Properties

Label 61.2.a.a.1.1
Level 61
Weight 2
Character 61.1
Self dual Yes
Analytic conductor 0.487
Analytic rank 1
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 61 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 61.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(0.48708745233\)
Analytic rank: \(1\)
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 \(\chi\) = 61.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -2.00000 q^{3} -1.00000 q^{4} -3.00000 q^{5} +2.00000 q^{6} +1.00000 q^{7} +3.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -2.00000 q^{3} -1.00000 q^{4} -3.00000 q^{5} +2.00000 q^{6} +1.00000 q^{7} +3.00000 q^{8} +1.00000 q^{9} +3.00000 q^{10} -5.00000 q^{11} +2.00000 q^{12} +1.00000 q^{13} -1.00000 q^{14} +6.00000 q^{15} -1.00000 q^{16} +4.00000 q^{17} -1.00000 q^{18} -4.00000 q^{19} +3.00000 q^{20} -2.00000 q^{21} +5.00000 q^{22} -9.00000 q^{23} -6.00000 q^{24} +4.00000 q^{25} -1.00000 q^{26} +4.00000 q^{27} -1.00000 q^{28} -6.00000 q^{29} -6.00000 q^{30} -5.00000 q^{32} +10.0000 q^{33} -4.00000 q^{34} -3.00000 q^{35} -1.00000 q^{36} +8.00000 q^{37} +4.00000 q^{38} -2.00000 q^{39} -9.00000 q^{40} +5.00000 q^{41} +2.00000 q^{42} -8.00000 q^{43} +5.00000 q^{44} -3.00000 q^{45} +9.00000 q^{46} +4.00000 q^{47} +2.00000 q^{48} -6.00000 q^{49} -4.00000 q^{50} -8.00000 q^{51} -1.00000 q^{52} +6.00000 q^{53} -4.00000 q^{54} +15.0000 q^{55} +3.00000 q^{56} +8.00000 q^{57} +6.00000 q^{58} +9.00000 q^{59} -6.00000 q^{60} -1.00000 q^{61} +1.00000 q^{63} +7.00000 q^{64} -3.00000 q^{65} -10.0000 q^{66} -7.00000 q^{67} -4.00000 q^{68} +18.0000 q^{69} +3.00000 q^{70} -8.00000 q^{71} +3.00000 q^{72} -11.0000 q^{73} -8.00000 q^{74} -8.00000 q^{75} +4.00000 q^{76} -5.00000 q^{77} +2.00000 q^{78} +3.00000 q^{79} +3.00000 q^{80} -11.0000 q^{81} -5.00000 q^{82} +4.00000 q^{83} +2.00000 q^{84} -12.0000 q^{85} +8.00000 q^{86} +12.0000 q^{87} -15.0000 q^{88} -4.00000 q^{89} +3.00000 q^{90} +1.00000 q^{91} +9.00000 q^{92} -4.00000 q^{94} +12.0000 q^{95} +10.0000 q^{96} -14.0000 q^{97} +6.00000 q^{98} -5.00000 q^{99} +O(q^{100})\)

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 \(-0.615027\pi\)
−0.353553 + 0.935414i \(0.615027\pi\)
\(3\) −2.00000 −1.15470 −0.577350 0.816497i \(-0.695913\pi\)
−0.577350 + 0.816497i \(0.695913\pi\)
\(4\) −1.00000 −0.500000
\(5\) −3.00000 −1.34164 −0.670820 0.741620i \(-0.734058\pi\)
−0.670820 + 0.741620i \(0.734058\pi\)
\(6\) 2.00000 0.816497
\(7\) 1.00000 0.377964 0.188982 0.981981i \(-0.439481\pi\)
0.188982 + 0.981981i \(0.439481\pi\)
\(8\) 3.00000 1.06066
\(9\) 1.00000 0.333333
\(10\) 3.00000 0.948683
\(11\) −5.00000 −1.50756 −0.753778 0.657129i \(-0.771771\pi\)
−0.753778 + 0.657129i \(0.771771\pi\)
\(12\) 2.00000 0.577350
\(13\) 1.00000 0.277350 0.138675 0.990338i \(-0.455716\pi\)
0.138675 + 0.990338i \(0.455716\pi\)
\(14\) −1.00000 −0.267261
\(15\) 6.00000 1.54919
\(16\) −1.00000 −0.250000
\(17\) 4.00000 0.970143 0.485071 0.874475i \(-0.338794\pi\)
0.485071 + 0.874475i \(0.338794\pi\)
\(18\) −1.00000 −0.235702
\(19\) −4.00000 −0.917663 −0.458831 0.888523i \(-0.651732\pi\)
−0.458831 + 0.888523i \(0.651732\pi\)
\(20\) 3.00000 0.670820
\(21\) −2.00000 −0.436436
\(22\) 5.00000 1.06600
\(23\) −9.00000 −1.87663 −0.938315 0.345782i \(-0.887614\pi\)
−0.938315 + 0.345782i \(0.887614\pi\)
\(24\) −6.00000 −1.22474
\(25\) 4.00000 0.800000
\(26\) −1.00000 −0.196116
\(27\) 4.00000 0.769800
\(28\) −1.00000 −0.188982
\(29\) −6.00000 −1.11417 −0.557086 0.830455i \(-0.688081\pi\)
−0.557086 + 0.830455i \(0.688081\pi\)
\(30\) −6.00000 −1.09545
\(31\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) −5.00000 −0.883883
\(33\) 10.0000 1.74078
\(34\) −4.00000 −0.685994
\(35\) −3.00000 −0.507093
\(36\) −1.00000 −0.166667
\(37\) 8.00000 1.31519 0.657596 0.753371i \(-0.271573\pi\)
0.657596 + 0.753371i \(0.271573\pi\)
\(38\) 4.00000 0.648886
\(39\) −2.00000 −0.320256
\(40\) −9.00000 −1.42302
\(41\) 5.00000 0.780869 0.390434 0.920631i \(-0.372325\pi\)
0.390434 + 0.920631i \(0.372325\pi\)
\(42\) 2.00000 0.308607
\(43\) −8.00000 −1.21999 −0.609994 0.792406i \(-0.708828\pi\)
−0.609994 + 0.792406i \(0.708828\pi\)
\(44\) 5.00000 0.753778
\(45\) −3.00000 −0.447214
\(46\) 9.00000 1.32698
\(47\) 4.00000 0.583460 0.291730 0.956501i \(-0.405769\pi\)
0.291730 + 0.956501i \(0.405769\pi\)
\(48\) 2.00000 0.288675
\(49\) −6.00000 −0.857143
\(50\) −4.00000 −0.565685
\(51\) −8.00000 −1.12022
\(52\) −1.00000 −0.138675
\(53\) 6.00000 0.824163 0.412082 0.911147i \(-0.364802\pi\)
0.412082 + 0.911147i \(0.364802\pi\)
\(54\) −4.00000 −0.544331
\(55\) 15.0000 2.02260
\(56\) 3.00000 0.400892
\(57\) 8.00000 1.05963
\(58\) 6.00000 0.787839
\(59\) 9.00000 1.17170 0.585850 0.810419i \(-0.300761\pi\)
0.585850 + 0.810419i \(0.300761\pi\)
\(60\) −6.00000 −0.774597
\(61\) −1.00000 −0.128037
\(62\) 0 0
\(63\) 1.00000 0.125988
\(64\) 7.00000 0.875000
\(65\) −3.00000 −0.372104
\(66\) −10.0000 −1.23091
