Properties

Label 66.2.a.a.1.1
Level $66$
Weight $2$
Character 66.1
Self dual yes
Analytic conductor $0.527$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 66 = 2 \cdot 3 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 66.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(0.527012653340\)
Analytic rank: \(0\)
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 \(\chi\) \(=\) 66.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +2.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +2.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{11} +1.00000 q^{12} -4.00000 q^{13} -2.00000 q^{14} +1.00000 q^{16} -6.00000 q^{17} -1.00000 q^{18} -4.00000 q^{19} +2.00000 q^{21} +1.00000 q^{22} +6.00000 q^{23} -1.00000 q^{24} -5.00000 q^{25} +4.00000 q^{26} +1.00000 q^{27} +2.00000 q^{28} +6.00000 q^{29} +8.00000 q^{31} -1.00000 q^{32} -1.00000 q^{33} +6.00000 q^{34} +1.00000 q^{36} -10.0000 q^{37} +4.00000 q^{38} -4.00000 q^{39} +6.00000 q^{41} -2.00000 q^{42} +8.00000 q^{43} -1.00000 q^{44} -6.00000 q^{46} -6.00000 q^{47} +1.00000 q^{48} -3.00000 q^{49} +5.00000 q^{50} -6.00000 q^{51} -4.00000 q^{52} -1.00000 q^{54} -2.00000 q^{56} -4.00000 q^{57} -6.00000 q^{58} +8.00000 q^{61} -8.00000 q^{62} +2.00000 q^{63} +1.00000 q^{64} +1.00000 q^{66} -4.00000 q^{67} -6.00000 q^{68} +6.00000 q^{69} +6.00000 q^{71} -1.00000 q^{72} +2.00000 q^{73} +10.0000 q^{74} -5.00000 q^{75} -4.00000 q^{76} -2.00000 q^{77} +4.00000 q^{78} +14.0000 q^{79} +1.00000 q^{81} -6.00000 q^{82} -12.0000 q^{83} +2.00000 q^{84} -8.00000 q^{86} +6.00000 q^{87} +1.00000 q^{88} -6.00000 q^{89} -8.00000 q^{91} +6.00000 q^{92} +8.00000 q^{93} +6.00000 q^{94} -1.00000 q^{96} +14.0000 q^{97} +3.00000 q^{98} -1.00000 q^{99} +O(q^{100})\)

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 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(6\) −1.00000 −0.408248
\(7\) 2.00000 0.755929 0.377964 0.925820i \(-0.376624\pi\)
0.377964 + 0.925820i \(0.376624\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −1.00000 −0.301511
\(12\) 1.00000 0.288675
\(13\) −4.00000 −1.10940 −0.554700 0.832050i \(-0.687167\pi\)
−0.554700 + 0.832050i \(0.687167\pi\)
\(14\) −2.00000 −0.534522
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) −6.00000 −1.45521 −0.727607 0.685994i \(-0.759367\pi\)
−0.727607 + 0.685994i \(0.759367\pi\)
\(18\) −1.00000 −0.235702
\(19\) −4.00000 −0.917663 −0.458831 0.888523i \(-0.651732\pi\)
−0.458831 + 0.888523i \(0.651732\pi\)
\(20\) 0 0
\(21\) 2.00000 0.436436
\(22\) 1.00000 0.213201
\(23\) 6.00000 1.25109 0.625543 0.780189i \(-0.284877\pi\)
0.625543 + 0.780189i \(0.284877\pi\)
\(24\) −1.00000 −0.204124
\(25\) −5.00000 −1.00000
\(26\) 4.00000 0.784465
\(27\) 1.00000 0.192450
\(28\) 2.00000 0.377964
\(29\) 6.00000 1.11417 0.557086 0.830455i \(-0.311919\pi\)
0.557086 + 0.830455i \(0.311919\pi\)
\(30\) 0 0
\(31\) 8.00000 1.43684 0.718421 0.695608i \(-0.244865\pi\)
0.718421 + 0.695608i \(0.244865\pi\)
\(32\) −1.00000 −0.176777
\(33\) −1.00000 −0.174078
\(34\) 6.00000 1.02899
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) −10.0000 −1.64399 −0.821995 0.569495i \(-0.807139\pi\)
−0.821995 + 0.569495i \(0.807139\pi\)
\(38\) 4.00000 0.648886
\(39\) −4.00000 −0.640513
\(40\) 0 0
\(41\) 6.00000 0.937043 0.468521 0.883452i \(-0.344787\pi\)
0.468521 + 0.883452i \(0.344787\pi\)
\(42\) −2.00000 −0.308607
\(43\) 8.00000 1.21999 0.609994 0.792406i \(-0.291172\pi\)
0.609994 + 0.792406i \(0.291172\pi\)
\(44\) −1.00000 −0.150756
\(45\) 0 0
\(46\) −6.00000 −0.884652
\(47\) −6.00000 −0.875190 −0.437595 0.899172i \(-0.644170\pi\)
−0.437595 + 0.899172i \(0.644170\pi\)
\(48\) 1.00000 0.144338
\(49\) −3.00000 −0.428571
\(50\) 5.00000 0.707107
\(51\) −6.00000 −0.840168
\(52\) −4.00000 −0.554700
\(53\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(54\) −1.00000 −0.136083
\(55\) 0 0
\(56\) −2.00000 −0.267261
\(57\) −4.00000 −0.529813
\(58\) −6.00000 −0.787839
\(59\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) 0 0
\(61\) 8.00000 1.02430 0.512148 0.858898i \(-0.328850\pi\)
0.512148 + 0.858898i \(0.328850\pi\)
\(62\) −8.00000 −1.01600
\(63\) 2.00000 0.251976
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 1.00000 0.123091
\(67\) −4.00000 −0.488678 −0.244339 0.969690i \(-0.578571\pi\)
−0.244339 + 0.969690i \(0.578571\pi\)
\(68\) −6.00000 −0.727607
\(69\) 6.00000 0.722315
\(70\) 0 0
\(71\) 6.00000 0.712069 0.356034 0.934473i \(-0.384129\pi\)
0.356034 + 0.934473i \(0.384129\pi\)
\(72\) −1.00000 −0.117851
\(73\) 2.00000 0.234082 0.117041 0.993127i \(-0.462659\pi\)
0.117041 + 0.993127i \(0.462659\pi\)
\(74\) 10.0000 1.16248
\(75\) −5.00000 −0.577350
\(76\) −4.00000 −0.458831
\(77\) −2.00000 −0.227921
\(78\) 4.00000 0.452911
\(79\) 14.0000 1.57512 0.787562 0.616236i \(-0.211343\pi\)
0.787562 + 0.616236i \(0.211343\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) −6.00000 −0.662589
