Properties

Label 574.2.a.g.1.1
Level $574$
Weight $2$
Character 574.1
Self dual yes
Analytic conductor $4.583$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 574 = 2 \cdot 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 574.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(4.58341307602\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 574.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -3.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -3.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +6.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -3.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -3.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +6.00000 q^{9} -1.00000 q^{10} -2.00000 q^{11} -3.00000 q^{12} +1.00000 q^{14} +3.00000 q^{15} +1.00000 q^{16} -3.00000 q^{17} +6.00000 q^{18} -8.00000 q^{19} -1.00000 q^{20} -3.00000 q^{21} -2.00000 q^{22} -4.00000 q^{23} -3.00000 q^{24} -4.00000 q^{25} -9.00000 q^{27} +1.00000 q^{28} -5.00000 q^{29} +3.00000 q^{30} -3.00000 q^{31} +1.00000 q^{32} +6.00000 q^{33} -3.00000 q^{34} -1.00000 q^{35} +6.00000 q^{36} +10.0000 q^{37} -8.00000 q^{38} -1.00000 q^{40} -1.00000 q^{41} -3.00000 q^{42} -5.00000 q^{43} -2.00000 q^{44} -6.00000 q^{45} -4.00000 q^{46} +6.00000 q^{47} -3.00000 q^{48} +1.00000 q^{49} -4.00000 q^{50} +9.00000 q^{51} -9.00000 q^{53} -9.00000 q^{54} +2.00000 q^{55} +1.00000 q^{56} +24.0000 q^{57} -5.00000 q^{58} -10.0000 q^{59} +3.00000 q^{60} +13.0000 q^{61} -3.00000 q^{62} +6.00000 q^{63} +1.00000 q^{64} +6.00000 q^{66} -2.00000 q^{67} -3.00000 q^{68} +12.0000 q^{69} -1.00000 q^{70} +9.00000 q^{71} +6.00000 q^{72} +4.00000 q^{73} +10.0000 q^{74} +12.0000 q^{75} -8.00000 q^{76} -2.00000 q^{77} -11.0000 q^{79} -1.00000 q^{80} +9.00000 q^{81} -1.00000 q^{82} -14.0000 q^{83} -3.00000 q^{84} +3.00000 q^{85} -5.00000 q^{86} +15.0000 q^{87} -2.00000 q^{88} -1.00000 q^{89} -6.00000 q^{90} -4.00000 q^{92} +9.00000 q^{93} +6.00000 q^{94} +8.00000 q^{95} -3.00000 q^{96} +7.00000 q^{97} +1.00000 q^{98} -12.0000 q^{99} +O(q^{100})\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −3.00000 −1.73205 −0.866025 0.500000i \(-0.833333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214 −0.223607 0.974679i \(-0.571783\pi\)
−0.223607 + 0.974679i \(0.571783\pi\)
\(6\) −3.00000 −1.22474
\(7\) 1.00000 0.377964
\(8\) 1.00000 0.353553
\(9\) 6.00000 2.00000
\(10\) −1.00000 −0.316228
\(11\) −2.00000 −0.603023 −0.301511 0.953463i \(-0.597491\pi\)
−0.301511 + 0.953463i \(0.597491\pi\)
\(12\) −3.00000 −0.866025
\(13\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) 1.00000 0.267261
\(15\) 3.00000 0.774597
\(16\) 1.00000 0.250000
\(17\) −3.00000 −0.727607 −0.363803 0.931476i \(-0.618522\pi\)
−0.363803 + 0.931476i \(0.618522\pi\)
\(18\) 6.00000 1.41421
\(19\) −8.00000 −1.83533 −0.917663 0.397360i \(-0.869927\pi\)
−0.917663 + 0.397360i \(0.869927\pi\)
\(20\) −1.00000 −0.223607
\(21\) −3.00000 −0.654654
\(22\) −2.00000 −0.426401
\(23\) −4.00000 −0.834058 −0.417029 0.908893i \(-0.636929\pi\)
−0.417029 + 0.908893i \(0.636929\pi\)
\(24\) −3.00000 −0.612372
\(25\) −4.00000 −0.800000
\(26\) 0 0
\(27\) −9.00000 −1.73205
\(28\) 1.00000 0.188982
\(29\) −5.00000 −0.928477 −0.464238 0.885710i \(-0.653672\pi\)
−0.464238 + 0.885710i \(0.653672\pi\)
\(30\) 3.00000 0.547723
\(31\) −3.00000 −0.538816 −0.269408 0.963026i \(-0.586828\pi\)
−0.269408 + 0.963026i \(0.586828\pi\)
\(32\) 1.00000 0.176777
\(33\) 6.00000 1.04447
\(34\) −3.00000 −0.514496
\(35\) −1.00000 −0.169031
\(36\) 6.00000 1.00000
\(37\) 10.0000 1.64399 0.821995 0.569495i \(-0.192861\pi\)
0.821995 + 0.569495i \(0.192861\pi\)
\(38\) −8.00000 −1.29777
\(39\) 0 0
\(40\) −1.00000 −0.158114
\(41\) −1.00000 −0.156174
\(42\) −3.00000 −0.462910
\(43\) −5.00000 −0.762493 −0.381246 0.924473i \(-0.624505\pi\)
−0.381246 + 0.924473i \(0.624505\pi\)
\(44\) −2.00000 −0.301511
\(45\) −6.00000 −0.894427
\(46\) −4.00000 −0.589768
\(47\) 6.00000 0.875190 0.437595 0.899172i \(-0.355830\pi\)
0.437595 + 0.899172i \(0.355830\pi\)
\(48\) −3.00000 −0.433013
\(49\) 1.00000 0.142857
\(50\) −4.00000 −0.565685
\(51\) 9.00000 1.26025
\(52\) 0 0
\(53\) −9.00000 −1.23625 −0.618123 0.786082i \(-0.712106\pi\)
−0.618123 + 0.786082i \(0.712106\pi\)
\(54\) −9.00000 −1.22474
\(55\) 2.00000 0.269680
\(56\) 1.00000 0.133631
\(57\) 24.0000 3.17888
\(58\) −5.00000 −0.656532
\(59\) −10.0000 −1.30189 −0.650945 0.759125i \(-0.725627\pi\)
−0.650945 + 0.759125i \(0.725627\pi\)
\(60\) 3.00000 0.387298
\(61\) 13.0000 1.66448 0.832240 0.554416i \(-0.187058\pi\)
0.832240 + 0.554416i \(0.187058\pi\)
\(62\) −3.00000 −0.381000
\(63\) 6.00000 0.755929
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 6.00000 0.738549
\(67\) −2.00000 −0.244339 −0.122169 0.992509i \(-0.538985\pi\)
−0.122169 + 0.992509i \(0.538985\pi\)
\(68\) −3.00000 −0.363803
\(69\) 12.0000 1.44463
\(70\) −1.00000 −0.119523
