Properties

Label 8033.2.a.a.1.1
Level 8033
Weight 2
Character 8033.1
Self dual Yes
Analytic conductor 64.144
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8033 = 29 \cdot 277 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8033.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.1438279437\)
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 \(\chi\) = 8033.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.00000 q^{3} -1.00000 q^{4} -3.00000 q^{5} +1.00000 q^{6} +2.00000 q^{7} -3.00000 q^{8} -2.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +1.00000 q^{3} -1.00000 q^{4} -3.00000 q^{5} +1.00000 q^{6} +2.00000 q^{7} -3.00000 q^{8} -2.00000 q^{9} -3.00000 q^{10} -3.00000 q^{11} -1.00000 q^{12} +1.00000 q^{13} +2.00000 q^{14} -3.00000 q^{15} -1.00000 q^{16} -2.00000 q^{17} -2.00000 q^{18} -4.00000 q^{19} +3.00000 q^{20} +2.00000 q^{21} -3.00000 q^{22} -4.00000 q^{23} -3.00000 q^{24} +4.00000 q^{25} +1.00000 q^{26} -5.00000 q^{27} -2.00000 q^{28} +1.00000 q^{29} -3.00000 q^{30} -9.00000 q^{31} +5.00000 q^{32} -3.00000 q^{33} -2.00000 q^{34} -6.00000 q^{35} +2.00000 q^{36} +8.00000 q^{37} -4.00000 q^{38} +1.00000 q^{39} +9.00000 q^{40} -6.00000 q^{41} +2.00000 q^{42} +13.0000 q^{43} +3.00000 q^{44} +6.00000 q^{45} -4.00000 q^{46} -7.00000 q^{47} -1.00000 q^{48} -3.00000 q^{49} +4.00000 q^{50} -2.00000 q^{51} -1.00000 q^{52} +9.00000 q^{53} -5.00000 q^{54} +9.00000 q^{55} -6.00000 q^{56} -4.00000 q^{57} +1.00000 q^{58} +3.00000 q^{60} +4.00000 q^{61} -9.00000 q^{62} -4.00000 q^{63} +7.00000 q^{64} -3.00000 q^{65} -3.00000 q^{66} +2.00000 q^{67} +2.00000 q^{68} -4.00000 q^{69} -6.00000 q^{70} -12.0000 q^{71} +6.00000 q^{72} +14.0000 q^{73} +8.00000 q^{74} +4.00000 q^{75} +4.00000 q^{76} -6.00000 q^{77} +1.00000 q^{78} +3.00000 q^{79} +3.00000 q^{80} +1.00000 q^{81} -6.00000 q^{82} +10.0000 q^{83} -2.00000 q^{84} +6.00000 q^{85} +13.0000 q^{86} +1.00000 q^{87} +9.00000 q^{88} -12.0000 q^{89} +6.00000 q^{90} +2.00000 q^{91} +4.00000 q^{92} -9.00000 q^{93} -7.00000 q^{94} +12.0000 q^{95} +5.00000 q^{96} +14.0000 q^{97} -3.00000 q^{98} +6.00000 q^{99} +O(q^{100})\)

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 0.288675 0.957427i \(-0.406785\pi\)
0.288675 + 0.957427i \(0.406785\pi\)
\(4\) −1.00000 −0.500000
\(5\) −3.00000 −1.34164 −0.670820 0.741620i \(-0.734058\pi\)
−0.670820 + 0.741620i \(0.734058\pi\)
\(6\) 1.00000 0.408248
\(7\) 2.00000 0.755929 0.377964 0.925820i \(-0.376624\pi\)
0.377964 + 0.925820i \(0.376624\pi\)
\(8\) −3.00000 −1.06066
\(9\) −2.00000 −0.666667
\(10\) −3.00000 −0.948683
\(11\) −3.00000 −0.904534 −0.452267 0.891883i \(-0.649385\pi\)
−0.452267 + 0.891883i \(0.649385\pi\)
\(12\) −1.00000 −0.288675
\(13\) 1.00000 0.277350 0.138675 0.990338i \(-0.455716\pi\)
0.138675 + 0.990338i \(0.455716\pi\)
\(14\) 2.00000 0.534522
\(15\) −3.00000 −0.774597
\(16\) −1.00000 −0.250000
\(17\) −2.00000 −0.485071 −0.242536 0.970143i \(-0.577979\pi\)
−0.242536 + 0.970143i \(0.577979\pi\)
\(18\) −2.00000 −0.471405
\(19\) −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
\(22\) −3.00000 −0.639602
\(23\) −4.00000 −0.834058 −0.417029 0.908893i \(-0.636929\pi\)
−0.417029 + 0.908893i \(0.636929\pi\)
\(24\) −3.00000 −0.612372
\(25\) 4.00000 0.800000
\(26\) 1.00000 0.196116
\(27\) −5.00000 −0.962250
\(28\) −2.00000 −0.377964
\(29\) 1.00000 0.185695
\(30\) −3.00000 −0.547723
\(31\) −9.00000 −1.61645 −0.808224 0.588875i \(-0.799571\pi\)
−0.808224 + 0.588875i \(0.799571\pi\)
\(32\) 5.00000 0.883883
\(33\) −3.00000 −0.522233
\(34\) −2.00000 −0.342997
\(35\) −6.00000 −1.01419
\(36\) 2.00000 0.333333
\(37\) 8.00000 1.31519 0.657596 0.753371i \(-0.271573\pi\)
0.657596 + 0.753371i \(0.271573\pi\)
\(38\) −4.00000 −0.648886
\(39\) 1.00000 0.160128
\(40\) 9.00000 1.42302
\(41\) −6.00000 −0.937043 −0.468521 0.883452i \(-0.655213\pi\)
−0.468521 + 0.883452i \(0.655213\pi\)
\(42\) 2.00000 0.308607
\(43\) 13.0000 1.98248 0.991241 0.132068i \(-0.0421616\pi\)
0.991241 + 0.132068i \(0.0421616\pi\)
\(44\) 3.00000 0.452267
\(45\) 6.00000 0.894427
\(46\) −4.00000 −0.589768
\(47\) −7.00000 −1.02105 −0.510527 0.859861i \(-0.670550\pi\)
−0.510527 + 0.859861i \(0.670550\pi\)
\(48\) −1.00000 −0.144338
\(49\) −3.00000 −0.428571
\(50\) 4.00000 0.565685
\(51\) −2.00000 −0.280056
\(52\) −1.00000 −0.138675
\(53\) 9.00000 1.23625 0.618123 0.786082i \(-0.287894\pi\)
0.618123 + 0.786082i \(0.287894\pi\)
\(54\) −5.00000 −0.680414
\(55\) 9.00000 1.21356
\(56\) −6.00000 −0.801784
\(57\) −4.00000 −0.529813
\(58\) 1.00000 0.131306
\(59\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) 3.00000 0.387298
\(61\) 4.00000 0.512148 0.256074 0.966657i \(-0.417571\pi\)
0.256074 + 0.966657i \(0.417571\pi\)
\(62\) −9.00000 −1.14300
\(63\) −4.00000 −0.503953
\(64\) 7.00000 0.875000
\(65\) −3.00000 −0.372104
\(66\) −3.00000 −0.369274
\(67\) 2.00000 0.244339 0.122169 0.992509i \(-0.461015\pi\)
0.122169 + 0.992509i \(0.461015\pi\)
\(68\) 2.00000 0.242536
\(69\) −4.00000 −0.481543
