Properties

Label 6026.2.a.d.1.1
Level 6026
Weight 2
Character 6026.1
Self dual Yes
Analytic conductor 48.118
Analytic rank 1
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6026 = 2 \cdot 23 \cdot 131 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6026.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.117852258\)
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 \(\chi\) = 6026.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(+2.00000 q^{3}\) \(+1.00000 q^{4}\) \(-1.00000 q^{5}\) \(+2.00000 q^{6}\) \(+2.00000 q^{7}\) \(+1.00000 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(+2.00000 q^{3}\) \(+1.00000 q^{4}\) \(-1.00000 q^{5}\) \(+2.00000 q^{6}\) \(+2.00000 q^{7}\) \(+1.00000 q^{8}\) \(+1.00000 q^{9}\) \(-1.00000 q^{10}\) \(-5.00000 q^{11}\) \(+2.00000 q^{12}\) \(-2.00000 q^{13}\) \(+2.00000 q^{14}\) \(-2.00000 q^{15}\) \(+1.00000 q^{16}\) \(-3.00000 q^{17}\) \(+1.00000 q^{18}\) \(-6.00000 q^{19}\) \(-1.00000 q^{20}\) \(+4.00000 q^{21}\) \(-5.00000 q^{22}\) \(-1.00000 q^{23}\) \(+2.00000 q^{24}\) \(-4.00000 q^{25}\) \(-2.00000 q^{26}\) \(-4.00000 q^{27}\) \(+2.00000 q^{28}\) \(-2.00000 q^{29}\) \(-2.00000 q^{30}\) \(+4.00000 q^{31}\) \(+1.00000 q^{32}\) \(-10.0000 q^{33}\) \(-3.00000 q^{34}\) \(-2.00000 q^{35}\) \(+1.00000 q^{36}\) \(+2.00000 q^{37}\) \(-6.00000 q^{38}\) \(-4.00000 q^{39}\) \(-1.00000 q^{40}\) \(+7.00000 q^{41}\) \(+4.00000 q^{42}\) \(-1.00000 q^{43}\) \(-5.00000 q^{44}\) \(-1.00000 q^{45}\) \(-1.00000 q^{46}\) \(-6.00000 q^{47}\) \(+2.00000 q^{48}\) \(-3.00000 q^{49}\) \(-4.00000 q^{50}\) \(-6.00000 q^{51}\) \(-2.00000 q^{52}\) \(+6.00000 q^{53}\) \(-4.00000 q^{54}\) \(+5.00000 q^{55}\) \(+2.00000 q^{56}\) \(-12.0000 q^{57}\) \(-2.00000 q^{58}\) \(+10.0000 q^{59}\) \(-2.00000 q^{60}\) \(-3.00000 q^{61}\) \(+4.00000 q^{62}\) \(+2.00000 q^{63}\) \(+1.00000 q^{64}\) \(+2.00000 q^{65}\) \(-10.0000 q^{66}\) \(-10.0000 q^{67}\) \(-3.00000 q^{68}\) \(-2.00000 q^{69}\) \(-2.00000 q^{70}\) \(-2.00000 q^{71}\) \(+1.00000 q^{72}\) \(-16.0000 q^{73}\) \(+2.00000 q^{74}\) \(-8.00000 q^{75}\) \(-6.00000 q^{76}\) \(-10.0000 q^{77}\) \(-4.00000 q^{78}\) \(+4.00000 q^{79}\) \(-1.00000 q^{80}\) \(-11.0000 q^{81}\) \(+7.00000 q^{82}\) \(-12.0000 q^{83}\) \(+4.00000 q^{84}\) \(+3.00000 q^{85}\) \(-1.00000 q^{86}\) \(-4.00000 q^{87}\) \(-5.00000 q^{88}\) \(-16.0000 q^{89}\) \(-1.00000 q^{90}\) \(-4.00000 q^{91}\) \(-1.00000 q^{92}\) \(+8.00000 q^{93}\) \(-6.00000 q^{94}\) \(+6.00000 q^{95}\) \(+2.00000 q^{96}\) \(+10.0000 q^{97}\) \(-3.00000 q^{98}\) \(-5.00000 q^{99}\) \(+O(q^{100})\)

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 −0.223607 0.974679i \(-0.571783\pi\)
−0.223607 + 0.974679i \(0.571783\pi\)
\(6\) 2.00000 0.816497
\(7\) 2.00000 0.755929 0.377964 0.925820i \(-0.376624\pi\)
0.377964 + 0.925820i \(0.376624\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.00000 0.333333
\(10\) −1.00000 −0.316228
\(11\) −5.00000 −1.50756 −0.753778 0.657129i \(-0.771771\pi\)
−0.753778 + 0.657129i \(0.771771\pi\)
\(12\) 2.00000 0.577350
\(13\) −2.00000 −0.554700 −0.277350 0.960769i \(-0.589456\pi\)
−0.277350 + 0.960769i \(0.589456\pi\)
\(14\) 2.00000 0.534522
\(15\) −2.00000 −0.516398
\(16\) 1.00000 0.250000
\(17\) −3.00000 −0.727607 −0.363803 0.931476i \(-0.618522\pi\)
−0.363803 + 0.931476i \(0.618522\pi\)
\(18\) 1.00000 0.235702
\(19\) −6.00000 −1.37649 −0.688247 0.725476i \(-0.741620\pi\)
−0.688247 + 0.725476i \(0.741620\pi\)
\(20\) −1.00000 −0.223607
\(21\) 4.00000 0.872872
\(22\) −5.00000 −1.06600
\(23\) −1.00000 −0.208514
\(24\) 2.00000 0.408248
\(25\) −4.00000 −0.800000
\(26\) −2.00000 −0.392232
\(27\) −4.00000 −0.769800
\(28\) 2.00000 0.377964
\(29\) −2.00000 −0.371391 −0.185695 0.982607i \(-0.559454\pi\)
−0.185695 + 0.982607i \(0.559454\pi\)
\(30\) −2.00000 −0.365148
\(31\) 4.00000 0.718421 0.359211 0.933257i \(-0.383046\pi\)
0.359211 + 0.933257i \(0.383046\pi\)
\(32\) 1.00000 0.176777
\(33\) −10.0000 −1.74078
\(34\) −3.00000 −0.514496
\(35\) −2.00000 −0.338062
\(36\) 1.00000 0.166667
\(37\) 2.00000 0.328798 0.164399 0.986394i \(-0.447432\pi\)
0.164399 + 0.986394i \(0.447432\pi\)
\(38\) −6.00000 −0.973329
\(39\) −4.00000 −0.640513
\(40\) −1.00000 −0.158114
\(41\) 7.00000 1.09322 0.546608 0.837389i \(-0.315919\pi\)
0.546608 + 0.837389i \(0.315919\pi\)
\(42\) 4.00000 0.617213
\(43\) −1.00000 −0.152499 −0.0762493 0.997089i \(-0.524294\pi\)
−0.0762493 + 0.997089i \(0.524294\pi\)
\(44\) −5.00000 −0.753778
\(45\) −1.00000 −0.149071
\(46\) −1.00000 −0.147442
\(47\) −6.00000 −0.875190 −0.437595 0.899172i \(-0.644170\pi\)
−0.437595 + 0.899172i \(0.644170\pi\)
\(48\) 2.00000 0.288675
\(49\) −3.00000 −0.428571
\(50\) −4.00000 −0.565685
\(51\) −6.00000 −0.840168
\(52\) −2.00000 −0.277350
\(53\) 6.00000 0.824163 0.412082 0.911147i \(-0.364802\pi\)
0.412082 + 0.911147i \(0.364802\pi\)
\(54\) −4.00000 −0.544331
\(55\) 5.00000 0.674200
\(56\) 2.00000 0.267261
\(57\) −12.0000 −1.58944
\(58\) −2.00000 −0.262613
\(59\) 10.0000 1.30189 0.650945 0.759125i \(-0.274373\pi\)
0.650945 + 0.759125i \(0.274373\pi\)
\(60\) −2.00000 −0.258199
