Properties

Label 75.2.a.c.1.1
Level 75
Weight 2
Character 75.1
Self dual Yes
Analytic conductor 0.599
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 75 = 3 \cdot 5^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 75.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(0.59887801516\)
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 \(\chi\) = 75.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+2.00000 q^{2}\) \(-1.00000 q^{3}\) \(+2.00000 q^{4}\) \(-2.00000 q^{6}\) \(-3.00000 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+2.00000 q^{2}\) \(-1.00000 q^{3}\) \(+2.00000 q^{4}\) \(-2.00000 q^{6}\) \(-3.00000 q^{7}\) \(+1.00000 q^{9}\) \(+2.00000 q^{11}\) \(-2.00000 q^{12}\) \(+1.00000 q^{13}\) \(-6.00000 q^{14}\) \(-4.00000 q^{16}\) \(+2.00000 q^{17}\) \(+2.00000 q^{18}\) \(-5.00000 q^{19}\) \(+3.00000 q^{21}\) \(+4.00000 q^{22}\) \(+6.00000 q^{23}\) \(+2.00000 q^{26}\) \(-1.00000 q^{27}\) \(-6.00000 q^{28}\) \(+10.0000 q^{29}\) \(-3.00000 q^{31}\) \(-8.00000 q^{32}\) \(-2.00000 q^{33}\) \(+4.00000 q^{34}\) \(+2.00000 q^{36}\) \(+2.00000 q^{37}\) \(-10.0000 q^{38}\) \(-1.00000 q^{39}\) \(-8.00000 q^{41}\) \(+6.00000 q^{42}\) \(+1.00000 q^{43}\) \(+4.00000 q^{44}\) \(+12.0000 q^{46}\) \(+2.00000 q^{47}\) \(+4.00000 q^{48}\) \(+2.00000 q^{49}\) \(-2.00000 q^{51}\) \(+2.00000 q^{52}\) \(-4.00000 q^{53}\) \(-2.00000 q^{54}\) \(+5.00000 q^{57}\) \(+20.0000 q^{58}\) \(-10.0000 q^{59}\) \(+7.00000 q^{61}\) \(-6.00000 q^{62}\) \(-3.00000 q^{63}\) \(-8.00000 q^{64}\) \(-4.00000 q^{66}\) \(-3.00000 q^{67}\) \(+4.00000 q^{68}\) \(-6.00000 q^{69}\) \(-8.00000 q^{71}\) \(-14.0000 q^{73}\) \(+4.00000 q^{74}\) \(-10.0000 q^{76}\) \(-6.00000 q^{77}\) \(-2.00000 q^{78}\) \(+1.00000 q^{81}\) \(-16.0000 q^{82}\) \(+6.00000 q^{83}\) \(+6.00000 q^{84}\) \(+2.00000 q^{86}\) \(-10.0000 q^{87}\) \(-3.00000 q^{91}\) \(+12.0000 q^{92}\) \(+3.00000 q^{93}\) \(+4.00000 q^{94}\) \(+8.00000 q^{96}\) \(+17.0000 q^{97}\) \(+4.00000 q^{98}\) \(+2.00000 q^{99}\) \(+O(q^{100})\)

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 \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(3\) −1.00000 −0.577350
\(4\) 2.00000 1.00000
\(5\) 0 0
\(6\) −2.00000 −0.816497
\(7\) −3.00000 −1.13389 −0.566947 0.823754i \(-0.691875\pi\)
−0.566947 + 0.823754i \(0.691875\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 2.00000 0.603023 0.301511 0.953463i \(-0.402509\pi\)
0.301511 + 0.953463i \(0.402509\pi\)
\(12\) −2.00000 −0.577350
\(13\) 1.00000 0.277350 0.138675 0.990338i \(-0.455716\pi\)
0.138675 + 0.990338i \(0.455716\pi\)
\(14\) −6.00000 −1.60357
\(15\) 0 0
\(16\) −4.00000 −1.00000
\(17\) 2.00000 0.485071 0.242536 0.970143i \(-0.422021\pi\)
0.242536 + 0.970143i \(0.422021\pi\)
\(18\) 2.00000 0.471405
\(19\) −5.00000 −1.14708 −0.573539 0.819178i \(-0.694430\pi\)
−0.573539 + 0.819178i \(0.694430\pi\)
\(20\) 0 0
\(21\) 3.00000 0.654654
\(22\) 4.00000 0.852803
\(23\) 6.00000 1.25109 0.625543 0.780189i \(-0.284877\pi\)
0.625543 + 0.780189i \(0.284877\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 2.00000 0.392232
\(27\) −1.00000 −0.192450
\(28\) −6.00000 −1.13389
\(29\) 10.0000 1.85695 0.928477 0.371391i \(-0.121119\pi\)
0.928477 + 0.371391i \(0.121119\pi\)
\(30\) 0 0
\(31\) −3.00000 −0.538816 −0.269408 0.963026i \(-0.586828\pi\)
−0.269408 + 0.963026i \(0.586828\pi\)
\(32\) −8.00000 −1.41421
\(33\) −2.00000 −0.348155
\(34\) 4.00000 0.685994
\(35\) 0 0
\(36\) 2.00000 0.333333
\(37\) 2.00000 0.328798 0.164399 0.986394i \(-0.447432\pi\)
0.164399 + 0.986394i \(0.447432\pi\)
\(38\) −10.0000 −1.62221
\(39\) −1.00000 −0.160128
\(40\) 0 0
\(41\) −8.00000 −1.24939 −0.624695 0.780869i \(-0.714777\pi\)
−0.624695 + 0.780869i \(0.714777\pi\)
\(42\) 6.00000 0.925820
\(43\) 1.00000 0.152499 0.0762493 0.997089i \(-0.475706\pi\)
0.0762493 + 0.997089i \(0.475706\pi\)
\(44\) 4.00000 0.603023
\(45\) 0 0
\(46\) 12.0000 1.76930
\(47\) 2.00000 0.291730 0.145865 0.989305i \(-0.453403\pi\)
0.145865 + 0.989305i \(0.453403\pi\)
\(48\) 4.00000 0.577350
\(49\) 2.00000 0.285714
\(50\) 0 0
\(51\) −2.00000 −0.280056
\(52\) 2.00000 0.277350
\(53\) −4.00000 −0.549442 −0.274721 0.961524i \(-0.588586\pi\)
−0.274721 + 0.961524i \(0.588586\pi\)
\(54\) −2.00000 −0.272166
\(55\) 0 0
\(56\) 0 0
\(57\) 5.00000 0.662266
\(58\) 20.0000 2.62613
\(59\) −10.0000 −1.30189 −0.650945 0.759125i \(-0.725627\pi\)
−0.650945 + 0.759125i \(0.725627\pi\)
\(60\) 0 0
\(61\) 7.00000 0.896258 0.448129 0.893969i \(-0.352090\pi\)
0.448129 + 0.893969i \(0.352090\pi\)
\(62\) −6.00000 −0.762001
\(63\) −3.00000 −0.377964