\(71\) 9.00000 1.06810 0.534052 0.845452i \(-0.320669\pi\)
0.534052 + 0.845452i \(0.320669\pi\)
\(72\) 6.00000 0.707107
\(73\) 4.00000 0.468165 0.234082 0.972217i \(-0.424791\pi\)
0.234082 + 0.972217i \(0.424791\pi\)
\(74\) 10.0000 1.16248
\(75\) 12.0000 1.38564
\(76\) −8.00000 −0.917663
\(77\) −2.00000 −0.227921
\(78\) 0 0
\(79\) −11.0000 −1.23760 −0.618798 0.785550i \(-0.712380\pi\)
−0.618798 + 0.785550i \(0.712380\pi\)
\(80\) −1.00000 −0.111803
\(81\) 9.00000 1.00000
\(82\) −1.00000 −0.110432
\(83\) −14.0000 −1.53670 −0.768350 0.640030i \(-0.778922\pi\)
−0.768350 + 0.640030i \(0.778922\pi\)
\(84\) −3.00000 −0.327327
\(85\) 3.00000 0.325396
\(86\) −5.00000 −0.539164
\(87\) 15.0000 1.60817
\(88\) −2.00000 −0.213201
\(89\) −1.00000 −0.106000 −0.0529999 0.998595i \(-0.516878\pi\)
−0.0529999 + 0.998595i \(0.516878\pi\)
\(90\) −6.00000 −0.632456
\(91\) 0 0
\(92\) −4.00000 −0.417029
\(93\) 9.00000 0.933257
\(94\) 6.00000 0.618853
\(95\) 8.00000 0.820783
\(96\) −3.00000 −0.306186
\(97\) 7.00000 0.710742 0.355371 0.934725i \(-0.384354\pi\)
0.355371 + 0.934725i \(0.384354\pi\)
\(98\) 1.00000 0.101015
\(99\) −12.0000 −1.20605
\(100\) −4.00000 −0.400000
\(101\) −10.0000 −0.995037 −0.497519 0.867453i \(-0.665755\pi\)
−0.497519 + 0.867453i \(0.665755\pi\)
\(102\) 9.00000 0.891133
\(103\) 13.0000 1.28093 0.640464 0.767988i \(-0.278742\pi\)
0.640464 + 0.767988i \(0.278742\pi\)
\(104\) 0 0
\(105\) 3.00000 0.292770
\(106\) −9.00000 −0.874157
\(107\) 3.00000 0.290021 0.145010 0.989430i \(-0.453678\pi\)
0.145010 + 0.989430i \(0.453678\pi\)
\(108\) −9.00000 −0.866025
\(109\) −2.00000 −0.191565 −0.0957826 0.995402i \(-0.530535\pi\)
−0.0957826 + 0.995402i \(0.530535\pi\)
\(110\) 2.00000 0.190693
\(111\) −30.0000 −2.84747
\(112\) 1.00000 0.0944911
\(113\) 9.00000 0.846649 0.423324 0.905978i \(-0.360863\pi\)
0.423324 + 0.905978i \(0.360863\pi\)
\(114\) 24.0000 2.24781
\(115\) 4.00000 0.373002
\(116\) −5.00000 −0.464238
\(117\) 0 0
\(118\) −10.0000 −0.920575
\(119\) −3.00000 −0.275010
\(120\) 3.00000 0.273861
\(121\) −7.00000 −0.636364
\(122\) 13.0000 1.17696
\(123\) 3.00000 0.270501
\(124\) −3.00000 −0.269408
\(125\) 9.00000 0.804984
\(126\) 6.00000 0.534522
\(127\) 2.00000 0.177471 0.0887357 0.996055i \(-0.471717\pi\)
0.0887357 + 0.996055i \(0.471717\pi\)
\(128\) 1.00000 0.0883883
\(129\) 15.0000 1.32068
\(130\) 0 0
\(131\) −8.00000 −0.698963 −0.349482 0.936943i \(-0.613642\pi\)
−0.349482 + 0.936943i \(0.613642\pi\)
\(132\) 6.00000 0.522233
\(133\) −8.00000 −0.693688
\(134\) −2.00000 −0.172774
\(135\) 9.00000 0.774597
\(136\) −3.00000 −0.257248
\(137\) 12.0000 1.02523 0.512615 0.858619i \(-0.328677\pi\)
0.512615 + 0.858619i \(0.328677\pi\)
\(138\) 12.0000 1.02151
\(139\) 14.0000 1.18746 0.593732 0.804663i \(-0.297654\pi\)
0.593732 + 0.804663i \(0.297654\pi\)
\(140\) −1.00000 −0.0845154
\(141\) −18.0000 −1.51587
\(142\) 9.00000 0.755263
\(143\) 0 0
\(144\) 6.00000 0.500000
\(145\) 5.00000 0.415227
\(146\) 4.00000 0.331042
\(147\) −3.00000 −0.247436
\(148\) 10.0000 0.821995
\(149\) 3.00000 0.245770 0.122885 0.992421i \(-0.460785\pi\)
0.122885 + 0.992421i \(0.460785\pi\)
\(150\) 12.0000 0.979796
\(151\) 19.0000 1.54620 0.773099 0.634285i \(-0.218706\pi\)
0.773099 + 0.634285i \(0.218706\pi\)
\(152\) −8.00000 −0.648886
\(153\) −18.0000 −1.45521
\(154\) −2.00000 −0.161165
\(155\) 3.00000 0.240966
\(156\) 0 0
\(157\) 4.00000 0.319235 0.159617 0.987179i \(-0.448974\pi\)
0.159617 + 0.987179i \(0.448974\pi\)
\(158\) −11.0000 −0.875113
\(159\) 27.0000 2.14124
\(160\) −1.00000 −0.0790569
\(161\) −4.00000 −0.315244
\(162\) 9.00000 0.707107
\(163\) −4.00000 −0.313304 −0.156652 0.987654i \(-0.550070\pi\)
−0.156652 + 0.987654i \(0.550070\pi\)
\(164\) −1.00000 −0.0780869
\(165\) −6.00000 −0.467099
\(166\) −14.0000 −1.08661
\(167\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(168\) −3.00000 −0.231455
\(169\) −13.0000 −1.00000
\(170\) 3.00000 0.230089
\(171\) −48.0000 −3.67065
\(172\) −5.00000 −0.381246
\(173\) −1.00000 −0.0760286 −0.0380143 0.999277i \(-0.512103\pi\)
−0.0380143 + 0.999277i \(0.512103\pi\)
\(174\) 15.0000 1.13715
\(175\) −4.00000 −0.302372
\(176\) −2.00000 −0.150756
\(177\) 30.0000 2.25494
\(178\) −1.00000 −0.0749532
\(179\) −16.0000 −1.19590 −0.597948 0.801535i \(-0.704017\pi\)
−0.597948 + 0.801535i \(0.704017\pi\)
\(180\) −6.00000 −0.447214
\(181\) −14.0000 −1.04061 −0.520306 0.853980i \(-0.674182\pi\)
−0.520306 + 0.853980i \(0.674182\pi\)
\(182\) 0 0
\(183\) −39.0000 −2.88296
\(184\) −4.00000 −0.294884
\(185\) −10.0000 −0.735215
\(186\) 9.00000 0.659912
\(187\) 6.00000 0.438763
\(188\) 6.00000 0.437595
\(189\) −9.00000 −0.654654
\(190\) 8.00000 0.580381
\(191\) −11.0000 −0.795932 −0.397966 0.917400i \(-0.630284\pi\)
−0.397966 + 0.917400i \(0.630284\pi\)
\(192\) −3.00000 −0.216506
\(193\) 12.0000 0.863779 0.431889 0.901927i \(-0.357847\pi\)
0.431889 + 0.901927i \(0.357847\pi\)
