Properties

Label 5166.2.a.o.1.1
Level $5166$
Weight $2$
Character 5166.1
Self dual yes
Analytic conductor $41.251$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 5166 = 2 \cdot 3^{2} \cdot 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5166.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(41.2507176842\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 574)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 5166.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{7} -1.00000 q^{8} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{7} -1.00000 q^{8} -1.00000 q^{10} +2.00000 q^{11} -1.00000 q^{14} +1.00000 q^{16} +3.00000 q^{17} -8.00000 q^{19} +1.00000 q^{20} -2.00000 q^{22} +4.00000 q^{23} -4.00000 q^{25} +1.00000 q^{28} +5.00000 q^{29} -3.00000 q^{31} -1.00000 q^{32} -3.00000 q^{34} +1.00000 q^{35} +10.0000 q^{37} +8.00000 q^{38} -1.00000 q^{40} +1.00000 q^{41} -5.00000 q^{43} +2.00000 q^{44} -4.00000 q^{46} -6.00000 q^{47} +1.00000 q^{49} +4.00000 q^{50} +9.00000 q^{53} +2.00000 q^{55} -1.00000 q^{56} -5.00000 q^{58} +10.0000 q^{59} +13.0000 q^{61} +3.00000 q^{62} +1.00000 q^{64} -2.00000 q^{67} +3.00000 q^{68} -1.00000 q^{70} -9.00000 q^{71} +4.00000 q^{73} -10.0000 q^{74} -8.00000 q^{76} +2.00000 q^{77} -11.0000 q^{79} +1.00000 q^{80} -1.00000 q^{82} +14.0000 q^{83} +3.00000 q^{85} +5.00000 q^{86} -2.00000 q^{88} +1.00000 q^{89} +4.00000 q^{92} +6.00000 q^{94} -8.00000 q^{95} +7.00000 q^{97} -1.00000 q^{98} +O(q^{100})\)

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 0.223607 0.974679i \(-0.428217\pi\)
0.223607 + 0.974679i \(0.428217\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) −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 \(0.5\pi\)
\(14\) −1.00000 −0.267261
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 3.00000 0.727607 0.363803 0.931476i \(-0.381478\pi\)
0.363803 + 0.931476i \(0.381478\pi\)
\(18\) 0 0
\(19\) −8.00000 −1.83533 −0.917663 0.397360i \(-0.869927\pi\)
−0.917663 + 0.397360i \(0.869927\pi\)
\(20\) 1.00000 0.223607
\(21\) 0 0
\(22\) −2.00000 −0.426401
\(23\) 4.00000 0.834058 0.417029 0.908893i \(-0.363071\pi\)
0.417029 + 0.908893i \(0.363071\pi\)
\(24\) 0 0
\(25\) −4.00000 −0.800000
\(26\) 0 0
\(27\) 0 0
\(28\) 1.00000 0.188982
\(29\) 5.00000 0.928477 0.464238 0.885710i \(-0.346328\pi\)
0.464238 + 0.885710i \(0.346328\pi\)
\(30\) 0 0
\(31\) −3.00000 −0.538816 −0.269408 0.963026i \(-0.586828\pi\)
−0.269408 + 0.963026i \(0.586828\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) −3.00000 −0.514496
\(35\) 1.00000 0.169031
\(36\) 0 0
\(37\) 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
\(42\) 0 0
\(43\) −5.00000 −0.762493 −0.381246 0.924473i \(-0.624505\pi\)
−0.381246 + 0.924473i \(0.624505\pi\)
\(44\) 2.00000 0.301511
\(45\) 0 0
\(46\) −4.00000 −0.589768
\(47\) −6.00000 −0.875190 −0.437595 0.899172i \(-0.644170\pi\)
−0.437595 + 0.899172i \(0.644170\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 4.00000 0.565685
\(51\) 0 0
\(52\) 0 0
\(53\) 9.00000 1.23625 0.618123 0.786082i \(-0.287894\pi\)
0.618123 + 0.786082i \(0.287894\pi\)
\(54\) 0 0
\(55\) 2.00000 0.269680
\(56\) −1.00000 −0.133631
\(57\) 0 0
\(58\) −5.00000 −0.656532
\(59\) 10.0000 1.30189 0.650945 0.759125i \(-0.274373\pi\)
0.650945 + 0.759125i \(0.274373\pi\)
\(60\) 0 0
\(61\) 13.0000 1.66448 0.832240 0.554416i \(-0.187058\pi\)
0.832240 + 0.554416i \(0.187058\pi\)
\(62\) 3.00000 0.381000
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) −2.00000 −0.244339 −0.122169 0.992509i \(-0.538985\pi\)
−0.122169 + 0.992509i \(0.538985\pi\)
\(68\) 3.00000 0.363803
\(69\) 0 0
\(70\) −1.00000 −0.119523
\(71\) −9.00000 −1.06810 −0.534052 0.845452i \(-0.679331\pi\)
−0.534052 + 0.845452i \(0.679331\pi\)
\(72\) 0 0
\(73\) 4.00000 0.468165 0.234082 0.972217i \(-0.424791\pi\)
0.234082 + 0.972217i \(0.424791\pi\)
\(74\) −10.0000 −1.16248
\(75\) 0 0
\(76\) −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
\(81\) 0 0
\(82\) −1.00000 −0.110432