\(67\) −7.00000 −0.855186 −0.427593 0.903971i \(-0.640638\pi\)
−0.427593 + 0.903971i \(0.640638\pi\)
\(68\) −4.00000 −0.485071
\(69\) 18.0000 2.16695
\(70\) 3.00000 0.358569
\(71\) −8.00000 −0.949425 −0.474713 0.880141i \(-0.657448\pi\)
−0.474713 + 0.880141i \(0.657448\pi\)
\(72\) 3.00000 0.353553
\(73\) −11.0000 −1.28745 −0.643726 0.765256i \(-0.722612\pi\)
−0.643726 + 0.765256i \(0.722612\pi\)
\(74\) −8.00000 −0.929981
\(75\) −8.00000 −0.923760
\(76\) 4.00000 0.458831
\(77\) −5.00000 −0.569803
\(78\) 2.00000 0.226455
\(79\) 3.00000 0.337526 0.168763 0.985657i \(-0.446023\pi\)
0.168763 + 0.985657i \(0.446023\pi\)
\(80\) 3.00000 0.335410
\(81\) −11.0000 −1.22222
\(82\) −5.00000 −0.552158
\(83\) 4.00000 0.439057 0.219529 0.975606i \(-0.429548\pi\)
0.219529 + 0.975606i \(0.429548\pi\)
\(84\) 2.00000 0.218218
\(85\) −12.0000 −1.30158
\(86\) 8.00000 0.862662
\(87\) 12.0000 1.28654
\(88\) −15.0000 −1.59901
\(89\) −4.00000 −0.423999 −0.212000 0.977270i \(-0.567998\pi\)
−0.212000 + 0.977270i \(0.567998\pi\)
\(90\) 3.00000 0.316228
\(91\) 1.00000 0.104828
\(92\) 9.00000 0.938315
\(93\) 0 0
\(94\) −4.00000 −0.412568
\(95\) 12.0000 1.23117
\(96\) 10.0000 1.02062
\(97\) −14.0000 −1.42148 −0.710742 0.703452i \(-0.751641\pi\)
−0.710742 + 0.703452i \(0.751641\pi\)
\(98\) 6.00000 0.606092
\(99\) −5.00000 −0.502519
\(100\) −4.00000 −0.400000
\(101\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(102\) 8.00000 0.792118
\(103\) 4.00000 0.394132 0.197066 0.980390i \(-0.436859\pi\)
0.197066 + 0.980390i \(0.436859\pi\)
\(104\) 3.00000 0.294174
\(105\) 6.00000 0.585540
\(106\) −6.00000 −0.582772
\(107\) −2.00000 −0.193347 −0.0966736 0.995316i \(-0.530820\pi\)
−0.0966736 + 0.995316i \(0.530820\pi\)
\(108\) −4.00000 −0.384900
\(109\) −17.0000 −1.62830 −0.814152 0.580651i \(-0.802798\pi\)
−0.814152 + 0.580651i \(0.802798\pi\)
\(110\) −15.0000 −1.43019
\(111\) −16.0000 −1.51865
\(112\) −1.00000 −0.0944911
\(113\) 1.00000 0.0940721 0.0470360 0.998893i \(-0.485022\pi\)
0.0470360 + 0.998893i \(0.485022\pi\)
\(114\) −8.00000 −0.749269
\(115\) 27.0000 2.51776
\(116\) 6.00000 0.557086
\(117\) 1.00000 0.0924500
\(118\) −9.00000 −0.828517
\(119\) 4.00000 0.366679
\(120\) 18.0000 1.64317
\(121\) 14.0000 1.27273
\(122\) 1.00000 0.0905357
\(123\) −10.0000 −0.901670
\(124\) 0 0
\(125\) 3.00000 0.268328
\(126\) −1.00000 −0.0890871
\(127\) 6.00000 0.532414 0.266207 0.963916i \(-0.414230\pi\)
0.266207 + 0.963916i \(0.414230\pi\)
\(128\) 3.00000 0.265165
\(129\) 16.0000 1.40872
\(130\) 3.00000 0.263117
\(131\) −16.0000 −1.39793 −0.698963 0.715158i \(-0.746355\pi\)
−0.698963 + 0.715158i \(0.746355\pi\)
\(132\) −10.0000 −0.870388
\(133\) −4.00000 −0.346844
\(134\) 7.00000 0.604708
\(135\) −12.0000 −1.03280
\(136\) 12.0000 1.02899
\(137\) 9.00000 0.768922 0.384461 0.923141i \(-0.374387\pi\)
0.384461 + 0.923141i \(0.374387\pi\)
\(138\) −18.0000 −1.53226
\(139\) −11.0000 −0.933008 −0.466504 0.884519i \(-0.654487\pi\)
−0.466504 + 0.884519i \(0.654487\pi\)
\(140\) 3.00000 0.253546
\(141\) −8.00000 −0.673722
\(142\) 8.00000 0.671345
\(143\) −5.00000 −0.418121
\(144\) −1.00000 −0.0833333
\(145\) 18.0000 1.49482
\(146\) 11.0000 0.910366
\(147\) 12.0000 0.989743
\(148\) −8.00000 −0.657596
\(149\) 19.0000 1.55654 0.778270 0.627929i \(-0.216097\pi\)
0.778270 + 0.627929i \(0.216097\pi\)
\(150\) 8.00000 0.653197
\(151\) 11.0000 0.895167 0.447584 0.894242i \(-0.352285\pi\)
0.447584 + 0.894242i \(0.352285\pi\)
\(152\) −12.0000 −0.973329
\(153\) 4.00000 0.323381
\(154\) 5.00000 0.402911
\(155\) 0 0
\(156\) 2.00000 0.160128
\(157\) −4.00000 −0.319235 −0.159617 0.987179i \(-0.551026\pi\)
−0.159617 + 0.987179i \(0.551026\pi\)
\(158\) −3.00000 −0.238667
\(159\) −12.0000 −0.951662
\(160\) 15.0000 1.18585
\(161\) −9.00000 −0.709299
\(162\) 11.0000 0.864242
\(163\) 18.0000 1.40987 0.704934 0.709273i \(-0.250976\pi\)
0.704934 + 0.709273i \(0.250976\pi\)
\(164\) −5.00000 −0.390434
\(165\) −30.0000 −2.33550
\(166\) −4.00000 −0.310460
\(167\) −12.0000 −0.928588 −0.464294 0.885681i \(-0.653692\pi\)
−0.464294 + 0.885681i \(0.653692\pi\)
\(168\) −6.00000 −0.462910
\(169\) −12.0000 −0.923077
\(170\) 12.0000 0.920358
\(171\) −4.00000 −0.305888
\(172\) 8.00000 0.609994
\(173\) 10.0000 0.760286 0.380143 0.924928i \(-0.375875\pi\)
0.380143 + 0.924928i \(0.375875\pi\)
\(174\) −12.0000 −0.909718
\(175\) 4.00000 0.302372
\(176\) 5.00000 0.376889
\(177\) −18.0000 −1.35296
\(178\) 4.00000 0.299813
\(179\) −18.0000 −1.34538 −0.672692 0.739923i \(-0.734862\pi\)
−0.672692 + 0.739923i \(0.734862\pi\)
\(180\) 3.00000 0.223607
\(181\) 8.00000 0.594635 0.297318 0.954779i \(-0.403908\pi\)
0.297318 + 0.954779i \(0.403908\pi\)
\(182\) −1.00000 −0.0741249
\(183\) 2.00000 0.147844
\(184\) −27.0000 −1.99047
\(185\) −24.0000 −1.76452
\(186\) 0 0
\(187\) −20.0000 −1.46254
\(188\) −4.00000 −0.291730
\(189\) 4.00000 0.290957
\(190\) −12.0000 −0.870572
\(191\) 3.00000 0.217072 0.108536 0.994092i \(-0.465384\pi\)
0.108536 + 0.994092i \(0.465384\pi\)