\(194\) 7.00000 0.502571
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) −12.0000 −0.854965 −0.427482 0.904024i \(-0.640599\pi\)
−0.427482 + 0.904024i \(0.640599\pi\)
\(198\) −12.0000 −0.852803
\(199\) −24.0000 −1.70131 −0.850657 0.525720i \(-0.823796\pi\)
−0.850657 + 0.525720i \(0.823796\pi\)
\(200\) −4.00000 −0.282843
\(201\) 6.00000 0.423207
\(202\) −10.0000 −0.703598
\(203\) −5.00000 −0.350931
\(204\) 9.00000 0.630126
\(205\) 1.00000 0.0698430
\(206\) 13.0000 0.905753
\(207\) −24.0000 −1.66812
\(208\) 0 0
\(209\) 16.0000 1.10674
\(210\) 3.00000 0.207020
\(211\) −12.0000 −0.826114 −0.413057 0.910705i \(-0.635539\pi\)
−0.413057 + 0.910705i \(0.635539\pi\)
\(212\) −9.00000 −0.618123
\(213\) −27.0000 −1.85001
\(214\) 3.00000 0.205076
\(215\) 5.00000 0.340997
\(216\) −9.00000 −0.612372
\(217\) −3.00000 −0.203653
\(218\) −2.00000 −0.135457
\(219\) −12.0000 −0.810885
\(220\) 2.00000 0.134840
\(221\) 0 0
\(222\) −30.0000 −2.01347
\(223\) 21.0000 1.40626 0.703132 0.711059i \(-0.251784\pi\)
0.703132 + 0.711059i \(0.251784\pi\)
\(224\) 1.00000 0.0668153
\(225\) −24.0000 −1.60000
\(226\) 9.00000 0.598671
\(227\) 25.0000 1.65931 0.829654 0.558278i \(-0.188538\pi\)
0.829654 + 0.558278i \(0.188538\pi\)
\(228\) 24.0000 1.58944
\(229\) 20.0000 1.32164 0.660819 0.750546i \(-0.270209\pi\)
0.660819 + 0.750546i \(0.270209\pi\)
\(230\) 4.00000 0.263752
\(231\) 6.00000 0.394771
\(232\) −5.00000 −0.328266
\(233\) 10.0000 0.655122 0.327561 0.944830i \(-0.393773\pi\)
0.327561 + 0.944830i \(0.393773\pi\)
\(234\) 0 0
\(235\) −6.00000 −0.391397
\(236\) −10.0000 −0.650945
\(237\) 33.0000 2.14358
\(238\) −3.00000 −0.194461
\(239\) −12.0000 −0.776215 −0.388108 0.921614i \(-0.626871\pi\)
−0.388108 + 0.921614i \(0.626871\pi\)
\(240\) 3.00000 0.193649
\(241\) −10.0000 −0.644157 −0.322078 0.946713i \(-0.604381\pi\)
−0.322078 + 0.946713i \(0.604381\pi\)
\(242\) −7.00000 −0.449977
\(243\) 0 0
\(244\) 13.0000 0.832240
\(245\) −1.00000 −0.0638877
\(246\) 3.00000 0.191273
\(247\) 0 0
\(248\) −3.00000 −0.190500
\(249\) 42.0000 2.66164
\(250\) 9.00000 0.569210
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 6.00000 0.377964
\(253\) 8.00000 0.502956
\(254\) 2.00000 0.125491
\(255\) −9.00000 −0.563602
\(256\) 1.00000 0.0625000
\(257\) −15.0000 −0.935674 −0.467837 0.883815i \(-0.654967\pi\)
−0.467837 + 0.883815i \(0.654967\pi\)
\(258\) 15.0000 0.933859
\(259\) 10.0000 0.621370
\(260\) 0 0
\(261\) −30.0000 −1.85695
\(262\) −8.00000 −0.494242
\(263\) −16.0000 −0.986602 −0.493301 0.869859i \(-0.664210\pi\)
−0.493301 + 0.869859i \(0.664210\pi\)
\(264\) 6.00000 0.369274
\(265\) 9.00000 0.552866
\(266\) −8.00000 −0.490511
\(267\) 3.00000 0.183597
\(268\) −2.00000 −0.122169
\(269\) −10.0000 −0.609711 −0.304855 0.952399i \(-0.598608\pi\)
−0.304855 + 0.952399i \(0.598608\pi\)
\(270\) 9.00000 0.547723
\(271\) 20.0000 1.21491 0.607457 0.794353i \(-0.292190\pi\)
0.607457 + 0.794353i \(0.292190\pi\)
\(272\) −3.00000 −0.181902
\(273\) 0 0
\(274\) 12.0000 0.724947
\(275\) 8.00000 0.482418
\(276\) 12.0000 0.722315
\(277\) 26.0000 1.56219 0.781094 0.624413i \(-0.214662\pi\)
0.781094 + 0.624413i \(0.214662\pi\)
\(278\) 14.0000 0.839664
\(279\) −18.0000 −1.07763
\(280\) −1.00000 −0.0597614
\(281\) 2.00000 0.119310 0.0596550 0.998219i \(-0.481000\pi\)
0.0596550 + 0.998219i \(0.481000\pi\)
\(282\) −18.0000 −1.07188
\(283\) 18.0000 1.06999 0.534994 0.844856i \(-0.320314\pi\)
0.534994 + 0.844856i \(0.320314\pi\)
\(284\) 9.00000 0.534052
\(285\) −24.0000 −1.42164
\(286\) 0 0
\(287\) −1.00000 −0.0590281
\(288\) 6.00000 0.353553
\(289\) −8.00000 −0.470588
\(290\) 5.00000 0.293610
\(291\) −21.0000 −1.23104
\(292\) 4.00000 0.234082
\(293\) 14.0000 0.817889 0.408944 0.912559i \(-0.365897\pi\)
0.408944 + 0.912559i \(0.365897\pi\)
\(294\) −3.00000 −0.174964
\(295\) 10.0000 0.582223
\(296\) 10.0000 0.581238
\(297\) 18.0000 1.04447
\(298\) 3.00000 0.173785
\(299\) 0 0
\(300\) 12.0000 0.692820
\(301\) −5.00000 −0.288195
\(302\) 19.0000 1.09333
\(303\) 30.0000 1.72345
\(304\) −8.00000 −0.458831
\(305\) −13.0000 −0.744378
\(306\) −18.0000 −1.02899
\(307\) −28.0000 −1.59804 −0.799022 0.601302i \(-0.794649\pi\)
−0.799022 + 0.601302i \(0.794649\pi\)
\(308\) −2.00000 −0.113961
\(309\) −39.0000 −2.21863
\(310\) 3.00000 0.170389
\(311\) 18.0000 1.02069 0.510343 0.859971i \(-0.329518\pi\)
0.510343 + 0.859971i \(0.329518\pi\)
\(312\) 0 0
\(313\) −22.0000 −1.24351 −0.621757 0.783210i \(-0.713581\pi\)
−0.621757 + 0.783210i \(0.713581\pi\)
\(314\) 4.00000 0.225733
\(315\) −6.00000 −0.338062
\(316\) −11.0000 −0.618798
\(317\) −18.0000 −1.01098 −0.505490 0.862832i \(-0.668688\pi\)
−0.505490 + 0.862832i \(0.668688\pi\)
\(318\) 27.0000 1.51408
\(319\) 10.0000 0.559893
\(320\) −1.00000 −0.0559017
\(321\) −9.00000 −0.502331
\(322\) −4.00000 −0.222911
\(323\) 24.0000 1.33540
\(324\) 9.00000 0.500000
\(325\) 0 0
\(326\) −4.00000 −0.221540
