Properties

Label 5577.2.a.g.1.1
Level $5577$
Weight $2$
Character 5577.1
Self dual yes
Analytic conductor $44.533$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 5577 = 3 \cdot 11 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5577.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(44.5325692073\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 429)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 5577.1

$q$-expansion

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

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 0.353553 0.935414i \(-0.384973\pi\)
0.353553 + 0.935414i \(0.384973\pi\)
\(3\) 1.00000 0.577350
\(4\) −1.00000 −0.500000
\(5\) 2.00000 0.894427 0.447214 0.894427i \(-0.352416\pi\)
0.447214 + 0.894427i \(0.352416\pi\)
\(6\) 1.00000 0.408248
\(7\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(8\) −3.00000 −1.06066
\(9\) 1.00000 0.333333
\(10\) 2.00000 0.632456
\(11\) 1.00000 0.301511
\(12\) −1.00000 −0.288675
\(13\) 0 0
\(14\) 0 0
\(15\) 2.00000 0.516398
\(16\) −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 \(-0.348268\pi\)
0.458831 + 0.888523i \(0.348268\pi\)
\(20\) −2.00000 −0.447214
\(21\) 0 0
\(22\) 1.00000 0.213201
\(23\) −8.00000 −1.66812 −0.834058 0.551677i \(-0.813988\pi\)
−0.834058 + 0.551677i \(0.813988\pi\)
\(24\) −3.00000 −0.612372
\(25\) −1.00000 −0.200000
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −10.0000 −1.85695 −0.928477 0.371391i \(-0.878881\pi\)
−0.928477 + 0.371391i \(0.878881\pi\)
\(30\) 2.00000 0.365148
\(31\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) 5.00000 0.883883
\(33\) 1.00000 0.174078
\(34\) −6.00000 −1.02899
\(35\) 0 0
\(36\) −1.00000 −0.166667
\(37\) −6.00000 −0.986394 −0.493197 0.869918i \(-0.664172\pi\)
−0.493197 + 0.869918i \(0.664172\pi\)
\(38\) 4.00000 0.648886
\(39\) 0 0
\(40\) −6.00000 −0.948683
\(41\) −10.0000 −1.56174 −0.780869 0.624695i \(-0.785223\pi\)
−0.780869 + 0.624695i \(0.785223\pi\)
\(42\) 0 0
\(43\) 4.00000 0.609994 0.304997 0.952353i \(-0.401344\pi\)
0.304997 + 0.952353i \(0.401344\pi\)
\(44\) −1.00000 −0.150756
\(45\) 2.00000 0.298142
\(46\) −8.00000 −1.17954
\(47\) −8.00000 −1.16692 −0.583460 0.812142i \(-0.698301\pi\)
−0.583460 + 0.812142i \(0.698301\pi\)
\(48\) −1.00000 −0.144338
\(49\) −7.00000 −1.00000
\(50\) −1.00000 −0.141421
\(51\) −6.00000 −0.840168
\(52\) 0 0
\(53\) −10.0000 −1.37361 −0.686803 0.726844i \(-0.740986\pi\)
−0.686803 + 0.726844i \(0.740986\pi\)
\(54\) 1.00000 0.136083
\(55\) 2.00000 0.269680
\(56\) 0 0
\(57\) 4.00000 0.529813
\(58\) −10.0000 −1.31306
\(59\) 12.0000 1.56227 0.781133 0.624364i \(-0.214642\pi\)
0.781133 + 0.624364i \(0.214642\pi\)
\(60\) −2.00000 −0.258199
\(61\) 14.0000 1.79252 0.896258 0.443533i \(-0.146275\pi\)
0.896258 + 0.443533i \(0.146275\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 7.00000 0.875000
\(65\) 0 0
\(66\) 1.00000 0.123091
\(67\) 12.0000 1.46603 0.733017 0.680211i \(-0.238112\pi\)
0.733017 + 0.680211i \(0.238112\pi\)
\(68\) 6.00000 0.727607
\(69\) −8.00000 −0.963087
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) −3.00000 −0.353553
\(73\) 6.00000 0.702247 0.351123 0.936329i \(-0.385800\pi\)
0.351123 + 0.936329i \(0.385800\pi\)
\(74\) −6.00000 −0.697486
\(75\) −1.00000 −0.115470
\(76\) −4.00000 −0.458831
\(77\) 0 0
\(78\) 0 0
\(79\) 8.00000 0.900070 0.450035 0.893011i \(-0.351411\pi\)
0.450035 + 0.893011i \(0.351411\pi\)
\(80\) −2.00000 −0.223607
\(81\) 1.00000 0.111111
\(82\) −10.0000 −1.10432
\(83\) −12.0000 −1.31717 −0.658586 0.752506i \(-0.728845\pi\)
−0.658586 + 0.752506i \(0.728845\pi\)
\(84\) 0 0
\(85\) −12.0000 −1.30158
\(86\) 4.00000 0.431331
\(87\) −10.0000 −1.07211
\(88\) −3.00000 −0.319801
\(89\) −2.00000 −0.212000 −0.106000 0.994366i \(-0.533804\pi\)
−0.106000 + 0.994366i \(0.533804\pi\)
\(90\) 2.00000 0.210819
\(91\) 0 0
\(92\) 8.00000 0.834058
\(93\) 0 0
\(94\) −8.00000 −0.825137
\(95\) 8.00000 0.820783
\(96\) 5.00000 0.510310
\(97\) 14.0000 1.42148 0.710742 0.703452i \(-0.248359\pi\)
0.710742 + 0.703452i \(0.248359\pi\)
\(98\) −7.00000 −0.707107
\(99\) 1.00000 0.100504
\(100\) 1.00000 0.100000
\(101\) −2.00000 −0.199007 −0.0995037 0.995037i \(-0.531726\pi\)
−0.0995037 + 0.995037i \(0.531726\pi\)
\(102\) −6.00000 −0.594089
\(103\) 8.00000 0.788263 0.394132 0.919054i \(-0.371045\pi\)
0.394132 + 0.919054i \(0.371045\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) −10.0000 −0.971286