\(61\) −3.00000 −0.384111 −0.192055 0.981384i \(-0.561515\pi\)
−0.192055 + 0.981384i \(0.561515\pi\)
\(62\) 4.00000 0.508001
\(63\) 2.00000 0.251976
\(64\) 1.00000 0.125000
\(65\) 2.00000 0.248069
\(66\) −10.0000 −1.23091
\(67\) −10.0000 −1.22169 −0.610847 0.791748i \(-0.709171\pi\)
−0.610847 + 0.791748i \(0.709171\pi\)
\(68\) −3.00000 −0.363803
\(69\) −2.00000 −0.240772
\(70\) −2.00000 −0.239046
\(71\) −2.00000 −0.237356 −0.118678 0.992933i \(-0.537866\pi\)
−0.118678 + 0.992933i \(0.537866\pi\)
\(72\) 1.00000 0.117851
\(73\) −16.0000 −1.87266 −0.936329 0.351123i \(-0.885800\pi\)
−0.936329 + 0.351123i \(0.885800\pi\)
\(74\) 2.00000 0.232495
\(75\) −8.00000 −0.923760
\(76\) −6.00000 −0.688247
\(77\) −10.0000 −1.13961
\(78\) −4.00000 −0.452911
\(79\) 4.00000 0.450035 0.225018 0.974355i \(-0.427756\pi\)
0.225018 + 0.974355i \(0.427756\pi\)
\(80\) −1.00000 −0.111803
\(81\) −11.0000 −1.22222
\(82\) 7.00000 0.773021
\(83\) −12.0000 −1.31717 −0.658586 0.752506i \(-0.728845\pi\)
−0.658586 + 0.752506i \(0.728845\pi\)
\(84\) 4.00000 0.436436
\(85\) 3.00000 0.325396
\(86\) −1.00000 −0.107833
\(87\) −4.00000 −0.428845
\(88\) −5.00000 −0.533002
\(89\) −16.0000 −1.69600 −0.847998 0.529999i \(-0.822192\pi\)
−0.847998 + 0.529999i \(0.822192\pi\)
\(90\) −1.00000 −0.105409
\(91\) −4.00000 −0.419314
\(92\) −1.00000 −0.104257
\(93\) 8.00000 0.829561
\(94\) −6.00000 −0.618853
\(95\) 6.00000 0.615587
\(96\) 2.00000 0.204124
\(97\) 10.0000 1.01535 0.507673 0.861550i \(-0.330506\pi\)
0.507673 + 0.861550i \(0.330506\pi\)
\(98\) −3.00000 −0.303046
\(99\) −5.00000 −0.502519
\(100\) −4.00000 −0.400000
\(101\) 16.0000 1.59206 0.796030 0.605257i \(-0.206930\pi\)
0.796030 + 0.605257i \(0.206930\pi\)
\(102\) −6.00000 −0.594089
\(103\) 1.00000 0.0985329 0.0492665 0.998786i \(-0.484312\pi\)
0.0492665 + 0.998786i \(0.484312\pi\)
\(104\) −2.00000 −0.196116
\(105\) −4.00000 −0.390360
\(106\) 6.00000 0.582772
\(107\) 13.0000 1.25676 0.628379 0.777908i \(-0.283719\pi\)
0.628379 + 0.777908i \(0.283719\pi\)
\(108\) −4.00000 −0.384900
\(109\) 1.00000 0.0957826 0.0478913 0.998853i \(-0.484750\pi\)
0.0478913 + 0.998853i \(0.484750\pi\)
\(110\) 5.00000 0.476731
\(111\) 4.00000 0.379663
\(112\) 2.00000 0.188982
\(113\) −12.0000 −1.12887 −0.564433 0.825479i \(-0.690905\pi\)
−0.564433 + 0.825479i \(0.690905\pi\)
\(114\) −12.0000 −1.12390
\(115\) 1.00000 0.0932505
\(116\) −2.00000 −0.185695
\(117\) −2.00000 −0.184900
\(118\) 10.0000 0.920575
\(119\) −6.00000 −0.550019
\(120\) −2.00000 −0.182574
\(121\) 14.0000 1.27273
\(122\) −3.00000 −0.271607
\(123\) 14.0000 1.26234
\(124\) 4.00000 0.359211
\(125\) 9.00000 0.804984
\(126\) 2.00000 0.178174
\(127\) 16.0000 1.41977 0.709885 0.704317i \(-0.248747\pi\)
0.709885 + 0.704317i \(0.248747\pi\)
\(128\) 1.00000 0.0883883
\(129\) −2.00000 −0.176090
\(130\) 2.00000 0.175412
\(131\) 1.00000 0.0873704
\(132\) −10.0000 −0.870388
\(133\) −12.0000 −1.04053
\(134\) −10.0000 −0.863868
\(135\) 4.00000 0.344265
\(136\) −3.00000 −0.257248
\(137\) 1.00000 0.0854358 0.0427179 0.999087i \(-0.486398\pi\)
0.0427179 + 0.999087i \(0.486398\pi\)
\(138\) −2.00000 −0.170251
\(139\) 3.00000 0.254457 0.127228 0.991873i \(-0.459392\pi\)
0.127228 + 0.991873i \(0.459392\pi\)
\(140\) −2.00000 −0.169031
\(141\) −12.0000 −1.01058
\(142\) −2.00000 −0.167836
\(143\) 10.0000 0.836242
\(144\) 1.00000 0.0833333
\(145\) 2.00000 0.166091
\(146\) −16.0000 −1.32417
\(147\) −6.00000 −0.494872
\(148\) 2.00000 0.164399
\(149\) −6.00000 −0.491539 −0.245770 0.969328i \(-0.579041\pi\)
−0.245770 + 0.969328i \(0.579041\pi\)
\(150\) −8.00000 −0.653197
\(151\) −11.0000 −0.895167 −0.447584 0.894242i \(-0.647715\pi\)
−0.447584 + 0.894242i \(0.647715\pi\)
\(152\) −6.00000 −0.486664
\(153\) −3.00000 −0.242536
\(154\) −10.0000 −0.805823
\(155\) −4.00000 −0.321288
\(156\) −4.00000 −0.320256
\(157\) −10.0000 −0.798087 −0.399043 0.916932i \(-0.630658\pi\)
−0.399043 + 0.916932i \(0.630658\pi\)
\(158\) 4.00000 0.318223
\(159\) 12.0000 0.951662
\(160\) −1.00000 −0.0790569
\(161\) −2.00000 −0.157622
\(162\) −11.0000 −0.864242
\(163\) 1.00000 0.0783260 0.0391630 0.999233i \(-0.487531\pi\)
0.0391630 + 0.999233i \(0.487531\pi\)
\(164\) 7.00000 0.546608
\(165\) 10.0000 0.778499
\(166\) −12.0000 −0.931381
\(167\) 9.00000 0.696441 0.348220 0.937413i \(-0.386786\pi\)
0.348220 + 0.937413i \(0.386786\pi\)
\(168\) 4.00000 0.308607
\(169\) −9.00000 −0.692308
\(170\) 3.00000 0.230089
\(171\) −6.00000 −0.458831
\(172\) −1.00000 −0.0762493
\(173\) 21.0000 1.59660 0.798300 0.602260i \(-0.205733\pi\)
0.798300 + 0.602260i \(0.205733\pi\)
\(174\) −4.00000 −0.303239
\(175\) −8.00000 −0.604743
\(176\) −5.00000 −0.376889
\(177\) 20.0000 1.50329
\(178\) −16.0000 −1.19925
\(179\) −12.0000 −0.896922 −0.448461 0.893802i \(-0.648028\pi\)
−0.448461 + 0.893802i \(0.648028\pi\)
\(180\) −1.00000 −0.0745356
\(181\) −20.0000 −1.48659 −0.743294 0.668965i \(-0.766738\pi\)
−0.743294 + 0.668965i \(0.766738\pi\)
\(182\) −4.00000 −0.296500
\(183\) −6.00000 −0.443533
\(184\) −1.00000 −0.0737210
\(185\) −2.00000 −0.147043
\(186\) 8.00000 0.586588