\(64\) −8.00000 −1.00000
\(65\) 0 0
\(66\) −4.00000 −0.492366
\(67\) −3.00000 −0.366508 −0.183254 0.983066i \(-0.558663\pi\)
−0.183254 + 0.983066i \(0.558663\pi\)
\(68\) 4.00000 0.485071
\(69\) −6.00000 −0.722315
\(70\) 0 0
\(71\) −8.00000 −0.949425 −0.474713 0.880141i \(-0.657448\pi\)
−0.474713 + 0.880141i \(0.657448\pi\)
\(72\) 0 0
\(73\) −14.0000 −1.63858 −0.819288 0.573382i \(-0.805631\pi\)
−0.819288 + 0.573382i \(0.805631\pi\)
\(74\) 4.00000 0.464991
\(75\) 0 0
\(76\) −10.0000 −1.14708
\(77\) −6.00000 −0.683763
\(78\) −2.00000 −0.226455
\(79\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) −16.0000 −1.76690
\(83\) 6.00000 0.658586 0.329293 0.944228i \(-0.393190\pi\)
0.329293 + 0.944228i \(0.393190\pi\)
\(84\) 6.00000 0.654654
\(85\) 0 0
\(86\) 2.00000 0.215666
\(87\) −10.0000 −1.07211
\(88\) 0 0
\(89\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(90\) 0 0
\(91\) −3.00000 −0.314485
\(92\) 12.0000 1.25109
\(93\) 3.00000 0.311086
\(94\) 4.00000 0.412568
\(95\) 0 0
\(96\) 8.00000 0.816497
\(97\) 17.0000 1.72609 0.863044 0.505128i \(-0.168555\pi\)
0.863044 + 0.505128i \(0.168555\pi\)
\(98\) 4.00000 0.404061
\(99\) 2.00000 0.201008
\(100\) 0 0
\(101\) 12.0000 1.19404 0.597022 0.802225i \(-0.296350\pi\)
0.597022 + 0.802225i \(0.296350\pi\)
\(102\) −4.00000 −0.396059
\(103\) −4.00000 −0.394132 −0.197066 0.980390i \(-0.563141\pi\)
−0.197066 + 0.980390i \(0.563141\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) −8.00000 −0.777029
\(107\) 12.0000 1.16008 0.580042 0.814587i \(-0.303036\pi\)
0.580042 + 0.814587i \(0.303036\pi\)
\(108\) −2.00000 −0.192450
\(109\) 5.00000 0.478913 0.239457 0.970907i \(-0.423031\pi\)
0.239457 + 0.970907i \(0.423031\pi\)
\(110\) 0 0
\(111\) −2.00000 −0.189832
\(112\) 12.0000 1.13389
\(113\) −4.00000 −0.376288 −0.188144 0.982141i \(-0.560247\pi\)
−0.188144 + 0.982141i \(0.560247\pi\)
\(114\) 10.0000 0.936586
\(115\) 0 0
\(116\) 20.0000 1.85695
\(117\) 1.00000 0.0924500
\(118\) −20.0000 −1.84115
\(119\) −6.00000 −0.550019
\(120\) 0 0
\(121\) −7.00000 −0.636364
\(122\) 14.0000 1.26750
\(123\) 8.00000 0.721336
\(124\) −6.00000 −0.538816
\(125\) 0 0
\(126\) −6.00000 −0.534522
\(127\) −8.00000 −0.709885 −0.354943 0.934888i \(-0.615500\pi\)
−0.354943 + 0.934888i \(0.615500\pi\)
\(128\) 0 0
\(129\) −1.00000 −0.0880451
\(130\) 0 0
\(131\) 12.0000 1.04844 0.524222 0.851581i \(-0.324356\pi\)
0.524222 + 0.851581i \(0.324356\pi\)
\(132\) −4.00000 −0.348155
\(133\) 15.0000 1.30066
\(134\) −6.00000 −0.518321
\(135\) 0 0
\(136\) 0 0
\(137\) −18.0000 −1.53784 −0.768922 0.639343i \(-0.779207\pi\)
−0.768922 + 0.639343i \(0.779207\pi\)
\(138\) −12.0000 −1.02151
\(139\) 20.0000 1.69638 0.848189 0.529694i \(-0.177693\pi\)
0.848189 + 0.529694i \(0.177693\pi\)
\(140\) 0 0
\(141\) −2.00000 −0.168430
\(142\) −16.0000 −1.34269
\(143\) 2.00000 0.167248
\(144\) −4.00000 −0.333333
\(145\) 0 0
\(146\) −28.0000 −2.31730
\(147\) −2.00000 −0.164957
\(148\) 4.00000 0.328798
\(149\) 10.0000 0.819232 0.409616 0.912258i \(-0.365663\pi\)
0.409616 + 0.912258i \(0.365663\pi\)
\(150\) 0 0
\(151\) 7.00000 0.569652 0.284826 0.958579i \(-0.408064\pi\)
0.284826 + 0.958579i \(0.408064\pi\)
\(152\) 0 0
\(153\) 2.00000 0.161690
\(154\) −12.0000 −0.966988
\(155\) 0 0
\(156\) −2.00000 −0.160128
\(157\) −13.0000 −1.03751 −0.518756 0.854922i \(-0.673605\pi\)
−0.518756 + 0.854922i \(0.673605\pi\)
\(158\) 0 0
\(159\) 4.00000 0.317221
\(160\) 0 0
\(161\) −18.0000 −1.41860
\(162\) 2.00000 0.157135
\(163\) 11.0000 0.861586 0.430793 0.902451i \(-0.358234\pi\)
0.430793 + 0.902451i \(0.358234\pi\)
\(164\) −16.0000 −1.24939
\(165\) 0 0
\(166\) 12.0000 0.931381
\(167\) 12.0000 0.928588 0.464294 0.885681i \(-0.346308\pi\)
0.464294 + 0.885681i \(0.346308\pi\)
\(168\) 0 0
\(169\) −12.0000 −0.923077
\(170\) 0 0
\(171\) −5.00000 −0.382360
\(172\) 2.00000 0.152499
\(173\) 6.00000 0.456172 0.228086 0.973641i \(-0.426753\pi\)
0.228086 + 0.973641i \(0.426753\pi\)
\(174\) −20.0000 −1.51620
\(175\) 0 0
\(176\) −8.00000 −0.603023
\(177\) 10.0000 0.751646
\(178\) 0 0
\(179\) −10.0000 −0.747435 −0.373718 0.927543i \(-0.621917\pi\)
−0.373718 + 0.927543i \(0.621917\pi\)
\(180\) 0 0
\(181\) 17.0000 1.26360 0.631800 0.775131i \(-0.282316\pi\)
0.631800 + 0.775131i \(0.282316\pi\)
\(182\) −6.00000 −0.444750
\(183\) −7.00000 −0.517455
\(184\) 0 0
\(185\) 0 0
\(186\) 6.00000 0.439941
\(187\) 4.00000 0.292509
\(188\) 4.00000 0.291730
\(189\) 3.00000 0.218218
\(190\) 0 0
\(191\) 22.0000 1.59186 0.795932 0.605386i \(-0.206981\pi\)
0.795932 + 0.605386i \(0.206981\pi\)