\(107\) 12.0000 1.16008 0.580042 0.814587i \(-0.303036\pi\)
0.580042 + 0.814587i \(0.303036\pi\)
\(108\) −1.00000 −0.0962250
\(109\) −14.0000 −1.34096 −0.670478 0.741929i \(-0.733911\pi\)
−0.670478 + 0.741929i \(0.733911\pi\)
\(110\) 2.00000 0.190693
\(111\) −6.00000 −0.569495
\(112\) 0 0
\(113\) −14.0000 −1.31701 −0.658505 0.752577i \(-0.728811\pi\)
−0.658505 + 0.752577i \(0.728811\pi\)
\(114\) 4.00000 0.374634
\(115\) −16.0000 −1.49201
\(116\) 10.0000 0.928477
\(117\) 0 0
\(118\) 12.0000 1.10469
\(119\) 0 0
\(120\) −6.00000 −0.547723
\(121\) 1.00000 0.0909091
\(122\) 14.0000 1.26750
\(123\) −10.0000 −0.901670
\(124\) 0 0
\(125\) −12.0000 −1.07331
\(126\) 0 0
\(127\) −8.00000 −0.709885 −0.354943 0.934888i \(-0.615500\pi\)
−0.354943 + 0.934888i \(0.615500\pi\)
\(128\) −3.00000 −0.265165
\(129\) 4.00000 0.352180
\(130\) 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
\(133\) 0 0
\(134\) 12.0000 1.03664
\(135\) 2.00000 0.172133
\(136\) 18.0000 1.54349
\(137\) −18.0000 −1.53784 −0.768922 0.639343i \(-0.779207\pi\)
−0.768922 + 0.639343i \(0.779207\pi\)
\(138\) −8.00000 −0.681005
\(139\) −12.0000 −1.01783 −0.508913 0.860818i \(-0.669953\pi\)
−0.508913 + 0.860818i \(0.669953\pi\)
\(140\) 0 0
\(141\) −8.00000 −0.673722
\(142\) 0 0
\(143\) 0 0
\(144\) −1.00000 −0.0833333
\(145\) −20.0000 −1.66091
\(146\) 6.00000 0.496564
\(147\) −7.00000 −0.577350
\(148\) 6.00000 0.493197
\(149\) 10.0000 0.819232 0.409616 0.912258i \(-0.365663\pi\)
0.409616 + 0.912258i \(0.365663\pi\)
\(150\) −1.00000 −0.0816497
\(151\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(152\) −12.0000 −0.973329
\(153\) −6.00000 −0.485071
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −2.00000 −0.159617 −0.0798087 0.996810i \(-0.525431\pi\)
−0.0798087 + 0.996810i \(0.525431\pi\)
\(158\) 8.00000 0.636446
\(159\) −10.0000 −0.793052
\(160\) 10.0000 0.790569
\(161\) 0 0
\(162\) 1.00000 0.0785674
\(163\) 12.0000 0.939913 0.469956 0.882690i \(-0.344270\pi\)
0.469956 + 0.882690i \(0.344270\pi\)
\(164\) 10.0000 0.780869
\(165\) 2.00000 0.155700
\(166\) −12.0000 −0.931381
\(167\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(168\) 0 0
\(169\) 0 0
\(170\) −12.0000 −0.920358
\(171\) 4.00000 0.305888
\(172\) −4.00000 −0.304997
\(173\) 6.00000 0.456172 0.228086 0.973641i \(-0.426753\pi\)
0.228086 + 0.973641i \(0.426753\pi\)
\(174\) −10.0000 −0.758098
\(175\) 0 0
\(176\) −1.00000 −0.0753778
\(177\) 12.0000 0.901975
\(178\) −2.00000 −0.149906
\(179\) 20.0000 1.49487 0.747435 0.664335i \(-0.231285\pi\)
0.747435 + 0.664335i \(0.231285\pi\)
\(180\) −2.00000 −0.149071
\(181\) −10.0000 −0.743294 −0.371647 0.928374i \(-0.621207\pi\)
−0.371647 + 0.928374i \(0.621207\pi\)
\(182\) 0 0
\(183\) 14.0000 1.03491
\(184\) 24.0000 1.76930
\(185\) −12.0000 −0.882258
\(186\) 0 0
\(187\) −6.00000 −0.438763
\(188\) 8.00000 0.583460
\(189\) 0 0
\(190\) 8.00000 0.580381
\(191\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(192\) 7.00000 0.505181
\(193\) −18.0000 −1.29567 −0.647834 0.761781i \(-0.724325\pi\)
−0.647834 + 0.761781i \(0.724325\pi\)
\(194\) 14.0000 1.00514
\(195\) 0 0
\(196\) 7.00000 0.500000
\(197\) −6.00000 −0.427482 −0.213741 0.976890i \(-0.568565\pi\)
−0.213741 + 0.976890i \(0.568565\pi\)
\(198\) 1.00000 0.0710669
\(199\) −24.0000 −1.70131 −0.850657 0.525720i \(-0.823796\pi\)
−0.850657 + 0.525720i \(0.823796\pi\)
\(200\) 3.00000 0.212132
\(201\) 12.0000 0.846415
\(202\) −2.00000 −0.140720
\(203\) 0 0
\(204\) 6.00000 0.420084
\(205\) −20.0000 −1.39686
\(206\) 8.00000 0.557386
\(207\) −8.00000 −0.556038
\(208\) 0 0
\(209\) 4.00000 0.276686
\(210\) 0 0
\(211\) −20.0000 −1.37686 −0.688428 0.725304i \(-0.741699\pi\)
−0.688428 + 0.725304i \(0.741699\pi\)
\(212\) 10.0000 0.686803
\(213\) 0 0
\(214\) 12.0000 0.820303
\(215\) 8.00000 0.545595
\(216\) −3.00000 −0.204124
\(217\) 0 0
\(218\) −14.0000 −0.948200
\(219\) 6.00000 0.405442
\(220\) −2.00000 −0.134840
\(221\) 0 0
\(222\) −6.00000 −0.402694
\(223\) −16.0000 −1.07144 −0.535720 0.844396i \(-0.679960\pi\)
−0.535720 + 0.844396i \(0.679960\pi\)
\(224\) 0 0
\(225\) −1.00000 −0.0666667
\(226\) −14.0000 −0.931266
\(227\) 20.0000 1.32745 0.663723 0.747978i \(-0.268975\pi\)
0.663723 + 0.747978i \(0.268975\pi\)
\(228\) −4.00000 −0.264906
\(229\) 10.0000 0.660819 0.330409 0.943838i \(-0.392813\pi\)
0.330409 + 0.943838i \(0.392813\pi\)
\(230\) −16.0000 −1.05501
\(231\) 0 0
\(232\) 30.0000 1.96960
\(233\) 18.0000 1.17922 0.589610 0.807688i \(-0.299282\pi\)
