Properties

Label 57.2.a.a.1.1
Level 57
Weight 2
Character 57.1
Self dual Yes
Analytic conductor 0.455
Analytic rank 1
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 57 = 3 \cdot 19 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 57.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(0.455147291521\)
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 \(\chi\) = 57.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.00000 q^{2} -1.00000 q^{3} +2.00000 q^{4} -3.00000 q^{5} +2.00000 q^{6} -5.00000 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q-2.00000 q^{2} -1.00000 q^{3} +2.00000 q^{4} -3.00000 q^{5} +2.00000 q^{6} -5.00000 q^{7} +1.00000 q^{9} +6.00000 q^{10} +1.00000 q^{11} -2.00000 q^{12} +2.00000 q^{13} +10.0000 q^{14} +3.00000 q^{15} -4.00000 q^{16} -1.00000 q^{17} -2.00000 q^{18} -1.00000 q^{19} -6.00000 q^{20} +5.00000 q^{21} -2.00000 q^{22} -4.00000 q^{23} +4.00000 q^{25} -4.00000 q^{26} -1.00000 q^{27} -10.0000 q^{28} -2.00000 q^{29} -6.00000 q^{30} -6.00000 q^{31} +8.00000 q^{32} -1.00000 q^{33} +2.00000 q^{34} +15.0000 q^{35} +2.00000 q^{36} +2.00000 q^{38} -2.00000 q^{39} -10.0000 q^{42} -1.00000 q^{43} +2.00000 q^{44} -3.00000 q^{45} +8.00000 q^{46} -9.00000 q^{47} +4.00000 q^{48} +18.0000 q^{49} -8.00000 q^{50} +1.00000 q^{51} +4.00000 q^{52} +10.0000 q^{53} +2.00000 q^{54} -3.00000 q^{55} +1.00000 q^{57} +4.00000 q^{58} -8.00000 q^{59} +6.00000 q^{60} -1.00000 q^{61} +12.0000 q^{62} -5.00000 q^{63} -8.00000 q^{64} -6.00000 q^{65} +2.00000 q^{66} +8.00000 q^{67} -2.00000 q^{68} +4.00000 q^{69} -30.0000 q^{70} -12.0000 q^{71} -11.0000 q^{73} -4.00000 q^{75} -2.00000 q^{76} -5.00000 q^{77} +4.00000 q^{78} +16.0000 q^{79} +12.0000 q^{80} +1.00000 q^{81} +12.0000 q^{83} +10.0000 q^{84} +3.00000 q^{85} +2.00000 q^{86} +2.00000 q^{87} -6.00000 q^{89} +6.00000 q^{90} -10.0000 q^{91} -8.00000 q^{92} +6.00000 q^{93} +18.0000 q^{94} +3.00000 q^{95} -8.00000 q^{96} -10.0000 q^{97} -36.0000 q^{98} +1.00000 q^{99} +O(q^{100})\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.00000 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(3\) −1.00000 −0.577350
\(4\) 2.00000 1.00000
\(5\) −3.00000 −1.34164 −0.670820 0.741620i \(-0.734058\pi\)
−0.670820 + 0.741620i \(0.734058\pi\)
\(6\) 2.00000 0.816497
\(7\) −5.00000 −1.88982 −0.944911 0.327327i \(-0.893852\pi\)
−0.944911 + 0.327327i \(0.893852\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 6.00000 1.89737
\(11\) 1.00000 0.301511 0.150756 0.988571i \(-0.451829\pi\)
0.150756 + 0.988571i \(0.451829\pi\)
\(12\) −2.00000 −0.577350
\(13\) 2.00000 0.554700 0.277350 0.960769i \(-0.410544\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) 10.0000 2.67261
\(15\) 3.00000 0.774597
\(16\) −4.00000 −1.00000
\(17\) −1.00000 −0.242536 −0.121268 0.992620i \(-0.538696\pi\)
−0.121268 + 0.992620i \(0.538696\pi\)
\(18\) −2.00000 −0.471405
\(19\) −1.00000 −0.229416
\(20\) −6.00000 −1.34164
\(21\) 5.00000 1.09109
\(22\) −2.00000 −0.426401
\(23\) −4.00000 −0.834058 −0.417029 0.908893i \(-0.636929\pi\)
−0.417029 + 0.908893i \(0.636929\pi\)
\(24\) 0 0
\(25\) 4.00000 0.800000
\(26\) −4.00000 −0.784465
\(27\) −1.00000 −0.192450
\(28\) −10.0000 −1.88982
\(29\) −2.00000 −0.371391 −0.185695 0.982607i \(-0.559454\pi\)
−0.185695 + 0.982607i \(0.559454\pi\)
\(30\) −6.00000 −1.09545
\(31\) −6.00000 −1.07763 −0.538816 0.842424i \(-0.681128\pi\)
−0.538816 + 0.842424i \(0.681128\pi\)
\(32\) 8.00000 1.41421
\(33\) −1.00000 −0.174078
\(34\) 2.00000 0.342997
\(35\) 15.0000 2.53546
\(36\) 2.00000 0.333333
\(37\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(38\) 2.00000 0.324443
\(39\) −2.00000 −0.320256
\(40\) 0 0
\(41\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) −10.0000 −1.54303
\(43\) −1.00000 −0.152499 −0.0762493 0.997089i \(-0.524294\pi\)
−0.0762493 + 0.997089i \(0.524294\pi\)
\(44\) 2.00000 0.301511
\(45\) −3.00000 −0.447214
\(46\) 8.00000 1.17954
\(47\) −9.00000 −1.31278 −0.656392 0.754420i \(-0.727918\pi\)
−0.656392 + 0.754420i \(0.727918\pi\)
\(48\) 4.00000 0.577350
\(49\) 18.0000 2.57143
\(50\) −8.00000 −1.13137
\(51\) 1.00000 0.140028
\(52\) 4.00000 0.554700
\(53\) 10.0000 1.37361 0.686803 0.726844i \(-0.259014\pi\)
0.686803 + 0.726844i \(0.259014\pi\)
\(54\) 2.00000 0.272166
\(55\) −3.00000 −0.404520
\(56\) 0 0
\(57\) 1.00000 0.132453
\(58\) 4.00000 0.525226
\(59\) −8.00000 −1.04151 −0.520756 0.853706i \(-0.674350\pi\)
−0.520756 + 0.853706i \(0.674350\pi\)
\(60\) 6.00000 0.774597
\(61\) −1.00000 −0.128037 −0.0640184 0.997949i \(-0.520392\pi\)
−0.0640184 + 0.997949i \(0.520392\pi\)
\(62\) 12.0000 1.52400
\(63\) −5.00000 −0.629941
\(64\) −8.00000 −1.00000
\(65\) −6.00000 −0.744208
\(66\) 2.00000 0.246183
\(67\) 8.00000 0.977356 0.488678 0.872464i \(-0.337479\pi\)
0.488678 + 0.872464i \(0.337479\pi\)