\(192\) −14.0000 −1.01036
\(193\) −8.00000 −0.575853 −0.287926 0.957653i \(-0.592966\pi\)
−0.287926 + 0.957653i \(0.592966\pi\)
\(194\) 14.0000 1.00514
\(195\) 6.00000 0.429669
\(196\) 6.00000 0.428571
\(197\) −3.00000 −0.213741 −0.106871 0.994273i \(-0.534083\pi\)
−0.106871 + 0.994273i \(0.534083\pi\)
\(198\) 5.00000 0.355335
\(199\) 6.00000 0.425329 0.212664 0.977125i \(-0.431786\pi\)
0.212664 + 0.977125i \(0.431786\pi\)
\(200\) 12.0000 0.848528
\(201\) 14.0000 0.987484
\(202\) 0 0
\(203\) −6.00000 −0.421117
\(204\) 8.00000 0.560112
\(205\) −15.0000 −1.04765
\(206\) −4.00000 −0.278693
\(207\) −9.00000 −0.625543
\(208\) −1.00000 −0.0693375
\(209\) 20.0000 1.38343
\(210\) −6.00000 −0.414039
\(211\) 4.00000 0.275371 0.137686 0.990476i \(-0.456034\pi\)
0.137686 + 0.990476i \(0.456034\pi\)
\(212\) −6.00000 −0.412082
\(213\) 16.0000 1.09630
\(214\) 2.00000 0.136717
\(215\) 24.0000 1.63679
\(216\) 12.0000 0.816497
\(217\) 0 0
\(218\) 17.0000 1.15139
\(219\) 22.0000 1.48662
\(220\) −15.0000 −1.01130
\(221\) 4.00000 0.269069
\(222\) 16.0000 1.07385
\(223\) 23.0000 1.54019 0.770097 0.637927i \(-0.220208\pi\)
0.770097 + 0.637927i \(0.220208\pi\)
\(224\) −5.00000 −0.334077
\(225\) 4.00000 0.266667
\(226\) −1.00000 −0.0665190
\(227\) 21.0000 1.39382 0.696909 0.717159i \(-0.254558\pi\)
0.696909 + 0.717159i \(0.254558\pi\)
\(228\) −8.00000 −0.529813
\(229\) 9.00000 0.594737 0.297368 0.954763i \(-0.403891\pi\)
0.297368 + 0.954763i \(0.403891\pi\)
\(230\) −27.0000 −1.78033
\(231\) 10.0000 0.657952
\(232\) −18.0000 −1.18176
\(233\) −14.0000 −0.917170 −0.458585 0.888650i \(-0.651644\pi\)
−0.458585 + 0.888650i \(0.651644\pi\)
\(234\) −1.00000 −0.0653720
\(235\) −12.0000 −0.782794
\(236\) −9.00000 −0.585850
\(237\) −6.00000 −0.389742
\(238\) −4.00000 −0.259281
\(239\) 2.00000 0.129369 0.0646846 0.997906i \(-0.479396\pi\)
0.0646846 + 0.997906i \(0.479396\pi\)
\(240\) −6.00000 −0.387298
\(241\) −3.00000 −0.193247 −0.0966235 0.995321i \(-0.530804\pi\)
−0.0966235 + 0.995321i \(0.530804\pi\)
\(242\) −14.0000 −0.899954
\(243\) 10.0000 0.641500
\(244\) 1.00000 0.0640184
\(245\) 18.0000 1.14998
\(246\) 10.0000 0.637577
\(247\) −4.00000 −0.254514
\(248\) 0 0
\(249\) −8.00000 −0.506979
\(250\) −3.00000 −0.189737
\(251\) −12.0000 −0.757433 −0.378717 0.925513i \(-0.623635\pi\)
−0.378717 + 0.925513i \(0.623635\pi\)
\(252\) −1.00000 −0.0629941
\(253\) 45.0000 2.82913
\(254\) −6.00000 −0.376473
\(255\) 24.0000 1.50294
\(256\) −17.0000 −1.06250
\(257\) −22.0000 −1.37232 −0.686161 0.727450i \(-0.740706\pi\)
−0.686161 + 0.727450i \(0.740706\pi\)
\(258\) −16.0000 −0.996116
\(259\) 8.00000 0.497096
\(260\) 3.00000 0.186052
\(261\) −6.00000 −0.371391
\(262\) 16.0000 0.988483
\(263\) −16.0000 −0.986602 −0.493301 0.869859i \(-0.664210\pi\)
−0.493301 + 0.869859i \(0.664210\pi\)
\(264\) 30.0000 1.84637
\(265\) −18.0000 −1.10573
\(266\) 4.00000 0.245256
\(267\) 8.00000 0.489592
\(268\) 7.00000 0.427593
\(269\) −18.0000 −1.09748 −0.548740 0.835993i \(-0.684892\pi\)
−0.548740 + 0.835993i \(0.684892\pi\)
\(270\) 12.0000 0.730297
\(271\) 14.0000 0.850439 0.425220 0.905090i \(-0.360197\pi\)
0.425220 + 0.905090i \(0.360197\pi\)
\(272\) −4.00000 −0.242536
\(273\) −2.00000 −0.121046
\(274\) −9.00000 −0.543710
\(275\) −20.0000 −1.20605
\(276\) −18.0000 −1.08347
\(277\) 10.0000 0.600842 0.300421 0.953807i \(-0.402873\pi\)
0.300421 + 0.953807i \(0.402873\pi\)
\(278\) 11.0000 0.659736
\(279\) 0 0
\(280\) −9.00000 −0.537853
\(281\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(282\) 8.00000 0.476393
\(283\) 6.00000 0.356663 0.178331 0.983970i \(-0.442930\pi\)
0.178331 + 0.983970i \(0.442930\pi\)
\(284\) 8.00000 0.474713
\(285\) −24.0000 −1.42164
\(286\) 5.00000 0.295656
\(287\) 5.00000 0.295141
\(288\) −5.00000 −0.294628
\(289\) −1.00000 −0.0588235
\(290\) −18.0000 −1.05700
\(291\) 28.0000 1.64139
\(292\) 11.0000 0.643726
\(293\) 18.0000 1.05157 0.525786 0.850617i \(-0.323771\pi\)
0.525786 + 0.850617i \(0.323771\pi\)
\(294\) −12.0000 −0.699854
\(295\) −27.0000 −1.57200
\(296\) 24.0000 1.39497
\(297\) −20.0000 −1.16052
\(298\) −19.0000 −1.10064
\(299\) −9.00000 −0.520483
\(300\) 8.00000 0.461880
\(301\) −8.00000 −0.461112
\(302\) −11.0000 −0.632979
\(303\) 0 0
\(304\) 4.00000 0.229416
\(305\) 3.00000 0.171780
\(306\) −4.00000 −0.228665
\(307\) −19.0000 −1.08439 −0.542194 0.840254i \(-0.682406\pi\)
−0.542194 + 0.840254i \(0.682406\pi\)
\(308\) 5.00000 0.284901
\(309\) −8.00000 −0.455104
\(310\) 0 0
\(311\) −15.0000 −0.850572 −0.425286 0.905059i \(-0.639826\pi\)
−0.425286 + 0.905059i \(0.639826\pi\)
\(312\) −6.00000 −0.339683
\(313\) −6.00000 −0.339140 −0.169570 0.985518i \(-0.554238\pi\)
−0.169570 + 0.985518i \(0.554238\pi\)
\(314\) 4.00000 0.225733
\(315\) −3.00000 −0.169031
\(316\) −3.00000 −0.168763
\(317\) −30.0000 −1.68497 −0.842484 0.538721i \(-0.818908\pi\)
−0.842484 + 0.538721i \(0.818908\pi\)
\(318\) 12.0000 0.672927
\(319\) 30.0000 1.67968
\(320\) −21.0000 −1.17394