\(70\) −6.00000 −0.717137
\(71\) −12.0000 −1.42414 −0.712069 0.702109i \(-0.752242\pi\)
−0.712069 + 0.702109i \(0.752242\pi\)
\(72\) 6.00000 0.707107
\(73\) 14.0000 1.63858 0.819288 0.573382i \(-0.194369\pi\)
0.819288 + 0.573382i \(0.194369\pi\)
\(74\) 8.00000 0.929981
\(75\) 4.00000 0.461880
\(76\) 4.00000 0.458831
\(77\) −6.00000 −0.683763
\(78\) 1.00000 0.113228
\(79\) 3.00000 0.337526 0.168763 0.985657i \(-0.446023\pi\)
0.168763 + 0.985657i \(0.446023\pi\)
\(80\) 3.00000 0.335410
\(81\) 1.00000 0.111111
\(82\) −6.00000 −0.662589
\(83\) 10.0000 1.09764 0.548821 0.835940i \(-0.315077\pi\)
0.548821 + 0.835940i \(0.315077\pi\)
\(84\) −2.00000 −0.218218
\(85\) 6.00000 0.650791
\(86\) 13.0000 1.40183
\(87\) 1.00000 0.107211
\(88\) 9.00000 0.959403
\(89\) −12.0000 −1.27200 −0.635999 0.771690i \(-0.719412\pi\)
−0.635999 + 0.771690i \(0.719412\pi\)
\(90\) 6.00000 0.632456
\(91\) 2.00000 0.209657
\(92\) 4.00000 0.417029
\(93\) −9.00000 −0.933257
\(94\) −7.00000 −0.721995
\(95\) 12.0000 1.23117
\(96\) 5.00000 0.510310
\(97\) 14.0000 1.42148 0.710742 0.703452i \(-0.248359\pi\)
0.710742 + 0.703452i \(0.248359\pi\)
\(98\) −3.00000 −0.303046
\(99\) 6.00000 0.603023
\(100\) −4.00000 −0.400000
\(101\) 2.00000 0.199007 0.0995037 0.995037i \(-0.468274\pi\)
0.0995037 + 0.995037i \(0.468274\pi\)
\(102\) −2.00000 −0.198030
\(103\) −14.0000 −1.37946 −0.689730 0.724066i \(-0.742271\pi\)
−0.689730 + 0.724066i \(0.742271\pi\)
\(104\) −3.00000 −0.294174
\(105\) −6.00000 −0.585540
\(106\) 9.00000 0.874157
\(107\) −6.00000 −0.580042 −0.290021 0.957020i \(-0.593662\pi\)
−0.290021 + 0.957020i \(0.593662\pi\)
\(108\) 5.00000 0.481125
\(109\) 1.00000 0.0957826 0.0478913 0.998853i \(-0.484750\pi\)
0.0478913 + 0.998853i \(0.484750\pi\)
\(110\) 9.00000 0.858116
\(111\) 8.00000 0.759326
\(112\) −2.00000 −0.188982
\(113\) −4.00000 −0.376288 −0.188144 0.982141i \(-0.560247\pi\)
−0.188144 + 0.982141i \(0.560247\pi\)
\(114\) −4.00000 −0.374634
\(115\) 12.0000 1.11901
\(116\) −1.00000 −0.0928477
\(117\) −2.00000 −0.184900
\(118\) 0 0
\(119\) −4.00000 −0.366679
\(120\) 9.00000 0.821584
\(121\) −2.00000 −0.181818
\(122\) 4.00000 0.362143
\(123\) −6.00000 −0.541002
\(124\) 9.00000 0.808224
\(125\) 3.00000 0.268328
\(126\) −4.00000 −0.356348
\(127\) 8.00000 0.709885 0.354943 0.934888i \(-0.384500\pi\)
0.354943 + 0.934888i \(0.384500\pi\)
\(128\) −3.00000 −0.265165
\(129\) 13.0000 1.14459
\(130\) −3.00000 −0.263117
\(131\) 12.0000 1.04844 0.524222 0.851581i \(-0.324356\pi\)
0.524222 + 0.851581i \(0.324356\pi\)
\(132\) 3.00000 0.261116
\(133\) −8.00000 −0.693688
\(134\) 2.00000 0.172774
\(135\) 15.0000 1.29099
\(136\) 6.00000 0.514496
\(137\) −22.0000 −1.87959 −0.939793 0.341743i \(-0.888983\pi\)
−0.939793 + 0.341743i \(0.888983\pi\)
\(138\) −4.00000 −0.340503
\(139\) 2.00000 0.169638 0.0848189 0.996396i \(-0.472969\pi\)
0.0848189 + 0.996396i \(0.472969\pi\)
\(140\) 6.00000 0.507093
\(141\) −7.00000 −0.589506
\(142\) −12.0000 −1.00702
\(143\) −3.00000 −0.250873
\(144\) 2.00000 0.166667
\(145\) −3.00000 −0.249136
\(146\) 14.0000 1.15865
\(147\) −3.00000 −0.247436
\(148\) −8.00000 −0.657596
\(149\) −13.0000 −1.06500 −0.532501 0.846430i \(-0.678748\pi\)
−0.532501 + 0.846430i \(0.678748\pi\)
\(150\) 4.00000 0.326599
\(151\) 20.0000 1.62758 0.813788 0.581161i \(-0.197401\pi\)
0.813788 + 0.581161i \(0.197401\pi\)
\(152\) 12.0000 0.973329
\(153\) 4.00000 0.323381
\(154\) −6.00000 −0.483494
\(155\) 27.0000 2.16869
\(156\) −1.00000 −0.0800641
\(157\) 10.0000 0.798087 0.399043 0.916932i \(-0.369342\pi\)
0.399043 + 0.916932i \(0.369342\pi\)
\(158\) 3.00000 0.238667
\(159\) 9.00000 0.713746
\(160\) −15.0000 −1.18585
\(161\) −8.00000 −0.630488
\(162\) 1.00000 0.0785674
\(163\) −3.00000 −0.234978 −0.117489 0.993074i \(-0.537485\pi\)
−0.117489 + 0.993074i \(0.537485\pi\)
\(164\) 6.00000 0.468521
\(165\) 9.00000 0.700649
\(166\) 10.0000 0.776151
\(167\) 22.0000 1.70241 0.851206 0.524832i \(-0.175872\pi\)
0.851206 + 0.524832i \(0.175872\pi\)
\(168\) −6.00000 −0.462910
\(169\) −12.0000 −0.923077
\(170\) 6.00000 0.460179
\(171\) 8.00000 0.611775
\(172\) −13.0000 −0.991241
\(173\) −6.00000 −0.456172 −0.228086 0.973641i \(-0.573247\pi\)
−0.228086 + 0.973641i \(0.573247\pi\)
\(174\) 1.00000 0.0758098
\(175\) 8.00000 0.604743
\(176\) 3.00000 0.226134
\(177\) 0 0
\(178\) −12.0000 −0.899438
\(179\) 6.00000 0.448461 0.224231 0.974536i \(-0.428013\pi\)
0.224231 + 0.974536i \(0.428013\pi\)
\(180\) −6.00000 −0.447214
\(181\) −17.0000 −1.26360 −0.631800 0.775131i \(-0.717684\pi\)
−0.631800 + 0.775131i \(0.717684\pi\)
\(182\) 2.00000 0.148250
\(183\) 4.00000 0.295689
\(184\) 12.0000 0.884652
\(185\) −24.0000 −1.76452
\(186\) −9.00000 −0.659912
\(187\) 6.00000 0.438763
\(188\) 7.00000 0.510527
\(189\) −10.0000 −0.727393
\(190\) 12.0000 0.870572
\(191\) −24.0000 −1.73658 −0.868290 0.496058i \(-0.834780\pi\)
−0.868290 + 0.496058i \(0.834780\pi\)
\(192\) 7.00000 0.505181
\(193\) −10.0000 −0.719816 −0.359908 0.932988i \(-0.617192\pi\)