\(68\) −2.00000 −0.242536
\(69\) 4.00000 0.481543
\(70\) −30.0000 −3.58569
\(71\) −12.0000 −1.42414 −0.712069 0.702109i \(-0.752242\pi\)
−0.712069 + 0.702109i \(0.752242\pi\)
\(72\) 0 0
\(73\) −11.0000 −1.28745 −0.643726 0.765256i \(-0.722612\pi\)
−0.643726 + 0.765256i \(0.722612\pi\)
\(74\) 0 0
\(75\) −4.00000 −0.461880
\(76\) −2.00000 −0.229416
\(77\) −5.00000 −0.569803
\(78\) 4.00000 0.452911
\(79\) 16.0000 1.80014 0.900070 0.435745i \(-0.143515\pi\)
0.900070 + 0.435745i \(0.143515\pi\)
\(80\) 12.0000 1.34164
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 12.0000 1.31717 0.658586 0.752506i \(-0.271155\pi\)
0.658586 + 0.752506i \(0.271155\pi\)
\(84\) 10.0000 1.09109
\(85\) 3.00000 0.325396
\(86\) 2.00000 0.215666
\(87\) 2.00000 0.214423
\(88\) 0 0
\(89\) −6.00000 −0.635999 −0.317999 0.948091i \(-0.603011\pi\)
−0.317999 + 0.948091i \(0.603011\pi\)
\(90\) 6.00000 0.632456
\(91\) −10.0000 −1.04828
\(92\) −8.00000 −0.834058
\(93\) 6.00000 0.622171
\(94\) 18.0000 1.85656
\(95\) 3.00000 0.307794
\(96\) −8.00000 −0.816497
\(97\) −10.0000 −1.01535 −0.507673 0.861550i \(-0.669494\pi\)
−0.507673 + 0.861550i \(0.669494\pi\)
\(98\) −36.0000 −3.63655
\(99\) 1.00000 0.100504
\(100\) 8.00000 0.800000
\(101\) 2.00000 0.199007 0.0995037 0.995037i \(-0.468274\pi\)
0.0995037 + 0.995037i \(0.468274\pi\)
\(102\) −2.00000 −0.198030
\(103\) −2.00000 −0.197066 −0.0985329 0.995134i \(-0.531415\pi\)
−0.0985329 + 0.995134i \(0.531415\pi\)
\(104\) 0 0
\(105\) −15.0000 −1.46385
\(106\) −20.0000 −1.94257
\(107\) 6.00000 0.580042 0.290021 0.957020i \(-0.406338\pi\)
0.290021 + 0.957020i \(0.406338\pi\)
\(108\) −2.00000 −0.192450
\(109\) 4.00000 0.383131 0.191565 0.981480i \(-0.438644\pi\)
0.191565 + 0.981480i \(0.438644\pi\)
\(110\) 6.00000 0.572078
\(111\) 0 0
\(112\) 20.0000 1.88982
\(113\) 2.00000 0.188144 0.0940721 0.995565i \(-0.470012\pi\)
0.0940721 + 0.995565i \(0.470012\pi\)
\(114\) −2.00000 −0.187317
\(115\) 12.0000 1.11901
\(116\) −4.00000 −0.371391
\(117\) 2.00000 0.184900
\(118\) 16.0000 1.47292
\(119\) 5.00000 0.458349
\(120\) 0 0
\(121\) −10.0000 −0.909091
\(122\) 2.00000 0.181071
\(123\) 0 0
\(124\) −12.0000 −1.07763
\(125\) 3.00000 0.268328
\(126\) 10.0000 0.890871
\(127\) −2.00000 −0.177471 −0.0887357 0.996055i \(-0.528283\pi\)
−0.0887357 + 0.996055i \(0.528283\pi\)
\(128\) 0 0
\(129\) 1.00000 0.0880451
\(130\) 12.0000 1.05247
\(131\) 7.00000 0.611593 0.305796 0.952097i \(-0.401077\pi\)
0.305796 + 0.952097i \(0.401077\pi\)
\(132\) −2.00000 −0.174078
\(133\) 5.00000 0.433555
\(134\) −16.0000 −1.38219
\(135\) 3.00000 0.258199
\(136\) 0 0
\(137\) −9.00000 −0.768922 −0.384461 0.923141i \(-0.625613\pi\)
−0.384461 + 0.923141i \(0.625613\pi\)
\(138\) −8.00000 −0.681005
\(139\) −13.0000 −1.10265 −0.551323 0.834292i \(-0.685877\pi\)
−0.551323 + 0.834292i \(0.685877\pi\)
\(140\) 30.0000 2.53546
\(141\) 9.00000 0.757937
\(142\) 24.0000 2.01404
\(143\) 2.00000 0.167248
\(144\) −4.00000 −0.333333
\(145\) 6.00000 0.498273
\(146\) 22.0000 1.82073
\(147\) −18.0000 −1.48461
\(148\) 0 0
\(149\) −21.0000 −1.72039 −0.860194 0.509968i \(-0.829657\pi\)
−0.860194 + 0.509968i \(0.829657\pi\)
\(150\) 8.00000 0.653197
\(151\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(152\) 0 0
\(153\) −1.00000 −0.0808452
\(154\) 10.0000 0.805823
\(155\) 18.0000 1.44579
\(156\) −4.00000 −0.320256
\(157\) −18.0000 −1.43656 −0.718278 0.695756i \(-0.755069\pi\)
−0.718278 + 0.695756i \(0.755069\pi\)
\(158\) −32.0000 −2.54578
\(159\) −10.0000 −0.793052
\(160\) −24.0000 −1.89737
\(161\) 20.0000 1.57622
\(162\) −2.00000 −0.157135
\(163\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(164\) 0 0
\(165\) 3.00000 0.233550
\(166\) −24.0000 −1.86276
\(167\) 10.0000 0.773823 0.386912 0.922117i \(-0.373542\pi\)
0.386912 + 0.922117i \(0.373542\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) −6.00000 −0.460179
\(171\) −1.00000 −0.0764719
\(172\) −2.00000 −0.152499
\(173\) 6.00000 0.456172 0.228086 0.973641i \(-0.426753\pi\)
0.228086 + 0.973641i \(0.426753\pi\)
\(174\) −4.00000 −0.303239
\(175\) −20.0000 −1.51186
\(176\) −4.00000 −0.301511
\(177\) 8.00000 0.601317
\(178\) 12.0000 0.899438
\(179\) −18.0000 −1.34538 −0.672692 0.739923i \(-0.734862\pi\)
−0.672692 + 0.739923i \(0.734862\pi\)
\(180\) −6.00000 −0.447214
\(181\) −14.0000 −1.04061 −0.520306 0.853980i \(-0.674182\pi\)
−0.520306 + 0.853980i \(0.674182\pi\)
\(182\) 20.0000 1.48250
\(183\) 1.00000 0.0739221
\(184\) 0 0
\(185\) 0 0
\(186\) −12.0000 −0.879883
\(187\) −1.00000 −0.0731272
\(188\) −18.0000 −1.31278
\(189\) 5.00000 0.363696
\(190\) −6.00000 −0.435286
\(191\) 9.00000 0.651217 0.325609 0.945505i \(-0.394431\pi\)
0.325609 + 0.945505i \(0.394431\pi\)
\(192\) 8.00000 0.577350
\(193\) 4.00000 0.287926 0.143963 0.989583i \(-0.454015\pi\)