\(83\) 14.0000 1.53670 0.768350 0.640030i \(-0.221078\pi\)
0.768350 + 0.640030i \(0.221078\pi\)
\(84\) 0 0
\(85\) 3.00000 0.325396
\(86\) 5.00000 0.539164
\(87\) 0 0
\(88\) −2.00000 −0.213201
\(89\) 1.00000 0.106000 0.0529999 0.998595i \(-0.483122\pi\)
0.0529999 + 0.998595i \(0.483122\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 4.00000 0.417029
\(93\) 0 0
\(94\) 6.00000 0.618853
\(95\) −8.00000 −0.820783
\(96\) 0 0
\(97\) 7.00000 0.710742 0.355371 0.934725i \(-0.384354\pi\)
0.355371 + 0.934725i \(0.384354\pi\)
\(98\) −1.00000 −0.101015
\(99\) 0 0
\(100\) −4.00000 −0.400000
\(101\) 10.0000 0.995037 0.497519 0.867453i \(-0.334245\pi\)
0.497519 + 0.867453i \(0.334245\pi\)
\(102\) 0 0
\(103\) 13.0000 1.28093 0.640464 0.767988i \(-0.278742\pi\)
0.640464 + 0.767988i \(0.278742\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) −9.00000 −0.874157
\(107\) −3.00000 −0.290021 −0.145010 0.989430i \(-0.546322\pi\)
−0.145010 + 0.989430i \(0.546322\pi\)
\(108\) 0 0
\(109\) −2.00000 −0.191565 −0.0957826 0.995402i \(-0.530535\pi\)
−0.0957826 + 0.995402i \(0.530535\pi\)
\(110\) −2.00000 −0.190693
\(111\) 0 0
\(112\) 1.00000 0.0944911
\(113\) −9.00000 −0.846649 −0.423324 0.905978i \(-0.639137\pi\)
−0.423324 + 0.905978i \(0.639137\pi\)
\(114\) 0 0
\(115\) 4.00000 0.373002
\(116\) 5.00000 0.464238
\(117\) 0 0
\(118\) −10.0000 −0.920575
\(119\) 3.00000 0.275010
\(120\) 0 0
\(121\) −7.00000 −0.636364
\(122\) −13.0000 −1.17696
\(123\) 0 0
\(124\) −3.00000 −0.269408
\(125\) −9.00000 −0.804984
\(126\) 0 0
\(127\) 2.00000 0.177471 0.0887357 0.996055i \(-0.471717\pi\)
0.0887357 + 0.996055i \(0.471717\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 0 0
\(130\) 0 0
\(131\) 8.00000 0.698963 0.349482 0.936943i \(-0.386358\pi\)
0.349482 + 0.936943i \(0.386358\pi\)
\(132\) 0 0
\(133\) −8.00000 −0.693688
\(134\) 2.00000 0.172774
\(135\) 0 0
\(136\) −3.00000 −0.257248
\(137\) −12.0000 −1.02523 −0.512615 0.858619i \(-0.671323\pi\)
−0.512615 + 0.858619i \(0.671323\pi\)
\(138\) 0 0
\(139\) 14.0000 1.18746 0.593732 0.804663i \(-0.297654\pi\)
0.593732 + 0.804663i \(0.297654\pi\)
\(140\) 1.00000 0.0845154
\(141\) 0 0
\(142\) 9.00000 0.755263
\(143\) 0 0
\(144\) 0 0
\(145\) 5.00000 0.415227
\(146\) −4.00000 −0.331042
\(147\) 0 0
\(148\) 10.0000 0.821995
\(149\) −3.00000 −0.245770 −0.122885 0.992421i \(-0.539215\pi\)
−0.122885 + 0.992421i \(0.539215\pi\)
\(150\) 0 0
\(151\) 19.0000 1.54620 0.773099 0.634285i \(-0.218706\pi\)
0.773099 + 0.634285i \(0.218706\pi\)
\(152\) 8.00000 0.648886
\(153\) 0 0
\(154\) −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
\(159\) 0 0
\(160\) −1.00000 −0.0790569
\(161\) 4.00000 0.315244
\(162\) 0 0
\(163\) −4.00000 −0.313304 −0.156652 0.987654i \(-0.550070\pi\)
−0.156652 + 0.987654i \(0.550070\pi\)
\(164\) 1.00000 0.0780869
\(165\) 0 0
\(166\) −14.0000 −1.08661
\(167\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(168\) 0 0
\(169\) −13.0000 −1.00000
\(170\) −3.00000 −0.230089
\(171\) 0 0
\(172\) −5.00000 −0.381246
\(173\) 1.00000 0.0760286 0.0380143 0.999277i \(-0.487897\pi\)
0.0380143 + 0.999277i \(0.487897\pi\)
\(174\) 0 0
\(175\) −4.00000 −0.302372
\(176\) 2.00000 0.150756
\(177\) 0 0
\(178\) −1.00000 −0.0749532
\(179\) 16.0000 1.19590 0.597948 0.801535i \(-0.295983\pi\)
0.597948 + 0.801535i \(0.295983\pi\)
\(180\) 0 0
\(181\) −14.0000 −1.04061 −0.520306 0.853980i \(-0.674182\pi\)
−0.520306 + 0.853980i \(0.674182\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −4.00000 −0.294884
\(185\) 10.0000 0.735215
\(186\) 0 0
\(187\) 6.00000 0.438763
\(188\) −6.00000 −0.437595
\(189\) 0 0
\(190\) 8.00000 0.580381
\(191\) 11.0000 0.795932 0.397966 0.917400i \(-0.369716\pi\)
0.397966 + 0.917400i \(0.369716\pi\)
\(192\) 0 0
\(193\) 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 \(-0.359401\pi\)
0.427482 + 0.904024i \(0.359401\pi\)
\(198\) 0 0
\(199\) −24.0000 −1.70131 −0.850657 0.525720i \(-0.823796\pi\)
−0.850657 + 0.525720i \(0.823796\pi\)
\(200\) 4.00000 0.282843
\(201\) 0 0
\(202\) −10.0000 −0.703598