\(187\) 15.0000 1.09691
\(188\) −6.00000 −0.437595
\(189\) −8.00000 −0.581914
\(190\) 6.00000 0.435286
\(191\) 14.0000 1.01300 0.506502 0.862239i \(-0.330938\pi\)
0.506502 + 0.862239i \(0.330938\pi\)
\(192\) 2.00000 0.144338
\(193\) 23.0000 1.65558 0.827788 0.561041i \(-0.189599\pi\)
0.827788 + 0.561041i \(0.189599\pi\)
\(194\) 10.0000 0.717958
\(195\) 4.00000 0.286446
\(196\) −3.00000 −0.214286
\(197\) 21.0000 1.49619 0.748094 0.663593i \(-0.230969\pi\)
0.748094 + 0.663593i \(0.230969\pi\)
\(198\) −5.00000 −0.355335
\(199\) −3.00000 −0.212664 −0.106332 0.994331i \(-0.533911\pi\)
−0.106332 + 0.994331i \(0.533911\pi\)
\(200\) −4.00000 −0.282843
\(201\) −20.0000 −1.41069
\(202\) 16.0000 1.12576
\(203\) −4.00000 −0.280745
\(204\) −6.00000 −0.420084
\(205\) −7.00000 −0.488901
\(206\) 1.00000 0.0696733
\(207\) −1.00000 −0.0695048
\(208\) −2.00000 −0.138675
\(209\) 30.0000 2.07514
\(210\) −4.00000 −0.276026
\(211\) −14.0000 −0.963800 −0.481900 0.876226i \(-0.660053\pi\)
−0.481900 + 0.876226i \(0.660053\pi\)
\(212\) 6.00000 0.412082
\(213\) −4.00000 −0.274075
\(214\) 13.0000 0.888662
\(215\) 1.00000 0.0681994
\(216\) −4.00000 −0.272166
\(217\) 8.00000 0.543075
\(218\) 1.00000 0.0677285
\(219\) −32.0000 −2.16236
\(220\) 5.00000 0.337100
\(221\) 6.00000 0.403604
\(222\) 4.00000 0.268462
\(223\) 14.0000 0.937509 0.468755 0.883328i \(-0.344703\pi\)
0.468755 + 0.883328i \(0.344703\pi\)
\(224\) 2.00000 0.133631
\(225\) −4.00000 −0.266667
\(226\) −12.0000 −0.798228
\(227\) 10.0000 0.663723 0.331862 0.943328i \(-0.392323\pi\)
0.331862 + 0.943328i \(0.392323\pi\)
\(228\) −12.0000 −0.794719
\(229\) 16.0000 1.05731 0.528655 0.848837i \(-0.322697\pi\)
0.528655 + 0.848837i \(0.322697\pi\)
\(230\) 1.00000 0.0659380
\(231\) −20.0000 −1.31590
\(232\) −2.00000 −0.131306
\(233\) −5.00000 −0.327561 −0.163780 0.986497i \(-0.552369\pi\)
−0.163780 + 0.986497i \(0.552369\pi\)
\(234\) −2.00000 −0.130744
\(235\) 6.00000 0.391397
\(236\) 10.0000 0.650945
\(237\) 8.00000 0.519656
\(238\) −6.00000 −0.388922
\(239\) −12.0000 −0.776215 −0.388108 0.921614i \(-0.626871\pi\)
−0.388108 + 0.921614i \(0.626871\pi\)
\(240\) −2.00000 −0.129099
\(241\) 11.0000 0.708572 0.354286 0.935137i \(-0.384724\pi\)
0.354286 + 0.935137i \(0.384724\pi\)
\(242\) 14.0000 0.899954
\(243\) −10.0000 −0.641500
\(244\) −3.00000 −0.192055
\(245\) 3.00000 0.191663
\(246\) 14.0000 0.892607
\(247\) 12.0000 0.763542
\(248\) 4.00000 0.254000
\(249\) −24.0000 −1.52094
\(250\) 9.00000 0.569210
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 2.00000 0.125988
\(253\) 5.00000 0.314347
\(254\) 16.0000 1.00393
\(255\) 6.00000 0.375735
\(256\) 1.00000 0.0625000
\(257\) −8.00000 −0.499026 −0.249513 0.968371i \(-0.580271\pi\)
−0.249513 + 0.968371i \(0.580271\pi\)
\(258\) −2.00000 −0.124515
\(259\) 4.00000 0.248548
\(260\) 2.00000 0.124035
\(261\) −2.00000 −0.123797
\(262\) 1.00000 0.0617802
\(263\) −10.0000 −0.616626 −0.308313 0.951285i \(-0.599764\pi\)
−0.308313 + 0.951285i \(0.599764\pi\)
\(264\) −10.0000 −0.615457
\(265\) −6.00000 −0.368577
\(266\) −12.0000 −0.735767
\(267\) −32.0000 −1.95837
\(268\) −10.0000 −0.610847
\(269\) 6.00000 0.365826 0.182913 0.983129i \(-0.441447\pi\)
0.182913 + 0.983129i \(0.441447\pi\)
\(270\) 4.00000 0.243432
\(271\) 7.00000 0.425220 0.212610 0.977137i \(-0.431804\pi\)
0.212610 + 0.977137i \(0.431804\pi\)
\(272\) −3.00000 −0.181902
\(273\) −8.00000 −0.484182
\(274\) 1.00000 0.0604122
\(275\) 20.0000 1.20605
\(276\) −2.00000 −0.120386
\(277\) −14.0000 −0.841178 −0.420589 0.907251i \(-0.638177\pi\)
−0.420589 + 0.907251i \(0.638177\pi\)
\(278\) 3.00000 0.179928
\(279\) 4.00000 0.239474
\(280\) −2.00000 −0.119523
\(281\) 1.00000 0.0596550 0.0298275 0.999555i \(-0.490504\pi\)
0.0298275 + 0.999555i \(0.490504\pi\)
\(282\) −12.0000 −0.714590
\(283\) −16.0000 −0.951101 −0.475551 0.879688i \(-0.657751\pi\)
−0.475551 + 0.879688i \(0.657751\pi\)
\(284\) −2.00000 −0.118678
\(285\) 12.0000 0.710819
\(286\) 10.0000 0.591312
\(287\) 14.0000 0.826394
\(288\) 1.00000 0.0589256
\(289\) −8.00000 −0.470588
\(290\) 2.00000 0.117444
\(291\) 20.0000 1.17242
\(292\) −16.0000 −0.936329
\(293\) 18.0000 1.05157 0.525786 0.850617i \(-0.323771\pi\)
0.525786 + 0.850617i \(0.323771\pi\)
\(294\) −6.00000 −0.349927
\(295\) −10.0000 −0.582223
\(296\) 2.00000 0.116248
\(297\) 20.0000 1.16052
\(298\) −6.00000 −0.347571
\(299\) 2.00000 0.115663
\(300\) −8.00000 −0.461880
\(301\) −2.00000 −0.115278
\(302\) −11.0000 −0.632979
\(303\) 32.0000 1.83835
\(304\) −6.00000 −0.344124
\(305\) 3.00000 0.171780
\(306\) −3.00000 −0.171499
\(307\) 6.00000 0.342438 0.171219 0.985233i \(-0.445229\pi\)
0.171219 + 0.985233i \(0.445229\pi\)
\(308\) −10.0000 −0.569803
\(309\) 2.00000 0.113776
\(310\) −4.00000 −0.227185
\(311\) −5.00000 −0.283524 −0.141762 0.989901i \(-0.545277\pi\)
−0.141762 + 0.989901i \(0.545277\pi\)
\(312\) −4.00000 −0.226455
\(313\) −22.0000 −1.24351 −0.621757 0.783210i \(-0.713581\pi\)
−0.621757 + 0.783210i \(0.713581\pi\)
\(314\) −10.0000 −0.564333
\(315\) −2.00000 −0.112687
\(316\) 4.00000 0.225018