0.589610 + 0.807688i \(0.299282\pi\)
\(234\) 0 0
\(235\) −16.0000 −1.04372
\(236\) −12.0000 −0.781133
\(237\) 8.00000 0.519656
\(238\) 0 0
\(239\) −8.00000 −0.517477 −0.258738 0.965947i \(-0.583307\pi\)
−0.258738 + 0.965947i \(0.583307\pi\)
\(240\) −2.00000 −0.129099
\(241\) −2.00000 −0.128831 −0.0644157 0.997923i \(-0.520518\pi\)
−0.0644157 + 0.997923i \(0.520518\pi\)
\(242\) 1.00000 0.0642824
\(243\) 1.00000 0.0641500
\(244\) −14.0000 −0.896258
\(245\) −14.0000 −0.894427
\(246\) −10.0000 −0.637577
\(247\) 0 0
\(248\) 0 0
\(249\) −12.0000 −0.760469
\(250\) −12.0000 −0.758947
\(251\) −20.0000 −1.26239 −0.631194 0.775625i \(-0.717435\pi\)
−0.631194 + 0.775625i \(0.717435\pi\)
\(252\) 0 0
\(253\) −8.00000 −0.502956
\(254\) −8.00000 −0.501965
\(255\) −12.0000 −0.751469
\(256\) −17.0000 −1.06250
\(257\) 18.0000 1.12281 0.561405 0.827541i \(-0.310261\pi\)
0.561405 + 0.827541i \(0.310261\pi\)
\(258\) 4.00000 0.249029
\(259\) 0 0
\(260\) 0 0
\(261\) −10.0000 −0.618984
\(262\) −12.0000 −0.741362
\(263\) 8.00000 0.493301 0.246651 0.969104i \(-0.420670\pi\)
0.246651 + 0.969104i \(0.420670\pi\)
\(264\) −3.00000 −0.184637
\(265\) −20.0000 −1.22859
\(266\) 0 0
\(267\) −2.00000 −0.122398
\(268\) −12.0000 −0.733017
\(269\) −2.00000 −0.121942 −0.0609711 0.998140i \(-0.519420\pi\)
−0.0609711 + 0.998140i \(0.519420\pi\)
\(270\) 2.00000 0.121716
\(271\) 8.00000 0.485965 0.242983 0.970031i \(-0.421874\pi\)
0.242983 + 0.970031i \(0.421874\pi\)
\(272\) 6.00000 0.363803
\(273\) 0 0
\(274\) −18.0000 −1.08742
\(275\) −1.00000 −0.0603023
\(276\) 8.00000 0.481543
\(277\) −10.0000 −0.600842 −0.300421 0.953807i \(-0.597127\pi\)
−0.300421 + 0.953807i \(0.597127\pi\)
\(278\) −12.0000 −0.719712
\(279\) 0 0
\(280\) 0 0
\(281\) 6.00000 0.357930 0.178965 0.983855i \(-0.442725\pi\)
0.178965 + 0.983855i \(0.442725\pi\)
\(282\) −8.00000 −0.476393
\(283\) 4.00000 0.237775 0.118888 0.992908i \(-0.462067\pi\)
0.118888 + 0.992908i \(0.462067\pi\)
\(284\) 0 0
\(285\) 8.00000 0.473879
\(286\) 0 0
\(287\) 0 0
\(288\) 5.00000 0.294628
\(289\) 19.0000 1.11765
\(290\) −20.0000 −1.17444
\(291\) 14.0000 0.820695
\(292\) −6.00000 −0.351123
\(293\) −6.00000 −0.350524 −0.175262 0.984522i \(-0.556077\pi\)
−0.175262 + 0.984522i \(0.556077\pi\)
\(294\) −7.00000 −0.408248
\(295\) 24.0000 1.39733
\(296\) 18.0000 1.04623
\(297\) 1.00000 0.0580259
\(298\) 10.0000 0.579284
\(299\) 0 0
\(300\) 1.00000 0.0577350
\(301\) 0 0
\(302\) 0 0
\(303\) −2.00000 −0.114897
\(304\) −4.00000 −0.229416
\(305\) 28.0000 1.60328
\(306\) −6.00000 −0.342997
\(307\) 20.0000 1.14146 0.570730 0.821138i \(-0.306660\pi\)
0.570730 + 0.821138i \(0.306660\pi\)
\(308\) 0 0
\(309\) 8.00000 0.455104
\(310\) 0 0
\(311\) −8.00000 −0.453638 −0.226819 0.973937i \(-0.572833\pi\)
−0.226819 + 0.973937i \(0.572833\pi\)
\(312\) 0 0
\(313\) −6.00000 −0.339140 −0.169570 0.985518i \(-0.554238\pi\)
−0.169570 + 0.985518i \(0.554238\pi\)
\(314\) −2.00000 −0.112867
\(315\) 0 0
\(316\) −8.00000 −0.450035
\(317\) −22.0000 −1.23564 −0.617822 0.786318i \(-0.711985\pi\)
−0.617822 + 0.786318i \(0.711985\pi\)
\(318\) −10.0000 −0.560772
\(319\) −10.0000 −0.559893
\(320\) 14.0000 0.782624
\(321\) 12.0000 0.669775
\(322\) 0 0
\(323\) −24.0000 −1.33540
\(324\) −1.00000 −0.0555556
\(325\) 0 0
\(326\) 12.0000 0.664619
\(327\) −14.0000 −0.774202
\(328\) 30.0000 1.65647
\(329\) 0 0
\(330\) 2.00000 0.110096
\(331\) 20.0000 1.09930 0.549650 0.835395i \(-0.314761\pi\)
0.549650 + 0.835395i \(0.314761\pi\)
\(332\) 12.0000 0.658586
\(333\) −6.00000 −0.328798
\(334\) 0 0
\(335\) 24.0000 1.31126
\(336\) 0 0
\(337\) 34.0000 1.85210 0.926049 0.377403i \(-0.123183\pi\)
0.926049 + 0.377403i \(0.123183\pi\)
\(338\) 0 0
\(339\) −14.0000 −0.760376
\(340\) 12.0000 0.650791
\(341\) 0 0
\(342\) 4.00000 0.216295
\(343\) 0 0
\(344\) −12.0000 −0.646997
\(345\) −16.0000 −0.861411
\(346\) 6.00000 0.322562
\(347\) −20.0000 −1.07366 −0.536828 0.843692i \(-0.680378\pi\)
−0.536828 + 0.843692i \(0.680378\pi\)
\(348\) 10.0000 0.536056
\(349\) 2.00000 0.107058 0.0535288 0.998566i \(-0.482953\pi\)
0.0535288 + 0.998566i \(0.482953\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 5.00000 0.266501
\(353\) 6.00000 0.319348 0.159674 0.987170i \(-0.448956\pi\)
0.159674 + 0.987170i \(0.448956\pi\)
\(354\) 12.0000 0.637793
\(355\) 0 0
\(356\) 2.00000 0.106000
\(357\) 0 0
\(358\) 20.0000 1.05703
\(359\) 16.0000 0.844448 0.422224 0.906492i \(-0.361250\pi\)
0.422224 + 0.906492i \(0.361250\pi\)
