Properties

Label 142.2.a.e.1.1
Level 142
Weight 2
Character 142.1
Self dual Yes
Analytic conductor 1.134
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 142 = 2 \cdot 71 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 142.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(1.1338757087\)
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 \(\chi\) = 142.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(+1.00000 q^{3}\) \(+1.00000 q^{4}\) \(+1.00000 q^{6}\) \(-1.00000 q^{7}\) \(+1.00000 q^{8}\) \(-2.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(+1.00000 q^{3}\) \(+1.00000 q^{4}\) \(+1.00000 q^{6}\) \(-1.00000 q^{7}\) \(+1.00000 q^{8}\) \(-2.00000 q^{9}\) \(+1.00000 q^{12}\) \(-1.00000 q^{13}\) \(-1.00000 q^{14}\) \(+1.00000 q^{16}\) \(-2.00000 q^{18}\) \(-1.00000 q^{19}\) \(-1.00000 q^{21}\) \(+3.00000 q^{23}\) \(+1.00000 q^{24}\) \(-5.00000 q^{25}\) \(-1.00000 q^{26}\) \(-5.00000 q^{27}\) \(-1.00000 q^{28}\) \(+5.00000 q^{31}\) \(+1.00000 q^{32}\) \(-2.00000 q^{36}\) \(-4.00000 q^{37}\) \(-1.00000 q^{38}\) \(-1.00000 q^{39}\) \(-1.00000 q^{42}\) \(-1.00000 q^{43}\) \(+3.00000 q^{46}\) \(+9.00000 q^{47}\) \(+1.00000 q^{48}\) \(-6.00000 q^{49}\) \(-5.00000 q^{50}\) \(-1.00000 q^{52}\) \(+6.00000 q^{53}\) \(-5.00000 q^{54}\) \(-1.00000 q^{56}\) \(-1.00000 q^{57}\) \(+6.00000 q^{59}\) \(+2.00000 q^{61}\) \(+5.00000 q^{62}\) \(+2.00000 q^{63}\) \(+1.00000 q^{64}\) \(+8.00000 q^{67}\) \(+3.00000 q^{69}\) \(-1.00000 q^{71}\) \(-2.00000 q^{72}\) \(-1.00000 q^{73}\) \(-4.00000 q^{74}\) \(-5.00000 q^{75}\) \(-1.00000 q^{76}\) \(-1.00000 q^{78}\) \(+8.00000 q^{79}\) \(+1.00000 q^{81}\) \(+12.0000 q^{83}\) \(-1.00000 q^{84}\) \(-1.00000 q^{86}\) \(-3.00000 q^{89}\) \(+1.00000 q^{91}\) \(+3.00000 q^{92}\) \(+5.00000 q^{93}\) \(+9.00000 q^{94}\) \(+1.00000 q^{96}\) \(-16.0000 q^{97}\) \(-6.00000 q^{98}\) \(+O(q^{100})\)

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
\(3\) 1.00000 0.577350 0.288675 0.957427i \(-0.406785\pi\)
0.288675 + 0.957427i \(0.406785\pi\)
\(4\) 1.00000 0.500000
\(5\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(6\) 1.00000 0.408248
\(7\) −1.00000 −0.377964 −0.188982 0.981981i \(-0.560519\pi\)
−0.188982 + 0.981981i \(0.560519\pi\)
\(8\) 1.00000 0.353553
\(9\) −2.00000 −0.666667
\(10\) 0 0
\(11\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) 1.00000 0.288675
\(13\) −1.00000 −0.277350 −0.138675 0.990338i \(-0.544284\pi\)
−0.138675 + 0.990338i \(0.544284\pi\)
\(14\) −1.00000 −0.267261
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(18\) −2.00000 −0.471405
\(19\) −1.00000 −0.229416 −0.114708 0.993399i \(-0.536593\pi\)
−0.114708 + 0.993399i \(0.536593\pi\)
\(20\) 0 0
\(21\) −1.00000 −0.218218
\(22\) 0 0
