Properties

Label 114.2.a.b.1.1
Level 114
Weight 2
Character 114.1
Self dual Yes
Analytic conductor 0.910
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 114 = 2 \cdot 3 \cdot 19 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 114.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(0.910294583043\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(0\)
Character \(\chi\) = 114.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.00000 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.00000 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +2.00000 q^{10} -4.00000 q^{11} -1.00000 q^{12} +2.00000 q^{13} -2.00000 q^{15} +1.00000 q^{16} -6.00000 q^{17} +1.00000 q^{18} -1.00000 q^{19} +2.00000 q^{20} -4.00000 q^{22} -4.00000 q^{23} -1.00000 q^{24} -1.00000 q^{25} +2.00000 q^{26} -1.00000 q^{27} -2.00000 q^{29} -2.00000 q^{30} +4.00000 q^{31} +1.00000 q^{32} +4.00000 q^{33} -6.00000 q^{34} +1.00000 q^{36} +10.0000 q^{37} -1.00000 q^{38} -2.00000 q^{39} +2.00000 q^{40} +10.0000 q^{41} +4.00000 q^{43} -4.00000 q^{44} +2.00000 q^{45} -4.00000 q^{46} -4.00000 q^{47} -1.00000 q^{48} -7.00000 q^{49} -1.00000 q^{50} +6.00000 q^{51} +2.00000 q^{52} -10.0000 q^{53} -1.00000 q^{54} -8.00000 q^{55} +1.00000 q^{57} -2.00000 q^{58} +12.0000 q^{59} -2.00000 q^{60} +14.0000 q^{61} +4.00000 q^{62} +1.00000 q^{64} +4.00000 q^{65} +4.00000 q^{66} -12.0000 q^{67} -6.00000 q^{68} +4.00000 q^{69} +8.00000 q^{71} +1.00000 q^{72} -6.00000 q^{73} +10.0000 q^{74} +1.00000 q^{75} -1.00000 q^{76} -2.00000 q^{78} -4.00000 q^{79} +2.00000 q^{80} +1.00000 q^{81} +10.0000 q^{82} +12.0000 q^{83} -12.0000 q^{85} +4.00000 q^{86} +2.00000 q^{87} -4.00000 q^{88} -6.00000 q^{89} +2.00000 q^{90} -4.00000 q^{92} -4.00000 q^{93} -4.00000 q^{94} -2.00000 q^{95} -1.00000 q^{96} +10.0000 q^{97} -7.00000 q^{98} -4.00000 q^{99} +O(q^{100})\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −1.00000 −0.577350
\(4\) 1.00000 0.500000
\(5\) 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 \(0.5\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.00000 0.333333
\(10\) 2.00000 0.632456
\(11\) −4.00000 −1.20605 −0.603023 0.797724i \(-0.706037\pi\)
−0.603023 + 0.797724i \(0.706037\pi\)
\(12\) −1.00000 −0.288675
\(13\) 2.00000 0.554700 0.277350 0.960769i \(-0.410544\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) 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
\(19\) −1.00000 −0.229416
\(20\) 2.00000 0.447214
\(21\) 0 0
\(22\) −4.00000 −0.852803
\(23\) −4.00000 −0.834058 −0.417029 0.908893i \(-0.636929\pi\)
−0.417029 + 0.908893i \(0.636929\pi\)
\(24\) −1.00000 −0.204124
\(25\) −1.00000 −0.200000
\(26\) 2.00000 0.392232
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −2.00000 −0.371391 −0.185695 0.982607i \(-0.559454\pi\)
−0.185695 + 0.982607i \(0.559454\pi\)
\(30\) −2.00000 −0.365148
\(31\) 4.00000 0.718421 0.359211 0.933257i \(-0.383046\pi\)
0.359211 + 0.933257i \(0.383046\pi\)
\(32\) 1.00000 0.176777
\(33\) 4.00000 0.696311
\(34\) −6.00000 −1.02899
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) 10.0000 1.64399 0.821995 0.569495i \(-0.192861\pi\)
0.821995 + 0.569495i \(0.192861\pi\)
\(38\) −1.00000 −0.162221
\(39\) −2.00000 −0.320256
\(40\) 2.00000 0.316228
\(41\) 10.0000 1.56174 0.780869 0.624695i \(-0.214777\pi\)
0.780869 + 0.624695i \(0.214777\pi\)
\(42\) 0 0
\(43\) 4.00000 0.609994 0.304997 0.952353i \(-0.401344\pi\)
0.304997 + 0.952353i \(0.401344\pi\)
\(44\) −4.00000 −0.603023
\(45\) 2.00000 0.298142
\(46\) −4.00000 −0.589768
\(47\) −4.00000 −0.583460 −0.291730 0.956501i \(-0.594231\pi\)
−0.291730 + 0.956501i \(0.594231\pi\)
\(48\) −1.00000 −0.144338
\(49\) −7.00000 −1.00000
\(50\) −1.00000 −0.141421
\(51\) 6.00000 0.840168
\(52\) 2.00000 0.277350
\(53\) −10.0000 −1.37361 −0.686803 0.726844i \(-0.740986\pi\)
−0.686803 + 0.726844i \(0.740986\pi\)
\(54\) −1.00000 −0.136083
\(55\) −8.00000 −1.07872
\(56\) 0 0
\(57\) 1.00000 0.132453
\(58\) −2.00000 −0.262613
\(59\) 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 \(0.146275\pi\)
\(62\) 4.00000 0.508001
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 4.00000 0.496139
\(66\) 4.00000 0.492366
\(67\) −12.0000 −1.46603 −0.733017 0.680211i \(-0.761888\pi\)
−0.733017 + 0.680211i \(0.761888\pi\)
\(68\) −6.00000 −0.727607
\(69\) 4.00000 0.481543
\(70\) 0 0
\(71\) 8.00000 0.949425 0.474713 0.880141i \(-0.342552\pi\)
0.474713 + 0.880141i \(0.342552\pi\)
\(72\) 1.00000 0.117851
\(73\) −6.00000 −0.702247 −0.351123 0.936329i \(-0.614200\pi\)
−0.351123 + 0.936329i \(0.614200\pi\)
\(74\) 10.0000 1.16248
\(75\) 1.00000 0.115470
\(76\) −1.00000 −0.114708
\(77\) 0 0
\(78\) −2.00000 −0.226455
