Properties

Label 26.2.a.b.1.1
Level 26
Weight 2
Character 26.1
Self dual Yes
Analytic conductor 0.208
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 26 = 2 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 26.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(0.207611045255\)
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 \(\chi\) = 26.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(-3.00000 q^{3}\) \(+1.00000 q^{4}\) \(-1.00000 q^{5}\) \(-3.00000 q^{6}\) \(+1.00000 q^{7}\) \(+1.00000 q^{8}\) \(+6.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(-3.00000 q^{3}\) \(+1.00000 q^{4}\) \(-1.00000 q^{5}\) \(-3.00000 q^{6}\) \(+1.00000 q^{7}\) \(+1.00000 q^{8}\) \(+6.00000 q^{9}\) \(-1.00000 q^{10}\) \(-2.00000 q^{11}\) \(-3.00000 q^{12}\) \(-1.00000 q^{13}\) \(+1.00000 q^{14}\) \(+3.00000 q^{15}\) \(+1.00000 q^{16}\) \(-3.00000 q^{17}\) \(+6.00000 q^{18}\) \(+6.00000 q^{19}\) \(-1.00000 q^{20}\) \(-3.00000 q^{21}\) \(-2.00000 q^{22}\) \(-4.00000 q^{23}\) \(-3.00000 q^{24}\) \(-4.00000 q^{25}\) \(-1.00000 q^{26}\) \(-9.00000 q^{27}\) \(+1.00000 q^{28}\) \(+2.00000 q^{29}\) \(+3.00000 q^{30}\) \(+4.00000 q^{31}\) \(+1.00000 q^{32}\) \(+6.00000 q^{33}\) \(-3.00000 q^{34}\) \(-1.00000 q^{35}\) \(+6.00000 q^{36}\) \(+3.00000 q^{37}\) \(+6.00000 q^{38}\) \(+3.00000 q^{39}\) \(-1.00000 q^{40}\) \(-3.00000 q^{42}\) \(-5.00000 q^{43}\) \(-2.00000 q^{44}\) \(-6.00000 q^{45}\) \(-4.00000 q^{46}\) \(+13.0000 q^{47}\) \(-3.00000 q^{48}\) \(-6.00000 q^{49}\) \(-4.00000 q^{50}\) \(+9.00000 q^{51}\) \(-1.00000 q^{52}\) \(+12.0000 q^{53}\) \(-9.00000 q^{54}\) \(+2.00000 q^{55}\) \(+1.00000 q^{56}\) \(-18.0000 q^{57}\) \(+2.00000 q^{58}\) \(-10.0000 q^{59}\) \(+3.00000 q^{60}\) \(-8.00000 q^{61}\) \(+4.00000 q^{62}\) \(+6.00000 q^{63}\) \(+1.00000 q^{64}\) \(+1.00000 q^{65}\) \(+6.00000 q^{66}\) \(-2.00000 q^{67}\) \(-3.00000 q^{68}\) \(+12.0000 q^{69}\) \(-1.00000 q^{70}\) \(-5.00000 q^{71}\) \(+6.00000 q^{72}\) \(-10.0000 q^{73}\) \(+3.00000 q^{74}\) \(+12.0000 q^{75}\) \(+6.00000 q^{76}\) \(-2.00000 q^{77}\) \(+3.00000 q^{78}\) \(-4.00000 q^{79}\) \(-1.00000 q^{80}\) \(+9.00000 q^{81}\) \(-3.00000 q^{84}\) \(+3.00000 q^{85}\) \(-5.00000 q^{86}\) \(-6.00000 q^{87}\) \(-2.00000 q^{88}\) \(+6.00000 q^{89}\) \(-6.00000 q^{90}\) \(-1.00000 q^{91}\) \(-4.00000 q^{92}\) \(-12.0000 q^{93}\) \(+13.0000 q^{94}\) \(-6.00000 q^{95}\) \(-3.00000 q^{96}\) \(+14.0000 q^{97}\) \(-6.00000 q^{98}\) \(-12.0000 q^{99}\) \(+O(q^{100})\)

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
\(3\) −3.00000 −1.73205 −0.866025 0.500000i \(-0.833333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214 −0.223607 0.974679i \(-0.571783\pi\)
−0.223607 + 0.974679i \(0.571783\pi\)
\(6\) −3.00000 −1.22474
\(7\) 1.00000 0.377964 0.188982 0.981981i \(-0.439481\pi\)
0.188982 + 0.981981i \(0.439481\pi\)
\(8\) 1.00000 0.353553
\(9\) 6.00000 2.00000
\(10\) −1.00000 −0.316228
\(11\) −2.00000 −0.603023 −0.301511 0.953463i \(-0.597491\pi\)
−0.301511 + 0.953463i \(0.597491\pi\)
\(12\) −3.00000 −0.866025
\(13\) −1.00000 −0.277350
\(14\) 1.00000 0.267261
\(15\) 3.00000 0.774597
\(16\) 1.00000 0.250000
\(17\) −3.00000 −0.727607 −0.363803 0.931476i \(-0.618522\pi\)
−0.363803 + 0.931476i \(0.618522\pi\)
\(18\) 6.00000 1.41421
\(19\) 6.00000 1.37649 0.688247 0.725476i \(-0.258380\pi\)
0.688247 + 0.725476i \(0.258380\pi\)
\(20\) −1.00000 −0.223607
\(21\) −3.00000 −0.654654
\(22\) −2.00000 −0.426401
\(23\) −4.00000 −0.834058 −0.417029 0.908893i \(-0.636929\pi\)
−0.417029 + 0.908893i \(0.636929\pi\)
\(24\) −3.00000 −0.612372
\(25\) −4.00000 −0.800000
\(26\) −1.00000 −0.196116
\(27\) −9.00000 −1.73205
\(28\) 1.00000 0.188982
\(29\) 2.00000 0.371391 0.185695 0.982607i \(-0.440546\pi\)
0.185695 + 0.982607i \(0.440546\pi\)
\(30\) 3.00000 0.547723
\(31\) 4.00000 0.718421 0.359211 0.933257i \(-0.383046\pi\)
0.359211 + 0.933257i \(0.383046\pi\)
\(32\) 1.00000 0.176777
\(33\) 6.00000 1.04447
\(34\) −3.00000 −0.514496
\(35\) −1.00000 −0.169031
\(36\) 6.00000 1.00000
\(37\) 3.00000 0.493197 0.246598 0.969118i \(-0.420687\pi\)
0.246598 + 0.969118i \(0.420687\pi\)
\(38\) 6.00000 0.973329
\(39\) 3.00000 0.480384
\(40\) −1.00000 −0.158114
\(41\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) −3.00000 −0.462910
\(43\) −5.00000 −0.762493 −0.381246 0.924473i \(-0.624505\pi\)
−0.381246 + 0.924473i \(0.624505\pi\)
\(44\) −2.00000 −0.301511
\(45\) −6.00000 −0.894427
\(46\) −4.00000 −0.589768
\(47\) 13.0000 1.89624 0.948122 0.317905i \(-0.102979\pi\)
0.948122 + 0.317905i \(0.102979\pi\)
\(48\) −3.00000 −0.433013
\(49\) −6.00000 −0.857143
\(50\) −4.00000 −0.565685
\(51\) 9.00000 1.26025
\(52\) −1.00000 −0.138675
\(53\) 12.0000 1.64833 0.824163 0.566352i \(-0.191646\pi\)
0.824163 + 0.566352i \(0.191646\pi\)
\(54\) −9.00000 −1.22474
\(55\) 2.00000 0.269680
\(56\) 1.00000 0.133631
\(57\) −18.0000 −2.38416
\(58\) 2.00000 0.262613
\(59\) −10.0000 −1.30189 −0.650945 0.759125i \(-0.725627\pi\)
−0.650945 + 0.759125i \(0.725627\pi\)