\(321\) 4.00000 0.223258
\(322\) 9.00000 0.501550
\(323\) −16.0000 −0.890264
\(324\) 11.0000 0.611111
\(325\) 4.00000 0.221880
\(326\) −18.0000 −0.996928
\(327\) 34.0000 1.88020
\(328\) 15.0000 0.828236
\(329\) 4.00000 0.220527
\(330\) 30.0000 1.65145
\(331\) −17.0000 −0.934405 −0.467202 0.884150i \(-0.654738\pi\)
−0.467202 + 0.884150i \(0.654738\pi\)
\(332\) −4.00000 −0.219529
\(333\) 8.00000 0.438397
\(334\) 12.0000 0.656611
\(335\) 21.0000 1.14735
\(336\) 2.00000 0.109109
\(337\) −2.00000 −0.108947 −0.0544735 0.998515i \(-0.517348\pi\)
−0.0544735 + 0.998515i \(0.517348\pi\)
\(338\) 12.0000 0.652714
\(339\) −2.00000 −0.108625
\(340\) 12.0000 0.650791
\(341\) 0 0
\(342\) 4.00000 0.216295
\(343\) −13.0000 −0.701934
\(344\) −24.0000 −1.29399
\(345\) −54.0000 −2.90726
\(346\) −10.0000 −0.537603
\(347\) 8.00000 0.429463 0.214731 0.976673i \(-0.431112\pi\)
0.214731 + 0.976673i \(0.431112\pi\)
\(348\) −12.0000 −0.643268
\(349\) −24.0000 −1.28469 −0.642345 0.766415i \(-0.722038\pi\)
−0.642345 + 0.766415i \(0.722038\pi\)
\(350\) −4.00000 −0.213809
\(351\) 4.00000 0.213504
\(352\) 25.0000 1.33250
\(353\) 19.0000 1.01127 0.505634 0.862748i \(-0.331259\pi\)
0.505634 + 0.862748i \(0.331259\pi\)
\(354\) 18.0000 0.956689
\(355\) 24.0000 1.27379
\(356\) 4.00000 0.212000
\(357\) −8.00000 −0.423405
\(358\) 18.0000 0.951330
\(359\) 12.0000 0.633336 0.316668 0.948536i \(-0.397436\pi\)
0.316668 + 0.948536i \(0.397436\pi\)
\(360\) −9.00000 −0.474342
\(361\) −3.00000 −0.157895
\(362\) −8.00000 −0.420471
\(363\) −28.0000 −1.46962
\(364\) −1.00000 −0.0524142
\(365\) 33.0000 1.72730
\(366\) −2.00000 −0.104542
\(367\) 14.0000 0.730794 0.365397 0.930852i \(-0.380933\pi\)
0.365397 + 0.930852i \(0.380933\pi\)
\(368\) 9.00000 0.469157
\(369\) 5.00000 0.260290
\(370\) 24.0000 1.24770
\(371\) 6.00000 0.311504
\(372\) 0 0
\(373\) −10.0000 −0.517780 −0.258890 0.965907i \(-0.583357\pi\)
−0.258890 + 0.965907i \(0.583357\pi\)
\(374\) 20.0000 1.03418
\(375\) −6.00000 −0.309839
\(376\) 12.0000 0.618853
\(377\) −6.00000 −0.309016
\(378\) −4.00000 −0.205738
\(379\) −14.0000 −0.719132 −0.359566 0.933120i \(-0.617075\pi\)
−0.359566 + 0.933120i \(0.617075\pi\)
\(380\) −12.0000 −0.615587
\(381\) −12.0000 −0.614779
\(382\) −3.00000 −0.153493
\(383\) 5.00000 0.255488 0.127744 0.991807i \(-0.459226\pi\)
0.127744 + 0.991807i \(0.459226\pi\)
\(384\) −6.00000 −0.306186
\(385\) 15.0000 0.764471
\(386\) 8.00000 0.407189
\(387\) −8.00000 −0.406663
\(388\) 14.0000 0.710742
\(389\) −14.0000 −0.709828 −0.354914 0.934899i \(-0.615490\pi\)
−0.354914 + 0.934899i \(0.615490\pi\)
\(390\) −6.00000 −0.303822
\(391\) −36.0000 −1.82060
\(392\) −18.0000 −0.909137
\(393\) 32.0000 1.61419
\(394\) 3.00000 0.151138
\(395\) −9.00000 −0.452839
\(396\) 5.00000 0.251259
\(397\) 8.00000 0.401508 0.200754 0.979642i \(-0.435661\pi\)
0.200754 + 0.979642i \(0.435661\pi\)
\(398\) −6.00000 −0.300753
\(399\) 8.00000 0.400501
\(400\) −4.00000 −0.200000
\(401\) 16.0000 0.799002 0.399501 0.916733i \(-0.369183\pi\)
0.399501 + 0.916733i \(0.369183\pi\)
\(402\) −14.0000 −0.698257
\(403\) 0 0
\(404\) 0 0
\(405\) 33.0000 1.63978
\(406\) 6.00000 0.297775
\(407\) −40.0000 −1.98273
\(408\) −24.0000 −1.18818
\(409\) 30.0000 1.48340 0.741702 0.670729i \(-0.234019\pi\)
0.741702 + 0.670729i \(0.234019\pi\)
\(410\) 15.0000 0.740797
\(411\) −18.0000 −0.887875
\(412\) −4.00000 −0.197066
\(413\) 9.00000 0.442861
\(414\) 9.00000 0.442326
\(415\) −12.0000 −0.589057
\(416\) −5.00000 −0.245145
\(417\) 22.0000 1.07734
\(418\) −20.0000 −0.978232
\(419\) 4.00000 0.195413 0.0977064 0.995215i \(-0.468849\pi\)
0.0977064 + 0.995215i \(0.468849\pi\)
\(420\) −6.00000 −0.292770
\(421\) 8.00000 0.389896 0.194948 0.980814i \(-0.437546\pi\)
0.194948 + 0.980814i \(0.437546\pi\)
\(422\) −4.00000 −0.194717
\(423\) 4.00000 0.194487
\(424\) 18.0000 0.874157
\(425\) 16.0000 0.776114
\(426\) −16.0000 −0.775203
\(427\) −1.00000 −0.0483934
\(428\) 2.00000 0.0966736
\(429\) 10.0000 0.482805
\(430\) −24.0000 −1.15738
\(431\) 6.00000 0.289010 0.144505 0.989504i \(-0.453841\pi\)
0.144505 + 0.989504i \(0.453841\pi\)
\(432\) −4.00000 −0.192450
\(433\) −8.00000 −0.384455 −0.192228 0.981350i \(-0.561571\pi\)
−0.192228 + 0.981350i \(0.561571\pi\)
\(434\) 0 0
\(435\) −36.0000 −1.72607
\(436\) 17.0000 0.814152
\(437\) 36.0000 1.72211
\(438\) −22.0000 −1.05120
\(439\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(440\) 45.0000 2.14529
\(441\) −6.00000 −0.285714
\(442\) −4.00000 −0.190261
\(443\) 12.0000 0.570137 0.285069 0.958507i \(-0.407984\pi\)
0.285069 + 0.958507i \(0.407984\pi\)
\(444\) 16.0000 0.759326
\(445\) 12.0000 0.568855
\(446\) −23.0000 −1.08908
\(447\) −38.0000 −1.79734
\(448\) 7.00000 0.330719
\(449\) −35.0000 −1.65175 −0.825876 0.563852i \(-0.809319\pi\)
−0.825876 + 0.563852i \(0.809319\pi\)
\(450\) −4.00000 −0.188562
\(451\) −25.0000 −1.17720
\(452\) −1.00000 −0.0470360
\(453\) −22.0000 −1.03365
\(454\) −21.0000 −0.985579
\(455\) −3.00000 −0.140642