−0.359908 + 0.932988i \(0.617192\pi\)
\(194\) 14.0000 1.00514
\(195\) −3.00000 −0.214834
\(196\) 3.00000 0.214286
\(197\) 2.00000 0.142494 0.0712470 0.997459i \(-0.477302\pi\)
0.0712470 + 0.997459i \(0.477302\pi\)
\(198\) 6.00000 0.426401
\(199\) 22.0000 1.55954 0.779769 0.626067i \(-0.215336\pi\)
0.779769 + 0.626067i \(0.215336\pi\)
\(200\) −12.0000 −0.848528
\(201\) 2.00000 0.141069
\(202\) 2.00000 0.140720
\(203\) 2.00000 0.140372
\(204\) 2.00000 0.140028
\(205\) 18.0000 1.25717
\(206\) −14.0000 −0.975426
\(207\) 8.00000 0.556038
\(208\) −1.00000 −0.0693375
\(209\) 12.0000 0.830057
\(210\) −6.00000 −0.414039
\(211\) 15.0000 1.03264 0.516321 0.856395i \(-0.327301\pi\)
0.516321 + 0.856395i \(0.327301\pi\)
\(212\) −9.00000 −0.618123
\(213\) −12.0000 −0.822226
\(214\) −6.00000 −0.410152
\(215\) −39.0000 −2.65978
\(216\) 15.0000 1.02062
\(217\) −18.0000 −1.22192
\(218\) 1.00000 0.0677285
\(219\) 14.0000 0.946032
\(220\) −9.00000 −0.606780
\(221\) −2.00000 −0.134535
\(222\) 8.00000 0.536925
\(223\) 16.0000 1.07144 0.535720 0.844396i \(-0.320040\pi\)
0.535720 + 0.844396i \(0.320040\pi\)
\(224\) 10.0000 0.668153
\(225\) −8.00000 −0.533333
\(226\) −4.00000 −0.266076
\(227\) −10.0000 −0.663723 −0.331862 0.943328i \(-0.607677\pi\)
−0.331862 + 0.943328i \(0.607677\pi\)
\(228\) 4.00000 0.264906
\(229\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(230\) 12.0000 0.791257
\(231\) −6.00000 −0.394771
\(232\) −3.00000 −0.196960
\(233\) 5.00000 0.327561 0.163780 0.986497i \(-0.447631\pi\)
0.163780 + 0.986497i \(0.447631\pi\)
\(234\) −2.00000 −0.130744
\(235\) 21.0000 1.36989
\(236\) 0 0
\(237\) 3.00000 0.194871
\(238\) −4.00000 −0.259281
\(239\) 26.0000 1.68180 0.840900 0.541190i \(-0.182026\pi\)
0.840900 + 0.541190i \(0.182026\pi\)
\(240\) 3.00000 0.193649
\(241\) 1.00000 0.0644157 0.0322078 0.999481i \(-0.489746\pi\)
0.0322078 + 0.999481i \(0.489746\pi\)
\(242\) −2.00000 −0.128565
\(243\) 16.0000 1.02640
\(244\) −4.00000 −0.256074
\(245\) 9.00000 0.574989
\(246\) −6.00000 −0.382546
\(247\) −4.00000 −0.254514
\(248\) 27.0000 1.71450
\(249\) 10.0000 0.633724
\(250\) 3.00000 0.189737
\(251\) 19.0000 1.19927 0.599635 0.800274i \(-0.295313\pi\)
0.599635 + 0.800274i \(0.295313\pi\)
\(252\) 4.00000 0.251976
\(253\) 12.0000 0.754434
\(254\) 8.00000 0.501965
\(255\) 6.00000 0.375735
\(256\) −17.0000 −1.06250
\(257\) 19.0000 1.18519 0.592594 0.805502i \(-0.298104\pi\)
0.592594 + 0.805502i \(0.298104\pi\)
\(258\) 13.0000 0.809345
\(259\) 16.0000 0.994192
\(260\) 3.00000 0.186052
\(261\) −2.00000 −0.123797
\(262\) 12.0000 0.741362
\(263\) −21.0000 −1.29492 −0.647458 0.762101i \(-0.724168\pi\)
−0.647458 + 0.762101i \(0.724168\pi\)
\(264\) 9.00000 0.553912
\(265\) −27.0000 −1.65860
\(266\) −8.00000 −0.490511
\(267\) −12.0000 −0.734388
\(268\) −2.00000 −0.122169
\(269\) 20.0000 1.21942 0.609711 0.792624i \(-0.291286\pi\)
0.609711 + 0.792624i \(0.291286\pi\)
\(270\) 15.0000 0.912871
\(271\) −11.0000 −0.668202 −0.334101 0.942537i \(-0.608433\pi\)
−0.334101 + 0.942537i \(0.608433\pi\)
\(272\) 2.00000 0.121268
\(273\) 2.00000 0.121046
\(274\) −22.0000 −1.32907
\(275\) −12.0000 −0.723627
\(276\) 4.00000 0.240772
\(277\) −1.00000 −0.0600842
\(278\) 2.00000 0.119952
\(279\) 18.0000 1.07763
\(280\) 18.0000 1.07571
\(281\) 27.0000 1.61068 0.805342 0.592810i \(-0.201981\pi\)
0.805342 + 0.592810i \(0.201981\pi\)
\(282\) −7.00000 −0.416844
\(283\) 14.0000 0.832214 0.416107 0.909316i \(-0.363394\pi\)
0.416107 + 0.909316i \(0.363394\pi\)
\(284\) 12.0000 0.712069
\(285\) 12.0000 0.710819
\(286\) −3.00000 −0.177394
\(287\) −12.0000 −0.708338
\(288\) −10.0000 −0.589256
\(289\) −13.0000 −0.764706
\(290\) −3.00000 −0.176166
\(291\) 14.0000 0.820695
\(292\) −14.0000 −0.819288
\(293\) 8.00000 0.467365 0.233682 0.972313i \(-0.424922\pi\)
0.233682 + 0.972313i \(0.424922\pi\)
\(294\) −3.00000 −0.174964
\(295\) 0 0
\(296\) −24.0000 −1.39497
\(297\) 15.0000 0.870388
\(298\) −13.0000 −0.753070
\(299\) −4.00000 −0.231326
\(300\) −4.00000 −0.230940
\(301\) 26.0000 1.49862
\(302\) 20.0000 1.15087
\(303\) 2.00000 0.114897
\(304\) 4.00000 0.229416
\(305\) −12.0000 −0.687118
\(306\) 4.00000 0.228665
\(307\) −29.0000 −1.65512 −0.827559 0.561379i \(-0.810271\pi\)
−0.827559 + 0.561379i \(0.810271\pi\)
\(308\) 6.00000 0.341882
\(309\) −14.0000 −0.796432
\(310\) 27.0000 1.53350
\(311\) 12.0000 0.680458 0.340229 0.940343i \(-0.389495\pi\)
0.340229 + 0.940343i \(0.389495\pi\)
\(312\) −3.00000 −0.169842
\(313\) 13.0000 0.734803 0.367402 0.930062i \(-0.380247\pi\)
0.367402 + 0.930062i \(0.380247\pi\)
\(314\) 10.0000 0.564333
\(315\) 12.0000 0.676123
\(316\) −3.00000 −0.168763
\(317\) 18.0000 1.01098 0.505490 0.862832i \(-0.331312\pi\)
0.505490 + 0.862832i \(0.331312\pi\)
\(318\) 9.00000 0.504695
\(319\) −3.00000 −0.167968
\(320\) −21.0000 −1.17394
\(321\) −6.00000 −0.334887
\(322\) −8.00000 −0.445823
\(323\) 8.00000 0.445132
\(324\) −1.00000 −0.0555556
\(325\) 4.00000 0.221880
\(326\) −3.00000 −0.166155
\(327\) 1.00000 0.0553001