\(327\) 6.00000 0.331801
\(328\) −1.00000 −0.0552158
\(329\) 6.00000 0.330791
\(330\) −6.00000 −0.330289
\(331\) −32.0000 −1.75888 −0.879440 0.476011i \(-0.842082\pi\)
−0.879440 + 0.476011i \(0.842082\pi\)
\(332\) −14.0000 −0.768350
\(333\) 60.0000 3.28798
\(334\) 0 0
\(335\) 2.00000 0.109272
\(336\) −3.00000 −0.163663
\(337\) −19.0000 −1.03500 −0.517498 0.855684i \(-0.673136\pi\)
−0.517498 + 0.855684i \(0.673136\pi\)
\(338\) −13.0000 −0.707107
\(339\) −27.0000 −1.46644
\(340\) 3.00000 0.162698
\(341\) 6.00000 0.324918
\(342\) −48.0000 −2.59554
\(343\) 1.00000 0.0539949
\(344\) −5.00000 −0.269582
\(345\) −12.0000 −0.646058
\(346\) −1.00000 −0.0537603
\(347\) 12.0000 0.644194 0.322097 0.946707i \(-0.395612\pi\)
0.322097 + 0.946707i \(0.395612\pi\)
\(348\) 15.0000 0.804084
\(349\) 14.0000 0.749403 0.374701 0.927146i \(-0.377745\pi\)
0.374701 + 0.927146i \(0.377745\pi\)
\(350\) −4.00000 −0.213809
\(351\) 0 0
\(352\) −2.00000 −0.106600
\(353\) −24.0000 −1.27739 −0.638696 0.769460i \(-0.720526\pi\)
−0.638696 + 0.769460i \(0.720526\pi\)
\(354\) 30.0000 1.59448
\(355\) −9.00000 −0.477670
\(356\) −1.00000 −0.0529999
\(357\) 9.00000 0.476331
\(358\) −16.0000 −0.845626
\(359\) 24.0000 1.26667 0.633336 0.773877i \(-0.281685\pi\)
0.633336 + 0.773877i \(0.281685\pi\)
\(360\) −6.00000 −0.316228
\(361\) 45.0000 2.36842
\(362\) −14.0000 −0.735824
\(363\) 21.0000 1.10221
\(364\) 0 0
\(365\) −4.00000 −0.209370
\(366\) −39.0000 −2.03856
\(367\) −17.0000 −0.887393 −0.443696 0.896177i \(-0.646333\pi\)
−0.443696 + 0.896177i \(0.646333\pi\)
\(368\) −4.00000 −0.208514
\(369\) −6.00000 −0.312348
\(370\) −10.0000 −0.519875
\(371\) −9.00000 −0.467257
\(372\) 9.00000 0.466628
\(373\) −18.0000 −0.932005 −0.466002 0.884783i \(-0.654306\pi\)
−0.466002 + 0.884783i \(0.654306\pi\)
\(374\) 6.00000 0.310253
\(375\) −27.0000 −1.39427
\(376\) 6.00000 0.309426
\(377\) 0 0
\(378\) −9.00000 −0.462910
\(379\) 37.0000 1.90056 0.950281 0.311393i \(-0.100796\pi\)
0.950281 + 0.311393i \(0.100796\pi\)
\(380\) 8.00000 0.410391
\(381\) −6.00000 −0.307389
\(382\) −11.0000 −0.562809
\(383\) −22.0000 −1.12415 −0.562074 0.827087i \(-0.689996\pi\)
−0.562074 + 0.827087i \(0.689996\pi\)
\(384\) −3.00000 −0.153093
\(385\) 2.00000 0.101929
\(386\) 12.0000 0.610784
\(387\) −30.0000 −1.52499
\(388\) 7.00000 0.355371
\(389\) −2.00000 −0.101404 −0.0507020 0.998714i \(-0.516146\pi\)
−0.0507020 + 0.998714i \(0.516146\pi\)
\(390\) 0 0
\(391\) 12.0000 0.606866
\(392\) 1.00000 0.0505076
\(393\) 24.0000 1.21064
\(394\) −12.0000 −0.604551
\(395\) 11.0000 0.553470
\(396\) −12.0000 −0.603023
\(397\) 20.0000 1.00377 0.501886 0.864934i \(-0.332640\pi\)
0.501886 + 0.864934i \(0.332640\pi\)
\(398\) −24.0000 −1.20301
\(399\) 24.0000 1.20150
\(400\) −4.00000 −0.200000
\(401\) −25.0000 −1.24844 −0.624220 0.781248i \(-0.714583\pi\)
−0.624220 + 0.781248i \(0.714583\pi\)
\(402\) 6.00000 0.299253
\(403\) 0 0
\(404\) −10.0000 −0.497519
\(405\) −9.00000 −0.447214
\(406\) −5.00000 −0.248146
\(407\) −20.0000 −0.991363
\(408\) 9.00000 0.445566
\(409\) −10.0000 −0.494468 −0.247234 0.968956i \(-0.579522\pi\)
−0.247234 + 0.968956i \(0.579522\pi\)
\(410\) 1.00000 0.0493865
\(411\) −36.0000 −1.77575
\(412\) 13.0000 0.640464
\(413\) −10.0000 −0.492068
\(414\) −24.0000 −1.17954
\(415\) 14.0000 0.687233
\(416\) 0 0
\(417\) −42.0000 −2.05675
\(418\) 16.0000 0.782586
\(419\) 28.0000 1.36789 0.683945 0.729534i \(-0.260263\pi\)
0.683945 + 0.729534i \(0.260263\pi\)
\(420\) 3.00000 0.146385
\(421\) −19.0000 −0.926003 −0.463002 0.886357i \(-0.653228\pi\)
−0.463002 + 0.886357i \(0.653228\pi\)
\(422\) −12.0000 −0.584151
\(423\) 36.0000 1.75038
\(424\) −9.00000 −0.437079
\(425\) 12.0000 0.582086
\(426\) −27.0000 −1.30815
\(427\) 13.0000 0.629114
\(428\) 3.00000 0.145010
\(429\) 0 0
\(430\) 5.00000 0.241121
\(431\) −16.0000 −0.770693 −0.385346 0.922772i \(-0.625918\pi\)
−0.385346 + 0.922772i \(0.625918\pi\)
\(432\) −9.00000 −0.433013
\(433\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(434\) −3.00000 −0.144005
\(435\) −15.0000 −0.719195
\(436\) −2.00000 −0.0957826
\(437\) 32.0000 1.53077
\(438\) −12.0000 −0.573382
\(439\) 34.0000 1.62273 0.811366 0.584539i \(-0.198725\pi\)
0.811366 + 0.584539i \(0.198725\pi\)
\(440\) 2.00000 0.0953463
\(441\) 6.00000 0.285714
\(442\) 0 0
\(443\) −25.0000 −1.18779 −0.593893 0.804544i \(-0.702410\pi\)
−0.593893 + 0.804544i \(0.702410\pi\)
\(444\) −30.0000 −1.42374
\(445\) 1.00000 0.0474045
\(446\) 21.0000 0.994379
\(447\) −9.00000 −0.425685
\(448\) 1.00000 0.0472456
\(449\) −33.0000 −1.55737 −0.778683 0.627417i \(-0.784112\pi\)
−0.778683 + 0.627417i \(0.784112\pi\)
\(450\) −24.0000 −1.13137
\(451\) 2.00000 0.0941763
\(452\) 9.00000 0.423324
\(453\) −57.0000 −2.67809
\(454\) 25.0000 1.17331
\(455\) 0 0
\(456\) 24.0000 1.12390
\(457\) −18.0000 −0.842004 −0.421002 0.907060i \(-0.638322\pi\)
−0.421002 + 0.907060i \(0.638322\pi\)
\(458\) 20.0000 0.934539