\(317\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(318\) 12.0000 0.672927
\(319\) 10.0000 0.559893
\(320\) −1.00000 −0.0559017
\(321\) 26.0000 1.45118
\(322\) −2.00000 −0.111456
\(323\) 18.0000 1.00155
\(324\) −11.0000 −0.611111
\(325\) 8.00000 0.443760
\(326\) 1.00000 0.0553849
\(327\) 2.00000 0.110600
\(328\) 7.00000 0.386510
\(329\) −12.0000 −0.661581
\(330\) 10.0000 0.550482
\(331\) −16.0000 −0.879440 −0.439720 0.898135i \(-0.644922\pi\)
−0.439720 + 0.898135i \(0.644922\pi\)
\(332\) −12.0000 −0.658586
\(333\) 2.00000 0.109599
\(334\) 9.00000 0.492458
\(335\) 10.0000 0.546358
\(336\) 4.00000 0.218218
\(337\) −28.0000 −1.52526 −0.762629 0.646837i \(-0.776092\pi\)
−0.762629 + 0.646837i \(0.776092\pi\)
\(338\) −9.00000 −0.489535
\(339\) −24.0000 −1.30350
\(340\) 3.00000 0.162698
\(341\) −20.0000 −1.08306
\(342\) −6.00000 −0.324443
\(343\) −20.0000 −1.07990
\(344\) −1.00000 −0.0539164
\(345\) 2.00000 0.107676
\(346\) 21.0000 1.12897
\(347\) 27.0000 1.44944 0.724718 0.689046i \(-0.241970\pi\)
0.724718 + 0.689046i \(0.241970\pi\)
\(348\) −4.00000 −0.214423
\(349\) −2.00000 −0.107058 −0.0535288 0.998566i \(-0.517047\pi\)
−0.0535288 + 0.998566i \(0.517047\pi\)
\(350\) −8.00000 −0.427618
\(351\) 8.00000 0.427008
\(352\) −5.00000 −0.266501
\(353\) −23.0000 −1.22417 −0.612083 0.790793i \(-0.709668\pi\)
−0.612083 + 0.790793i \(0.709668\pi\)
\(354\) 20.0000 1.06299
\(355\) 2.00000 0.106149
\(356\) −16.0000 −0.847998
\(357\) −12.0000 −0.635107
\(358\) −12.0000 −0.634220
\(359\) −11.0000 −0.580558 −0.290279 0.956942i \(-0.593748\pi\)
−0.290279 + 0.956942i \(0.593748\pi\)
\(360\) −1.00000 −0.0527046
\(361\) 17.0000 0.894737
\(362\) −20.0000 −1.05118
\(363\) 28.0000 1.46962
\(364\) −4.00000 −0.209657
\(365\) 16.0000 0.837478
\(366\) −6.00000 −0.313625
\(367\) 14.0000 0.730794 0.365397 0.930852i \(-0.380933\pi\)
0.365397 + 0.930852i \(0.380933\pi\)
\(368\) −1.00000 −0.0521286
\(369\) 7.00000 0.364405
\(370\) −2.00000 −0.103975
\(371\) 12.0000 0.623009
\(372\) 8.00000 0.414781
\(373\) −16.0000 −0.828449 −0.414224 0.910175i \(-0.635947\pi\)
−0.414224 + 0.910175i \(0.635947\pi\)
\(374\) 15.0000 0.775632
\(375\) 18.0000 0.929516
\(376\) −6.00000 −0.309426
\(377\) 4.00000 0.206010
\(378\) −8.00000 −0.411476
\(379\) −23.0000 −1.18143 −0.590715 0.806880i \(-0.701154\pi\)
−0.590715 + 0.806880i \(0.701154\pi\)
\(380\) 6.00000 0.307794
\(381\) 32.0000 1.63941
\(382\) 14.0000 0.716302
\(383\) −26.0000 −1.32854 −0.664269 0.747494i \(-0.731257\pi\)
−0.664269 + 0.747494i \(0.731257\pi\)
\(384\) 2.00000 0.102062
\(385\) 10.0000 0.509647
\(386\) 23.0000 1.17067
\(387\) −1.00000 −0.0508329
\(388\) 10.0000 0.507673
\(389\) 24.0000 1.21685 0.608424 0.793612i \(-0.291802\pi\)
0.608424 + 0.793612i \(0.291802\pi\)
\(390\) 4.00000 0.202548
\(391\) 3.00000 0.151717
\(392\) −3.00000 −0.151523
\(393\) 2.00000 0.100887
\(394\) 21.0000 1.05796
\(395\) −4.00000 −0.201262
\(396\) −5.00000 −0.251259
\(397\) −36.0000 −1.80679 −0.903394 0.428811i \(-0.858933\pi\)
−0.903394 + 0.428811i \(0.858933\pi\)
\(398\) −3.00000 −0.150376
\(399\) −24.0000 −1.20150
\(400\) −4.00000 −0.200000
\(401\) −22.0000 −1.09863 −0.549314 0.835616i \(-0.685111\pi\)
−0.549314 + 0.835616i \(0.685111\pi\)
\(402\) −20.0000 −0.997509
\(403\) −8.00000 −0.398508
\(404\) 16.0000 0.796030
\(405\) 11.0000 0.546594
\(406\) −4.00000 −0.198517
\(407\) −10.0000 −0.495682
\(408\) −6.00000 −0.297044
\(409\) 9.00000 0.445021 0.222511 0.974930i \(-0.428575\pi\)
0.222511 + 0.974930i \(0.428575\pi\)
\(410\) −7.00000 −0.345705
\(411\) 2.00000 0.0986527
\(412\) 1.00000 0.0492665
\(413\) 20.0000 0.984136
\(414\) −1.00000 −0.0491473
\(415\) 12.0000 0.589057
\(416\) −2.00000 −0.0980581
\(417\) 6.00000 0.293821
\(418\) 30.0000 1.46735
\(419\) −16.0000 −0.781651 −0.390826 0.920465i \(-0.627810\pi\)
−0.390826 + 0.920465i \(0.627810\pi\)
\(420\) −4.00000 −0.195180
\(421\) 22.0000 1.07221 0.536107 0.844150i \(-0.319894\pi\)
0.536107 + 0.844150i \(0.319894\pi\)
\(422\) −14.0000 −0.681509
\(423\) −6.00000 −0.291730
\(424\) 6.00000 0.291386
\(425\) 12.0000 0.582086
\(426\) −4.00000 −0.193801
\(427\) −6.00000 −0.290360
\(428\) 13.0000 0.628379
\(429\) 20.0000 0.965609
\(430\) 1.00000 0.0482243
\(431\) −16.0000 −0.770693 −0.385346 0.922772i \(-0.625918\pi\)
−0.385346 + 0.922772i \(0.625918\pi\)
\(432\) −4.00000 −0.192450
\(433\) 19.0000 0.913082 0.456541 0.889702i \(-0.349088\pi\)
0.456541 + 0.889702i \(0.349088\pi\)
\(434\) 8.00000 0.384012
\(435\) 4.00000 0.191785
\(436\) 1.00000 0.0478913
\(437\) 6.00000 0.287019
\(438\) −32.0000 −1.52902
\(439\) −19.0000 −0.906821 −0.453410 0.891302i \(-0.649793\pi\)
−0.453410 + 0.891302i \(0.649793\pi\)
\(440\) 5.00000 0.238366
\(441\) −3.00000 −0.142857
\(442\) 6.00000 0.285391
\(443\) 12.0000 0.570137 0.285069 0.958507i \(-0.407984\pi\)
0.285069 + 0.958507i \(0.407984\pi\)
\(444\) 4.00000 0.189832
\(445\) 16.0000 0.758473
\(446\) 14.0000 0.662919
\(447\) −12.0000 −0.567581
\(448\) 2.00000 0.0944911
\(449\) −22.0000 −1.03824 −0.519122 0.854700i \(-0.673741\pi\)
−0.519122 + 0.854700i \(0.673741\pi\)
\(450\) −4.00000 −0.188562