\(328\) 18.0000 0.993884
\(329\) −14.0000 −0.771845
\(330\) 9.00000 0.495434
\(331\) 1.00000 0.0549650 0.0274825 0.999622i \(-0.491251\pi\)
0.0274825 + 0.999622i \(0.491251\pi\)
\(332\) −10.0000 −0.548821
\(333\) −16.0000 −0.876795
\(334\) 22.0000 1.20379
\(335\) −6.00000 −0.327815
\(336\) −2.00000 −0.109109
\(337\) 14.0000 0.762629 0.381314 0.924445i \(-0.375472\pi\)
0.381314 + 0.924445i \(0.375472\pi\)
\(338\) −12.0000 −0.652714
\(339\) −4.00000 −0.217250
\(340\) −6.00000 −0.325396
\(341\) 27.0000 1.46213
\(342\) 8.00000 0.432590
\(343\) −20.0000 −1.07990
\(344\) −39.0000 −2.10274
\(345\) 12.0000 0.646058
\(346\) −6.00000 −0.322562
\(347\) 16.0000 0.858925 0.429463 0.903085i \(-0.358703\pi\)
0.429463 + 0.903085i \(0.358703\pi\)
\(348\) −1.00000 −0.0536056
\(349\) 5.00000 0.267644 0.133822 0.991005i \(-0.457275\pi\)
0.133822 + 0.991005i \(0.457275\pi\)
\(350\) 8.00000 0.427618
\(351\) −5.00000 −0.266880
\(352\) −15.0000 −0.799503
\(353\) 14.0000 0.745145 0.372572 0.928003i \(-0.378476\pi\)
0.372572 + 0.928003i \(0.378476\pi\)
\(354\) 0 0
\(355\) 36.0000 1.91068
\(356\) 12.0000 0.635999
\(357\) −4.00000 −0.211702
\(358\) 6.00000 0.317110
\(359\) 25.0000 1.31945 0.659725 0.751507i \(-0.270673\pi\)
0.659725 + 0.751507i \(0.270673\pi\)
\(360\) −18.0000 −0.948683
\(361\) −3.00000 −0.157895
\(362\) −17.0000 −0.893500
\(363\) −2.00000 −0.104973
\(364\) −2.00000 −0.104828
\(365\) −42.0000 −2.19838
\(366\) 4.00000 0.209083
\(367\) −16.0000 −0.835193 −0.417597 0.908633i \(-0.637127\pi\)
−0.417597 + 0.908633i \(0.637127\pi\)
\(368\) 4.00000 0.208514
\(369\) 12.0000 0.624695
\(370\) −24.0000 −1.24770
\(371\) 18.0000 0.934513
\(372\) 9.00000 0.466628
\(373\) −29.0000 −1.50156 −0.750782 0.660551i \(-0.770323\pi\)
−0.750782 + 0.660551i \(0.770323\pi\)
\(374\) 6.00000 0.310253
\(375\) 3.00000 0.154919
\(376\) 21.0000 1.08299
\(377\) 1.00000 0.0515026
\(378\) −10.0000 −0.514344
\(379\) 4.00000 0.205466 0.102733 0.994709i \(-0.467241\pi\)
0.102733 + 0.994709i \(0.467241\pi\)
\(380\) −12.0000 −0.615587
\(381\) 8.00000 0.409852
\(382\) −24.0000 −1.22795
\(383\) −20.0000 −1.02195 −0.510976 0.859595i \(-0.670716\pi\)
−0.510976 + 0.859595i \(0.670716\pi\)
\(384\) −3.00000 −0.153093
\(385\) 18.0000 0.917365
\(386\) −10.0000 −0.508987
\(387\) −26.0000 −1.32165
\(388\) −14.0000 −0.710742
\(389\) −18.0000 −0.912636 −0.456318 0.889817i \(-0.650832\pi\)
−0.456318 + 0.889817i \(0.650832\pi\)
\(390\) −3.00000 −0.151911
\(391\) 8.00000 0.404577
\(392\) 9.00000 0.454569
\(393\) 12.0000 0.605320
\(394\) 2.00000 0.100759
\(395\) −9.00000 −0.452839
\(396\) −6.00000 −0.301511
\(397\) −7.00000 −0.351320 −0.175660 0.984451i \(-0.556206\pi\)
−0.175660 + 0.984451i \(0.556206\pi\)
\(398\) 22.0000 1.10276
\(399\) −8.00000 −0.400501
\(400\) −4.00000 −0.200000
\(401\) 17.0000 0.848939 0.424470 0.905442i \(-0.360461\pi\)
0.424470 + 0.905442i \(0.360461\pi\)
\(402\) 2.00000 0.0997509
\(403\) −9.00000 −0.448322
\(404\) −2.00000 −0.0995037
\(405\) −3.00000 −0.149071
\(406\) 2.00000 0.0992583
\(407\) −24.0000 −1.18964
\(408\) 6.00000 0.297044
\(409\) −14.0000 −0.692255 −0.346128 0.938187i \(-0.612504\pi\)
−0.346128 + 0.938187i \(0.612504\pi\)
\(410\) 18.0000 0.888957
\(411\) −22.0000 −1.08518
\(412\) 14.0000 0.689730
\(413\) 0 0
\(414\) 8.00000 0.393179
\(415\) −30.0000 −1.47264
\(416\) 5.00000 0.245145
\(417\) 2.00000 0.0979404
\(418\) 12.0000 0.586939
\(419\) −34.0000 −1.66101 −0.830504 0.557012i \(-0.811948\pi\)
−0.830504 + 0.557012i \(0.811948\pi\)
\(420\) 6.00000 0.292770
\(421\) 34.0000 1.65706 0.828529 0.559946i \(-0.189178\pi\)
0.828529 + 0.559946i \(0.189178\pi\)
\(422\) 15.0000 0.730189
\(423\) 14.0000 0.680703
\(424\) −27.0000 −1.31124
\(425\) −8.00000 −0.388057
\(426\) −12.0000 −0.581402
\(427\) 8.00000 0.387147
\(428\) 6.00000 0.290021
\(429\) −3.00000 −0.144841
\(430\) −39.0000 −1.88075
\(431\) 12.0000 0.578020 0.289010 0.957326i \(-0.406674\pi\)
0.289010 + 0.957326i \(0.406674\pi\)
\(432\) 5.00000 0.240563
\(433\) 22.0000 1.05725 0.528626 0.848855i \(-0.322707\pi\)
0.528626 + 0.848855i \(0.322707\pi\)
\(434\) −18.0000 −0.864028
\(435\) −3.00000 −0.143839
\(436\) −1.00000 −0.0478913
\(437\) 16.0000 0.765384
\(438\) 14.0000 0.668946
\(439\) 4.00000 0.190910 0.0954548 0.995434i \(-0.469569\pi\)
0.0954548 + 0.995434i \(0.469569\pi\)
\(440\) −27.0000 −1.28717
\(441\) 6.00000 0.285714
\(442\) −2.00000 −0.0951303
\(443\) −36.0000 −1.71041 −0.855206 0.518289i \(-0.826569\pi\)
−0.855206 + 0.518289i \(0.826569\pi\)
\(444\) −8.00000 −0.379663
\(445\) 36.0000 1.70656
\(446\) 16.0000 0.757622
\(447\) −13.0000 −0.614879
\(448\) 14.0000 0.661438
\(449\) 6.00000 0.283158 0.141579 0.989927i \(-0.454782\pi\)
0.141579 + 0.989927i \(0.454782\pi\)
\(450\) −8.00000 −0.377124
\(451\) 18.0000 0.847587
\(452\) 4.00000 0.188144
\(453\) 20.0000 0.939682
\(454\) −10.0000 −0.469323
\(455\) −6.00000 −0.281284
\(456\) 12.0000 0.561951
\(457\) 18.0000 0.842004 0.421002 0.907060i \(-0.361678\pi\)
0.421002 + 0.907060i \(0.361678\pi\)