\(60\) 3.00000 0.387298
\(61\) −8.00000 −1.02430 −0.512148 0.858898i \(-0.671150\pi\)
−0.512148 + 0.858898i \(0.671150\pi\)
\(62\) 4.00000 0.508001
\(63\) 6.00000 0.755929
\(64\) 1.00000 0.125000
\(65\) 1.00000 0.124035
\(66\) 6.00000 0.738549
\(67\) −2.00000 −0.244339 −0.122169 0.992509i \(-0.538985\pi\)
−0.122169 + 0.992509i \(0.538985\pi\)
\(68\) −3.00000 −0.363803
\(69\) 12.0000 1.44463
\(70\) −1.00000 −0.119523
\(71\) −5.00000 −0.593391 −0.296695 0.954972i \(-0.595885\pi\)
−0.296695 + 0.954972i \(0.595885\pi\)
\(72\) 6.00000 0.707107
\(73\) −10.0000 −1.17041 −0.585206 0.810885i \(-0.698986\pi\)
−0.585206 + 0.810885i \(0.698986\pi\)
\(74\) 3.00000 0.348743
\(75\) 12.0000 1.38564
\(76\) 6.00000 0.688247
\(77\) −2.00000 −0.227921
\(78\) 3.00000 0.339683
\(79\) −4.00000 −0.450035 −0.225018 0.974355i \(-0.572244\pi\)
−0.225018 + 0.974355i \(0.572244\pi\)
\(80\) −1.00000 −0.111803
\(81\) 9.00000 1.00000
\(82\) 0 0
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) −3.00000 −0.327327
\(85\) 3.00000 0.325396
\(86\) −5.00000 −0.539164
\(87\) −6.00000 −0.643268
\(88\) −2.00000 −0.213201
\(89\) 6.00000 0.635999 0.317999 0.948091i \(-0.396989\pi\)
0.317999 + 0.948091i \(0.396989\pi\)
\(90\) −6.00000 −0.632456
\(91\) −1.00000 −0.104828
\(92\) −4.00000 −0.417029
\(93\) −12.0000 −1.24434
\(94\) 13.0000 1.34085
\(95\) −6.00000 −0.615587
\(96\) −3.00000 −0.306186
\(97\) 14.0000 1.42148 0.710742 0.703452i \(-0.248359\pi\)
0.710742 + 0.703452i \(0.248359\pi\)
\(98\) −6.00000 −0.606092
\(99\) −12.0000 −1.20605
\(100\) −4.00000 −0.400000
\(101\) 4.00000 0.398015 0.199007 0.979998i \(-0.436228\pi\)
0.199007 + 0.979998i \(0.436228\pi\)
\(102\) 9.00000 0.891133
\(103\) −8.00000 −0.788263 −0.394132 0.919054i \(-0.628955\pi\)
−0.394132 + 0.919054i \(0.628955\pi\)
\(104\) −1.00000 −0.0980581
\(105\) 3.00000 0.292770
\(106\) 12.0000 1.16554
\(107\) −4.00000 −0.386695 −0.193347 0.981130i \(-0.561934\pi\)
−0.193347 + 0.981130i \(0.561934\pi\)
\(108\) −9.00000 −0.866025
\(109\) 19.0000 1.81987 0.909935 0.414751i \(-0.136131\pi\)
0.909935 + 0.414751i \(0.136131\pi\)
\(110\) 2.00000 0.190693
\(111\) −9.00000 −0.854242
\(112\) 1.00000 0.0944911
\(113\) 2.00000 0.188144 0.0940721 0.995565i \(-0.470012\pi\)
0.0940721 + 0.995565i \(0.470012\pi\)
\(114\) −18.0000 −1.68585
\(115\) 4.00000 0.373002
\(116\) 2.00000 0.185695
\(117\) −6.00000 −0.554700
\(118\) −10.0000 −0.920575
\(119\) −3.00000 −0.275010
\(120\) 3.00000 0.273861
\(121\) −7.00000 −0.636364
\(122\) −8.00000 −0.724286
\(123\) 0 0
\(124\) 4.00000 0.359211
\(125\) 9.00000 0.804984
\(126\) 6.00000 0.534522
\(127\) 16.0000 1.41977 0.709885 0.704317i \(-0.248747\pi\)
0.709885 + 0.704317i \(0.248747\pi\)
\(128\) 1.00000 0.0883883
\(129\) 15.0000 1.32068
\(130\) 1.00000 0.0877058
\(131\) −1.00000 −0.0873704 −0.0436852 0.999045i \(-0.513910\pi\)
−0.0436852 + 0.999045i \(0.513910\pi\)
\(132\) 6.00000 0.522233
\(133\) 6.00000 0.520266
\(134\) −2.00000 −0.172774
\(135\) 9.00000 0.774597
\(136\) −3.00000 −0.257248
\(137\) 12.0000 1.02523 0.512615 0.858619i \(-0.328677\pi\)
0.512615 + 0.858619i \(0.328677\pi\)
\(138\) 12.0000 1.02151
\(139\) 7.00000 0.593732 0.296866 0.954919i \(-0.404058\pi\)
0.296866 + 0.954919i \(0.404058\pi\)
\(140\) −1.00000 −0.0845154
\(141\) −39.0000 −3.28439
\(142\) −5.00000 −0.419591
\(143\) 2.00000 0.167248
\(144\) 6.00000 0.500000
\(145\) −2.00000 −0.166091
\(146\) −10.0000 −0.827606
\(147\) 18.0000 1.48461
\(148\) 3.00000 0.246598
\(149\) −18.0000 −1.47462 −0.737309 0.675556i \(-0.763904\pi\)
−0.737309 + 0.675556i \(0.763904\pi\)
\(150\) 12.0000 0.979796
\(151\) −9.00000 −0.732410 −0.366205 0.930534i \(-0.619343\pi\)
−0.366205 + 0.930534i \(0.619343\pi\)
\(152\) 6.00000 0.486664
\(153\) −18.0000 −1.45521
\(154\) −2.00000 −0.161165
\(155\) −4.00000 −0.321288
\(156\) 3.00000 0.240192
\(157\) −10.0000 −0.798087 −0.399043 0.916932i \(-0.630658\pi\)
−0.399043 + 0.916932i \(0.630658\pi\)
\(158\) −4.00000 −0.318223
\(159\) −36.0000 −2.85499
\(160\) −1.00000 −0.0790569
\(161\) −4.00000 −0.315244
\(162\) 9.00000 0.707107
\(163\) −4.00000 −0.313304 −0.156652 0.987654i \(-0.550070\pi\)
−0.156652 + 0.987654i \(0.550070\pi\)
\(164\) 0 0
\(165\) −6.00000 −0.467099
\(166\) 0 0
\(167\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(168\) −3.00000 −0.231455
\(169\) 1.00000 0.0769231
\(170\) 3.00000 0.230089
\(171\) 36.0000 2.75299
\(172\) −5.00000 −0.381246
\(173\) 20.0000 1.52057 0.760286 0.649589i \(-0.225059\pi\)
0.760286 + 0.649589i \(0.225059\pi\)
\(174\) −6.00000 −0.454859
\(175\) −4.00000 −0.302372
\(176\) −2.00000 −0.150756
\(177\) 30.0000 2.25494
\(178\) 6.00000 0.449719
\(179\) −9.00000 −0.672692 −0.336346 0.941739i \(-0.609191\pi\)
−0.336346 + 0.941739i \(0.609191\pi\)
\(180\) −6.00000 −0.447214
\(181\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(182\) −1.00000 −0.0741249
\(183\) 24.0000 1.77413
\(184\) −4.00000 −0.294884
\(185\) −3.00000 −0.220564
\(186\) −12.0000 −0.879883
\(187\) 6.00000 0.438763