\(456\) 24.0000 1.12390
\(457\) −20.0000 −0.935561 −0.467780 0.883845i \(-0.654946\pi\)
−0.467780 + 0.883845i \(0.654946\pi\)
\(458\) −9.00000 −0.420542
\(459\) 16.0000 0.746816
\(460\) −27.0000 −1.25888
\(461\) −18.0000 −0.838344 −0.419172 0.907907i \(-0.637680\pi\)
−0.419172 + 0.907907i \(0.637680\pi\)
\(462\) −10.0000 −0.465242
\(463\) −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
\(466\) 14.0000 0.648537
\(467\) 11.0000 0.509019 0.254510 0.967070i \(-0.418086\pi\)
0.254510 + 0.967070i \(0.418086\pi\)
\(468\) −1.00000 −0.0462250
\(469\) −7.00000 −0.323230
\(470\) 12.0000 0.553519
\(471\) 8.00000 0.368621
\(472\) 27.0000 1.24278
\(473\) 40.0000 1.83920
\(474\) 6.00000 0.275589
\(475\) −16.0000 −0.734130
\(476\) −4.00000 −0.183340
\(477\) 6.00000 0.274721
\(478\) −2.00000 −0.0914779
\(479\) 14.0000 0.639676 0.319838 0.947472i \(-0.396371\pi\)
0.319838 + 0.947472i \(0.396371\pi\)
\(480\) −30.0000 −1.36931
\(481\) 8.00000 0.364769
\(482\) 3.00000 0.136646
\(483\) 18.0000 0.819028
\(484\) −14.0000 −0.636364
\(485\) 42.0000 1.90712
\(486\) −10.0000 −0.453609
\(487\) −12.0000 −0.543772 −0.271886 0.962329i \(-0.587647\pi\)
−0.271886 + 0.962329i \(0.587647\pi\)
\(488\) −3.00000 −0.135804
\(489\) −36.0000 −1.62798
\(490\) −18.0000 −0.813157
\(491\) −28.0000 −1.26362 −0.631811 0.775122i \(-0.717688\pi\)
−0.631811 + 0.775122i \(0.717688\pi\)
\(492\) 10.0000 0.450835
\(493\) −24.0000 −1.08091
\(494\) 4.00000 0.179969
\(495\) 15.0000 0.674200
\(496\) 0 0
\(497\) −8.00000 −0.358849
\(498\) 8.00000 0.358489
\(499\) 13.0000 0.581960 0.290980 0.956729i \(-0.406019\pi\)
0.290980 + 0.956729i \(0.406019\pi\)
\(500\) −3.00000 −0.134164
\(501\) 24.0000 1.07224
\(502\) 12.0000 0.535586
\(503\) 10.0000 0.445878 0.222939 0.974832i \(-0.428435\pi\)
0.222939 + 0.974832i \(0.428435\pi\)
\(504\) 3.00000 0.133631
\(505\) 0 0
\(506\) −45.0000 −2.00049
\(507\) 24.0000 1.06588
\(508\) −6.00000 −0.266207
\(509\) 28.0000 1.24108 0.620539 0.784176i \(-0.286914\pi\)
0.620539 + 0.784176i \(0.286914\pi\)
\(510\) −24.0000 −1.06274
\(511\) −11.0000 −0.486611
\(512\) 11.0000 0.486136
\(513\) −16.0000 −0.706417
\(514\) 22.0000 0.970378
\(515\) −12.0000 −0.528783
\(516\) −16.0000 −0.704361
\(517\) −20.0000 −0.879599
\(518\) −8.00000 −0.351500
\(519\) −20.0000 −0.877903
\(520\) −9.00000 −0.394676
\(521\) −20.0000 −0.876216 −0.438108 0.898922i \(-0.644351\pi\)
−0.438108 + 0.898922i \(0.644351\pi\)
\(522\) 6.00000 0.262613
\(523\) −9.00000 −0.393543 −0.196771 0.980449i \(-0.563046\pi\)
−0.196771 + 0.980449i \(0.563046\pi\)
\(524\) 16.0000 0.698963
\(525\) −8.00000 −0.349149
\(526\) 16.0000 0.697633
\(527\) 0 0
\(528\) −10.0000 −0.435194
\(529\) 58.0000 2.52174
\(530\) 18.0000 0.781870
\(531\) 9.00000 0.390567
\(532\) 4.00000 0.173422
\(533\) 5.00000 0.216574
\(534\) −8.00000 −0.346194
\(535\) 6.00000 0.259403
\(536\) −21.0000 −0.907062
\(537\) 36.0000 1.55351
\(538\) 18.0000 0.776035
\(539\) 30.0000 1.29219
\(540\) 12.0000 0.516398
\(541\) 28.0000 1.20381 0.601907 0.798566i \(-0.294408\pi\)
0.601907 + 0.798566i \(0.294408\pi\)
\(542\) −14.0000 −0.601351
\(543\) −16.0000 −0.686626
\(544\) −20.0000 −0.857493
\(545\) 51.0000 2.18460
\(546\) 2.00000 0.0855921
\(547\) −29.0000 −1.23995 −0.619975 0.784621i \(-0.712857\pi\)
−0.619975 + 0.784621i \(0.712857\pi\)
\(548\) −9.00000 −0.384461
\(549\) −1.00000 −0.0426790
\(550\) 20.0000 0.852803
\(551\) 24.0000 1.02243
\(552\) 54.0000 2.29839
\(553\) 3.00000 0.127573
\(554\) −10.0000 −0.424859
\(555\) 48.0000 2.03749
\(556\) 11.0000 0.466504
\(557\) −28.0000 −1.18640 −0.593199 0.805056i \(-0.702135\pi\)
−0.593199 + 0.805056i \(0.702135\pi\)
\(558\) 0 0
\(559\) −8.00000 −0.338364
\(560\) 3.00000 0.126773
\(561\) 40.0000 1.68880
\(562\) 0 0
\(563\) −10.0000 −0.421450 −0.210725 0.977545i \(-0.567582\pi\)
−0.210725 + 0.977545i \(0.567582\pi\)
\(564\) 8.00000 0.336861
\(565\) −3.00000 −0.126211
\(566\) −6.00000 −0.252199
\(567\) −11.0000 −0.461957
\(568\) −24.0000 −1.00702
\(569\) −15.0000 −0.628833 −0.314416 0.949285i \(-0.601809\pi\)
−0.314416 + 0.949285i \(0.601809\pi\)
\(570\) 24.0000 1.00525
\(571\) 38.0000 1.59025 0.795125 0.606445i \(-0.207405\pi\)
0.795125 + 0.606445i \(0.207405\pi\)
\(572\) 5.00000 0.209061
\(573\) −6.00000 −0.250654
\(574\) −5.00000 −0.208696
\(575\) −36.0000 −1.50130
\(576\) 7.00000 0.291667
\(577\) 10.0000 0.416305 0.208153 0.978096i \(-0.433255\pi\)
0.208153 + 0.978096i \(0.433255\pi\)
\(578\) 1.00000 0.0415945
\(579\) 16.0000 0.664937
\(580\) −18.0000 −0.747409
\(581\) 4.00000 0.165948
\(582\) −28.0000 −1.16064
\(583\) −30.0000 −1.24247
\(584\) −33.0000 −1.36555
\(585\) −3.00000 −0.124035
\(586\) −18.0000 −0.743573
\(587\) 32.0000 1.32078 0.660391 0.750922i \(-0.270391\pi\)
0.660391 + 0.750922i \(0.270391\pi\)
\(588\) −12.0000 −0.494872
\(589\) 0 0
\(590\) 27.0000 1.11157
\(591\) 6.00000 0.246807
\(592\) −8.00000 −0.328798
\(593\) −6.00000 −0.246390 −0.123195 0.992382i \(-0.539314\pi\)