\(458\) 0 0
\(459\) 10.0000 0.466760
\(460\) −12.0000 −0.559503
\(461\) −28.0000 −1.30409 −0.652045 0.758180i \(-0.726089\pi\)
−0.652045 + 0.758180i \(0.726089\pi\)
\(462\) −6.00000 −0.279145
\(463\) −40.0000 −1.85896 −0.929479 0.368875i \(-0.879743\pi\)
−0.929479 + 0.368875i \(0.879743\pi\)
\(464\) −1.00000 −0.0464238
\(465\) 27.0000 1.25210
\(466\) 5.00000 0.231621
\(467\) 27.0000 1.24941 0.624705 0.780860i \(-0.285219\pi\)
0.624705 + 0.780860i \(0.285219\pi\)
\(468\) 2.00000 0.0924500
\(469\) 4.00000 0.184703
\(470\) 21.0000 0.968658
\(471\) 10.0000 0.460776
\(472\) 0 0
\(473\) −39.0000 −1.79322
\(474\) 3.00000 0.137795
\(475\) −16.0000 −0.734130
\(476\) 4.00000 0.183340
\(477\) −18.0000 −0.824163
\(478\) 26.0000 1.18921
\(479\) 3.00000 0.137073 0.0685367 0.997649i \(-0.478167\pi\)
0.0685367 + 0.997649i \(0.478167\pi\)
\(480\) −15.0000 −0.684653
\(481\) 8.00000 0.364769
\(482\) 1.00000 0.0455488
\(483\) −8.00000 −0.364013
\(484\) 2.00000 0.0909091
\(485\) −42.0000 −1.90712
\(486\) 16.0000 0.725775
\(487\) 28.0000 1.26880 0.634401 0.773004i \(-0.281247\pi\)
0.634401 + 0.773004i \(0.281247\pi\)
\(488\) −12.0000 −0.543214
\(489\) −3.00000 −0.135665
\(490\) 9.00000 0.406579
\(491\) 1.00000 0.0451294 0.0225647 0.999745i \(-0.492817\pi\)
0.0225647 + 0.999745i \(0.492817\pi\)
\(492\) 6.00000 0.270501
\(493\) −2.00000 −0.0900755
\(494\) −4.00000 −0.179969
\(495\) −18.0000 −0.809040
\(496\) 9.00000 0.404112
\(497\) −24.0000 −1.07655
\(498\) 10.0000 0.448111
\(499\) −34.0000 −1.52205 −0.761025 0.648723i \(-0.775303\pi\)
−0.761025 + 0.648723i \(0.775303\pi\)
\(500\) −3.00000 −0.134164
\(501\) 22.0000 0.982888
\(502\) 19.0000 0.848012
\(503\) −3.00000 −0.133763 −0.0668817 0.997761i \(-0.521305\pi\)
−0.0668817 + 0.997761i \(0.521305\pi\)
\(504\) 12.0000 0.534522
\(505\) −6.00000 −0.266996
\(506\) 12.0000 0.533465
\(507\) −12.0000 −0.532939
\(508\) −8.00000 −0.354943
\(509\) 45.0000 1.99459 0.997295 0.0735034i \(-0.0234180\pi\)
0.997295 + 0.0735034i \(0.0234180\pi\)
\(510\) 6.00000 0.265684
\(511\) 28.0000 1.23865
\(512\) −11.0000 −0.486136
\(513\) 20.0000 0.883022
\(514\) 19.0000 0.838054
\(515\) 42.0000 1.85074
\(516\) −13.0000 −0.572293
\(517\) 21.0000 0.923579
\(518\) 16.0000 0.703000
\(519\) −6.00000 −0.263371
\(520\) 9.00000 0.394676
\(521\) −39.0000 −1.70862 −0.854311 0.519763i \(-0.826020\pi\)
−0.854311 + 0.519763i \(0.826020\pi\)
\(522\) −2.00000 −0.0875376
\(523\) 14.0000 0.612177 0.306089 0.952003i \(-0.400980\pi\)
0.306089 + 0.952003i \(0.400980\pi\)
\(524\) −12.0000 −0.524222
\(525\) 8.00000 0.349149
\(526\) −21.0000 −0.915644
\(527\) 18.0000 0.784092
\(528\) 3.00000 0.130558
\(529\) −7.00000 −0.304348
\(530\) −27.0000 −1.17281
\(531\) 0 0
\(532\) 8.00000 0.346844
\(533\) −6.00000 −0.259889
\(534\) −12.0000 −0.519291
\(535\) 18.0000 0.778208
\(536\) −6.00000 −0.259161
\(537\) 6.00000 0.258919
\(538\) 20.0000 0.862261
\(539\) 9.00000 0.387657
\(540\) −15.0000 −0.645497
\(541\) −18.0000 −0.773880 −0.386940 0.922105i \(-0.626468\pi\)
−0.386940 + 0.922105i \(0.626468\pi\)
\(542\) −11.0000 −0.472490
\(543\) −17.0000 −0.729540
\(544\) −10.0000 −0.428746
\(545\) −3.00000 −0.128506
\(546\) 2.00000 0.0855921
\(547\) 18.0000 0.769624 0.384812 0.922995i \(-0.374266\pi\)
0.384812 + 0.922995i \(0.374266\pi\)
\(548\) 22.0000 0.939793
\(549\) −8.00000 −0.341432
\(550\) −12.0000 −0.511682
\(551\) −4.00000 −0.170406
\(552\) 12.0000 0.510754
\(553\) 6.00000 0.255146
\(554\) −1.00000 −0.0424859
\(555\) −24.0000 −1.01874
\(556\) −2.00000 −0.0848189
\(557\) −46.0000 −1.94908 −0.974541 0.224208i \(-0.928020\pi\)
−0.974541 + 0.224208i \(0.928020\pi\)
\(558\) 18.0000 0.762001
\(559\) 13.0000 0.549841
\(560\) 6.00000 0.253546
\(561\) 6.00000 0.253320
\(562\) 27.0000 1.13893
\(563\) −9.00000 −0.379305 −0.189652 0.981851i \(-0.560736\pi\)
−0.189652 + 0.981851i \(0.560736\pi\)
\(564\) 7.00000 0.294753
\(565\) 12.0000 0.504844
\(566\) 14.0000 0.588464
\(567\) 2.00000 0.0839921
\(568\) 36.0000 1.51053
\(569\) 22.0000 0.922288 0.461144 0.887325i \(-0.347439\pi\)
0.461144 + 0.887325i \(0.347439\pi\)
\(570\) 12.0000 0.502625
\(571\) −10.0000 −0.418487 −0.209243 0.977864i \(-0.567100\pi\)
−0.209243 + 0.977864i \(0.567100\pi\)
\(572\) 3.00000 0.125436
\(573\) −24.0000 −1.00261
\(574\) −12.0000 −0.500870
\(575\) −16.0000 −0.667246
\(576\) −14.0000 −0.583333
\(577\) −14.0000 −0.582828 −0.291414 0.956597i \(-0.594126\pi\)
−0.291414 + 0.956597i \(0.594126\pi\)
\(578\) −13.0000 −0.540729
\(579\) −10.0000 −0.415586
\(580\) 3.00000 0.124568
\(581\) 20.0000 0.829740
\(582\) 14.0000 0.580319
\(583\) −27.0000 −1.11823
\(584\) −42.0000 −1.73797
\(585\) 6.00000 0.248069
\(586\) 8.00000 0.330477
\(587\) 20.0000 0.825488 0.412744 0.910847i \(-0.364570\pi\)
0.412744 + 0.910847i \(0.364570\pi\)
\(588\) 3.00000 0.123718
\(589\) 36.0000 1.48335
\(590\) 0 0
\(591\) 2.00000 0.0822690
\(592\) −8.00000 −0.328798
\(593\) −9.00000 −0.369586 −0.184793 0.982777i \(-0.559161\pi\)
−0.184793 + 0.982777i \(0.559161\pi\)
