Properties

Label 4010.2.a.b.1.1
Level 4010
Weight 2
Character 4010.1
Self dual Yes
Analytic conductor 32.020
Analytic rank 1
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4010 = 2 \cdot 5 \cdot 401 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4010.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0200112105\)
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 \(\chi\) = 4010.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +2.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +2.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +3.00000 q^{11} +2.00000 q^{12} +1.00000 q^{13} -2.00000 q^{15} +1.00000 q^{16} -8.00000 q^{17} -1.00000 q^{18} -1.00000 q^{20} -3.00000 q^{22} -2.00000 q^{24} +1.00000 q^{25} -1.00000 q^{26} -4.00000 q^{27} -4.00000 q^{29} +2.00000 q^{30} +1.00000 q^{31} -1.00000 q^{32} +6.00000 q^{33} +8.00000 q^{34} +1.00000 q^{36} -10.0000 q^{37} +2.00000 q^{39} +1.00000 q^{40} +7.00000 q^{41} -11.0000 q^{43} +3.00000 q^{44} -1.00000 q^{45} +4.00000 q^{47} +2.00000 q^{48} -7.00000 q^{49} -1.00000 q^{50} -16.0000 q^{51} +1.00000 q^{52} -5.00000 q^{53} +4.00000 q^{54} -3.00000 q^{55} +4.00000 q^{58} +4.00000 q^{59} -2.00000 q^{60} -13.0000 q^{61} -1.00000 q^{62} +1.00000 q^{64} -1.00000 q^{65} -6.00000 q^{66} -8.00000 q^{68} +9.00000 q^{71} -1.00000 q^{72} +9.00000 q^{73} +10.0000 q^{74} +2.00000 q^{75} -2.00000 q^{78} +3.00000 q^{79} -1.00000 q^{80} -11.0000 q^{81} -7.00000 q^{82} -5.00000 q^{83} +8.00000 q^{85} +11.0000 q^{86} -8.00000 q^{87} -3.00000 q^{88} +7.00000 q^{89} +1.00000 q^{90} +2.00000 q^{93} -4.00000 q^{94} -2.00000 q^{96} -18.0000 q^{97} +7.00000 q^{98} +3.00000 q^{99} +O(q^{100})\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 2.00000 1.15470 0.577350 0.816497i \(-0.304087\pi\)
0.577350 + 0.816497i \(0.304087\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214
\(6\) −2.00000 −0.816497
\(7\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) 1.00000 0.316228
\(11\) 3.00000 0.904534 0.452267 0.891883i \(-0.350615\pi\)
0.452267 + 0.891883i \(0.350615\pi\)
\(12\) 2.00000 0.577350
\(13\) 1.00000 0.277350 0.138675 0.990338i \(-0.455716\pi\)
0.138675 + 0.990338i \(0.455716\pi\)
\(14\) 0 0
\(15\) −2.00000 −0.516398
\(16\) 1.00000 0.250000
\(17\) −8.00000 −1.94029 −0.970143 0.242536i \(-0.922021\pi\)
−0.970143 + 0.242536i \(0.922021\pi\)
\(18\) −1.00000 −0.235702
\(19\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(20\) −1.00000 −0.223607
\(21\) 0 0
\(22\) −3.00000 −0.639602
\(23\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) −2.00000 −0.408248
\(25\) 1.00000 0.200000
\(26\) −1.00000 −0.196116
\(27\) −4.00000 −0.769800
\(28\) 0 0
\(29\) −4.00000 −0.742781 −0.371391 0.928477i \(-0.621119\pi\)
−0.371391 + 0.928477i \(0.621119\pi\)
\(30\) 2.00000 0.365148
\(31\) 1.00000 0.179605 0.0898027 0.995960i \(-0.471376\pi\)
0.0898027 + 0.995960i \(0.471376\pi\)
\(32\) −1.00000 −0.176777
\(33\) 6.00000 1.04447
\(34\) 8.00000 1.37199
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) −10.0000 −1.64399 −0.821995 0.569495i \(-0.807139\pi\)
−0.821995 + 0.569495i \(0.807139\pi\)
\(38\) 0 0
\(39\) 2.00000 0.320256
\(40\) 1.00000 0.158114
\(41\) 7.00000 1.09322 0.546608 0.837389i \(-0.315919\pi\)
0.546608 + 0.837389i \(0.315919\pi\)
\(42\) 0 0
\(43\) −11.0000 −1.67748 −0.838742 0.544529i \(-0.816708\pi\)
−0.838742 + 0.544529i \(0.816708\pi\)
\(44\) 3.00000 0.452267
\(45\) −1.00000 −0.149071
\(46\) 0 0
\(47\) 4.00000 0.583460 0.291730 0.956501i \(-0.405769\pi\)
0.291730 + 0.956501i \(0.405769\pi\)
\(48\) 2.00000 0.288675
\(49\) −7.00000 −1.00000
\(50\) −1.00000 −0.141421
\(51\) −16.0000 −2.24045
\(52\) 1.00000 0.138675
\(53\) −5.00000 −0.686803 −0.343401 0.939189i \(-0.611579\pi\)
−0.343401 + 0.939189i \(0.611579\pi\)
\(54\) 4.00000 0.544331
\(55\) −3.00000 −0.404520
\(56\) 0 0
\(57\) 0 0
\(58\) 4.00000 0.525226
\(59\) 4.00000 0.520756 0.260378 0.965507i \(-0.416153\pi\)
0.260378 + 0.965507i \(0.416153\pi\)
\(60\) −2.00000 −0.258199
\(61\) −13.0000 −1.66448 −0.832240 0.554416i \(-0.812942\pi\)
−0.832240 + 0.554416i \(0.812942\pi\)
\(62\) −1.00000 −0.127000
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −1.00000 −0.124035
\(66\) −6.00000 −0.738549
\(67\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(68\) −8.00000 −0.970143
\(69\) 0 0
\(70\) 0 0
\(71\) 9.00000 1.06810 0.534052 0.845452i \(-0.320669\pi\)
0.534052 + 0.845452i \(0.320669\pi\)
\(72\) −1.00000 −0.117851
\(73\) 9.00000 1.05337 0.526685 0.850060i \(-0.323435\pi\)
0.526685 + 0.850060i \(0.323435\pi\)
\(74\) 10.0000 1.16248
\(75\) 2.00000 0.230940
\(76\) 0 0
\(77\) 0 0