0.143963 + 0.989583i \(0.454015\pi\)
\(194\) 20.0000 1.43592
\(195\) 6.00000 0.429669
\(196\) 36.0000 2.57143
\(197\) −2.00000 −0.142494 −0.0712470 0.997459i \(-0.522698\pi\)
−0.0712470 + 0.997459i \(0.522698\pi\)
\(198\) −2.00000 −0.142134
\(199\) −21.0000 −1.48865 −0.744325 0.667817i \(-0.767229\pi\)
−0.744325 + 0.667817i \(0.767229\pi\)
\(200\) 0 0
\(201\) −8.00000 −0.564276
\(202\) −4.00000 −0.281439
\(203\) 10.0000 0.701862
\(204\) 2.00000 0.140028
\(205\) 0 0
\(206\) 4.00000 0.278693
\(207\) −4.00000 −0.278019
\(208\) −8.00000 −0.554700
\(209\) −1.00000 −0.0691714
\(210\) 30.0000 2.07020
\(211\) 12.0000 0.826114 0.413057 0.910705i \(-0.364461\pi\)
0.413057 + 0.910705i \(0.364461\pi\)
\(212\) 20.0000 1.37361
\(213\) 12.0000 0.822226
\(214\) −12.0000 −0.820303
\(215\) 3.00000 0.204598
\(216\) 0 0
\(217\) 30.0000 2.03653
\(218\) −8.00000 −0.541828
\(219\) 11.0000 0.743311
\(220\) −6.00000 −0.404520
\(221\) −2.00000 −0.134535
\(222\) 0 0
\(223\) 12.0000 0.803579 0.401790 0.915732i \(-0.368388\pi\)
0.401790 + 0.915732i \(0.368388\pi\)
\(224\) −40.0000 −2.67261
\(225\) 4.00000 0.266667
\(226\) −4.00000 −0.266076
\(227\) 18.0000 1.19470 0.597351 0.801980i \(-0.296220\pi\)
0.597351 + 0.801980i \(0.296220\pi\)
\(228\) 2.00000 0.132453
\(229\) 25.0000 1.65205 0.826023 0.563636i \(-0.190598\pi\)
0.826023 + 0.563636i \(0.190598\pi\)
\(230\) −24.0000 −1.58251
\(231\) 5.00000 0.328976
\(232\) 0 0
\(233\) 9.00000 0.589610 0.294805 0.955557i \(-0.404745\pi\)
0.294805 + 0.955557i \(0.404745\pi\)
\(234\) −4.00000 −0.261488
\(235\) 27.0000 1.76129
\(236\) −16.0000 −1.04151
\(237\) −16.0000 −1.03931
\(238\) −10.0000 −0.648204
\(239\) −3.00000 −0.194054 −0.0970269 0.995282i \(-0.530933\pi\)
−0.0970269 + 0.995282i \(0.530933\pi\)
\(240\) −12.0000 −0.774597
\(241\) 20.0000 1.28831 0.644157 0.764894i \(-0.277208\pi\)
0.644157 + 0.764894i \(0.277208\pi\)
\(242\) 20.0000 1.28565
\(243\) −1.00000 −0.0641500
\(244\) −2.00000 −0.128037
\(245\) −54.0000 −3.44993
\(246\) 0 0
\(247\) −2.00000 −0.127257
\(248\) 0 0
\(249\) −12.0000 −0.760469
\(250\) −6.00000 −0.379473
\(251\) 7.00000 0.441836 0.220918 0.975292i \(-0.429095\pi\)
0.220918 + 0.975292i \(0.429095\pi\)
\(252\) −10.0000 −0.629941
\(253\) −4.00000 −0.251478
\(254\) 4.00000 0.250982
\(255\) −3.00000 −0.187867
\(256\) 16.0000 1.00000
\(257\) −8.00000 −0.499026 −0.249513 0.968371i \(-0.580271\pi\)
−0.249513 + 0.968371i \(0.580271\pi\)
\(258\) −2.00000 −0.124515
\(259\) 0 0
\(260\) −12.0000 −0.744208
\(261\) −2.00000 −0.123797
\(262\) −14.0000 −0.864923
\(263\) 23.0000 1.41824 0.709120 0.705087i \(-0.249092\pi\)
0.709120 + 0.705087i \(0.249092\pi\)
\(264\) 0 0
\(265\) −30.0000 −1.84289
\(266\) −10.0000 −0.613139
\(267\) 6.00000 0.367194
\(268\) 16.0000 0.977356
\(269\) −14.0000 −0.853595 −0.426798 0.904347i \(-0.640358\pi\)
−0.426798 + 0.904347i \(0.640358\pi\)
\(270\) −6.00000 −0.365148
\(271\) 12.0000 0.728948 0.364474 0.931214i \(-0.381249\pi\)
0.364474 + 0.931214i \(0.381249\pi\)
\(272\) 4.00000 0.242536
\(273\) 10.0000 0.605228
\(274\) 18.0000 1.08742
\(275\) 4.00000 0.241209
\(276\) 8.00000 0.481543
\(277\) −11.0000 −0.660926 −0.330463 0.943819i \(-0.607205\pi\)
−0.330463 + 0.943819i \(0.607205\pi\)
\(278\) 26.0000 1.55938
\(279\) −6.00000 −0.359211
\(280\) 0 0
\(281\) 10.0000 0.596550 0.298275 0.954480i \(-0.403589\pi\)
0.298275 + 0.954480i \(0.403589\pi\)
\(282\) −18.0000 −1.07188
\(283\) −13.0000 −0.772770 −0.386385 0.922338i \(-0.626276\pi\)
−0.386385 + 0.922338i \(0.626276\pi\)
\(284\) −24.0000 −1.42414
\(285\) −3.00000 −0.177705
\(286\) −4.00000 −0.236525
\(287\) 0 0
\(288\) 8.00000 0.471405
\(289\) −16.0000 −0.941176
\(290\) −12.0000 −0.704664
\(291\) 10.0000 0.586210
\(292\) −22.0000 −1.28745
\(293\) −28.0000 −1.63578 −0.817889 0.575376i \(-0.804856\pi\)
−0.817889 + 0.575376i \(0.804856\pi\)
\(294\) 36.0000 2.09956
\(295\) 24.0000 1.39733
\(296\) 0 0
\(297\) −1.00000 −0.0580259
\(298\) 42.0000 2.43299
\(299\) −8.00000 −0.462652
\(300\) −8.00000 −0.461880
\(301\) 5.00000 0.288195
\(302\) 0 0
\(303\) −2.00000 −0.114897
\(304\) 4.00000 0.229416
\(305\) 3.00000 0.171780
\(306\) 2.00000 0.114332
\(307\) −12.0000 −0.684876 −0.342438 0.939540i \(-0.611253\pi\)
−0.342438 + 0.939540i \(0.611253\pi\)
\(308\) −10.0000 −0.569803
\(309\) 2.00000 0.113776
\(310\) −36.0000 −2.04466
\(311\) −21.0000 −1.19080 −0.595400 0.803429i \(-0.703007\pi\)
−0.595400 + 0.803429i \(0.703007\pi\)
\(312\) 0 0
\(313\) −2.00000 −0.113047 −0.0565233 0.998401i \(-0.518002\pi\)
−0.0565233 + 0.998401i \(0.518002\pi\)
\(314\) 36.0000 2.03160
\(315\) 15.0000 0.845154
\(316\) 32.0000 1.80014
\(317\) −4.00000 −0.224662 −0.112331 0.993671i \(-0.535832\pi\)
−0.112331 + 0.993671i \(0.535832\pi\)
\(318\) 20.0000 1.12154
\(319\) −2.00000 −0.111979
\(320\) 24.0000 1.34164