\(188\) 13.0000 0.948122
\(189\) −9.00000 −0.654654
\(190\) −6.00000 −0.435286
\(191\) 10.0000 0.723575 0.361787 0.932261i \(-0.382167\pi\)
0.361787 + 0.932261i \(0.382167\pi\)
\(192\) −3.00000 −0.216506
\(193\) −16.0000 −1.15171 −0.575853 0.817554i \(-0.695330\pi\)
−0.575853 + 0.817554i \(0.695330\pi\)
\(194\) 14.0000 1.00514
\(195\) −3.00000 −0.214834
\(196\) −6.00000 −0.428571
\(197\) 9.00000 0.641223 0.320612 0.947211i \(-0.396112\pi\)
0.320612 + 0.947211i \(0.396112\pi\)
\(198\) −12.0000 −0.852803
\(199\) −10.0000 −0.708881 −0.354441 0.935079i \(-0.615329\pi\)
−0.354441 + 0.935079i \(0.615329\pi\)
\(200\) −4.00000 −0.282843
\(201\) 6.00000 0.423207
\(202\) 4.00000 0.281439
\(203\) 2.00000 0.140372
\(204\) 9.00000 0.630126
\(205\) 0 0
\(206\) −8.00000 −0.557386
\(207\) −24.0000 −1.66812
\(208\) −1.00000 −0.0693375
\(209\) −12.0000 −0.830057
\(210\) 3.00000 0.207020
\(211\) 23.0000 1.58339 0.791693 0.610920i \(-0.209200\pi\)
0.791693 + 0.610920i \(0.209200\pi\)
\(212\) 12.0000 0.824163
\(213\) 15.0000 1.02778
\(214\) −4.00000 −0.273434
\(215\) 5.00000 0.340997
\(216\) −9.00000 −0.612372
\(217\) 4.00000 0.271538
\(218\) 19.0000 1.28684
\(219\) 30.0000 2.02721
\(220\) 2.00000 0.134840
\(221\) 3.00000 0.201802
\(222\) −9.00000 −0.604040
\(223\) −21.0000 −1.40626 −0.703132 0.711059i \(-0.748216\pi\)
−0.703132 + 0.711059i \(0.748216\pi\)
\(224\) 1.00000 0.0668153
\(225\) −24.0000 −1.60000
\(226\) 2.00000 0.133038
\(227\) −24.0000 −1.59294 −0.796468 0.604681i \(-0.793301\pi\)
−0.796468 + 0.604681i \(0.793301\pi\)
\(228\) −18.0000 −1.19208
\(229\) −15.0000 −0.991228 −0.495614 0.868543i \(-0.665057\pi\)
−0.495614 + 0.868543i \(0.665057\pi\)
\(230\) 4.00000 0.263752
\(231\) 6.00000 0.394771
\(232\) 2.00000 0.131306
\(233\) −11.0000 −0.720634 −0.360317 0.932830i \(-0.617331\pi\)
−0.360317 + 0.932830i \(0.617331\pi\)
\(234\) −6.00000 −0.392232
\(235\) −13.0000 −0.848026
\(236\) −10.0000 −0.650945
\(237\) 12.0000 0.779484
\(238\) −3.00000 −0.194461
\(239\) 9.00000 0.582162 0.291081 0.956698i \(-0.405985\pi\)
0.291081 + 0.956698i \(0.405985\pi\)
\(240\) 3.00000 0.193649
\(241\) 18.0000 1.15948 0.579741 0.814801i \(-0.303154\pi\)
0.579741 + 0.814801i \(0.303154\pi\)
\(242\) −7.00000 −0.449977
\(243\) 0 0
\(244\) −8.00000 −0.512148
\(245\) 6.00000 0.383326
\(246\) 0 0
\(247\) −6.00000 −0.381771
\(248\) 4.00000 0.254000
\(249\) 0 0
\(250\) 9.00000 0.569210
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 6.00000 0.377964
\(253\) 8.00000 0.502956
\(254\) 16.0000 1.00393
\(255\) −9.00000 −0.563602
\(256\) 1.00000 0.0625000
\(257\) −15.0000 −0.935674 −0.467837 0.883815i \(-0.654967\pi\)
−0.467837 + 0.883815i \(0.654967\pi\)
\(258\) 15.0000 0.933859
\(259\) 3.00000 0.186411
\(260\) 1.00000 0.0620174
\(261\) 12.0000 0.742781
\(262\) −1.00000 −0.0617802
\(263\) 12.0000 0.739952 0.369976 0.929041i \(-0.379366\pi\)
0.369976 + 0.929041i \(0.379366\pi\)
\(264\) 6.00000 0.369274
\(265\) −12.0000 −0.737154
\(266\) 6.00000 0.367884
\(267\) −18.0000 −1.10158
\(268\) −2.00000 −0.122169
\(269\) −24.0000 −1.46331 −0.731653 0.681677i \(-0.761251\pi\)
−0.731653 + 0.681677i \(0.761251\pi\)
\(270\) 9.00000 0.547723
\(271\) 13.0000 0.789694 0.394847 0.918747i \(-0.370798\pi\)
0.394847 + 0.918747i \(0.370798\pi\)
\(272\) −3.00000 −0.181902
\(273\) 3.00000 0.181568
\(274\) 12.0000 0.724947
\(275\) 8.00000 0.482418
\(276\) 12.0000 0.722315
\(277\) 12.0000 0.721010 0.360505 0.932757i \(-0.382604\pi\)
0.360505 + 0.932757i \(0.382604\pi\)
\(278\) 7.00000 0.419832
\(279\) 24.0000 1.43684
\(280\) −1.00000 −0.0597614
\(281\) −26.0000 −1.55103 −0.775515 0.631329i \(-0.782510\pi\)
−0.775515 + 0.631329i \(0.782510\pi\)
\(282\) −39.0000 −2.32242
\(283\) 4.00000 0.237775 0.118888 0.992908i \(-0.462067\pi\)
0.118888 + 0.992908i \(0.462067\pi\)
\(284\) −5.00000 −0.296695
\(285\) 18.0000 1.06623
\(286\) 2.00000 0.118262
\(287\) 0 0
\(288\) 6.00000 0.353553
\(289\) −8.00000 −0.470588
\(290\) −2.00000 −0.117444
\(291\) −42.0000 −2.46208
\(292\) −10.0000 −0.585206
\(293\) 7.00000 0.408944 0.204472 0.978872i \(-0.434452\pi\)
0.204472 + 0.978872i \(0.434452\pi\)
\(294\) 18.0000 1.04978
\(295\) 10.0000 0.582223
\(296\) 3.00000 0.174371
\(297\) 18.0000 1.04447
\(298\) −18.0000 −1.04271
\(299\) 4.00000 0.231326
\(300\) 12.0000 0.692820
\(301\) −5.00000 −0.288195
\(302\) −9.00000 −0.517892
\(303\) −12.0000 −0.689382
\(304\) 6.00000 0.344124
\(305\) 8.00000 0.458079
\(306\) −18.0000 −1.02899
\(307\) 14.0000 0.799022 0.399511 0.916728i \(-0.369180\pi\)
0.399511 + 0.916728i \(0.369180\pi\)
\(308\) −2.00000 −0.113961
\(309\) 24.0000 1.36531
\(310\) −4.00000 −0.227185
\(311\) 18.0000 1.02069 0.510343 0.859971i \(-0.329518\pi\)
0.510343 + 0.859971i \(0.329518\pi\)
\(312\) 3.00000 0.169842
\(313\) −1.00000 −0.0565233 −0.0282617 0.999601i \(-0.508997\pi\)
−0.0282617 + 0.999601i \(0.508997\pi\)
\(314\) −10.0000 −0.564333
\(315\) −6.00000 −0.338062
\(316\) −4.00000 −0.225018
\(317\) −18.0000 −1.01098 −0.505490 0.862832i \(-0.668688\pi\)