\(203\) 5.00000 0.350931
\(204\) 0 0
\(205\) 1.00000 0.0698430
\(206\) −13.0000 −0.905753
\(207\) 0 0
\(208\) 0 0
\(209\) −16.0000 −1.10674
\(210\) 0 0
\(211\) −12.0000 −0.826114 −0.413057 0.910705i \(-0.635539\pi\)
−0.413057 + 0.910705i \(0.635539\pi\)
\(212\) 9.00000 0.618123
\(213\) 0 0
\(214\) 3.00000 0.205076
\(215\) −5.00000 −0.340997
\(216\) 0 0
\(217\) −3.00000 −0.203653
\(218\) 2.00000 0.135457
\(219\) 0 0
\(220\) 2.00000 0.134840
\(221\) 0 0
\(222\) 0 0
\(223\) 21.0000 1.40626 0.703132 0.711059i \(-0.251784\pi\)
0.703132 + 0.711059i \(0.251784\pi\)
\(224\) −1.00000 −0.0668153
\(225\) 0 0
\(226\) 9.00000 0.598671
\(227\) −25.0000 −1.65931 −0.829654 0.558278i \(-0.811462\pi\)
−0.829654 + 0.558278i \(0.811462\pi\)
\(228\) 0 0
\(229\) 20.0000 1.32164 0.660819 0.750546i \(-0.270209\pi\)
0.660819 + 0.750546i \(0.270209\pi\)
\(230\) −4.00000 −0.263752
\(231\) 0 0
\(232\) −5.00000 −0.328266
\(233\) −10.0000 −0.655122 −0.327561 0.944830i \(-0.606227\pi\)
−0.327561 + 0.944830i \(0.606227\pi\)
\(234\) 0 0
\(235\) −6.00000 −0.391397
\(236\) 10.0000 0.650945
\(237\) 0 0
\(238\) −3.00000 −0.194461
\(239\) 12.0000 0.776215 0.388108 0.921614i \(-0.373129\pi\)
0.388108 + 0.921614i \(0.373129\pi\)
\(240\) 0 0
\(241\) −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
\(246\) 0 0
\(247\) 0 0
\(248\) 3.00000 0.190500
\(249\) 0 0
\(250\) 9.00000 0.569210
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) 8.00000 0.502956
\(254\) −2.00000 −0.125491
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 15.0000 0.935674 0.467837 0.883815i \(-0.345033\pi\)
0.467837 + 0.883815i \(0.345033\pi\)
\(258\) 0 0
\(259\) 10.0000 0.621370
\(260\) 0 0
\(261\) 0 0
\(262\) −8.00000 −0.494242
\(263\) 16.0000 0.986602 0.493301 0.869859i \(-0.335790\pi\)
0.493301 + 0.869859i \(0.335790\pi\)
\(264\) 0 0
\(265\) 9.00000 0.552866
\(266\) 8.00000 0.490511
\(267\) 0 0
\(268\) −2.00000 −0.122169
\(269\) 10.0000 0.609711 0.304855 0.952399i \(-0.401392\pi\)
0.304855 + 0.952399i \(0.401392\pi\)
\(270\) 0 0
\(271\) 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
\(276\) 0 0
\(277\) 26.0000 1.56219 0.781094 0.624413i \(-0.214662\pi\)
0.781094 + 0.624413i \(0.214662\pi\)
\(278\) −14.0000 −0.839664
\(279\) 0 0
\(280\) −1.00000 −0.0597614
\(281\) −2.00000 −0.119310 −0.0596550 0.998219i \(-0.519000\pi\)
−0.0596550 + 0.998219i \(0.519000\pi\)
\(282\) 0 0
\(283\) 18.0000 1.06999 0.534994 0.844856i \(-0.320314\pi\)
0.534994 + 0.844856i \(0.320314\pi\)
\(284\) −9.00000 −0.534052
\(285\) 0 0
\(286\) 0 0
\(287\) 1.00000 0.0590281
\(288\) 0 0
\(289\) −8.00000 −0.470588
\(290\) −5.00000 −0.293610
\(291\) 0 0
\(292\) 4.00000 0.234082
\(293\) −14.0000 −0.817889 −0.408944 0.912559i \(-0.634103\pi\)
−0.408944 + 0.912559i \(0.634103\pi\)
\(294\) 0 0
\(295\) 10.0000 0.582223
\(296\) −10.0000 −0.581238
\(297\) 0 0
\(298\) 3.00000 0.173785
\(299\) 0 0
\(300\) 0 0
\(301\) −5.00000 −0.288195
\(302\) −19.0000 −1.09333
\(303\) 0 0
\(304\) −8.00000 −0.458831
\(305\) 13.0000 0.744378
\(306\) 0 0
\(307\) −28.0000 −1.59804 −0.799022 0.601302i \(-0.794649\pi\)
−0.799022 + 0.601302i \(0.794649\pi\)
\(308\) 2.00000 0.113961
\(309\) 0 0
\(310\) 3.00000 0.170389
\(311\) −18.0000 −1.02069 −0.510343 0.859971i \(-0.670482\pi\)
−0.510343 + 0.859971i \(0.670482\pi\)
\(312\) 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
\(315\) 0 0
\(316\) −11.0000 −0.618798
\(317\) 18.0000 1.01098 0.505490 0.862832i \(-0.331312\pi\)
0.505490 + 0.862832i \(0.331312\pi\)
\(318\) 0 0
\(319\) 10.0000 0.559893
\(320\) 1.00000 0.0559017
\(321\) 0 0
\(322\) −4.00000 −0.222911
\(323\) −24.0000 −1.33540
\(324\) 0 0
\(325\) 0 0
\(326\) 4.00000 0.221540
\(327\) 0 0
\(328\) −1.00000 −0.0552158
\(329\) −6.00000 −0.330791
\(330\) 0 0
\(331\) −32.0000 −1.75888 −0.879440 0.476011i \(-0.842082\pi\)
−0.879440 + 0.476011i \(0.842082\pi\)
\(332\) 14.0000 0.768350
\(333\) 0 0
\(334\) 0 0
\(335\) −2.00000 −0.109272
\(336\) 0 0
\(337\) −19.0000 −1.03500 −0.517498 0.855684i \(-0.673136\pi\)