\(83\) −12.0000 −1.31717 −0.658586 0.752506i \(-0.728845\pi\)
−0.658586 + 0.752506i \(0.728845\pi\)
\(84\) 2.00000 0.218218
\(85\) 0 0
\(86\) −8.00000 −0.862662
\(87\) 6.00000 0.643268
\(88\) 1.00000 0.106600
\(89\) −6.00000 −0.635999 −0.317999 0.948091i \(-0.603011\pi\)
−0.317999 + 0.948091i \(0.603011\pi\)
\(90\) 0 0
\(91\) −8.00000 −0.838628
\(92\) 6.00000 0.625543
\(93\) 8.00000 0.829561
\(94\) 6.00000 0.618853
\(95\) 0 0
\(96\) −1.00000 −0.102062
\(97\) 14.0000 1.42148 0.710742 0.703452i \(-0.248359\pi\)
0.710742 + 0.703452i \(0.248359\pi\)
\(98\) 3.00000 0.303046
\(99\) −1.00000 −0.100504
\(100\) −5.00000 −0.500000
\(101\) 6.00000 0.597022 0.298511 0.954406i \(-0.403510\pi\)
0.298511 + 0.954406i \(0.403510\pi\)
\(102\) 6.00000 0.594089
\(103\) −4.00000 −0.394132 −0.197066 0.980390i \(-0.563141\pi\)
−0.197066 + 0.980390i \(0.563141\pi\)
\(104\) 4.00000 0.392232
\(105\) 0 0
\(106\) 0 0
\(107\) −12.0000 −1.16008 −0.580042 0.814587i \(-0.696964\pi\)
−0.580042 + 0.814587i \(0.696964\pi\)
\(108\) 1.00000 0.0962250
\(109\) −4.00000 −0.383131 −0.191565 0.981480i \(-0.561356\pi\)
−0.191565 + 0.981480i \(0.561356\pi\)
\(110\) 0 0
\(111\) −10.0000 −0.949158
\(112\) 2.00000 0.188982
\(113\) 18.0000 1.69330 0.846649 0.532152i \(-0.178617\pi\)
0.846649 + 0.532152i \(0.178617\pi\)
\(114\) 4.00000 0.374634
\(115\) 0 0
\(116\) 6.00000 0.557086
\(117\) −4.00000 −0.369800
\(118\) 0 0
\(119\) −12.0000 −1.10004
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) −8.00000 −0.724286
\(123\) 6.00000 0.541002
\(124\) 8.00000 0.718421
\(125\) 0 0
\(126\) −2.00000 −0.178174
\(127\) 14.0000 1.24230 0.621150 0.783692i \(-0.286666\pi\)
0.621150 + 0.783692i \(0.286666\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 8.00000 0.704361
\(130\) 0 0
\(131\) −12.0000 −1.04844 −0.524222 0.851581i \(-0.675644\pi\)
−0.524222 + 0.851581i \(0.675644\pi\)
\(132\) −1.00000 −0.0870388
\(133\) −8.00000 −0.693688
\(134\) 4.00000 0.345547
\(135\) 0 0
\(136\) 6.00000 0.514496
\(137\) −18.0000 −1.53784 −0.768922 0.639343i \(-0.779207\pi\)
−0.768922 + 0.639343i \(0.779207\pi\)
\(138\) −6.00000 −0.510754
\(139\) −4.00000 −0.339276 −0.169638 0.985506i \(-0.554260\pi\)
−0.169638 + 0.985506i \(0.554260\pi\)
\(140\) 0 0
\(141\) −6.00000 −0.505291
\(142\) −6.00000 −0.503509
\(143\) 4.00000 0.334497
\(144\) 1.00000 0.0833333
\(145\) 0 0
\(146\) −2.00000 −0.165521
\(147\) −3.00000 −0.247436
\(148\) −10.0000 −0.821995
\(149\) −6.00000 −0.491539 −0.245770 0.969328i \(-0.579041\pi\)
−0.245770 + 0.969328i \(0.579041\pi\)
\(150\) 5.00000 0.408248
\(151\) −10.0000 −0.813788 −0.406894 0.913475i \(-0.633388\pi\)
−0.406894 + 0.913475i \(0.633388\pi\)
\(152\) 4.00000 0.324443
\(153\) −6.00000 −0.485071
\(154\) 2.00000 0.161165
\(155\) 0 0
\(156\) −4.00000 −0.320256
\(157\) 2.00000 0.159617 0.0798087 0.996810i \(-0.474569\pi\)
0.0798087 + 0.996810i \(0.474569\pi\)
\(158\) −14.0000 −1.11378
\(159\) 0 0
\(160\) 0 0
\(161\) 12.0000 0.945732
\(162\) −1.00000 −0.0785674
\(163\) −4.00000 −0.313304 −0.156652 0.987654i \(-0.550070\pi\)
−0.156652 + 0.987654i \(0.550070\pi\)
\(164\) 6.00000 0.468521
\(165\) 0 0
\(166\) 12.0000 0.931381
\(167\) 12.0000 0.928588 0.464294 0.885681i \(-0.346308\pi\)
0.464294 + 0.885681i \(0.346308\pi\)
\(168\) −2.00000 −0.154303
\(169\) 3.00000 0.230769
\(170\) 0 0
\(171\) −4.00000 −0.305888
\(172\) 8.00000 0.609994
\(173\) 6.00000 0.456172 0.228086 0.973641i \(-0.426753\pi\)
0.228086 + 0.973641i \(0.426753\pi\)
\(174\) −6.00000 −0.454859
\(175\) −10.0000 −0.755929
\(176\) −1.00000 −0.0753778
\(177\) 0 0
\(178\) 6.00000 0.449719
\(179\) 24.0000 1.79384 0.896922 0.442189i \(-0.145798\pi\)
0.896922 + 0.442189i \(0.145798\pi\)
\(180\) 0 0
\(181\) −22.0000 −1.63525 −0.817624 0.575753i \(-0.804709\pi\)
−0.817624 + 0.575753i \(0.804709\pi\)
\(182\) 8.00000 0.592999
\(183\) 8.00000 0.591377
\(184\) −6.00000 −0.442326
\(185\) 0 0
\(186\) −8.00000 −0.586588
\(187\) 6.00000 0.438763
\(188\) −6.00000 −0.437595
\(189\) 2.00000 0.145479
\(190\) 0 0
\(191\) 18.0000 1.30243 0.651217 0.758891i \(-0.274259\pi\)
0.651217 + 0.758891i \(0.274259\pi\)
\(192\) 1.00000 0.0721688
\(193\) 14.0000 1.00774 0.503871 0.863779i \(-0.331909\pi\)
0.503871 + 0.863779i \(0.331909\pi\)
\(194\) −14.0000 −1.00514
\(195\) 0 0
\(196\) −3.00000 −0.214286
\(197\) 6.00000 0.427482 0.213741 0.976890i \(-0.431435\pi\)
0.213741 + 0.976890i \(0.431435\pi\)
\(198\) 1.00000 0.0710669
\(199\) −4.00000 −0.283552 −0.141776 0.989899i \(-0.545281\pi\)
−0.141776 + 0.989899i \(0.545281\pi\)
\(200\) 5.00000 0.353553
\(201\) −4.00000 −0.282138
\(202\) −6.00000 −0.422159
\(203\) 12.0000 0.842235
\(204\) −6.00000 −0.420084
\(205\) 0 0
\(206\) 4.00000 0.278693
\(207\) 6.00000 0.417029
\(208\) −4.00000 −0.277350
\(209\) 4.00000 0.276686
\(210\) 0 0
\(211\) 8.00000 0.550743 0.275371 0.961338i \(-0.411199\pi\)