\(459\) 27.0000 1.26025
\(460\) 4.00000 0.186501
\(461\) −21.0000 −0.978068 −0.489034 0.872265i \(-0.662651\pi\)
−0.489034 + 0.872265i \(0.662651\pi\)
\(462\) 6.00000 0.279145
\(463\) 16.0000 0.743583 0.371792 0.928316i \(-0.378744\pi\)
0.371792 + 0.928316i \(0.378744\pi\)
\(464\) −5.00000 −0.232119
\(465\) −9.00000 −0.417365
\(466\) 10.0000 0.463241
\(467\) 6.00000 0.277647 0.138823 0.990317i \(-0.455668\pi\)
0.138823 + 0.990317i \(0.455668\pi\)
\(468\) 0 0
\(469\) −2.00000 −0.0923514
\(470\) −6.00000 −0.276759
\(471\) −12.0000 −0.552931
\(472\) −10.0000 −0.460287
\(473\) 10.0000 0.459800
\(474\) 33.0000 1.51574
\(475\) 32.0000 1.46826
\(476\) −3.00000 −0.137505
\(477\) −54.0000 −2.47249
\(478\) −12.0000 −0.548867
\(479\) −10.0000 −0.456912 −0.228456 0.973554i \(-0.573368\pi\)
−0.228456 + 0.973554i \(0.573368\pi\)
\(480\) 3.00000 0.136931
\(481\) 0 0
\(482\) −10.0000 −0.455488
\(483\) 12.0000 0.546019
\(484\) −7.00000 −0.318182
\(485\) −7.00000 −0.317854
\(486\) 0 0
\(487\) 12.0000 0.543772 0.271886 0.962329i \(-0.412353\pi\)
0.271886 + 0.962329i \(0.412353\pi\)
\(488\) 13.0000 0.588482
\(489\) 12.0000 0.542659
\(490\) −1.00000 −0.0451754
\(491\) 37.0000 1.66979 0.834893 0.550412i \(-0.185529\pi\)
0.834893 + 0.550412i \(0.185529\pi\)
\(492\) 3.00000 0.135250
\(493\) 15.0000 0.675566
\(494\) 0 0
\(495\) 12.0000 0.539360
\(496\) −3.00000 −0.134704
\(497\) 9.00000 0.403705
\(498\) 42.0000 1.88207
\(499\) 10.0000 0.447661 0.223831 0.974628i \(-0.428144\pi\)
0.223831 + 0.974628i \(0.428144\pi\)
\(500\) 9.00000 0.402492
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 6.00000 0.267261
\(505\) 10.0000 0.444994
\(506\) 8.00000 0.355643
\(507\) 39.0000 1.73205
\(508\) 2.00000 0.0887357
\(509\) −36.0000 −1.59567 −0.797836 0.602875i \(-0.794022\pi\)
−0.797836 + 0.602875i \(0.794022\pi\)
\(510\) −9.00000 −0.398527
\(511\) 4.00000 0.176950
\(512\) 1.00000 0.0441942
\(513\) 72.0000 3.17888
\(514\) −15.0000 −0.661622
\(515\) −13.0000 −0.572848
\(516\) 15.0000 0.660338
\(517\) −12.0000 −0.527759
\(518\) 10.0000 0.439375
\(519\) 3.00000 0.131685
\(520\) 0 0
\(521\) −38.0000 −1.66481 −0.832405 0.554168i \(-0.813037\pi\)
−0.832405 + 0.554168i \(0.813037\pi\)
\(522\) −30.0000 −1.31306
\(523\) 20.0000 0.874539 0.437269 0.899331i \(-0.355946\pi\)
0.437269 + 0.899331i \(0.355946\pi\)
\(524\) −8.00000 −0.349482
\(525\) 12.0000 0.523723
\(526\) −16.0000 −0.697633
\(527\) 9.00000 0.392046
\(528\) 6.00000 0.261116
\(529\) −7.00000 −0.304348
\(530\) 9.00000 0.390935
\(531\) −60.0000 −2.60378
\(532\) −8.00000 −0.346844
\(533\) 0 0
\(534\) 3.00000 0.129823
\(535\) −3.00000 −0.129701
\(536\) −2.00000 −0.0863868
\(537\) 48.0000 2.07135
\(538\) −10.0000 −0.431131
\(539\) −2.00000 −0.0861461
\(540\) 9.00000 0.387298
\(541\) 10.0000 0.429934 0.214967 0.976621i \(-0.431036\pi\)
0.214967 + 0.976621i \(0.431036\pi\)
\(542\) 20.0000 0.859074
\(543\) 42.0000 1.80239
\(544\) −3.00000 −0.128624
\(545\) 2.00000 0.0856706
\(546\) 0 0
\(547\) 2.00000 0.0855138 0.0427569 0.999086i \(-0.486386\pi\)
0.0427569 + 0.999086i \(0.486386\pi\)
\(548\) 12.0000 0.512615
\(549\) 78.0000 3.32896
\(550\) 8.00000 0.341121
\(551\) 40.0000 1.70406
\(552\) 12.0000 0.510754
\(553\) −11.0000 −0.467768
\(554\) 26.0000 1.10463
\(555\) 30.0000 1.27343
\(556\) 14.0000 0.593732
\(557\) 33.0000 1.39825 0.699127 0.714997i \(-0.253572\pi\)
0.699127 + 0.714997i \(0.253572\pi\)
\(558\) −18.0000 −0.762001
\(559\) 0 0
\(560\) −1.00000 −0.0422577
\(561\) −18.0000 −0.759961
\(562\) 2.00000 0.0843649
\(563\) 4.00000 0.168580 0.0842900 0.996441i \(-0.473138\pi\)
0.0842900 + 0.996441i \(0.473138\pi\)
\(564\) −18.0000 −0.757937
\(565\) −9.00000 −0.378633
\(566\) 18.0000 0.756596
\(567\) 9.00000 0.377964
\(568\) 9.00000 0.377632
\(569\) −25.0000 −1.04805 −0.524027 0.851701i \(-0.675571\pi\)
−0.524027 + 0.851701i \(0.675571\pi\)
\(570\) −24.0000 −1.00525
\(571\) −44.0000 −1.84134 −0.920671 0.390339i \(-0.872358\pi\)
−0.920671 + 0.390339i \(0.872358\pi\)
\(572\) 0 0
\(573\) 33.0000 1.37859
\(574\) −1.00000 −0.0417392
\(575\) 16.0000 0.667246
\(576\) 6.00000 0.250000
\(577\) 46.0000 1.91501 0.957503 0.288425i \(-0.0931316\pi\)
0.957503 + 0.288425i \(0.0931316\pi\)
\(578\) −8.00000 −0.332756
\(579\) −36.0000 −1.49611
\(580\) 5.00000 0.207614
\(581\) −14.0000 −0.580818
\(582\) −21.0000 −0.870478
\(583\) 18.0000 0.745484
\(584\) 4.00000 0.165521
\(585\) 0 0
\(586\) 14.0000 0.578335
\(587\) −21.0000 −0.866763 −0.433381 0.901211i \(-0.642680\pi\)
−0.433381 + 0.901211i \(0.642680\pi\)
\(588\) −3.00000 −0.123718
\(589\) 24.0000 0.988903
\(590\) 10.0000 0.411693
\(591\) 36.0000 1.48084
\(592\) 10.0000 0.410997
\(593\) −43.0000 −1.76580 −0.882899 0.469563i \(-0.844412\pi\)
−0.882899 + 0.469563i \(0.844412\pi\)
\(594\) 18.0000 0.738549
\(595\) 3.00000 0.122988
\(596\) 3.00000 0.122885
\(597\) 72.0000 2.94676
\(598\) 0 0