\(23\) 3.00000 0.625543 0.312772 0.949828i \(-0.398743\pi\)
0.312772 + 0.949828i \(0.398743\pi\)
\(24\) 1.00000 0.204124
\(25\) −5.00000 −1.00000
\(26\) −1.00000 −0.196116
\(27\) −5.00000 −0.962250
\(28\) −1.00000 −0.188982
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 0 0
\(31\) 5.00000 0.898027 0.449013 0.893525i \(-0.351776\pi\)
0.449013 + 0.893525i \(0.351776\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) −2.00000 −0.333333
\(37\) −4.00000 −0.657596 −0.328798 0.944400i \(-0.606644\pi\)
−0.328798 + 0.944400i \(0.606644\pi\)
\(38\) −1.00000 −0.162221
\(39\) −1.00000 −0.160128
\(40\) 0 0
\(41\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) −1.00000 −0.154303
\(43\) −1.00000 −0.152499 −0.0762493 0.997089i \(-0.524294\pi\)
−0.0762493 + 0.997089i \(0.524294\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 3.00000 0.442326
\(47\) 9.00000 1.31278 0.656392 0.754420i \(-0.272082\pi\)
0.656392 + 0.754420i \(0.272082\pi\)
\(48\) 1.00000 0.144338
\(49\) −6.00000 −0.857143
\(50\) −5.00000 −0.707107
\(51\) 0 0
\(52\) −1.00000 −0.138675
\(53\) 6.00000 0.824163 0.412082 0.911147i \(-0.364802\pi\)
0.412082 + 0.911147i \(0.364802\pi\)
\(54\) −5.00000 −0.680414
\(55\) 0 0
\(56\) −1.00000 −0.133631
\(57\) −1.00000 −0.132453
\(58\) 0 0
\(59\) 6.00000 0.781133 0.390567 0.920575i \(-0.372279\pi\)
0.390567 + 0.920575i \(0.372279\pi\)
\(60\) 0 0
\(61\) 2.00000 0.256074 0.128037 0.991769i \(-0.459132\pi\)
0.128037 + 0.991769i \(0.459132\pi\)
\(62\) 5.00000 0.635001
\(63\) 2.00000 0.251976
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) 8.00000 0.977356 0.488678 0.872464i \(-0.337479\pi\)
0.488678 + 0.872464i \(0.337479\pi\)
\(68\) 0 0
\(69\) 3.00000 0.361158
\(70\) 0 0
\(71\) −1.00000 −0.118678
\(72\) −2.00000 −0.235702
\(73\) −1.00000 −0.117041 −0.0585206 0.998286i \(-0.518638\pi\)
−0.0585206 + 0.998286i \(0.518638\pi\)
\(74\) −4.00000 −0.464991
\(75\) −5.00000 −0.577350
\(76\) −1.00000 −0.114708
\(77\) 0 0
\(78\) −1.00000 −0.113228
\(79\) 8.00000 0.900070 0.450035 0.893011i \(-0.351411\pi\)
0.450035 + 0.893011i \(0.351411\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 12.0000 1.31717 0.658586 0.752506i \(-0.271155\pi\)
0.658586 + 0.752506i \(0.271155\pi\)
\(84\) −1.00000 −0.109109
\(85\) 0 0
\(86\) −1.00000 −0.107833
\(87\) 0 0
\(88\) 0 0
\(89\) −3.00000 −0.317999 −0.159000 0.987279i \(-0.550827\pi\)
−0.159000 + 0.987279i \(0.550827\pi\)
\(90\) 0 0
\(91\) 1.00000 0.104828
\(92\) 3.00000 0.312772
\(93\) 5.00000 0.518476
\(94\) 9.00000 0.928279
\(95\) 0 0
\(96\) 1.00000 0.102062
\(97\) −16.0000 −1.62455 −0.812277 0.583272i \(-0.801772\pi\)
−0.812277 + 0.583272i \(0.801772\pi\)
\(98\) −6.00000 −0.606092
\(99\) 0 0
\(100\) −5.00000 −0.500000
\(101\) 12.0000 1.19404 0.597022 0.802225i \(-0.296350\pi\)