\(360\) −6.00000 −0.316228
\(361\) −3.00000 −0.157895
\(362\) −10.0000 −0.525588
\(363\) 1.00000 0.0524864
\(364\) 0 0
\(365\) 12.0000 0.628109
\(366\) 14.0000 0.731792
\(367\) −16.0000 −0.835193 −0.417597 0.908633i \(-0.637127\pi\)
−0.417597 + 0.908633i \(0.637127\pi\)
\(368\) 8.00000 0.417029
\(369\) −10.0000 −0.520579
\(370\) −12.0000 −0.623850
\(371\) 0 0
\(372\) 0 0
\(373\) 38.0000 1.96757 0.983783 0.179364i \(-0.0574041\pi\)
0.983783 + 0.179364i \(0.0574041\pi\)
\(374\) −6.00000 −0.310253
\(375\) −12.0000 −0.619677
\(376\) 24.0000 1.23771
\(377\) 0 0
\(378\) 0 0
\(379\) 20.0000 1.02733 0.513665 0.857991i \(-0.328287\pi\)
0.513665 + 0.857991i \(0.328287\pi\)
\(380\) −8.00000 −0.410391
\(381\) −8.00000 −0.409852
\(382\) 0 0
\(383\) 8.00000 0.408781 0.204390 0.978889i \(-0.434479\pi\)
0.204390 + 0.978889i \(0.434479\pi\)
\(384\) −3.00000 −0.153093
\(385\) 0 0
\(386\) −18.0000 −0.916176
\(387\) 4.00000 0.203331
\(388\) −14.0000 −0.710742
\(389\) −10.0000 −0.507020 −0.253510 0.967333i \(-0.581585\pi\)
−0.253510 + 0.967333i \(0.581585\pi\)
\(390\) 0 0
\(391\) 48.0000 2.42746
\(392\) 21.0000 1.06066
\(393\) −12.0000 −0.605320
\(394\) −6.00000 −0.302276
\(395\) 16.0000 0.805047
\(396\) −1.00000 −0.0502519
\(397\) −14.0000 −0.702640 −0.351320 0.936255i \(-0.614267\pi\)
−0.351320 + 0.936255i \(0.614267\pi\)
\(398\) −24.0000 −1.20301
\(399\) 0 0
\(400\) 1.00000 0.0500000
\(401\) 22.0000 1.09863 0.549314 0.835616i \(-0.314889\pi\)
0.549314 + 0.835616i \(0.314889\pi\)
\(402\) 12.0000 0.598506
\(403\) 0 0
\(404\) 2.00000 0.0995037
\(405\) 2.00000 0.0993808
\(406\) 0 0
\(407\) −6.00000 −0.297409
\(408\) 18.0000 0.891133
\(409\) −10.0000 −0.494468 −0.247234 0.968956i \(-0.579522\pi\)
−0.247234 + 0.968956i \(0.579522\pi\)
\(410\) −20.0000 −0.987730
\(411\) −18.0000 −0.887875
\(412\) −8.00000 −0.394132
\(413\) 0 0
\(414\) −8.00000 −0.393179
\(415\) −24.0000 −1.17811
\(416\) 0 0
\(417\) −12.0000 −0.587643
\(418\) 4.00000 0.195646
\(419\) −12.0000 −0.586238 −0.293119 0.956076i \(-0.594693\pi\)
−0.293119 + 0.956076i \(0.594693\pi\)
\(420\) 0 0
\(421\) −22.0000 −1.07221 −0.536107 0.844150i \(-0.680106\pi\)
−0.536107 + 0.844150i \(0.680106\pi\)
\(422\) −20.0000 −0.973585
\(423\) −8.00000 −0.388973
\(424\) 30.0000 1.45693
\(425\) 6.00000 0.291043
\(426\) 0 0
\(427\) 0 0
\(428\) −12.0000 −0.580042
\(429\) 0 0
\(430\) 8.00000 0.385794
\(431\) −24.0000 −1.15604 −0.578020 0.816023i \(-0.696174\pi\)
−0.578020 + 0.816023i \(0.696174\pi\)
\(432\) −1.00000 −0.0481125
\(433\) −14.0000 −0.672797 −0.336399 0.941720i \(-0.609209\pi\)
−0.336399 + 0.941720i \(0.609209\pi\)
\(434\) 0 0
\(435\) −20.0000 −0.958927
\(436\) 14.0000 0.670478
\(437\) −32.0000 −1.53077
\(438\) 6.00000 0.286691
\(439\) −16.0000 −0.763638 −0.381819 0.924237i \(-0.624702\pi\)
−0.381819 + 0.924237i \(0.624702\pi\)
\(440\) −6.00000 −0.286039
\(441\) −7.00000 −0.333333
\(442\) 0 0
\(443\) −4.00000 −0.190046 −0.0950229 0.995475i \(-0.530292\pi\)
−0.0950229 + 0.995475i \(0.530292\pi\)
\(444\) 6.00000 0.284747
\(445\) −4.00000 −0.189618
\(446\) −16.0000 −0.757622
\(447\) 10.0000 0.472984
\(448\) 0 0
\(449\) 22.0000 1.03824 0.519122 0.854700i \(-0.326259\pi\)
0.519122 + 0.854700i \(0.326259\pi\)
\(450\) −1.00000 −0.0471405
\(451\) −10.0000 −0.470882
\(452\) 14.0000 0.658505
\(453\) 0 0
\(454\) 20.0000 0.938647
\(455\) 0 0
\(456\) −12.0000 −0.561951
\(457\) 6.00000 0.280668 0.140334 0.990104i \(-0.455182\pi\)
0.140334 + 0.990104i \(0.455182\pi\)
\(458\) 10.0000 0.467269
\(459\) −6.00000 −0.280056
\(460\) 16.0000 0.746004
\(461\) 2.00000 0.0931493 0.0465746 0.998915i \(-0.485169\pi\)
0.0465746 + 0.998915i \(0.485169\pi\)
\(462\) 0 0
\(463\) −16.0000 −0.743583 −0.371792 0.928316i \(-0.621256\pi\)
−0.371792 + 0.928316i \(0.621256\pi\)
\(464\) 10.0000 0.464238
\(465\) 0 0
\(466\) 18.0000 0.833834
\(467\) −12.0000 −0.555294 −0.277647 0.960683i \(-0.589555\pi\)
−0.277647 + 0.960683i \(0.589555\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −16.0000 −0.738025
\(471\) −2.00000 −0.0921551
\(472\) −36.0000 −1.65703
\(473\) 4.00000 0.183920
\(474\) 8.00000 0.367452
\(475\) −4.00000 −0.183533
\(476\) 0 0
\(477\) −10.0000 −0.457869
\(478\) −8.00000 −0.365911
\(479\) 24.0000 1.09659 0.548294 0.836286i \(-0.315277\pi\)
0.548294 + 0.836286i \(0.315277\pi\)
\(480\) 10.0000 0.456435
\(481\) 0 0
\(482\) −2.00000 −0.0910975
\(483\) 0 0
\(484\) −1.00000 −0.0454545
\(485\) 28.0000 1.27141