−0.517498 + 0.855684i \(0.673136\pi\)
\(338\) 13.0000 0.707107
\(339\) 0 0
\(340\) 3.00000 0.162698
\(341\) −6.00000 −0.324918
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 5.00000 0.269582
\(345\) 0 0
\(346\) −1.00000 −0.0537603
\(347\) −12.0000 −0.644194 −0.322097 0.946707i \(-0.604388\pi\)
−0.322097 + 0.946707i \(0.604388\pi\)
\(348\) 0 0
\(349\) 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 \(-0.279474\pi\)
0.638696 + 0.769460i \(0.279474\pi\)
\(354\) 0 0
\(355\) −9.00000 −0.477670
\(356\) 1.00000 0.0529999
\(357\) 0 0
\(358\) −16.0000 −0.845626
\(359\) −24.0000 −1.26667 −0.633336 0.773877i \(-0.718315\pi\)
−0.633336 + 0.773877i \(0.718315\pi\)
\(360\) 0 0
\(361\) 45.0000 2.36842
\(362\) 14.0000 0.735824
\(363\) 0 0
\(364\) 0 0
\(365\) 4.00000 0.209370
\(366\) 0 0
\(367\) −17.0000 −0.887393 −0.443696 0.896177i \(-0.646333\pi\)
−0.443696 + 0.896177i \(0.646333\pi\)
\(368\) 4.00000 0.208514
\(369\) 0 0
\(370\) −10.0000 −0.519875
\(371\) 9.00000 0.467257
\(372\) 0 0
\(373\) −18.0000 −0.932005 −0.466002 0.884783i \(-0.654306\pi\)
−0.466002 + 0.884783i \(0.654306\pi\)
\(374\) −6.00000 −0.310253
\(375\) 0 0
\(376\) 6.00000 0.309426
\(377\) 0 0
\(378\) 0 0
\(379\) 37.0000 1.90056 0.950281 0.311393i \(-0.100796\pi\)
0.950281 + 0.311393i \(0.100796\pi\)
\(380\) −8.00000 −0.410391
\(381\) 0 0
\(382\) −11.0000 −0.562809
\(383\) 22.0000 1.12415 0.562074 0.827087i \(-0.310004\pi\)
0.562074 + 0.827087i \(0.310004\pi\)
\(384\) 0 0
\(385\) 2.00000 0.101929
\(386\) −12.0000 −0.610784
\(387\) 0 0
\(388\) 7.00000 0.355371
\(389\) 2.00000 0.101404 0.0507020 0.998714i \(-0.483854\pi\)
0.0507020 + 0.998714i \(0.483854\pi\)
\(390\) 0 0
\(391\) 12.0000 0.606866
\(392\) −1.00000 −0.0505076
\(393\) 0 0
\(394\) −12.0000 −0.604551
\(395\) −11.0000 −0.553470
\(396\) 0 0
\(397\) 20.0000 1.00377 0.501886 0.864934i \(-0.332640\pi\)
0.501886 + 0.864934i \(0.332640\pi\)
\(398\) 24.0000 1.20301
\(399\) 0 0
\(400\) −4.00000 −0.200000
\(401\) 25.0000 1.24844 0.624220 0.781248i \(-0.285417\pi\)
0.624220 + 0.781248i \(0.285417\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 10.0000 0.497519
\(405\) 0 0
\(406\) −5.00000 −0.248146
\(407\) 20.0000 0.991363
\(408\) 0 0
\(409\) −10.0000 −0.494468 −0.247234 0.968956i \(-0.579522\pi\)
−0.247234 + 0.968956i \(0.579522\pi\)
\(410\) −1.00000 −0.0493865
\(411\) 0 0
\(412\) 13.0000 0.640464
\(413\) 10.0000 0.492068
\(414\) 0 0
\(415\) 14.0000 0.687233
\(416\) 0 0
\(417\) 0 0
\(418\) 16.0000 0.782586
\(419\) −28.0000 −1.36789 −0.683945 0.729534i \(-0.739737\pi\)
−0.683945 + 0.729534i \(0.739737\pi\)
\(420\) 0 0
\(421\) −19.0000 −0.926003 −0.463002 0.886357i \(-0.653228\pi\)
−0.463002 + 0.886357i \(0.653228\pi\)
\(422\) 12.0000 0.584151
\(423\) 0 0
\(424\) −9.00000 −0.437079
\(425\) −12.0000 −0.582086
\(426\) 0 0
\(427\) 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 \(-0.374082\pi\)
0.385346 + 0.922772i \(0.374082\pi\)
\(432\) 0 0
\(433\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(434\) 3.00000 0.144005
\(435\) 0 0
\(436\) −2.00000 −0.0957826
\(437\) −32.0000 −1.53077
\(438\) 0 0
\(439\) 34.0000 1.62273 0.811366 0.584539i \(-0.198725\pi\)
0.811366 + 0.584539i \(0.198725\pi\)
\(440\) −2.00000 −0.0953463
\(441\) 0 0
\(442\) 0 0
\(443\) 25.0000 1.18779 0.593893 0.804544i \(-0.297590\pi\)
0.593893 + 0.804544i \(0.297590\pi\)
\(444\) 0 0
\(445\) 1.00000 0.0474045
\(446\) −21.0000 −0.994379
\(447\) 0 0
\(448\) 1.00000 0.0472456
\(449\) 33.0000 1.55737 0.778683 0.627417i \(-0.215888\pi\)
0.778683 + 0.627417i \(0.215888\pi\)
\(450\) 0 0
\(451\) 2.00000 0.0941763
\(452\) −9.00000 −0.423324
\(453\) 0 0
\(454\) 25.0000 1.17331
\(455\) 0 0
\(456\) 0 0
\(457\) −18.0000 −0.842004 −0.421002 0.907060i \(-0.638322\pi\)
−0.421002 + 0.907060i \(0.638322\pi\)
\(458\) −20.0000 −0.934539
\(459\) 0 0
\(460\) 4.00000 0.186501
\(461\) 21.0000 0.978068 0.489034 0.872265i \(-0.337349\pi\)
0.489034 + 0.872265i \(0.337349\pi\)
\(462\) 0 0
\(463\) 16.0000 0.743583 0.371792 0.928316i \(-0.378744\pi\)