−0.123195 + 0.992382i \(0.539314\pi\)
\(594\) 20.0000 0.820610
\(595\) −12.0000 −0.491952
\(596\) −19.0000 −0.778270
\(597\) −12.0000 −0.491127
\(598\) 9.00000 0.368037
\(599\) −35.0000 −1.43006 −0.715031 0.699093i \(-0.753587\pi\)
−0.715031 + 0.699093i \(0.753587\pi\)
\(600\) −24.0000 −0.979796
\(601\) −43.0000 −1.75401 −0.877003 0.480484i \(-0.840461\pi\)
−0.877003 + 0.480484i \(0.840461\pi\)
\(602\) 8.00000 0.326056
\(603\) −7.00000 −0.285062
\(604\) −11.0000 −0.447584
\(605\) −42.0000 −1.70754
\(606\) 0 0
\(607\) −26.0000 −1.05531 −0.527654 0.849460i \(-0.676928\pi\)
−0.527654 + 0.849460i \(0.676928\pi\)
\(608\) 20.0000 0.811107
\(609\) 12.0000 0.486265
\(610\) −3.00000 −0.121466
\(611\) 4.00000 0.161823
\(612\) −4.00000 −0.161690
\(613\) −6.00000 −0.242338 −0.121169 0.992632i \(-0.538664\pi\)
−0.121169 + 0.992632i \(0.538664\pi\)
\(614\) 19.0000 0.766778
\(615\) 30.0000 1.20972
\(616\) −15.0000 −0.604367
\(617\) 10.0000 0.402585 0.201292 0.979531i \(-0.435486\pi\)
0.201292 + 0.979531i \(0.435486\pi\)
\(618\) 8.00000 0.321807
\(619\) −28.0000 −1.12542 −0.562708 0.826656i \(-0.690240\pi\)
−0.562708 + 0.826656i \(0.690240\pi\)
\(620\) 0 0
\(621\) −36.0000 −1.44463
\(622\) 15.0000 0.601445
\(623\) −4.00000 −0.160257
\(624\) 2.00000 0.0800641
\(625\) −29.0000 −1.16000
\(626\) 6.00000 0.239808
\(627\) −40.0000 −1.59745
\(628\) 4.00000 0.159617
\(629\) 32.0000 1.27592
\(630\) 3.00000 0.119523
\(631\) 25.0000 0.995234 0.497617 0.867397i \(-0.334208\pi\)
0.497617 + 0.867397i \(0.334208\pi\)
\(632\) 9.00000 0.358001
\(633\) −8.00000 −0.317971
\(634\) 30.0000 1.19145
\(635\) −18.0000 −0.714308
\(636\) 12.0000 0.475831
\(637\) −6.00000 −0.237729
\(638\) −30.0000 −1.18771
\(639\) −8.00000 −0.316475
\(640\) −9.00000 −0.355756
\(641\) 46.0000 1.81689 0.908445 0.418004i \(-0.137270\pi\)
0.908445 + 0.418004i \(0.137270\pi\)
\(642\) −4.00000 −0.157867
\(643\) −4.00000 −0.157745 −0.0788723 0.996885i \(-0.525132\pi\)
−0.0788723 + 0.996885i \(0.525132\pi\)
\(644\) 9.00000 0.354650
\(645\) −48.0000 −1.89000
\(646\) 16.0000 0.629512
\(647\) 39.0000 1.53325 0.766624 0.642096i \(-0.221935\pi\)
0.766624 + 0.642096i \(0.221935\pi\)
\(648\) −33.0000 −1.29636
\(649\) −45.0000 −1.76640
\(650\) −4.00000 −0.156893
\(651\) 0 0
\(652\) −18.0000 −0.704934
\(653\) 46.0000 1.80012 0.900060 0.435767i \(-0.143523\pi\)
0.900060 + 0.435767i \(0.143523\pi\)
\(654\) −34.0000 −1.32951
\(655\) 48.0000 1.87552
\(656\) −5.00000 −0.195217
\(657\) −11.0000 −0.429151
\(658\) −4.00000 −0.155936
\(659\) −34.0000 −1.32445 −0.662226 0.749304i \(-0.730388\pi\)
−0.662226 + 0.749304i \(0.730388\pi\)
\(660\) 30.0000 1.16775
\(661\) 34.0000 1.32245 0.661223 0.750189i \(-0.270038\pi\)
0.661223 + 0.750189i \(0.270038\pi\)
\(662\) 17.0000 0.660724
\(663\) −8.00000 −0.310694
\(664\) 12.0000 0.465690
\(665\) 12.0000 0.465340
\(666\) −8.00000 −0.309994
\(667\) 54.0000 2.09089
\(668\) 12.0000 0.464294
\(669\) −46.0000 −1.77846
\(670\) −21.0000 −0.811301
\(671\) 5.00000 0.193023
\(672\) 10.0000 0.385758
\(673\) 32.0000 1.23351 0.616755 0.787155i \(-0.288447\pi\)
0.616755 + 0.787155i \(0.288447\pi\)
\(674\) 2.00000 0.0770371
\(675\) 16.0000 0.615840
\(676\) 12.0000 0.461538
\(677\) −32.0000 −1.22986 −0.614930 0.788582i \(-0.710816\pi\)
−0.614930 + 0.788582i \(0.710816\pi\)
\(678\) 2.00000 0.0768095
\(679\) −14.0000 −0.537271
\(680\) −36.0000 −1.38054
\(681\) −42.0000 −1.60944
\(682\) 0 0
\(683\) 26.0000 0.994862 0.497431 0.867503i \(-0.334277\pi\)
0.497431 + 0.867503i \(0.334277\pi\)
\(684\) 4.00000 0.152944
\(685\) −27.0000 −1.03162
\(686\) 13.0000 0.496342
\(687\) −18.0000 −0.686743
\(688\) 8.00000 0.304997
\(689\) 6.00000 0.228582
\(690\) 54.0000 2.05574
\(691\) 16.0000 0.608669 0.304334 0.952565i \(-0.401566\pi\)
0.304334 + 0.952565i \(0.401566\pi\)
\(692\) −10.0000 −0.380143
\(693\) −5.00000 −0.189934
\(694\) −8.00000 −0.303676
\(695\) 33.0000 1.25176
\(696\) 36.0000 1.36458
\(697\) 20.0000 0.757554
\(698\) 24.0000 0.908413
\(699\) 28.0000 1.05906
\(700\) −4.00000 −0.151186
\(701\) 18.0000 0.679851 0.339925 0.940452i \(-0.389598\pi\)
0.339925 + 0.940452i \(0.389598\pi\)
\(702\) −4.00000 −0.150970
\(703\) −32.0000 −1.20690
\(704\) −35.0000 −1.31911
\(705\) 24.0000 0.903892
\(706\) −19.0000 −0.715074
\(707\) 0 0
\(708\) 18.0000 0.676481
\(709\) −34.0000 −1.27690 −0.638448 0.769665i \(-0.720423\pi\)
−0.638448 + 0.769665i \(0.720423\pi\)
\(710\) −24.0000 −0.900704
\(711\) 3.00000 0.112509
\(712\) −12.0000 −0.449719
\(713\) 0 0
\(714\) 8.00000 0.299392
\(715\) 15.0000 0.560968
\(716\) 18.0000 0.672692
\(717\) −4.00000 −0.149383
\(718\) −12.0000 −0.447836
\(719\) −46.0000 −1.71551 −0.857755 0.514058i \(-0.828142\pi\)
−0.857755 + 0.514058i \(0.828142\pi\)
\(720\) 3.00000 0.111803
\(721\) 4.00000 0.148968
\(722\) 3.00000 0.111648
\(723\) 6.00000 0.223142
\(724\) −8.00000 −0.297318
\(725\) −24.0000 −0.891338
\(726\) 28.0000 1.03918
\(727\) 8.00000 0.296704 0.148352 0.988935i \(-0.452603\pi\)