\(79\) −4.00000 −0.450035 −0.225018 0.974355i \(-0.572244\pi\)
−0.225018 + 0.974355i \(0.572244\pi\)
\(80\) 2.00000 0.223607
\(81\) 1.00000 0.111111
\(82\) 10.0000 1.10432
\(83\) 12.0000 1.31717 0.658586 0.752506i \(-0.271155\pi\)
0.658586 + 0.752506i \(0.271155\pi\)
\(84\) 0 0
\(85\) −12.0000 −1.30158
\(86\) 4.00000 0.431331
\(87\) 2.00000 0.214423
\(88\) −4.00000 −0.426401
\(89\) −6.00000 −0.635999 −0.317999 0.948091i \(-0.603011\pi\)
−0.317999 + 0.948091i \(0.603011\pi\)
\(90\) 2.00000 0.210819
\(91\) 0 0
\(92\) −4.00000 −0.417029
\(93\) −4.00000 −0.414781
\(94\) −4.00000 −0.412568
\(95\) −2.00000 −0.205196
\(96\) −1.00000 −0.102062
\(97\) 10.0000 1.01535 0.507673 0.861550i \(-0.330506\pi\)
0.507673 + 0.861550i \(0.330506\pi\)
\(98\) −7.00000 −0.707107
\(99\) −4.00000 −0.402015
\(100\) −1.00000 −0.100000
\(101\) 2.00000 0.199007 0.0995037 0.995037i \(-0.468274\pi\)
0.0995037 + 0.995037i \(0.468274\pi\)
\(102\) 6.00000 0.594089
\(103\) −12.0000 −1.18240 −0.591198 0.806527i \(-0.701345\pi\)
−0.591198 + 0.806527i \(0.701345\pi\)
\(104\) 2.00000 0.196116
\(105\) 0 0
\(106\) −10.0000 −0.971286
\(107\) −4.00000 −0.386695 −0.193347 0.981130i \(-0.561934\pi\)
−0.193347 + 0.981130i \(0.561934\pi\)
\(108\) −1.00000 −0.0962250
\(109\) −6.00000 −0.574696 −0.287348 0.957826i \(-0.592774\pi\)
−0.287348 + 0.957826i \(0.592774\pi\)
\(110\) −8.00000 −0.762770
\(111\) −10.0000 −0.949158
\(112\) 0 0
\(113\) 2.00000 0.188144 0.0940721 0.995565i \(-0.470012\pi\)
0.0940721 + 0.995565i \(0.470012\pi\)
\(114\) 1.00000 0.0936586
\(115\) −8.00000 −0.746004
\(116\) −2.00000 −0.185695
\(117\) 2.00000 0.184900
\(118\) 12.0000 1.10469
\(119\) 0 0
\(120\) −2.00000 −0.182574
\(121\) 5.00000 0.454545
\(122\) 14.0000 1.26750
\(123\) −10.0000 −0.901670
\(124\) 4.00000 0.359211
\(125\) −12.0000 −1.07331
\(126\) 0 0
\(127\) −12.0000 −1.06483 −0.532414 0.846484i \(-0.678715\pi\)
−0.532414 + 0.846484i \(0.678715\pi\)
\(128\) 1.00000 0.0883883
\(129\) −4.00000 −0.352180
\(130\) 4.00000 0.350823
\(131\) 12.0000 1.04844 0.524222 0.851581i \(-0.324356\pi\)
0.524222 + 0.851581i \(0.324356\pi\)
\(132\) 4.00000 0.348155
\(133\) 0 0
\(134\) −12.0000 −1.03664
\(135\) −2.00000 −0.172133
\(136\) −6.00000 −0.514496
\(137\) −14.0000 −1.19610 −0.598050 0.801459i \(-0.704058\pi\)
−0.598050 + 0.801459i \(0.704058\pi\)
\(138\) 4.00000 0.340503
\(139\) 12.0000 1.01783 0.508913 0.860818i \(-0.330047\pi\)
0.508913 + 0.860818i \(0.330047\pi\)
\(140\) 0 0
\(141\) 4.00000 0.336861
\(142\) 8.00000 0.671345
\(143\) −8.00000 −0.668994
\(144\) 1.00000 0.0833333
\(145\) −4.00000 −0.332182
\(146\) −6.00000 −0.496564
\(147\) 7.00000 0.577350
\(148\) 10.0000 0.821995
\(149\) −6.00000 −0.491539 −0.245770 0.969328i \(-0.579041\pi\)
−0.245770 + 0.969328i \(0.579041\pi\)
\(150\) 1.00000 0.0816497
\(151\) 20.0000 1.62758 0.813788 0.581161i \(-0.197401\pi\)
0.813788 + 0.581161i \(0.197401\pi\)
\(152\) −1.00000 −0.0811107
\(153\) −6.00000 −0.485071
\(154\) 0 0
\(155\) 8.00000 0.642575
\(156\) −2.00000 −0.160128
\(157\) 22.0000 1.75579 0.877896 0.478852i \(-0.158947\pi\)
0.877896 + 0.478852i \(0.158947\pi\)
\(158\) −4.00000 −0.318223
\(159\) 10.0000 0.793052
\(160\) 2.00000 0.158114
\(161\) 0 0
\(162\) 1.00000 0.0785674
\(163\) 20.0000 1.56652 0.783260 0.621694i \(-0.213555\pi\)
0.783260 + 0.621694i \(0.213555\pi\)
\(164\) 10.0000 0.780869
\(165\) 8.00000 0.622799
\(166\) 12.0000 0.931381
\(167\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) −12.0000 −0.920358
\(171\) −1.00000 −0.0764719
\(172\) 4.00000 0.304997
\(173\) 6.00000 0.456172 0.228086 0.973641i \(-0.426753\pi\)
0.228086 + 0.973641i \(0.426753\pi\)
\(174\) 2.00000 0.151620
\(175\) 0 0
\(176\) −4.00000 −0.301511
\(177\) −12.0000 −0.901975
\(178\) −6.00000 −0.449719
\(179\) 12.0000 0.896922 0.448461 0.893802i \(-0.351972\pi\)
0.448461 + 0.893802i \(0.351972\pi\)
\(180\) 2.00000 0.149071
\(181\) −14.0000 −1.04061 −0.520306 0.853980i \(-0.674182\pi\)
−0.520306 + 0.853980i \(0.674182\pi\)
\(182\) 0 0
\(183\) −14.0000 −1.03491
\(184\) −4.00000 −0.294884
\(185\) 20.0000 1.47043
\(186\) −4.00000 −0.293294
\(187\) 24.0000 1.75505
\(188\) −4.00000 −0.291730
\(189\) 0 0
\(190\) −2.00000 −0.145095
\(191\) 4.00000 0.289430 0.144715 0.989473i \(-0.453773\pi\)
0.144715 + 0.989473i \(0.453773\pi\)
\(192\) −1.00000 −0.0721688
\(193\) −6.00000 −0.431889 −0.215945 0.976406i \(-0.569283\pi\)
−0.215945 + 0.976406i \(0.569283\pi\)
\(194\) 10.0000 0.717958
\(195\) −4.00000 −0.286446
\(196\) −7.00000 −0.500000
\(197\) −22.0000 −1.56744 −0.783718 0.621117i \(-0.786679\pi\)
−0.783718 + 0.621117i \(0.786679\pi\)
\(198\) −4.00000 −0.284268
\(199\) −16.0000 −1.13421 −0.567105 0.823646i \(-0.691937\pi\)
−0.567105 + 0.823646i \(0.691937\pi\)