\(599\) −44.0000 −1.79779 −0.898896 0.438163i \(-0.855629\pi\)
−0.898896 + 0.438163i \(0.855629\pi\)
\(600\) 12.0000 0.489898
\(601\) 21.0000 0.856608 0.428304 0.903635i \(-0.359111\pi\)
0.428304 + 0.903635i \(0.359111\pi\)
\(602\) −5.00000 −0.203785
\(603\) −12.0000 −0.488678
\(604\) 19.0000 0.773099
\(605\) 7.00000 0.284590
\(606\) 30.0000 1.21867
\(607\) −43.0000 −1.74532 −0.872658 0.488332i \(-0.837606\pi\)
−0.872658 + 0.488332i \(0.837606\pi\)
\(608\) −8.00000 −0.324443
\(609\) 15.0000 0.607831
\(610\) −13.0000 −0.526355
\(611\) 0 0
\(612\) −18.0000 −0.727607
\(613\) −16.0000 −0.646234 −0.323117 0.946359i \(-0.604731\pi\)
−0.323117 + 0.946359i \(0.604731\pi\)
\(614\) −28.0000 −1.12999
\(615\) −3.00000 −0.120972
\(616\) −2.00000 −0.0805823
\(617\) 30.0000 1.20775 0.603877 0.797077i \(-0.293622\pi\)
0.603877 + 0.797077i \(0.293622\pi\)
\(618\) −39.0000 −1.56881
\(619\) −24.0000 −0.964641 −0.482321 0.875995i \(-0.660206\pi\)
−0.482321 + 0.875995i \(0.660206\pi\)
\(620\) 3.00000 0.120483
\(621\) 36.0000 1.44463
\(622\) 18.0000 0.721734
\(623\) −1.00000 −0.0400642
\(624\) 0 0
\(625\) 11.0000 0.440000
\(626\) −22.0000 −0.879297
\(627\) −48.0000 −1.91694
\(628\) 4.00000 0.159617
\(629\) −30.0000 −1.19618
\(630\) −6.00000 −0.239046
\(631\) 30.0000 1.19428 0.597141 0.802137i \(-0.296303\pi\)
0.597141 + 0.802137i \(0.296303\pi\)
\(632\) −11.0000 −0.437557
\(633\) 36.0000 1.43087
\(634\) −18.0000 −0.714871
\(635\) −2.00000 −0.0793676
\(636\) 27.0000 1.07062
\(637\) 0 0
\(638\) 10.0000 0.395904
\(639\) 54.0000 2.13621
\(640\) −1.00000 −0.0395285
\(641\) −30.0000 −1.18493 −0.592464 0.805597i \(-0.701845\pi\)
−0.592464 + 0.805597i \(0.701845\pi\)
\(642\) −9.00000 −0.355202
\(643\) −7.00000 −0.276053 −0.138027 0.990429i \(-0.544076\pi\)
−0.138027 + 0.990429i \(0.544076\pi\)
\(644\) −4.00000 −0.157622
\(645\) −15.0000 −0.590624
\(646\) 24.0000 0.944267
\(647\) −3.00000 −0.117942 −0.0589711 0.998260i \(-0.518782\pi\)
−0.0589711 + 0.998260i \(0.518782\pi\)
\(648\) 9.00000 0.353553
\(649\) 20.0000 0.785069
\(650\) 0 0
\(651\) 9.00000 0.352738
\(652\) −4.00000 −0.156652
\(653\) 3.00000 0.117399 0.0586995 0.998276i \(-0.481305\pi\)
0.0586995 + 0.998276i \(0.481305\pi\)
\(654\) 6.00000 0.234619
\(655\) 8.00000 0.312586
\(656\) −1.00000 −0.0390434
\(657\) 24.0000 0.936329
\(658\) 6.00000 0.233904
\(659\) 44.0000 1.71400 0.856998 0.515319i \(-0.172327\pi\)
0.856998 + 0.515319i \(0.172327\pi\)
\(660\) −6.00000 −0.233550
\(661\) −38.0000 −1.47803 −0.739014 0.673690i \(-0.764708\pi\)
−0.739014 + 0.673690i \(0.764708\pi\)
\(662\) −32.0000 −1.24372
\(663\) 0 0
\(664\) −14.0000 −0.543305
\(665\) 8.00000 0.310227
\(666\) 60.0000 2.32495
\(667\) 20.0000 0.774403
\(668\) 0 0
\(669\) −63.0000 −2.43572
\(670\) 2.00000 0.0772667
\(671\) −26.0000 −1.00372
\(672\) −3.00000 −0.115728
\(673\) 30.0000 1.15642 0.578208 0.815890i \(-0.303752\pi\)
0.578208 + 0.815890i \(0.303752\pi\)
\(674\) −19.0000 −0.731853
\(675\) 36.0000 1.38564
\(676\) −13.0000 −0.500000
\(677\) 6.00000 0.230599 0.115299 0.993331i \(-0.463217\pi\)
0.115299 + 0.993331i \(0.463217\pi\)
\(678\) −27.0000 −1.03693
\(679\) 7.00000 0.268635
\(680\) 3.00000 0.115045
\(681\) −75.0000 −2.87401
\(682\) 6.00000 0.229752
\(683\) 40.0000 1.53056 0.765279 0.643699i \(-0.222601\pi\)
0.765279 + 0.643699i \(0.222601\pi\)
\(684\) −48.0000 −1.83533
\(685\) −12.0000 −0.458496
\(686\) 1.00000 0.0381802
\(687\) −60.0000 −2.28914
\(688\) −5.00000 −0.190623
\(689\) 0 0
\(690\) −12.0000 −0.456832
\(691\) 13.0000 0.494543 0.247272 0.968946i \(-0.420466\pi\)
0.247272 + 0.968946i \(0.420466\pi\)
\(692\) −1.00000 −0.0380143
\(693\) −12.0000 −0.455842
\(694\) 12.0000 0.455514
\(695\) −14.0000 −0.531050
\(696\) 15.0000 0.568574
\(697\) 3.00000 0.113633
\(698\) 14.0000 0.529908
\(699\) −30.0000 −1.13470
\(700\) −4.00000 −0.151186
\(701\) 16.0000 0.604312 0.302156 0.953259i \(-0.402294\pi\)
0.302156 + 0.953259i \(0.402294\pi\)
\(702\) 0 0
\(703\) −80.0000 −3.01726
\(704\) −2.00000 −0.0753778
\(705\) 18.0000 0.677919
\(706\) −24.0000 −0.903252
\(707\) −10.0000 −0.376089
\(708\) 30.0000 1.12747
\(709\) 3.00000 0.112667 0.0563337 0.998412i \(-0.482059\pi\)
0.0563337 + 0.998412i \(0.482059\pi\)
\(710\) −9.00000 −0.337764
\(711\) −66.0000 −2.47519
\(712\) −1.00000 −0.0374766
\(713\) 12.0000 0.449404
\(714\) 9.00000 0.336817
\(715\) 0 0
\(716\) −16.0000 −0.597948
\(717\) 36.0000 1.34444
\(718\) 24.0000 0.895672
\(719\) −8.00000 −0.298350 −0.149175 0.988811i \(-0.547662\pi\)
−0.149175 + 0.988811i \(0.547662\pi\)
\(720\) −6.00000 −0.223607
\(721\) 13.0000 0.484145
\(722\) 45.0000 1.67473
\(723\) 30.0000 1.11571
\(724\) −14.0000 −0.520306
\(725\) 20.0000 0.742781
\(726\) 21.0000 0.779383
\(727\) −28.0000 −1.03846 −0.519231 0.854634i \(-0.673782\pi\)
−0.519231 + 0.854634i \(0.673782\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) −4.00000 −0.148047
\(731\) 15.0000 0.554795
\(732\) −39.0000 −1.44148