\(594\) 15.0000 0.615457
\(595\) 12.0000 0.491952
\(596\) 13.0000 0.532501
\(597\) 22.0000 0.900400
\(598\) −4.00000 −0.163572
\(599\) −31.0000 −1.26663 −0.633313 0.773896i \(-0.718305\pi\)
−0.633313 + 0.773896i \(0.718305\pi\)
\(600\) −12.0000 −0.489898
\(601\) −12.0000 −0.489490 −0.244745 0.969587i \(-0.578704\pi\)
−0.244745 + 0.969587i \(0.578704\pi\)
\(602\) 26.0000 1.05968
\(603\) −4.00000 −0.162893
\(604\) −20.0000 −0.813788
\(605\) 6.00000 0.243935
\(606\) 2.00000 0.0812444
\(607\) 25.0000 1.01472 0.507359 0.861735i \(-0.330622\pi\)
0.507359 + 0.861735i \(0.330622\pi\)
\(608\) −20.0000 −0.811107
\(609\) 2.00000 0.0810441
\(610\) −12.0000 −0.485866
\(611\) −7.00000 −0.283190
\(612\) −4.00000 −0.161690
\(613\) −13.0000 −0.525065 −0.262533 0.964923i \(-0.584558\pi\)
−0.262533 + 0.964923i \(0.584558\pi\)
\(614\) −29.0000 −1.17034
\(615\) 18.0000 0.725830
\(616\) 18.0000 0.725241
\(617\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(618\) −14.0000 −0.563163
\(619\) 17.0000 0.683288 0.341644 0.939829i \(-0.389016\pi\)
0.341644 + 0.939829i \(0.389016\pi\)
\(620\) −27.0000 −1.08435
\(621\) 20.0000 0.802572
\(622\) 12.0000 0.481156
\(623\) −24.0000 −0.961540
\(624\) −1.00000 −0.0400320
\(625\) −29.0000 −1.16000
\(626\) 13.0000 0.519584
\(627\) 12.0000 0.479234
\(628\) −10.0000 −0.399043
\(629\) −16.0000 −0.637962
\(630\) 12.0000 0.478091
\(631\) −8.00000 −0.318475 −0.159237 0.987240i \(-0.550904\pi\)
−0.159237 + 0.987240i \(0.550904\pi\)
\(632\) −9.00000 −0.358001
\(633\) 15.0000 0.596196
\(634\) 18.0000 0.714871
\(635\) −24.0000 −0.952411
\(636\) −9.00000 −0.356873
\(637\) −3.00000 −0.118864
\(638\) −3.00000 −0.118771
\(639\) 24.0000 0.949425
\(640\) 9.00000 0.355756
\(641\) 20.0000 0.789953 0.394976 0.918691i \(-0.370753\pi\)
0.394976 + 0.918691i \(0.370753\pi\)
\(642\) −6.00000 −0.236801
\(643\) −2.00000 −0.0788723 −0.0394362 0.999222i \(-0.512556\pi\)
−0.0394362 + 0.999222i \(0.512556\pi\)
\(644\) 8.00000 0.315244
\(645\) −39.0000 −1.53562
\(646\) 8.00000 0.314756
\(647\) 40.0000 1.57256 0.786281 0.617869i \(-0.212004\pi\)
0.786281 + 0.617869i \(0.212004\pi\)
\(648\) −3.00000 −0.117851
\(649\) 0 0
\(650\) 4.00000 0.156893
\(651\) −18.0000 −0.705476
\(652\) 3.00000 0.117489
\(653\) −6.00000 −0.234798 −0.117399 0.993085i \(-0.537456\pi\)
−0.117399 + 0.993085i \(0.537456\pi\)
\(654\) 1.00000 0.0391031
\(655\) −36.0000 −1.40664
\(656\) 6.00000 0.234261
\(657\) −28.0000 −1.09238
\(658\) −14.0000 −0.545777
\(659\) 19.0000 0.740135 0.370067 0.929005i \(-0.379335\pi\)
0.370067 + 0.929005i \(0.379335\pi\)
\(660\) −9.00000 −0.350325
\(661\) −22.0000 −0.855701 −0.427850 0.903850i \(-0.640729\pi\)
−0.427850 + 0.903850i \(0.640729\pi\)
\(662\) 1.00000 0.0388661
\(663\) −2.00000 −0.0776736
\(664\) −30.0000 −1.16423
\(665\) 24.0000 0.930680
\(666\) −16.0000 −0.619987
\(667\) −4.00000 −0.154881
\(668\) −22.0000 −0.851206
\(669\) 16.0000 0.618596
\(670\) −6.00000 −0.231800
\(671\) −12.0000 −0.463255
\(672\) 10.0000 0.385758
\(673\) −1.00000 −0.0385472 −0.0192736 0.999814i \(-0.506135\pi\)
−0.0192736 + 0.999814i \(0.506135\pi\)
\(674\) 14.0000 0.539260
\(675\) −20.0000 −0.769800
\(676\) 12.0000 0.461538
\(677\) 30.0000 1.15299 0.576497 0.817099i \(-0.304419\pi\)
0.576497 + 0.817099i \(0.304419\pi\)
\(678\) −4.00000 −0.153619
\(679\) 28.0000 1.07454
\(680\) −18.0000 −0.690268
\(681\) −10.0000 −0.383201
\(682\) 27.0000 1.03388
\(683\) −12.0000 −0.459167 −0.229584 0.973289i \(-0.573736\pi\)
−0.229584 + 0.973289i \(0.573736\pi\)
\(684\) −8.00000 −0.305888
\(685\) 66.0000 2.52173
\(686\) −20.0000 −0.763604
\(687\) 0 0
\(688\) −13.0000 −0.495620
\(689\) 9.00000 0.342873
\(690\) 12.0000 0.456832
\(691\) 20.0000 0.760836 0.380418 0.924815i \(-0.375780\pi\)
0.380418 + 0.924815i \(0.375780\pi\)
\(692\) 6.00000 0.228086
\(693\) 12.0000 0.455842
\(694\) 16.0000 0.607352
\(695\) −6.00000 −0.227593
\(696\) −3.00000 −0.113715
\(697\) 12.0000 0.454532
\(698\) 5.00000 0.189253
\(699\) 5.00000 0.189117
\(700\) −8.00000 −0.302372
\(701\) −15.0000 −0.566542 −0.283271 0.959040i \(-0.591420\pi\)
−0.283271 + 0.959040i \(0.591420\pi\)
\(702\) −5.00000 −0.188713
\(703\) −32.0000 −1.20690
\(704\) −21.0000 −0.791467
\(705\) 21.0000 0.790906
\(706\) 14.0000 0.526897
\(707\) 4.00000 0.150435
\(708\) 0 0
\(709\) −23.0000 −0.863783 −0.431892 0.901926i \(-0.642154\pi\)
−0.431892 + 0.901926i \(0.642154\pi\)
\(710\) 36.0000 1.35106
\(711\) −6.00000 −0.225018
\(712\) 36.0000 1.34916
\(713\) 36.0000 1.34821
\(714\) −4.00000 −0.149696
\(715\) 9.00000 0.336581
\(716\) −6.00000 −0.224231
\(717\) 26.0000 0.970988
\(718\) 25.0000 0.932992
\(719\) 6.00000 0.223762 0.111881 0.993722i \(-0.464312\pi\)
0.111881 + 0.993722i \(0.464312\pi\)
\(720\) −6.00000 −0.223607
\(721\) −28.0000 −1.04277
\(722\) −3.00000 −0.111648
\(723\) 1.00000 0.0371904
\(724\) 17.0000 0.631800
\(725\) 4.00000 0.148556
\(726\) −2.00000 −0.0742270
\(727\) −20.0000 −0.741759 −0.370879 0.928681i \(-0.620944\pi\)
−0.370879 + 0.928681i \(0.620944\pi\)