\(321\) −6.00000 −0.334887
\(322\) −40.0000 −2.22911
\(323\) 1.00000 0.0556415
\(324\) 2.00000 0.111111
\(325\) 8.00000 0.443760
\(326\) 0 0
\(327\) −4.00000 −0.221201
\(328\) 0 0
\(329\) 45.0000 2.48093
\(330\) −6.00000 −0.330289
\(331\) −4.00000 −0.219860 −0.109930 0.993939i \(-0.535063\pi\)
−0.109930 + 0.993939i \(0.535063\pi\)
\(332\) 24.0000 1.31717
\(333\) 0 0
\(334\) −20.0000 −1.09435
\(335\) −24.0000 −1.31126
\(336\) −20.0000 −1.09109
\(337\) −14.0000 −0.762629 −0.381314 0.924445i \(-0.624528\pi\)
−0.381314 + 0.924445i \(0.624528\pi\)
\(338\) 18.0000 0.979071
\(339\) −2.00000 −0.108625
\(340\) 6.00000 0.325396
\(341\) −6.00000 −0.324918
\(342\) 2.00000 0.108148
\(343\) −55.0000 −2.96972
\(344\) 0 0
\(345\) −12.0000 −0.646058
\(346\) −12.0000 −0.645124
\(347\) −25.0000 −1.34207 −0.671035 0.741426i \(-0.734150\pi\)
−0.671035 + 0.741426i \(0.734150\pi\)
\(348\) 4.00000 0.214423
\(349\) 9.00000 0.481759 0.240879 0.970555i \(-0.422564\pi\)
0.240879 + 0.970555i \(0.422564\pi\)
\(350\) 40.0000 2.13809
\(351\) −2.00000 −0.106752
\(352\) 8.00000 0.426401
\(353\) −2.00000 −0.106449 −0.0532246 0.998583i \(-0.516950\pi\)
−0.0532246 + 0.998583i \(0.516950\pi\)
\(354\) −16.0000 −0.850390
\(355\) 36.0000 1.91068
\(356\) −12.0000 −0.635999
\(357\) −5.00000 −0.264628
\(358\) 36.0000 1.90266
\(359\) 37.0000 1.95279 0.976393 0.216003i \(-0.0693022\pi\)
0.976393 + 0.216003i \(0.0693022\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 28.0000 1.47165
\(363\) 10.0000 0.524864
\(364\) −20.0000 −1.04828
\(365\) 33.0000 1.72730
\(366\) −2.00000 −0.104542
\(367\) −8.00000 −0.417597 −0.208798 0.977959i \(-0.566955\pi\)
−0.208798 + 0.977959i \(0.566955\pi\)
\(368\) 16.0000 0.834058
\(369\) 0 0
\(370\) 0 0
\(371\) −50.0000 −2.59587
\(372\) 12.0000 0.622171
\(373\) 16.0000 0.828449 0.414224 0.910175i \(-0.364053\pi\)
0.414224 + 0.910175i \(0.364053\pi\)
\(374\) 2.00000 0.103418
\(375\) −3.00000 −0.154919
\(376\) 0 0
\(377\) −4.00000 −0.206010
\(378\) −10.0000 −0.514344
\(379\) 34.0000 1.74646 0.873231 0.487306i \(-0.162020\pi\)
0.873231 + 0.487306i \(0.162020\pi\)
\(380\) 6.00000 0.307794
\(381\) 2.00000 0.102463
\(382\) −18.0000 −0.920960
\(383\) −34.0000 −1.73732 −0.868659 0.495410i \(-0.835018\pi\)
−0.868659 + 0.495410i \(0.835018\pi\)
\(384\) 0 0
\(385\) 15.0000 0.764471
\(386\) −8.00000 −0.407189
\(387\) −1.00000 −0.0508329
\(388\) −20.0000 −1.01535
\(389\) −27.0000 −1.36895 −0.684477 0.729034i \(-0.739969\pi\)
−0.684477 + 0.729034i \(0.739969\pi\)
\(390\) −12.0000 −0.607644
\(391\) 4.00000 0.202289
\(392\) 0 0
\(393\) −7.00000 −0.353103
\(394\) 4.00000 0.201517
\(395\) −48.0000 −2.41514
\(396\) 2.00000 0.100504
\(397\) 25.0000 1.25471 0.627357 0.778732i \(-0.284137\pi\)
0.627357 + 0.778732i \(0.284137\pi\)
\(398\) 42.0000 2.10527
\(399\) −5.00000 −0.250313
\(400\) −16.0000 −0.800000
\(401\) 36.0000 1.79775 0.898877 0.438201i \(-0.144384\pi\)
0.898877 + 0.438201i \(0.144384\pi\)
\(402\) 16.0000 0.798007
\(403\) −12.0000 −0.597763
\(404\) 4.00000 0.199007
\(405\) −3.00000 −0.149071
\(406\) −20.0000 −0.992583
\(407\) 0 0
\(408\) 0 0
\(409\) −14.0000 −0.692255 −0.346128 0.938187i \(-0.612504\pi\)
−0.346128 + 0.938187i \(0.612504\pi\)
\(410\) 0 0
\(411\) 9.00000 0.443937
\(412\) −4.00000 −0.197066
\(413\) 40.0000 1.96827
\(414\) 8.00000 0.393179
\(415\) −36.0000 −1.76717
\(416\) 16.0000 0.784465
\(417\) 13.0000 0.636613
\(418\) 2.00000 0.0978232
\(419\) 28.0000 1.36789 0.683945 0.729534i \(-0.260263\pi\)
0.683945 + 0.729534i \(0.260263\pi\)
\(420\) −30.0000 −1.46385
\(421\) 26.0000 1.26716 0.633581 0.773676i \(-0.281584\pi\)
0.633581 + 0.773676i \(0.281584\pi\)
\(422\) −24.0000 −1.16830
\(423\) −9.00000 −0.437595
\(424\) 0 0
\(425\) −4.00000 −0.194029
\(426\) −24.0000 −1.16280
\(427\) 5.00000 0.241967
\(428\) 12.0000 0.580042
\(429\) −2.00000 −0.0965609
\(430\) −6.00000 −0.289346
\(431\) −34.0000 −1.63772 −0.818861 0.573992i \(-0.805394\pi\)
−0.818861 + 0.573992i \(0.805394\pi\)
\(432\) 4.00000 0.192450
\(433\) 6.00000 0.288342 0.144171 0.989553i \(-0.453949\pi\)
0.144171 + 0.989553i \(0.453949\pi\)
\(434\) −60.0000 −2.88009
\(435\) −6.00000 −0.287678
\(436\) 8.00000 0.383131
\(437\) 4.00000 0.191346
\(438\) −22.0000 −1.05120
\(439\) 26.0000 1.24091 0.620456 0.784241i \(-0.286947\pi\)
0.620456 + 0.784241i \(0.286947\pi\)
\(440\) 0 0
\(441\) 18.0000 0.857143
\(442\) 4.00000 0.190261
\(443\) −5.00000 −0.237557 −0.118779 0.992921i \(-0.537898\pi\)
−0.118779 + 0.992921i \(0.537898\pi\)
\(444\) 0 0
\(445\) 18.0000 0.853282
\(446\) −24.0000 −1.13643
\(447\) 21.0000 0.993266
\(448\) 40.0000 1.88982
\(449\) −36.0000 −1.69895 −0.849473 0.527633i \(-0.823080\pi\)
−0.849473 + 0.527633i \(0.823080\pi\)
\(450\) −8.00000 −0.377124
\(451\) 0 0
\(452\) 4.00000 0.188144
\(453\) 0 0