\(78\) −2.00000 −0.226455
\(79\) 3.00000 0.337526 0.168763 0.985657i \(-0.446023\pi\)
0.168763 + 0.985657i \(0.446023\pi\)
\(80\) −1.00000 −0.111803
\(81\) −11.0000 −1.22222
\(82\) −7.00000 −0.773021
\(83\) −5.00000 −0.548821 −0.274411 0.961613i \(-0.588483\pi\)
−0.274411 + 0.961613i \(0.588483\pi\)
\(84\) 0 0
\(85\) 8.00000 0.867722
\(86\) 11.0000 1.18616
\(87\) −8.00000 −0.857690
\(88\) −3.00000 −0.319801
\(89\) 7.00000 0.741999 0.370999 0.928633i \(-0.379015\pi\)
0.370999 + 0.928633i \(0.379015\pi\)
\(90\) 1.00000 0.105409
\(91\) 0 0
\(92\) 0 0
\(93\) 2.00000 0.207390
\(94\) −4.00000 −0.412568
\(95\) 0 0
\(96\) −2.00000 −0.204124
\(97\) −18.0000 −1.82762 −0.913812 0.406138i \(-0.866875\pi\)
−0.913812 + 0.406138i \(0.866875\pi\)
\(98\) 7.00000 0.707107
\(99\) 3.00000 0.301511
\(100\) 1.00000 0.100000
\(101\) 10.0000 0.995037 0.497519 0.867453i \(-0.334245\pi\)
0.497519 + 0.867453i \(0.334245\pi\)
\(102\) 16.0000 1.58424
\(103\) 6.00000 0.591198 0.295599 0.955312i \(-0.404481\pi\)
0.295599 + 0.955312i \(0.404481\pi\)
\(104\) −1.00000 −0.0980581
\(105\) 0 0
\(106\) 5.00000 0.485643
\(107\) 12.0000 1.16008 0.580042 0.814587i \(-0.303036\pi\)
0.580042 + 0.814587i \(0.303036\pi\)
\(108\) −4.00000 −0.384900
\(109\) −14.0000 −1.34096 −0.670478 0.741929i \(-0.733911\pi\)
−0.670478 + 0.741929i \(0.733911\pi\)
\(110\) 3.00000 0.286039
\(111\) −20.0000 −1.89832
\(112\) 0 0
\(113\) 15.0000 1.41108 0.705541 0.708669i \(-0.250704\pi\)
0.705541 + 0.708669i \(0.250704\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −4.00000 −0.371391
\(117\) 1.00000 0.0924500
\(118\) −4.00000 −0.368230
\(119\) 0 0
\(120\) 2.00000 0.182574
\(121\) −2.00000 −0.181818
\(122\) 13.0000 1.17696
\(123\) 14.0000 1.26234
\(124\) 1.00000 0.0898027
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −3.00000 −0.266207 −0.133103 0.991102i \(-0.542494\pi\)
−0.133103 + 0.991102i \(0.542494\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −22.0000 −1.93699
\(130\) 1.00000 0.0877058
\(131\) −8.00000 −0.698963 −0.349482 0.936943i \(-0.613642\pi\)
−0.349482 + 0.936943i \(0.613642\pi\)
\(132\) 6.00000 0.522233
\(133\) 0 0
\(134\) 0 0
\(135\) 4.00000 0.344265
\(136\) 8.00000 0.685994
\(137\) −22.0000 −1.87959 −0.939793 0.341743i \(-0.888983\pi\)
−0.939793 + 0.341743i \(0.888983\pi\)
\(138\) 0 0
\(139\) 4.00000 0.339276 0.169638 0.985506i \(-0.445740\pi\)
0.169638 + 0.985506i \(0.445740\pi\)
\(140\) 0 0
\(141\) 8.00000 0.673722
\(142\) −9.00000 −0.755263
\(143\) 3.00000 0.250873
\(144\) 1.00000 0.0833333
\(145\) 4.00000 0.332182
\(146\) −9.00000 −0.744845
\(147\) −14.0000 −1.15470
\(148\) −10.0000 −0.821995
\(149\) −10.0000 −0.819232 −0.409616 0.912258i \(-0.634337\pi\)
−0.409616 + 0.912258i \(0.634337\pi\)
\(150\) −2.00000 −0.163299
\(151\) 12.0000 0.976546 0.488273 0.872691i \(-0.337627\pi\)
0.488273 + 0.872691i \(0.337627\pi\)
\(152\) 0 0
\(153\) −8.00000 −0.646762
\(154\) 0 0
\(155\) −1.00000 −0.0803219
\(156\) 2.00000 0.160128
\(157\) −18.0000 −1.43656 −0.718278 0.695756i \(-0.755069\pi\)
−0.718278 + 0.695756i \(0.755069\pi\)
\(158\) −3.00000 −0.238667
\(159\) −10.0000 −0.793052
\(160\) 1.00000 0.0790569
\(161\) 0 0
\(162\) 11.0000 0.864242
\(163\) −10.0000 −0.783260 −0.391630 0.920123i \(-0.628089\pi\)
−0.391630 + 0.920123i \(0.628089\pi\)
\(164\) 7.00000 0.546608
\(165\) −6.00000 −0.467099
\(166\) 5.00000 0.388075
\(167\) 19.0000 1.47026 0.735132 0.677924i \(-0.237120\pi\)
0.735132 + 0.677924i \(0.237120\pi\)
\(168\) 0 0
\(169\) −12.0000 −0.923077
\(170\) −8.00000 −0.613572
\(171\) 0 0
\(172\) −11.0000 −0.838742
\(173\) −16.0000 −1.21646 −0.608229 0.793762i \(-0.708120\pi\)
−0.608229 + 0.793762i \(0.708120\pi\)
\(174\) 8.00000 0.606478
\(175\) 0 0
\(176\) 3.00000 0.226134
\(177\) 8.00000 0.601317
\(178\) −7.00000 −0.524672
\(179\) −23.0000 −1.71910 −0.859550 0.511051i \(-0.829256\pi\)
−0.859550 + 0.511051i \(0.829256\pi\)
\(180\) −1.00000 −0.0745356
\(181\) −4.00000 −0.297318 −0.148659 0.988889i \(-0.547496\pi\)
−0.148659 + 0.988889i \(0.547496\pi\)
\(182\) 0 0
\(183\) −26.0000 −1.92198
\(184\) 0 0
\(185\) 10.0000 0.735215
\(186\) −2.00000 −0.146647
\(187\) −24.0000 −1.75505
\(188\) 4.00000 0.291730
\(189\) 0 0
\(190\) 0 0
\(191\) 3.00000 0.217072 0.108536 0.994092i \(-0.465384\pi\)
0.108536 + 0.994092i \(0.465384\pi\)
\(192\) 2.00000 0.144338
\(193\) −4.00000 −0.287926 −0.143963 0.989583i \(-0.545985\pi\)
−0.143963 + 0.989583i \(0.545985\pi\)
\(194\) 18.0000 1.29232
\(195\) −2.00000 −0.143223
\(196\) −7.00000 −0.500000
\(197\) 6.00000 0.427482 0.213741 0.976890i \(-0.431435\pi\)
0.213741 + 0.976890i \(0.431435\pi\)
\(198\) −3.00000 −0.213201