0.597022 + 0.802225i \(0.296350\pi\)
\(102\) 0 0
\(103\) 8.00000 0.788263 0.394132 0.919054i \(-0.371045\pi\)
0.394132 + 0.919054i \(0.371045\pi\)
\(104\) −1.00000 −0.0980581
\(105\) 0 0
\(106\) 6.00000 0.582772
\(107\) −3.00000 −0.290021 −0.145010 0.989430i \(-0.546322\pi\)
−0.145010 + 0.989430i \(0.546322\pi\)
\(108\) −5.00000 −0.481125
\(109\) −16.0000 −1.53252 −0.766261 0.642529i \(-0.777885\pi\)
−0.766261 + 0.642529i \(0.777885\pi\)
\(110\) 0 0
\(111\) −4.00000 −0.379663
\(112\) −1.00000 −0.0944911
\(113\) 6.00000 0.564433 0.282216 0.959351i \(-0.408930\pi\)
0.282216 + 0.959351i \(0.408930\pi\)
\(114\) −1.00000 −0.0936586
\(115\) 0 0
\(116\) 0 0
\(117\) 2.00000 0.184900
\(118\) 6.00000 0.552345
\(119\) 0 0
\(120\) 0 0
\(121\) −11.0000 −1.00000
\(122\) 2.00000 0.181071
\(123\) 0 0
\(124\) 5.00000 0.449013
\(125\) 0 0
\(126\) 2.00000 0.178174
\(127\) −16.0000 −1.41977 −0.709885 0.704317i \(-0.751253\pi\)
−0.709885 + 0.704317i \(0.751253\pi\)
\(128\) 1.00000 0.0883883
\(129\) −1.00000 −0.0880451
\(130\) 0 0
\(131\) −3.00000 −0.262111 −0.131056 0.991375i \(-0.541837\pi\)
−0.131056 + 0.991375i \(0.541837\pi\)
\(132\) 0 0
\(133\) 1.00000 0.0867110
\(134\) 8.00000 0.691095
\(135\) 0 0
\(136\) 0 0
\(137\) −12.0000 −1.02523 −0.512615 0.858619i \(-0.671323\pi\)
−0.512615 + 0.858619i \(0.671323\pi\)
\(138\) 3.00000 0.255377
\(139\) −16.0000 −1.35710 −0.678551 0.734553i \(-0.737392\pi\)
−0.678551 + 0.734553i \(0.737392\pi\)
\(140\) 0 0
\(141\) 9.00000 0.757937
\(142\) −1.00000 −0.0839181
\(143\) 0 0
\(144\) −2.00000 −0.166667
\(145\) 0 0
\(146\) −1.00000 −0.0827606
\(147\) −6.00000 −0.494872
\(148\) −4.00000 −0.328798
\(149\) −15.0000 −1.22885 −0.614424 0.788976i \(-0.710612\pi\)
−0.614424 + 0.788976i \(0.710612\pi\)
\(150\) −5.00000 −0.408248
\(151\) −16.0000 −1.30206 −0.651031 0.759051i \(-0.725663\pi\)
−0.651031 + 0.759051i \(0.725663\pi\)
\(152\) −1.00000 −0.0811107
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) −1.00000 −0.0800641
\(157\) 14.0000 1.11732 0.558661 0.829396i \(-0.311315\pi\)
0.558661 + 0.829396i \(0.311315\pi\)
\(158\) 8.00000 0.636446
\(159\) 6.00000 0.475831
\(160\) 0 0
\(161\) −3.00000 −0.236433
\(162\) 1.00000 0.0785674
\(163\) −4.00000 −0.313304 −0.156652 0.987654i \(-0.550070\pi\)
−0.156652 + 0.987654i \(0.550070\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 12.0000 0.931381
\(167\) −18.0000 −1.39288 −0.696441 0.717614i \(-0.745234\pi\)
−0.696441 + 0.717614i \(0.745234\pi\)
\(168\) −1.00000 −0.0771517
\(169\) −12.0000 −0.923077
\(170\) 0 0
\(171\) 2.00000 0.152944
\(172\) −1.00000 −0.0762493
\(173\) 21.0000 1.59660 0.798300 0.602260i \(-0.205733\pi\)
0.798300 + 0.602260i \(0.205733\pi\)
\(174\) 0 0
\(175\) 5.00000 0.377964
\(176\) 0 0