\(200\) −1.00000 −0.0707107
\(201\) 12.0000 0.846415
\(202\) 2.00000 0.140720
\(203\) 0 0
\(204\) 6.00000 0.420084
\(205\) 20.0000 1.39686
\(206\) −12.0000 −0.836080
\(207\) −4.00000 −0.278019
\(208\) 2.00000 0.138675
\(209\) 4.00000 0.276686
\(210\) 0 0
\(211\) 12.0000 0.826114 0.413057 0.910705i \(-0.364461\pi\)
0.413057 + 0.910705i \(0.364461\pi\)
\(212\) −10.0000 −0.686803
\(213\) −8.00000 −0.548151
\(214\) −4.00000 −0.273434
\(215\) 8.00000 0.545595
\(216\) −1.00000 −0.0680414
\(217\) 0 0
\(218\) −6.00000 −0.406371
\(219\) 6.00000 0.405442
\(220\) −8.00000 −0.539360
\(221\) −12.0000 −0.807207
\(222\) −10.0000 −0.671156
\(223\) −28.0000 −1.87502 −0.937509 0.347960i \(-0.886874\pi\)
−0.937509 + 0.347960i \(0.886874\pi\)
\(224\) 0 0
\(225\) −1.00000 −0.0666667
\(226\) 2.00000 0.133038
\(227\) 28.0000 1.85843 0.929213 0.369546i \(-0.120487\pi\)
0.929213 + 0.369546i \(0.120487\pi\)
\(228\) 1.00000 0.0662266
\(229\) −10.0000 −0.660819 −0.330409 0.943838i \(-0.607187\pi\)
−0.330409 + 0.943838i \(0.607187\pi\)
\(230\) −8.00000 −0.527504
\(231\) 0 0
\(232\) −2.00000 −0.131306
\(233\) −6.00000 −0.393073 −0.196537 0.980497i \(-0.562969\pi\)
−0.196537 + 0.980497i \(0.562969\pi\)
\(234\) 2.00000 0.130744
\(235\) −8.00000 −0.521862
\(236\) 12.0000 0.781133
\(237\) 4.00000 0.259828
\(238\) 0 0
\(239\) 12.0000 0.776215 0.388108 0.921614i \(-0.373129\pi\)
0.388108 + 0.921614i \(0.373129\pi\)
\(240\) −2.00000 −0.129099
\(241\) 10.0000 0.644157 0.322078 0.946713i \(-0.395619\pi\)
0.322078 + 0.946713i \(0.395619\pi\)
\(242\) 5.00000 0.321412
\(243\) −1.00000 −0.0641500
\(244\) 14.0000 0.896258
\(245\) −14.0000 −0.894427
\(246\) −10.0000 −0.637577
\(247\) −2.00000 −0.127257
\(248\) 4.00000 0.254000
\(249\) −12.0000 −0.760469
\(250\) −12.0000 −0.758947
\(251\) −28.0000 −1.76734 −0.883672 0.468106i \(-0.844936\pi\)
−0.883672 + 0.468106i \(0.844936\pi\)
\(252\) 0 0
\(253\) 16.0000 1.00591
\(254\) −12.0000 −0.752947
\(255\) 12.0000 0.751469
\(256\) 1.00000 0.0625000
\(257\) 2.00000 0.124757 0.0623783 0.998053i \(-0.480131\pi\)
0.0623783 + 0.998053i \(0.480131\pi\)
\(258\) −4.00000 −0.249029
\(259\) 0 0
\(260\) 4.00000 0.248069
\(261\) −2.00000 −0.123797
\(262\) 12.0000 0.741362
\(263\) −12.0000 −0.739952 −0.369976 0.929041i \(-0.620634\pi\)
−0.369976 + 0.929041i \(0.620634\pi\)
\(264\) 4.00000 0.246183
\(265\) −20.0000 −1.22859
\(266\) 0 0
\(267\) 6.00000 0.367194
\(268\) −12.0000 −0.733017
\(269\) 6.00000 0.365826 0.182913 0.983129i \(-0.441447\pi\)
0.182913 + 0.983129i \(0.441447\pi\)
\(270\) −2.00000 −0.121716
\(271\) −8.00000 −0.485965 −0.242983 0.970031i \(-0.578126\pi\)
−0.242983 + 0.970031i \(0.578126\pi\)
\(272\) −6.00000 −0.363803
\(273\) 0 0
\(274\) −14.0000 −0.845771
\(275\) 4.00000 0.241209
\(276\) 4.00000 0.240772
\(277\) −26.0000 −1.56219 −0.781094 0.624413i \(-0.785338\pi\)
−0.781094 + 0.624413i \(0.785338\pi\)
\(278\) 12.0000 0.719712
\(279\) 4.00000 0.239474
\(280\) 0 0
\(281\) 10.0000 0.596550 0.298275 0.954480i \(-0.403589\pi\)
0.298275 + 0.954480i \(0.403589\pi\)
\(282\) 4.00000 0.238197
\(283\) 12.0000 0.713326 0.356663 0.934233i \(-0.383914\pi\)
0.356663 + 0.934233i \(0.383914\pi\)
\(284\) 8.00000 0.474713
\(285\) 2.00000 0.118470
\(286\) −8.00000 −0.473050
\(287\) 0 0
\(288\) 1.00000 0.0589256
\(289\) 19.0000 1.11765
\(290\) −4.00000 −0.234888
\(291\) −10.0000 −0.586210
\(292\) −6.00000 −0.351123
\(293\) −18.0000 −1.05157 −0.525786 0.850617i \(-0.676229\pi\)
−0.525786 + 0.850617i \(0.676229\pi\)
\(294\) 7.00000 0.408248
\(295\) 24.0000 1.39733
\(296\) 10.0000 0.581238
\(297\) 4.00000 0.232104
\(298\) −6.00000 −0.347571
\(299\) −8.00000 −0.462652
\(300\) 1.00000 0.0577350
\(301\) 0 0
\(302\) 20.0000 1.15087
\(303\) −2.00000 −0.114897
\(304\) −1.00000 −0.0573539
\(305\) 28.0000 1.60328
\(306\) −6.00000 −0.342997
\(307\) −12.0000 −0.684876 −0.342438 0.939540i \(-0.611253\pi\)
−0.342438 + 0.939540i \(0.611253\pi\)
\(308\) 0 0
\(309\) 12.0000 0.682656
\(310\) 8.00000 0.454369
\(311\) 4.00000 0.226819 0.113410 0.993548i \(-0.463823\pi\)
0.113410 + 0.993548i \(0.463823\pi\)
\(312\) −2.00000 −0.113228
\(313\) −22.0000 −1.24351 −0.621757 0.783210i \(-0.713581\pi\)
−0.621757 + 0.783210i \(0.713581\pi\)
\(314\) 22.0000 1.24153
\(315\) 0 0
\(316\) −4.00000 −0.225018
\(317\) 6.00000 0.336994 0.168497 0.985702i \(-0.446109\pi\)
0.168497 + 0.985702i \(0.446109\pi\)
\(318\) 10.0000 0.560772
\(319\) 8.00000 0.447914
\(320\) 2.00000 0.111803
\(321\) 4.00000 0.223258
\(322\) 0 0
\(323\) 6.00000 0.333849
\(324\) 1.00000 0.0555556
\(325\) −2.00000 −0.110940
\(326\) 20.0000 1.10770
\(327\) 6.00000 0.331801
\(328\) 10.0000 0.552158
\(329\) 0 0
\(330\) 8.00000 0.440386