\(486\) 1.00000 0.0453609
\(487\) −8.00000 −0.362515 −0.181257 0.983436i \(-0.558017\pi\)
−0.181257 + 0.983436i \(0.558017\pi\)
\(488\) −42.0000 −1.90125
\(489\) 12.0000 0.542659
\(490\) −14.0000 −0.632456
\(491\) 12.0000 0.541552 0.270776 0.962642i \(-0.412720\pi\)
0.270776 + 0.962642i \(0.412720\pi\)
\(492\) 10.0000 0.450835
\(493\) 60.0000 2.70226
\(494\) 0 0
\(495\) 2.00000 0.0898933
\(496\) 0 0
\(497\) 0 0
\(498\) −12.0000 −0.537733
\(499\) 28.0000 1.25345 0.626726 0.779240i \(-0.284395\pi\)
0.626726 + 0.779240i \(0.284395\pi\)
\(500\) 12.0000 0.536656
\(501\) 0 0
\(502\) −20.0000 −0.892644
\(503\) 24.0000 1.07011 0.535054 0.844818i \(-0.320291\pi\)
0.535054 + 0.844818i \(0.320291\pi\)
\(504\) 0 0
\(505\) −4.00000 −0.177998
\(506\) −8.00000 −0.355643
\(507\) 0 0
\(508\) 8.00000 0.354943
\(509\) −6.00000 −0.265945 −0.132973 0.991120i \(-0.542452\pi\)
−0.132973 + 0.991120i \(0.542452\pi\)
\(510\) −12.0000 −0.531369
\(511\) 0 0
\(512\) −11.0000 −0.486136
\(513\) 4.00000 0.176604
\(514\) 18.0000 0.793946
\(515\) 16.0000 0.705044
\(516\) −4.00000 −0.176090
\(517\) −8.00000 −0.351840
\(518\) 0 0
\(519\) 6.00000 0.263371
\(520\) 0 0
\(521\) 42.0000 1.84005 0.920027 0.391856i \(-0.128167\pi\)
0.920027 + 0.391856i \(0.128167\pi\)
\(522\) −10.0000 −0.437688
\(523\) −28.0000 −1.22435 −0.612177 0.790721i \(-0.709706\pi\)
−0.612177 + 0.790721i \(0.709706\pi\)
\(524\) 12.0000 0.524222
\(525\) 0 0
\(526\) 8.00000 0.348817
\(527\) 0 0
\(528\) −1.00000 −0.0435194
\(529\) 41.0000 1.78261
\(530\) −20.0000 −0.868744
\(531\) 12.0000 0.520756
\(532\) 0 0
\(533\) 0 0
\(534\) −2.00000 −0.0865485
\(535\) 24.0000 1.03761
\(536\) −36.0000 −1.55496
\(537\) 20.0000 0.863064
\(538\) −2.00000 −0.0862261
\(539\) −7.00000 −0.301511
\(540\) −2.00000 −0.0860663
\(541\) 34.0000 1.46177 0.730887 0.682498i \(-0.239107\pi\)
0.730887 + 0.682498i \(0.239107\pi\)
\(542\) 8.00000 0.343629
\(543\) −10.0000 −0.429141
\(544\) −30.0000 −1.28624
\(545\) −28.0000 −1.19939
\(546\) 0 0
\(547\) −4.00000 −0.171028 −0.0855138 0.996337i \(-0.527253\pi\)
−0.0855138 + 0.996337i \(0.527253\pi\)
\(548\) 18.0000 0.768922
\(549\) 14.0000 0.597505
\(550\) −1.00000 −0.0426401
\(551\) −40.0000 −1.70406
\(552\) 24.0000 1.02151
\(553\) 0 0
\(554\) −10.0000 −0.424859
\(555\) −12.0000 −0.509372
\(556\) 12.0000 0.508913
\(557\) 18.0000 0.762684 0.381342 0.924434i \(-0.375462\pi\)
0.381342 + 0.924434i \(0.375462\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) −6.00000 −0.253320
\(562\) 6.00000 0.253095
\(563\) −44.0000 −1.85438 −0.927189 0.374593i \(-0.877783\pi\)
−0.927189 + 0.374593i \(0.877783\pi\)
\(564\) 8.00000 0.336861
\(565\) −28.0000 −1.17797
\(566\) 4.00000 0.168133
\(567\) 0 0
\(568\) 0 0
\(569\) 18.0000 0.754599 0.377300 0.926091i \(-0.376853\pi\)
0.377300 + 0.926091i \(0.376853\pi\)
\(570\) 8.00000 0.335083
\(571\) 4.00000 0.167395 0.0836974 0.996491i \(-0.473327\pi\)
0.0836974 + 0.996491i \(0.473327\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 8.00000 0.333623
\(576\) 7.00000 0.291667
\(577\) −2.00000 −0.0832611 −0.0416305 0.999133i \(-0.513255\pi\)
−0.0416305 + 0.999133i \(0.513255\pi\)
\(578\) 19.0000 0.790296
\(579\) −18.0000 −0.748054
\(580\) 20.0000 0.830455
\(581\) 0 0
\(582\) 14.0000 0.580319
\(583\) −10.0000 −0.414158
\(584\) −18.0000 −0.744845
\(585\) 0 0
\(586\) −6.00000 −0.247858
\(587\) 12.0000 0.495293 0.247647 0.968850i \(-0.420343\pi\)
0.247647 + 0.968850i \(0.420343\pi\)
\(588\) 7.00000 0.288675
\(589\) 0 0
\(590\) 24.0000 0.988064
\(591\) −6.00000 −0.246807
\(592\) 6.00000 0.246598
\(593\) 30.0000 1.23195 0.615976 0.787765i \(-0.288762\pi\)
0.615976 + 0.787765i \(0.288762\pi\)
\(594\) 1.00000 0.0410305
\(595\) 0 0
\(596\) −10.0000 −0.409616
\(597\) −24.0000 −0.982255
\(598\) 0 0
\(599\) −8.00000 −0.326871 −0.163436 0.986554i \(-0.552258\pi\)
−0.163436 + 0.986554i \(0.552258\pi\)
\(600\) 3.00000 0.122474
\(601\) −6.00000 −0.244745 −0.122373 0.992484i \(-0.539050\pi\)
−0.122373 + 0.992484i \(0.539050\pi\)
\(602\) 0 0
\(603\) 12.0000 0.488678
\(604\) 0 0
\(605\) 2.00000 0.0813116
\(606\) −2.00000 −0.0812444
\(607\) 8.00000 0.324710 0.162355 0.986732i \(-0.448091\pi\)
0.162355 + 0.986732i \(0.448091\pi\)
\(608\) 20.0000 0.811107
\(609\) 0 0
\(610\) 28.0000 1.13369
\(611\) 0 0
\(612\) 6.00000 0.242536
\(613\) −38.0000 −1.53481 −0.767403 0.641165i \(-0.778451\pi\)
−0.767403 + 0.641165i \(0.778451\pi\)
\(614\) 20.0000 0.807134
\(615\) −20.0000 −0.806478