\(177\) 6.00000 0.450988
\(178\) −3.00000 −0.224860
\(179\) −9.00000 −0.672692 −0.336346 0.941739i \(-0.609191\pi\)
−0.336346 + 0.941739i \(0.609191\pi\)
\(180\) 0 0
\(181\) 11.0000 0.817624 0.408812 0.912619i \(-0.365943\pi\)
0.408812 + 0.912619i \(0.365943\pi\)
\(182\) 1.00000 0.0741249
\(183\) 2.00000 0.147844
\(184\) 3.00000 0.221163
\(185\) 0 0
\(186\) 5.00000 0.366618
\(187\) 0 0
\(188\) 9.00000 0.656392
\(189\) 5.00000 0.363696
\(190\) 0 0
\(191\) 6.00000 0.434145 0.217072 0.976156i \(-0.430349\pi\)
0.217072 + 0.976156i \(0.430349\pi\)
\(192\) 1.00000 0.0721688
\(193\) −4.00000 −0.287926 −0.143963 0.989583i \(-0.545985\pi\)
−0.143963 + 0.989583i \(0.545985\pi\)
\(194\) −16.0000 −1.14873
\(195\) 0 0
\(196\) −6.00000 −0.428571
\(197\) 21.0000 1.49619 0.748094 0.663593i \(-0.230969\pi\)
0.748094 + 0.663593i \(0.230969\pi\)
\(198\) 0 0
\(199\) 8.00000 0.567105 0.283552 0.958957i \(-0.408487\pi\)
0.283552 + 0.958957i \(0.408487\pi\)
\(200\) −5.00000 −0.353553
\(201\) 8.00000 0.564276
\(202\) 12.0000 0.844317
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 8.00000 0.557386
\(207\) −6.00000 −0.417029
\(208\) −1.00000 −0.0693375
\(209\) 0 0
\(210\) 0 0
\(211\) 14.0000 0.963800 0.481900 0.876226i \(-0.339947\pi\)
0.481900 + 0.876226i \(0.339947\pi\)
\(212\) 6.00000 0.412082
\(213\) −1.00000 −0.0685189
\(214\) −3.00000 −0.205076
\(215\) 0 0
\(216\) −5.00000 −0.340207
\(217\) −5.00000 −0.339422
\(218\) −16.0000 −1.08366
\(219\) −1.00000 −0.0675737
\(220\) 0 0
\(221\) 0 0
\(222\) −4.00000 −0.268462
\(223\) 8.00000 0.535720 0.267860 0.963458i \(-0.413684\pi\)
0.267860 + 0.963458i \(0.413684\pi\)
\(224\) −1.00000 −0.0668153
\(225\) 10.0000 0.666667
\(226\) 6.00000 0.399114
\(227\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(228\) −1.00000 −0.0662266
\(229\) 14.0000 0.925146 0.462573 0.886581i \(-0.346926\pi\)
0.462573 + 0.886581i \(0.346926\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 15.0000 0.982683 0.491341 0.870967i \(-0.336507\pi\)
0.491341 + 0.870967i \(0.336507\pi\)
\(234\) 2.00000 0.130744
\(235\) 0 0
\(236\) 6.00000 0.390567
\(237\) 8.00000 0.519656
\(238\) 0 0
\(239\) −15.0000 −0.970269 −0.485135 0.874439i \(-0.661229\pi\)
−0.485135 + 0.874439i \(0.661229\pi\)
\(240\) 0 0
\(241\) 14.0000 0.901819 0.450910 0.892570i \(-0.351100\pi\)
0.450910 + 0.892570i \(0.351100\pi\)
\(242\) −11.0000 −0.707107
\(243\) 16.0000 1.02640
\(244\) 2.00000 0.128037
\(245\) 0 0
\(246\) 0 0
\(247\) 1.00000 0.0636285
\(248\) 5.00000 0.317500
\(249\) 12.0000 0.760469
\(250\) 0 0
\(251\) −15.0000 −0.946792 −0.473396 0.880850i \(-0.656972\pi\)
−0.473396 + 0.880850i \(0.656972\pi\)
\(252\) 2.00000 0.125988
\(253\) 0 0
\(254\) −16.0000 −1.00393
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 6.00000 0.374270 0.187135 0.982334i \(-0.440080\pi\)
