 2.00000 0.0647524
\(955\) 0 0
\(956\) 3.00000 0.0970269
\(957\) 16.0000 0.517207
\(958\) −1.00000 −0.0323085
\(959\) 0 0
\(960\) 0 0
\(961\) −6.00000 −0.193548
\(962\) −8.00000 −0.257930
\(963\) −14.0000 −0.451144
\(964\) 2.00000 0.0644157
\(965\) 0 0
\(966\) 0 0
\(967\) 29.0000 0.932577 0.466289 0.884633i \(-0.345591\pi\)
0.466289 + 0.884633i \(0.345591\pi\)
\(968\) 5.00000 0.160706
\(969\) 18.0000 0.578243
\(970\) 0 0
\(971\) 24.0000 0.770197 0.385098 0.922876i \(-0.374168\pi\)
0.385098 + 0.922876i \(0.374168\pi\)
\(972\) −1.00000 −0.0320750
\(973\) 0 0
\(974\) −5.00000 −0.160210
\(975\) 0 0
\(976\) −12.0000 −0.384111
\(977\) −3.00000 −0.0959785 −0.0479893 0.998848i \(-0.515281\pi\)
−0.0479893 + 0.998848i \(0.515281\pi\)
\(978\) −8.00000 −0.255812
\(979\) −28.0000 −0.894884
\(980\) 0 0
\(981\) 6.00000 0.191565
\(982\) 38.0000 1.21263
\(983\) 28.0000 0.893061 0.446531 0.894768i \(-0.352659\pi\)
0.446531 + 0.894768i \(0.352659\pi\)
\(984\) 7.00000 0.223152
\(985\) 0 0
\(986\) 12.0000 0.382158
\(987\) 0 0
\(988\) −24.0000 −0.763542
\(989\) 14.0000 0.445174
\(990\) 0 0
\(991\) 7.00000 0.222362 0.111181 0.993800i \(-0.464537\pi\)
0.111181 + 0.993800i \(0.464537\pi\)
\(992\) 5.00000 0.158750
\(993\) 34.0000 1.07896
\(994\) 0 0
\(995\) 0 0
\(996\) 4.00000 0.126745
\(997\) −16.0000 −0.506725 −0.253363 0.967371i \(-0.581537\pi\)
−0.253363 + 0.967371i \(0.581537\pi\)
\(998\) 28.0000 0.886325
\(999\) 2.00000 0.0632772
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 7350.2.a.bs.1.1 1
5.4 even 2 7350.2.a.v.1.1 1
7.3 odd 6 1050.2.i.d.751.1 yes 2
7.5 odd 6 1050.2.i.d.151.1 2
7.6 odd 2 7350.2.a.ci.1.1 1
35.3 even 12 1050.2.o.l.499.2 4
35.12 even 12 1050.2.o.l.949.2 4
35.17 even 12 1050.2.o.l.499.1 4
35.19 odd 6 1050.2.i.r.151.1 yes 2
35.24 odd 6 1050.2.i.r.751.1 yes 2
35.33 even 12 1050.2.o.l.949.1 4
35.34 odd 2 7350.2.a.e.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1050.2.i.d.151.1 2 7.5 odd 6
1050.2.i.d.751.1 yes 2 7.3 odd 6
1050.2.i.r.151.1 yes 2 35.19 odd 6
1050.2.i.r.751.1 yes 2 35.24 odd 6
1050.2.o.l.499.1 4 35.17 even 12
1050.2.o.l.499.2 4 35.3 even 12
1050.2.o.l.949.1 4 35.33 even 12
1050.2.o.l.949.2 4 35.12 even 12
7350.2.a.e.1.1 1 35.34 odd 2
7350.2.a.v.1.1 1 5.4 even 2
7350.2.a.bs.1.1 1 1.1 even 1 trivial
7350.2.a.ci.1.1 1 7.6 odd 2