\(199\) −4.00000 −0.283552 −0.141776 0.989899i \(-0.545281\pi\)
−0.141776 + 0.989899i \(0.545281\pi\)
\(200\) −1.00000 −0.0707107
\(201\) 0 0
\(202\) −10.0000 −0.703598
\(203\) 0 0
\(204\) −16.0000 −1.12022
\(205\) −7.00000 −0.488901
\(206\) −6.00000 −0.418040
\(207\) 0 0
\(208\) 1.00000 0.0693375
\(209\) 0 0
\(210\) 0 0
\(211\) 16.0000 1.10149 0.550743 0.834675i \(-0.314345\pi\)
0.550743 + 0.834675i \(0.314345\pi\)
\(212\) −5.00000 −0.343401
\(213\) 18.0000 1.23334
\(214\) −12.0000 −0.820303
\(215\) 11.0000 0.750194
\(216\) 4.00000 0.272166
\(217\) 0 0
\(218\) 14.0000 0.948200
\(219\) 18.0000 1.21633
\(220\) −3.00000 −0.202260
\(221\) −8.00000 −0.538138
\(222\) 20.0000 1.34231
\(223\) 20.0000 1.33930 0.669650 0.742677i \(-0.266444\pi\)
0.669650 + 0.742677i \(0.266444\pi\)
\(224\) 0 0
\(225\) 1.00000 0.0666667
\(226\) −15.0000 −0.997785
\(227\) −4.00000 −0.265489 −0.132745 0.991150i \(-0.542379\pi\)
−0.132745 + 0.991150i \(0.542379\pi\)
\(228\) 0 0
\(229\) −10.0000 −0.660819 −0.330409 0.943838i \(-0.607187\pi\)
−0.330409 + 0.943838i \(0.607187\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 4.00000 0.262613
\(233\) 12.0000 0.786146 0.393073 0.919507i \(-0.371412\pi\)
0.393073 + 0.919507i \(0.371412\pi\)
\(234\) −1.00000 −0.0653720
\(235\) −4.00000 −0.260931
\(236\) 4.00000 0.260378
\(237\) 6.00000 0.389742
\(238\) 0 0
\(239\) −6.00000 −0.388108 −0.194054 0.980991i \(-0.562164\pi\)
−0.194054 + 0.980991i \(0.562164\pi\)
\(240\) −2.00000 −0.129099
\(241\) 17.0000 1.09507 0.547533 0.836784i \(-0.315567\pi\)
0.547533 + 0.836784i \(0.315567\pi\)
\(242\) 2.00000 0.128565
\(243\) −10.0000 −0.641500
\(244\) −13.0000 −0.832240
\(245\) 7.00000 0.447214
\(246\) −14.0000 −0.892607
\(247\) 0 0
\(248\) −1.00000 −0.0635001
\(249\) −10.0000 −0.633724
\(250\) 1.00000 0.0632456
\(251\) −20.0000 −1.26239 −0.631194 0.775625i \(-0.717435\pi\)
−0.631194 + 0.775625i \(0.717435\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 3.00000 0.188237
\(255\) 16.0000 1.00196
\(256\) 1.00000 0.0625000
\(257\) −17.0000 −1.06043 −0.530215 0.847863i \(-0.677889\pi\)
−0.530215 + 0.847863i \(0.677889\pi\)
\(258\) 22.0000 1.36966
\(259\) 0 0
\(260\) −1.00000 −0.0620174
\(261\) −4.00000 −0.247594
\(262\) 8.00000 0.494242
\(263\) 18.0000 1.10993 0.554964 0.831875i \(-0.312732\pi\)
0.554964 + 0.831875i \(0.312732\pi\)
\(264\) −6.00000 −0.369274
\(265\) 5.00000 0.307148
\(266\) 0 0
\(267\) 14.0000 0.856786
\(268\) 0 0
\(269\) −3.00000 −0.182913 −0.0914566 0.995809i \(-0.529152\pi\)
−0.0914566 + 0.995809i \(0.529152\pi\)
\(270\) −4.00000 −0.243432
\(271\) 8.00000 0.485965 0.242983 0.970031i \(-0.421874\pi\)
0.242983 + 0.970031i \(0.421874\pi\)
\(272\) −8.00000 −0.485071
\(273\) 0 0
\(274\) 22.0000 1.32907
\(275\) 3.00000 0.180907
\(276\) 0 0
\(277\) 1.00000 0.0600842 0.0300421 0.999549i \(-0.490436\pi\)
0.0300421 + 0.999549i \(0.490436\pi\)
\(278\) −4.00000 −0.239904
\(279\) 1.00000 0.0598684
\(280\) 0 0
\(281\) −22.0000 −1.31241 −0.656205 0.754583i \(-0.727839\pi\)
−0.656205 + 0.754583i \(0.727839\pi\)
\(282\) −8.00000 −0.476393
\(283\) −12.0000 −0.713326 −0.356663 0.934233i \(-0.616086\pi\)
−0.356663 + 0.934233i \(0.616086\pi\)
\(284\) 9.00000 0.534052
\(285\) 0 0
\(286\) −3.00000 −0.177394
\(287\) 0 0
\(288\) −1.00000 −0.0589256
\(289\) 47.0000 2.76471
\(290\) −4.00000 −0.234888
\(291\) −36.0000 −2.11036
\(292\) 9.00000 0.526685
\(293\) −1.00000 −0.0584206 −0.0292103 0.999573i \(-0.509299\pi\)
−0.0292103 + 0.999573i \(0.509299\pi\)
\(294\) 14.0000 0.816497
\(295\) −4.00000 −0.232889
\(296\) 10.0000 0.581238
\(297\) −12.0000 −0.696311
\(298\) 10.0000 0.579284
\(299\) 0 0
\(300\) 2.00000 0.115470
\(301\) 0 0
\(302\) −12.0000 −0.690522
\(303\) 20.0000 1.14897
\(304\) 0 0
\(305\) 13.0000 0.744378
\(306\) 8.00000 0.457330
\(307\) 23.0000 1.31268 0.656340 0.754466i \(-0.272104\pi\)
0.656340 + 0.754466i \(0.272104\pi\)
\(308\) 0 0
\(309\) 12.0000 0.682656
\(310\) 1.00000 0.0567962
\(311\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) −2.00000 −0.113228
\(313\) −31.0000 −1.75222 −0.876112 0.482108i \(-0.839871\pi\)
−0.876112 + 0.482108i \(0.839871\pi\)
\(314\) 18.0000 1.01580
\(315\) 0 0
\(316\) 3.00000 0.168763
\(317\) −9.00000 −0.505490 −0.252745 0.967533i \(-0.581333\pi\)
−0.252745 + 0.967533i \(0.581333\pi\)
\(318\) 10.0000 0.560772
\(319\) −12.0000 −0.671871
\(320\) −1.00000 −0.0559017
\(321\) 24.0000 1.33955
\(322\) 0 0
\(323\) 0 0
\(324\) −11.0000 −0.611111
\(325\) 1.00000 0.0554700
\(326\) 10.0000 0.553849
\(327\) −28.0000 −1.54840
\(328\) −7.00000 −0.386510
\(329\) 0 0
\(330\) 6.00000 0.330289