\(192\) 8.00000 0.577350
\(193\) 11.0000 0.791797 0.395899 0.918294i \(-0.370433\pi\)
0.395899 + 0.918294i \(0.370433\pi\)
\(194\) 34.0000 2.44106
\(195\) 0 0
\(196\) 4.00000 0.285714
\(197\) −18.0000 −1.28245 −0.641223 0.767354i \(-0.721573\pi\)
−0.641223 + 0.767354i \(0.721573\pi\)
\(198\) 4.00000 0.284268
\(199\) −5.00000 −0.354441 −0.177220 0.984171i \(-0.556711\pi\)
−0.177220 + 0.984171i \(0.556711\pi\)
\(200\) 0 0
\(201\) 3.00000 0.211604
\(202\) 24.0000 1.68863
\(203\) −30.0000 −2.10559
\(204\) −4.00000 −0.280056
\(205\) 0 0
\(206\) −8.00000 −0.557386
\(207\) 6.00000 0.417029
\(208\) −4.00000 −0.277350
\(209\) −10.0000 −0.691714
\(210\) 0 0
\(211\) −13.0000 −0.894957 −0.447478 0.894295i \(-0.647678\pi\)
−0.447478 + 0.894295i \(0.647678\pi\)
\(212\) −8.00000 −0.549442
\(213\) 8.00000 0.548151
\(214\) 24.0000 1.64061
\(215\) 0 0
\(216\) 0 0
\(217\) 9.00000 0.610960
\(218\) 10.0000 0.677285
\(219\) 14.0000 0.946032
\(220\) 0 0
\(221\) 2.00000 0.134535
\(222\) −4.00000 −0.268462
\(223\) −19.0000 −1.27233 −0.636167 0.771551i \(-0.719481\pi\)
−0.636167 + 0.771551i \(0.719481\pi\)
\(224\) 24.0000 1.60357
\(225\) 0 0
\(226\) −8.00000 −0.532152
\(227\) −8.00000 −0.530979 −0.265489 0.964114i \(-0.585534\pi\)
−0.265489 + 0.964114i \(0.585534\pi\)
\(228\) 10.0000 0.662266
\(229\) −15.0000 −0.991228 −0.495614 0.868543i \(-0.665057\pi\)
−0.495614 + 0.868543i \(0.665057\pi\)
\(230\) 0 0
\(231\) 6.00000 0.394771
\(232\) 0 0
\(233\) −24.0000 −1.57229 −0.786146 0.618041i \(-0.787927\pi\)
−0.786146 + 0.618041i \(0.787927\pi\)
\(234\) 2.00000 0.130744
\(235\) 0 0
\(236\) −20.0000 −1.30189
\(237\) 0 0
\(238\) −12.0000 −0.777844
\(239\) 20.0000 1.29369 0.646846 0.762620i \(-0.276088\pi\)
0.646846 + 0.762620i \(0.276088\pi\)
\(240\) 0 0
\(241\) −23.0000 −1.48156 −0.740780 0.671748i \(-0.765544\pi\)
−0.740780 + 0.671748i \(0.765544\pi\)
\(242\) −14.0000 −0.899954
\(243\) −1.00000 −0.0641500
\(244\) 14.0000 0.896258
\(245\) 0 0
\(246\) 16.0000 1.02012
\(247\) −5.00000 −0.318142
\(248\) 0 0
\(249\) −6.00000 −0.380235
\(250\) 0 0
\(251\) 12.0000 0.757433 0.378717 0.925513i \(-0.376365\pi\)
0.378717 + 0.925513i \(0.376365\pi\)
\(252\) −6.00000 −0.377964
\(253\) 12.0000 0.754434
\(254\) −16.0000 −1.00393
\(255\) 0 0
\(256\) 16.0000 1.00000
\(257\) 12.0000 0.748539 0.374270 0.927320i \(-0.377893\pi\)
0.374270 + 0.927320i \(0.377893\pi\)
\(258\) −2.00000 −0.124515
\(259\) −6.00000 −0.372822
\(260\) 0 0
\(261\) 10.0000 0.618984
\(262\) 24.0000 1.48272
\(263\) 16.0000 0.986602 0.493301 0.869859i \(-0.335790\pi\)
0.493301 + 0.869859i \(0.335790\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 30.0000 1.83942
\(267\) 0 0
\(268\) −6.00000 −0.366508
\(269\) −10.0000 −0.609711 −0.304855 0.952399i \(-0.598608\pi\)
−0.304855 + 0.952399i \(0.598608\pi\)
\(270\) 0 0
\(271\) −8.00000 −0.485965 −0.242983 0.970031i \(-0.578126\pi\)
−0.242983 + 0.970031i \(0.578126\pi\)
\(272\) −8.00000 −0.485071
\(273\) 3.00000 0.181568
\(274\) −36.0000 −2.17484
\(275\) 0 0
\(276\) −12.0000 −0.722315
\(277\) −3.00000 −0.180253 −0.0901263 0.995930i \(-0.528727\pi\)
−0.0901263 + 0.995930i \(0.528727\pi\)
\(278\) 40.0000 2.39904
\(279\) −3.00000 −0.179605
\(280\) 0 0
\(281\) −18.0000 −1.07379 −0.536895 0.843649i \(-0.680403\pi\)
−0.536895 + 0.843649i \(0.680403\pi\)
\(282\) −4.00000 −0.238197
\(283\) −9.00000 −0.534994 −0.267497 0.963559i \(-0.586197\pi\)
−0.267497 + 0.963559i \(0.586197\pi\)
\(284\) −16.0000 −0.949425
\(285\) 0 0
\(286\) 4.00000 0.236525
\(287\) 24.0000 1.41668
\(288\) −8.00000 −0.471405
\(289\) −13.0000 −0.764706
\(290\) 0 0
\(291\) −17.0000 −0.996558
\(292\) −28.0000 −1.63858
\(293\) 6.00000 0.350524 0.175262 0.984522i \(-0.443923\pi\)
0.175262 + 0.984522i \(0.443923\pi\)
\(294\) −4.00000 −0.233285
\(295\) 0 0
\(296\) 0 0
\(297\) −2.00000 −0.116052
\(298\) 20.0000 1.15857
\(299\) 6.00000 0.346989
\(300\) 0 0
\(301\) −3.00000 −0.172917
\(302\) 14.0000 0.805609
\(303\) −12.0000 −0.689382
\(304\) 20.0000 1.14708
\(305\) 0 0
\(306\) 4.00000 0.228665
\(307\) 7.00000 0.399511 0.199756 0.979846i \(-0.435985\pi\)
0.199756 + 0.979846i \(0.435985\pi\)
\(308\) −12.0000 −0.683763
\(309\) 4.00000 0.227552
\(310\) 0 0
\(311\) −18.0000 −1.02069 −0.510343 0.859971i \(-0.670482\pi\)
−0.510343 + 0.859971i \(0.670482\pi\)
\(312\) 0 0
\(313\) 11.0000 0.621757 0.310878 0.950450i \(-0.399377\pi\)
0.310878 + 0.950450i \(0.399377\pi\)
\(314\) −26.0000 −1.46726
\(315\) 0 0
\(316\) 0 0
\(317\) −8.00000 −0.449325 −0.224662 0.974437i \(-0.572128\pi\)
−0.224662 + 0.974437i \(0.572128\pi\)
\(318\) 8.00000 0.448618