0.275371 + 0.961338i \(0.411199\pi\)
\(212\) 0 0
\(213\) 6.00000 0.411113
\(214\) 12.0000 0.820303
\(215\) 0 0
\(216\) −1.00000 −0.0680414
\(217\) 16.0000 1.08615
\(218\) 4.00000 0.270914
\(219\) 2.00000 0.135147
\(220\) 0 0
\(221\) 24.0000 1.61441
\(222\) 10.0000 0.671156
\(223\) −16.0000 −1.07144 −0.535720 0.844396i \(-0.679960\pi\)
−0.535720 + 0.844396i \(0.679960\pi\)
\(224\) −2.00000 −0.133631
\(225\) −5.00000 −0.333333
\(226\) −18.0000 −1.19734
\(227\) −12.0000 −0.796468 −0.398234 0.917284i \(-0.630377\pi\)
−0.398234 + 0.917284i \(0.630377\pi\)
\(228\) −4.00000 −0.264906
\(229\) −22.0000 −1.45380 −0.726900 0.686743i \(-0.759040\pi\)
−0.726900 + 0.686743i \(0.759040\pi\)
\(230\) 0 0
\(231\) −2.00000 −0.131590
\(232\) −6.00000 −0.393919
\(233\) −18.0000 −1.17922 −0.589610 0.807688i \(-0.700718\pi\)
−0.589610 + 0.807688i \(0.700718\pi\)
\(234\) 4.00000 0.261488
\(235\) 0 0
\(236\) 0 0
\(237\) 14.0000 0.909398
\(238\) 12.0000 0.777844
\(239\) −12.0000 −0.776215 −0.388108 0.921614i \(-0.626871\pi\)
−0.388108 + 0.921614i \(0.626871\pi\)
\(240\) 0 0
\(241\) −10.0000 −0.644157 −0.322078 0.946713i \(-0.604381\pi\)
−0.322078 + 0.946713i \(0.604381\pi\)
\(242\) −1.00000 −0.0642824
\(243\) 1.00000 0.0641500
\(244\) 8.00000 0.512148
\(245\) 0 0
\(246\) −6.00000 −0.382546
\(247\) 16.0000 1.01806
\(248\) −8.00000 −0.508001
\(249\) −12.0000 −0.760469
\(250\) 0 0
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 2.00000 0.125988
\(253\) −6.00000 −0.377217
\(254\) −14.0000 −0.878438
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −30.0000 −1.87135 −0.935674 0.352865i \(-0.885208\pi\)
−0.935674 + 0.352865i \(0.885208\pi\)
\(258\) −8.00000 −0.498058
\(259\) −20.0000 −1.24274
\(260\) 0 0
\(261\) 6.00000 0.371391
\(262\) 12.0000 0.741362
\(263\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(264\) 1.00000 0.0615457
\(265\) 0 0
\(266\) 8.00000 0.490511
\(267\) −6.00000 −0.367194
\(268\) −4.00000 −0.244339
\(269\) −24.0000 −1.46331 −0.731653 0.681677i \(-0.761251\pi\)
−0.731653 + 0.681677i \(0.761251\pi\)
\(270\) 0 0
\(271\) 2.00000 0.121491 0.0607457 0.998153i \(-0.480652\pi\)
0.0607457 + 0.998153i \(0.480652\pi\)
\(272\) −6.00000 −0.363803
\(273\) −8.00000 −0.484182
\(274\) 18.0000 1.08742
\(275\) 5.00000 0.301511
\(276\) 6.00000 0.361158
\(277\) −16.0000 −0.961347 −0.480673 0.876900i \(-0.659608\pi\)
−0.480673 + 0.876900i \(0.659608\pi\)
\(278\) 4.00000 0.239904
\(279\) 8.00000 0.478947
\(280\) 0 0
\(281\) −6.00000 −0.357930 −0.178965 0.983855i \(-0.557275\pi\)
−0.178965 + 0.983855i \(0.557275\pi\)
\(282\) 6.00000 0.357295
\(283\) 8.00000 0.475551 0.237775 0.971320i \(-0.423582\pi\)
0.237775 + 0.971320i \(0.423582\pi\)
\(284\) 6.00000 0.356034
\(285\) 0 0
\(286\) −4.00000 −0.236525
\(287\) 12.0000 0.708338
\(288\) −1.00000 −0.0589256
\(289\) 19.0000 1.11765
\(290\) 0 0
\(291\) 14.0000 0.820695
\(292\) 2.00000 0.117041
\(293\) −6.00000 −0.350524 −0.175262 0.984522i \(-0.556077\pi\)
−0.175262 + 0.984522i \(0.556077\pi\)
\(294\) 3.00000 0.174964
\(295\) 0 0
\(296\) 10.0000 0.581238
\(297\) −1.00000 −0.0580259
\(298\) 6.00000 0.347571
\(299\) −24.0000 −1.38796
\(300\) −5.00000 −0.288675
\(301\) 16.0000 0.922225
\(302\) 10.0000 0.575435
\(303\) 6.00000 0.344691
\(304\) −4.00000 −0.229416
\(305\) 0 0
\(306\) 6.00000 0.342997
\(307\) 20.0000 1.14146 0.570730 0.821138i \(-0.306660\pi\)
0.570730 + 0.821138i \(0.306660\pi\)
\(308\) −2.00000 −0.113961
\(309\) −4.00000 −0.227552
\(310\) 0 0
\(311\) −18.0000 −1.02069 −0.510343 0.859971i \(-0.670482\pi\)
−0.510343 + 0.859971i \(0.670482\pi\)
\(312\) 4.00000 0.226455
\(313\) 26.0000 1.46961 0.734803 0.678280i \(-0.237274\pi\)
0.734803 + 0.678280i \(0.237274\pi\)
\(314\) −2.00000 −0.112867
\(315\) 0 0
\(316\) 14.0000 0.787562
\(317\) 12.0000 0.673987 0.336994 0.941507i \(-0.390590\pi\)
0.336994 + 0.941507i \(0.390590\pi\)
\(318\) 0 0
\(319\) −6.00000 −0.335936
\(320\) 0 0
\(321\) −12.0000 −0.669775
\(322\) −12.0000 −0.668734
\(323\) 24.0000 1.33540
\(324\) 1.00000 0.0555556
\(325\) 20.0000 1.10940
\(326\) 4.00000 0.221540
\(327\) −4.00000 −0.221201
\(328\) −6.00000 −0.331295
\(329\) −12.0000 −0.661581
\(330\) 0 0
\(331\) −4.00000 −0.219860 −0.109930 0.993939i \(-0.535063\pi\)
−0.109930 + 0.993939i \(0.535063\pi\)
\(332\) −12.0000 −0.658586
\(333\) −10.0000 −0.547997
\(334\) −12.0000 −0.656611
\(335\) 0 0
\(336\) 2.00000 0.109109
\(337\) 2.00000 0.108947 0.0544735 0.998515i \(-0.482652\pi\)
0.0544735 + 0.998515i \(0.482652\pi\)
\(338\) −3.00000 −0.163178
\(339\) 18.0000 0.977626
\(340\) 0 0
\(341\) −8.00000 −0.433224
\(342\) 4.00000 0.216295
\(343\) −20.0000 −1.07990
\(344\) −8.00000 −0.431331
\(345\) 0 0
\(346\) −6.00000 −0.322562
\(347\) 36.0000 1.93258 0.966291 0.257454i \(-0.0828835\pi\)
0.966291 + 0.257454i \(0.0828835\pi\)
\(348\) 6.00000 0.321634