0.371792 + 0.928316i \(0.378744\pi\)
\(464\) 5.00000 0.232119
\(465\) 0 0
\(466\) 10.0000 0.463241
\(467\) −6.00000 −0.277647 −0.138823 0.990317i \(-0.544332\pi\)
−0.138823 + 0.990317i \(0.544332\pi\)
\(468\) 0 0
\(469\) −2.00000 −0.0923514
\(470\) 6.00000 0.276759
\(471\) 0 0
\(472\) −10.0000 −0.460287
\(473\) −10.0000 −0.459800
\(474\) 0 0
\(475\) 32.0000 1.46826
\(476\) 3.00000 0.137505
\(477\) 0 0
\(478\) −12.0000 −0.548867
\(479\) 10.0000 0.456912 0.228456 0.973554i \(-0.426632\pi\)
0.228456 + 0.973554i \(0.426632\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 10.0000 0.455488
\(483\) 0 0
\(484\) −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
\(489\) 0 0
\(490\) −1.00000 −0.0451754
\(491\) −37.0000 −1.66979 −0.834893 0.550412i \(-0.814471\pi\)
−0.834893 + 0.550412i \(0.814471\pi\)
\(492\) 0 0
\(493\) 15.0000 0.675566
\(494\) 0 0
\(495\) 0 0
\(496\) −3.00000 −0.134704
\(497\) −9.00000 −0.403705
\(498\) 0 0
\(499\) 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 \(0.5\pi\)
\(504\) 0 0
\(505\) 10.0000 0.444994
\(506\) −8.00000 −0.355643
\(507\) 0 0
\(508\) 2.00000 0.0887357
\(509\) 36.0000 1.59567 0.797836 0.602875i \(-0.205978\pi\)
0.797836 + 0.602875i \(0.205978\pi\)
\(510\) 0 0
\(511\) 4.00000 0.176950
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) −15.0000 −0.661622
\(515\) 13.0000 0.572848
\(516\) 0 0
\(517\) −12.0000 −0.527759
\(518\) −10.0000 −0.439375
\(519\) 0 0
\(520\) 0 0
\(521\) 38.0000 1.66481 0.832405 0.554168i \(-0.186963\pi\)
0.832405 + 0.554168i \(0.186963\pi\)
\(522\) 0 0
\(523\) 20.0000 0.874539 0.437269 0.899331i \(-0.355946\pi\)
0.437269 + 0.899331i \(0.355946\pi\)
\(524\) 8.00000 0.349482
\(525\) 0 0
\(526\) −16.0000 −0.697633
\(527\) −9.00000 −0.392046
\(528\) 0 0
\(529\) −7.00000 −0.304348
\(530\) −9.00000 −0.390935
\(531\) 0 0
\(532\) −8.00000 −0.346844
\(533\) 0 0
\(534\) 0 0
\(535\) −3.00000 −0.129701
\(536\) 2.00000 0.0863868
\(537\) 0 0
\(538\) −10.0000 −0.431131
\(539\) 2.00000 0.0861461
\(540\) 0 0
\(541\) 10.0000 0.429934 0.214967 0.976621i \(-0.431036\pi\)
0.214967 + 0.976621i \(0.431036\pi\)
\(542\) −20.0000 −0.859074
\(543\) 0 0
\(544\) −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
\(549\) 0 0
\(550\) 8.00000 0.341121
\(551\) −40.0000 −1.70406
\(552\) 0 0
\(553\) −11.0000 −0.467768
\(554\) −26.0000 −1.10463
\(555\) 0 0
\(556\) 14.0000 0.593732
\(557\) −33.0000 −1.39825 −0.699127 0.714997i \(-0.746428\pi\)
−0.699127 + 0.714997i \(0.746428\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 1.00000 0.0422577
\(561\) 0 0
\(562\) 2.00000 0.0843649
\(563\) −4.00000 −0.168580 −0.0842900 0.996441i \(-0.526862\pi\)
−0.0842900 + 0.996441i \(0.526862\pi\)
\(564\) 0 0
\(565\) −9.00000 −0.378633
\(566\) −18.0000 −0.756596
\(567\) 0 0
\(568\) 9.00000 0.377632
\(569\) 25.0000 1.04805 0.524027 0.851701i \(-0.324429\pi\)
0.524027 + 0.851701i \(0.324429\pi\)
\(570\) 0 0
\(571\) −44.0000 −1.84134 −0.920671 0.390339i \(-0.872358\pi\)
−0.920671 + 0.390339i \(0.872358\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) −1.00000 −0.0417392
\(575\) −16.0000 −0.667246
\(576\) 0 0
\(577\) 46.0000 1.91501 0.957503 0.288425i \(-0.0931316\pi\)
0.957503 + 0.288425i \(0.0931316\pi\)
\(578\) 8.00000 0.332756
\(579\) 0 0
\(580\) 5.00000 0.207614
\(581\) 14.0000 0.580818
\(582\) 0 0
\(583\) 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 \(-0.357320\pi\)
0.433381 + 0.901211i \(0.357320\pi\)
\(588\) 0 0
\(589\) 24.0000 0.988903
\(590\) −10.0000 −0.411693
\(591\) 0 0
\(592\) 10.0000 0.410997
\(593\) 43.0000 1.76580 0.882899 0.469563i \(-0.155588\pi\)
0.882899 + 0.469563i \(0.155588\pi\)
\(594\) 0 0
\(595\) 3.00000 0.122988
\(596\) −3.00000 −0.122885
\(597\) 0 0
\(598\) 0 0
\(599\) 44.0000 1.79779 0.898896 0.438163i \(-0.144371\pi\)
0.898896 + 0.438163i \(0.144371\pi\)
\(600\) 0 0
\(601\) 21.0000 0.856608 0.428304 0.903635i \(-0.359111\pi\)
0.428304 + 0.903635i \(0.359111\pi\)
\(602\) 5.00000 0.203785
\(603\) 0 0
\(604\) 19.0000 0.773099
\(605\) −7.00000 −0.284590