\(454\) −36.0000 −1.68956
\(455\) 30.0000 1.40642
\(456\) 0 0
\(457\) −29.0000 −1.35656 −0.678281 0.734802i \(-0.737275\pi\)
−0.678281 + 0.734802i \(0.737275\pi\)
\(458\) −50.0000 −2.33635
\(459\) 1.00000 0.0466760
\(460\) 24.0000 1.11901
\(461\) 27.0000 1.25752 0.628758 0.777601i \(-0.283564\pi\)
0.628758 + 0.777601i \(0.283564\pi\)
\(462\) −10.0000 −0.465242
\(463\) 17.0000 0.790057 0.395029 0.918669i \(-0.370735\pi\)
0.395029 + 0.918669i \(0.370735\pi\)
\(464\) 8.00000 0.371391
\(465\) −18.0000 −0.834730
\(466\) −18.0000 −0.833834
\(467\) −5.00000 −0.231372 −0.115686 0.993286i \(-0.536907\pi\)
−0.115686 + 0.993286i \(0.536907\pi\)
\(468\) 4.00000 0.184900
\(469\) −40.0000 −1.84703
\(470\) −54.0000 −2.49083
\(471\) 18.0000 0.829396
\(472\) 0 0
\(473\) −1.00000 −0.0459800
\(474\) 32.0000 1.46981
\(475\) −4.00000 −0.183533
\(476\) 10.0000 0.458349
\(477\) 10.0000 0.457869
\(478\) 6.00000 0.274434
\(479\) −16.0000 −0.731059 −0.365529 0.930800i \(-0.619112\pi\)
−0.365529 + 0.930800i \(0.619112\pi\)
\(480\) 24.0000 1.09545
\(481\) 0 0
\(482\) −40.0000 −1.82195
\(483\) −20.0000 −0.910032
\(484\) −20.0000 −0.909091
\(485\) 30.0000 1.36223
\(486\) 2.00000 0.0907218
\(487\) −16.0000 −0.725029 −0.362515 0.931978i \(-0.618082\pi\)
−0.362515 + 0.931978i \(0.618082\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 108.000 4.87894
\(491\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(492\) 0 0
\(493\) 2.00000 0.0900755
\(494\) 4.00000 0.179969
\(495\) −3.00000 −0.134840
\(496\) 24.0000 1.07763
\(497\) 60.0000 2.69137
\(498\) 24.0000 1.07547
\(499\) 5.00000 0.223831 0.111915 0.993718i \(-0.464301\pi\)
0.111915 + 0.993718i \(0.464301\pi\)
\(500\) 6.00000 0.268328
\(501\) −10.0000 −0.446767
\(502\) −14.0000 −0.624851
\(503\) 16.0000 0.713405 0.356702 0.934218i \(-0.383901\pi\)
0.356702 + 0.934218i \(0.383901\pi\)
\(504\) 0 0
\(505\) −6.00000 −0.266996
\(506\) 8.00000 0.355643
\(507\) 9.00000 0.399704
\(508\) −4.00000 −0.177471
\(509\) 6.00000 0.265945 0.132973 0.991120i \(-0.457548\pi\)
0.132973 + 0.991120i \(0.457548\pi\)
\(510\) 6.00000 0.265684
\(511\) 55.0000 2.43306
\(512\) −32.0000 −1.41421
\(513\) 1.00000 0.0441511
\(514\) 16.0000 0.705730
\(515\) 6.00000 0.264392
\(516\) 2.00000 0.0880451
\(517\) −9.00000 −0.395820
\(518\) 0 0
\(519\) −6.00000 −0.263371
\(520\) 0 0
\(521\) 36.0000 1.57719 0.788594 0.614914i \(-0.210809\pi\)
0.788594 + 0.614914i \(0.210809\pi\)
\(522\) 4.00000 0.175075
\(523\) −34.0000 −1.48672 −0.743358 0.668894i \(-0.766768\pi\)
−0.743358 + 0.668894i \(0.766768\pi\)
\(524\) 14.0000 0.611593
\(525\) 20.0000 0.872872
\(526\) −46.0000 −2.00570
\(527\) 6.00000 0.261364
\(528\) 4.00000 0.174078
\(529\) −7.00000 −0.304348
\(530\) 60.0000 2.60623
\(531\) −8.00000 −0.347170
\(532\) 10.0000 0.433555
\(533\) 0 0
\(534\) −12.0000 −0.519291
\(535\) −18.0000 −0.778208
\(536\) 0 0
\(537\) 18.0000 0.776757
\(538\) 28.0000 1.20717
\(539\) 18.0000 0.775315
\(540\) 6.00000 0.258199
\(541\) 3.00000 0.128980 0.0644900 0.997918i \(-0.479458\pi\)
0.0644900 + 0.997918i \(0.479458\pi\)
\(542\) −24.0000 −1.03089
\(543\) 14.0000 0.600798
\(544\) −8.00000 −0.342997
\(545\) −12.0000 −0.514024
\(546\) −20.0000 −0.855921
\(547\) −26.0000 −1.11168 −0.555840 0.831289i \(-0.687603\pi\)
−0.555840 + 0.831289i \(0.687603\pi\)
\(548\) −18.0000 −0.768922
\(549\) −1.00000 −0.0426790
\(550\) −8.00000 −0.341121
\(551\) 2.00000 0.0852029
\(552\) 0 0
\(553\) −80.0000 −3.40195
\(554\) 22.0000 0.934690
\(555\) 0 0
\(556\) −26.0000 −1.10265
\(557\) −41.0000 −1.73723 −0.868613 0.495491i \(-0.834988\pi\)
−0.868613 + 0.495491i \(0.834988\pi\)
\(558\) 12.0000 0.508001
\(559\) −2.00000 −0.0845910
\(560\) −60.0000 −2.53546
\(561\) 1.00000 0.0422200
\(562\) −20.0000 −0.843649
\(563\) −12.0000 −0.505740 −0.252870 0.967500i \(-0.581374\pi\)
−0.252870 + 0.967500i \(0.581374\pi\)
\(564\) 18.0000 0.757937
\(565\) −6.00000 −0.252422
\(566\) 26.0000 1.09286
\(567\) −5.00000 −0.209980
\(568\) 0 0
\(569\) −18.0000 −0.754599 −0.377300 0.926091i \(-0.623147\pi\)
−0.377300 + 0.926091i \(0.623147\pi\)
\(570\) 6.00000 0.251312
\(571\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(572\) 4.00000 0.167248
\(573\) −9.00000 −0.375980
\(574\) 0 0
\(575\) −16.0000 −0.667246
\(576\) −8.00000 −0.333333
\(577\) 27.0000 1.12402 0.562012 0.827129i \(-0.310027\pi\)
0.562012 + 0.827129i \(0.310027\pi\)
\(578\) 32.0000 1.33102
\(579\) −4.00000 −0.166234
\(580\) 12.0000 0.498273
\(581\) −60.0000 −2.48922
\(582\) −20.0000 −0.829027
\(583\) 10.0000 0.414158
\(584\) 0 0
\(585\) −6.00000 −0.248069
\(586\) 56.0000 2.31334
\(587\) 7.00000 0.288921 0.144460 0.989511i \(-0.453855\pi\)
0.144460 + 0.989511i \(0.453855\pi\)
\(588\) −36.0000 −1.48461
\(589\) 6.00000 0.247226
\(590\) −48.0000 −1.97613
\(591\) 2.00000 0.0822690
\(592\) 0 0