\(349\) −4.00000 −0.214115 −0.107058 0.994253i \(-0.534143\pi\)
−0.107058 + 0.994253i \(0.534143\pi\)
\(350\) 10.0000 0.534522
\(351\) −4.00000 −0.213504
\(352\) 1.00000 0.0533002
\(353\) −6.00000 −0.319348 −0.159674 0.987170i \(-0.551044\pi\)
−0.159674 + 0.987170i \(0.551044\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −6.00000 −0.317999
\(357\) −12.0000 −0.635107
\(358\) −24.0000 −1.26844
\(359\) −12.0000 −0.633336 −0.316668 0.948536i \(-0.602564\pi\)
−0.316668 + 0.948536i \(0.602564\pi\)
\(360\) 0 0
\(361\) −3.00000 −0.157895
\(362\) 22.0000 1.15629
\(363\) 1.00000 0.0524864
\(364\) −8.00000 −0.419314
\(365\) 0 0
\(366\) −8.00000 −0.418167
\(367\) 8.00000 0.417597 0.208798 0.977959i \(-0.433045\pi\)
0.208798 + 0.977959i \(0.433045\pi\)
\(368\) 6.00000 0.312772
\(369\) 6.00000 0.312348
\(370\) 0 0
\(371\) 0 0
\(372\) 8.00000 0.414781
\(373\) 20.0000 1.03556 0.517780 0.855514i \(-0.326758\pi\)
0.517780 + 0.855514i \(0.326758\pi\)
\(374\) −6.00000 −0.310253
\(375\) 0 0
\(376\) 6.00000 0.309426
\(377\) −24.0000 −1.23606
\(378\) −2.00000 −0.102869
\(379\) 20.0000 1.02733 0.513665 0.857991i \(-0.328287\pi\)
0.513665 + 0.857991i \(0.328287\pi\)
\(380\) 0 0
\(381\) 14.0000 0.717242
\(382\) −18.0000 −0.920960
\(383\) 6.00000 0.306586 0.153293 0.988181i \(-0.451012\pi\)
0.153293 + 0.988181i \(0.451012\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) −14.0000 −0.712581
\(387\) 8.00000 0.406663
\(388\) 14.0000 0.710742
\(389\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(390\) 0 0
\(391\) −36.0000 −1.82060
\(392\) 3.00000 0.151523
\(393\) −12.0000 −0.605320
\(394\) −6.00000 −0.302276
\(395\) 0 0
\(396\) −1.00000 −0.0502519
\(397\) 26.0000 1.30490 0.652451 0.757831i \(-0.273741\pi\)
0.652451 + 0.757831i \(0.273741\pi\)
\(398\) 4.00000 0.200502
\(399\) −8.00000 −0.400501
\(400\) −5.00000 −0.250000
\(401\) 30.0000 1.49813 0.749064 0.662497i \(-0.230503\pi\)
0.749064 + 0.662497i \(0.230503\pi\)
\(402\) 4.00000 0.199502
\(403\) −32.0000 −1.59403
\(404\) 6.00000 0.298511
\(405\) 0 0
\(406\) −12.0000 −0.595550
\(407\) 10.0000 0.495682
\(408\) 6.00000 0.297044
\(409\) −34.0000 −1.68119 −0.840596 0.541663i \(-0.817795\pi\)
−0.840596 + 0.541663i \(0.817795\pi\)
\(410\) 0 0
\(411\) −18.0000 −0.887875
\(412\) −4.00000 −0.197066
\(413\) 0 0
\(414\) −6.00000 −0.294884
\(415\) 0 0
\(416\) 4.00000 0.196116
\(417\) −4.00000 −0.195881
\(418\) −4.00000 −0.195646
\(419\) 24.0000 1.17248 0.586238 0.810139i \(-0.300608\pi\)
0.586238 + 0.810139i \(0.300608\pi\)
\(420\) 0 0
\(421\) −10.0000 −0.487370 −0.243685 0.969854i \(-0.578356\pi\)
−0.243685 + 0.969854i \(0.578356\pi\)
\(422\) −8.00000 −0.389434
\(423\) −6.00000 −0.291730
\(424\) 0 0
\(425\) 30.0000 1.45521
\(426\) −6.00000 −0.290701
\(427\) 16.0000 0.774294
\(428\) −12.0000 −0.580042
\(429\) 4.00000 0.193122
\(430\) 0 0
\(431\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(432\) 1.00000 0.0481125
\(433\) 26.0000 1.24948 0.624740 0.780833i \(-0.285205\pi\)
0.624740 + 0.780833i \(0.285205\pi\)
\(434\) −16.0000 −0.768025
\(435\) 0 0
\(436\) −4.00000 −0.191565
\(437\) −24.0000 −1.14808
\(438\) −2.00000 −0.0955637
\(439\) −10.0000 −0.477274 −0.238637 0.971109i \(-0.576701\pi\)
−0.238637 + 0.971109i \(0.576701\pi\)
\(440\) 0 0
\(441\) −3.00000 −0.142857
\(442\) −24.0000 −1.14156
\(443\) −24.0000 −1.14027 −0.570137 0.821549i \(-0.693110\pi\)
−0.570137 + 0.821549i \(0.693110\pi\)
\(444\) −10.0000 −0.474579
\(445\) 0 0
\(446\) 16.0000 0.757622
\(447\) −6.00000 −0.283790
\(448\) 2.00000 0.0944911
\(449\) 6.00000 0.283158 0.141579 0.989927i \(-0.454782\pi\)
0.141579 + 0.989927i \(0.454782\pi\)
\(450\) 5.00000 0.235702
\(451\) −6.00000 −0.282529
\(452\) 18.0000 0.846649
\(453\) −10.0000 −0.469841
\(454\) 12.0000 0.563188
\(455\) 0 0
\(456\) 4.00000 0.187317
\(457\) −10.0000 −0.467780 −0.233890 0.972263i \(-0.575146\pi\)
−0.233890 + 0.972263i \(0.575146\pi\)
\(458\) 22.0000 1.02799
\(459\) −6.00000 −0.280056
\(460\) 0 0
\(461\) 42.0000 1.95614 0.978068 0.208288i \(-0.0667892\pi\)
0.978068 + 0.208288i \(0.0667892\pi\)
\(462\) 2.00000 0.0930484
\(463\) −4.00000 −0.185896 −0.0929479 0.995671i \(-0.529629\pi\)
−0.0929479 + 0.995671i \(0.529629\pi\)
\(464\) 6.00000 0.278543
\(465\) 0 0
\(466\) 18.0000 0.833834
\(467\) −12.0000 −0.555294 −0.277647 0.960683i \(-0.589555\pi\)
−0.277647 + 0.960683i \(0.589555\pi\)
\(468\) −4.00000 −0.184900
\(469\) −8.00000 −0.369406
\(470\) 0 0
\(471\) 2.00000 0.0921551
\(472\) 0 0
\(473\) −8.00000 −0.367840
\(474\) −14.0000 −0.643041
\(475\) 20.0000 0.917663
\(476\) −12.0000 −0.550019
\(477\) 0 0
\(478\) 12.0000 0.548867
\(479\) −24.0000 −1.09659 −0.548294 0.836286i \(-0.684723\pi\)
−0.548294 + 0.836286i \(0.684723\pi\)
\(480\) 0 0
\(481\) 40.0000 1.82384
\(482\) 10.0000 0.455488
\(483\) 12.0000 0.546019
\(484\) 1.00000 0.0454545
\(485\) 0 0
\(486\) −1.00000 −0.0453609