\(606\) 0 0
\(607\) −43.0000 −1.74532 −0.872658 0.488332i \(-0.837606\pi\)
−0.872658 + 0.488332i \(0.837606\pi\)
\(608\) 8.00000 0.324443
\(609\) 0 0
\(610\) −13.0000 −0.526355
\(611\) 0 0
\(612\) 0 0
\(613\) −16.0000 −0.646234 −0.323117 0.946359i \(-0.604731\pi\)
−0.323117 + 0.946359i \(0.604731\pi\)
\(614\) 28.0000 1.12999
\(615\) 0 0
\(616\) −2.00000 −0.0805823
\(617\) −30.0000 −1.20775 −0.603877 0.797077i \(-0.706378\pi\)
−0.603877 + 0.797077i \(0.706378\pi\)
\(618\) 0 0
\(619\) −24.0000 −0.964641 −0.482321 0.875995i \(-0.660206\pi\)
−0.482321 + 0.875995i \(0.660206\pi\)
\(620\) −3.00000 −0.120483
\(621\) 0 0
\(622\) 18.0000 0.721734
\(623\) 1.00000 0.0400642
\(624\) 0 0
\(625\) 11.0000 0.440000
\(626\) 22.0000 0.879297
\(627\) 0 0
\(628\) 4.00000 0.159617
\(629\) 30.0000 1.19618
\(630\) 0 0
\(631\) 30.0000 1.19428 0.597141 0.802137i \(-0.296303\pi\)
0.597141 + 0.802137i \(0.296303\pi\)
\(632\) 11.0000 0.437557
\(633\) 0 0
\(634\) −18.0000 −0.714871
\(635\) 2.00000 0.0793676
\(636\) 0 0
\(637\) 0 0
\(638\) −10.0000 −0.395904
\(639\) 0 0
\(640\) −1.00000 −0.0395285
\(641\) 30.0000 1.18493 0.592464 0.805597i \(-0.298155\pi\)
0.592464 + 0.805597i \(0.298155\pi\)
\(642\) 0 0
\(643\) −7.00000 −0.276053 −0.138027 0.990429i \(-0.544076\pi\)
−0.138027 + 0.990429i \(0.544076\pi\)
\(644\) 4.00000 0.157622
\(645\) 0 0
\(646\) 24.0000 0.944267
\(647\) 3.00000 0.117942 0.0589711 0.998260i \(-0.481218\pi\)
0.0589711 + 0.998260i \(0.481218\pi\)
\(648\) 0 0
\(649\) 20.0000 0.785069
\(650\) 0 0
\(651\) 0 0
\(652\) −4.00000 −0.156652
\(653\) −3.00000 −0.117399 −0.0586995 0.998276i \(-0.518695\pi\)
−0.0586995 + 0.998276i \(0.518695\pi\)
\(654\) 0 0
\(655\) 8.00000 0.312586
\(656\) 1.00000 0.0390434
\(657\) 0 0
\(658\) 6.00000 0.233904
\(659\) −44.0000 −1.71400 −0.856998 0.515319i \(-0.827673\pi\)
−0.856998 + 0.515319i \(0.827673\pi\)
\(660\) 0 0
\(661\) −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
\(666\) 0 0
\(667\) 20.0000 0.774403
\(668\) 0 0
\(669\) 0 0
\(670\) 2.00000 0.0772667
\(671\) 26.0000 1.00372
\(672\) 0 0
\(673\) 30.0000 1.15642 0.578208 0.815890i \(-0.303752\pi\)
0.578208 + 0.815890i \(0.303752\pi\)
\(674\) 19.0000 0.731853
\(675\) 0 0
\(676\) −13.0000 −0.500000
\(677\) −6.00000 −0.230599 −0.115299 0.993331i \(-0.536783\pi\)
−0.115299 + 0.993331i \(0.536783\pi\)
\(678\) 0 0
\(679\) 7.00000 0.268635
\(680\) −3.00000 −0.115045
\(681\) 0 0
\(682\) 6.00000 0.229752
\(683\) −40.0000 −1.53056 −0.765279 0.643699i \(-0.777399\pi\)
−0.765279 + 0.643699i \(0.777399\pi\)
\(684\) 0 0
\(685\) −12.0000 −0.458496
\(686\) −1.00000 −0.0381802
\(687\) 0 0
\(688\) −5.00000 −0.190623
\(689\) 0 0
\(690\) 0 0
\(691\) 13.0000 0.494543 0.247272 0.968946i \(-0.420466\pi\)
0.247272 + 0.968946i \(0.420466\pi\)
\(692\) 1.00000 0.0380143
\(693\) 0 0
\(694\) 12.0000 0.455514
\(695\) 14.0000 0.531050
\(696\) 0 0
\(697\) 3.00000 0.113633
\(698\) −14.0000 −0.529908
\(699\) 0 0
\(700\) −4.00000 −0.151186
\(701\) −16.0000 −0.604312 −0.302156 0.953259i \(-0.597706\pi\)
−0.302156 + 0.953259i \(0.597706\pi\)
\(702\) 0 0
\(703\) −80.0000 −3.01726
\(704\) 2.00000 0.0753778
\(705\) 0 0
\(706\) −24.0000 −0.903252
\(707\) 10.0000 0.376089
\(708\) 0 0
\(709\) 3.00000 0.112667 0.0563337 0.998412i \(-0.482059\pi\)
0.0563337 + 0.998412i \(0.482059\pi\)
\(710\) 9.00000 0.337764
\(711\) 0 0
\(712\) −1.00000 −0.0374766
\(713\) −12.0000 −0.449404
\(714\) 0 0
\(715\) 0 0
\(716\) 16.0000 0.597948
\(717\) 0 0
\(718\) 24.0000 0.895672
\(719\) 8.00000 0.298350 0.149175 0.988811i \(-0.452338\pi\)
0.149175 + 0.988811i \(0.452338\pi\)
\(720\) 0 0
\(721\) 13.0000 0.484145
\(722\) −45.0000 −1.67473
\(723\) 0 0
\(724\) −14.0000 −0.520306
\(725\) −20.0000 −0.742781
\(726\) 0 0
\(727\) −28.0000 −1.03846 −0.519231 0.854634i \(-0.673782\pi\)
−0.519231 + 0.854634i \(0.673782\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −4.00000 −0.148047
\(731\) −15.0000 −0.554795
\(732\) 0 0
\(733\) 13.0000 0.480166 0.240083 0.970752i \(-0.422825\pi\)
0.240083 + 0.970752i \(0.422825\pi\)