\(331\) −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
\(334\) 0 0
\(335\) −24.0000 −1.31126
\(336\) 0 0
\(337\) −14.0000 −0.762629 −0.381314 0.924445i \(-0.624528\pi\)
−0.381314 + 0.924445i \(0.624528\pi\)
\(338\) −9.00000 −0.489535
\(339\) −2.00000 −0.108625
\(340\) −12.0000 −0.650791
\(341\) −16.0000 −0.866449
\(342\) −1.00000 −0.0540738
\(343\) 0 0
\(344\) 4.00000 0.215666
\(345\) 8.00000 0.430706
\(346\) 6.00000 0.322562
\(347\) −20.0000 −1.07366 −0.536828 0.843692i \(-0.680378\pi\)
−0.536828 + 0.843692i \(0.680378\pi\)
\(348\) 2.00000 0.107211
\(349\) −26.0000 −1.39175 −0.695874 0.718164i \(-0.744983\pi\)
−0.695874 + 0.718164i \(0.744983\pi\)
\(350\) 0 0
\(351\) −2.00000 −0.106752
\(352\) −4.00000 −0.213201
\(353\) 18.0000 0.958043 0.479022 0.877803i \(-0.340992\pi\)
0.479022 + 0.877803i \(0.340992\pi\)
\(354\) −12.0000 −0.637793
\(355\) 16.0000 0.849192
\(356\) −6.00000 −0.317999
\(357\) 0 0
\(358\) 12.0000 0.634220
\(359\) 12.0000 0.633336 0.316668 0.948536i \(-0.397436\pi\)
0.316668 + 0.948536i \(0.397436\pi\)
\(360\) 2.00000 0.105409
\(361\) 1.00000 0.0526316
\(362\) −14.0000 −0.735824
\(363\) −5.00000 −0.262432
\(364\) 0 0
\(365\) −12.0000 −0.628109
\(366\) −14.0000 −0.731792
\(367\) −8.00000 −0.417597 −0.208798 0.977959i \(-0.566955\pi\)
−0.208798 + 0.977959i \(0.566955\pi\)
\(368\) −4.00000 −0.208514
\(369\) 10.0000 0.520579
\(370\) 20.0000 1.03975
\(371\) 0 0
\(372\) −4.00000 −0.207390
\(373\) 26.0000 1.34623 0.673114 0.739538i \(-0.264956\pi\)
0.673114 + 0.739538i \(0.264956\pi\)
\(374\) 24.0000 1.24101
\(375\) 12.0000 0.619677
\(376\) −4.00000 −0.206284
\(377\) −4.00000 −0.206010
\(378\) 0 0
\(379\) −36.0000 −1.84920 −0.924598 0.380945i \(-0.875599\pi\)
−0.924598 + 0.380945i \(0.875599\pi\)
\(380\) −2.00000 −0.102598
\(381\) 12.0000 0.614779
\(382\) 4.00000 0.204658
\(383\) 16.0000 0.817562 0.408781 0.912633i \(-0.365954\pi\)
0.408781 + 0.912633i \(0.365954\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) −6.00000 −0.305392
\(387\) 4.00000 0.203331
\(388\) 10.0000 0.507673
\(389\) 18.0000 0.912636 0.456318 0.889817i \(-0.349168\pi\)
0.456318 + 0.889817i \(0.349168\pi\)
\(390\) −4.00000 −0.202548
\(391\) 24.0000 1.21373
\(392\) −7.00000 −0.353553
\(393\) −12.0000 −0.605320
\(394\) −22.0000 −1.10834
\(395\) −8.00000 −0.402524
\(396\) −4.00000 −0.201008
\(397\) −10.0000 −0.501886 −0.250943 0.968002i \(-0.580741\pi\)
−0.250943 + 0.968002i \(0.580741\pi\)
\(398\) −16.0000 −0.802008
\(399\) 0 0
\(400\) −1.00000 −0.0500000
\(401\) −14.0000 −0.699127 −0.349563 0.936913i \(-0.613670\pi\)
−0.349563 + 0.936913i \(0.613670\pi\)
\(402\) 12.0000 0.598506
\(403\) 8.00000 0.398508
\(404\) 2.00000 0.0995037
\(405\) 2.00000 0.0993808
\(406\) 0 0
\(407\) −40.0000 −1.98273
\(408\) 6.00000 0.297044
\(409\) −14.0000 −0.692255 −0.346128 0.938187i \(-0.612504\pi\)
−0.346128 + 0.938187i \(0.612504\pi\)
\(410\) 20.0000 0.987730
\(411\) 14.0000 0.690569
\(412\) −12.0000 −0.591198
\(413\) 0 0
\(414\) −4.00000 −0.196589
\(415\) 24.0000 1.17811
\(416\) 2.00000 0.0980581
\(417\) −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
\(421\) 26.0000 1.26716 0.633581 0.773676i \(-0.281584\pi\)
0.633581 + 0.773676i \(0.281584\pi\)
\(422\) 12.0000 0.584151
\(423\) −4.00000 −0.194487
\(424\) −10.0000 −0.485643
\(425\) 6.00000 0.291043
\(426\) −8.00000 −0.387601
\(427\) 0 0
\(428\) −4.00000 −0.193347
\(429\) 8.00000 0.386244
\(430\) 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
\(433\) 26.0000 1.24948 0.624740 0.780833i \(-0.285205\pi\)
0.624740 + 0.780833i \(0.285205\pi\)
\(434\) 0 0
\(435\) 4.00000 0.191785
\(436\) −6.00000 −0.287348
\(437\) 4.00000 0.191346
\(438\) 6.00000 0.286691
\(439\) −4.00000 −0.190910 −0.0954548 0.995434i \(-0.530431\pi\)
−0.0954548 + 0.995434i \(0.530431\pi\)
\(440\) −8.00000 −0.381385
\(441\) −7.00000 −0.333333
\(442\) −12.0000 −0.570782
\(443\) −20.0000 −0.950229 −0.475114 0.879924i \(-0.657593\pi\)
−0.475114 + 0.879924i \(0.657593\pi\)
\(444\) −10.0000 −0.474579
\(445\) −12.0000 −0.568855
\(446\) −28.0000 −1.32584
\(447\) 6.00000 0.283790
\(448\) 0 0
\(449\) 34.0000 1.60456 0.802280 0.596948i \(-0.203620\pi\)
0.802280 + 0.596948i \(0.203620\pi\)
\(450\) −1.00000 −0.0471405
\(451\) −40.0000 −1.88353
\(452\) 2.00000 0.0940721
\(453\) −20.0000 −0.939682
\(454\) 28.0000 1.31411
\(455\) 0 0
\(456\) 1.00000 0.0468293
\(457\) 26.0000 1.21623 0.608114 0.793849i \(-0.291926\pi\)
0.608114 + 0.793849i \(0.291926\pi\)
\(458\) −10.0000 −0.467269
\(459\) 6.00000 0.280056
\(460\) −8.00000 −0.373002
\(461\) 2.00000 0.0931493 0.0465746 0.998915i \(-0.485169\pi\)
0.0465746 + 0.998915i \(0.485169\pi\)
\(462\) 0 0