\(451\) −35.0000 −1.64809
\(452\) −12.0000 −0.564433
\(453\) −22.0000 −1.03365
\(454\) 10.0000 0.469323
\(455\) 4.00000 0.187523
\(456\) −12.0000 −0.561951
\(457\) −28.0000 −1.30978 −0.654892 0.755722i \(-0.727286\pi\)
−0.654892 + 0.755722i \(0.727286\pi\)
\(458\) 16.0000 0.747631
\(459\) 12.0000 0.560112
\(460\) 1.00000 0.0466252
\(461\) −21.0000 −0.978068 −0.489034 0.872265i \(-0.662651\pi\)
−0.489034 + 0.872265i \(0.662651\pi\)
\(462\) −20.0000 −0.930484
\(463\) 32.0000 1.48717 0.743583 0.668644i \(-0.233125\pi\)
0.743583 + 0.668644i \(0.233125\pi\)
\(464\) −2.00000 −0.0928477
\(465\) −8.00000 −0.370991
\(466\) −5.00000 −0.231621
\(467\) −3.00000 −0.138823 −0.0694117 0.997588i \(-0.522112\pi\)
−0.0694117 + 0.997588i \(0.522112\pi\)
\(468\) −2.00000 −0.0924500
\(469\) −20.0000 −0.923514
\(470\) 6.00000 0.276759
\(471\) −20.0000 −0.921551
\(472\) 10.0000 0.460287
\(473\) 5.00000 0.229900
\(474\) 8.00000 0.367452
\(475\) 24.0000 1.10120
\(476\) −6.00000 −0.275010
\(477\) 6.00000 0.274721
\(478\) −12.0000 −0.548867
\(479\) −39.0000 −1.78196 −0.890978 0.454047i \(-0.849980\pi\)
−0.890978 + 0.454047i \(0.849980\pi\)
\(480\) −2.00000 −0.0912871
\(481\) −4.00000 −0.182384
\(482\) 11.0000 0.501036
\(483\) −4.00000 −0.182006
\(484\) 14.0000 0.636364
\(485\) −10.0000 −0.454077
\(486\) −10.0000 −0.453609
\(487\) 17.0000 0.770344 0.385172 0.922845i \(-0.374142\pi\)
0.385172 + 0.922845i \(0.374142\pi\)
\(488\) −3.00000 −0.135804
\(489\) 2.00000 0.0904431
\(490\) 3.00000 0.135526
\(491\) −7.00000 −0.315906 −0.157953 0.987447i \(-0.550489\pi\)
−0.157953 + 0.987447i \(0.550489\pi\)
\(492\) 14.0000 0.631169
\(493\) 6.00000 0.270226
\(494\) 12.0000 0.539906
\(495\) 5.00000 0.224733
\(496\) 4.00000 0.179605
\(497\) −4.00000 −0.179425
\(498\) −24.0000 −1.07547
\(499\) 29.0000 1.29822 0.649109 0.760695i \(-0.275142\pi\)
0.649109 + 0.760695i \(0.275142\pi\)
\(500\) 9.00000 0.402492
\(501\) 18.0000 0.804181
\(502\) 0 0
\(503\) −39.0000 −1.73892 −0.869462 0.494000i \(-0.835534\pi\)
−0.869462 + 0.494000i \(0.835534\pi\)
\(504\) 2.00000 0.0890871
\(505\) −16.0000 −0.711991
\(506\) 5.00000 0.222277
\(507\) −18.0000 −0.799408
\(508\) 16.0000 0.709885
\(509\) 25.0000 1.10811 0.554053 0.832482i \(-0.313081\pi\)
0.554053 + 0.832482i \(0.313081\pi\)
\(510\) 6.00000 0.265684
\(511\) −32.0000 −1.41560
\(512\) 1.00000 0.0441942
\(513\) 24.0000 1.05963
\(514\) −8.00000 −0.352865
\(515\) −1.00000 −0.0440653
\(516\) −2.00000 −0.0880451
\(517\) 30.0000 1.31940
\(518\) 4.00000 0.175750
\(519\) 42.0000 1.84360
\(520\) 2.00000 0.0877058
\(521\) 35.0000 1.53338 0.766689 0.642019i \(-0.221903\pi\)
0.766689 + 0.642019i \(0.221903\pi\)
\(522\) −2.00000 −0.0875376
\(523\) −34.0000 −1.48672 −0.743358 0.668894i \(-0.766768\pi\)
−0.743358 + 0.668894i \(0.766768\pi\)
\(524\) 1.00000 0.0436852
\(525\) −16.0000 −0.698297
\(526\) −10.0000 −0.436021
\(527\) −12.0000 −0.522728
\(528\) −10.0000 −0.435194
\(529\) 1.00000 0.0434783
\(530\) −6.00000 −0.260623
\(531\) 10.0000 0.433963
\(532\) −12.0000 −0.520266
\(533\) −14.0000 −0.606407
\(534\) −32.0000 −1.38478
\(535\) −13.0000 −0.562039
\(536\) −10.0000 −0.431934
\(537\) −24.0000 −1.03568
\(538\) 6.00000 0.258678
\(539\) 15.0000 0.646096
\(540\) 4.00000 0.172133
\(541\) −9.00000 −0.386940 −0.193470 0.981106i \(-0.561974\pi\)
−0.193470 + 0.981106i \(0.561974\pi\)
\(542\) 7.00000 0.300676
\(543\) −40.0000 −1.71656
\(544\) −3.00000 −0.128624
\(545\) −1.00000 −0.0428353
\(546\) −8.00000 −0.342368
\(547\) −29.0000 −1.23995 −0.619975 0.784621i \(-0.712857\pi\)
−0.619975 + 0.784621i \(0.712857\pi\)
\(548\) 1.00000 0.0427179
\(549\) −3.00000 −0.128037
\(550\) 20.0000 0.852803
\(551\) 12.0000 0.511217
\(552\) −2.00000 −0.0851257
\(553\) 8.00000 0.340195
\(554\) −14.0000 −0.594803
\(555\) −4.00000 −0.169791
\(556\) 3.00000 0.127228
\(557\) 5.00000 0.211857 0.105928 0.994374i \(-0.466219\pi\)
0.105928 + 0.994374i \(0.466219\pi\)
\(558\) 4.00000 0.169334
\(559\) 2.00000 0.0845910
\(560\) −2.00000 −0.0845154
\(561\) 30.0000 1.26660
\(562\) 1.00000 0.0421825
\(563\) 24.0000 1.01148 0.505740 0.862686i \(-0.331220\pi\)
0.505740 + 0.862686i \(0.331220\pi\)
\(564\) −12.0000 −0.505291
\(565\) 12.0000 0.504844
\(566\) −16.0000 −0.672530
\(567\) −22.0000 −0.923913
\(568\) −2.00000 −0.0839181
\(569\) 40.0000 1.67689 0.838444 0.544988i \(-0.183466\pi\)
0.838444 + 0.544988i \(0.183466\pi\)
\(570\) 12.0000 0.502625
\(571\) 32.0000 1.33916 0.669579 0.742741i \(-0.266474\pi\)
0.669579 + 0.742741i \(0.266474\pi\)
\(572\) 10.0000 0.418121
\(573\) 28.0000 1.16972
\(574\) 14.0000 0.584349
\(575\) 4.00000 0.166812
\(576\) 1.00000 0.0416667
\(577\) 23.0000 0.957503 0.478751 0.877951i \(-0.341090\pi\)
0.478751 + 0.877951i \(0.341090\pi\)
\(578\) −8.00000 −0.332756
\(579\) 46.0000 1.91169
\(580\) 2.00000 0.0830455
\(581\) −24.0000 −0.995688
\(582\) 20.0000 0.829027
\(583\) −30.0000 −1.24247
\(584\) −16.0000 −0.662085
\(585\) 2.00000 0.0826898
\(586\) 18.0000 0.743573
\(587\) 30.0000 1.23823 0.619116 0.785299i \(-0.287491\pi\)
0.619116 + 0.785299i \(0.287491\pi\)
\(588\) −6.00000 −0.247436