\(319\) 20.0000 1.11979
\(320\) 0 0
\(321\) −12.0000 −0.669775
\(322\) −36.0000 −2.00620
\(323\) −10.0000 −0.556415
\(324\) 2.00000 0.111111
\(325\) 0 0
\(326\) 22.0000 1.21847
\(327\) −5.00000 −0.276501
\(328\) 0 0
\(329\) −6.00000 −0.330791
\(330\) 0 0
\(331\) 12.0000 0.659580 0.329790 0.944054i \(-0.393022\pi\)
0.329790 + 0.944054i \(0.393022\pi\)
\(332\) 12.0000 0.658586
\(333\) 2.00000 0.109599
\(334\) 24.0000 1.31322
\(335\) 0 0
\(336\) −12.0000 −0.654654
\(337\) −23.0000 −1.25289 −0.626445 0.779466i \(-0.715491\pi\)
−0.626445 + 0.779466i \(0.715491\pi\)
\(338\) −24.0000 −1.30543
\(339\) 4.00000 0.217250
\(340\) 0 0
\(341\) −6.00000 −0.324918
\(342\) −10.0000 −0.540738
\(343\) 15.0000 0.809924
\(344\) 0 0
\(345\) 0 0
\(346\) 12.0000 0.645124
\(347\) 2.00000 0.107366 0.0536828 0.998558i \(-0.482904\pi\)
0.0536828 + 0.998558i \(0.482904\pi\)
\(348\) −20.0000 −1.07211
\(349\) 10.0000 0.535288 0.267644 0.963518i \(-0.413755\pi\)
0.267644 + 0.963518i \(0.413755\pi\)
\(350\) 0 0
\(351\) −1.00000 −0.0533761
\(352\) −16.0000 −0.852803
\(353\) 6.00000 0.319348 0.159674 0.987170i \(-0.448956\pi\)
0.159674 + 0.987170i \(0.448956\pi\)
\(354\) 20.0000 1.06299
\(355\) 0 0
\(356\) 0 0
\(357\) 6.00000 0.317554
\(358\) −20.0000 −1.05703
\(359\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(360\) 0 0
\(361\) 6.00000 0.315789
\(362\) 34.0000 1.78700
\(363\) 7.00000 0.367405
\(364\) −6.00000 −0.314485
\(365\) 0 0
\(366\) −14.0000 −0.731792
\(367\) 27.0000 1.40939 0.704694 0.709511i \(-0.251084\pi\)
0.704694 + 0.709511i \(0.251084\pi\)
\(368\) −24.0000 −1.25109
\(369\) −8.00000 −0.416463
\(370\) 0 0
\(371\) 12.0000 0.623009
\(372\) 6.00000 0.311086
\(373\) −29.0000 −1.50156 −0.750782 0.660551i \(-0.770323\pi\)
−0.750782 + 0.660551i \(0.770323\pi\)
\(374\) 8.00000 0.413670
\(375\) 0 0
\(376\) 0 0
\(377\) 10.0000 0.515026
\(378\) 6.00000 0.308607
\(379\) 25.0000 1.28416 0.642082 0.766636i \(-0.278071\pi\)
0.642082 + 0.766636i \(0.278071\pi\)
\(380\) 0 0
\(381\) 8.00000 0.409852
\(382\) 44.0000 2.25124
\(383\) 36.0000 1.83951 0.919757 0.392488i \(-0.128386\pi\)
0.919757 + 0.392488i \(0.128386\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 22.0000 1.11977
\(387\) 1.00000 0.0508329
\(388\) 34.0000 1.72609
\(389\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(390\) 0 0
\(391\) 12.0000 0.606866
\(392\) 0 0
\(393\) −12.0000 −0.605320
\(394\) −36.0000 −1.81365
\(395\) 0 0
\(396\) 4.00000 0.201008
\(397\) 7.00000 0.351320 0.175660 0.984451i \(-0.443794\pi\)
0.175660 + 0.984451i \(0.443794\pi\)
\(398\) −10.0000 −0.501255
\(399\) −15.0000 −0.750939
\(400\) 0 0
\(401\) 12.0000 0.599251 0.299626 0.954057i \(-0.403138\pi\)
0.299626 + 0.954057i \(0.403138\pi\)
\(402\) 6.00000 0.299253
\(403\) −3.00000 −0.149441
\(404\) 24.0000 1.19404
\(405\) 0 0
\(406\) −60.0000 −2.97775
\(407\) 4.00000 0.198273
\(408\) 0 0
\(409\) 5.00000 0.247234 0.123617 0.992330i \(-0.460551\pi\)
0.123617 + 0.992330i \(0.460551\pi\)
\(410\) 0 0
\(411\) 18.0000 0.887875
\(412\) −8.00000 −0.394132
\(413\) 30.0000 1.47620
\(414\) 12.0000 0.589768
\(415\) 0 0
\(416\) −8.00000 −0.392232
\(417\) −20.0000 −0.979404
\(418\) −20.0000 −0.978232
\(419\) −20.0000 −0.977064 −0.488532 0.872546i \(-0.662467\pi\)
−0.488532 + 0.872546i \(0.662467\pi\)
\(420\) 0 0
\(421\) 22.0000 1.07221 0.536107 0.844150i \(-0.319894\pi\)
0.536107 + 0.844150i \(0.319894\pi\)
\(422\) −26.0000 −1.26566
\(423\) 2.00000 0.0972433
\(424\) 0 0
\(425\) 0 0
\(426\) 16.0000 0.775203
\(427\) −21.0000 −1.01626
\(428\) 24.0000 1.16008
\(429\) −2.00000 −0.0965609
\(430\) 0 0
\(431\) −18.0000 −0.867029 −0.433515 0.901146i \(-0.642727\pi\)
−0.433515 + 0.901146i \(0.642727\pi\)
\(432\) 4.00000 0.192450
\(433\) −29.0000 −1.39365 −0.696826 0.717241i \(-0.745405\pi\)
−0.696826 + 0.717241i \(0.745405\pi\)
\(434\) 18.0000 0.864028
\(435\) 0 0
\(436\) 10.0000 0.478913
\(437\) −30.0000 −1.43509
\(438\) 28.0000 1.33789
\(439\) −35.0000 −1.67046 −0.835229 0.549902i \(-0.814665\pi\)
−0.835229 + 0.549902i \(0.814665\pi\)
\(440\) 0 0
\(441\) 2.00000 0.0952381
\(442\) 4.00000 0.190261
\(443\) −24.0000 −1.14027 −0.570137 0.821549i \(-0.693110\pi\)
−0.570137 + 0.821549i \(0.693110\pi\)
\(444\) −4.00000 −0.189832
\(445\) 0 0
\(446\) −38.0000 −1.79935
\(447\) −10.0000 −0.472984
\(448\) 24.0000 1.13389
\(449\) 20.0000 0.943858 0.471929 0.881636i \(-0.343558\pi\)
0.471929 + 0.881636i \(0.343558\pi\)
\(450\) 0 0
\(451\) −16.0000 −0.753411
\(452\) −8.00000 −0.376288
\(453\) −7.00000 −0.328889
\(454\) −16.0000 −0.750917
\(455\) 0 0
\(456\) 0 0