\(331\) 11.0000 0.604615 0.302307 0.953211i \(-0.402243\pi\)
0.302307 + 0.953211i \(0.402243\pi\)
\(332\) −5.00000 −0.274411
\(333\) −10.0000 −0.547997
\(334\) −19.0000 −1.03963
\(335\) 0 0
\(336\) 0 0
\(337\) −3.00000 −0.163420 −0.0817102 0.996656i \(-0.526038\pi\)
−0.0817102 + 0.996656i \(0.526038\pi\)
\(338\) 12.0000 0.652714
\(339\) 30.0000 1.62938
\(340\) 8.00000 0.433861
\(341\) 3.00000 0.162459
\(342\) 0 0
\(343\) 0 0
\(344\) 11.0000 0.593080
\(345\) 0 0
\(346\) 16.0000 0.860165
\(347\) 10.0000 0.536828 0.268414 0.963304i \(-0.413500\pi\)
0.268414 + 0.963304i \(0.413500\pi\)
\(348\) −8.00000 −0.428845
\(349\) −10.0000 −0.535288 −0.267644 0.963518i \(-0.586245\pi\)
−0.267644 + 0.963518i \(0.586245\pi\)
\(350\) 0 0
\(351\) −4.00000 −0.213504
\(352\) −3.00000 −0.159901
\(353\) 6.00000 0.319348 0.159674 0.987170i \(-0.448956\pi\)
0.159674 + 0.987170i \(0.448956\pi\)
\(354\) −8.00000 −0.425195
\(355\) −9.00000 −0.477670
\(356\) 7.00000 0.370999
\(357\) 0 0
\(358\) 23.0000 1.21559
\(359\) 27.0000 1.42501 0.712503 0.701669i \(-0.247562\pi\)
0.712503 + 0.701669i \(0.247562\pi\)
\(360\) 1.00000 0.0527046
\(361\) −19.0000 −1.00000
\(362\) 4.00000 0.210235
\(363\) −4.00000 −0.209946
\(364\) 0 0
\(365\) −9.00000 −0.471082
\(366\) 26.0000 1.35904
\(367\) −35.0000 −1.82699 −0.913493 0.406855i \(-0.866625\pi\)
−0.913493 + 0.406855i \(0.866625\pi\)
\(368\) 0 0
\(369\) 7.00000 0.364405
\(370\) −10.0000 −0.519875
\(371\) 0 0
\(372\) 2.00000 0.103695
\(373\) 8.00000 0.414224 0.207112 0.978317i \(-0.433593\pi\)
0.207112 + 0.978317i \(0.433593\pi\)
\(374\) 24.0000 1.24101
\(375\) −2.00000 −0.103280
\(376\) −4.00000 −0.206284
\(377\) −4.00000 −0.206010
\(378\) 0 0
\(379\) 35.0000 1.79783 0.898915 0.438124i \(-0.144357\pi\)
0.898915 + 0.438124i \(0.144357\pi\)
\(380\) 0 0
\(381\) −6.00000 −0.307389
\(382\) −3.00000 −0.153493
\(383\) 12.0000 0.613171 0.306586 0.951843i \(-0.400813\pi\)
0.306586 + 0.951843i \(0.400813\pi\)
\(384\) −2.00000 −0.102062
\(385\) 0 0
\(386\) 4.00000 0.203595
\(387\) −11.0000 −0.559161
\(388\) −18.0000 −0.913812
\(389\) 37.0000 1.87597 0.937987 0.346670i \(-0.112688\pi\)
0.937987 + 0.346670i \(0.112688\pi\)
\(390\) 2.00000 0.101274
\(391\) 0 0
\(392\) 7.00000 0.353553
\(393\) −16.0000 −0.807093
\(394\) −6.00000 −0.302276
\(395\) −3.00000 −0.150946
\(396\) 3.00000 0.150756
\(397\) −14.0000 −0.702640 −0.351320 0.936255i \(-0.614267\pi\)
−0.351320 + 0.936255i \(0.614267\pi\)
\(398\) 4.00000 0.200502
\(399\) 0 0
\(400\) 1.00000 0.0500000
\(401\) −1.00000 −0.0499376
\(402\) 0 0
\(403\) 1.00000 0.0498135
\(404\) 10.0000 0.497519
\(405\) 11.0000 0.546594
\(406\) 0 0
\(407\) −30.0000 −1.48704
\(408\) 16.0000 0.792118
\(409\) −18.0000 −0.890043 −0.445021 0.895520i \(-0.646804\pi\)
−0.445021 + 0.895520i \(0.646804\pi\)
\(410\) 7.00000 0.345705
\(411\) −44.0000 −2.17036
\(412\) 6.00000 0.295599
\(413\) 0 0
\(414\) 0 0
\(415\) 5.00000 0.245440
\(416\) −1.00000 −0.0490290
\(417\) 8.00000 0.391762
\(418\) 0 0
\(419\) −28.0000 −1.36789 −0.683945 0.729534i \(-0.739737\pi\)
−0.683945 + 0.729534i \(0.739737\pi\)
\(420\) 0 0
\(421\) −2.00000 −0.0974740 −0.0487370 0.998812i \(-0.515520\pi\)
−0.0487370 + 0.998812i \(0.515520\pi\)
\(422\) −16.0000 −0.778868
\(423\) 4.00000 0.194487
\(424\) 5.00000 0.242821
\(425\) −8.00000 −0.388057
\(426\) −18.0000 −0.872103
\(427\) 0 0
\(428\) 12.0000 0.580042
\(429\) 6.00000 0.289683
\(430\) −11.0000 −0.530467
\(431\) 1.00000 0.0481683 0.0240842 0.999710i \(-0.492333\pi\)
0.0240842 + 0.999710i \(0.492333\pi\)
\(432\) −4.00000 −0.192450
\(433\) 10.0000 0.480569 0.240285 0.970702i \(-0.422759\pi\)
0.240285 + 0.970702i \(0.422759\pi\)
\(434\) 0 0
\(435\) 8.00000 0.383571
\(436\) −14.0000 −0.670478
\(437\) 0 0
\(438\) −18.0000 −0.860073
\(439\) 28.0000 1.33637 0.668184 0.743996i \(-0.267072\pi\)
0.668184 + 0.743996i \(0.267072\pi\)
\(440\) 3.00000 0.143019
\(441\) −7.00000 −0.333333
\(442\) 8.00000 0.380521
\(443\) 20.0000 0.950229 0.475114 0.879924i \(-0.342407\pi\)
0.475114 + 0.879924i \(0.342407\pi\)
\(444\) −20.0000 −0.949158
\(445\) −7.00000 −0.331832
\(446\) −20.0000 −0.947027
\(447\) −20.0000 −0.945968
\(448\) 0 0
\(449\) 14.0000 0.660701 0.330350 0.943858i \(-0.392833\pi\)
0.330350 + 0.943858i \(0.392833\pi\)
\(450\) −1.00000 −0.0471405
\(451\) 21.0000 0.988851
\(452\) 15.0000 0.705541
\(453\) 24.0000 1.12762
\(454\) 4.00000 0.187729
\(455\) 0 0
\(456\) 0 0
\(457\) 1.00000 0.0467780 0.0233890 0.999726i \(-0.492554\pi\)
0.0233890 + 0.999726i \(0.492554\pi\)
\(458\) 10.0000 0.467269
\(459\) 32.0000 1.49363
\(460\) 0 0
\(461\) 10.0000 0.465746 0.232873 0.972507i \(-0.425187\pi\)
0.232873 + 0.972507i \(0.425187\pi\)