\(463\) −8.00000 −0.371792 −0.185896 0.982569i \(-0.559519\pi\)
−0.185896 + 0.982569i \(0.559519\pi\)
\(464\) −2.00000 −0.0928477
\(465\) −8.00000 −0.370991
\(466\) −6.00000 −0.277945
\(467\) −20.0000 −0.925490 −0.462745 0.886492i \(-0.653135\pi\)
−0.462745 + 0.886492i \(0.653135\pi\)
\(468\) 2.00000 0.0924500
\(469\) 0 0
\(470\) −8.00000 −0.369012
\(471\) −22.0000 −1.01371
\(472\) 12.0000 0.552345
\(473\) −16.0000 −0.735681
\(474\) 4.00000 0.183726
\(475\) 1.00000 0.0458831
\(476\) 0 0
\(477\) −10.0000 −0.457869
\(478\) 12.0000 0.548867
\(479\) 4.00000 0.182765 0.0913823 0.995816i \(-0.470871\pi\)
0.0913823 + 0.995816i \(0.470871\pi\)
\(480\) −2.00000 −0.0912871
\(481\) 20.0000 0.911922
\(482\) 10.0000 0.455488
\(483\) 0 0
\(484\) 5.00000 0.227273
\(485\) 20.0000 0.908153
\(486\) −1.00000 −0.0453609
\(487\) 4.00000 0.181257 0.0906287 0.995885i \(-0.471112\pi\)
0.0906287 + 0.995885i \(0.471112\pi\)
\(488\) 14.0000 0.633750
\(489\) −20.0000 −0.904431
\(490\) −14.0000 −0.632456
\(491\) 20.0000 0.902587 0.451294 0.892375i \(-0.350963\pi\)
0.451294 + 0.892375i \(0.350963\pi\)
\(492\) −10.0000 −0.450835
\(493\) 12.0000 0.540453
\(494\) −2.00000 −0.0899843
\(495\) −8.00000 −0.359573
\(496\) 4.00000 0.179605
\(497\) 0 0
\(498\) −12.0000 −0.537733
\(499\) −20.0000 −0.895323 −0.447661 0.894203i \(-0.647743\pi\)
−0.447661 + 0.894203i \(0.647743\pi\)
\(500\) −12.0000 −0.536656
\(501\) 0 0
\(502\) −28.0000 −1.24970
\(503\) 36.0000 1.60516 0.802580 0.596544i \(-0.203460\pi\)
0.802580 + 0.596544i \(0.203460\pi\)
\(504\) 0 0
\(505\) 4.00000 0.177998
\(506\) 16.0000 0.711287
\(507\) 9.00000 0.399704
\(508\) −12.0000 −0.532414
\(509\) 6.00000 0.265945 0.132973 0.991120i \(-0.457548\pi\)
0.132973 + 0.991120i \(0.457548\pi\)
\(510\) 12.0000 0.531369
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) 1.00000 0.0441511
\(514\) 2.00000 0.0882162
\(515\) −24.0000 −1.05757
\(516\) −4.00000 −0.176090
\(517\) 16.0000 0.703679
\(518\) 0 0
\(519\) −6.00000 −0.263371
\(520\) 4.00000 0.175412
\(521\) 26.0000 1.13908 0.569540 0.821963i \(-0.307121\pi\)
0.569540 + 0.821963i \(0.307121\pi\)
\(522\) −2.00000 −0.0875376
\(523\) −4.00000 −0.174908 −0.0874539 0.996169i \(-0.527873\pi\)
−0.0874539 + 0.996169i \(0.527873\pi\)
\(524\) 12.0000 0.524222
\(525\) 0 0
\(526\) −12.0000 −0.523225
\(527\) −24.0000 −1.04546
\(528\) 4.00000 0.174078
\(529\) −7.00000 −0.304348
\(530\) −20.0000 −0.868744
\(531\) 12.0000 0.520756
\(532\) 0 0
\(533\) 20.0000 0.866296
\(534\) 6.00000 0.259645
\(535\) −8.00000 −0.345870
\(536\) −12.0000 −0.518321
\(537\) −12.0000 −0.517838
\(538\) 6.00000 0.258678
\(539\) 28.0000 1.20605
\(540\) −2.00000 −0.0860663
\(541\) 38.0000 1.63375 0.816874 0.576816i \(-0.195705\pi\)
0.816874 + 0.576816i \(0.195705\pi\)
\(542\) −8.00000 −0.343629
\(543\) 14.0000 0.600798
\(544\) −6.00000 −0.257248
\(545\) −12.0000 −0.514024
\(546\) 0 0
\(547\) 4.00000 0.171028 0.0855138 0.996337i \(-0.472747\pi\)
0.0855138 + 0.996337i \(0.472747\pi\)
\(548\) −14.0000 −0.598050
\(549\) 14.0000 0.597505
\(550\) 4.00000 0.170561
\(551\) 2.00000 0.0852029
\(552\) 4.00000 0.170251
\(553\) 0 0
\(554\) −26.0000 −1.10463
\(555\) −20.0000 −0.848953
\(556\) 12.0000 0.508913
\(557\) 34.0000 1.44063 0.720313 0.693649i \(-0.243998\pi\)
0.720313 + 0.693649i \(0.243998\pi\)
\(558\) 4.00000 0.169334
\(559\) 8.00000 0.338364
\(560\) 0 0
\(561\) −24.0000 −1.01328
\(562\) 10.0000 0.421825
\(563\) −12.0000 −0.505740 −0.252870 0.967500i \(-0.581374\pi\)
−0.252870 + 0.967500i \(0.581374\pi\)
\(564\) 4.00000 0.168430
\(565\) 4.00000 0.168281
\(566\) 12.0000 0.504398
\(567\) 0 0
\(568\) 8.00000 0.335673
\(569\) −38.0000 −1.59304 −0.796521 0.604610i \(-0.793329\pi\)
−0.796521 + 0.604610i \(0.793329\pi\)
\(570\) 2.00000 0.0837708
\(571\) 20.0000 0.836974 0.418487 0.908223i \(-0.362561\pi\)
0.418487 + 0.908223i \(0.362561\pi\)
\(572\) −8.00000 −0.334497
\(573\) −4.00000 −0.167102
\(574\) 0 0
\(575\) 4.00000 0.166812
\(576\) 1.00000 0.0416667
\(577\) 2.00000 0.0832611 0.0416305 0.999133i \(-0.486745\pi\)
0.0416305 + 0.999133i \(0.486745\pi\)
\(578\) 19.0000 0.790296
\(579\) 6.00000 0.249351
\(580\) −4.00000 −0.166091
\(581\) 0 0
\(582\) −10.0000 −0.414513
\(583\) 40.0000 1.65663
\(584\) −6.00000 −0.248282
\(585\) 4.00000 0.165380
\(586\) −18.0000 −0.743573
\(587\) 12.0000 0.495293 0.247647 0.968850i \(-0.420343\pi\)
0.247647 + 0.968850i \(0.420343\pi\)
\(588\) 7.00000 0.288675
\(589\) −4.00000 −0.164817
\(590\) 24.0000 0.988064
\(591\) 22.0000 0.904959
\(592\) 10.0000 0.410997
\(593\) 34.0000 1.39621 0.698106 0.715994i \(-0.254026\pi\)
0.698106 + 0.715994i \(0.254026\pi\)
\(594\) 4.00000 0.164122
\(595\) 0 0
\(596\) −6.00000 −0.245770
\(597\) 16.0000 0.654836