\(593\) −6.00000 −0.246390 −0.123195 0.992382i \(-0.539314\pi\)
−0.123195 + 0.992382i \(0.539314\pi\)
\(594\) 2.00000 0.0820610
\(595\) −15.0000 −0.614940
\(596\) −42.0000 −1.72039
\(597\) 21.0000 0.859473
\(598\) 16.0000 0.654289
\(599\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) 0 0
\(601\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(602\) −10.0000 −0.407570
\(603\) 8.00000 0.325785
\(604\) 0 0
\(605\) 30.0000 1.21967
\(606\) 4.00000 0.162489
\(607\) 26.0000 1.05531 0.527654 0.849460i \(-0.323072\pi\)
0.527654 + 0.849460i \(0.323072\pi\)
\(608\) −8.00000 −0.324443
\(609\) −10.0000 −0.405220
\(610\) −6.00000 −0.242933
\(611\) −18.0000 −0.728202
\(612\) −2.00000 −0.0808452
\(613\) 33.0000 1.33286 0.666429 0.745569i \(-0.267822\pi\)
0.666429 + 0.745569i \(0.267822\pi\)
\(614\) 24.0000 0.968561
\(615\) 0 0
\(616\) 0 0
\(617\) 27.0000 1.08698 0.543490 0.839416i \(-0.317103\pi\)
0.543490 + 0.839416i \(0.317103\pi\)
\(618\) −4.00000 −0.160904
\(619\) 4.00000 0.160774 0.0803868 0.996764i \(-0.474384\pi\)
0.0803868 + 0.996764i \(0.474384\pi\)
\(620\) 36.0000 1.44579
\(621\) 4.00000 0.160514
\(622\) 42.0000 1.68405
\(623\) 30.0000 1.20192
\(624\) 8.00000 0.320256
\(625\) −29.0000 −1.16000
\(626\) 4.00000 0.159872
\(627\) 1.00000 0.0399362
\(628\) −36.0000 −1.43656
\(629\) 0 0
\(630\) −30.0000 −1.19523
\(631\) 15.0000 0.597141 0.298570 0.954388i \(-0.403490\pi\)
0.298570 + 0.954388i \(0.403490\pi\)
\(632\) 0 0
\(633\) −12.0000 −0.476957
\(634\) 8.00000 0.317721
\(635\) 6.00000 0.238103
\(636\) −20.0000 −0.793052
\(637\) 36.0000 1.42637
\(638\) 4.00000 0.158362
\(639\) −12.0000 −0.474713
\(640\) 0 0
\(641\) 18.0000 0.710957 0.355479 0.934684i \(-0.384318\pi\)
0.355479 + 0.934684i \(0.384318\pi\)
\(642\) 12.0000 0.473602
\(643\) −1.00000 −0.0394362 −0.0197181 0.999806i \(-0.506277\pi\)
−0.0197181 + 0.999806i \(0.506277\pi\)
\(644\) 40.0000 1.57622
\(645\) −3.00000 −0.118125
\(646\) −2.00000 −0.0786889
\(647\) −39.0000 −1.53325 −0.766624 0.642096i \(-0.778065\pi\)
−0.766624 + 0.642096i \(0.778065\pi\)
\(648\) 0 0
\(649\) −8.00000 −0.314027
\(650\) −16.0000 −0.627572
\(651\) −30.0000 −1.17579
\(652\) 0 0
\(653\) 3.00000 0.117399 0.0586995 0.998276i \(-0.481305\pi\)
0.0586995 + 0.998276i \(0.481305\pi\)
\(654\) 8.00000 0.312825
\(655\) −21.0000 −0.820538
\(656\) 0 0
\(657\) −11.0000 −0.429151
\(658\) −90.0000 −3.50857
\(659\) −14.0000 −0.545363 −0.272681 0.962104i \(-0.587910\pi\)
−0.272681 + 0.962104i \(0.587910\pi\)
\(660\) 6.00000 0.233550
\(661\) 12.0000 0.466746 0.233373 0.972387i \(-0.425024\pi\)
0.233373 + 0.972387i \(0.425024\pi\)
\(662\) 8.00000 0.310929
\(663\) 2.00000 0.0776736
\(664\) 0 0
\(665\) −15.0000 −0.581675
\(666\) 0 0
\(667\) 8.00000 0.309761
\(668\) 20.0000 0.773823
\(669\) −12.0000 −0.463947
\(670\) 48.0000 1.85440
\(671\) −1.00000 −0.0386046
\(672\) 40.0000 1.54303
\(673\) −24.0000 −0.925132 −0.462566 0.886585i \(-0.653071\pi\)
−0.462566 + 0.886585i \(0.653071\pi\)
\(674\) 28.0000 1.07852
\(675\) −4.00000 −0.153960
\(676\) −18.0000 −0.692308
\(677\) 34.0000 1.30673 0.653363 0.757045i \(-0.273358\pi\)
0.653363 + 0.757045i \(0.273358\pi\)
\(678\) 4.00000 0.153619
\(679\) 50.0000 1.91882
\(680\) 0 0
\(681\) −18.0000 −0.689761
\(682\) 12.0000 0.459504
\(683\) −6.00000 −0.229584 −0.114792 0.993390i \(-0.536620\pi\)
−0.114792 + 0.993390i \(0.536620\pi\)
\(684\) −2.00000 −0.0764719
\(685\) 27.0000 1.03162
\(686\) 110.000 4.19982
\(687\) −25.0000 −0.953809
\(688\) 4.00000 0.152499
\(689\) 20.0000 0.761939
\(690\) 24.0000 0.913664
\(691\) −31.0000 −1.17930 −0.589648 0.807661i \(-0.700733\pi\)
−0.589648 + 0.807661i \(0.700733\pi\)
\(692\) 12.0000 0.456172
\(693\) −5.00000 −0.189934
\(694\) 50.0000 1.89797
\(695\) 39.0000 1.47935
\(696\) 0 0
\(697\) 0 0
\(698\) −18.0000 −0.681310
\(699\) −9.00000 −0.340411
\(700\) −40.0000 −1.51186
\(701\) −22.0000 −0.830929 −0.415464 0.909610i \(-0.636381\pi\)
−0.415464 + 0.909610i \(0.636381\pi\)
\(702\) 4.00000 0.150970
\(703\) 0 0
\(704\) −8.00000 −0.301511
\(705\) −27.0000 −1.01688
\(706\) 4.00000 0.150542
\(707\) −10.0000 −0.376089
\(708\) 16.0000 0.601317
\(709\) −42.0000 −1.57734 −0.788672 0.614815i \(-0.789231\pi\)
−0.788672 + 0.614815i \(0.789231\pi\)
\(710\) −72.0000 −2.70211
\(711\) 16.0000 0.600047
\(712\) 0 0
\(713\) 24.0000 0.898807
\(714\) 10.0000 0.374241
\(715\) −6.00000 −0.224387
\(716\) −36.0000 −1.34538
\(717\) 3.00000 0.112037
\(718\) −74.0000 −2.76166
\(719\) 33.0000 1.23069 0.615346 0.788257i \(-0.289016\pi\)
0.615346 + 0.788257i \(0.289016\pi\)
\(720\) 12.0000 0.447214
\(721\) 10.0000 0.372419
\(722\) −2.00000 −0.0744323
\(723\) −20.0000 −0.743808
\(724\) −28.0000 −1.04061
\(725\) −8.00000 −0.297113
\(726\) −20.0000 −0.742270
\(727\) −23.0000 −0.853023 −0.426511 0.904482i \(-0.640258\pi\)