\(733\) 13.0000 0.480166 0.240083 0.970752i \(-0.422825\pi\)
0.240083 + 0.970752i \(0.422825\pi\)
\(734\) −17.0000 −0.627481
\(735\) 3.00000 0.110657
\(736\) −4.00000 −0.147442
\(737\) 4.00000 0.147342
\(738\) −6.00000 −0.220863
\(739\) 19.0000 0.698926 0.349463 0.936950i \(-0.386364\pi\)
0.349463 + 0.936950i \(0.386364\pi\)
\(740\) −10.0000 −0.367607
\(741\) 0 0
\(742\) −9.00000 −0.330400
\(743\) −12.0000 −0.440237 −0.220119 0.975473i \(-0.570644\pi\)
−0.220119 + 0.975473i \(0.570644\pi\)
\(744\) 9.00000 0.329956
\(745\) −3.00000 −0.109911
\(746\) −18.0000 −0.659027
\(747\) −84.0000 −3.07340
\(748\) 6.00000 0.219382
\(749\) 3.00000 0.109618
\(750\) −27.0000 −0.985901
\(751\) 24.0000 0.875772 0.437886 0.899030i \(-0.355727\pi\)
0.437886 + 0.899030i \(0.355727\pi\)
\(752\) 6.00000 0.218797
\(753\) 0 0
\(754\) 0 0
\(755\) −19.0000 −0.691481
\(756\) −9.00000 −0.327327
\(757\) −5.00000 −0.181728 −0.0908640 0.995863i \(-0.528963\pi\)
−0.0908640 + 0.995863i \(0.528963\pi\)
\(758\) 37.0000 1.34390
\(759\) −24.0000 −0.871145
\(760\) 8.00000 0.290191
\(761\) 6.00000 0.217500 0.108750 0.994069i \(-0.465315\pi\)
0.108750 + 0.994069i \(0.465315\pi\)
\(762\) −6.00000 −0.217357
\(763\) −2.00000 −0.0724049
\(764\) −11.0000 −0.397966
\(765\) 18.0000 0.650791
\(766\) −22.0000 −0.794892
\(767\) 0 0
\(768\) −3.00000 −0.108253
\(769\) −14.0000 −0.504853 −0.252426 0.967616i \(-0.581229\pi\)
−0.252426 + 0.967616i \(0.581229\pi\)
\(770\) 2.00000 0.0720750
\(771\) 45.0000 1.62064
\(772\) 12.0000 0.431889
\(773\) −38.0000 −1.36677 −0.683383 0.730061i \(-0.739492\pi\)
−0.683383 + 0.730061i \(0.739492\pi\)
\(774\) −30.0000 −1.07833
\(775\) 12.0000 0.431053
\(776\) 7.00000 0.251285
\(777\) −30.0000 −1.07624
\(778\) −2.00000 −0.0717035
\(779\) 8.00000 0.286630
\(780\) 0 0
\(781\) −18.0000 −0.644091
\(782\) 12.0000 0.429119
\(783\) 45.0000 1.60817
\(784\) 1.00000 0.0357143
\(785\) −4.00000 −0.142766
\(786\) 24.0000 0.856052
\(787\) −52.0000 −1.85360 −0.926800 0.375555i \(-0.877452\pi\)
−0.926800 + 0.375555i \(0.877452\pi\)
\(788\) −12.0000 −0.427482
\(789\) 48.0000 1.70885
\(790\) 11.0000 0.391362
\(791\) 9.00000 0.320003
\(792\) −12.0000 −0.426401
\(793\) 0 0
\(794\) 20.0000 0.709773
\(795\) −27.0000 −0.957591
\(796\) −24.0000 −0.850657
\(797\) 21.0000 0.743858 0.371929 0.928261i \(-0.378696\pi\)
0.371929 + 0.928261i \(0.378696\pi\)
\(798\) 24.0000 0.849591
\(799\) −18.0000 −0.636794
\(800\) −4.00000 −0.141421
\(801\) −6.00000 −0.212000
\(802\) −25.0000 −0.882781
\(803\) −8.00000 −0.282314
\(804\) 6.00000 0.211604
\(805\) 4.00000 0.140981
\(806\) 0 0
\(807\) 30.0000 1.05605
\(808\) −10.0000 −0.351799
\(809\) 54.0000 1.89854 0.949269 0.314464i \(-0.101825\pi\)
0.949269 + 0.314464i \(0.101825\pi\)
\(810\) −9.00000 −0.316228
\(811\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(812\) −5.00000 −0.175466
\(813\) −60.0000 −2.10429
\(814\) −20.0000 −0.701000
\(815\) 4.00000 0.140114
\(816\) 9.00000 0.315063
\(817\) 40.0000 1.39942
\(818\) −10.0000 −0.349642
\(819\) 0 0
\(820\) 1.00000 0.0349215
\(821\) −4.00000 −0.139601 −0.0698005 0.997561i \(-0.522236\pi\)
−0.0698005 + 0.997561i \(0.522236\pi\)
\(822\) −36.0000 −1.25564
\(823\) −51.0000 −1.77775 −0.888874 0.458151i \(-0.848512\pi\)
−0.888874 + 0.458151i \(0.848512\pi\)
\(824\) 13.0000 0.452876
\(825\) −24.0000 −0.835573
\(826\) −10.0000 −0.347945
\(827\) 30.0000 1.04320 0.521601 0.853189i \(-0.325335\pi\)
0.521601 + 0.853189i \(0.325335\pi\)
\(828\) −24.0000 −0.834058
\(829\) 11.0000 0.382046 0.191023 0.981586i \(-0.438820\pi\)
0.191023 + 0.981586i \(0.438820\pi\)
\(830\) 14.0000 0.485947
\(831\) −78.0000 −2.70579
\(832\) 0 0
\(833\) −3.00000 −0.103944
\(834\) −42.0000 −1.45434
\(835\) 0 0
\(836\) 16.0000 0.553372
\(837\) 27.0000 0.933257
\(838\) 28.0000 0.967244
\(839\) 14.0000 0.483334 0.241667 0.970359i \(-0.422306\pi\)
0.241667 + 0.970359i \(0.422306\pi\)
\(840\) 3.00000 0.103510
\(841\) −4.00000 −0.137931
\(842\) −19.0000 −0.654783
\(843\) −6.00000 −0.206651
\(844\) −12.0000 −0.413057
\(845\) 13.0000 0.447214
\(846\) 36.0000 1.23771
\(847\) −7.00000 −0.240523
\(848\) −9.00000 −0.309061
\(849\) −54.0000 −1.85328
\(850\) 12.0000 0.411597
\(851\) −40.0000 −1.37118
\(852\) −27.0000 −0.925005
\(853\) −21.0000 −0.719026 −0.359513 0.933140i \(-0.617057\pi\)
−0.359513 + 0.933140i \(0.617057\pi\)
\(854\) 13.0000 0.444851
\(855\) 48.0000 1.64157
\(856\) 3.00000 0.102538
\(857\) −38.0000 −1.29806 −0.649028 0.760765i \(-0.724824\pi\)
−0.649028 + 0.760765i \(0.724824\pi\)
\(858\) 0 0
\(859\) −8.00000 −0.272956 −0.136478 0.990643i \(-0.543578\pi\)
−0.136478 + 0.990643i \(0.543578\pi\)
\(860\) 5.00000 0.170499
\(861\) 3.00000 0.102240
\(862\) −16.0000 −0.544962
\(863\) −32.0000 −1.08929 −0.544646 0.838666i \(-0.683336\pi\)
−0.544646 + 0.838666i \(0.683336\pi\)
\(864\) −9.00000 −0.306186
\(865\) 1.00000 0.0340010
\(866\) 0 0
\(867\) 24.0000 0.815083