\(598\) −8.00000 −0.327144
\(599\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) 1.00000 0.0408248
\(601\) 10.0000 0.407909 0.203954 0.978980i \(-0.434621\pi\)
0.203954 + 0.978980i \(0.434621\pi\)
\(602\) 0 0
\(603\) −12.0000 −0.488678
\(604\) 20.0000 0.813788
\(605\) 10.0000 0.406558
\(606\) −2.00000 −0.0812444
\(607\) −4.00000 −0.162355 −0.0811775 0.996700i \(-0.525868\pi\)
−0.0811775 + 0.996700i \(0.525868\pi\)
\(608\) −1.00000 −0.0405554
\(609\) 0 0
\(610\) 28.0000 1.13369
\(611\) −8.00000 −0.323645
\(612\) −6.00000 −0.242536
\(613\) −2.00000 −0.0807792 −0.0403896 0.999184i \(-0.512860\pi\)
−0.0403896 + 0.999184i \(0.512860\pi\)
\(614\) −12.0000 −0.484281
\(615\) −20.0000 −0.806478
\(616\) 0 0
\(617\) 42.0000 1.69086 0.845428 0.534089i \(-0.179345\pi\)
0.845428 + 0.534089i \(0.179345\pi\)
\(618\) 12.0000 0.482711
\(619\) 4.00000 0.160774 0.0803868 0.996764i \(-0.474384\pi\)
0.0803868 + 0.996764i \(0.474384\pi\)
\(620\) 8.00000 0.321288
\(621\) 4.00000 0.160514
\(622\) 4.00000 0.160385
\(623\) 0 0
\(624\) −2.00000 −0.0800641
\(625\) −19.0000 −0.760000
\(626\) −22.0000 −0.879297
\(627\) −4.00000 −0.159745
\(628\) 22.0000 0.877896
\(629\) −60.0000 −2.39236
\(630\) 0 0
\(631\) −40.0000 −1.59237 −0.796187 0.605050i \(-0.793153\pi\)
−0.796187 + 0.605050i \(0.793153\pi\)
\(632\) −4.00000 −0.159111
\(633\) −12.0000 −0.476957
\(634\) 6.00000 0.238290
\(635\) −24.0000 −0.952411
\(636\) 10.0000 0.396526
\(637\) −14.0000 −0.554700
\(638\) 8.00000 0.316723
\(639\) 8.00000 0.316475
\(640\) 2.00000 0.0790569
\(641\) 18.0000 0.710957 0.355479 0.934684i \(-0.384318\pi\)
0.355479 + 0.934684i \(0.384318\pi\)
\(642\) 4.00000 0.157867
\(643\) 4.00000 0.157745 0.0788723 0.996885i \(-0.474868\pi\)
0.0788723 + 0.996885i \(0.474868\pi\)
\(644\) 0 0
\(645\) −8.00000 −0.315000
\(646\) 6.00000 0.236067
\(647\) −4.00000 −0.157256 −0.0786281 0.996904i \(-0.525054\pi\)
−0.0786281 + 0.996904i \(0.525054\pi\)
\(648\) 1.00000 0.0392837
\(649\) −48.0000 −1.88416
\(650\) −2.00000 −0.0784465
\(651\) 0 0
\(652\) 20.0000 0.783260
\(653\) 18.0000 0.704394 0.352197 0.935926i \(-0.385435\pi\)
0.352197 + 0.935926i \(0.385435\pi\)
\(654\) 6.00000 0.234619
\(655\) 24.0000 0.937758
\(656\) 10.0000 0.390434
\(657\) −6.00000 −0.234082
\(658\) 0 0
\(659\) −4.00000 −0.155818 −0.0779089 0.996960i \(-0.524824\pi\)
−0.0779089 + 0.996960i \(0.524824\pi\)
\(660\) 8.00000 0.311400
\(661\) −38.0000 −1.47803 −0.739014 0.673690i \(-0.764708\pi\)
−0.739014 + 0.673690i \(0.764708\pi\)
\(662\) −4.00000 −0.155464
\(663\) 12.0000 0.466041
\(664\) 12.0000 0.465690
\(665\) 0 0
\(666\) 10.0000 0.387492
\(667\) 8.00000 0.309761
\(668\) 0 0
\(669\) 28.0000 1.08254
\(670\) −24.0000 −0.927201
\(671\) −56.0000 −2.16186
\(672\) 0 0
\(673\) 26.0000 1.00223 0.501113 0.865382i \(-0.332924\pi\)
0.501113 + 0.865382i \(0.332924\pi\)
\(674\) −14.0000 −0.539260
\(675\) 1.00000 0.0384900
\(676\) −9.00000 −0.346154
\(677\) −26.0000 −0.999261 −0.499631 0.866239i \(-0.666531\pi\)
−0.499631 + 0.866239i \(0.666531\pi\)
\(678\) −2.00000 −0.0768095
\(679\) 0 0
\(680\) −12.0000 −0.460179
\(681\) −28.0000 −1.07296
\(682\) −16.0000 −0.612672
\(683\) 4.00000 0.153056 0.0765279 0.997067i \(-0.475617\pi\)
0.0765279 + 0.997067i \(0.475617\pi\)
\(684\) −1.00000 −0.0382360
\(685\) −28.0000 −1.06983
\(686\) 0 0
\(687\) 10.0000 0.381524
\(688\) 4.00000 0.152499
\(689\) −20.0000 −0.761939
\(690\) 8.00000 0.304555
\(691\) −36.0000 −1.36950 −0.684752 0.728776i \(-0.740090\pi\)
−0.684752 + 0.728776i \(0.740090\pi\)
\(692\) 6.00000 0.228086
\(693\) 0 0
\(694\) −20.0000 −0.759190
\(695\) 24.0000 0.910372
\(696\) 2.00000 0.0758098
\(697\) −60.0000 −2.27266
\(698\) −26.0000 −0.984115
\(699\) 6.00000 0.226941
\(700\) 0 0
\(701\) −22.0000 −0.830929 −0.415464 0.909610i \(-0.636381\pi\)
−0.415464 + 0.909610i \(0.636381\pi\)
\(702\) −2.00000 −0.0754851
\(703\) −10.0000 −0.377157
\(704\) −4.00000 −0.150756
\(705\) 8.00000 0.301297
\(706\) 18.0000 0.677439
\(707\) 0 0
\(708\) −12.0000 −0.450988
\(709\) −42.0000 −1.57734 −0.788672 0.614815i \(-0.789231\pi\)
−0.788672 + 0.614815i \(0.789231\pi\)
\(710\) 16.0000 0.600469
\(711\) −4.00000 −0.150012
\(712\) −6.00000 −0.224860
\(713\) −16.0000 −0.599205
\(714\) 0 0
\(715\) −16.0000 −0.598366
\(716\) 12.0000 0.448461
\(717\) −12.0000 −0.448148
\(718\) 12.0000 0.447836
\(719\) 28.0000 1.04422 0.522112 0.852877i \(-0.325144\pi\)
0.522112 + 0.852877i \(0.325144\pi\)
\(720\) 2.00000 0.0745356
\(721\) 0 0
\(722\) 1.00000 0.0372161
\(723\) −10.0000 −0.371904
\(724\) −14.0000 −0.520306
\(725\) 2.00000 0.0742781
\(726\) −5.00000 −0.185567
\(727\) −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