\(589\) −24.0000 −0.988903
\(590\) −10.0000 −0.411693
\(591\) 42.0000 1.72765
\(592\) 2.00000 0.0821995
\(593\) 44.0000 1.80686 0.903432 0.428732i \(-0.141040\pi\)
0.903432 + 0.428732i \(0.141040\pi\)
\(594\) 20.0000 0.820610
\(595\) 6.00000 0.245976
\(596\) −6.00000 −0.245770
\(597\) −6.00000 −0.245564
\(598\) 2.00000 0.0817861
\(599\) 45.0000 1.83865 0.919325 0.393499i \(-0.128735\pi\)
0.919325 + 0.393499i \(0.128735\pi\)
\(600\) −8.00000 −0.326599
\(601\) 3.00000 0.122373 0.0611863 0.998126i \(-0.480512\pi\)
0.0611863 + 0.998126i \(0.480512\pi\)
\(602\) −2.00000 −0.0815139
\(603\) −10.0000 −0.407231
\(604\) −11.0000 −0.447584
\(605\) −14.0000 −0.569181
\(606\) 32.0000 1.29991
\(607\) −22.0000 −0.892952 −0.446476 0.894795i \(-0.647321\pi\)
−0.446476 + 0.894795i \(0.647321\pi\)
\(608\) −6.00000 −0.243332
\(609\) −8.00000 −0.324176
\(610\) 3.00000 0.121466
\(611\) 12.0000 0.485468
\(612\) −3.00000 −0.121268
\(613\) −3.00000 −0.121169 −0.0605844 0.998163i \(-0.519296\pi\)
−0.0605844 + 0.998163i \(0.519296\pi\)
\(614\) 6.00000 0.242140
\(615\) −14.0000 −0.564534
\(616\) −10.0000 −0.402911
\(617\) −27.0000 −1.08698 −0.543490 0.839416i \(-0.682897\pi\)
−0.543490 + 0.839416i \(0.682897\pi\)
\(618\) 2.00000 0.0804518
\(619\) −2.00000 −0.0803868 −0.0401934 0.999192i \(-0.512797\pi\)
−0.0401934 + 0.999192i \(0.512797\pi\)
\(620\) −4.00000 −0.160644
\(621\) 4.00000 0.160514
\(622\) −5.00000 −0.200482
\(623\) −32.0000 −1.28205
\(624\) −4.00000 −0.160128
\(625\) 11.0000 0.440000
\(626\) −22.0000 −0.879297
\(627\) 60.0000 2.39617
\(628\) −10.0000 −0.399043
\(629\) −6.00000 −0.239236
\(630\) −2.00000 −0.0796819
\(631\) −30.0000 −1.19428 −0.597141 0.802137i \(-0.703697\pi\)
−0.597141 + 0.802137i \(0.703697\pi\)
\(632\) 4.00000 0.159111
\(633\) −28.0000 −1.11290
\(634\) 0 0
\(635\) −16.0000 −0.634941
\(636\) 12.0000 0.475831
\(637\) 6.00000 0.237729
\(638\) 10.0000 0.395904
\(639\) −2.00000 −0.0791188
\(640\) −1.00000 −0.0395285
\(641\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(642\) 26.0000 1.02614
\(643\) −16.0000 −0.630978 −0.315489 0.948929i \(-0.602169\pi\)
−0.315489 + 0.948929i \(0.602169\pi\)
\(644\) −2.00000 −0.0788110
\(645\) 2.00000 0.0787499
\(646\) 18.0000 0.708201
\(647\) 3.00000 0.117942 0.0589711 0.998260i \(-0.481218\pi\)
0.0589711 + 0.998260i \(0.481218\pi\)
\(648\) −11.0000 −0.432121
\(649\) −50.0000 −1.96267
\(650\) 8.00000 0.313786
\(651\) 16.0000 0.627089
\(652\) 1.00000 0.0391630
\(653\) 24.0000 0.939193 0.469596 0.882881i \(-0.344399\pi\)
0.469596 + 0.882881i \(0.344399\pi\)
\(654\) 2.00000 0.0782062
\(655\) −1.00000 −0.0390732
\(656\) 7.00000 0.273304
\(657\) −16.0000 −0.624219
\(658\) −12.0000 −0.467809
\(659\) 15.0000 0.584317 0.292159 0.956370i \(-0.405627\pi\)
0.292159 + 0.956370i \(0.405627\pi\)
\(660\) 10.0000 0.389249
\(661\) −8.00000 −0.311164 −0.155582 0.987823i \(-0.549725\pi\)
−0.155582 + 0.987823i \(0.549725\pi\)
\(662\) −16.0000 −0.621858
\(663\) 12.0000 0.466041
\(664\) −12.0000 −0.465690
\(665\) 12.0000 0.465340
\(666\) 2.00000 0.0774984
\(667\) 2.00000 0.0774403
\(668\) 9.00000 0.348220
\(669\) 28.0000 1.08254
\(670\) 10.0000 0.386334
\(671\) 15.0000 0.579069
\(672\) 4.00000 0.154303
\(673\) −46.0000 −1.77317 −0.886585 0.462566i \(-0.846929\pi\)
−0.886585 + 0.462566i \(0.846929\pi\)
\(674\) −28.0000 −1.07852
\(675\) 16.0000 0.615840
\(676\) −9.00000 −0.346154
\(677\) 18.0000 0.691796 0.345898 0.938272i \(-0.387574\pi\)
0.345898 + 0.938272i \(0.387574\pi\)
\(678\) −24.0000 −0.921714
\(679\) 20.0000 0.767530
\(680\) 3.00000 0.115045
\(681\) 20.0000 0.766402
\(682\) −20.0000 −0.765840
\(683\) 2.00000 0.0765279 0.0382639 0.999268i \(-0.487817\pi\)
0.0382639 + 0.999268i \(0.487817\pi\)
\(684\) −6.00000 −0.229416
\(685\) −1.00000 −0.0382080
\(686\) −20.0000 −0.763604
\(687\) 32.0000 1.22088
\(688\) −1.00000 −0.0381246
\(689\) −12.0000 −0.457164
\(690\) 2.00000 0.0761387
\(691\) −28.0000 −1.06517 −0.532585 0.846376i \(-0.678779\pi\)
−0.532585 + 0.846376i \(0.678779\pi\)
\(692\) 21.0000 0.798300
\(693\) −10.0000 −0.379869
\(694\) 27.0000 1.02491
\(695\) −3.00000 −0.113796
\(696\) −4.00000 −0.151620
\(697\) −21.0000 −0.795432
\(698\) −2.00000 −0.0757011
\(699\) −10.0000 −0.378235
\(700\) −8.00000 −0.302372
\(701\) 26.0000 0.982006 0.491003 0.871158i \(-0.336630\pi\)
0.491003 + 0.871158i \(0.336630\pi\)
\(702\) 8.00000 0.301941
\(703\) −12.0000 −0.452589
\(704\) −5.00000 −0.188445
\(705\) 12.0000 0.451946
\(706\) −23.0000 −0.865616
\(707\) 32.0000 1.20348
\(708\) 20.0000 0.751646
\(709\) −10.0000 −0.375558 −0.187779 0.982211i \(-0.560129\pi\)
−0.187779 + 0.982211i \(0.560129\pi\)
\(710\) 2.00000 0.0750587
\(711\) 4.00000 0.150012
\(712\) −16.0000 −0.599625
\(713\) −4.00000 −0.149801
\(714\) −12.0000 −0.449089
\(715\) −10.0000 −0.373979
\(716\) −12.0000 −0.448461
\(717\) −24.0000 −0.896296
\(718\) −11.0000 −0.410516
\(719\) −43.0000 −1.60363 −0.801815 0.597573i \(-0.796132\pi\)
−0.801815 + 0.597573i \(0.796132\pi\)
\(720\) −1.00000 −0.0372678
\(721\) 2.00000 0.0744839
\(722\) 17.0000 0.632674
\(723\) 22.0000 0.818189