\(487\) 20.0000 0.906287 0.453143 0.891438i \(-0.350303\pi\)
0.453143 + 0.891438i \(0.350303\pi\)
\(488\) −8.00000 −0.362143
\(489\) −4.00000 −0.180886
\(490\) 0 0
\(491\) 12.0000 0.541552 0.270776 0.962642i \(-0.412720\pi\)
0.270776 + 0.962642i \(0.412720\pi\)
\(492\) 6.00000 0.270501
\(493\) −36.0000 −1.62136
\(494\) −16.0000 −0.719874
\(495\) 0 0
\(496\) 8.00000 0.359211
\(497\) 12.0000 0.538274
\(498\) 12.0000 0.537733
\(499\) −4.00000 −0.179065 −0.0895323 0.995984i \(-0.528537\pi\)
−0.0895323 + 0.995984i \(0.528537\pi\)
\(500\) 0 0
\(501\) 12.0000 0.536120
\(502\) 0 0
\(503\) 12.0000 0.535054 0.267527 0.963550i \(-0.413794\pi\)
0.267527 + 0.963550i \(0.413794\pi\)
\(504\) −2.00000 −0.0890871
\(505\) 0 0
\(506\) 6.00000 0.266733
\(507\) 3.00000 0.133235
\(508\) 14.0000 0.621150
\(509\) 24.0000 1.06378 0.531891 0.846813i \(-0.321482\pi\)
0.531891 + 0.846813i \(0.321482\pi\)
\(510\) 0 0
\(511\) 4.00000 0.176950
\(512\) −1.00000 −0.0441942
\(513\) −4.00000 −0.176604
\(514\) 30.0000 1.32324
\(515\) 0 0
\(516\) 8.00000 0.352180
\(517\) 6.00000 0.263880
\(518\) 20.0000 0.878750
\(519\) 6.00000 0.263371
\(520\) 0 0
\(521\) −18.0000 −0.788594 −0.394297 0.918983i \(-0.629012\pi\)
−0.394297 + 0.918983i \(0.629012\pi\)
\(522\) −6.00000 −0.262613
\(523\) −16.0000 −0.699631 −0.349816 0.936819i \(-0.613756\pi\)
−0.349816 + 0.936819i \(0.613756\pi\)
\(524\) −12.0000 −0.524222
\(525\) −10.0000 −0.436436
\(526\) 0 0
\(527\) −48.0000 −2.09091
\(528\) −1.00000 −0.0435194
\(529\) 13.0000 0.565217
\(530\) 0 0
\(531\) 0 0
\(532\) −8.00000 −0.346844
\(533\) −24.0000 −1.03956
\(534\) 6.00000 0.259645
\(535\) 0 0
\(536\) 4.00000 0.172774
\(537\) 24.0000 1.03568
\(538\) 24.0000 1.03471
\(539\) 3.00000 0.129219
\(540\) 0 0
\(541\) 20.0000 0.859867 0.429934 0.902861i \(-0.358537\pi\)
0.429934 + 0.902861i \(0.358537\pi\)
\(542\) −2.00000 −0.0859074
\(543\) −22.0000 −0.944110
\(544\) 6.00000 0.257248
\(545\) 0 0
\(546\) 8.00000 0.342368
\(547\) −28.0000 −1.19719 −0.598597 0.801050i \(-0.704275\pi\)
−0.598597 + 0.801050i \(0.704275\pi\)
\(548\) −18.0000 −0.768922
\(549\) 8.00000 0.341432
\(550\) −5.00000 −0.213201
\(551\) −24.0000 −1.02243
\(552\) −6.00000 −0.255377
\(553\) 28.0000 1.19068
\(554\) 16.0000 0.679775
\(555\) 0 0
\(556\) −4.00000 −0.169638
\(557\) 18.0000 0.762684 0.381342 0.924434i \(-0.375462\pi\)
0.381342 + 0.924434i \(0.375462\pi\)
\(558\) −8.00000 −0.338667
\(559\) −32.0000 −1.35346
\(560\) 0 0
\(561\) 6.00000 0.253320
\(562\) 6.00000 0.253095
\(563\) −12.0000 −0.505740 −0.252870 0.967500i \(-0.581374\pi\)
−0.252870 + 0.967500i \(0.581374\pi\)
\(564\) −6.00000 −0.252646
\(565\) 0 0
\(566\) −8.00000 −0.336265
\(567\) 2.00000 0.0839921
\(568\) −6.00000 −0.251754
\(569\) 18.0000 0.754599 0.377300 0.926091i \(-0.376853\pi\)
0.377300 + 0.926091i \(0.376853\pi\)
\(570\) 0 0
\(571\) −28.0000 −1.17176 −0.585882 0.810397i \(-0.699252\pi\)
−0.585882 + 0.810397i \(0.699252\pi\)
\(572\) 4.00000 0.167248
\(573\) 18.0000 0.751961
\(574\) −12.0000 −0.500870
\(575\) −30.0000 −1.25109
\(576\) 1.00000 0.0416667
\(577\) −34.0000 −1.41544 −0.707719 0.706494i \(-0.750276\pi\)
−0.707719 + 0.706494i \(0.750276\pi\)
\(578\) −19.0000 −0.790296
\(579\) 14.0000 0.581820
\(580\) 0 0
\(581\) −24.0000 −0.995688
\(582\) −14.0000 −0.580319
\(583\) 0 0
\(584\) −2.00000 −0.0827606
\(585\) 0 0
\(586\) 6.00000 0.247858
\(587\) 24.0000 0.990586 0.495293 0.868726i \(-0.335061\pi\)
0.495293 + 0.868726i \(0.335061\pi\)
\(588\) −3.00000 −0.123718
\(589\) −32.0000 −1.31854
\(590\) 0 0
\(591\) 6.00000 0.246807
\(592\) −10.0000 −0.410997
\(593\) −30.0000 −1.23195 −0.615976 0.787765i \(-0.711238\pi\)
−0.615976 + 0.787765i \(0.711238\pi\)
\(594\) 1.00000 0.0410305
\(595\) 0 0
\(596\) −6.00000 −0.245770
\(597\) −4.00000 −0.163709
\(598\) 24.0000 0.981433
\(599\) 30.0000 1.22577 0.612883 0.790173i \(-0.290010\pi\)
0.612883 + 0.790173i \(0.290010\pi\)
\(600\) 5.00000 0.204124
\(601\) −22.0000 −0.897399 −0.448699 0.893683i \(-0.648113\pi\)
−0.448699 + 0.893683i \(0.648113\pi\)
\(602\) −16.0000 −0.652111
\(603\) −4.00000 −0.162893
\(604\) −10.0000 −0.406894
\(605\) 0 0
\(606\) −6.00000 −0.243733
\(607\) 14.0000 0.568242 0.284121 0.958788i \(-0.408298\pi\)
0.284121 + 0.958788i \(0.408298\pi\)
\(608\) 4.00000 0.162221
\(609\) 12.0000 0.486265
\(610\) 0 0
\(611\) 24.0000 0.970936
\(612\) −6.00000 −0.242536
\(613\) −16.0000 −0.646234 −0.323117 0.946359i \(-0.604731\pi\)
−0.323117 + 0.946359i \(0.604731\pi\)
\(614\) −20.0000 −0.807134
\(615\) 0 0
\(616\) 2.00000 0.0805823
\(617\) −30.0000 −1.20775 −0.603877 0.797077i \(-0.706378\pi\)
−0.603877 + 0.797077i \(0.706378\pi\)
\(618\) 4.00000 0.160904
\(619\) 44.0000 1.76851 0.884255 0.467005i \(-0.154667\pi\)
0.884255 + 0.467005i \(0.154667\pi\)
\(620\) 0 0
\(621\) 6.00000 0.240772
\(622\) 18.0000 0.721734
\(623\) −12.0000 −0.480770
\(624\) −4.00000 −0.160128