0.187135 + 0.982334i \(0.440080\pi\)
\(258\) −1.00000 −0.0622573
\(259\) 4.00000 0.248548
\(260\) 0 0
\(261\) 0 0
\(262\) −3.00000 −0.185341
\(263\) −12.0000 −0.739952 −0.369976 0.929041i \(-0.620634\pi\)
−0.369976 + 0.929041i \(0.620634\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 1.00000 0.0613139
\(267\) −3.00000 −0.183597
\(268\) 8.00000 0.488678
\(269\) −27.0000 −1.64622 −0.823110 0.567883i \(-0.807763\pi\)
−0.823110 + 0.567883i \(0.807763\pi\)
\(270\) 0 0
\(271\) −10.0000 −0.607457 −0.303728 0.952759i \(-0.598232\pi\)
−0.303728 + 0.952759i \(0.598232\pi\)
\(272\) 0 0
\(273\) 1.00000 0.0605228
\(274\) −12.0000 −0.724947
\(275\) 0 0
\(276\) 3.00000 0.180579
\(277\) 8.00000 0.480673 0.240337 0.970690i \(-0.422742\pi\)
0.240337 + 0.970690i \(0.422742\pi\)
\(278\) −16.0000 −0.959616
\(279\) −10.0000 −0.598684
\(280\) 0 0
\(281\) −30.0000 −1.78965 −0.894825 0.446417i \(-0.852700\pi\)
−0.894825 + 0.446417i \(0.852700\pi\)
\(282\) 9.00000 0.535942
\(283\) 14.0000 0.832214 0.416107 0.909316i \(-0.363394\pi\)
0.416107 + 0.909316i \(0.363394\pi\)
\(284\) −1.00000 −0.0593391
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −2.00000 −0.117851
\(289\) −17.0000 −1.00000
\(290\) 0 0
\(291\) −16.0000 −0.937937
\(292\) −1.00000 −0.0585206
\(293\) −18.0000 −1.05157 −0.525786 0.850617i \(-0.676229\pi\)
−0.525786 + 0.850617i \(0.676229\pi\)
\(294\) −6.00000 −0.349927
\(295\) 0 0
\(296\) −4.00000 −0.232495
\(297\) 0 0
\(298\) −15.0000 −0.868927
\(299\) −3.00000 −0.173494
\(300\) −5.00000 −0.288675
\(301\) 1.00000 0.0576390
\(302\) −16.0000 −0.920697
\(303\) 12.0000 0.689382
\(304\) −1.00000 −0.0573539
\(305\) 0 0
\(306\) 0 0
\(307\) 2.00000 0.114146 0.0570730 0.998370i \(-0.481823\pi\)
0.0570730 + 0.998370i \(0.481823\pi\)
\(308\) 0 0
\(309\) 8.00000 0.455104
\(310\) 0 0
\(311\) −12.0000 −0.680458 −0.340229 0.940343i \(-0.610505\pi\)
−0.340229 + 0.940343i \(0.610505\pi\)
\(312\) −1.00000 −0.0566139
\(313\) −1.00000 −0.0565233 −0.0282617 0.999601i \(-0.508997\pi\)
−0.0282617 + 0.999601i \(0.508997\pi\)
\(314\) 14.0000 0.790066
\(315\) 0 0
\(316\) 8.00000 0.450035
\(317\) 18.0000 1.01098 0.505490 0.862832i \(-0.331312\pi\)
0.505490 + 0.862832i \(0.331312\pi\)
\(318\) 6.00000 0.336463
\(319\) 0 0
\(320\) 0 0
\(321\) −3.00000 −0.167444
\(322\) −3.00000 −0.167183
\(323\) 0 0
\(324\) 1.00000 0.0555556
\(325\) 5.00000 0.277350
\(326\) −4.00000 −0.221540
\(327\) −16.0000 −0.884802
\(328\) 0 0
\(329\) −9.00000 −0.496186
\(330\) 0 0
\(331\) 20.0000 1.09930 0.549650 0.835395i \(-0.314761\pi\)
0.549650 + 0.835395i \(0.314761\pi\)
\(332\) 12.0000 0.658586
\(333\) 8.00000 0.438397
\(334\) −18.0000 −0.984916
\(335\) 0 0
\(336\) −1.00000 −0.0545545