\(457\) 22.0000 1.02912 0.514558 0.857455i \(-0.327956\pi\)
0.514558 + 0.857455i \(0.327956\pi\)
\(458\) −30.0000 −1.40181
\(459\) −2.00000 −0.0933520
\(460\) 0 0
\(461\) 12.0000 0.558896 0.279448 0.960161i \(-0.409849\pi\)
0.279448 + 0.960161i \(0.409849\pi\)
\(462\) 12.0000 0.558291
\(463\) −24.0000 −1.11537 −0.557687 0.830051i \(-0.688311\pi\)
−0.557687 + 0.830051i \(0.688311\pi\)
\(464\) −40.0000 −1.85695
\(465\) 0 0
\(466\) −48.0000 −2.22356
\(467\) −38.0000 −1.75843 −0.879215 0.476425i \(-0.841932\pi\)
−0.879215 + 0.476425i \(0.841932\pi\)
\(468\) 2.00000 0.0924500
\(469\) 9.00000 0.415581
\(470\) 0 0
\(471\) 13.0000 0.599008
\(472\) 0 0
\(473\) 2.00000 0.0919601
\(474\) 0 0
\(475\) 0 0
\(476\) −12.0000 −0.550019
\(477\) −4.00000 −0.183147
\(478\) 40.0000 1.82956
\(479\) 30.0000 1.37073 0.685367 0.728197i \(-0.259642\pi\)
0.685367 + 0.728197i \(0.259642\pi\)
\(480\) 0 0
\(481\) 2.00000 0.0911922
\(482\) −46.0000 −2.09524
\(483\) 18.0000 0.819028
\(484\) −14.0000 −0.636364
\(485\) 0 0
\(486\) −2.00000 −0.0907218
\(487\) −13.0000 −0.589086 −0.294543 0.955638i \(-0.595167\pi\)
−0.294543 + 0.955638i \(0.595167\pi\)
\(488\) 0 0
\(489\) −11.0000 −0.497437
\(490\) 0 0
\(491\) −8.00000 −0.361035 −0.180517 0.983572i \(-0.557777\pi\)
−0.180517 + 0.983572i \(0.557777\pi\)
\(492\) 16.0000 0.721336
\(493\) 20.0000 0.900755
\(494\) −10.0000 −0.449921
\(495\) 0 0
\(496\) 12.0000 0.538816
\(497\) 24.0000 1.07655
\(498\) −12.0000 −0.537733
\(499\) −5.00000 −0.223831 −0.111915 0.993718i \(-0.535699\pi\)
−0.111915 + 0.993718i \(0.535699\pi\)
\(500\) 0 0
\(501\) −12.0000 −0.536120
\(502\) 24.0000 1.07117
\(503\) 16.0000 0.713405 0.356702 0.934218i \(-0.383901\pi\)
0.356702 + 0.934218i \(0.383901\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 24.0000 1.06693
\(507\) 12.0000 0.532939
\(508\) −16.0000 −0.709885
\(509\) −10.0000 −0.443242 −0.221621 0.975133i \(-0.571135\pi\)
−0.221621 + 0.975133i \(0.571135\pi\)
\(510\) 0 0
\(511\) 42.0000 1.85797
\(512\) 32.0000 1.41421
\(513\) 5.00000 0.220755
\(514\) 24.0000 1.05859
\(515\) 0 0
\(516\) −2.00000 −0.0880451
\(517\) 4.00000 0.175920
\(518\) −12.0000 −0.527250
\(519\) −6.00000 −0.263371
\(520\) 0 0
\(521\) 22.0000 0.963837 0.481919 0.876216i \(-0.339940\pi\)
0.481919 + 0.876216i \(0.339940\pi\)
\(522\) 20.0000 0.875376
\(523\) 31.0000 1.35554 0.677768 0.735276i \(-0.262948\pi\)
0.677768 + 0.735276i \(0.262948\pi\)
\(524\) 24.0000 1.04844
\(525\) 0 0
\(526\) 32.0000 1.39527
\(527\) −6.00000 −0.261364
\(528\) 8.00000 0.348155
\(529\) 13.0000 0.565217
\(530\) 0 0
\(531\) −10.0000 −0.433963
\(532\) 30.0000 1.30066
\(533\) −8.00000 −0.346518
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 10.0000 0.431532
\(538\) −20.0000 −0.862261
\(539\) 4.00000 0.172292
\(540\) 0 0
\(541\) −3.00000 −0.128980 −0.0644900 0.997918i \(-0.520542\pi\)
−0.0644900 + 0.997918i \(0.520542\pi\)
\(542\) −16.0000 −0.687259
\(543\) −17.0000 −0.729540
\(544\) −16.0000 −0.685994
\(545\) 0 0
\(546\) 6.00000 0.256776
\(547\) −8.00000 −0.342055 −0.171028 0.985266i \(-0.554709\pi\)
−0.171028 + 0.985266i \(0.554709\pi\)
\(548\) −36.0000 −1.53784
\(549\) 7.00000 0.298753
\(550\) 0 0
\(551\) −50.0000 −2.13007
\(552\) 0 0
\(553\) 0 0
\(554\) −6.00000 −0.254916
\(555\) 0 0
\(556\) 40.0000 1.69638
\(557\) 42.0000 1.77960 0.889799 0.456354i \(-0.150845\pi\)
0.889799 + 0.456354i \(0.150845\pi\)
\(558\) −6.00000 −0.254000
\(559\) 1.00000 0.0422955
\(560\) 0 0
\(561\) −4.00000 −0.168880
\(562\) −36.0000 −1.51857
\(563\) 6.00000 0.252870 0.126435 0.991975i \(-0.459647\pi\)
0.126435 + 0.991975i \(0.459647\pi\)
\(564\) −4.00000 −0.168430
\(565\) 0 0
\(566\) −18.0000 −0.756596
\(567\) −3.00000 −0.125988
\(568\) 0 0
\(569\) 30.0000 1.25767 0.628833 0.777541i \(-0.283533\pi\)
0.628833 + 0.777541i \(0.283533\pi\)
\(570\) 0 0
\(571\) −13.0000 −0.544033 −0.272017 0.962293i \(-0.587691\pi\)
−0.272017 + 0.962293i \(0.587691\pi\)
\(572\) 4.00000 0.167248
\(573\) −22.0000 −0.919063
\(574\) 48.0000 2.00348
\(575\) 0 0
\(576\) −8.00000 −0.333333
\(577\) −13.0000 −0.541197 −0.270599 0.962692i \(-0.587222\pi\)
−0.270599 + 0.962692i \(0.587222\pi\)
\(578\) −26.0000 −1.08146
\(579\) −11.0000 −0.457144
\(580\) 0 0
\(581\) −18.0000 −0.746766
\(582\) −34.0000 −1.40935
\(583\) −8.00000 −0.331326
\(584\) 0 0
\(585\) 0 0
\(586\) 12.0000 0.495715
\(587\) 12.0000 0.495293 0.247647 0.968850i \(-0.420343\pi\)
0.247647 + 0.968850i \(0.420343\pi\)
\(588\) −4.00000 −0.164957
\(589\) 15.0000 0.618064
\(590\) 0 0
\(591\) 18.0000 0.740421
\(592\) −8.00000 −0.328798