\(625\) 25.0000 1.00000
\(626\) −26.0000 −1.03917
\(627\) 4.00000 0.159745
\(628\) 2.00000 0.0798087
\(629\) 60.0000 2.39236
\(630\) 0 0
\(631\) −16.0000 −0.636950 −0.318475 0.947931i \(-0.603171\pi\)
−0.318475 + 0.947931i \(0.603171\pi\)
\(632\) −14.0000 −0.556890
\(633\) 8.00000 0.317971
\(634\) −12.0000 −0.476581
\(635\) 0 0
\(636\) 0 0
\(637\) 12.0000 0.475457
\(638\) 6.00000 0.237542
\(639\) 6.00000 0.237356
\(640\) 0 0
\(641\) 6.00000 0.236986 0.118493 0.992955i \(-0.462194\pi\)
0.118493 + 0.992955i \(0.462194\pi\)
\(642\) 12.0000 0.473602
\(643\) −4.00000 −0.157745 −0.0788723 0.996885i \(-0.525132\pi\)
−0.0788723 + 0.996885i \(0.525132\pi\)
\(644\) 12.0000 0.472866
\(645\) 0 0
\(646\) −24.0000 −0.944267
\(647\) 6.00000 0.235884 0.117942 0.993020i \(-0.462370\pi\)
0.117942 + 0.993020i \(0.462370\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 0 0
\(650\) −20.0000 −0.784465
\(651\) 16.0000 0.627089
\(652\) −4.00000 −0.156652
\(653\) −36.0000 −1.40879 −0.704394 0.709809i \(-0.748781\pi\)
−0.704394 + 0.709809i \(0.748781\pi\)
\(654\) 4.00000 0.156412
\(655\) 0 0
\(656\) 6.00000 0.234261
\(657\) 2.00000 0.0780274
\(658\) 12.0000 0.467809
\(659\) 36.0000 1.40236 0.701180 0.712984i \(-0.252657\pi\)
0.701180 + 0.712984i \(0.252657\pi\)
\(660\) 0 0
\(661\) −22.0000 −0.855701 −0.427850 0.903850i \(-0.640729\pi\)
−0.427850 + 0.903850i \(0.640729\pi\)
\(662\) 4.00000 0.155464
\(663\) 24.0000 0.932083
\(664\) 12.0000 0.465690
\(665\) 0 0
\(666\) 10.0000 0.387492
\(667\) 36.0000 1.39393
\(668\) 12.0000 0.464294
\(669\) −16.0000 −0.618596
\(670\) 0 0
\(671\) −8.00000 −0.308837
\(672\) −2.00000 −0.0771517
\(673\) 14.0000 0.539660 0.269830 0.962908i \(-0.413032\pi\)
0.269830 + 0.962908i \(0.413032\pi\)
\(674\) −2.00000 −0.0770371
\(675\) −5.00000 −0.192450
\(676\) 3.00000 0.115385
\(677\) 30.0000 1.15299 0.576497 0.817099i \(-0.304419\pi\)
0.576497 + 0.817099i \(0.304419\pi\)
\(678\) −18.0000 −0.691286
\(679\) 28.0000 1.07454
\(680\) 0 0
\(681\) −12.0000 −0.459841
\(682\) 8.00000 0.306336
\(683\) −24.0000 −0.918334 −0.459167 0.888350i \(-0.651852\pi\)
−0.459167 + 0.888350i \(0.651852\pi\)
\(684\) −4.00000 −0.152944
\(685\) 0 0
\(686\) 20.0000 0.763604
\(687\) −22.0000 −0.839352
\(688\) 8.00000 0.304997
\(689\) 0 0
\(690\) 0 0
\(691\) 20.0000 0.760836 0.380418 0.924815i \(-0.375780\pi\)
0.380418 + 0.924815i \(0.375780\pi\)
\(692\) 6.00000 0.228086
\(693\) −2.00000 −0.0759737
\(694\) −36.0000 −1.36654
\(695\) 0 0
\(696\) −6.00000 −0.227429
\(697\) −36.0000 −1.36360
\(698\) 4.00000 0.151402
\(699\) −18.0000 −0.680823
\(700\) −10.0000 −0.377964
\(701\) −6.00000 −0.226617 −0.113308 0.993560i \(-0.536145\pi\)
−0.113308 + 0.993560i \(0.536145\pi\)
\(702\) 4.00000 0.150970
\(703\) 40.0000 1.50863
\(704\) −1.00000 −0.0376889
\(705\) 0 0
\(706\) 6.00000 0.225813
\(707\) 12.0000 0.451306
\(708\) 0 0
\(709\) 26.0000 0.976450 0.488225 0.872718i \(-0.337644\pi\)
0.488225 + 0.872718i \(0.337644\pi\)
\(710\) 0 0
\(711\) 14.0000 0.525041
\(712\) 6.00000 0.224860
\(713\) 48.0000 1.79761
\(714\) 12.0000 0.449089
\(715\) 0 0
\(716\) 24.0000 0.896922
\(717\) −12.0000 −0.448148
\(718\) 12.0000 0.447836
\(719\) 30.0000 1.11881 0.559406 0.828894i \(-0.311029\pi\)
0.559406 + 0.828894i \(0.311029\pi\)
\(720\) 0 0
\(721\) −8.00000 −0.297936
\(722\) 3.00000 0.111648
\(723\) −10.0000 −0.371904
\(724\) −22.0000 −0.817624
\(725\) −30.0000 −1.11417
\(726\) −1.00000 −0.0371135
\(727\) −28.0000 −1.03846 −0.519231 0.854634i \(-0.673782\pi\)
−0.519231 + 0.854634i \(0.673782\pi\)
\(728\) 8.00000 0.296500
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −48.0000 −1.77534
\(732\) 8.00000 0.295689
\(733\) −4.00000 −0.147743 −0.0738717 0.997268i \(-0.523536\pi\)
−0.0738717 + 0.997268i \(0.523536\pi\)
\(734\) −8.00000 −0.295285
\(735\) 0 0
\(736\) −6.00000 −0.221163
\(737\) 4.00000 0.147342
\(738\) −6.00000 −0.220863
\(739\) 8.00000 0.294285 0.147142 0.989115i \(-0.452992\pi\)
0.147142 + 0.989115i \(0.452992\pi\)
\(740\) 0 0
\(741\) 16.0000 0.587775
\(742\) 0 0
\(743\) 36.0000 1.32071 0.660356 0.750953i \(-0.270405\pi\)
0.660356 + 0.750953i \(0.270405\pi\)
\(744\) −8.00000 −0.293294
\(745\) 0 0
\(746\) −20.0000 −0.732252
\(747\) −12.0000 −0.439057
\(748\) 6.00000 0.219382
\(749\) −24.0000 −0.876941
\(750\) 0 0
\(751\) 8.00000 0.291924 0.145962 0.989290i \(-0.453372\pi\)
0.145962 + 0.989290i \(0.453372\pi\)
\(752\) −6.00000 −0.218797
\(753\) 0 0
\(754\) 24.0000 0.874028
\(755\) 0 0
\(756\) 2.00000 0.0727393
\(757\) −34.0000 −1.23575 −0.617876 0.786276i \(-0.712006\pi\)
−0.617876 + 0.786276i \(0.712006\pi\)
\(758\) −20.0000 −0.726433
\(759\) −6.00000 −0.217786
\(760\) 0 0
\(761\) 18.0000 0.652499 0.326250 0.945284i \(-0.394215\pi\)
0.326250 + 0.945284i \(0.394215\pi\)
\(762\) −14.0000 −0.507166
\(763\) −8.00000 −0.289619
\(764\) 18.0000 0.651217
\(765\) 0 0