−0.505490 + 0.862832i \(0.668688\pi\)
\(318\) −36.0000 −2.01878
\(319\) −4.00000 −0.223957
\(320\) −1.00000 −0.0559017
\(321\) 12.0000 0.669775
\(322\) −4.00000 −0.222911
\(323\) −18.0000 −1.00155
\(324\) 9.00000 0.500000
\(325\) 4.00000 0.221880
\(326\) −4.00000 −0.221540
\(327\) −57.0000 −3.15211
\(328\) 0 0
\(329\) 13.0000 0.716713
\(330\) −6.00000 −0.330289
\(331\) −4.00000 −0.219860 −0.109930 0.993939i \(-0.535063\pi\)
−0.109930 + 0.993939i \(0.535063\pi\)
\(332\) 0 0
\(333\) 18.0000 0.986394
\(334\) 0 0
\(335\) 2.00000 0.109272
\(336\) −3.00000 −0.163663
\(337\) 23.0000 1.25289 0.626445 0.779466i \(-0.284509\pi\)
0.626445 + 0.779466i \(0.284509\pi\)
\(338\) 1.00000 0.0543928
\(339\) −6.00000 −0.325875
\(340\) 3.00000 0.162698
\(341\) −8.00000 −0.433224
\(342\) 36.0000 1.94666
\(343\) −13.0000 −0.701934
\(344\) −5.00000 −0.269582
\(345\) −12.0000 −0.646058
\(346\) 20.0000 1.07521
\(347\) −9.00000 −0.483145 −0.241573 0.970383i \(-0.577663\pi\)
−0.241573 + 0.970383i \(0.577663\pi\)
\(348\) −6.00000 −0.321634
\(349\) 7.00000 0.374701 0.187351 0.982293i \(-0.440010\pi\)
0.187351 + 0.982293i \(0.440010\pi\)
\(350\) −4.00000 −0.213809
\(351\) 9.00000 0.480384
\(352\) −2.00000 −0.106600
\(353\) 4.00000 0.212899 0.106449 0.994318i \(-0.466052\pi\)
0.106449 + 0.994318i \(0.466052\pi\)
\(354\) 30.0000 1.59448
\(355\) 5.00000 0.265372
\(356\) 6.00000 0.317999
\(357\) 9.00000 0.476331
\(358\) −9.00000 −0.475665
\(359\) 24.0000 1.26667 0.633336 0.773877i \(-0.281685\pi\)
0.633336 + 0.773877i \(0.281685\pi\)
\(360\) −6.00000 −0.316228
\(361\) 17.0000 0.894737
\(362\) 0 0
\(363\) 21.0000 1.10221
\(364\) −1.00000 −0.0524142
\(365\) 10.0000 0.523424
\(366\) 24.0000 1.25450
\(367\) −10.0000 −0.521996 −0.260998 0.965339i \(-0.584052\pi\)
−0.260998 + 0.965339i \(0.584052\pi\)
\(368\) −4.00000 −0.208514
\(369\) 0 0
\(370\) −3.00000 −0.155963
\(371\) 12.0000 0.623009
\(372\) −12.0000 −0.622171
\(373\) −4.00000 −0.207112 −0.103556 0.994624i \(-0.533022\pi\)
−0.103556 + 0.994624i \(0.533022\pi\)
\(374\) 6.00000 0.310253
\(375\) −27.0000 −1.39427
\(376\) 13.0000 0.670424
\(377\) −2.00000 −0.103005
\(378\) −9.00000 −0.462910
\(379\) 16.0000 0.821865 0.410932 0.911666i \(-0.365203\pi\)
0.410932 + 0.911666i \(0.365203\pi\)
\(380\) −6.00000 −0.307794
\(381\) −48.0000 −2.45911
\(382\) 10.0000 0.511645
\(383\) 27.0000 1.37964 0.689818 0.723983i \(-0.257691\pi\)
0.689818 + 0.723983i \(0.257691\pi\)
\(384\) −3.00000 −0.153093
\(385\) 2.00000 0.101929
\(386\) −16.0000 −0.814379
\(387\) −30.0000 −1.52499
\(388\) 14.0000 0.710742
\(389\) −30.0000 −1.52106 −0.760530 0.649303i \(-0.775061\pi\)
−0.760530 + 0.649303i \(0.775061\pi\)
\(390\) −3.00000 −0.151911
\(391\) 12.0000 0.606866
\(392\) −6.00000 −0.303046
\(393\) 3.00000 0.151330
\(394\) 9.00000 0.453413
\(395\) 4.00000 0.201262
\(396\) −12.0000 −0.603023
\(397\) −22.0000 −1.10415 −0.552074 0.833795i \(-0.686163\pi\)
−0.552074 + 0.833795i \(0.686163\pi\)
\(398\) −10.0000 −0.501255
\(399\) −18.0000 −0.901127
\(400\) −4.00000 −0.200000
\(401\) 24.0000 1.19850 0.599251 0.800561i \(-0.295465\pi\)
0.599251 + 0.800561i \(0.295465\pi\)
\(402\) 6.00000 0.299253
\(403\) −4.00000 −0.199254
\(404\) 4.00000 0.199007
\(405\) −9.00000 −0.447214
\(406\) 2.00000 0.0992583
\(407\) −6.00000 −0.297409
\(408\) 9.00000 0.445566
\(409\) 4.00000 0.197787 0.0988936 0.995098i \(-0.468470\pi\)
0.0988936 + 0.995098i \(0.468470\pi\)
\(410\) 0 0
\(411\) −36.0000 −1.77575
\(412\) −8.00000 −0.394132
\(413\) −10.0000 −0.492068
\(414\) −24.0000 −1.17954
\(415\) 0 0
\(416\) −1.00000 −0.0490290
\(417\) −21.0000 −1.02837
\(418\) −12.0000 −0.586939
\(419\) 21.0000 1.02592 0.512959 0.858413i \(-0.328549\pi\)
0.512959 + 0.858413i \(0.328549\pi\)
\(420\) 3.00000 0.146385
\(421\) −5.00000 −0.243685 −0.121843 0.992549i \(-0.538880\pi\)
−0.121843 + 0.992549i \(0.538880\pi\)
\(422\) 23.0000 1.11962
\(423\) 78.0000 3.79249
\(424\) 12.0000 0.582772
\(425\) 12.0000 0.582086
\(426\) 15.0000 0.726752
\(427\) −8.00000 −0.387147
\(428\) −4.00000 −0.193347
\(429\) −6.00000 −0.289683
\(430\) 5.00000 0.241121
\(431\) 33.0000 1.58955 0.794777 0.606902i \(-0.207588\pi\)
0.794777 + 0.606902i \(0.207588\pi\)
\(432\) −9.00000 −0.433013
\(433\) 7.00000 0.336399 0.168199 0.985753i \(-0.446205\pi\)
0.168199 + 0.985753i \(0.446205\pi\)
\(434\) 4.00000 0.192006
\(435\) 6.00000 0.287678
\(436\) 19.0000 0.909935
\(437\) −24.0000 −1.14808
\(438\) 30.0000 1.43346
\(439\) −22.0000 −1.05000 −0.525001 0.851101i \(-0.675935\pi\)
−0.525001 + 0.851101i \(0.675935\pi\)
\(440\) 2.00000 0.0953463
\(441\) −36.0000 −1.71429
\(442\) 3.00000 0.142695
\(443\) −39.0000 −1.85295 −0.926473 0.376361i \(-0.877175\pi\)
−0.926473 + 0.376361i \(0.877175\pi\)
\(444\) −9.00000 −0.427121
\(445\) −6.00000 −0.284427
\(446\) −21.0000 −0.994379
\(447\) 54.0000 2.55411
\(448\) 1.00000 0.0472456
\(449\) −26.0000 −1.22702 −0.613508 0.789689i \(-0.710242\pi\)
−0.613508 + 0.789689i \(0.710242\pi\)
\(450\) −24.0000 −1.13137