\(733\) 6.00000 0.221615 0.110808 0.993842i \(-0.464656\pi\)
0.110808 + 0.993842i \(0.464656\pi\)
\(734\) −8.00000 −0.295285
\(735\) 14.0000 0.516398
\(736\) −4.00000 −0.147442
\(737\) 48.0000 1.76810
\(738\) 10.0000 0.368105
\(739\) 20.0000 0.735712 0.367856 0.929883i \(-0.380092\pi\)
0.367856 + 0.929883i \(0.380092\pi\)
\(740\) 20.0000 0.735215
\(741\) 2.00000 0.0734718
\(742\) 0 0
\(743\) 32.0000 1.17397 0.586983 0.809599i \(-0.300316\pi\)
0.586983 + 0.809599i \(0.300316\pi\)
\(744\) −4.00000 −0.146647
\(745\) −12.0000 −0.439646
\(746\) 26.0000 0.951928
\(747\) 12.0000 0.439057
\(748\) 24.0000 0.877527
\(749\) 0 0
\(750\) 12.0000 0.438178
\(751\) 44.0000 1.60558 0.802791 0.596260i \(-0.203347\pi\)
0.802791 + 0.596260i \(0.203347\pi\)
\(752\) −4.00000 −0.145865
\(753\) 28.0000 1.02038
\(754\) −4.00000 −0.145671
\(755\) 40.0000 1.45575
\(756\) 0 0
\(757\) −2.00000 −0.0726912 −0.0363456 0.999339i \(-0.511572\pi\)
−0.0363456 + 0.999339i \(0.511572\pi\)
\(758\) −36.0000 −1.30758
\(759\) −16.0000 −0.580763
\(760\) −2.00000 −0.0725476
\(761\) −30.0000 −1.08750 −0.543750 0.839248i \(-0.682996\pi\)
−0.543750 + 0.839248i \(0.682996\pi\)
\(762\) 12.0000 0.434714
\(763\) 0 0
\(764\) 4.00000 0.144715
\(765\) −12.0000 −0.433861
\(766\) 16.0000 0.578103
\(767\) 24.0000 0.866590
\(768\) −1.00000 −0.0360844
\(769\) −14.0000 −0.504853 −0.252426 0.967616i \(-0.581229\pi\)
−0.252426 + 0.967616i \(0.581229\pi\)
\(770\) 0 0
\(771\) −2.00000 −0.0720282
\(772\) −6.00000 −0.215945
\(773\) 30.0000 1.07903 0.539513 0.841978i \(-0.318609\pi\)
0.539513 + 0.841978i \(0.318609\pi\)
\(774\) 4.00000 0.143777
\(775\) −4.00000 −0.143684
\(776\) 10.0000 0.358979
\(777\) 0 0
\(778\) 18.0000 0.645331
\(779\) −10.0000 −0.358287
\(780\) −4.00000 −0.143223
\(781\) −32.0000 −1.14505
\(782\) 24.0000 0.858238
\(783\) 2.00000 0.0714742
\(784\) −7.00000 −0.250000
\(785\) 44.0000 1.57043
\(786\) −12.0000 −0.428026
\(787\) −20.0000 −0.712923 −0.356462 0.934310i \(-0.616017\pi\)
−0.356462 + 0.934310i \(0.616017\pi\)
\(788\) −22.0000 −0.783718
\(789\) 12.0000 0.427211
\(790\) −8.00000 −0.284627
\(791\) 0 0
\(792\) −4.00000 −0.142134
\(793\) 28.0000 0.994309
\(794\) −10.0000 −0.354887
\(795\) 20.0000 0.709327
\(796\) −16.0000 −0.567105
\(797\) 6.00000 0.212531 0.106265 0.994338i \(-0.466111\pi\)
0.106265 + 0.994338i \(0.466111\pi\)
\(798\) 0 0
\(799\) 24.0000 0.849059
\(800\) −1.00000 −0.0353553
\(801\) −6.00000 −0.212000
\(802\) −14.0000 −0.494357
\(803\) 24.0000 0.846942
\(804\) 12.0000 0.423207
\(805\) 0 0
\(806\) 8.00000 0.281788
\(807\) −6.00000 −0.211210
\(808\) 2.00000 0.0703598
\(809\) −30.0000 −1.05474 −0.527372 0.849635i \(-0.676823\pi\)
−0.527372 + 0.849635i \(0.676823\pi\)
\(810\) 2.00000 0.0702728
\(811\) 12.0000 0.421377 0.210688 0.977553i \(-0.432429\pi\)
0.210688 + 0.977553i \(0.432429\pi\)
\(812\) 0 0
\(813\) 8.00000 0.280572
\(814\) −40.0000 −1.40200
\(815\) 40.0000 1.40114
\(816\) 6.00000 0.210042
\(817\) −4.00000 −0.139942
\(818\) −14.0000 −0.489499
\(819\) 0 0
\(820\) 20.0000 0.698430
\(821\) −30.0000 −1.04701 −0.523504 0.852023i \(-0.675375\pi\)
−0.523504 + 0.852023i \(0.675375\pi\)
\(822\) 14.0000 0.488306
\(823\) 8.00000 0.278862 0.139431 0.990232i \(-0.455473\pi\)
0.139431 + 0.990232i \(0.455473\pi\)
\(824\) −12.0000 −0.418040
\(825\) −4.00000 −0.139262
\(826\) 0 0
\(827\) −28.0000 −0.973655 −0.486828 0.873498i \(-0.661846\pi\)
−0.486828 + 0.873498i \(0.661846\pi\)
\(828\) −4.00000 −0.139010
\(829\) 42.0000 1.45872 0.729360 0.684130i \(-0.239818\pi\)
0.729360 + 0.684130i \(0.239818\pi\)
\(830\) 24.0000 0.833052
\(831\) 26.0000 0.901930
\(832\) 2.00000 0.0693375
\(833\) 42.0000 1.45521
\(834\) −12.0000 −0.415526
\(835\) 0 0
\(836\) 4.00000 0.138343
\(837\) −4.00000 −0.138260
\(838\) −12.0000 −0.414533
\(839\) −16.0000 −0.552381 −0.276191 0.961103i \(-0.589072\pi\)
−0.276191 + 0.961103i \(0.589072\pi\)
\(840\) 0 0
\(841\) −25.0000 −0.862069
\(842\) 26.0000 0.896019
\(843\) −10.0000 −0.344418
\(844\) 12.0000 0.413057
\(845\) −18.0000 −0.619219
\(846\) −4.00000 −0.137523
\(847\) 0 0
\(848\) −10.0000 −0.343401
\(849\) −12.0000 −0.411839
\(850\) 6.00000 0.205798
\(851\) −40.0000 −1.37118
\(852\) −8.00000 −0.274075
\(853\) 6.00000 0.205436 0.102718 0.994711i \(-0.467246\pi\)
0.102718 + 0.994711i \(0.467246\pi\)
\(854\) 0 0
\(855\) −2.00000 −0.0683986
\(856\) −4.00000 −0.136717
\(857\) 42.0000 1.43469 0.717346 0.696717i \(-0.245357\pi\)
0.717346 + 0.696717i \(0.245357\pi\)
\(858\) 8.00000 0.273115
\(859\) 52.0000 1.77422 0.887109 0.461561i \(-0.152710\pi\)
0.887109 + 0.461561i \(0.152710\pi\)
\(860\) 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 \(0.633943\pi\)
\(864\) −1.00000 −0.0340207
\(865\) 12.0000 0.408012