\(766\) −6.00000 −0.216789
\(767\) 0 0
\(768\) 1.00000 0.0360844
\(769\) −34.0000 −1.22607 −0.613036 0.790055i \(-0.710052\pi\)
−0.613036 + 0.790055i \(0.710052\pi\)
\(770\) 0 0
\(771\) −30.0000 −1.08042
\(772\) 14.0000 0.503871
\(773\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(774\) −8.00000 −0.287554
\(775\) −40.0000 −1.43684
\(776\) −14.0000 −0.502571
\(777\) −20.0000 −0.717496
\(778\) 0 0
\(779\) −24.0000 −0.859889
\(780\) 0 0
\(781\) −6.00000 −0.214697
\(782\) 36.0000 1.28736
\(783\) 6.00000 0.214423
\(784\) −3.00000 −0.107143
\(785\) 0 0
\(786\) 12.0000 0.428026
\(787\) 32.0000 1.14068 0.570338 0.821410i \(-0.306812\pi\)
0.570338 + 0.821410i \(0.306812\pi\)
\(788\) 6.00000 0.213741
\(789\) 0 0
\(790\) 0 0
\(791\) 36.0000 1.28001
\(792\) 1.00000 0.0355335
\(793\) −32.0000 −1.13635
\(794\) −26.0000 −0.922705
\(795\) 0 0
\(796\) −4.00000 −0.141776
\(797\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(798\) 8.00000 0.283197
\(799\) 36.0000 1.27359
\(800\) 5.00000 0.176777
\(801\) −6.00000 −0.212000
\(802\) −30.0000 −1.05934
\(803\) −2.00000 −0.0705785
\(804\) −4.00000 −0.141069
\(805\) 0 0
\(806\) 32.0000 1.12715
\(807\) −24.0000 −0.844840
\(808\) −6.00000 −0.211079
\(809\) −42.0000 −1.47664 −0.738321 0.674450i \(-0.764381\pi\)
−0.738321 + 0.674450i \(0.764381\pi\)
\(810\) 0 0
\(811\) 8.00000 0.280918 0.140459 0.990086i \(-0.455142\pi\)
0.140459 + 0.990086i \(0.455142\pi\)
\(812\) 12.0000 0.421117
\(813\) 2.00000 0.0701431
\(814\) −10.0000 −0.350500
\(815\) 0 0
\(816\) −6.00000 −0.210042
\(817\) −32.0000 −1.11954
\(818\) 34.0000 1.18878
\(819\) −8.00000 −0.279543
\(820\) 0 0
\(821\) −18.0000 −0.628204 −0.314102 0.949389i \(-0.601703\pi\)
−0.314102 + 0.949389i \(0.601703\pi\)
\(822\) 18.0000 0.627822
\(823\) 8.00000 0.278862 0.139431 0.990232i \(-0.455473\pi\)
0.139431 + 0.990232i \(0.455473\pi\)
\(824\) 4.00000 0.139347
\(825\) 5.00000 0.174078
\(826\) 0 0
\(827\) −12.0000 −0.417281 −0.208640 0.977992i \(-0.566904\pi\)
−0.208640 + 0.977992i \(0.566904\pi\)
\(828\) 6.00000 0.208514
\(829\) 14.0000 0.486240 0.243120 0.969996i \(-0.421829\pi\)
0.243120 + 0.969996i \(0.421829\pi\)
\(830\) 0 0
\(831\) −16.0000 −0.555034
\(832\) −4.00000 −0.138675
\(833\) 18.0000 0.623663
\(834\) 4.00000 0.138509
\(835\) 0 0
\(836\) 4.00000 0.138343
\(837\) 8.00000 0.276520
\(838\) −24.0000 −0.829066
\(839\) 18.0000 0.621429 0.310715 0.950503i \(-0.399432\pi\)
0.310715 + 0.950503i \(0.399432\pi\)
\(840\) 0 0
\(841\) 7.00000 0.241379
\(842\) 10.0000 0.344623
\(843\) −6.00000 −0.206651
\(844\) 8.00000 0.275371
\(845\) 0 0
\(846\) 6.00000 0.206284
\(847\) 2.00000 0.0687208
\(848\) 0 0
\(849\) 8.00000 0.274559
\(850\) −30.0000 −1.02899
\(851\) −60.0000 −2.05677
\(852\) 6.00000 0.205557
\(853\) 8.00000 0.273915 0.136957 0.990577i \(-0.456268\pi\)
0.136957 + 0.990577i \(0.456268\pi\)
\(854\) −16.0000 −0.547509
\(855\) 0 0
\(856\) 12.0000 0.410152
\(857\) 54.0000 1.84460 0.922302 0.386469i \(-0.126305\pi\)
0.922302 + 0.386469i \(0.126305\pi\)
\(858\) −4.00000 −0.136558
\(859\) 20.0000 0.682391 0.341196 0.939992i \(-0.389168\pi\)
0.341196 + 0.939992i \(0.389168\pi\)
\(860\) 0 0
\(861\) 12.0000 0.408959
\(862\) 0 0
\(863\) 42.0000 1.42970 0.714848 0.699280i \(-0.246496\pi\)
0.714848 + 0.699280i \(0.246496\pi\)
\(864\) −1.00000 −0.0340207
\(865\) 0 0
\(866\) −26.0000 −0.883516
\(867\) 19.0000 0.645274
\(868\) 16.0000 0.543075
\(869\) −14.0000 −0.474917
\(870\) 0 0
\(871\) 16.0000 0.542139
\(872\) 4.00000 0.135457
\(873\) 14.0000 0.473828
\(874\) 24.0000 0.811812
\(875\) 0 0
\(876\) 2.00000 0.0675737
\(877\) −52.0000 −1.75592 −0.877958 0.478738i \(-0.841094\pi\)
−0.877958 + 0.478738i \(0.841094\pi\)
\(878\) 10.0000 0.337484
\(879\) −6.00000 −0.202375
\(880\) 0 0
\(881\) −30.0000 −1.01073 −0.505363 0.862907i \(-0.668641\pi\)
−0.505363 + 0.862907i \(0.668641\pi\)
\(882\) 3.00000 0.101015
\(883\) −28.0000 −0.942275 −0.471138 0.882060i \(-0.656156\pi\)
−0.471138 + 0.882060i \(0.656156\pi\)
\(884\) 24.0000 0.807207
\(885\) 0 0
\(886\) 24.0000 0.806296
\(887\) −36.0000 −1.20876 −0.604381 0.796696i \(-0.706579\pi\)
−0.604381 + 0.796696i \(0.706579\pi\)
\(888\) 10.0000 0.335578
\(889\) 28.0000 0.939090
\(890\) 0 0
\(891\) −1.00000 −0.0335013
\(892\) −16.0000 −0.535720
\(893\) 24.0000 0.803129
\(894\) 6.00000 0.200670
\(895\) 0 0
\(896\) −2.00000 −0.0668153
\(897\) −24.0000 −0.801337
\(898\) −6.00000 −0.200223
\(899\) 48.0000 1.60089
\(900\) −5.00000 −0.166667
\(901\) 0 0
\(902\) 6.00000 0.199778
\(903\) 16.0000 0.532447
\(904\) −18.0000 −0.598671
\(905\) 0 0
\(906\) 10.0000 0.332228
\(907\) 20.0000 0.664089 0.332045 0.943264i \(-0.392262\pi\)
0.332045 + 0.943264i \(0.392262\pi\)
\(908\) −12.0000 −0.398234
\(909\) 6.00000 0.199007
\(910\) 0 0
\(911\) −42.0000 −1.39152 −0.695761 0.718273i \(-0.744933\pi\)
−0.695761 + 0.718273i \(0.744933\pi\)