\(451\) 0 0
\(452\) 2.00000 0.0940721
\(453\) 27.0000 1.26857
\(454\) −24.0000 −1.12638
\(455\) 1.00000 0.0468807
\(456\) −18.0000 −0.842927
\(457\) 10.0000 0.467780 0.233890 0.972263i \(-0.424854\pi\)
0.233890 + 0.972263i \(0.424854\pi\)
\(458\) −15.0000 −0.700904
\(459\) 27.0000 1.26025
\(460\) 4.00000 0.186501
\(461\) −21.0000 −0.978068 −0.489034 0.872265i \(-0.662651\pi\)
−0.489034 + 0.872265i \(0.662651\pi\)
\(462\) 6.00000 0.279145
\(463\) 16.0000 0.743583 0.371792 0.928316i \(-0.378744\pi\)
0.371792 + 0.928316i \(0.378744\pi\)
\(464\) 2.00000 0.0928477
\(465\) 12.0000 0.556487
\(466\) −11.0000 −0.509565
\(467\) 20.0000 0.925490 0.462745 0.886492i \(-0.346865\pi\)
0.462745 + 0.886492i \(0.346865\pi\)
\(468\) −6.00000 −0.277350
\(469\) −2.00000 −0.0923514
\(470\) −13.0000 −0.599645
\(471\) 30.0000 1.38233
\(472\) −10.0000 −0.460287
\(473\) 10.0000 0.459800
\(474\) 12.0000 0.551178
\(475\) −24.0000 −1.10120
\(476\) −3.00000 −0.137505
\(477\) 72.0000 3.29665
\(478\) 9.00000 0.411650
\(479\) −3.00000 −0.137073 −0.0685367 0.997649i \(-0.521833\pi\)
−0.0685367 + 0.997649i \(0.521833\pi\)
\(480\) 3.00000 0.136931
\(481\) −3.00000 −0.136788
\(482\) 18.0000 0.819878
\(483\) 12.0000 0.546019
\(484\) −7.00000 −0.318182
\(485\) −14.0000 −0.635707
\(486\) 0 0
\(487\) −16.0000 −0.725029 −0.362515 0.931978i \(-0.618082\pi\)
−0.362515 + 0.931978i \(0.618082\pi\)
\(488\) −8.00000 −0.362143
\(489\) 12.0000 0.542659
\(490\) 6.00000 0.271052
\(491\) −5.00000 −0.225647 −0.112823 0.993615i \(-0.535989\pi\)
−0.112823 + 0.993615i \(0.535989\pi\)
\(492\) 0 0
\(493\) −6.00000 −0.270226
\(494\) −6.00000 −0.269953
\(495\) 12.0000 0.539360
\(496\) 4.00000 0.179605
\(497\) −5.00000 −0.224281
\(498\) 0 0
\(499\) −32.0000 −1.43252 −0.716258 0.697835i \(-0.754147\pi\)
−0.716258 + 0.697835i \(0.754147\pi\)
\(500\) 9.00000 0.402492
\(501\) 0 0
\(502\) 0 0
\(503\) −14.0000 −0.624229 −0.312115 0.950044i \(-0.601037\pi\)
−0.312115 + 0.950044i \(0.601037\pi\)
\(504\) 6.00000 0.267261
\(505\) −4.00000 −0.177998
\(506\) 8.00000 0.355643
\(507\) −3.00000 −0.133235
\(508\) 16.0000 0.709885
\(509\) 34.0000 1.50702 0.753512 0.657434i \(-0.228358\pi\)
0.753512 + 0.657434i \(0.228358\pi\)
\(510\) −9.00000 −0.398527
\(511\) −10.0000 −0.442374
\(512\) 1.00000 0.0441942
\(513\) −54.0000 −2.38416
\(514\) −15.0000 −0.661622
\(515\) 8.00000 0.352522
\(516\) 15.0000 0.660338
\(517\) −26.0000 −1.14348
\(518\) 3.00000 0.131812
\(519\) −60.0000 −2.63371
\(520\) 1.00000 0.0438529
\(521\) 39.0000 1.70862 0.854311 0.519763i \(-0.173980\pi\)
0.854311 + 0.519763i \(0.173980\pi\)
\(522\) 12.0000 0.525226
\(523\) −36.0000 −1.57417 −0.787085 0.616844i \(-0.788411\pi\)
−0.787085 + 0.616844i \(0.788411\pi\)
\(524\) −1.00000 −0.0436852
\(525\) 12.0000 0.523723
\(526\) 12.0000 0.523225
\(527\) −12.0000 −0.522728
\(528\) 6.00000 0.261116
\(529\) −7.00000 −0.304348
\(530\) −12.0000 −0.521247
\(531\) −60.0000 −2.60378
\(532\) 6.00000 0.260133
\(533\) 0 0
\(534\) −18.0000 −0.778936
\(535\) 4.00000 0.172935
\(536\) −2.00000 −0.0863868
\(537\) 27.0000 1.16514
\(538\) −24.0000 −1.03471
\(539\) 12.0000 0.516877
\(540\) 9.00000 0.387298
\(541\) 17.0000 0.730887 0.365444 0.930834i \(-0.380917\pi\)
0.365444 + 0.930834i \(0.380917\pi\)
\(542\) 13.0000 0.558398
\(543\) 0 0
\(544\) −3.00000 −0.128624
\(545\) −19.0000 −0.813871
\(546\) 3.00000 0.128388
\(547\) 37.0000 1.58201 0.791003 0.611812i \(-0.209559\pi\)
0.791003 + 0.611812i \(0.209559\pi\)
\(548\) 12.0000 0.512615
\(549\) −48.0000 −2.04859
\(550\) 8.00000 0.341121
\(551\) 12.0000 0.511217
\(552\) 12.0000 0.510754
\(553\) −4.00000 −0.170097
\(554\) 12.0000 0.509831
\(555\) 9.00000 0.382029
\(556\) 7.00000 0.296866
\(557\) 33.0000 1.39825 0.699127 0.714997i \(-0.253572\pi\)
0.699127 + 0.714997i \(0.253572\pi\)
\(558\) 24.0000 1.01600
\(559\) 5.00000 0.211477
\(560\) −1.00000 −0.0422577
\(561\) −18.0000 −0.759961
\(562\) −26.0000 −1.09674
\(563\) 11.0000 0.463595 0.231797 0.972764i \(-0.425539\pi\)
0.231797 + 0.972764i \(0.425539\pi\)
\(564\) −39.0000 −1.64220
\(565\) −2.00000 −0.0841406
\(566\) 4.00000 0.168133
\(567\) 9.00000 0.377964
\(568\) −5.00000 −0.209795
\(569\) 31.0000 1.29959 0.649794 0.760111i \(-0.274855\pi\)
0.649794 + 0.760111i \(0.274855\pi\)
\(570\) 18.0000 0.753937
\(571\) 33.0000 1.38101 0.690504 0.723329i \(-0.257389\pi\)
0.690504 + 0.723329i \(0.257389\pi\)
\(572\) 2.00000 0.0836242
\(573\) −30.0000 −1.25327
\(574\) 0 0
\(575\) 16.0000 0.667246
\(576\) 6.00000 0.250000
\(577\) 18.0000 0.749350 0.374675 0.927156i \(-0.377754\pi\)
0.374675 + 0.927156i \(0.377754\pi\)
\(578\) −8.00000 −0.332756
\(579\) 48.0000 1.99481
\(580\) −2.00000 −0.0830455
\(581\) 0 0
\(582\) −42.0000 −1.74096
\(583\) −24.0000 −0.993978
\(584\) −10.0000 −0.413803
\(585\) 6.00000 0.248069
\(586\) 7.00000 0.289167
\(587\) −28.0000 −1.15568 −0.577842 0.816149i \(-0.696105\pi\)
−0.577842 + 0.816149i \(0.696105\pi\)
\(588\) 18.0000 0.742307
\(589\) 24.0000 0.988903
\(590\) 10.0000 0.411693