\(616\) 0 0
\(617\) −18.0000 −0.724653 −0.362326 0.932051i \(-0.618017\pi\)
−0.362326 + 0.932051i \(0.618017\pi\)
\(618\) 8.00000 0.321807
\(619\) 20.0000 0.803868 0.401934 0.915669i \(-0.368338\pi\)
0.401934 + 0.915669i \(0.368338\pi\)
\(620\) 0 0
\(621\) −8.00000 −0.321029
\(622\) −8.00000 −0.320771
\(623\) 0 0
\(624\) 0 0
\(625\) −19.0000 −0.760000
\(626\) −6.00000 −0.239808
\(627\) 4.00000 0.159745
\(628\) 2.00000 0.0798087
\(629\) 36.0000 1.43541
\(630\) 0 0
\(631\) −24.0000 −0.955425 −0.477712 0.878516i \(-0.658534\pi\)
−0.477712 + 0.878516i \(0.658534\pi\)
\(632\) −24.0000 −0.954669
\(633\) −20.0000 −0.794929
\(634\) −22.0000 −0.873732
\(635\) −16.0000 −0.634941
\(636\) 10.0000 0.396526
\(637\) 0 0
\(638\) −10.0000 −0.395904
\(639\) 0 0
\(640\) −6.00000 −0.237171
\(641\) −30.0000 −1.18493 −0.592464 0.805597i \(-0.701845\pi\)
−0.592464 + 0.805597i \(0.701845\pi\)
\(642\) 12.0000 0.473602
\(643\) −36.0000 −1.41970 −0.709851 0.704352i \(-0.751238\pi\)
−0.709851 + 0.704352i \(0.751238\pi\)
\(644\) 0 0
\(645\) 8.00000 0.315000
\(646\) −24.0000 −0.944267
\(647\) −8.00000 −0.314512 −0.157256 0.987558i \(-0.550265\pi\)
−0.157256 + 0.987558i \(0.550265\pi\)
\(648\) −3.00000 −0.117851
\(649\) 12.0000 0.471041
\(650\) 0 0
\(651\) 0 0
\(652\) −12.0000 −0.469956
\(653\) −34.0000 −1.33052 −0.665261 0.746611i \(-0.731680\pi\)
−0.665261 + 0.746611i \(0.731680\pi\)
\(654\) −14.0000 −0.547443
\(655\) −24.0000 −0.937758
\(656\) 10.0000 0.390434
\(657\) 6.00000 0.234082
\(658\) 0 0
\(659\) 20.0000 0.779089 0.389545 0.921008i \(-0.372632\pi\)
0.389545 + 0.921008i \(0.372632\pi\)
\(660\) −2.00000 −0.0778499
\(661\) 10.0000 0.388955 0.194477 0.980907i \(-0.437699\pi\)
0.194477 + 0.980907i \(0.437699\pi\)
\(662\) 20.0000 0.777322
\(663\) 0 0
\(664\) 36.0000 1.39707
\(665\) 0 0
\(666\) −6.00000 −0.232495
\(667\) 80.0000 3.09761
\(668\) 0 0
\(669\) −16.0000 −0.618596
\(670\) 24.0000 0.927201
\(671\) 14.0000 0.540464
\(672\) 0 0
\(673\) 2.00000 0.0770943 0.0385472 0.999257i \(-0.487727\pi\)
0.0385472 + 0.999257i \(0.487727\pi\)
\(674\) 34.0000 1.30963
\(675\) −1.00000 −0.0384900
\(676\) 0 0
\(677\) −18.0000 −0.691796 −0.345898 0.938272i \(-0.612426\pi\)
−0.345898 + 0.938272i \(0.612426\pi\)
\(678\) −14.0000 −0.537667
\(679\) 0 0
\(680\) 36.0000 1.38054
\(681\) 20.0000 0.766402
\(682\) 0 0
\(683\) −36.0000 −1.37750 −0.688751 0.724998i \(-0.741841\pi\)
−0.688751 + 0.724998i \(0.741841\pi\)
\(684\) −4.00000 −0.152944
\(685\) −36.0000 −1.37549
\(686\) 0 0
\(687\) 10.0000 0.381524
\(688\) −4.00000 −0.152499
\(689\) 0 0
\(690\) −16.0000 −0.609110
\(691\) 44.0000 1.67384 0.836919 0.547326i \(-0.184354\pi\)
0.836919 + 0.547326i \(0.184354\pi\)
\(692\) −6.00000 −0.228086
\(693\) 0 0
\(694\) −20.0000 −0.759190
\(695\) −24.0000 −0.910372
\(696\) 30.0000 1.13715
\(697\) 60.0000 2.27266
\(698\) 2.00000 0.0757011
\(699\) 18.0000 0.680823
\(700\) 0 0
\(701\) −10.0000 −0.377695 −0.188847 0.982006i \(-0.560475\pi\)
−0.188847 + 0.982006i \(0.560475\pi\)
\(702\) 0 0
\(703\) −24.0000 −0.905177
\(704\) 7.00000 0.263822
\(705\) −16.0000 −0.602595
\(706\) 6.00000 0.225813
\(707\) 0 0
\(708\) −12.0000 −0.450988
\(709\) 10.0000 0.375558 0.187779 0.982211i \(-0.439871\pi\)
0.187779 + 0.982211i \(0.439871\pi\)
\(710\) 0 0
\(711\) 8.00000 0.300023
\(712\) 6.00000 0.224860
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) −20.0000 −0.747435
\(717\) −8.00000 −0.298765
\(718\) 16.0000 0.597115
\(719\) 32.0000 1.19340 0.596699 0.802465i \(-0.296479\pi\)
0.596699 + 0.802465i \(0.296479\pi\)
\(720\) −2.00000 −0.0745356
\(721\) 0 0
\(722\) −3.00000 −0.111648
\(723\) −2.00000 −0.0743808
\(724\) 10.0000 0.371647
\(725\) 10.0000 0.371391
\(726\) 1.00000 0.0371135
\(727\) −8.00000 −0.296704 −0.148352 0.988935i \(-0.547397\pi\)
−0.148352 + 0.988935i \(0.547397\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 12.0000 0.444140
\(731\) −24.0000 −0.887672
\(732\) −14.0000 −0.517455
\(733\) 34.0000 1.25582 0.627909 0.778287i \(-0.283911\pi\)
0.627909 + 0.778287i \(0.283911\pi\)
\(734\) −16.0000 −0.590571
\(735\) −14.0000 −0.516398
\(736\) −40.0000 −1.47442
\(737\) 12.0000 0.442026
\(738\) −10.0000 −0.368105
\(739\) 20.0000 0.735712 0.367856 0.929883i \(-0.380092\pi\)
0.367856 + 0.929883i \(0.380092\pi\)
\(740\) 12.0000 0.441129
\(741\) 0 0
\(742\) 0 0
\(743\) 48.0000 1.76095 0.880475 0.474093i \(-0.157224\pi\)
0.880475 + 0.474093i \(0.157224\pi\)
\(744\) 0 0
\(745\) 20.0000 0.732743