0.148352 + 0.988935i \(0.452603\pi\)
\(728\) 3.00000 0.111187
\(729\) 13.0000 0.481481
\(730\) −33.0000 −1.22138
\(731\) −32.0000 −1.18356
\(732\) −2.00000 −0.0739221
\(733\) 49.0000 1.80986 0.904928 0.425564i \(-0.139924\pi\)
0.904928 + 0.425564i \(0.139924\pi\)
\(734\) −14.0000 −0.516749
\(735\) −36.0000 −1.32788
\(736\) 45.0000 1.65872
\(737\) 35.0000 1.28924
\(738\) −5.00000 −0.184053
\(739\) 45.0000 1.65535 0.827676 0.561206i \(-0.189663\pi\)
0.827676 + 0.561206i \(0.189663\pi\)
\(740\) 24.0000 0.882258
\(741\) 8.00000 0.293887
\(742\) −6.00000 −0.220267
\(743\) 27.0000 0.990534 0.495267 0.868741i \(-0.335070\pi\)
0.495267 + 0.868741i \(0.335070\pi\)
\(744\) 0 0
\(745\) −57.0000 −2.08832
\(746\) 10.0000 0.366126
\(747\) 4.00000 0.146352
\(748\) 20.0000 0.731272
\(749\) −2.00000 −0.0730784
\(750\) 6.00000 0.219089
\(751\) −10.0000 −0.364905 −0.182453 0.983215i \(-0.558404\pi\)
−0.182453 + 0.983215i \(0.558404\pi\)
\(752\) −4.00000 −0.145865
\(753\) 24.0000 0.874609
\(754\) 6.00000 0.218507
\(755\) −33.0000 −1.20099
\(756\) −4.00000 −0.145479
\(757\) 27.0000 0.981332 0.490666 0.871348i \(-0.336754\pi\)
0.490666 + 0.871348i \(0.336754\pi\)
\(758\) 14.0000 0.508503
\(759\) −90.0000 −3.26679
\(760\) 36.0000 1.30586
\(761\) −26.0000 −0.942499 −0.471250 0.882000i \(-0.656197\pi\)
−0.471250 + 0.882000i \(0.656197\pi\)
\(762\) 12.0000 0.434714
\(763\) −17.0000 −0.615441
\(764\) −3.00000 −0.108536
\(765\) −12.0000 −0.433861
\(766\) −5.00000 −0.180657
\(767\) 9.00000 0.324971
\(768\) 34.0000 1.22687
\(769\) −52.0000 −1.87517 −0.937584 0.347759i \(-0.886943\pi\)
−0.937584 + 0.347759i \(0.886943\pi\)
\(770\) −15.0000 −0.540562
\(771\) 44.0000 1.58462
\(772\) 8.00000 0.287926
\(773\) −46.0000 −1.65451 −0.827253 0.561830i \(-0.810097\pi\)
−0.827253 + 0.561830i \(0.810097\pi\)
\(774\) 8.00000 0.287554
\(775\) 0 0
\(776\) −42.0000 −1.50771
\(777\) −16.0000 −0.573997
\(778\) 14.0000 0.501924
\(779\) −20.0000 −0.716574
\(780\) −6.00000 −0.214834
\(781\) 40.0000 1.43131
\(782\) 36.0000 1.28736
\(783\) −24.0000 −0.857690
\(784\) 6.00000 0.214286
\(785\) 12.0000 0.428298
\(786\) −32.0000 −1.14140
\(787\) 48.0000 1.71102 0.855508 0.517790i \(-0.173245\pi\)
0.855508 + 0.517790i \(0.173245\pi\)
\(788\) 3.00000 0.106871
\(789\) 32.0000 1.13923
\(790\) 9.00000 0.320206
\(791\) 1.00000 0.0355559
\(792\) −15.0000 −0.533002
\(793\) −1.00000 −0.0355110
\(794\) −8.00000 −0.283909
\(795\) 36.0000 1.27679
\(796\) −6.00000 −0.212664
\(797\) −23.0000 −0.814702 −0.407351 0.913272i \(-0.633547\pi\)
−0.407351 + 0.913272i \(0.633547\pi\)
\(798\) −8.00000 −0.283197
\(799\) 16.0000 0.566039
\(800\) −20.0000 −0.707107
\(801\) −4.00000 −0.141333
\(802\) −16.0000 −0.564980
\(803\) 55.0000 1.94091
\(804\) −14.0000 −0.493742
\(805\) 27.0000 0.951625
\(806\) 0 0
\(807\) 36.0000 1.26726
\(808\) 0 0
\(809\) −15.0000 −0.527372 −0.263686 0.964609i \(-0.584938\pi\)
−0.263686 + 0.964609i \(0.584938\pi\)
\(810\) −33.0000 −1.15950
\(811\) 7.00000 0.245803 0.122902 0.992419i \(-0.460780\pi\)
0.122902 + 0.992419i \(0.460780\pi\)
\(812\) 6.00000 0.210559
\(813\) −28.0000 −0.982003
\(814\) 40.0000 1.40200
\(815\) −54.0000 −1.89154
\(816\) 8.00000 0.280056
\(817\) 32.0000 1.11954
\(818\) −30.0000 −1.04893
\(819\) 1.00000 0.0349428
\(820\) 15.0000 0.523823
\(821\) −36.0000 −1.25641 −0.628204 0.778048i \(-0.716210\pi\)
−0.628204 + 0.778048i \(0.716210\pi\)
\(822\) 18.0000 0.627822
\(823\) −12.0000 −0.418294 −0.209147 0.977884i \(-0.567069\pi\)
−0.209147 + 0.977884i \(0.567069\pi\)
\(824\) 12.0000 0.418040
\(825\) 40.0000 1.39262
\(826\) −9.00000 −0.313150
\(827\) 8.00000 0.278187 0.139094 0.990279i \(-0.455581\pi\)
0.139094 + 0.990279i \(0.455581\pi\)
\(828\) 9.00000 0.312772
\(829\) 3.00000 0.104194 0.0520972 0.998642i \(-0.483409\pi\)
0.0520972 + 0.998642i \(0.483409\pi\)
\(830\) 12.0000 0.416526
\(831\) −20.0000 −0.693792
\(832\) 7.00000 0.242681
\(833\) −24.0000 −0.831551
\(834\) −22.0000 −0.761798
\(835\) 36.0000 1.24583
\(836\) −20.0000 −0.691714
\(837\) 0 0
\(838\) −4.00000 −0.138178
\(839\) −30.0000 −1.03572 −0.517858 0.855467i \(-0.673270\pi\)
−0.517858 + 0.855467i \(0.673270\pi\)
\(840\) 18.0000 0.621059
\(841\) 7.00000 0.241379
\(842\) −8.00000 −0.275698
\(843\) 0 0
\(844\) −4.00000 −0.137686
\(845\) 36.0000 1.23844
\(846\) −4.00000 −0.137523
\(847\) 14.0000 0.481046
\(848\) −6.00000 −0.206041
\(849\) −12.0000 −0.411839
\(850\) −16.0000 −0.548795
\(851\) −72.0000 −2.46813
\(852\) −16.0000 −0.548151
\(853\) −43.0000 −1.47229 −0.736146 0.676823i \(-0.763356\pi\)
−0.736146 + 0.676823i \(0.763356\pi\)
\(854\) 1.00000 0.0342193
\(855\) 12.0000 0.410391
\(856\) −6.00000 −0.205076
\(857\) 37.0000 1.26390 0.631948 0.775011i \(-0.282256\pi\)
0.631948 + 0.775011i \(0.282256\pi\)
\(858\) −10.0000 −0.341394
\(859\) 6.00000 0.204717 0.102359 0.994748i \(-0.467361\pi\)
0.102359 + 0.994748i \(0.467361\pi\)
\(860\) −24.0000 −0.818393
\(861\) −10.0000 −0.340799
\(862\) −6.00000 −0.204361