\(868\) −3.00000 −0.101827
\(869\) 22.0000 0.746299
\(870\) −15.0000 −0.508548
\(871\) 0 0
\(872\) −2.00000 −0.0677285
\(873\) 42.0000 1.42148
\(874\) 32.0000 1.08242
\(875\) 9.00000 0.304256
\(876\) −12.0000 −0.405442
\(877\) −32.0000 −1.08056 −0.540282 0.841484i \(-0.681682\pi\)
−0.540282 + 0.841484i \(0.681682\pi\)
\(878\) 34.0000 1.14744
\(879\) −42.0000 −1.41662
\(880\) 2.00000 0.0674200
\(881\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(882\) 6.00000 0.202031
\(883\) −26.0000 −0.874970 −0.437485 0.899226i \(-0.644131\pi\)
−0.437485 + 0.899226i \(0.644131\pi\)
\(884\) 0 0
\(885\) −30.0000 −1.00844
\(886\) −25.0000 −0.839891
\(887\) 20.0000 0.671534 0.335767 0.941945i \(-0.391004\pi\)
0.335767 + 0.941945i \(0.391004\pi\)
\(888\) −30.0000 −1.00673
\(889\) 2.00000 0.0670778
\(890\) 1.00000 0.0335201
\(891\) −18.0000 −0.603023
\(892\) 21.0000 0.703132
\(893\) −48.0000 −1.60626
\(894\) −9.00000 −0.301005
\(895\) 16.0000 0.534821
\(896\) 1.00000 0.0334077
\(897\) 0 0
\(898\) −33.0000 −1.10122
\(899\) 15.0000 0.500278
\(900\) −24.0000 −0.800000
\(901\) 27.0000 0.899500
\(902\) 2.00000 0.0665927
\(903\) 15.0000 0.499169
\(904\) 9.00000 0.299336
\(905\) 14.0000 0.465376
\(906\) −57.0000 −1.89370
\(907\) 19.0000 0.630885 0.315442 0.948945i \(-0.397847\pi\)
0.315442 + 0.948945i \(0.397847\pi\)
\(908\) 25.0000 0.829654
\(909\) −60.0000 −1.99007
\(910\) 0 0
\(911\) 2.00000 0.0662630 0.0331315 0.999451i \(-0.489452\pi\)
0.0331315 + 0.999451i \(0.489452\pi\)
\(912\) 24.0000 0.794719
\(913\) 28.0000 0.926665
\(914\) −18.0000 −0.595387
\(915\) 39.0000 1.28930
\(916\) 20.0000 0.660819
\(917\) −8.00000 −0.264183
\(918\) 27.0000 0.891133
\(919\) 3.00000 0.0989609 0.0494804 0.998775i \(-0.484243\pi\)
0.0494804 + 0.998775i \(0.484243\pi\)
\(920\) 4.00000 0.131876
\(921\) 84.0000 2.76789
\(922\) −21.0000 −0.691598
\(923\) 0 0
\(924\) 6.00000 0.197386
\(925\) −40.0000 −1.31519
\(926\) 16.0000 0.525793
\(927\) 78.0000 2.56186
\(928\) −5.00000 −0.164133
\(929\) −50.0000 −1.64045 −0.820223 0.572043i \(-0.806151\pi\)
−0.820223 + 0.572043i \(0.806151\pi\)
\(930\) −9.00000 −0.295122
\(931\) −8.00000 −0.262189
\(932\) 10.0000 0.327561
\(933\) −54.0000 −1.76788
\(934\) 6.00000 0.196326
\(935\) −6.00000 −0.196221
\(936\) 0 0
\(937\) 7.00000 0.228680 0.114340 0.993442i \(-0.463525\pi\)
0.114340 + 0.993442i \(0.463525\pi\)
\(938\) −2.00000 −0.0653023
\(939\) 66.0000 2.15383
\(940\) −6.00000 −0.195698
\(941\) 18.0000 0.586783 0.293392 0.955992i \(-0.405216\pi\)
0.293392 + 0.955992i \(0.405216\pi\)
\(942\) −12.0000 −0.390981
\(943\) 4.00000 0.130258
\(944\) −10.0000 −0.325472
\(945\) 9.00000 0.292770
\(946\) 10.0000 0.325128
\(947\) −4.00000 −0.129983 −0.0649913 0.997886i \(-0.520702\pi\)
−0.0649913 + 0.997886i \(0.520702\pi\)
\(948\) 33.0000 1.07179
\(949\) 0 0
\(950\) 32.0000 1.03822
\(951\) 54.0000 1.75107
\(952\) −3.00000 −0.0972306
\(953\) 30.0000 0.971795 0.485898 0.874016i \(-0.338493\pi\)
0.485898 + 0.874016i \(0.338493\pi\)
\(954\) −54.0000 −1.74831
\(955\) 11.0000 0.355952
\(956\) −12.0000 −0.388108
\(957\) −30.0000 −0.969762
\(958\) −10.0000 −0.323085
\(959\) 12.0000 0.387500
\(960\) 3.00000 0.0968246
\(961\) −22.0000 −0.709677
\(962\) 0 0
\(963\) 18.0000 0.580042
\(964\) −10.0000 −0.322078
\(965\) −12.0000 −0.386294
\(966\) 12.0000 0.386094
\(967\) −47.0000 −1.51142 −0.755709 0.654907i \(-0.772708\pi\)
−0.755709 + 0.654907i \(0.772708\pi\)
\(968\) −7.00000 −0.224989
\(969\) −72.0000 −2.31297
\(970\) −7.00000 −0.224756
\(971\) 13.0000 0.417190 0.208595 0.978002i \(-0.433111\pi\)
0.208595 + 0.978002i \(0.433111\pi\)
\(972\) 0 0
\(973\) 14.0000 0.448819
\(974\) 12.0000 0.384505
\(975\) 0 0
\(976\) 13.0000 0.416120
\(977\) 54.0000 1.72761 0.863807 0.503824i \(-0.168074\pi\)
0.863807 + 0.503824i \(0.168074\pi\)
\(978\) 12.0000 0.383718
\(979\) 2.00000 0.0639203
\(980\) −1.00000 −0.0319438
\(981\) −12.0000 −0.383131
\(982\) 37.0000 1.18072
\(983\) −3.00000 −0.0956851 −0.0478426 0.998855i \(-0.515235\pi\)
−0.0478426 + 0.998855i \(0.515235\pi\)
\(984\) 3.00000 0.0956365
\(985\) 12.0000 0.382352
\(986\) 15.0000 0.477697
\(987\) −18.0000 −0.572946
\(988\) 0 0
\(989\) 20.0000 0.635963
\(990\) 12.0000 0.381385
\(991\) 40.0000 1.27064 0.635321 0.772248i \(-0.280868\pi\)
0.635321 + 0.772248i \(0.280868\pi\)
\(992\) −3.00000 −0.0952501
\(993\) 96.0000 3.04647
\(994\) 9.00000 0.285463
\(995\) 24.0000 0.760851
\(996\) 42.0000 1.33082
\(997\) 4.00000 0.126681 0.0633406 0.997992i \(-0.479825\pi\)
0.0633406 + 0.997992i \(0.479825\pi\)
\(998\) 10.0000 0.316544
\(999\) −90.0000 −2.84747
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 574.2.a.g.1.1 1
3.2 odd 2 5166.2.a.o.1.1 1
4.3 odd 2 4592.2.a.l.1.1 1
7.6 odd 2 4018.2.a.s.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
574.2.a.g.1.1 1 1.1 even 1 trivial
4018.2.a.s.1.1 1 7.6 odd 2
4592.2.a.l.1.1 1 4.3 odd 2
5166.2.a.o.1.1 1 3.2 odd 2