\(746\) 38.0000 1.39128
\(747\) −12.0000 −0.439057
\(748\) 6.00000 0.219382
\(749\) 0 0
\(750\) −12.0000 −0.438178
\(751\) −32.0000 −1.16770 −0.583848 0.811863i \(-0.698454\pi\)
−0.583848 + 0.811863i \(0.698454\pi\)
\(752\) 8.00000 0.291730
\(753\) −20.0000 −0.728841
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 22.0000 0.799604 0.399802 0.916602i \(-0.369079\pi\)
0.399802 + 0.916602i \(0.369079\pi\)
\(758\) 20.0000 0.726433
\(759\) −8.00000 −0.290382
\(760\) −24.0000 −0.870572
\(761\) 54.0000 1.95750 0.978749 0.205061i \(-0.0657392\pi\)
0.978749 + 0.205061i \(0.0657392\pi\)
\(762\) −8.00000 −0.289809
\(763\) 0 0
\(764\) 0 0
\(765\) −12.0000 −0.433861
\(766\) 8.00000 0.289052
\(767\) 0 0
\(768\) −17.0000 −0.613435
\(769\) −18.0000 −0.649097 −0.324548 0.945869i \(-0.605212\pi\)
−0.324548 + 0.945869i \(0.605212\pi\)
\(770\) 0 0
\(771\) 18.0000 0.648254
\(772\) 18.0000 0.647834
\(773\) −30.0000 −1.07903 −0.539513 0.841978i \(-0.681391\pi\)
−0.539513 + 0.841978i \(0.681391\pi\)
\(774\) 4.00000 0.143777
\(775\) 0 0
\(776\) −42.0000 −1.50771
\(777\) 0 0
\(778\) −10.0000 −0.358517
\(779\) −40.0000 −1.43315
\(780\) 0 0
\(781\) 0 0
\(782\) 48.0000 1.71648
\(783\) −10.0000 −0.357371
\(784\) 7.00000 0.250000
\(785\) −4.00000 −0.142766
\(786\) −12.0000 −0.428026
\(787\) −28.0000 −0.998092 −0.499046 0.866575i \(-0.666316\pi\)
−0.499046 + 0.866575i \(0.666316\pi\)
\(788\) 6.00000 0.213741
\(789\) 8.00000 0.284808
\(790\) 16.0000 0.569254
\(791\) 0 0
\(792\) −3.00000 −0.106600
\(793\) 0 0
\(794\) −14.0000 −0.496841
\(795\) −20.0000 −0.709327
\(796\) 24.0000 0.850657
\(797\) −18.0000 −0.637593 −0.318796 0.947823i \(-0.603279\pi\)
−0.318796 + 0.947823i \(0.603279\pi\)
\(798\) 0 0
\(799\) 48.0000 1.69812
\(800\) −5.00000 −0.176777
\(801\) −2.00000 −0.0706665
\(802\) 22.0000 0.776847
\(803\) 6.00000 0.211735
\(804\) −12.0000 −0.423207
\(805\) 0 0
\(806\) 0 0
\(807\) −2.00000 −0.0704033
\(808\) 6.00000 0.211079
\(809\) 2.00000 0.0703163 0.0351581 0.999382i \(-0.488807\pi\)
0.0351581 + 0.999382i \(0.488807\pi\)
\(810\) 2.00000 0.0702728
\(811\) −20.0000 −0.702295 −0.351147 0.936320i \(-0.614208\pi\)
−0.351147 + 0.936320i \(0.614208\pi\)
\(812\) 0 0
\(813\) 8.00000 0.280572
\(814\) −6.00000 −0.210300
\(815\) 24.0000 0.840683
\(816\) 6.00000 0.210042
\(817\) 16.0000 0.559769
\(818\) −10.0000 −0.349642
\(819\) 0 0
\(820\) 20.0000 0.698430
\(821\) −6.00000 −0.209401 −0.104701 0.994504i \(-0.533388\pi\)
−0.104701 + 0.994504i \(0.533388\pi\)
\(822\) −18.0000 −0.627822
\(823\) −8.00000 −0.278862 −0.139431 0.990232i \(-0.544527\pi\)
−0.139431 + 0.990232i \(0.544527\pi\)
\(824\) −24.0000 −0.836080
\(825\) −1.00000 −0.0348155
\(826\) 0 0
\(827\) −20.0000 −0.695468 −0.347734 0.937593i \(-0.613049\pi\)
−0.347734 + 0.937593i \(0.613049\pi\)
\(828\) 8.00000 0.278019
\(829\) −34.0000 −1.18087 −0.590434 0.807086i \(-0.701044\pi\)
−0.590434 + 0.807086i \(0.701044\pi\)
\(830\) −24.0000 −0.833052
\(831\) −10.0000 −0.346896
\(832\) 0 0
\(833\) 42.0000 1.45521
\(834\) −12.0000 −0.415526
\(835\) 0 0
\(836\) −4.00000 −0.138343
\(837\) 0 0
\(838\) −12.0000 −0.414533
\(839\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(840\) 0 0
\(841\) 71.0000 2.44828
\(842\) −22.0000 −0.758170
\(843\) 6.00000 0.206651
\(844\) 20.0000 0.688428
\(845\) 0 0
\(846\) −8.00000 −0.275046
\(847\) 0 0
\(848\) 10.0000 0.343401
\(849\) 4.00000 0.137280
\(850\) 6.00000 0.205798
\(851\) 48.0000 1.64542
\(852\) 0 0
\(853\) −22.0000 −0.753266 −0.376633 0.926363i \(-0.622918\pi\)
−0.376633 + 0.926363i \(0.622918\pi\)
\(854\) 0 0
\(855\) 8.00000 0.273594
\(856\) −36.0000 −1.23045
\(857\) 18.0000 0.614868 0.307434 0.951569i \(-0.400530\pi\)
0.307434 + 0.951569i \(0.400530\pi\)
\(858\) 0 0
\(859\) −20.0000 −0.682391 −0.341196 0.939992i \(-0.610832\pi\)
−0.341196 + 0.939992i \(0.610832\pi\)
\(860\) −8.00000 −0.272798
\(861\) 0 0
\(862\) −24.0000 −0.817443
\(863\) −24.0000 −0.816970 −0.408485 0.912765i \(-0.633943\pi\)
−0.408485 + 0.912765i \(0.633943\pi\)
\(864\) 5.00000 0.170103
\(865\) 12.0000 0.408012
\(866\) −14.0000 −0.475739
\(867\) 19.0000 0.645274
\(868\) 0 0
\(869\) 8.00000 0.271381
\(870\) −20.0000 −0.678064
\(871\) 0 0
\(872\) 42.0000 1.42230
\(873\) 14.0000 0.473828
\(874\) −32.0000 −1.08242
\(875\) 0 0
\(876\) −6.00000 −0.202721
\(877\) 18.0000 0.607817 0.303908 0.952701i \(-0.401708\pi\)
0.303908 + 0.952701i \(0.401708\pi\)
\(878\) −16.0000 −0.539974
\(879\) −6.00000 −0.202375