\(593\) 16.0000 0.657041 0.328521 0.944497i \(-0.393450\pi\)
0.328521 + 0.944497i \(0.393450\pi\)
\(594\) −4.00000 −0.164122
\(595\) 0 0
\(596\) 20.0000 0.819232
\(597\) 5.00000 0.204636
\(598\) 12.0000 0.490716
\(599\) −20.0000 −0.817178 −0.408589 0.912719i \(-0.633979\pi\)
−0.408589 + 0.912719i \(0.633979\pi\)
\(600\) 0 0
\(601\) −13.0000 −0.530281 −0.265141 0.964210i \(-0.585418\pi\)
−0.265141 + 0.964210i \(0.585418\pi\)
\(602\) −6.00000 −0.244542
\(603\) −3.00000 −0.122169
\(604\) 14.0000 0.569652
\(605\) 0 0
\(606\) −24.0000 −0.974933
\(607\) −8.00000 −0.324710 −0.162355 0.986732i \(-0.551909\pi\)
−0.162355 + 0.986732i \(0.551909\pi\)
\(608\) 40.0000 1.62221
\(609\) 30.0000 1.21566
\(610\) 0 0
\(611\) 2.00000 0.0809113
\(612\) 4.00000 0.161690
\(613\) −14.0000 −0.565455 −0.282727 0.959200i \(-0.591239\pi\)
−0.282727 + 0.959200i \(0.591239\pi\)
\(614\) 14.0000 0.564994
\(615\) 0 0
\(616\) 0 0
\(617\) 12.0000 0.483102 0.241551 0.970388i \(-0.422344\pi\)
0.241551 + 0.970388i \(0.422344\pi\)
\(618\) 8.00000 0.321807
\(619\) −25.0000 −1.00483 −0.502417 0.864625i \(-0.667556\pi\)
−0.502417 + 0.864625i \(0.667556\pi\)
\(620\) 0 0
\(621\) −6.00000 −0.240772
\(622\) −36.0000 −1.44347
\(623\) 0 0
\(624\) 4.00000 0.160128
\(625\) 0 0
\(626\) 22.0000 0.879297
\(627\) 10.0000 0.399362
\(628\) −26.0000 −1.03751
\(629\) 4.00000 0.159490
\(630\) 0 0
\(631\) −23.0000 −0.915616 −0.457808 0.889051i \(-0.651365\pi\)
−0.457808 + 0.889051i \(0.651365\pi\)
\(632\) 0 0
\(633\) 13.0000 0.516704
\(634\) −16.0000 −0.635441
\(635\) 0 0
\(636\) 8.00000 0.317221
\(637\) 2.00000 0.0792429
\(638\) 40.0000 1.58362
\(639\) −8.00000 −0.316475
\(640\) 0 0
\(641\) 12.0000 0.473972 0.236986 0.971513i \(-0.423841\pi\)
0.236986 + 0.971513i \(0.423841\pi\)
\(642\) −24.0000 −0.947204
\(643\) 36.0000 1.41970 0.709851 0.704352i \(-0.248762\pi\)
0.709851 + 0.704352i \(0.248762\pi\)
\(644\) −36.0000 −1.41860
\(645\) 0 0
\(646\) −20.0000 −0.786889
\(647\) −28.0000 −1.10079 −0.550397 0.834903i \(-0.685524\pi\)
−0.550397 + 0.834903i \(0.685524\pi\)
\(648\) 0 0
\(649\) −20.0000 −0.785069
\(650\) 0 0
\(651\) −9.00000 −0.352738
\(652\) 22.0000 0.861586
\(653\) −14.0000 −0.547862 −0.273931 0.961749i \(-0.588324\pi\)
−0.273931 + 0.961749i \(0.588324\pi\)
\(654\) −10.0000 −0.391031
\(655\) 0 0
\(656\) 32.0000 1.24939
\(657\) −14.0000 −0.546192
\(658\) −12.0000 −0.467809
\(659\) −40.0000 −1.55818 −0.779089 0.626913i \(-0.784318\pi\)
−0.779089 + 0.626913i \(0.784318\pi\)
\(660\) 0 0
\(661\) −38.0000 −1.47803 −0.739014 0.673690i \(-0.764708\pi\)
−0.739014 + 0.673690i \(0.764708\pi\)
\(662\) 24.0000 0.932786
\(663\) −2.00000 −0.0776736
\(664\) 0 0
\(665\) 0 0
\(666\) 4.00000 0.154997
\(667\) 60.0000 2.32321
\(668\) 24.0000 0.928588
\(669\) 19.0000 0.734582
\(670\) 0 0
\(671\) 14.0000 0.540464
\(672\) −24.0000 −0.925820
\(673\) 6.00000 0.231283 0.115642 0.993291i \(-0.463108\pi\)
0.115642 + 0.993291i \(0.463108\pi\)
\(674\) −46.0000 −1.77185
\(675\) 0 0
\(676\) −24.0000 −0.923077
\(677\) 42.0000 1.61419 0.807096 0.590421i \(-0.201038\pi\)
0.807096 + 0.590421i \(0.201038\pi\)
\(678\) 8.00000 0.307238
\(679\) −51.0000 −1.95720
\(680\) 0 0
\(681\) 8.00000 0.306561
\(682\) −12.0000 −0.459504
\(683\) −24.0000 −0.918334 −0.459167 0.888350i \(-0.651852\pi\)
−0.459167 + 0.888350i \(0.651852\pi\)
\(684\) −10.0000 −0.382360
\(685\) 0 0
\(686\) 30.0000 1.14541
\(687\) 15.0000 0.572286
\(688\) −4.00000 −0.152499
\(689\) −4.00000 −0.152388
\(690\) 0 0
\(691\) −8.00000 −0.304334 −0.152167 0.988355i \(-0.548625\pi\)
−0.152167 + 0.988355i \(0.548625\pi\)
\(692\) 12.0000 0.456172
\(693\) −6.00000 −0.227921
\(694\) 4.00000 0.151838
\(695\) 0 0
\(696\) 0 0
\(697\) −16.0000 −0.606043
\(698\) 20.0000 0.757011
\(699\) 24.0000 0.907763
\(700\) 0 0
\(701\) 22.0000 0.830929 0.415464 0.909610i \(-0.363619\pi\)
0.415464 + 0.909610i \(0.363619\pi\)
\(702\) −2.00000 −0.0754851
\(703\) −10.0000 −0.377157
\(704\) −16.0000 −0.603023
\(705\) 0 0
\(706\) 12.0000 0.451626
\(707\) −36.0000 −1.35392
\(708\) 20.0000 0.751646
\(709\) 25.0000 0.938895 0.469447 0.882960i \(-0.344453\pi\)
0.469447 + 0.882960i \(0.344453\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −18.0000 −0.674105
\(714\) 12.0000 0.449089
\(715\) 0 0
\(716\) −20.0000 −0.747435
\(717\) −20.0000 −0.746914
\(718\) 0 0
\(719\) 30.0000 1.11881 0.559406 0.828894i \(-0.311029\pi\)
0.559406 + 0.828894i \(0.311029\pi\)
\(720\) 0 0
\(721\) 12.0000 0.446903
\(722\) 12.0000 0.446594
\(723\) 23.0000 0.855379
\(724\) 34.0000 1.26360
\(725\) 0 0
\(726\) 14.0000 0.519589