\(591\) −27.0000 −1.11063
\(592\) 3.00000 0.123299
\(593\) −22.0000 −0.903432 −0.451716 0.892162i \(-0.649188\pi\)
−0.451716 + 0.892162i \(0.649188\pi\)
\(594\) 18.0000 0.738549
\(595\) 3.00000 0.122988
\(596\) −18.0000 −0.737309
\(597\) 30.0000 1.22782
\(598\) 4.00000 0.163572
\(599\) −2.00000 −0.0817178 −0.0408589 0.999165i \(-0.513009\pi\)
−0.0408589 + 0.999165i \(0.513009\pi\)
\(600\) 12.0000 0.489898
\(601\) −35.0000 −1.42768 −0.713840 0.700309i \(-0.753046\pi\)
−0.713840 + 0.700309i \(0.753046\pi\)
\(602\) −5.00000 −0.203785
\(603\) −12.0000 −0.488678
\(604\) −9.00000 −0.366205
\(605\) 7.00000 0.284590
\(606\) −12.0000 −0.487467
\(607\) 6.00000 0.243532 0.121766 0.992559i \(-0.461144\pi\)
0.121766 + 0.992559i \(0.461144\pi\)
\(608\) 6.00000 0.243332
\(609\) −6.00000 −0.243132
\(610\) 8.00000 0.323911
\(611\) −13.0000 −0.525924
\(612\) −18.0000 −0.727607
\(613\) 26.0000 1.05013 0.525065 0.851062i \(-0.324041\pi\)
0.525065 + 0.851062i \(0.324041\pi\)
\(614\) 14.0000 0.564994
\(615\) 0 0
\(616\) −2.00000 −0.0805823
\(617\) 16.0000 0.644136 0.322068 0.946717i \(-0.395622\pi\)
0.322068 + 0.946717i \(0.395622\pi\)
\(618\) 24.0000 0.965422
\(619\) 4.00000 0.160774 0.0803868 0.996764i \(-0.474384\pi\)
0.0803868 + 0.996764i \(0.474384\pi\)
\(620\) −4.00000 −0.160644
\(621\) 36.0000 1.44463
\(622\) 18.0000 0.721734
\(623\) 6.00000 0.240385
\(624\) 3.00000 0.120096
\(625\) 11.0000 0.440000
\(626\) −1.00000 −0.0399680
\(627\) 36.0000 1.43770
\(628\) −10.0000 −0.399043
\(629\) −9.00000 −0.358854
\(630\) −6.00000 −0.239046
\(631\) −5.00000 −0.199047 −0.0995234 0.995035i \(-0.531732\pi\)
−0.0995234 + 0.995035i \(0.531732\pi\)
\(632\) −4.00000 −0.159111
\(633\) −69.0000 −2.74250
\(634\) −18.0000 −0.714871
\(635\) −16.0000 −0.634941
\(636\) −36.0000 −1.42749
\(637\) 6.00000 0.237729
\(638\) −4.00000 −0.158362
\(639\) −30.0000 −1.18678
\(640\) −1.00000 −0.0395285
\(641\) −2.00000 −0.0789953 −0.0394976 0.999220i \(-0.512576\pi\)
−0.0394976 + 0.999220i \(0.512576\pi\)
\(642\) 12.0000 0.473602
\(643\) 14.0000 0.552106 0.276053 0.961142i \(-0.410973\pi\)
0.276053 + 0.961142i \(0.410973\pi\)
\(644\) −4.00000 −0.157622
\(645\) −15.0000 −0.590624
\(646\) −18.0000 −0.708201
\(647\) −38.0000 −1.49393 −0.746967 0.664861i \(-0.768491\pi\)
−0.746967 + 0.664861i \(0.768491\pi\)
\(648\) 9.00000 0.353553
\(649\) 20.0000 0.785069
\(650\) 4.00000 0.156893
\(651\) −12.0000 −0.470317
\(652\) −4.00000 −0.156652
\(653\) 24.0000 0.939193 0.469596 0.882881i \(-0.344399\pi\)
0.469596 + 0.882881i \(0.344399\pi\)
\(654\) −57.0000 −2.22888
\(655\) 1.00000 0.0390732
\(656\) 0 0
\(657\) −60.0000 −2.34082
\(658\) 13.0000 0.506793
\(659\) −12.0000 −0.467454 −0.233727 0.972302i \(-0.575092\pi\)
−0.233727 + 0.972302i \(0.575092\pi\)
\(660\) −6.00000 −0.233550
\(661\) −10.0000 −0.388955 −0.194477 0.980907i \(-0.562301\pi\)
−0.194477 + 0.980907i \(0.562301\pi\)
\(662\) −4.00000 −0.155464
\(663\) −9.00000 −0.349531
\(664\) 0 0
\(665\) −6.00000 −0.232670
\(666\) 18.0000 0.697486
\(667\) −8.00000 −0.309761
\(668\) 0 0
\(669\) 63.0000 2.43572
\(670\) 2.00000 0.0772667
\(671\) 16.0000 0.617673
\(672\) −3.00000 −0.115728
\(673\) 37.0000 1.42625 0.713123 0.701039i \(-0.247280\pi\)
0.713123 + 0.701039i \(0.247280\pi\)
\(674\) 23.0000 0.885927
\(675\) 36.0000 1.38564
\(676\) 1.00000 0.0384615
\(677\) −36.0000 −1.38359 −0.691796 0.722093i \(-0.743180\pi\)
−0.691796 + 0.722093i \(0.743180\pi\)
\(678\) −6.00000 −0.230429
\(679\) 14.0000 0.537271
\(680\) 3.00000 0.115045
\(681\) 72.0000 2.75905
\(682\) −8.00000 −0.306336
\(683\) −44.0000 −1.68361 −0.841807 0.539779i \(-0.818508\pi\)
−0.841807 + 0.539779i \(0.818508\pi\)
\(684\) 36.0000 1.37649
\(685\) −12.0000 −0.458496
\(686\) −13.0000 −0.496342
\(687\) 45.0000 1.71686
\(688\) −5.00000 −0.190623
\(689\) −12.0000 −0.457164
\(690\) −12.0000 −0.456832
\(691\) −8.00000 −0.304334 −0.152167 0.988355i \(-0.548625\pi\)
−0.152167 + 0.988355i \(0.548625\pi\)
\(692\) 20.0000 0.760286
\(693\) −12.0000 −0.455842
\(694\) −9.00000 −0.341635
\(695\) −7.00000 −0.265525
\(696\) −6.00000 −0.227429
\(697\) 0 0
\(698\) 7.00000 0.264954
\(699\) 33.0000 1.24817
\(700\) −4.00000 −0.151186
\(701\) −12.0000 −0.453234 −0.226617 0.973984i \(-0.572767\pi\)
−0.226617 + 0.973984i \(0.572767\pi\)
\(702\) 9.00000 0.339683
\(703\) 18.0000 0.678883
\(704\) −2.00000 −0.0753778
\(705\) 39.0000 1.46882
\(706\) 4.00000 0.150542
\(707\) 4.00000 0.150435
\(708\) 30.0000 1.12747
\(709\) 38.0000 1.42712 0.713560 0.700594i \(-0.247082\pi\)
0.713560 + 0.700594i \(0.247082\pi\)
\(710\) 5.00000 0.187647
\(711\) −24.0000 −0.900070
\(712\) 6.00000 0.224860
\(713\) −16.0000 −0.599205
\(714\) 9.00000 0.336817
\(715\) −2.00000 −0.0747958
\(716\) −9.00000 −0.336346
\(717\) −27.0000 −1.00833
\(718\) 24.0000 0.895672
\(719\) −22.0000 −0.820462 −0.410231 0.911982i \(-0.634552\pi\)
−0.410231 + 0.911982i \(0.634552\pi\)
\(720\) −6.00000 −0.223607
\(721\) −8.00000 −0.297936
\(722\) 17.0000 0.632674
\(723\) −54.0000 −2.00828
\(724\) 0 0