\(880\) −2.00000 −0.0674200
\(881\) 50.0000 1.68454 0.842271 0.539054i \(-0.181218\pi\)
0.842271 + 0.539054i \(0.181218\pi\)
\(882\) −7.00000 −0.235702
\(883\) −44.0000 −1.48072 −0.740359 0.672212i \(-0.765344\pi\)
−0.740359 + 0.672212i \(0.765344\pi\)
\(884\) 0 0
\(885\) 24.0000 0.806751
\(886\) −4.00000 −0.134383
\(887\) 24.0000 0.805841 0.402921 0.915235i \(-0.367995\pi\)
0.402921 + 0.915235i \(0.367995\pi\)
\(888\) 18.0000 0.604040
\(889\) 0 0
\(890\) −4.00000 −0.134080
\(891\) 1.00000 0.0335013
\(892\) 16.0000 0.535720
\(893\) −32.0000 −1.07084
\(894\) 10.0000 0.334450
\(895\) 40.0000 1.33705
\(896\) 0 0
\(897\) 0 0
\(898\) 22.0000 0.734150
\(899\) 0 0
\(900\) 1.00000 0.0333333
\(901\) 60.0000 1.99889
\(902\) −10.0000 −0.332964
\(903\) 0 0
\(904\) 42.0000 1.39690
\(905\) −20.0000 −0.664822
\(906\) 0 0
\(907\) −4.00000 −0.132818 −0.0664089 0.997792i \(-0.521154\pi\)
−0.0664089 + 0.997792i \(0.521154\pi\)
\(908\) −20.0000 −0.663723
\(909\) −2.00000 −0.0663358
\(910\) 0 0
\(911\) −16.0000 −0.530104 −0.265052 0.964234i \(-0.585389\pi\)
−0.265052 + 0.964234i \(0.585389\pi\)
\(912\) −4.00000 −0.132453
\(913\) −12.0000 −0.397142
\(914\) 6.00000 0.198462
\(915\) 28.0000 0.925651
\(916\) −10.0000 −0.330409
\(917\) 0 0
\(918\) −6.00000 −0.198030
\(919\) 32.0000 1.05558 0.527791 0.849374i \(-0.323020\pi\)
0.527791 + 0.849374i \(0.323020\pi\)
\(920\) 48.0000 1.58251
\(921\) 20.0000 0.659022
\(922\) 2.00000 0.0658665
\(923\) 0 0
\(924\) 0 0
\(925\) 6.00000 0.197279
\(926\) −16.0000 −0.525793
\(927\) 8.00000 0.262754
\(928\) −50.0000 −1.64133
\(929\) −10.0000 −0.328089 −0.164045 0.986453i \(-0.552454\pi\)
−0.164045 + 0.986453i \(0.552454\pi\)
\(930\) 0 0
\(931\) −28.0000 −0.917663
\(932\) −18.0000 −0.589610
\(933\) −8.00000 −0.261908
\(934\) −12.0000 −0.392652
\(935\) −12.0000 −0.392442
\(936\) 0 0
\(937\) 10.0000 0.326686 0.163343 0.986569i \(-0.447772\pi\)
0.163343 + 0.986569i \(0.447772\pi\)
\(938\) 0 0
\(939\) −6.00000 −0.195803
\(940\) 16.0000 0.521862
\(941\) 2.00000 0.0651981 0.0325991 0.999469i \(-0.489622\pi\)
0.0325991 + 0.999469i \(0.489622\pi\)
\(942\) −2.00000 −0.0651635
\(943\) 80.0000 2.60516
\(944\) −12.0000 −0.390567
\(945\) 0 0
\(946\) 4.00000 0.130051
\(947\) 36.0000 1.16984 0.584921 0.811090i \(-0.301125\pi\)
0.584921 + 0.811090i \(0.301125\pi\)
\(948\) −8.00000 −0.259828
\(949\) 0 0
\(950\) −4.00000 −0.129777
\(951\) −22.0000 −0.713399
\(952\) 0 0
\(953\) −46.0000 −1.49009 −0.745043 0.667016i \(-0.767571\pi\)
−0.745043 + 0.667016i \(0.767571\pi\)
\(954\) −10.0000 −0.323762
\(955\) 0 0
\(956\) 8.00000 0.258738
\(957\) −10.0000 −0.323254
\(958\) 24.0000 0.775405
\(959\) 0 0
\(960\) 14.0000 0.451848
\(961\) −31.0000 −1.00000
\(962\) 0 0
\(963\) 12.0000 0.386695
\(964\) 2.00000 0.0644157
\(965\) −36.0000 −1.15888
\(966\) 0 0
\(967\) −16.0000 −0.514525 −0.257263 0.966342i \(-0.582821\pi\)
−0.257263 + 0.966342i \(0.582821\pi\)
\(968\) −3.00000 −0.0964237
\(969\) −24.0000 −0.770991
\(970\) 28.0000 0.899026
\(971\) −36.0000 −1.15529 −0.577647 0.816286i \(-0.696029\pi\)
−0.577647 + 0.816286i \(0.696029\pi\)
\(972\) −1.00000 −0.0320750
\(973\) 0 0
\(974\) −8.00000 −0.256337
\(975\) 0 0
\(976\) −14.0000 −0.448129
\(977\) −42.0000 −1.34370 −0.671850 0.740688i \(-0.734500\pi\)
−0.671850 + 0.740688i \(0.734500\pi\)
\(978\) 12.0000 0.383718
\(979\) −2.00000 −0.0639203
\(980\) 14.0000 0.447214
\(981\) −14.0000 −0.446986
\(982\) 12.0000 0.382935
\(983\) −48.0000 −1.53096 −0.765481 0.643458i \(-0.777499\pi\)
−0.765481 + 0.643458i \(0.777499\pi\)
\(984\) 30.0000 0.956365
\(985\) −12.0000 −0.382352
\(986\) 60.0000 1.91079
\(987\) 0 0
\(988\) 0 0
\(989\) −32.0000 −1.01754
\(990\) 2.00000 0.0635642
\(991\) 48.0000 1.52477 0.762385 0.647124i \(-0.224028\pi\)
0.762385 + 0.647124i \(0.224028\pi\)
\(992\) 0 0
\(993\) 20.0000 0.634681
\(994\) 0 0
\(995\) −48.0000 −1.52170
\(996\) 12.0000 0.380235
\(997\) 22.0000 0.696747 0.348373 0.937356i \(-0.386734\pi\)
0.348373 + 0.937356i \(0.386734\pi\)
\(998\) 28.0000 0.886325
\(999\) −6.00000 −0.189832
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 5577.2.a.g.1.1 1
13.12 even 2 429.2.a.b.1.1 1
39.38 odd 2 1287.2.a.e.1.1 1
52.51 odd 2 6864.2.a.e.1.1 1
143.142 odd 2 4719.2.a.k.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
429.2.a.b.1.1 1 13.12 even 2
1287.2.a.e.1.1 1 39.38 odd 2
4719.2.a.k.1.1 1 143.142 odd 2
5577.2.a.g.1.1 1 1.1 even 1 trivial
6864.2.a.e.1.1 1 52.51 odd 2