\(724\) −20.0000 −0.743294
\(725\) 8.00000 0.297113
\(726\) 28.0000 1.03918
\(727\) −7.00000 −0.259616 −0.129808 0.991539i \(-0.541436\pi\)
−0.129808 + 0.991539i \(0.541436\pi\)
\(728\) −4.00000 −0.148250
\(729\) 13.0000 0.481481
\(730\) 16.0000 0.592187
\(731\) 3.00000 0.110959
\(732\) −6.00000 −0.221766
\(733\) −8.00000 −0.295487 −0.147743 0.989026i \(-0.547201\pi\)
−0.147743 + 0.989026i \(0.547201\pi\)
\(734\) 14.0000 0.516749
\(735\) 6.00000 0.221313
\(736\) −1.00000 −0.0368605
\(737\) 50.0000 1.84177
\(738\) 7.00000 0.257674
\(739\) −34.0000 −1.25071 −0.625355 0.780340i \(-0.715046\pi\)
−0.625355 + 0.780340i \(0.715046\pi\)
\(740\) −2.00000 −0.0735215
\(741\) 24.0000 0.881662
\(742\) 12.0000 0.440534
\(743\) 39.0000 1.43077 0.715386 0.698730i \(-0.246251\pi\)
0.715386 + 0.698730i \(0.246251\pi\)
\(744\) 8.00000 0.293294
\(745\) 6.00000 0.219823
\(746\) −16.0000 −0.585802
\(747\) −12.0000 −0.439057
\(748\) 15.0000 0.548454
\(749\) 26.0000 0.950019
\(750\) 18.0000 0.657267
\(751\) 7.00000 0.255434 0.127717 0.991811i \(-0.459235\pi\)
0.127717 + 0.991811i \(0.459235\pi\)
\(752\) −6.00000 −0.218797
\(753\) 0 0
\(754\) 4.00000 0.145671
\(755\) 11.0000 0.400331
\(756\) −8.00000 −0.290957
\(757\) 17.0000 0.617876 0.308938 0.951082i \(-0.400027\pi\)
0.308938 + 0.951082i \(0.400027\pi\)
\(758\) −23.0000 −0.835398
\(759\) 10.0000 0.362977
\(760\) 6.00000 0.217643
\(761\) −10.0000 −0.362500 −0.181250 0.983437i \(-0.558014\pi\)
−0.181250 + 0.983437i \(0.558014\pi\)
\(762\) 32.0000 1.15924
\(763\) 2.00000 0.0724049
\(764\) 14.0000 0.506502
\(765\) 3.00000 0.108465
\(766\) −26.0000 −0.939418
\(767\) −20.0000 −0.722158
\(768\) 2.00000 0.0721688
\(769\) −20.0000 −0.721218 −0.360609 0.932717i \(-0.617431\pi\)
−0.360609 + 0.932717i \(0.617431\pi\)
\(770\) 10.0000 0.360375
\(771\) −16.0000 −0.576226
\(772\) 23.0000 0.827788
\(773\) 18.0000 0.647415 0.323708 0.946157i \(-0.395071\pi\)
0.323708 + 0.946157i \(0.395071\pi\)
\(774\) −1.00000 −0.0359443
\(775\) −16.0000 −0.574737
\(776\) 10.0000 0.358979
\(777\) 8.00000 0.286998
\(778\) 24.0000 0.860442
\(779\) −42.0000 −1.50481
\(780\) 4.00000 0.143223
\(781\) 10.0000 0.357828
\(782\) 3.00000 0.107280
\(783\) 8.00000 0.285897
\(784\) −3.00000 −0.107143
\(785\) 10.0000 0.356915
\(786\) 2.00000 0.0713376
\(787\) 43.0000 1.53278 0.766392 0.642373i \(-0.222050\pi\)
0.766392 + 0.642373i \(0.222050\pi\)
\(788\) 21.0000 0.748094
\(789\) −20.0000 −0.712019
\(790\) −4.00000 −0.142314
\(791\) −24.0000 −0.853342
\(792\) −5.00000 −0.177667
\(793\) 6.00000 0.213066
\(794\) −36.0000 −1.27759
\(795\) −12.0000 −0.425596
\(796\) −3.00000 −0.106332
\(797\) −29.0000 −1.02723 −0.513616 0.858020i \(-0.671695\pi\)
−0.513616 + 0.858020i \(0.671695\pi\)
\(798\) −24.0000 −0.849591
\(799\) 18.0000 0.636794
\(800\) −4.00000 −0.141421
\(801\) −16.0000 −0.565332
\(802\) −22.0000 −0.776847
\(803\) 80.0000 2.82314
\(804\) −20.0000 −0.705346
\(805\) 2.00000 0.0704907
\(806\) −8.00000 −0.281788
\(807\) 12.0000 0.422420
\(808\) 16.0000 0.562878
\(809\) 24.0000 0.843795 0.421898 0.906644i \(-0.361364\pi\)
0.421898 + 0.906644i \(0.361364\pi\)
\(810\) 11.0000 0.386501
\(811\) −10.0000 −0.351147 −0.175574 0.984466i \(-0.556178\pi\)
−0.175574 + 0.984466i \(0.556178\pi\)
\(812\) −4.00000 −0.140372
\(813\) 14.0000 0.491001
\(814\) −10.0000 −0.350500
\(815\) −1.00000 −0.0350285
\(816\) −6.00000 −0.210042
\(817\) 6.00000 0.209913
\(818\) 9.00000 0.314678
\(819\) −4.00000 −0.139771
\(820\) −7.00000 −0.244451
\(821\) −6.00000 −0.209401 −0.104701 0.994504i \(-0.533388\pi\)
−0.104701 + 0.994504i \(0.533388\pi\)
\(822\) 2.00000 0.0697580
\(823\) −44.0000 −1.53374 −0.766872 0.641800i \(-0.778188\pi\)
−0.766872 + 0.641800i \(0.778188\pi\)
\(824\) 1.00000 0.0348367
\(825\) 40.0000 1.39262
\(826\) 20.0000 0.695889
\(827\) −52.0000 −1.80822 −0.904109 0.427303i \(-0.859464\pi\)
−0.904109 + 0.427303i \(0.859464\pi\)
\(828\) −1.00000 −0.0347524
\(829\) 2.00000 0.0694629 0.0347314 0.999397i \(-0.488942\pi\)
0.0347314 + 0.999397i \(0.488942\pi\)
\(830\) 12.0000 0.416526
\(831\) −28.0000 −0.971309
\(832\) −2.00000 −0.0693375
\(833\) 9.00000 0.311832
\(834\) 6.00000 0.207763
\(835\) −9.00000 −0.311458
\(836\) 30.0000 1.03757
\(837\) −16.0000 −0.553041
\(838\) −16.0000 −0.552711
\(839\) −6.00000 −0.207143 −0.103572 0.994622i \(-0.533027\pi\)
−0.103572 + 0.994622i \(0.533027\pi\)
\(840\) −4.00000 −0.138013
\(841\) −25.0000 −0.862069
\(842\) 22.0000 0.758170
\(843\) 2.00000 0.0688837
\(844\) −14.0000 −0.481900
\(845\) 9.00000 0.309609
\(846\) −6.00000 −0.206284
\(847\) 28.0000 0.962091
\(848\) 6.00000 0.206041
\(849\) −32.0000 −1.09824
\(850\) 12.0000 0.411597
\(851\) −2.00000 −0.0685591
\(852\) −4.00000 −0.137038
\(853\) −26.0000 −0.890223 −0.445112 0.895475i \(-0.646836\pi\)
−0.445112 + 0.895475i \(0.646836\pi\)
\(854\) −6.00000 −0.205316
\(855\) 6.00000 0.205196
\(856\) 13.0000 0.444331
\(857\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(858\) 20.0000 0.682789
\(859\) 56.0000 1.91070 0.955348 0.295484i \(-0.0954809\pi\)
0.955348 + 0.295484i \(0.0954809\pi\)