\(462\) 0 0
\(463\) 5.00000 0.232370 0.116185 0.993228i \(-0.462933\pi\)
0.116185 + 0.993228i \(0.462933\pi\)
\(464\) −4.00000 −0.185695
\(465\) −2.00000 −0.0927478
\(466\) −12.0000 −0.555889
\(467\) −6.00000 −0.277647 −0.138823 0.990317i \(-0.544332\pi\)
−0.138823 + 0.990317i \(0.544332\pi\)
\(468\) 1.00000 0.0462250
\(469\) 0 0
\(470\) 4.00000 0.184506
\(471\) −36.0000 −1.65879
\(472\) −4.00000 −0.184115
\(473\) −33.0000 −1.51734
\(474\) −6.00000 −0.275589
\(475\) 0 0
\(476\) 0 0
\(477\) −5.00000 −0.228934
\(478\) 6.00000 0.274434
\(479\) −40.0000 −1.82765 −0.913823 0.406112i \(-0.866884\pi\)
−0.913823 + 0.406112i \(0.866884\pi\)
\(480\) 2.00000 0.0912871
\(481\) −10.0000 −0.455961
\(482\) −17.0000 −0.774329
\(483\) 0 0
\(484\) −2.00000 −0.0909091
\(485\) 18.0000 0.817338
\(486\) 10.0000 0.453609
\(487\) 14.0000 0.634401 0.317200 0.948359i \(-0.397257\pi\)
0.317200 + 0.948359i \(0.397257\pi\)
\(488\) 13.0000 0.588482
\(489\) −20.0000 −0.904431
\(490\) −7.00000 −0.316228
\(491\) −15.0000 −0.676941 −0.338470 0.940977i \(-0.609909\pi\)
−0.338470 + 0.940977i \(0.609909\pi\)
\(492\) 14.0000 0.631169
\(493\) 32.0000 1.44121
\(494\) 0 0
\(495\) −3.00000 −0.134840
\(496\) 1.00000 0.0449013
\(497\) 0 0
\(498\) 10.0000 0.448111
\(499\) −4.00000 −0.179065 −0.0895323 0.995984i \(-0.528537\pi\)
−0.0895323 + 0.995984i \(0.528537\pi\)
\(500\) −1.00000 −0.0447214
\(501\) 38.0000 1.69771
\(502\) 20.0000 0.892644
\(503\) −42.0000 −1.87269 −0.936344 0.351085i \(-0.885813\pi\)
−0.936344 + 0.351085i \(0.885813\pi\)
\(504\) 0 0
\(505\) −10.0000 −0.444994
\(506\) 0 0
\(507\) −24.0000 −1.06588
\(508\) −3.00000 −0.133103
\(509\) 10.0000 0.443242 0.221621 0.975133i \(-0.428865\pi\)
0.221621 + 0.975133i \(0.428865\pi\)
\(510\) −16.0000 −0.708492
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 17.0000 0.749838
\(515\) −6.00000 −0.264392
\(516\) −22.0000 −0.968496
\(517\) 12.0000 0.527759
\(518\) 0 0
\(519\) −32.0000 −1.40464
\(520\) 1.00000 0.0438529
\(521\) −12.0000 −0.525730 −0.262865 0.964833i \(-0.584667\pi\)
−0.262865 + 0.964833i \(0.584667\pi\)
\(522\) 4.00000 0.175075
\(523\) −2.00000 −0.0874539 −0.0437269 0.999044i \(-0.513923\pi\)
−0.0437269 + 0.999044i \(0.513923\pi\)
\(524\) −8.00000 −0.349482
\(525\) 0 0
\(526\) −18.0000 −0.784837
\(527\) −8.00000 −0.348485
\(528\) 6.00000 0.261116
\(529\) −23.0000 −1.00000
\(530\) −5.00000 −0.217186
\(531\) 4.00000 0.173585
\(532\) 0 0
\(533\) 7.00000 0.303204
\(534\) −14.0000 −0.605839
\(535\) −12.0000 −0.518805
\(536\) 0 0
\(537\) −46.0000 −1.98505
\(538\) 3.00000 0.129339
\(539\) −21.0000 −0.904534
\(540\) 4.00000 0.172133
\(541\) 20.0000 0.859867 0.429934 0.902861i \(-0.358537\pi\)
0.429934 + 0.902861i \(0.358537\pi\)
\(542\) −8.00000 −0.343629
\(543\) −8.00000 −0.343313
\(544\) 8.00000 0.342997
\(545\) 14.0000 0.599694
\(546\) 0 0
\(547\) 15.0000 0.641354 0.320677 0.947189i \(-0.396090\pi\)
0.320677 + 0.947189i \(0.396090\pi\)
\(548\) −22.0000 −0.939793
\(549\) −13.0000 −0.554826
\(550\) −3.00000 −0.127920
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) −1.00000 −0.0424859
\(555\) 20.0000 0.848953
\(556\) 4.00000 0.169638
\(557\) −6.00000 −0.254228 −0.127114 0.991888i \(-0.540571\pi\)
−0.127114 + 0.991888i \(0.540571\pi\)
\(558\) −1.00000 −0.0423334
\(559\) −11.0000 −0.465250
\(560\) 0 0
\(561\) −48.0000 −2.02656
\(562\) 22.0000 0.928014
\(563\) 4.00000 0.168580 0.0842900 0.996441i \(-0.473138\pi\)
0.0842900 + 0.996441i \(0.473138\pi\)
\(564\) 8.00000 0.336861
\(565\) −15.0000 −0.631055
\(566\) 12.0000 0.504398
\(567\) 0 0
\(568\) −9.00000 −0.377632
\(569\) 40.0000 1.67689 0.838444 0.544988i \(-0.183466\pi\)
0.838444 + 0.544988i \(0.183466\pi\)
\(570\) 0 0
\(571\) −38.0000 −1.59025 −0.795125 0.606445i \(-0.792595\pi\)
−0.795125 + 0.606445i \(0.792595\pi\)
\(572\) 3.00000 0.125436
\(573\) 6.00000 0.250654
\(574\) 0 0
\(575\) 0 0
\(576\) 1.00000 0.0416667
\(577\) −33.0000 −1.37381 −0.686904 0.726748i \(-0.741031\pi\)
−0.686904 + 0.726748i \(0.741031\pi\)
\(578\) −47.0000 −1.95494
\(579\) −8.00000 −0.332469
\(580\) 4.00000 0.166091
\(581\) 0 0
\(582\) 36.0000 1.49225
\(583\) −15.0000 −0.621237
\(584\) −9.00000 −0.372423
\(585\) −1.00000 −0.0413449
\(586\) 1.00000 0.0413096
\(587\) −5.00000 −0.206372 −0.103186 0.994662i \(-0.532904\pi\)
−0.103186 + 0.994662i \(0.532904\pi\)
\(588\) −14.0000 −0.577350
\(589\) 0 0
\(590\) 4.00000 0.164677
\(591\) 12.0000 0.493614
\(592\) −10.0000 −0.410997
\(593\) −18.0000 −0.739171 −0.369586 0.929197i \(-0.620500\pi\)
−0.369586 + 0.929197i \(0.620500\pi\)
\(594\) 12.0000 0.492366
\(595\) 0 0
\(596\) −10.0000 −0.409616