\(725\) −8.00000 −0.297113
\(726\) 21.0000 0.779383
\(727\) −14.0000 −0.519231 −0.259616 0.965712i \(-0.583596\pi\)
−0.259616 + 0.965712i \(0.583596\pi\)
\(728\) −1.00000 −0.0370625
\(729\) −27.0000 −1.00000
\(730\) 10.0000 0.370117
\(731\) 15.0000 0.554795
\(732\) 24.0000 0.887066
\(733\) −43.0000 −1.58824 −0.794121 0.607760i \(-0.792068\pi\)
−0.794121 + 0.607760i \(0.792068\pi\)
\(734\) −10.0000 −0.369107
\(735\) −18.0000 −0.663940
\(736\) −4.00000 −0.147442
\(737\) 4.00000 0.147342
\(738\) 0 0
\(739\) 12.0000 0.441427 0.220714 0.975339i \(-0.429161\pi\)
0.220714 + 0.975339i \(0.429161\pi\)
\(740\) −3.00000 −0.110282
\(741\) 18.0000 0.661247
\(742\) 12.0000 0.440534
\(743\) −47.0000 −1.72426 −0.862131 0.506685i \(-0.830871\pi\)
−0.862131 + 0.506685i \(0.830871\pi\)
\(744\) −12.0000 −0.439941
\(745\) 18.0000 0.659469
\(746\) −4.00000 −0.146450
\(747\) 0 0
\(748\) 6.00000 0.219382
\(749\) −4.00000 −0.146157
\(750\) −27.0000 −0.985901
\(751\) 24.0000 0.875772 0.437886 0.899030i \(-0.355727\pi\)
0.437886 + 0.899030i \(0.355727\pi\)
\(752\) 13.0000 0.474061
\(753\) 0 0
\(754\) −2.00000 −0.0728357
\(755\) 9.00000 0.327544
\(756\) −9.00000 −0.327327
\(757\) −12.0000 −0.436147 −0.218074 0.975932i \(-0.569977\pi\)
−0.218074 + 0.975932i \(0.569977\pi\)
\(758\) 16.0000 0.581146
\(759\) −24.0000 −0.871145
\(760\) −6.00000 −0.217643
\(761\) 6.00000 0.217500 0.108750 0.994069i \(-0.465315\pi\)
0.108750 + 0.994069i \(0.465315\pi\)
\(762\) −48.0000 −1.73886
\(763\) 19.0000 0.687846
\(764\) 10.0000 0.361787
\(765\) 18.0000 0.650791
\(766\) 27.0000 0.975550
\(767\) 10.0000 0.361079
\(768\) −3.00000 −0.108253
\(769\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(770\) 2.00000 0.0720750
\(771\) 45.0000 1.62064
\(772\) −16.0000 −0.575853
\(773\) 11.0000 0.395643 0.197821 0.980238i \(-0.436613\pi\)
0.197821 + 0.980238i \(0.436613\pi\)
\(774\) −30.0000 −1.07833
\(775\) −16.0000 −0.574737
\(776\) 14.0000 0.502571
\(777\) −9.00000 −0.322873
\(778\) −30.0000 −1.07555
\(779\) 0 0
\(780\) −3.00000 −0.107417
\(781\) 10.0000 0.357828
\(782\) 12.0000 0.429119
\(783\) −18.0000 −0.643268
\(784\) −6.00000 −0.214286
\(785\) 10.0000 0.356915
\(786\) 3.00000 0.107006
\(787\) 32.0000 1.14068 0.570338 0.821410i \(-0.306812\pi\)
0.570338 + 0.821410i \(0.306812\pi\)
\(788\) 9.00000 0.320612
\(789\) −36.0000 −1.28163
\(790\) 4.00000 0.142314
\(791\) 2.00000 0.0711118
\(792\) −12.0000 −0.426401
\(793\) 8.00000 0.284088
\(794\) −22.0000 −0.780751
\(795\) 36.0000 1.27679
\(796\) −10.0000 −0.354441
\(797\) −42.0000 −1.48772 −0.743858 0.668338i \(-0.767006\pi\)
−0.743858 + 0.668338i \(0.767006\pi\)
\(798\) −18.0000 −0.637193
\(799\) −39.0000 −1.37972
\(800\) −4.00000 −0.141421
\(801\) 36.0000 1.27200
\(802\) 24.0000 0.847469
\(803\) 20.0000 0.705785
\(804\) 6.00000 0.211604
\(805\) 4.00000 0.140981
\(806\) −4.00000 −0.140894
\(807\) 72.0000 2.53452
\(808\) 4.00000 0.140720
\(809\) −9.00000 −0.316423 −0.158212 0.987405i \(-0.550573\pi\)
−0.158212 + 0.987405i \(0.550573\pi\)
\(810\) −9.00000 −0.316228
\(811\) −28.0000 −0.983213 −0.491606 0.870817i \(-0.663590\pi\)
−0.491606 + 0.870817i \(0.663590\pi\)
\(812\) 2.00000 0.0701862
\(813\) −39.0000 −1.36779
\(814\) −6.00000 −0.210300
\(815\) 4.00000 0.140114
\(816\) 9.00000 0.315063
\(817\) −30.0000 −1.04957
\(818\) 4.00000 0.139857
\(819\) −6.00000 −0.209657
\(820\) 0 0
\(821\) −25.0000 −0.872506 −0.436253 0.899824i \(-0.643695\pi\)
−0.436253 + 0.899824i \(0.643695\pi\)
\(822\) −36.0000 −1.25564
\(823\) 54.0000 1.88232 0.941161 0.337959i \(-0.109737\pi\)
0.941161 + 0.337959i \(0.109737\pi\)
\(824\) −8.00000 −0.278693
\(825\) −24.0000 −0.835573
\(826\) −10.0000 −0.347945
\(827\) 30.0000 1.04320 0.521601 0.853189i \(-0.325335\pi\)
0.521601 + 0.853189i \(0.325335\pi\)
\(828\) −24.0000 −0.834058
\(829\) −38.0000 −1.31979 −0.659897 0.751356i \(-0.729400\pi\)
−0.659897 + 0.751356i \(0.729400\pi\)
\(830\) 0 0
\(831\) −36.0000 −1.24883
\(832\) −1.00000 −0.0346688
\(833\) 18.0000 0.623663
\(834\) −21.0000 −0.727171
\(835\) 0 0
\(836\) −12.0000 −0.415029
\(837\) −36.0000 −1.24434
\(838\) 21.0000 0.725433
\(839\) 56.0000 1.93333 0.966667 0.256036i \(-0.0824164\pi\)
0.966667 + 0.256036i \(0.0824164\pi\)
\(840\) 3.00000 0.103510
\(841\) −25.0000 −0.862069
\(842\) −5.00000 −0.172311
\(843\) 78.0000 2.68646
\(844\) 23.0000 0.791693
\(845\) −1.00000 −0.0344010
\(846\) 78.0000 2.68170
\(847\) −7.00000 −0.240523
\(848\) 12.0000 0.412082
\(849\) −12.0000 −0.411839
\(850\) 12.0000 0.411597
\(851\) −12.0000 −0.411355
\(852\) 15.0000 0.513892
\(853\) 49.0000 1.67773 0.838864 0.544341i \(-0.183220\pi\)
0.838864 + 0.544341i \(0.183220\pi\)
\(854\) −8.00000 −0.273754
\(855\) −36.0000 −1.23117
\(856\) −4.00000 −0.136717
\(857\) 46.0000 1.57133 0.785665 0.618652i \(-0.212321\pi\)
0.785665 + 0.618652i \(0.212321\pi\)
\(858\) −6.00000 −0.204837
\(859\) 20.0000 0.682391 0.341196 0.939992i \(-0.389168\pi\)
0.341196 + 0.939992i \(0.389168\pi\)
\(860\) 5.00000 0.170499
\(861\) 0 0