\(727\) −43.0000 −1.59478 −0.797391 0.603463i \(-0.793787\pi\)
−0.797391 + 0.603463i \(0.793787\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 2.00000 0.0739727
\(732\) −14.0000 −0.517455
\(733\) −34.0000 −1.25582 −0.627909 0.778287i \(-0.716089\pi\)
−0.627909 + 0.778287i \(0.716089\pi\)
\(734\) 54.0000 1.99318
\(735\) 0 0
\(736\) −48.0000 −1.76930
\(737\) −6.00000 −0.221013
\(738\) −16.0000 −0.588968
\(739\) −20.0000 −0.735712 −0.367856 0.929883i \(-0.619908\pi\)
−0.367856 + 0.929883i \(0.619908\pi\)
\(740\) 0 0
\(741\) 5.00000 0.183680
\(742\) 24.0000 0.881068
\(743\) −4.00000 −0.146746 −0.0733729 0.997305i \(-0.523376\pi\)
−0.0733729 + 0.997305i \(0.523376\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −58.0000 −2.12353
\(747\) 6.00000 0.219529
\(748\) 8.00000 0.292509
\(749\) −36.0000 −1.31541
\(750\) 0 0
\(751\) −8.00000 −0.291924 −0.145962 0.989290i \(-0.546628\pi\)
−0.145962 + 0.989290i \(0.546628\pi\)
\(752\) −8.00000 −0.291730
\(753\) −12.0000 −0.437304
\(754\) 20.0000 0.728357
\(755\) 0 0
\(756\) 6.00000 0.218218
\(757\) −23.0000 −0.835949 −0.417975 0.908459i \(-0.637260\pi\)
−0.417975 + 0.908459i \(0.637260\pi\)
\(758\) 50.0000 1.81608
\(759\) −12.0000 −0.435572
\(760\) 0 0
\(761\) 12.0000 0.435000 0.217500 0.976060i \(-0.430210\pi\)
0.217500 + 0.976060i \(0.430210\pi\)
\(762\) 16.0000 0.579619
\(763\) −15.0000 −0.543036
\(764\) 44.0000 1.59186
\(765\) 0 0
\(766\) 72.0000 2.60147
\(767\) −10.0000 −0.361079
\(768\) −16.0000 −0.577350
\(769\) 35.0000 1.26213 0.631066 0.775729i \(-0.282618\pi\)
0.631066 + 0.775729i \(0.282618\pi\)
\(770\) 0 0
\(771\) −12.0000 −0.432169
\(772\) 22.0000 0.791797
\(773\) −24.0000 −0.863220 −0.431610 0.902060i \(-0.642054\pi\)
−0.431610 + 0.902060i \(0.642054\pi\)
\(774\) 2.00000 0.0718885
\(775\) 0 0
\(776\) 0 0
\(777\) 6.00000 0.215249
\(778\) 0 0
\(779\) 40.0000 1.43315
\(780\) 0 0
\(781\) −16.0000 −0.572525
\(782\) 24.0000 0.858238
\(783\) −10.0000 −0.357371
\(784\) −8.00000 −0.285714
\(785\) 0 0
\(786\) −24.0000 −0.856052
\(787\) 7.00000 0.249523 0.124762 0.992187i \(-0.460183\pi\)
0.124762 + 0.992187i \(0.460183\pi\)
\(788\) −36.0000 −1.28245
\(789\) −16.0000 −0.569615
\(790\) 0 0
\(791\) 12.0000 0.426671
\(792\) 0 0
\(793\) 7.00000 0.248577
\(794\) 14.0000 0.496841
\(795\) 0 0
\(796\) −10.0000 −0.354441
\(797\) 52.0000 1.84193 0.920967 0.389640i \(-0.127401\pi\)
0.920967 + 0.389640i \(0.127401\pi\)
\(798\) −30.0000 −1.06199
\(799\) 4.00000 0.141510
\(800\) 0 0
\(801\) 0 0
\(802\) 24.0000 0.847469
\(803\) −28.0000 −0.988099
\(804\) 6.00000 0.211604
\(805\) 0 0
\(806\) −6.00000 −0.211341
\(807\) 10.0000 0.352017
\(808\) 0 0
\(809\) −20.0000 −0.703163 −0.351581 0.936157i \(-0.614356\pi\)
−0.351581 + 0.936157i \(0.614356\pi\)
\(810\) 0 0
\(811\) 27.0000 0.948098 0.474049 0.880498i \(-0.342792\pi\)
0.474049 + 0.880498i \(0.342792\pi\)
\(812\) −60.0000 −2.10559
\(813\) 8.00000 0.280572
\(814\) 8.00000 0.280400
\(815\) 0 0
\(816\) 8.00000 0.280056
\(817\) −5.00000 −0.174928
\(818\) 10.0000 0.349642
\(819\) −3.00000 −0.104828
\(820\) 0 0
\(821\) −18.0000 −0.628204 −0.314102 0.949389i \(-0.601703\pi\)
−0.314102 + 0.949389i \(0.601703\pi\)
\(822\) 36.0000 1.25564
\(823\) 41.0000 1.42917 0.714585 0.699549i \(-0.246616\pi\)
0.714585 + 0.699549i \(0.246616\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 60.0000 2.08767
\(827\) −28.0000 −0.973655 −0.486828 0.873498i \(-0.661846\pi\)
−0.486828 + 0.873498i \(0.661846\pi\)
\(828\) 12.0000 0.417029
\(829\) −30.0000 −1.04194 −0.520972 0.853574i \(-0.674430\pi\)
−0.520972 + 0.853574i \(0.674430\pi\)
\(830\) 0 0
\(831\) 3.00000 0.104069
\(832\) −8.00000 −0.277350
\(833\) 4.00000 0.138592
\(834\) −40.0000 −1.38509
\(835\) 0 0
\(836\) −20.0000 −0.691714
\(837\) 3.00000 0.103695
\(838\) −40.0000 −1.38178
\(839\) 10.0000 0.345238 0.172619 0.984989i \(-0.444777\pi\)
0.172619 + 0.984989i \(0.444777\pi\)
\(840\) 0 0
\(841\) 71.0000 2.44828
\(842\) 44.0000 1.51634
\(843\) 18.0000 0.619953
\(844\) −26.0000 −0.894957
\(845\) 0 0
\(846\) 4.00000 0.137523
\(847\) 21.0000 0.721569
\(848\) 16.0000 0.549442
\(849\) 9.00000 0.308879
\(850\) 0 0
\(851\) 12.0000 0.411355
\(852\) 16.0000 0.548151
\(853\) 51.0000 1.74621 0.873103 0.487535i \(-0.162104\pi\)
0.873103 + 0.487535i \(0.162104\pi\)
\(854\) −42.0000 −1.43721
\(855\) 0 0
\(856\) 0 0
\(857\) −28.0000 −0.956462 −0.478231 0.878234i \(-0.658722\pi\)
−0.478231 + 0.878234i \(0.658722\pi\)
\(858\) −4.00000 −0.136558
\(859\) 40.0000 1.36478 0.682391 0.730987i \(-0.260940\pi\)
0.682391 + 0.730987i \(0.260940\pi\)
\(860\) 0 0