\(728\) −6.00000 −0.222375
\(729\) 13.0000 0.481481
\(730\) −42.0000 −1.55449
\(731\) −26.0000 −0.961645
\(732\) −4.00000 −0.147844
\(733\) 10.0000 0.369358 0.184679 0.982799i \(-0.440875\pi\)
0.184679 + 0.982799i \(0.440875\pi\)
\(734\) −16.0000 −0.590571
\(735\) 9.00000 0.331970
\(736\) −20.0000 −0.737210
\(737\) −6.00000 −0.221013
\(738\) 12.0000 0.441726
\(739\) 25.0000 0.919640 0.459820 0.888012i \(-0.347914\pi\)
0.459820 + 0.888012i \(0.347914\pi\)
\(740\) 24.0000 0.882258
\(741\) −4.00000 −0.146944
\(742\) 18.0000 0.660801
\(743\) −48.0000 −1.76095 −0.880475 0.474093i \(-0.842776\pi\)
−0.880475 + 0.474093i \(0.842776\pi\)
\(744\) 27.0000 0.989868
\(745\) 39.0000 1.42885
\(746\) −29.0000 −1.06177
\(747\) −20.0000 −0.731762
\(748\) −6.00000 −0.219382
\(749\) −12.0000 −0.438470
\(750\) 3.00000 0.109545
\(751\) 20.0000 0.729810 0.364905 0.931045i \(-0.381101\pi\)
0.364905 + 0.931045i \(0.381101\pi\)
\(752\) 7.00000 0.255264
\(753\) 19.0000 0.692398
\(754\) 1.00000 0.0364179
\(755\) −60.0000 −2.18362
\(756\) 10.0000 0.363696
\(757\) −6.00000 −0.218074 −0.109037 0.994038i \(-0.534777\pi\)
−0.109037 + 0.994038i \(0.534777\pi\)
\(758\) 4.00000 0.145287
\(759\) 12.0000 0.435572
\(760\) −36.0000 −1.30586
\(761\) −54.0000 −1.95750 −0.978749 0.205061i \(-0.934261\pi\)
−0.978749 + 0.205061i \(0.934261\pi\)
\(762\) 8.00000 0.289809
\(763\) 2.00000 0.0724049
\(764\) 24.0000 0.868290
\(765\) −12.0000 −0.433861
\(766\) −20.0000 −0.722629
\(767\) 0 0
\(768\) −17.0000 −0.613435
\(769\) −8.00000 −0.288487 −0.144244 0.989542i \(-0.546075\pi\)
−0.144244 + 0.989542i \(0.546075\pi\)
\(770\) 18.0000 0.648675
\(771\) 19.0000 0.684268
\(772\) 10.0000 0.359908
\(773\) −24.0000 −0.863220 −0.431610 0.902060i \(-0.642054\pi\)
−0.431610 + 0.902060i \(0.642054\pi\)
\(774\) −26.0000 −0.934551
\(775\) −36.0000 −1.29316
\(776\) −42.0000 −1.50771
\(777\) 16.0000 0.573997
\(778\) −18.0000 −0.645331
\(779\) 24.0000 0.859889
\(780\) 3.00000 0.107417
\(781\) 36.0000 1.28818
\(782\) 8.00000 0.286079
\(783\) −5.00000 −0.178685
\(784\) 3.00000 0.107143
\(785\) −30.0000 −1.07075
\(786\) 12.0000 0.428026
\(787\) 46.0000 1.63972 0.819861 0.572562i \(-0.194050\pi\)
0.819861 + 0.572562i \(0.194050\pi\)
\(788\) −2.00000 −0.0712470
\(789\) −21.0000 −0.747620
\(790\) −9.00000 −0.320206
\(791\) −8.00000 −0.284447
\(792\) −18.0000 −0.639602
\(793\) 4.00000 0.142044
\(794\) −7.00000 −0.248421
\(795\) −27.0000 −0.957591
\(796\) −22.0000 −0.779769
\(797\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(798\) −8.00000 −0.283197
\(799\) 14.0000 0.495284
\(800\) 20.0000 0.707107
\(801\) 24.0000 0.847998
\(802\) 17.0000 0.600291
\(803\) −42.0000 −1.48215
\(804\) −2.00000 −0.0705346
\(805\) 24.0000 0.845889
\(806\) −9.00000 −0.317011
\(807\) 20.0000 0.704033
\(808\) −6.00000 −0.211079
\(809\) −52.0000 −1.82822 −0.914111 0.405463i \(-0.867110\pi\)
−0.914111 + 0.405463i \(0.867110\pi\)
\(810\) −3.00000 −0.105409
\(811\) −40.0000 −1.40459 −0.702295 0.711886i \(-0.747841\pi\)
−0.702295 + 0.711886i \(0.747841\pi\)
\(812\) −2.00000 −0.0701862
\(813\) −11.0000 −0.385787
\(814\) −24.0000 −0.841200
\(815\) 9.00000 0.315256
\(816\) 2.00000 0.0700140
\(817\) −52.0000 −1.81925
\(818\) −14.0000 −0.489499
\(819\) −4.00000 −0.139771
\(820\) −18.0000 −0.628587
\(821\) 21.0000 0.732905 0.366453 0.930437i \(-0.380572\pi\)
0.366453 + 0.930437i \(0.380572\pi\)
\(822\) −22.0000 −0.767338
\(823\) 16.0000 0.557725 0.278862 0.960331i \(-0.410043\pi\)
0.278862 + 0.960331i \(0.410043\pi\)
\(824\) 42.0000 1.46314
\(825\) −12.0000 −0.417786
\(826\) 0 0
\(827\) 31.0000 1.07798 0.538988 0.842314i \(-0.318807\pi\)
0.538988 + 0.842314i \(0.318807\pi\)
\(828\) −8.00000 −0.278019
\(829\) −30.0000 −1.04194 −0.520972 0.853574i \(-0.674430\pi\)
−0.520972 + 0.853574i \(0.674430\pi\)
\(830\) −30.0000 −1.04132
\(831\) −1.00000 −0.0346896
\(832\) 7.00000 0.242681
\(833\) 6.00000 0.207888
\(834\) 2.00000 0.0692543
\(835\) −66.0000 −2.28402
\(836\) −12.0000 −0.415029
\(837\) 45.0000 1.55543
\(838\) −34.0000 −1.17451
\(839\) −21.0000 −0.725001 −0.362500 0.931984i \(-0.618077\pi\)
−0.362500 + 0.931984i \(0.618077\pi\)
\(840\) 18.0000 0.621059
\(841\) 1.00000 0.0344828
\(842\) 34.0000 1.17172
\(843\) 27.0000 0.929929
\(844\) −15.0000 −0.516321
\(845\) 36.0000 1.23844
\(846\) 14.0000 0.481330
\(847\) −4.00000 −0.137442
\(848\) −9.00000 −0.309061
\(849\) 14.0000 0.480479
\(850\) −8.00000 −0.274398
\(851\) −32.0000 −1.09695
\(852\) 12.0000 0.411113
\(853\) −34.0000 −1.16414 −0.582069 0.813139i \(-0.697757\pi\)
−0.582069 + 0.813139i \(0.697757\pi\)
\(854\) 8.00000 0.273754
\(855\) −24.0000 −0.820783
\(856\) 18.0000 0.615227
\(857\) 7.00000 0.239115 0.119558 0.992827i \(-0.461852\pi\)
0.119558 + 0.992827i \(0.461852\pi\)
\(858\) −3.00000 −0.102418
\(859\) 49.0000 1.67186 0.835929 0.548837i \(-0.184929\pi\)
0.835929 + 0.548837i \(0.184929\pi\)
\(860\) 39.0000 1.32989
\(861\) −12.0000 −0.408959
\(862\) 12.0000 0.408722