\(863\) 16.0000 0.544646 0.272323 0.962206i \(-0.412208\pi\)
0.272323 + 0.962206i \(0.412208\pi\)
\(864\) −20.0000 −0.680414
\(865\) −30.0000 −1.02003
\(866\) 8.00000 0.271851
\(867\) 2.00000 0.0679236
\(868\) 0 0
\(869\) −15.0000 −0.508840
\(870\) 36.0000 1.22051
\(871\) −7.00000 −0.237186
\(872\) −51.0000 −1.72708
\(873\) −14.0000 −0.473828
\(874\) −36.0000 −1.21772
\(875\) 3.00000 0.101419
\(876\) −22.0000 −0.743311
\(877\) −12.0000 −0.405211 −0.202606 0.979260i \(-0.564941\pi\)
−0.202606 + 0.979260i \(0.564941\pi\)
\(878\) 0 0
\(879\) −36.0000 −1.21425
\(880\) −15.0000 −0.505650
\(881\) −29.0000 −0.977035 −0.488517 0.872554i \(-0.662462\pi\)
−0.488517 + 0.872554i \(0.662462\pi\)
\(882\) 6.00000 0.202031
\(883\) 9.00000 0.302874 0.151437 0.988467i \(-0.451610\pi\)
0.151437 + 0.988467i \(0.451610\pi\)
\(884\) −4.00000 −0.134535
\(885\) 54.0000 1.81519
\(886\) −12.0000 −0.403148
\(887\) 16.0000 0.537227 0.268614 0.963248i \(-0.413434\pi\)
0.268614 + 0.963248i \(0.413434\pi\)
\(888\) −48.0000 −1.61077
\(889\) 6.00000 0.201234
\(890\) −12.0000 −0.402241
\(891\) 55.0000 1.84257
\(892\) −23.0000 −0.770097
\(893\) −16.0000 −0.535420
\(894\) 38.0000 1.27091
\(895\) 54.0000 1.80502
\(896\) 3.00000 0.100223
\(897\) 18.0000 0.601003
\(898\) 35.0000 1.16797
\(899\) 0 0
\(900\) −4.00000 −0.133333
\(901\) 24.0000 0.799556
\(902\) 25.0000 0.832409
\(903\) 16.0000 0.532447
\(904\) 3.00000 0.0997785
\(905\) −24.0000 −0.797787
\(906\) 22.0000 0.730901
\(907\) 12.0000 0.398453 0.199227 0.979953i \(-0.436157\pi\)
0.199227 + 0.979953i \(0.436157\pi\)
\(908\) −21.0000 −0.696909
\(909\) 0 0
\(910\) 3.00000 0.0994490
\(911\) 2.00000 0.0662630 0.0331315 0.999451i \(-0.489452\pi\)
0.0331315 + 0.999451i \(0.489452\pi\)
\(912\) −8.00000 −0.264906
\(913\) −20.0000 −0.661903
\(914\) 20.0000 0.661541
\(915\) −6.00000 −0.198354
\(916\) −9.00000 −0.297368
\(917\) −16.0000 −0.528367
\(918\) −16.0000 −0.528079
\(919\) −56.0000 −1.84727 −0.923635 0.383274i \(-0.874797\pi\)
−0.923635 + 0.383274i \(0.874797\pi\)
\(920\) 81.0000 2.67049
\(921\) 38.0000 1.25214
\(922\) 18.0000 0.592798
\(923\) −8.00000 −0.263323
\(924\) −10.0000 −0.328976
\(925\) 32.0000 1.05215
\(926\) 4.00000 0.131448
\(927\) 4.00000 0.131377
\(928\) 30.0000 0.984798
\(929\) −3.00000 −0.0984268 −0.0492134 0.998788i \(-0.515671\pi\)
−0.0492134 + 0.998788i \(0.515671\pi\)
\(930\) 0 0
\(931\) 24.0000 0.786568
\(932\) 14.0000 0.458585
\(933\) 30.0000 0.982156
\(934\) −11.0000 −0.359931
\(935\) 60.0000 1.96221
\(936\) 3.00000 0.0980581
\(937\) −21.0000 −0.686040 −0.343020 0.939328i \(-0.611450\pi\)
−0.343020 + 0.939328i \(0.611450\pi\)
\(938\) 7.00000 0.228558
\(939\) 12.0000 0.391605
\(940\) 12.0000 0.391397
\(941\) −6.00000 −0.195594 −0.0977972 0.995206i \(-0.531180\pi\)
−0.0977972 + 0.995206i \(0.531180\pi\)
\(942\) −8.00000 −0.260654
\(943\) −45.0000 −1.46540
\(944\) −9.00000 −0.292925
\(945\) −12.0000 −0.390360
\(946\) −40.0000 −1.30051
\(947\) −41.0000 −1.33232 −0.666160 0.745808i \(-0.732063\pi\)
−0.666160 + 0.745808i \(0.732063\pi\)
\(948\) 6.00000 0.194871
\(949\) −11.0000 −0.357075
\(950\) 16.0000 0.519109
\(951\) 60.0000 1.94563
\(952\) 12.0000 0.388922
\(953\) 14.0000 0.453504 0.226752 0.973952i \(-0.427189\pi\)
0.226752 + 0.973952i \(0.427189\pi\)
\(954\) −6.00000 −0.194257
\(955\) −9.00000 −0.291233
\(956\) −2.00000 −0.0646846
\(957\) −60.0000 −1.93952
\(958\) −14.0000 −0.452319
\(959\) 9.00000 0.290625
\(960\) 42.0000 1.35554
\(961\) −31.0000 −1.00000
\(962\) −8.00000 −0.257930
\(963\) −2.00000 −0.0644491
\(964\) 3.00000 0.0966235
\(965\) 24.0000 0.772587
\(966\) −18.0000 −0.579141
\(967\) 14.0000 0.450210 0.225105 0.974335i \(-0.427728\pi\)
0.225105 + 0.974335i \(0.427728\pi\)
\(968\) 42.0000 1.34993
\(969\) 32.0000 1.02799
\(970\) −42.0000 −1.34854
\(971\) −6.00000 −0.192549 −0.0962746 0.995355i \(-0.530693\pi\)
−0.0962746 + 0.995355i \(0.530693\pi\)
\(972\) −10.0000 −0.320750
\(973\) −11.0000 −0.352644
\(974\) 12.0000 0.384505
\(975\) −8.00000 −0.256205
\(976\) 1.00000 0.0320092
\(977\) −18.0000 −0.575871 −0.287936 0.957650i \(-0.592969\pi\)
−0.287936 + 0.957650i \(0.592969\pi\)
\(978\) 36.0000 1.15115
\(979\) 20.0000 0.639203
\(980\) −18.0000 −0.574989
\(981\) −17.0000 −0.542768
\(982\) 28.0000 0.893516
\(983\) −36.0000 −1.14822 −0.574111 0.818778i \(-0.694652\pi\)
−0.574111 + 0.818778i \(0.694652\pi\)
\(984\) −30.0000 −0.956365
\(985\) 9.00000 0.286764
\(986\) 24.0000 0.764316
\(987\) −8.00000 −0.254643
\(988\) 4.00000 0.127257
\(989\) 72.0000 2.28947
\(990\) −15.0000 −0.476731
\(991\) −48.0000 −1.52477 −0.762385 0.647124i \(-0.775972\pi\)
−0.762385 + 0.647124i \(0.775972\pi\)
\(992\) 0 0
\(993\) 34.0000 1.07896
\(994\) 8.00000 0.253745
\(995\) −18.0000 −0.570638
\(996\) 8.00000 0.253490
\(997\) −56.0000 −1.77354 −0.886769 0.462213i \(-0.847056\pi\)
−0.886769 + 0.462213i \(0.847056\pi\)
\(998\) −13.0000 −0.411508
\(999\) 32.0000 1.01244
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 \(a_p\))