\(337\) 8.00000 0.435788 0.217894 0.975972i \(-0.430081\pi\)
0.217894 + 0.975972i \(0.430081\pi\)
\(338\) −12.0000 −0.652714
\(339\) 6.00000 0.325875
\(340\) 0 0
\(341\) 0 0
\(342\) 2.00000 0.108148
\(343\) 13.0000 0.701934
\(344\) −1.00000 −0.0539164
\(345\) 0 0
\(346\) 21.0000 1.12897
\(347\) −24.0000 −1.28839 −0.644194 0.764862i \(-0.722807\pi\)
−0.644194 + 0.764862i \(0.722807\pi\)
\(348\) 0 0
\(349\) −13.0000 −0.695874 −0.347937 0.937518i \(-0.613118\pi\)
−0.347937 + 0.937518i \(0.613118\pi\)
\(350\) 5.00000 0.267261
\(351\) 5.00000 0.266880
\(352\) 0 0
\(353\) 30.0000 1.59674 0.798369 0.602168i \(-0.205696\pi\)
0.798369 + 0.602168i \(0.205696\pi\)
\(354\) 6.00000 0.318896
\(355\) 0 0
\(356\) −3.00000 −0.159000
\(357\) 0 0
\(358\) −9.00000 −0.475665
\(359\) −24.0000 −1.26667 −0.633336 0.773877i \(-0.718315\pi\)
−0.633336 + 0.773877i \(0.718315\pi\)
\(360\) 0 0
\(361\) −18.0000 −0.947368
\(362\) 11.0000 0.578147
\(363\) −11.0000 −0.577350
\(364\) 1.00000 0.0524142
\(365\) 0 0
\(366\) 2.00000 0.104542
\(367\) 38.0000 1.98358 0.991792 0.127862i \(-0.0408116\pi\)
0.991792 + 0.127862i \(0.0408116\pi\)
\(368\) 3.00000 0.156386
\(369\) 0 0
\(370\) 0 0
\(371\) −6.00000 −0.311504
\(372\) 5.00000 0.259238
\(373\) 26.0000 1.34623 0.673114 0.739538i \(-0.264956\pi\)
0.673114 + 0.739538i \(0.264956\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 9.00000 0.464140
\(377\) 0 0
\(378\) 5.00000 0.257172
\(379\) −4.00000 −0.205466 −0.102733 0.994709i \(-0.532759\pi\)
−0.102733 + 0.994709i \(0.532759\pi\)
\(380\) 0 0
\(381\) −16.0000 −0.819705
\(382\) 6.00000 0.306987
\(383\) 21.0000 1.07305 0.536525 0.843884i \(-0.319737\pi\)
0.536525 + 0.843884i \(0.319737\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) −4.00000 −0.203595
\(387\) 2.00000 0.101666
\(388\) −16.0000 −0.812277
\(389\) 21.0000 1.06474 0.532371 0.846511i \(-0.321301\pi\)
0.532371 + 0.846511i \(0.321301\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −6.00000 −0.303046
\(393\) −3.00000 −0.151330
\(394\) 21.0000 1.05796
\(395\) 0 0
\(396\) 0 0
\(397\) 2.00000 0.100377 0.0501886 0.998740i \(-0.484018\pi\)
0.0501886 + 0.998740i \(0.484018\pi\)
\(398\) 8.00000 0.401004
\(399\) 1.00000 0.0500626
\(400\) −5.00000 −0.250000
\(401\) −12.0000 −0.599251 −0.299626 0.954057i \(-0.596862\pi\)
−0.299626 + 0.954057i \(0.596862\pi\)
\(402\) 8.00000 0.399004
\(403\) −5.00000 −0.249068
\(404\) 12.0000 0.597022
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −7.00000 −0.346128 −0.173064 0.984911i \(-0.555367\pi\)
−0.173064 + 0.984911i \(0.555367\pi\)
\(410\) 0 0
\(411\) −12.0000 −0.591916
\(412\) 8.00000 0.394132
\(413\) −6.00000 −0.295241
\(414\) −6.00000 −0.294884
\(415\) 0 0
\(416\) −1.00000 −0.0490290
\(417\) −16.0000 −0.783523
\(418\) 0 0