\(734\) 17.0000 0.627481
\(735\) 0 0
\(736\) −4.00000 −0.147442
\(737\) −4.00000 −0.147342
\(738\) 0 0
\(739\) 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 \(-0.429356\pi\)
0.220119 + 0.975473i \(0.429356\pi\)
\(744\) 0 0
\(745\) −3.00000 −0.109911
\(746\) 18.0000 0.659027
\(747\) 0 0
\(748\) 6.00000 0.219382
\(749\) −3.00000 −0.109618
\(750\) 0 0
\(751\) 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
\(756\) 0 0
\(757\) −5.00000 −0.181728 −0.0908640 0.995863i \(-0.528963\pi\)
−0.0908640 + 0.995863i \(0.528963\pi\)
\(758\) −37.0000 −1.34390
\(759\) 0 0
\(760\) 8.00000 0.290191
\(761\) −6.00000 −0.217500 −0.108750 0.994069i \(-0.534685\pi\)
−0.108750 + 0.994069i \(0.534685\pi\)
\(762\) 0 0
\(763\) −2.00000 −0.0724049
\(764\) 11.0000 0.397966
\(765\) 0 0
\(766\) −22.0000 −0.794892
\(767\) 0 0
\(768\) 0 0
\(769\) −14.0000 −0.504853 −0.252426 0.967616i \(-0.581229\pi\)
−0.252426 + 0.967616i \(0.581229\pi\)
\(770\) −2.00000 −0.0720750
\(771\) 0 0
\(772\) 12.0000 0.431889
\(773\) 38.0000 1.36677 0.683383 0.730061i \(-0.260508\pi\)
0.683383 + 0.730061i \(0.260508\pi\)
\(774\) 0 0
\(775\) 12.0000 0.431053
\(776\) −7.00000 −0.251285
\(777\) 0 0
\(778\) −2.00000 −0.0717035
\(779\) −8.00000 −0.286630
\(780\) 0 0
\(781\) −18.0000 −0.644091
\(782\) −12.0000 −0.429119
\(783\) 0 0
\(784\) 1.00000 0.0357143
\(785\) 4.00000 0.142766
\(786\) 0 0
\(787\) −52.0000 −1.85360 −0.926800 0.375555i \(-0.877452\pi\)
−0.926800 + 0.375555i \(0.877452\pi\)
\(788\) 12.0000 0.427482
\(789\) 0 0
\(790\) 11.0000 0.391362
\(791\) −9.00000 −0.320003
\(792\) 0 0
\(793\) 0 0
\(794\) −20.0000 −0.709773
\(795\) 0 0
\(796\) −24.0000 −0.850657
\(797\) −21.0000 −0.743858 −0.371929 0.928261i \(-0.621304\pi\)
−0.371929 + 0.928261i \(0.621304\pi\)
\(798\) 0 0
\(799\) −18.0000 −0.636794
\(800\) 4.00000 0.141421
\(801\) 0 0
\(802\) −25.0000 −0.882781
\(803\) 8.00000 0.282314
\(804\) 0 0
\(805\) 4.00000 0.140981
\(806\) 0 0
\(807\) 0 0
\(808\) −10.0000 −0.351799
\(809\) −54.0000 −1.89854 −0.949269 0.314464i \(-0.898175\pi\)
−0.949269 + 0.314464i \(0.898175\pi\)
\(810\) 0 0
\(811\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(812\) 5.00000 0.175466
\(813\) 0 0
\(814\) −20.0000 −0.701000
\(815\) −4.00000 −0.140114
\(816\) 0 0
\(817\) 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 \(-0.477764\pi\)
0.0698005 + 0.997561i \(0.477764\pi\)
\(822\) 0 0
\(823\) −51.0000 −1.77775 −0.888874 0.458151i \(-0.848512\pi\)
−0.888874 + 0.458151i \(0.848512\pi\)
\(824\) −13.0000 −0.452876
\(825\) 0 0
\(826\) −10.0000 −0.347945
\(827\) −30.0000 −1.04320 −0.521601 0.853189i \(-0.674665\pi\)
−0.521601 + 0.853189i \(0.674665\pi\)
\(828\) 0 0
\(829\) 11.0000 0.382046 0.191023 0.981586i \(-0.438820\pi\)
0.191023 + 0.981586i \(0.438820\pi\)
\(830\) −14.0000 −0.485947
\(831\) 0 0
\(832\) 0 0
\(833\) 3.00000 0.103944
\(834\) 0 0
\(835\) 0 0
\(836\) −16.0000 −0.553372
\(837\) 0 0
\(838\) 28.0000 0.967244
\(839\) −14.0000 −0.483334 −0.241667 0.970359i \(-0.577694\pi\)
−0.241667 + 0.970359i \(0.577694\pi\)
\(840\) 0 0
\(841\) −4.00000 −0.137931
\(842\) 19.0000 0.654783
\(843\) 0 0
\(844\) −12.0000 −0.413057
\(845\) −13.0000 −0.447214
\(846\) 0 0
\(847\) −7.00000 −0.240523
\(848\) 9.00000 0.309061
\(849\) 0 0
\(850\) 12.0000 0.411597
\(851\) 40.0000 1.37118
\(852\) 0 0
\(853\) −21.0000 −0.719026 −0.359513 0.933140i \(-0.617057\pi\)
−0.359513 + 0.933140i \(0.617057\pi\)
\(854\) −13.0000 −0.444851
\(855\) 0 0
\(856\) 3.00000 0.102538
\(857\) 38.0000 1.29806 0.649028 0.760765i \(-0.275176\pi\)
0.649028 + 0.760765i \(0.275176\pi\)
\(858\) 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
\(861\) 0 0
\(862\) −16.0000 −0.544962
\(863\) 32.0000 1.08929 0.544646 0.838666i \(-0.316664\pi\)
0.544646 + 0.838666i \(0.316664\pi\)
\(864\) 0 0
\(865\) 1.00000 0.0340010
\(866\) 0 0
\(867\) 0 0
\(868\) −3.00000 −0.101827
\(869\) −22.0000 −0.746299
\(870\) 0 0
\(871\) 0 0
\(872\) 2.00000 0.0677285
\(873\) 0 0
\(874\) 32.0000 1.08242
\(875\) −9.00000 −0.304256