−0.426511 + 0.904482i \(0.640258\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −66.0000 −2.44277
\(731\) 1.00000 0.0369863
\(732\) 2.00000 0.0739221
\(733\) −14.0000 −0.517102 −0.258551 0.965998i \(-0.583245\pi\)
−0.258551 + 0.965998i \(0.583245\pi\)
\(734\) 16.0000 0.590571
\(735\) 54.0000 1.99182
\(736\) −32.0000 −1.17954
\(737\) 8.00000 0.294684
\(738\) 0 0
\(739\) −5.00000 −0.183928 −0.0919640 0.995762i \(-0.529314\pi\)
−0.0919640 + 0.995762i \(0.529314\pi\)
\(740\) 0 0
\(741\) 2.00000 0.0734718
\(742\) 100.000 3.67112
\(743\) −8.00000 −0.293492 −0.146746 0.989174i \(-0.546880\pi\)
−0.146746 + 0.989174i \(0.546880\pi\)
\(744\) 0 0
\(745\) 63.0000 2.30814
\(746\) −32.0000 −1.17160
\(747\) 12.0000 0.439057
\(748\) −2.00000 −0.0731272
\(749\) −30.0000 −1.09618
\(750\) 6.00000 0.219089
\(751\) 24.0000 0.875772 0.437886 0.899030i \(-0.355727\pi\)
0.437886 + 0.899030i \(0.355727\pi\)
\(752\) 36.0000 1.31278
\(753\) −7.00000 −0.255094
\(754\) 8.00000 0.291343
\(755\) 0 0
\(756\) 10.0000 0.363696
\(757\) −17.0000 −0.617876 −0.308938 0.951082i \(-0.599973\pi\)
−0.308938 + 0.951082i \(0.599973\pi\)
\(758\) −68.0000 −2.46987
\(759\) 4.00000 0.145191
\(760\) 0 0
\(761\) 15.0000 0.543750 0.271875 0.962333i \(-0.412356\pi\)
0.271875 + 0.962333i \(0.412356\pi\)
\(762\) −4.00000 −0.144905
\(763\) −20.0000 −0.724049
\(764\) 18.0000 0.651217
\(765\) 3.00000 0.108465
\(766\) 68.0000 2.45694
\(767\) −16.0000 −0.577727
\(768\) −16.0000 −0.577350
\(769\) 11.0000 0.396670 0.198335 0.980134i \(-0.436447\pi\)
0.198335 + 0.980134i \(0.436447\pi\)
\(770\) −30.0000 −1.08112
\(771\) 8.00000 0.288113
\(772\) 8.00000 0.287926
\(773\) 20.0000 0.719350 0.359675 0.933078i \(-0.382888\pi\)
0.359675 + 0.933078i \(0.382888\pi\)
\(774\) 2.00000 0.0718885
\(775\) −24.0000 −0.862105
\(776\) 0 0
\(777\) 0 0
\(778\) 54.0000 1.93599
\(779\) 0 0
\(780\) 12.0000 0.429669
\(781\) −12.0000 −0.429394
\(782\) −8.00000 −0.286079
\(783\) 2.00000 0.0714742
\(784\) −72.0000 −2.57143
\(785\) 54.0000 1.92734
\(786\) 14.0000 0.499363
\(787\) 40.0000 1.42585 0.712923 0.701242i \(-0.247371\pi\)
0.712923 + 0.701242i \(0.247371\pi\)
\(788\) −4.00000 −0.142494
\(789\) −23.0000 −0.818822
\(790\) 96.0000 3.41553
\(791\) −10.0000 −0.355559
\(792\) 0 0
\(793\) −2.00000 −0.0710221
\(794\) −50.0000 −1.77443
\(795\) 30.0000 1.06399
\(796\) −42.0000 −1.48865
\(797\) −44.0000 −1.55856 −0.779280 0.626676i \(-0.784415\pi\)
−0.779280 + 0.626676i \(0.784415\pi\)
\(798\) 10.0000 0.353996
\(799\) 9.00000 0.318397
\(800\) 32.0000 1.13137
\(801\) −6.00000 −0.212000
\(802\) −72.0000 −2.54241
\(803\) −11.0000 −0.388182
\(804\) −16.0000 −0.564276
\(805\) −60.0000 −2.11472
\(806\) 24.0000 0.845364
\(807\) 14.0000 0.492823
\(808\) 0 0
\(809\) −55.0000 −1.93370 −0.966849 0.255351i \(-0.917809\pi\)
−0.966849 + 0.255351i \(0.917809\pi\)
\(810\) 6.00000 0.210819
\(811\) −38.0000 −1.33436 −0.667180 0.744896i \(-0.732499\pi\)
−0.667180 + 0.744896i \(0.732499\pi\)
\(812\) 20.0000 0.701862
\(813\) −12.0000 −0.420858
\(814\) 0 0
\(815\) 0 0
\(816\) −4.00000 −0.140028
\(817\) 1.00000 0.0349856
\(818\) 28.0000 0.978997
\(819\) −10.0000 −0.349428
\(820\) 0 0
\(821\) −45.0000 −1.57051 −0.785255 0.619172i \(-0.787468\pi\)
−0.785255 + 0.619172i \(0.787468\pi\)
\(822\) −18.0000 −0.627822
\(823\) 43.0000 1.49889 0.749443 0.662069i \(-0.230321\pi\)
0.749443 + 0.662069i \(0.230321\pi\)
\(824\) 0 0
\(825\) −4.00000 −0.139262
\(826\) −80.0000 −2.78356
\(827\) 12.0000 0.417281 0.208640 0.977992i \(-0.433096\pi\)
0.208640 + 0.977992i \(0.433096\pi\)
\(828\) −8.00000 −0.278019
\(829\) 52.0000 1.80603 0.903017 0.429604i \(-0.141347\pi\)
0.903017 + 0.429604i \(0.141347\pi\)
\(830\) 72.0000 2.49916
\(831\) 11.0000 0.381586
\(832\) −16.0000 −0.554700
\(833\) −18.0000 −0.623663
\(834\) −26.0000 −0.900306
\(835\) −30.0000 −1.03819
\(836\) −2.00000 −0.0691714
\(837\) 6.00000 0.207390
\(838\) −56.0000 −1.93449
\(839\) 54.0000 1.86429 0.932144 0.362089i \(-0.117936\pi\)
0.932144 + 0.362089i \(0.117936\pi\)
\(840\) 0 0
\(841\) −25.0000 −0.862069
\(842\) −52.0000 −1.79204
\(843\) −10.0000 −0.344418
\(844\) 24.0000 0.826114
\(845\) 27.0000 0.928828
\(846\) 18.0000 0.618853
\(847\) 50.0000 1.71802
\(848\) −40.0000 −1.37361
\(849\) 13.0000 0.446159
\(850\) 8.00000 0.274398
\(851\) 0 0
\(852\) 24.0000 0.822226
\(853\) −14.0000 −0.479351 −0.239675 0.970853i \(-0.577041\pi\)
−0.239675 + 0.970853i \(0.577041\pi\)
\(854\) −10.0000 −0.342193
\(855\) 3.00000 0.102598
\(856\) 0 0
\(857\) −8.00000 −0.273275 −0.136637 0.990621i \(-0.543630\pi\)
−0.136637 + 0.990621i \(0.543630\pi\)
\(858\) 4.00000 0.136558
\(859\) 27.0000 0.921228 0.460614 0.887601i \(-0.347629\pi\)
0.460614 + 0.887601i \(0.347629\pi\)
\(860\) 6.00000 0.204598
\(861\) 0 0
\(862\) 68.0000 2.31609