\(863\) 20.0000 0.680808 0.340404 0.940279i \(-0.389436\pi\)
0.340404 + 0.940279i \(0.389436\pi\)
\(864\) −25.0000 −0.850517
\(865\) 18.0000 0.612018
\(866\) 22.0000 0.747590
\(867\) −13.0000 −0.441503
\(868\) 18.0000 0.610960
\(869\) −9.00000 −0.305304
\(870\) −3.00000 −0.101710
\(871\) 2.00000 0.0677674
\(872\) −3.00000 −0.101593
\(873\) −28.0000 −0.947656
\(874\) 16.0000 0.541208
\(875\) 6.00000 0.202837
\(876\) −14.0000 −0.473016
\(877\) −11.0000 −0.371444 −0.185722 0.982602i \(-0.559462\pi\)
−0.185722 + 0.982602i \(0.559462\pi\)
\(878\) 4.00000 0.134993
\(879\) 8.00000 0.269833
\(880\) −9.00000 −0.303390
\(881\) −38.0000 −1.28025 −0.640126 0.768270i \(-0.721118\pi\)
−0.640126 + 0.768270i \(0.721118\pi\)
\(882\) 6.00000 0.202031
\(883\) 44.0000 1.48072 0.740359 0.672212i \(-0.234656\pi\)
0.740359 + 0.672212i \(0.234656\pi\)
\(884\) 2.00000 0.0672673
\(885\) 0 0
\(886\) −36.0000 −1.20944
\(887\) 55.0000 1.84672 0.923360 0.383936i \(-0.125432\pi\)
0.923360 + 0.383936i \(0.125432\pi\)
\(888\) −24.0000 −0.805387
\(889\) 16.0000 0.536623
\(890\) 36.0000 1.20672
\(891\) −3.00000 −0.100504
\(892\) −16.0000 −0.535720
\(893\) 28.0000 0.936984
\(894\) −13.0000 −0.434785
\(895\) −18.0000 −0.601674
\(896\) −6.00000 −0.200446
\(897\) −4.00000 −0.133556
\(898\) 6.00000 0.200223
\(899\) −9.00000 −0.300167
\(900\) 8.00000 0.266667
\(901\) −18.0000 −0.599667
\(902\) 18.0000 0.599334
\(903\) 26.0000 0.865226
\(904\) 12.0000 0.399114
\(905\) 51.0000 1.69530
\(906\) 20.0000 0.664455
\(907\) 44.0000 1.46100 0.730498 0.682915i \(-0.239288\pi\)
0.730498 + 0.682915i \(0.239288\pi\)
\(908\) 10.0000 0.331862
\(909\) −4.00000 −0.132672
\(910\) −6.00000 −0.198898
\(911\) 5.00000 0.165657 0.0828287 0.996564i \(-0.473605\pi\)
0.0828287 + 0.996564i \(0.473605\pi\)
\(912\) 4.00000 0.132453
\(913\) −30.0000 −0.992855
\(914\) 18.0000 0.595387
\(915\) −12.0000 −0.396708
\(916\) 0 0
\(917\) 24.0000 0.792550
\(918\) 10.0000 0.330049
\(919\) −56.0000 −1.84727 −0.923635 0.383274i \(-0.874797\pi\)
−0.923635 + 0.383274i \(0.874797\pi\)
\(920\) −36.0000 −1.18688
\(921\) −29.0000 −0.955582
\(922\) −28.0000 −0.922131
\(923\) −12.0000 −0.394985
\(924\) 6.00000 0.197386
\(925\) 32.0000 1.05215
\(926\) −40.0000 −1.31448
\(927\) 28.0000 0.919641
\(928\) 5.00000 0.164133
\(929\) −18.0000 −0.590561 −0.295280 0.955411i \(-0.595413\pi\)
−0.295280 + 0.955411i \(0.595413\pi\)
\(930\) 27.0000 0.885365
\(931\) 12.0000 0.393284
\(932\) −5.00000 −0.163780
\(933\) 12.0000 0.392862
\(934\) 27.0000 0.883467
\(935\) −18.0000 −0.588663
\(936\) 6.00000 0.196116
\(937\) 26.0000 0.849383 0.424691 0.905338i \(-0.360383\pi\)
0.424691 + 0.905338i \(0.360383\pi\)
\(938\) 4.00000 0.130605
\(939\) 13.0000 0.424239
\(940\) −21.0000 −0.684944
\(941\) −3.00000 −0.0977972 −0.0488986 0.998804i \(-0.515571\pi\)
−0.0488986 + 0.998804i \(0.515571\pi\)
\(942\) 10.0000 0.325818
\(943\) 24.0000 0.781548
\(944\) 0 0
\(945\) 30.0000 0.975900
\(946\) −39.0000 −1.26800
\(947\) −21.0000 −0.682408 −0.341204 0.939989i \(-0.610835\pi\)
−0.341204 + 0.939989i \(0.610835\pi\)
\(948\) −3.00000 −0.0974355
\(949\) 14.0000 0.454459
\(950\) −16.0000 −0.519109
\(951\) 18.0000 0.583690
\(952\) 12.0000 0.388922
\(953\) −49.0000 −1.58727 −0.793633 0.608397i \(-0.791813\pi\)
−0.793633 + 0.608397i \(0.791813\pi\)
\(954\) −18.0000 −0.582772
\(955\) 72.0000 2.32987
\(956\) −26.0000 −0.840900
\(957\) −3.00000 −0.0969762
\(958\) 3.00000 0.0969256
\(959\) −44.0000 −1.42083
\(960\) −21.0000 −0.677772
\(961\) 50.0000 1.61290
\(962\) 8.00000 0.257930
\(963\) 12.0000 0.386695
\(964\) −1.00000 −0.0322078
\(965\) 30.0000 0.965734
\(966\) −8.00000 −0.257396
\(967\) −39.0000 −1.25416 −0.627078 0.778957i \(-0.715749\pi\)
−0.627078 + 0.778957i \(0.715749\pi\)
\(968\) 6.00000 0.192847
\(969\) 8.00000 0.256997
\(970\) −42.0000 −1.34854
\(971\) −28.0000 −0.898563 −0.449281 0.893390i \(-0.648320\pi\)
−0.449281 + 0.893390i \(0.648320\pi\)
\(972\) −16.0000 −0.513200
\(973\) 4.00000 0.128234
\(974\) 28.0000 0.897178
\(975\) 4.00000 0.128103
\(976\) −4.00000 −0.128037
\(977\) 41.0000 1.31171 0.655853 0.754889i \(-0.272309\pi\)
0.655853 + 0.754889i \(0.272309\pi\)
\(978\) −3.00000 −0.0959294
\(979\) 36.0000 1.15056
\(980\) −9.00000 −0.287494
\(981\) −2.00000 −0.0638551
\(982\) 1.00000 0.0319113
\(983\) −49.0000 −1.56286 −0.781429 0.623995i \(-0.785509\pi\)
−0.781429 + 0.623995i \(0.785509\pi\)
\(984\) 18.0000 0.573819
\(985\) −6.00000 −0.191176
\(986\) −2.00000 −0.0636930
\(987\) −14.0000 −0.445625
\(988\) 4.00000 0.127257
\(989\) −52.0000 −1.65350
\(990\) −18.0000 −0.572078
\(991\) 24.0000 0.762385 0.381193 0.924496i \(-0.375513\pi\)
0.381193 + 0.924496i \(0.375513\pi\)
\(992\) −45.0000 −1.42875
\(993\) 1.00000 0.0317340
\(994\) −24.0000 −0.761234
\(995\) −66.0000 −2.09234
\(996\) −10.0000 −0.316862
\(997\) 26.0000 0.823428 0.411714 0.911313i \(-0.364930\pi\)
0.411714 + 0.911313i \(0.364930\pi\)
\(998\) −34.0000 −1.07625
\(999\) −40.0000 −1.26554
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 \(a_p\))