\(876\) 0 0
\(877\) −32.0000 −1.08056 −0.540282 0.841484i \(-0.681682\pi\)
−0.540282 + 0.841484i \(0.681682\pi\)
\(878\) −34.0000 −1.14744
\(879\) 0 0
\(880\) 2.00000 0.0674200
\(881\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(882\) 0 0
\(883\) −26.0000 −0.874970 −0.437485 0.899226i \(-0.644131\pi\)
−0.437485 + 0.899226i \(0.644131\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) −25.0000 −0.839891
\(887\) −20.0000 −0.671534 −0.335767 0.941945i \(-0.608996\pi\)
−0.335767 + 0.941945i \(0.608996\pi\)
\(888\) 0 0
\(889\) 2.00000 0.0670778
\(890\) −1.00000 −0.0335201
\(891\) 0 0
\(892\) 21.0000 0.703132
\(893\) 48.0000 1.60626
\(894\) 0 0
\(895\) 16.0000 0.534821
\(896\) −1.00000 −0.0334077
\(897\) 0 0
\(898\) −33.0000 −1.10122
\(899\) −15.0000 −0.500278
\(900\) 0 0
\(901\) 27.0000 0.899500
\(902\) −2.00000 −0.0665927
\(903\) 0 0
\(904\) 9.00000 0.299336
\(905\) −14.0000 −0.465376
\(906\) 0 0
\(907\) 19.0000 0.630885 0.315442 0.948945i \(-0.397847\pi\)
0.315442 + 0.948945i \(0.397847\pi\)
\(908\) −25.0000 −0.829654
\(909\) 0 0
\(910\) 0 0
\(911\) −2.00000 −0.0662630 −0.0331315 0.999451i \(-0.510548\pi\)
−0.0331315 + 0.999451i \(0.510548\pi\)
\(912\) 0 0
\(913\) 28.0000 0.926665
\(914\) 18.0000 0.595387
\(915\) 0 0
\(916\) 20.0000 0.660819
\(917\) 8.00000 0.264183
\(918\) 0 0
\(919\) 3.00000 0.0989609 0.0494804 0.998775i \(-0.484243\pi\)
0.0494804 + 0.998775i \(0.484243\pi\)
\(920\) −4.00000 −0.131876
\(921\) 0 0
\(922\) −21.0000 −0.691598
\(923\) 0 0
\(924\) 0 0
\(925\) −40.0000 −1.31519
\(926\) −16.0000 −0.525793
\(927\) 0 0
\(928\) −5.00000 −0.164133
\(929\) 50.0000 1.64045 0.820223 0.572043i \(-0.193849\pi\)
0.820223 + 0.572043i \(0.193849\pi\)
\(930\) 0 0
\(931\) −8.00000 −0.262189
\(932\) −10.0000 −0.327561
\(933\) 0 0
\(934\) 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
\(939\) 0 0
\(940\) −6.00000 −0.195698
\(941\) −18.0000 −0.586783 −0.293392 0.955992i \(-0.594784\pi\)
−0.293392 + 0.955992i \(0.594784\pi\)
\(942\) 0 0
\(943\) 4.00000 0.130258
\(944\) 10.0000 0.325472
\(945\) 0 0
\(946\) 10.0000 0.325128
\(947\) 4.00000 0.129983 0.0649913 0.997886i \(-0.479298\pi\)
0.0649913 + 0.997886i \(0.479298\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) −32.0000 −1.03822
\(951\) 0 0
\(952\) −3.00000 −0.0972306
\(953\) −30.0000 −0.971795 −0.485898 0.874016i \(-0.661507\pi\)
−0.485898 + 0.874016i \(0.661507\pi\)
\(954\) 0 0
\(955\) 11.0000 0.355952
\(956\) 12.0000 0.388108
\(957\) 0 0
\(958\) −10.0000 −0.323085
\(959\) −12.0000 −0.387500
\(960\) 0 0
\(961\) −22.0000 −0.709677
\(962\) 0 0
\(963\) 0 0
\(964\) −10.0000 −0.322078
\(965\) 12.0000 0.386294
\(966\) 0 0
\(967\) −47.0000 −1.51142 −0.755709 0.654907i \(-0.772708\pi\)
−0.755709 + 0.654907i \(0.772708\pi\)
\(968\) 7.00000 0.224989
\(969\) 0 0
\(970\) −7.00000 −0.224756
\(971\) −13.0000 −0.417190 −0.208595 0.978002i \(-0.566889\pi\)
−0.208595 + 0.978002i \(0.566889\pi\)
\(972\) 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 \(-0.831926\pi\)
−0.863807 + 0.503824i \(0.831926\pi\)
\(978\) 0 0
\(979\) 2.00000 0.0639203
\(980\) 1.00000 0.0319438
\(981\) 0 0
\(982\) 37.0000 1.18072
\(983\) 3.00000 0.0956851 0.0478426 0.998855i \(-0.484765\pi\)
0.0478426 + 0.998855i \(0.484765\pi\)
\(984\) 0 0
\(985\) 12.0000 0.382352
\(986\) −15.0000 −0.477697
\(987\) 0 0
\(988\) 0 0
\(989\) −20.0000 −0.635963
\(990\) 0 0
\(991\) 40.0000 1.27064 0.635321 0.772248i \(-0.280868\pi\)
0.635321 + 0.772248i \(0.280868\pi\)
\(992\) 3.00000 0.0952501
\(993\) 0 0
\(994\) 9.00000 0.285463
\(995\) −24.0000 −0.760851
\(996\) 0 0
\(997\) 4.00000 0.126681 0.0633406 0.997992i \(-0.479825\pi\)
0.0633406 + 0.997992i \(0.479825\pi\)
\(998\) −10.0000 −0.316544
\(999\) 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 5166.2.a.o.1.1 1
3.2 odd 2 574.2.a.g.1.1 1
12.11 even 2 4592.2.a.l.1.1 1
21.20 even 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 3.2 odd 2
4018.2.a.s.1.1 1 21.20 even 2
4592.2.a.l.1.1 1 12.11 even 2
5166.2.a.o.1.1 1 1.1 even 1 trivial