\(597\) −8.00000 −0.327418
\(598\) 0 0
\(599\) 18.0000 0.735460 0.367730 0.929933i \(-0.380135\pi\)
0.367730 + 0.929933i \(0.380135\pi\)
\(600\) −2.00000 −0.0816497
\(601\) −34.0000 −1.38689 −0.693444 0.720510i \(-0.743908\pi\)
−0.693444 + 0.720510i \(0.743908\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 12.0000 0.488273
\(605\) 2.00000 0.0813116
\(606\) −20.0000 −0.812444
\(607\) 36.0000 1.46119 0.730597 0.682808i \(-0.239242\pi\)
0.730597 + 0.682808i \(0.239242\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) −13.0000 −0.526355
\(611\) 4.00000 0.161823
\(612\) −8.00000 −0.323381
\(613\) −41.0000 −1.65597 −0.827987 0.560747i \(-0.810514\pi\)
−0.827987 + 0.560747i \(0.810514\pi\)
\(614\) −23.0000 −0.928204
\(615\) −14.0000 −0.564534
\(616\) 0 0
\(617\) 28.0000 1.12724 0.563619 0.826035i \(-0.309409\pi\)
0.563619 + 0.826035i \(0.309409\pi\)
\(618\) −12.0000 −0.482711
\(619\) −17.0000 −0.683288 −0.341644 0.939829i \(-0.610984\pi\)
−0.341644 + 0.939829i \(0.610984\pi\)
\(620\) −1.00000 −0.0401610
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 2.00000 0.0800641
\(625\) 1.00000 0.0400000
\(626\) 31.0000 1.23901
\(627\) 0 0
\(628\) −18.0000 −0.718278
\(629\) 80.0000 3.18981
\(630\) 0 0
\(631\) 28.0000 1.11466 0.557331 0.830290i \(-0.311825\pi\)
0.557331 + 0.830290i \(0.311825\pi\)
\(632\) −3.00000 −0.119334
\(633\) 32.0000 1.27189
\(634\) 9.00000 0.357436
\(635\) 3.00000 0.119051
\(636\) −10.0000 −0.396526
\(637\) −7.00000 −0.277350
\(638\) 12.0000 0.475085
\(639\) 9.00000 0.356034
\(640\) 1.00000 0.0395285
\(641\) −4.00000 −0.157991 −0.0789953 0.996875i \(-0.525171\pi\)
−0.0789953 + 0.996875i \(0.525171\pi\)
\(642\) −24.0000 −0.947204
\(643\) 28.0000 1.10421 0.552106 0.833774i \(-0.313824\pi\)
0.552106 + 0.833774i \(0.313824\pi\)
\(644\) 0 0
\(645\) 22.0000 0.866249
\(646\) 0 0
\(647\) −3.00000 −0.117942 −0.0589711 0.998260i \(-0.518782\pi\)
−0.0589711 + 0.998260i \(0.518782\pi\)
\(648\) 11.0000 0.432121
\(649\) 12.0000 0.471041
\(650\) −1.00000 −0.0392232
\(651\) 0 0
\(652\) −10.0000 −0.391630
\(653\) −22.0000 −0.860927 −0.430463 0.902608i \(-0.641650\pi\)
−0.430463 + 0.902608i \(0.641650\pi\)
\(654\) 28.0000 1.09489
\(655\) 8.00000 0.312586
\(656\) 7.00000 0.273304
\(657\) 9.00000 0.351123
\(658\) 0 0
\(659\) 42.0000 1.63609 0.818044 0.575156i \(-0.195059\pi\)
0.818044 + 0.575156i \(0.195059\pi\)
\(660\) −6.00000 −0.233550
\(661\) −41.0000 −1.59472 −0.797358 0.603507i \(-0.793769\pi\)
−0.797358 + 0.603507i \(0.793769\pi\)
\(662\) −11.0000 −0.427527
\(663\) −16.0000 −0.621389
\(664\) 5.00000 0.194038
\(665\) 0 0
\(666\) 10.0000 0.387492
\(667\) 0 0
\(668\) 19.0000 0.735132
\(669\) 40.0000 1.54649
\(670\) 0 0
\(671\) −39.0000 −1.50558
\(672\) 0 0
\(673\) −42.0000 −1.61898 −0.809491 0.587133i \(-0.800257\pi\)
−0.809491 + 0.587133i \(0.800257\pi\)
\(674\) 3.00000 0.115556
\(675\) −4.00000 −0.153960
\(676\) −12.0000 −0.461538
\(677\) 12.0000 0.461197 0.230599 0.973049i \(-0.425932\pi\)
0.230599 + 0.973049i \(0.425932\pi\)
\(678\) −30.0000 −1.15214
\(679\) 0 0
\(680\) −8.00000 −0.306786
\(681\) −8.00000 −0.306561
\(682\) −3.00000 −0.114876
\(683\) 6.00000 0.229584 0.114792 0.993390i \(-0.463380\pi\)
0.114792 + 0.993390i \(0.463380\pi\)
\(684\) 0 0
\(685\) 22.0000 0.840577
\(686\) 0 0
\(687\) −20.0000 −0.763048
\(688\) −11.0000 −0.419371
\(689\) −5.00000 −0.190485
\(690\) 0 0
\(691\) 35.0000 1.33146 0.665731 0.746191i \(-0.268120\pi\)
0.665731 + 0.746191i \(0.268120\pi\)
\(692\) −16.0000 −0.608229
\(693\) 0 0
\(694\) −10.0000 −0.379595
\(695\) −4.00000 −0.151729
\(696\) 8.00000 0.303239
\(697\) −56.0000 −2.12115
\(698\) 10.0000 0.378506
\(699\) 24.0000 0.907763
\(700\) 0 0
\(701\) 45.0000 1.69963 0.849813 0.527084i \(-0.176715\pi\)
0.849813 + 0.527084i \(0.176715\pi\)
\(702\) 4.00000 0.150970
\(703\) 0 0
\(704\) 3.00000 0.113067
\(705\) −8.00000 −0.301297
\(706\) −6.00000 −0.225813
\(707\) 0 0
\(708\) 8.00000 0.300658
\(709\) −8.00000 −0.300446 −0.150223 0.988652i \(-0.547999\pi\)
−0.150223 + 0.988652i \(0.547999\pi\)
\(710\) 9.00000 0.337764
\(711\) 3.00000 0.112509
\(712\) −7.00000 −0.262336
\(713\) 0 0
\(714\) 0 0
\(715\) −3.00000 −0.112194
\(716\) −23.0000 −0.859550
\(717\) −12.0000 −0.448148
\(718\) −27.0000 −1.00763
\(719\) 48.0000 1.79010 0.895049 0.445968i \(-0.147140\pi\)
0.895049 + 0.445968i \(0.147140\pi\)
\(720\) −1.00000 −0.0372678
\(721\) 0 0
\(722\) 19.0000 0.707107
\(723\) 34.0000 1.26447
\(724\) −4.00000 −0.148659
\(725\) −4.00000 −0.148556
\(726\) 4.00000 0.148454
\(727\) −29.0000 −1.07555 −0.537775 0.843088i \(-0.680735\pi\)