\(862\) 33.0000 1.12398
\(863\) −11.0000 −0.374444 −0.187222 0.982318i \(-0.559948\pi\)
−0.187222 + 0.982318i \(0.559948\pi\)
\(864\) −9.00000 −0.306186
\(865\) −20.0000 −0.680020
\(866\) 7.00000 0.237870
\(867\) 24.0000 0.815083
\(868\) 4.00000 0.135769
\(869\) 8.00000 0.271381
\(870\) 6.00000 0.203419
\(871\) 2.00000 0.0677674
\(872\) 19.0000 0.643421
\(873\) 84.0000 2.84297
\(874\) −24.0000 −0.811812
\(875\) 9.00000 0.304256
\(876\) 30.0000 1.01361
\(877\) −39.0000 −1.31694 −0.658468 0.752609i \(-0.728795\pi\)
−0.658468 + 0.752609i \(0.728795\pi\)
\(878\) −22.0000 −0.742464
\(879\) −21.0000 −0.708312
\(880\) 2.00000 0.0674200
\(881\) 21.0000 0.707508 0.353754 0.935339i \(-0.384905\pi\)
0.353754 + 0.935339i \(0.384905\pi\)
\(882\) −36.0000 −1.21218
\(883\) −47.0000 −1.58168 −0.790838 0.612026i \(-0.790355\pi\)
−0.790838 + 0.612026i \(0.790355\pi\)
\(884\) 3.00000 0.100901
\(885\) −30.0000 −1.00844
\(886\) −39.0000 −1.31023
\(887\) −8.00000 −0.268614 −0.134307 0.990940i \(-0.542881\pi\)
−0.134307 + 0.990940i \(0.542881\pi\)
\(888\) −9.00000 −0.302020
\(889\) 16.0000 0.536623
\(890\) −6.00000 −0.201120
\(891\) −18.0000 −0.603023
\(892\) −21.0000 −0.703132
\(893\) 78.0000 2.61017
\(894\) 54.0000 1.80603
\(895\) 9.00000 0.300837
\(896\) 1.00000 0.0334077
\(897\) −12.0000 −0.400668
\(898\) −26.0000 −0.867631
\(899\) 8.00000 0.266815
\(900\) −24.0000 −0.800000
\(901\) −36.0000 −1.19933
\(902\) 0 0
\(903\) 15.0000 0.499169
\(904\) 2.00000 0.0665190
\(905\) 0 0
\(906\) 27.0000 0.897015
\(907\) −9.00000 −0.298840 −0.149420 0.988774i \(-0.547741\pi\)
−0.149420 + 0.988774i \(0.547741\pi\)
\(908\) −24.0000 −0.796468
\(909\) 24.0000 0.796030
\(910\) 1.00000 0.0331497
\(911\) −54.0000 −1.78910 −0.894550 0.446968i \(-0.852504\pi\)
−0.894550 + 0.446968i \(0.852504\pi\)
\(912\) −18.0000 −0.596040
\(913\) 0 0
\(914\) 10.0000 0.330771
\(915\) −24.0000 −0.793416
\(916\) −15.0000 −0.495614
\(917\) −1.00000 −0.0330229
\(918\) 27.0000 0.891133
\(919\) 24.0000 0.791687 0.395843 0.918318i \(-0.370452\pi\)
0.395843 + 0.918318i \(0.370452\pi\)
\(920\) 4.00000 0.131876
\(921\) −42.0000 −1.38395
\(922\) −21.0000 −0.691598
\(923\) 5.00000 0.164577
\(924\) 6.00000 0.197386
\(925\) −12.0000 −0.394558
\(926\) 16.0000 0.525793
\(927\) −48.0000 −1.57653
\(928\) 2.00000 0.0656532
\(929\) −36.0000 −1.18112 −0.590561 0.806993i \(-0.701093\pi\)
−0.590561 + 0.806993i \(0.701093\pi\)
\(930\) 12.0000 0.393496
\(931\) −36.0000 −1.17985
\(932\) −11.0000 −0.360317
\(933\) −54.0000 −1.76788
\(934\) 20.0000 0.654420
\(935\) −6.00000 −0.196221
\(936\) −6.00000 −0.196116
\(937\) −42.0000 −1.37208 −0.686040 0.727564i \(-0.740653\pi\)
−0.686040 + 0.727564i \(0.740653\pi\)
\(938\) −2.00000 −0.0653023
\(939\) 3.00000 0.0979013
\(940\) −13.0000 −0.424013
\(941\) 25.0000 0.814977 0.407488 0.913210i \(-0.366405\pi\)
0.407488 + 0.913210i \(0.366405\pi\)
\(942\) 30.0000 0.977453
\(943\) 0 0
\(944\) −10.0000 −0.325472
\(945\) 9.00000 0.292770
\(946\) 10.0000 0.325128
\(947\) −18.0000 −0.584921 −0.292461 0.956278i \(-0.594474\pi\)
−0.292461 + 0.956278i \(0.594474\pi\)
\(948\) 12.0000 0.389742
\(949\) 10.0000 0.324614
\(950\) −24.0000 −0.778663
\(951\) 54.0000 1.75107
\(952\) −3.00000 −0.0972306
\(953\) 23.0000 0.745043 0.372522 0.928024i \(-0.378493\pi\)
0.372522 + 0.928024i \(0.378493\pi\)
\(954\) 72.0000 2.33109
\(955\) −10.0000 −0.323592
\(956\) 9.00000 0.291081
\(957\) 12.0000 0.387905
\(958\) −3.00000 −0.0969256
\(959\) 12.0000 0.387500
\(960\) 3.00000 0.0968246
\(961\) −15.0000 −0.483871
\(962\) −3.00000 −0.0967239
\(963\) −24.0000 −0.773389
\(964\) 18.0000 0.579741
\(965\) 16.0000 0.515058
\(966\) 12.0000 0.386094
\(967\) 23.0000 0.739630 0.369815 0.929105i \(-0.379421\pi\)
0.369815 + 0.929105i \(0.379421\pi\)
\(968\) −7.00000 −0.224989
\(969\) 54.0000 1.73473
\(970\) −14.0000 −0.449513
\(971\) −15.0000 −0.481373 −0.240686 0.970603i \(-0.577373\pi\)
−0.240686 + 0.970603i \(0.577373\pi\)
\(972\) 0 0
\(973\) 7.00000 0.224410
\(974\) −16.0000 −0.512673
\(975\) −12.0000 −0.384308
\(976\) −8.00000 −0.256074
\(977\) −30.0000 −0.959785 −0.479893 0.877327i \(-0.659324\pi\)
−0.479893 + 0.877327i \(0.659324\pi\)
\(978\) 12.0000 0.383718
\(979\) −12.0000 −0.383522
\(980\) 6.00000 0.191663
\(981\) 114.000 3.63974
\(982\) −5.00000 −0.159556
\(983\) −31.0000 −0.988746 −0.494373 0.869250i \(-0.664602\pi\)
−0.494373 + 0.869250i \(0.664602\pi\)
\(984\) 0 0
\(985\) −9.00000 −0.286764
\(986\) −6.00000 −0.191079
\(987\) −39.0000 −1.24138
\(988\) −6.00000 −0.190885
\(989\) 20.0000 0.635963
\(990\) 12.0000 0.381385
\(991\) −30.0000 −0.952981 −0.476491 0.879180i \(-0.658091\pi\)
−0.476491 + 0.879180i \(0.658091\pi\)
\(992\) 4.00000 0.127000
\(993\) 12.0000 0.380808
\(994\) −5.00000 −0.158590
\(995\) 10.0000 0.317021
\(996\) 0 0
\(997\) −10.0000 −0.316703 −0.158352 0.987383i \(-0.550618\pi\)
−0.158352 + 0.987383i \(0.550618\pi\)
\(998\) −32.0000 −1.01294
\(999\) −27.0000 −0.854242
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 \(a_p\))