\(912\) −4.00000 −0.132453
\(913\) 12.0000 0.397142
\(914\) 10.0000 0.330771
\(915\) 0 0
\(916\) −22.0000 −0.726900
\(917\) −24.0000 −0.792550
\(918\) 6.00000 0.198030
\(919\) 2.00000 0.0659739 0.0329870 0.999456i \(-0.489498\pi\)
0.0329870 + 0.999456i \(0.489498\pi\)
\(920\) 0 0
\(921\) 20.0000 0.659022
\(922\) −42.0000 −1.38320
\(923\) −24.0000 −0.789970
\(924\) −2.00000 −0.0657952
\(925\) 50.0000 1.64399
\(926\) 4.00000 0.131448
\(927\) −4.00000 −0.131377
\(928\) −6.00000 −0.196960
\(929\) 30.0000 0.984268 0.492134 0.870519i \(-0.336217\pi\)
0.492134 + 0.870519i \(0.336217\pi\)
\(930\) 0 0
\(931\) 12.0000 0.393284
\(932\) −18.0000 −0.589610
\(933\) −18.0000 −0.589294
\(934\) 12.0000 0.392652
\(935\) 0 0
\(936\) 4.00000 0.130744
\(937\) −22.0000 −0.718709 −0.359354 0.933201i \(-0.617003\pi\)
−0.359354 + 0.933201i \(0.617003\pi\)
\(938\) 8.00000 0.261209
\(939\) 26.0000 0.848478
\(940\) 0 0
\(941\) −18.0000 −0.586783 −0.293392 0.955992i \(-0.594784\pi\)
−0.293392 + 0.955992i \(0.594784\pi\)
\(942\) −2.00000 −0.0651635
\(943\) 36.0000 1.17232
\(944\) 0 0
\(945\) 0 0
\(946\) 8.00000 0.260102
\(947\) 12.0000 0.389948 0.194974 0.980808i \(-0.437538\pi\)
0.194974 + 0.980808i \(0.437538\pi\)
\(948\) 14.0000 0.454699
\(949\) −8.00000 −0.259691
\(950\) −20.0000 −0.648886
\(951\) 12.0000 0.389127
\(952\) 12.0000 0.388922
\(953\) −42.0000 −1.36051 −0.680257 0.732974i \(-0.738132\pi\)
−0.680257 + 0.732974i \(0.738132\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) −12.0000 −0.388108
\(957\) −6.00000 −0.193952
\(958\) 24.0000 0.775405
\(959\) −36.0000 −1.16250
\(960\) 0 0
\(961\) 33.0000 1.06452
\(962\) −40.0000 −1.28965
\(963\) −12.0000 −0.386695
\(964\) −10.0000 −0.322078
\(965\) 0 0
\(966\) −12.0000 −0.386094
\(967\) 14.0000 0.450210 0.225105 0.974335i \(-0.427728\pi\)
0.225105 + 0.974335i \(0.427728\pi\)
\(968\) −1.00000 −0.0321412
\(969\) 24.0000 0.770991
\(970\) 0 0
\(971\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(972\) 1.00000 0.0320750
\(973\) −8.00000 −0.256468
\(974\) −20.0000 −0.640841
\(975\) 20.0000 0.640513
\(976\) 8.00000 0.256074
\(977\) 54.0000 1.72761 0.863807 0.503824i \(-0.168074\pi\)
0.863807 + 0.503824i \(0.168074\pi\)
\(978\) 4.00000 0.127906
\(979\) 6.00000 0.191761
\(980\) 0 0
\(981\) −4.00000 −0.127710
\(982\) −12.0000 −0.382935
\(983\) 30.0000 0.956851 0.478426 0.878128i \(-0.341208\pi\)
0.478426 + 0.878128i \(0.341208\pi\)
\(984\) −6.00000 −0.191273
\(985\) 0 0
\(986\) 36.0000 1.14647
\(987\) −12.0000 −0.381964
\(988\) 16.0000 0.509028
\(989\) 48.0000 1.52631
\(990\) 0 0
\(991\) 56.0000 1.77890 0.889449 0.457034i \(-0.151088\pi\)
0.889449 + 0.457034i \(0.151088\pi\)
\(992\) −8.00000 −0.254000
\(993\) −4.00000 −0.126936
\(994\) −12.0000 −0.380617
\(995\) 0 0
\(996\) −12.0000 −0.380235
\(997\) 44.0000 1.39349 0.696747 0.717317i \(-0.254630\pi\)
0.696747 + 0.717317i \(0.254630\pi\)
\(998\) 4.00000 0.126618
\(999\) −10.0000 −0.316386
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 66.2.a.a.1.1 1
3.2 odd 2 198.2.a.e.1.1 1
4.3 odd 2 528.2.a.d.1.1 1
5.2 odd 4 1650.2.c.d.199.1 2
5.3 odd 4 1650.2.c.d.199.2 2
5.4 even 2 1650.2.a.m.1.1 1
7.6 odd 2 3234.2.a.d.1.1 1
8.3 odd 2 2112.2.a.v.1.1 1
8.5 even 2 2112.2.a.i.1.1 1
9.2 odd 6 1782.2.e.f.595.1 2
9.4 even 3 1782.2.e.s.1189.1 2
9.5 odd 6 1782.2.e.f.1189.1 2
9.7 even 3 1782.2.e.s.595.1 2
11.2 odd 10 726.2.e.b.565.1 4
11.3 even 5 726.2.e.k.493.1 4
11.4 even 5 726.2.e.k.511.1 4
11.5 even 5 726.2.e.k.487.1 4
11.6 odd 10 726.2.e.b.487.1 4
11.7 odd 10 726.2.e.b.511.1 4
11.8 odd 10 726.2.e.b.493.1 4
11.9 even 5 726.2.e.k.565.1 4
11.10 odd 2 726.2.a.i.1.1 1
12.11 even 2 1584.2.a.h.1.1 1
15.2 even 4 4950.2.c.r.199.2 2
15.8 even 4 4950.2.c.r.199.1 2
15.14 odd 2 4950.2.a.g.1.1 1
21.20 even 2 9702.2.a.bu.1.1 1
24.5 odd 2 6336.2.a.bj.1.1 1
24.11 even 2 6336.2.a.bf.1.1 1
33.32 even 2 2178.2.a.b.1.1 1
44.43 even 2 5808.2.a.l.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
66.2.a.a.1.1 1 1.1 even 1 trivial
198.2.a.e.1.1 1 3.2 odd 2
528.2.a.d.1.1 1 4.3 odd 2
726.2.a.i.1.1 1 11.10 odd 2
726.2.e.b.487.1 4 11.6 odd 10
726.2.e.b.493.1 4 11.8 odd 10
726.2.e.b.511.1 4 11.7 odd 10
726.2.e.b.565.1 4 11.2 odd 10
726.2.e.k.487.1 4 11.5 even 5
726.2.e.k.493.1 4 11.3 even 5
726.2.e.k.511.1 4 11.4 even 5
726.2.e.k.565.1 4 11.9 even 5
1584.2.a.h.1.1 1 12.11 even 2
1650.2.a.m.1.1 1 5.4 even 2
1650.2.c.d.199.1 2 5.2 odd 4
1650.2.c.d.199.2 2 5.3 odd 4
1782.2.e.f.595.1 2 9.2 odd 6
1782.2.e.f.1189.1 2 9.5 odd 6
1782.2.e.s.595.1 2 9.7 even 3
1782.2.e.s.1189.1 2 9.4 even 3
2112.2.a.i.1.1 1 8.5 even 2
2112.2.a.v.1.1 1 8.3 odd 2
2178.2.a.b.1.1 1 33.32 even 2
3234.2.a.d.1.1 1 7.6 odd 2
4950.2.a.g.1.1 1 15.14 odd 2
4950.2.c.r.199.1 2 15.8 even 4
4950.2.c.r.199.2 2 15.2 even 4
5808.2.a.l.1.1 1 44.43 even 2
6336.2.a.bf.1.1 1 24.11 even 2
6336.2.a.bj.1.1 1 24.5 odd 2
9702.2.a.bu.1.1 1 21.20 even 2