−0.537775 + 0.843088i \(0.680735\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 9.00000 0.333105
\(731\) 88.0000 3.25480
\(732\) −26.0000 −0.960988
\(733\) 8.00000 0.295487 0.147743 0.989026i \(-0.452799\pi\)
0.147743 + 0.989026i \(0.452799\pi\)
\(734\) 35.0000 1.29187
\(735\) 14.0000 0.516398
\(736\) 0 0
\(737\) 0 0
\(738\) −7.00000 −0.257674
\(739\) 12.0000 0.441427 0.220714 0.975339i \(-0.429161\pi\)
0.220714 + 0.975339i \(0.429161\pi\)
\(740\) 10.0000 0.367607
\(741\) 0 0
\(742\) 0 0
\(743\) 37.0000 1.35740 0.678699 0.734416i \(-0.262544\pi\)
0.678699 + 0.734416i \(0.262544\pi\)
\(744\) −2.00000 −0.0733236
\(745\) 10.0000 0.366372
\(746\) −8.00000 −0.292901
\(747\) −5.00000 −0.182940
\(748\) −24.0000 −0.877527
\(749\) 0 0
\(750\) 2.00000 0.0730297
\(751\) −12.0000 −0.437886 −0.218943 0.975738i \(-0.570261\pi\)
−0.218943 + 0.975738i \(0.570261\pi\)
\(752\) 4.00000 0.145865
\(753\) −40.0000 −1.45768
\(754\) 4.00000 0.145671
\(755\) −12.0000 −0.436725
\(756\) 0 0
\(757\) 46.0000 1.67190 0.835949 0.548807i \(-0.184918\pi\)
0.835949 + 0.548807i \(0.184918\pi\)
\(758\) −35.0000 −1.27126
\(759\) 0 0
\(760\) 0 0
\(761\) 33.0000 1.19625 0.598125 0.801403i \(-0.295913\pi\)
0.598125 + 0.801403i \(0.295913\pi\)
\(762\) 6.00000 0.217357
\(763\) 0 0
\(764\) 3.00000 0.108536
\(765\) 8.00000 0.289241
\(766\) −12.0000 −0.433578
\(767\) 4.00000 0.144432
\(768\) 2.00000 0.0721688
\(769\) 22.0000 0.793340 0.396670 0.917961i \(-0.370166\pi\)
0.396670 + 0.917961i \(0.370166\pi\)
\(770\) 0 0
\(771\) −34.0000 −1.22448
\(772\) −4.00000 −0.143963
\(773\) −12.0000 −0.431610 −0.215805 0.976436i \(-0.569238\pi\)
−0.215805 + 0.976436i \(0.569238\pi\)
\(774\) 11.0000 0.395387
\(775\) 1.00000 0.0359211
\(776\) 18.0000 0.646162
\(777\) 0 0
\(778\) −37.0000 −1.32651
\(779\) 0 0
\(780\) −2.00000 −0.0716115
\(781\) 27.0000 0.966136
\(782\) 0 0
\(783\) 16.0000 0.571793
\(784\) −7.00000 −0.250000
\(785\) 18.0000 0.642448
\(786\) 16.0000 0.570701
\(787\) −14.0000 −0.499046 −0.249523 0.968369i \(-0.580274\pi\)
−0.249523 + 0.968369i \(0.580274\pi\)
\(788\) 6.00000 0.213741
\(789\) 36.0000 1.28163
\(790\) 3.00000 0.106735
\(791\) 0 0
\(792\) −3.00000 −0.106600
\(793\) −13.0000 −0.461644
\(794\) 14.0000 0.496841
\(795\) 10.0000 0.354663
\(796\) −4.00000 −0.141776
\(797\) −18.0000 −0.637593 −0.318796 0.947823i \(-0.603279\pi\)
−0.318796 + 0.947823i \(0.603279\pi\)
\(798\) 0 0
\(799\) −32.0000 −1.13208
\(800\) −1.00000 −0.0353553
\(801\) 7.00000 0.247333
\(802\) 1.00000 0.0353112
\(803\) 27.0000 0.952809
\(804\) 0 0
\(805\) 0 0
\(806\) −1.00000 −0.0352235
\(807\) −6.00000 −0.211210
\(808\) −10.0000 −0.351799
\(809\) −9.00000 −0.316423 −0.158212 0.987405i \(-0.550573\pi\)
−0.158212 + 0.987405i \(0.550573\pi\)
\(810\) −11.0000 −0.386501
\(811\) −24.0000 −0.842754 −0.421377 0.906886i \(-0.638453\pi\)
−0.421377 + 0.906886i \(0.638453\pi\)
\(812\) 0 0
\(813\) 16.0000 0.561144
\(814\) 30.0000 1.05150
\(815\) 10.0000 0.350285
\(816\) −16.0000 −0.560112
\(817\) 0 0
\(818\) 18.0000 0.629355
\(819\) 0 0
\(820\) −7.00000 −0.244451
\(821\) −3.00000 −0.104701 −0.0523504 0.998629i \(-0.516671\pi\)
−0.0523504 + 0.998629i \(0.516671\pi\)
\(822\) 44.0000 1.53468
\(823\) 19.0000 0.662298 0.331149 0.943578i \(-0.392564\pi\)
0.331149 + 0.943578i \(0.392564\pi\)
\(824\) −6.00000 −0.209020
\(825\) 6.00000 0.208893
\(826\) 0 0
\(827\) 28.0000 0.973655 0.486828 0.873498i \(-0.338154\pi\)
0.486828 + 0.873498i \(0.338154\pi\)
\(828\) 0 0
\(829\) 33.0000 1.14614 0.573069 0.819507i \(-0.305753\pi\)
0.573069 + 0.819507i \(0.305753\pi\)
\(830\) −5.00000 −0.173553
\(831\) 2.00000 0.0693792
\(832\) 1.00000 0.0346688
\(833\) 56.0000 1.94029
\(834\) −8.00000 −0.277017
\(835\) −19.0000 −0.657522
\(836\) 0 0
\(837\) −4.00000 −0.138260
\(838\) 28.0000 0.967244
\(839\) 27.0000 0.932144 0.466072 0.884747i \(-0.345669\pi\)
0.466072 + 0.884747i \(0.345669\pi\)
\(840\) 0 0
\(841\) −13.0000 −0.448276
\(842\) 2.00000 0.0689246
\(843\) −44.0000 −1.51544
\(844\) 16.0000 0.550743
\(845\) 12.0000 0.412813
\(846\) −4.00000 −0.137523
\(847\) 0 0
\(848\) −5.00000 −0.171701
\(849\) −24.0000 −0.823678
\(850\) 8.00000 0.274398
\(851\) 0 0
\(852\) 18.0000 0.616670
\(853\) −34.0000 −1.16414 −0.582069 0.813139i \(-0.697757\pi\)
−0.582069 + 0.813139i \(0.697757\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) −12.0000 −0.410152
\(857\) −7.00000 −0.239115 −0.119558 0.992827i \(-0.538148\pi\)
−0.119558 + 0.992827i \(0.538148\pi\)
\(858\) −6.00000 −0.204837
\(859\) 35.0000 1.19418 0.597092 0.802173i \(-0.296323\pi\)
0.597092 + 0.802173i \(0.296323\pi\)
\(860\) 11.0000 0.375097
\(861\) 0 0
\(862\) −1.00000 −0.0340601