\(863\) −44.0000 −1.49778 −0.748889 0.662696i \(-0.769412\pi\)
−0.748889 + 0.662696i \(0.769412\pi\)
\(864\) −8.00000 −0.272166
\(865\) −18.0000 −0.612018
\(866\) −12.0000 −0.407777
\(867\) 16.0000 0.543388
\(868\) 60.0000 2.03653
\(869\) 16.0000 0.542763
\(870\) 12.0000 0.406838
\(871\) 16.0000 0.542139
\(872\) 0 0
\(873\) −10.0000 −0.338449
\(874\) −8.00000 −0.270604
\(875\) −15.0000 −0.507093
\(876\) 22.0000 0.743311
\(877\) −6.00000 −0.202606 −0.101303 0.994856i \(-0.532301\pi\)
−0.101303 + 0.994856i \(0.532301\pi\)
\(878\) −52.0000 −1.75491
\(879\) 28.0000 0.944417
\(880\) 12.0000 0.404520
\(881\) −37.0000 −1.24656 −0.623281 0.781998i \(-0.714201\pi\)
−0.623281 + 0.781998i \(0.714201\pi\)
\(882\) −36.0000 −1.21218
\(883\) 35.0000 1.17784 0.588922 0.808190i \(-0.299553\pi\)
0.588922 + 0.808190i \(0.299553\pi\)
\(884\) −4.00000 −0.134535
\(885\) −24.0000 −0.806751
\(886\) 10.0000 0.335957
\(887\) −12.0000 −0.402921 −0.201460 0.979497i \(-0.564569\pi\)
−0.201460 + 0.979497i \(0.564569\pi\)
\(888\) 0 0
\(889\) 10.0000 0.335389
\(890\) −36.0000 −1.20672
\(891\) 1.00000 0.0335013
\(892\) 24.0000 0.803579
\(893\) 9.00000 0.301174
\(894\) −42.0000 −1.40469
\(895\) 54.0000 1.80502
\(896\) 0 0
\(897\) 8.00000 0.267112
\(898\) 72.0000 2.40267
\(899\) 12.0000 0.400222
\(900\) 8.00000 0.266667
\(901\) −10.0000 −0.333148
\(902\) 0 0
\(903\) −5.00000 −0.166390
\(904\) 0 0
\(905\) 42.0000 1.39613
\(906\) 0 0
\(907\) −26.0000 −0.863316 −0.431658 0.902037i \(-0.642071\pi\)
−0.431658 + 0.902037i \(0.642071\pi\)
\(908\) 36.0000 1.19470
\(909\) 2.00000 0.0663358
\(910\) −60.0000 −1.98898
\(911\) −6.00000 −0.198789 −0.0993944 0.995048i \(-0.531691\pi\)
−0.0993944 + 0.995048i \(0.531691\pi\)
\(912\) −4.00000 −0.132453
\(913\) 12.0000 0.397142
\(914\) 58.0000 1.91847
\(915\) −3.00000 −0.0991769
\(916\) 50.0000 1.65205
\(917\) −35.0000 −1.15580
\(918\) −2.00000 −0.0660098
\(919\) 8.00000 0.263896 0.131948 0.991257i \(-0.457877\pi\)
0.131948 + 0.991257i \(0.457877\pi\)
\(920\) 0 0
\(921\) 12.0000 0.395413
\(922\) −54.0000 −1.77840
\(923\) −24.0000 −0.789970
\(924\) 10.0000 0.328976
\(925\) 0 0
\(926\) −34.0000 −1.11731
\(927\) −2.00000 −0.0656886
\(928\) −16.0000 −0.525226
\(929\) −2.00000 −0.0656179 −0.0328089 0.999462i \(-0.510445\pi\)
−0.0328089 + 0.999462i \(0.510445\pi\)
\(930\) 36.0000 1.18049
\(931\) −18.0000 −0.589926
\(932\) 18.0000 0.589610
\(933\) 21.0000 0.687509
\(934\) 10.0000 0.327210
\(935\) 3.00000 0.0981105
\(936\) 0 0
\(937\) 21.0000 0.686040 0.343020 0.939328i \(-0.388550\pi\)
0.343020 + 0.939328i \(0.388550\pi\)
\(938\) 80.0000 2.61209
\(939\) 2.00000 0.0652675
\(940\) 54.0000 1.76129
\(941\) 42.0000 1.36916 0.684580 0.728937i \(-0.259985\pi\)
0.684580 + 0.728937i \(0.259985\pi\)
\(942\) −36.0000 −1.17294
\(943\) 0 0
\(944\) 32.0000 1.04151
\(945\) −15.0000 −0.487950
\(946\) 2.00000 0.0650256
\(947\) −28.0000 −0.909878 −0.454939 0.890523i \(-0.650339\pi\)
−0.454939 + 0.890523i \(0.650339\pi\)
\(948\) −32.0000 −1.03931
\(949\) −22.0000 −0.714150
\(950\) 8.00000 0.259554
\(951\) 4.00000 0.129709
\(952\) 0 0
\(953\) −32.0000 −1.03658 −0.518291 0.855204i \(-0.673432\pi\)
−0.518291 + 0.855204i \(0.673432\pi\)
\(954\) −20.0000 −0.647524
\(955\) −27.0000 −0.873699
\(956\) −6.00000 −0.194054
\(957\) 2.00000 0.0646508
\(958\) 32.0000 1.03387
\(959\) 45.0000 1.45313
\(960\) −24.0000 −0.774597
\(961\) 5.00000 0.161290
\(962\) 0 0
\(963\) 6.00000 0.193347
\(964\) 40.0000 1.28831
\(965\) −12.0000 −0.386294
\(966\) 40.0000 1.28698
\(967\) −32.0000 −1.02905 −0.514525 0.857475i \(-0.672032\pi\)
−0.514525 + 0.857475i \(0.672032\pi\)
\(968\) 0 0
\(969\) −1.00000 −0.0321246
\(970\) −60.0000 −1.92648
\(971\) 12.0000 0.385098 0.192549 0.981287i \(-0.438325\pi\)
0.192549 + 0.981287i \(0.438325\pi\)
\(972\) −2.00000 −0.0641500
\(973\) 65.0000 2.08380
\(974\) 32.0000 1.02535
\(975\) −8.00000 −0.256205
\(976\) 4.00000 0.128037
\(977\) 54.0000 1.72761 0.863807 0.503824i \(-0.168074\pi\)
0.863807 + 0.503824i \(0.168074\pi\)
\(978\) 0 0
\(979\) −6.00000 −0.191761
\(980\) −108.000 −3.44993
\(981\) 4.00000 0.127710
\(982\) 0 0
\(983\) −44.0000 −1.40338 −0.701691 0.712481i \(-0.747571\pi\)
−0.701691 + 0.712481i \(0.747571\pi\)
\(984\) 0 0
\(985\) 6.00000 0.191176
\(986\) −4.00000 −0.127386
\(987\) −45.0000 −1.43237
\(988\) −4.00000 −0.127257
\(989\) 4.00000 0.127193
\(990\) 6.00000 0.190693
\(991\) −16.0000 −0.508257 −0.254128 0.967170i \(-0.581789\pi\)
−0.254128 + 0.967170i \(0.581789\pi\)
\(992\) −48.0000 −1.52400
\(993\) 4.00000 0.126936
\(994\) −120.000 −3.80617
\(995\) 63.0000 1.99723
\(996\) −24.0000 −0.760469
\(997\) −47.0000 −1.48850 −0.744252 0.667898i \(-0.767194\pi\)
−0.744252 + 0.667898i \(0.767194\pi\)
\(998\) −10.0000 −0.316544
\(999\) 0 0
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 \(a_p\))