\(860\) 1.00000 0.0340997
\(861\) 28.0000 0.954237
\(862\) −16.0000 −0.544962
\(863\) −32.0000 −1.08929 −0.544646 0.838666i \(-0.683336\pi\)
−0.544646 + 0.838666i \(0.683336\pi\)
\(864\) −4.00000 −0.136083
\(865\) −21.0000 −0.714021
\(866\) 19.0000 0.645646
\(867\) −16.0000 −0.543388
\(868\) 8.00000 0.271538
\(869\) −20.0000 −0.678454
\(870\) 4.00000 0.135613
\(871\) 20.0000 0.677674
\(872\) 1.00000 0.0338643
\(873\) 10.0000 0.338449
\(874\) 6.00000 0.202953
\(875\) 18.0000 0.608511
\(876\) −32.0000 −1.08118
\(877\) 32.0000 1.08056 0.540282 0.841484i \(-0.318318\pi\)
0.540282 + 0.841484i \(0.318318\pi\)
\(878\) −19.0000 −0.641219
\(879\) 36.0000 1.21425
\(880\) 5.00000 0.168550
\(881\) 2.00000 0.0673817 0.0336909 0.999432i \(-0.489274\pi\)
0.0336909 + 0.999432i \(0.489274\pi\)
\(882\) −3.00000 −0.101015
\(883\) 29.0000 0.975928 0.487964 0.872864i \(-0.337740\pi\)
0.487964 + 0.872864i \(0.337740\pi\)
\(884\) 6.00000 0.201802
\(885\) −20.0000 −0.672293
\(886\) 12.0000 0.403148
\(887\) 47.0000 1.57811 0.789053 0.614325i \(-0.210572\pi\)
0.789053 + 0.614325i \(0.210572\pi\)
\(888\) 4.00000 0.134231
\(889\) 32.0000 1.07325
\(890\) 16.0000 0.536321
\(891\) 55.0000 1.84257
\(892\) 14.0000 0.468755
\(893\) 36.0000 1.20469
\(894\) −12.0000 −0.401340
\(895\) 12.0000 0.401116
\(896\) 2.00000 0.0668153
\(897\) 4.00000 0.133556
\(898\) −22.0000 −0.734150
\(899\) −8.00000 −0.266815
\(900\) −4.00000 −0.133333
\(901\) −18.0000 −0.599667
\(902\) −35.0000 −1.16537
\(903\) −4.00000 −0.133112
\(904\) −12.0000 −0.399114
\(905\) 20.0000 0.664822
\(906\) −22.0000 −0.730901
\(907\) −29.0000 −0.962929 −0.481465 0.876466i \(-0.659895\pi\)
−0.481465 + 0.876466i \(0.659895\pi\)
\(908\) 10.0000 0.331862
\(909\) 16.0000 0.530687
\(910\) 4.00000 0.132599
\(911\) 40.0000 1.32526 0.662630 0.748947i \(-0.269440\pi\)
0.662630 + 0.748947i \(0.269440\pi\)
\(912\) −12.0000 −0.397360
\(913\) 60.0000 1.98571
\(914\) −28.0000 −0.926158
\(915\) 6.00000 0.198354
\(916\) 16.0000 0.528655
\(917\) 2.00000 0.0660458
\(918\) 12.0000 0.396059
\(919\) 51.0000 1.68233 0.841167 0.540775i \(-0.181869\pi\)
0.841167 + 0.540775i \(0.181869\pi\)
\(920\) 1.00000 0.0329690
\(921\) 12.0000 0.395413
\(922\) −21.0000 −0.691598
\(923\) 4.00000 0.131662
\(924\) −20.0000 −0.657952
\(925\) −8.00000 −0.263038
\(926\) 32.0000 1.05159
\(927\) 1.00000 0.0328443
\(928\) −2.00000 −0.0656532
\(929\) 41.0000 1.34517 0.672583 0.740022i \(-0.265185\pi\)
0.672583 + 0.740022i \(0.265185\pi\)
\(930\) −8.00000 −0.262330
\(931\) 18.0000 0.589926
\(932\) −5.00000 −0.163780
\(933\) −10.0000 −0.327385
\(934\) −3.00000 −0.0981630
\(935\) −15.0000 −0.490552
\(936\) −2.00000 −0.0653720
\(937\) −14.0000 −0.457360 −0.228680 0.973502i \(-0.573441\pi\)
−0.228680 + 0.973502i \(0.573441\pi\)
\(938\) −20.0000 −0.653023
\(939\) −44.0000 −1.43589
\(940\) 6.00000 0.195698
\(941\) 30.0000 0.977972 0.488986 0.872292i \(-0.337367\pi\)
0.488986 + 0.872292i \(0.337367\pi\)
\(942\) −20.0000 −0.651635
\(943\) −7.00000 −0.227951
\(944\) 10.0000 0.325472
\(945\) 8.00000 0.260240
\(946\) 5.00000 0.162564
\(947\) −36.0000 −1.16984 −0.584921 0.811090i \(-0.698875\pi\)
−0.584921 + 0.811090i \(0.698875\pi\)
\(948\) 8.00000 0.259828
\(949\) 32.0000 1.03876
\(950\) 24.0000 0.778663
\(951\) 0 0
\(952\) −6.00000 −0.194461
\(953\) −12.0000 −0.388718 −0.194359 0.980930i \(-0.562263\pi\)
−0.194359 + 0.980930i \(0.562263\pi\)
\(954\) 6.00000 0.194257
\(955\) −14.0000 −0.453029
\(956\) −12.0000 −0.388108
\(957\) 20.0000 0.646508
\(958\) −39.0000 −1.26003
\(959\) 2.00000 0.0645834
\(960\) −2.00000 −0.0645497
\(961\) −15.0000 −0.483871
\(962\) −4.00000 −0.128965
\(963\) 13.0000 0.418919
\(964\) 11.0000 0.354286
\(965\) −23.0000 −0.740396
\(966\) −4.00000 −0.128698
\(967\) −12.0000 −0.385894 −0.192947 0.981209i \(-0.561805\pi\)
−0.192947 + 0.981209i \(0.561805\pi\)
\(968\) 14.0000 0.449977
\(969\) 36.0000 1.15649
\(970\) −10.0000 −0.321081
\(971\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(972\) −10.0000 −0.320750
\(973\) 6.00000 0.192351
\(974\) 17.0000 0.544715
\(975\) 16.0000 0.512410
\(976\) −3.00000 −0.0960277
\(977\) −58.0000 −1.85558 −0.927792 0.373097i \(-0.878296\pi\)
−0.927792 + 0.373097i \(0.878296\pi\)
\(978\) 2.00000 0.0639529
\(979\) 80.0000 2.55681
\(980\) 3.00000 0.0958315
\(981\) 1.00000 0.0319275
\(982\) −7.00000 −0.223379
\(983\) −48.0000 −1.53096 −0.765481 0.643458i \(-0.777499\pi\)
−0.765481 + 0.643458i \(0.777499\pi\)
\(984\) 14.0000 0.446304
\(985\) −21.0000 −0.669116
\(986\) 6.00000 0.191079
\(987\) −24.0000 −0.763928
\(988\) 12.0000 0.381771
\(989\) 1.00000 0.0317982
\(990\) 5.00000 0.158910
\(991\) −8.00000 −0.254128 −0.127064 0.991894i \(-0.540555\pi\)
−0.127064 + 0.991894i \(0.540555\pi\)
\(992\) 4.00000 0.127000
\(993\) −32.0000 −1.01549
\(994\) −4.00000 −0.126872
\(995\) 3.00000 0.0951064
\(996\) −24.0000 −0.760469
\(997\) −14.0000 −0.443384 −0.221692 0.975117i \(-0.571158\pi\)
−0.221692 + 0.975117i \(0.571158\pi\)
\(998\) 29.0000 0.917979
\(999\) −8.00000 −0.253109
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 \(a_p\))