\(863\) −4.00000 −0.136162 −0.0680808 0.997680i \(-0.521688\pi\)
−0.0680808 + 0.997680i \(0.521688\pi\)
\(864\) 4.00000 0.136083
\(865\) 16.0000 0.544016
\(866\) −10.0000 −0.339814
\(867\) 94.0000 3.19241
\(868\) 0 0
\(869\) 9.00000 0.305304
\(870\) −8.00000 −0.271225
\(871\) 0 0
\(872\) 14.0000 0.474100
\(873\) −18.0000 −0.609208
\(874\) 0 0
\(875\) 0 0
\(876\) 18.0000 0.608164
\(877\) 34.0000 1.14810 0.574049 0.818821i \(-0.305372\pi\)
0.574049 + 0.818821i \(0.305372\pi\)
\(878\) −28.0000 −0.944954
\(879\) −2.00000 −0.0674583
\(880\) −3.00000 −0.101130
\(881\) 38.0000 1.28025 0.640126 0.768270i \(-0.278882\pi\)
0.640126 + 0.768270i \(0.278882\pi\)
\(882\) 7.00000 0.235702
\(883\) −44.0000 −1.48072 −0.740359 0.672212i \(-0.765344\pi\)
−0.740359 + 0.672212i \(0.765344\pi\)
\(884\) −8.00000 −0.269069
\(885\) −8.00000 −0.268917
\(886\) −20.0000 −0.671913
\(887\) 12.0000 0.402921 0.201460 0.979497i \(-0.435431\pi\)
0.201460 + 0.979497i \(0.435431\pi\)
\(888\) 20.0000 0.671156
\(889\) 0 0
\(890\) 7.00000 0.234641
\(891\) −33.0000 −1.10554
\(892\) 20.0000 0.669650
\(893\) 0 0
\(894\) 20.0000 0.668900
\(895\) 23.0000 0.768805
\(896\) 0 0
\(897\) 0 0
\(898\) −14.0000 −0.467186
\(899\) −4.00000 −0.133407
\(900\) 1.00000 0.0333333
\(901\) 40.0000 1.33259
\(902\) −21.0000 −0.699224
\(903\) 0 0
\(904\) −15.0000 −0.498893
\(905\) 4.00000 0.132964
\(906\) −24.0000 −0.797347
\(907\) −38.0000 −1.26177 −0.630885 0.775877i \(-0.717308\pi\)
−0.630885 + 0.775877i \(0.717308\pi\)
\(908\) −4.00000 −0.132745
\(909\) 10.0000 0.331679
\(910\) 0 0
\(911\) −58.0000 −1.92163 −0.960813 0.277198i \(-0.910594\pi\)
−0.960813 + 0.277198i \(0.910594\pi\)
\(912\) 0 0
\(913\) −15.0000 −0.496428
\(914\) −1.00000 −0.0330771
\(915\) 26.0000 0.859533
\(916\) −10.0000 −0.330409
\(917\) 0 0
\(918\) −32.0000 −1.05616
\(919\) −53.0000 −1.74831 −0.874154 0.485648i \(-0.838584\pi\)
−0.874154 + 0.485648i \(0.838584\pi\)
\(920\) 0 0
\(921\) 46.0000 1.51575
\(922\) −10.0000 −0.329332
\(923\) 9.00000 0.296239
\(924\) 0 0
\(925\) −10.0000 −0.328798
\(926\) −5.00000 −0.164310
\(927\) 6.00000 0.197066
\(928\) 4.00000 0.131306
\(929\) 8.00000 0.262471 0.131236 0.991351i \(-0.458106\pi\)
0.131236 + 0.991351i \(0.458106\pi\)
\(930\) 2.00000 0.0655826
\(931\) 0 0
\(932\) 12.0000 0.393073
\(933\) 0 0
\(934\) 6.00000 0.196326
\(935\) 24.0000 0.784884
\(936\) −1.00000 −0.0326860
\(937\) −22.0000 −0.718709 −0.359354 0.933201i \(-0.617003\pi\)
−0.359354 + 0.933201i \(0.617003\pi\)
\(938\) 0 0
\(939\) −62.0000 −2.02329
\(940\) −4.00000 −0.130466
\(941\) 1.00000 0.0325991 0.0162995 0.999867i \(-0.494811\pi\)
0.0162995 + 0.999867i \(0.494811\pi\)
\(942\) 36.0000 1.17294
\(943\) 0 0
\(944\) 4.00000 0.130189
\(945\) 0 0
\(946\) 33.0000 1.07292
\(947\) −47.0000 −1.52729 −0.763647 0.645634i \(-0.776593\pi\)
−0.763647 + 0.645634i \(0.776593\pi\)
\(948\) 6.00000 0.194871
\(949\) 9.00000 0.292152
\(950\) 0 0
\(951\) −18.0000 −0.583690
\(952\) 0 0
\(953\) 9.00000 0.291539 0.145769 0.989319i \(-0.453434\pi\)
0.145769 + 0.989319i \(0.453434\pi\)
\(954\) 5.00000 0.161881
\(955\) −3.00000 −0.0970777
\(956\) −6.00000 −0.194054
\(957\) −24.0000 −0.775810
\(958\) 40.0000 1.29234
\(959\) 0 0
\(960\) −2.00000 −0.0645497
\(961\) −30.0000 −0.967742
\(962\) 10.0000 0.322413
\(963\) 12.0000 0.386695
\(964\) 17.0000 0.547533
\(965\) 4.00000 0.128765
\(966\) 0 0
\(967\) 8.00000 0.257263 0.128631 0.991692i \(-0.458942\pi\)
0.128631 + 0.991692i \(0.458942\pi\)
\(968\) 2.00000 0.0642824
\(969\) 0 0
\(970\) −18.0000 −0.577945
\(971\) 32.0000 1.02693 0.513464 0.858111i \(-0.328362\pi\)
0.513464 + 0.858111i \(0.328362\pi\)
\(972\) −10.0000 −0.320750
\(973\) 0 0
\(974\) −14.0000 −0.448589
\(975\) 2.00000 0.0640513
\(976\) −13.0000 −0.416120
\(977\) −11.0000 −0.351921 −0.175961 0.984397i \(-0.556303\pi\)
−0.175961 + 0.984397i \(0.556303\pi\)
\(978\) 20.0000 0.639529
\(979\) 21.0000 0.671163
\(980\) 7.00000 0.223607
\(981\) −14.0000 −0.446986
\(982\) 15.0000 0.478669
\(983\) 38.0000 1.21201 0.606006 0.795460i \(-0.292771\pi\)
0.606006 + 0.795460i \(0.292771\pi\)
\(984\) −14.0000 −0.446304
\(985\) −6.00000 −0.191176
\(986\) −32.0000 −1.01909
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 3.00000 0.0953463
\(991\) 61.0000 1.93773 0.968864 0.247592i \(-0.0796392\pi\)
0.968864 + 0.247592i \(0.0796392\pi\)
\(992\) −1.00000 −0.0317500
\(993\) 22.0000 0.698149
\(994\) 0 0
\(995\) 4.00000 0.126809
\(996\) −10.0000 −0.316862
\(997\) −22.0000 −0.696747 −0.348373 0.937356i \(-0.613266\pi\)
−0.348373 + 0.937356i \(0.613266\pi\)
\(998\) 4.00000 0.126618
\(999\) 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 \(a_p\))