\(419\) 36.0000 1.75872 0.879358 0.476162i \(-0.157972\pi\)
0.879358 + 0.476162i \(0.157972\pi\)
\(420\) 0 0
\(421\) 11.0000 0.536107 0.268054 0.963404i \(-0.413620\pi\)
0.268054 + 0.963404i \(0.413620\pi\)
\(422\) 14.0000 0.681509
\(423\) −18.0000 −0.875190
\(424\) 6.00000 0.291386
\(425\) 0 0
\(426\) −1.00000 −0.0484502
\(427\) −2.00000 −0.0967868
\(428\) −3.00000 −0.145010
\(429\) 0 0
\(430\) 0 0
\(431\) −12.0000 −0.578020 −0.289010 0.957326i \(-0.593326\pi\)
−0.289010 + 0.957326i \(0.593326\pi\)
\(432\) −5.00000 −0.240563
\(433\) −34.0000 −1.63394 −0.816968 0.576683i \(-0.804347\pi\)
−0.816968 + 0.576683i \(0.804347\pi\)
\(434\) −5.00000 −0.240008
\(435\) 0 0
\(436\) −16.0000 −0.766261
\(437\) −3.00000 −0.143509
\(438\) −1.00000 −0.0477818
\(439\) 8.00000 0.381819 0.190910 0.981608i \(-0.438856\pi\)
0.190910 + 0.981608i \(0.438856\pi\)
\(440\) 0 0
\(441\) 12.0000 0.571429
\(442\) 0 0
\(443\) 18.0000 0.855206 0.427603 0.903967i \(-0.359358\pi\)
0.427603 + 0.903967i \(0.359358\pi\)
\(444\) −4.00000 −0.189832
\(445\) 0 0
\(446\) 8.00000 0.378811
\(447\) −15.0000 −0.709476
\(448\) −1.00000 −0.0472456
\(449\) −12.0000 −0.566315 −0.283158 0.959073i \(-0.591382\pi\)
−0.283158 + 0.959073i \(0.591382\pi\)
\(450\) 10.0000 0.471405
\(451\) 0 0
\(452\) 6.00000 0.282216
\(453\) −16.0000 −0.751746
\(454\) 0 0
\(455\) 0 0
\(456\) −1.00000 −0.0468293
\(457\) 26.0000 1.21623 0.608114 0.793849i \(-0.291926\pi\)
0.608114 + 0.793849i \(0.291926\pi\)
\(458\) 14.0000 0.654177
\(459\) 0 0
\(460\) 0 0
\(461\) −21.0000 −0.978068 −0.489034 0.872265i \(-0.662651\pi\)
−0.489034 + 0.872265i \(0.662651\pi\)
\(462\) 0 0
\(463\) −22.0000 −1.02243 −0.511213 0.859454i \(-0.670804\pi\)
−0.511213 + 0.859454i \(0.670804\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 15.0000 0.694862
\(467\) 30.0000 1.38823 0.694117 0.719862i \(-0.255795\pi\)
0.694117 + 0.719862i \(0.255795\pi\)
\(468\) 2.00000 0.0924500
\(469\) −8.00000 −0.369406
\(470\) 0 0
\(471\) 14.0000 0.645086
\(472\) 6.00000 0.276172
\(473\) 0 0
\(474\) 8.00000 0.367452
\(475\) 5.00000 0.229416
\(476\) 0 0
\(477\) −12.0000 −0.549442
\(478\) −15.0000 −0.686084
\(479\) 15.0000 0.685367 0.342684 0.939451i \(-0.388664\pi\)
0.342684 + 0.939451i \(0.388664\pi\)
\(480\) 0 0
\(481\) 4.00000 0.182384
\(482\) 14.0000 0.637683
\(483\) −3.00000 −0.136505
\(484\) −11.0000 −0.500000
\(485\) 0 0
\(486\) 16.0000 0.725775
\(487\) 8.00000 0.362515 0.181257 0.983436i \(-0.441983\pi\)
0.181257 + 0.983436i \(0.441983\pi\)
\(488\) 2.00000 0.0905357
\(489\) −4.00000 −0.180886
\(490\) 0 0
\(491\) −24.0000 −1.08310 −0.541552 0.840667i \(-0.682163\pi\)
−0.541552 + 0.840667i \(0.682163\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 1.00000 0.0449921
\(495\) 0 0