\(861\) −24.0000 −0.817918
\(862\) −36.0000 −1.22616
\(863\) 16.0000 0.544646 0.272323 0.962206i \(-0.412208\pi\)
0.272323 + 0.962206i \(0.412208\pi\)
\(864\) 8.00000 0.272166
\(865\) 0 0
\(866\) −58.0000 −1.97092
\(867\) 13.0000 0.441503
\(868\) 18.0000 0.610960
\(869\) 0 0
\(870\) 0 0
\(871\) −3.00000 −0.101651
\(872\) 0 0
\(873\) 17.0000 0.575363
\(874\) −60.0000 −2.02953
\(875\) 0 0
\(876\) 28.0000 0.946032
\(877\) 27.0000 0.911725 0.455863 0.890050i \(-0.349331\pi\)
0.455863 + 0.890050i \(0.349331\pi\)
\(878\) −70.0000 −2.36239
\(879\) −6.00000 −0.202375
\(880\) 0 0
\(881\) 32.0000 1.07811 0.539054 0.842271i \(-0.318782\pi\)
0.539054 + 0.842271i \(0.318782\pi\)
\(882\) 4.00000 0.134687
\(883\) 41.0000 1.37976 0.689880 0.723924i \(-0.257663\pi\)
0.689880 + 0.723924i \(0.257663\pi\)
\(884\) 4.00000 0.134535
\(885\) 0 0
\(886\) −48.0000 −1.61259
\(887\) −18.0000 −0.604381 −0.302190 0.953248i \(-0.597718\pi\)
−0.302190 + 0.953248i \(0.597718\pi\)
\(888\) 0 0
\(889\) 24.0000 0.804934
\(890\) 0 0
\(891\) 2.00000 0.0670025
\(892\) −38.0000 −1.27233
\(893\) −10.0000 −0.334637
\(894\) −20.0000 −0.668900
\(895\) 0 0
\(896\) 0 0
\(897\) −6.00000 −0.200334
\(898\) 40.0000 1.33482
\(899\) −30.0000 −1.00056
\(900\) 0 0
\(901\) −8.00000 −0.266519
\(902\) −32.0000 −1.06548
\(903\) 3.00000 0.0998337
\(904\) 0 0
\(905\) 0 0
\(906\) −14.0000 −0.465119
\(907\) 12.0000 0.398453 0.199227 0.979953i \(-0.436157\pi\)
0.199227 + 0.979953i \(0.436157\pi\)
\(908\) −16.0000 −0.530979
\(909\) 12.0000 0.398015
\(910\) 0 0
\(911\) −58.0000 −1.92163 −0.960813 0.277198i \(-0.910594\pi\)
−0.960813 + 0.277198i \(0.910594\pi\)
\(912\) −20.0000 −0.662266
\(913\) 12.0000 0.397142
\(914\) 44.0000 1.45539
\(915\) 0 0
\(916\) −30.0000 −0.991228
\(917\) −36.0000 −1.18882
\(918\) −4.00000 −0.132020
\(919\) 55.0000 1.81428 0.907141 0.420826i \(-0.138260\pi\)
0.907141 + 0.420826i \(0.138260\pi\)
\(920\) 0 0
\(921\) −7.00000 −0.230658
\(922\) 24.0000 0.790398
\(923\) −8.00000 −0.263323
\(924\) 12.0000 0.394771
\(925\) 0 0
\(926\) −48.0000 −1.57738
\(927\) −4.00000 −0.131377
\(928\) −80.0000 −2.62613
\(929\) −50.0000 −1.64045 −0.820223 0.572043i \(-0.806151\pi\)
−0.820223 + 0.572043i \(0.806151\pi\)
\(930\) 0 0
\(931\) −10.0000 −0.327737
\(932\) −48.0000 −1.57229
\(933\) 18.0000 0.589294
\(934\) −76.0000 −2.48680
\(935\) 0 0
\(936\) 0 0
\(937\) −33.0000 −1.07806 −0.539032 0.842286i \(-0.681210\pi\)
−0.539032 + 0.842286i \(0.681210\pi\)
\(938\) 18.0000 0.587721
\(939\) −11.0000 −0.358971
\(940\) 0 0
\(941\) 22.0000 0.717180 0.358590 0.933495i \(-0.383258\pi\)
0.358590 + 0.933495i \(0.383258\pi\)
\(942\) 26.0000 0.847126
\(943\) −48.0000 −1.56310
\(944\) 40.0000 1.30189
\(945\) 0 0
\(946\) 4.00000 0.130051
\(947\) −18.0000 −0.584921 −0.292461 0.956278i \(-0.594474\pi\)
−0.292461 + 0.956278i \(0.594474\pi\)
\(948\) 0 0
\(949\) −14.0000 −0.454459
\(950\) 0 0
\(951\) 8.00000 0.259418
\(952\) 0 0
\(953\) 56.0000 1.81402 0.907009 0.421111i \(-0.138360\pi\)
0.907009 + 0.421111i \(0.138360\pi\)
\(954\) −8.00000 −0.259010
\(955\) 0 0
\(956\) 40.0000 1.29369
\(957\) −20.0000 −0.646508
\(958\) 60.0000 1.93851
\(959\) 54.0000 1.74375
\(960\) 0 0
\(961\) −22.0000 −0.709677
\(962\) 4.00000 0.128965
\(963\) 12.0000 0.386695
\(964\) −46.0000 −1.48156
\(965\) 0 0
\(966\) 36.0000 1.15828
\(967\) 32.0000 1.02905 0.514525 0.857475i \(-0.327968\pi\)
0.514525 + 0.857475i \(0.327968\pi\)
\(968\) 0 0
\(969\) 10.0000 0.321246
\(970\) 0 0
\(971\) 42.0000 1.34784 0.673922 0.738802i \(-0.264608\pi\)
0.673922 + 0.738802i \(0.264608\pi\)
\(972\) −2.00000 −0.0641500
\(973\) −60.0000 −1.92351
\(974\) −26.0000 −0.833094
\(975\) 0 0
\(976\) −28.0000 −0.896258
\(977\) 2.00000 0.0639857 0.0319928 0.999488i \(-0.489815\pi\)
0.0319928 + 0.999488i \(0.489815\pi\)
\(978\) −22.0000 −0.703482
\(979\) 0 0
\(980\) 0 0
\(981\) 5.00000 0.159638
\(982\) −16.0000 −0.510581
\(983\) 36.0000 1.14822 0.574111 0.818778i \(-0.305348\pi\)
0.574111 + 0.818778i \(0.305348\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 40.0000 1.27386
\(987\) 6.00000 0.190982
\(988\) −10.0000 −0.318142
\(989\) 6.00000 0.190789
\(990\) 0 0
\(991\) 17.0000 0.540023 0.270011 0.962857i \(-0.412973\pi\)
0.270011 + 0.962857i \(0.412973\pi\)
\(992\) 24.0000 0.762001
\(993\) −12.0000 −0.380808
\(994\) 48.0000 1.52247
\(995\) 0 0
\(996\) −12.0000 −0.380235
\(997\) 42.0000 1.33015 0.665077 0.746775i \(-0.268399\pi\)
0.665077 + 0.746775i \(0.268399\pi\)
\(998\) −10.0000 −0.316544
\(999\) −2.00000 −0.0632772
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 \(a_p\))