\(866\) 26.0000 0.883516
\(867\) −19.0000 −0.645274
\(868\) 0 0
\(869\) 16.0000 0.542763
\(870\) 4.00000 0.135613
\(871\) −24.0000 −0.813209
\(872\) −6.00000 −0.203186
\(873\) 10.0000 0.338449
\(874\) 4.00000 0.135302
\(875\) 0 0
\(876\) 6.00000 0.202721
\(877\) 34.0000 1.14810 0.574049 0.818821i \(-0.305372\pi\)
0.574049 + 0.818821i \(0.305372\pi\)
\(878\) −4.00000 −0.134993
\(879\) 18.0000 0.607125
\(880\) −8.00000 −0.269680
\(881\) 18.0000 0.606435 0.303218 0.952921i \(-0.401939\pi\)
0.303218 + 0.952921i \(0.401939\pi\)
\(882\) −7.00000 −0.235702
\(883\) −20.0000 −0.673054 −0.336527 0.941674i \(-0.609252\pi\)
−0.336527 + 0.941674i \(0.609252\pi\)
\(884\) −12.0000 −0.403604
\(885\) −24.0000 −0.806751
\(886\) −20.0000 −0.671913
\(887\) −32.0000 −1.07445 −0.537227 0.843437i \(-0.680528\pi\)
−0.537227 + 0.843437i \(0.680528\pi\)
\(888\) −10.0000 −0.335578
\(889\) 0 0
\(890\) −12.0000 −0.402241
\(891\) −4.00000 −0.134005
\(892\) −28.0000 −0.937509
\(893\) 4.00000 0.133855
\(894\) 6.00000 0.200670
\(895\) 24.0000 0.802232
\(896\) 0 0
\(897\) 8.00000 0.267112
\(898\) 34.0000 1.13459
\(899\) −8.00000 −0.266815
\(900\) −1.00000 −0.0333333
\(901\) 60.0000 1.99889
\(902\) −40.0000 −1.33185
\(903\) 0 0
\(904\) 2.00000 0.0665190
\(905\) −28.0000 −0.930751
\(906\) −20.0000 −0.664455
\(907\) 44.0000 1.46100 0.730498 0.682915i \(-0.239288\pi\)
0.730498 + 0.682915i \(0.239288\pi\)
\(908\) 28.0000 0.929213
\(909\) 2.00000 0.0663358
\(910\) 0 0
\(911\) 24.0000 0.795155 0.397578 0.917568i \(-0.369851\pi\)
0.397578 + 0.917568i \(0.369851\pi\)
\(912\) 1.00000 0.0331133
\(913\) −48.0000 −1.58857
\(914\) 26.0000 0.860004
\(915\) −28.0000 −0.925651
\(916\) −10.0000 −0.330409
\(917\) 0 0
\(918\) 6.00000 0.198030
\(919\) 8.00000 0.263896 0.131948 0.991257i \(-0.457877\pi\)
0.131948 + 0.991257i \(0.457877\pi\)
\(920\) −8.00000 −0.263752
\(921\) 12.0000 0.395413
\(922\) 2.00000 0.0658665
\(923\) 16.0000 0.526646
\(924\) 0 0
\(925\) −10.0000 −0.328798
\(926\) −8.00000 −0.262896
\(927\) −12.0000 −0.394132
\(928\) −2.00000 −0.0656532
\(929\) −22.0000 −0.721797 −0.360898 0.932605i \(-0.617530\pi\)
−0.360898 + 0.932605i \(0.617530\pi\)
\(930\) −8.00000 −0.262330
\(931\) 7.00000 0.229416
\(932\) −6.00000 −0.196537
\(933\) −4.00000 −0.130954
\(934\) −20.0000 −0.654420
\(935\) 48.0000 1.56977
\(936\) 2.00000 0.0653720
\(937\) 26.0000 0.849383 0.424691 0.905338i \(-0.360383\pi\)
0.424691 + 0.905338i \(0.360383\pi\)
\(938\) 0 0
\(939\) 22.0000 0.717943
\(940\) −8.00000 −0.260931
\(941\) 22.0000 0.717180 0.358590 0.933495i \(-0.383258\pi\)
0.358590 + 0.933495i \(0.383258\pi\)
\(942\) −22.0000 −0.716799
\(943\) −40.0000 −1.30258
\(944\) 12.0000 0.390567
\(945\) 0 0
\(946\) −16.0000 −0.520205
\(947\) 12.0000 0.389948 0.194974 0.980808i \(-0.437538\pi\)
0.194974 + 0.980808i \(0.437538\pi\)
\(948\) 4.00000 0.129914
\(949\) −12.0000 −0.389536
\(950\) 1.00000 0.0324443
\(951\) −6.00000 −0.194563
\(952\) 0 0
\(953\) −22.0000 −0.712650 −0.356325 0.934362i \(-0.615970\pi\)
−0.356325 + 0.934362i \(0.615970\pi\)
\(954\) −10.0000 −0.323762
\(955\) 8.00000 0.258874
\(956\) 12.0000 0.388108
\(957\) −8.00000 −0.258603
\(958\) 4.00000 0.129234
\(959\) 0 0
\(960\) −2.00000 −0.0645497
\(961\) −15.0000 −0.483871
\(962\) 20.0000 0.644826
\(963\) −4.00000 −0.128898
\(964\) 10.0000 0.322078
\(965\) −12.0000 −0.386294
\(966\) 0 0
\(967\) 48.0000 1.54358 0.771788 0.635880i \(-0.219363\pi\)
0.771788 + 0.635880i \(0.219363\pi\)
\(968\) 5.00000 0.160706
\(969\) −6.00000 −0.192748
\(970\) 20.0000 0.642161
\(971\) −28.0000 −0.898563 −0.449281 0.893390i \(-0.648320\pi\)
−0.449281 + 0.893390i \(0.648320\pi\)
\(972\) −1.00000 −0.0320750
\(973\) 0 0
\(974\) 4.00000 0.128168
\(975\) 2.00000 0.0640513
\(976\) 14.0000 0.448129
\(977\) −46.0000 −1.47167 −0.735835 0.677161i \(-0.763210\pi\)
−0.735835 + 0.677161i \(0.763210\pi\)
\(978\) −20.0000 −0.639529
\(979\) 24.0000 0.767043
\(980\) −14.0000 −0.447214
\(981\) −6.00000 −0.191565
\(982\) 20.0000 0.638226
\(983\) −24.0000 −0.765481 −0.382741 0.923856i \(-0.625020\pi\)
−0.382741 + 0.923856i \(0.625020\pi\)
\(984\) −10.0000 −0.318788
\(985\) −44.0000 −1.40196
\(986\) 12.0000 0.382158
\(987\) 0 0
\(988\) −2.00000 −0.0636285
\(989\) −16.0000 −0.508770
\(990\) −8.00000 −0.254257
\(991\) 4.00000 0.127064 0.0635321 0.997980i \(-0.479763\pi\)
0.0635321 + 0.997980i \(0.479763\pi\)
\(992\) 4.00000 0.127000
\(993\) 4.00000 0.126936
\(994\) 0 0
\(995\) −32.0000 −1.01447
\(996\) −12.0000 −0.380235
\(997\) −2.00000 −0.0633406 −0.0316703 0.999498i \(-0.510083\pi\)
−0.0316703 + 0.999498i \(0.510083\pi\)
\(998\) −20.0000 −0.633089
\(999\) −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 \(a_p\))