\(496\) 5.00000 0.224507
\(497\) 1.00000 0.0448561
\(498\) 12.0000 0.537733
\(499\) 41.0000 1.83541 0.917706 0.397260i \(-0.130039\pi\)
0.917706 + 0.397260i \(0.130039\pi\)
\(500\) 0 0
\(501\) −18.0000 −0.804181
\(502\) −15.0000 −0.669483
\(503\) −18.0000 −0.802580 −0.401290 0.915951i \(-0.631438\pi\)
−0.401290 + 0.915951i \(0.631438\pi\)
\(504\) 2.00000 0.0890871
\(505\) 0 0
\(506\) 0 0
\(507\) −12.0000 −0.532939
\(508\) −16.0000 −0.709885
\(509\) 12.0000 0.531891 0.265945 0.963988i \(-0.414316\pi\)
0.265945 + 0.963988i \(0.414316\pi\)
\(510\) 0 0
\(511\) 1.00000 0.0442374
\(512\) 1.00000 0.0441942
\(513\) 5.00000 0.220755
\(514\) 6.00000 0.264649
\(515\) 0 0
\(516\) −1.00000 −0.0440225
\(517\) 0 0
\(518\) 4.00000 0.175750
\(519\) 21.0000 0.921798
\(520\) 0 0
\(521\) 18.0000 0.788594 0.394297 0.918983i \(-0.370988\pi\)
0.394297 + 0.918983i \(0.370988\pi\)
\(522\) 0 0
\(523\) −10.0000 −0.437269 −0.218635 0.975807i \(-0.570160\pi\)
−0.218635 + 0.975807i \(0.570160\pi\)
\(524\) −3.00000 −0.131056
\(525\) 5.00000 0.218218
\(526\) −12.0000 −0.523225
\(527\) 0 0
\(528\) 0 0
\(529\) −14.0000 −0.608696
\(530\) 0 0
\(531\) −12.0000 −0.520756
\(532\) 1.00000 0.0433555
\(533\) 0 0
\(534\) −3.00000 −0.129823
\(535\) 0 0
\(536\) 8.00000 0.345547
\(537\) −9.00000 −0.388379
\(538\) −27.0000 −1.16405
\(539\) 0 0
\(540\) 0 0
\(541\) 2.00000 0.0859867 0.0429934 0.999075i \(-0.486311\pi\)
0.0429934 + 0.999075i \(0.486311\pi\)
\(542\) −10.0000 −0.429537
\(543\) 11.0000 0.472055
\(544\) 0 0
\(545\) 0 0
\(546\) 1.00000 0.0427960
\(547\) −31.0000 −1.32546 −0.662732 0.748857i \(-0.730603\pi\)
−0.662732 + 0.748857i \(0.730603\pi\)
\(548\) −12.0000 −0.512615
\(549\) −4.00000 −0.170716
\(550\) 0 0
\(551\) 0 0
\(552\) 3.00000 0.127688
\(553\) −8.00000 −0.340195
\(554\) 8.00000 0.339887
\(555\) 0 0
\(556\) −16.0000 −0.678551
\(557\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(558\) −10.0000 −0.423334
\(559\) 1.00000 0.0422955
\(560\) 0 0
\(561\) 0 0
\(562\) −30.0000 −1.26547
\(563\) 6.00000 0.252870 0.126435 0.991975i \(-0.459647\pi\)
0.126435 + 0.991975i \(0.459647\pi\)
\(564\) 9.00000 0.378968
\(565\) 0 0
\(566\) 14.0000 0.588464
\(567\) −1.00000 −0.0419961
\(568\) −1.00000 −0.0419591
\(569\) −9.00000 −0.377300 −0.188650 0.982044i \(-0.560411\pi\)
−0.188650 + 0.982044i \(0.560411\pi\)
\(570\) 0 0
\(571\) 44.0000 1.84134 0.920671 0.390339i \(-0.127642\pi\)
0.920671 + 0.390339i \(0.127642\pi\)
\(572\) 0 0
\(573\) 6.00000 0.250654
\(574\) 0 0
\(575\) −15.0000 −0.625543
\(576\) −2.00000 −0.0833333
\(577\) −34.0000 −1.41544 −0.707719 0.706494i \(-0.750276\pi\)
−0.707719 + 0.706494i \(0.750276\pi\)
\(578\) −17.0000 −0.707107
\(579\) −4.00000 −0.166234
\(580\) 0 0
\(581\) −12.0000 −0.497844
\(582\) −16.0000 −0.663221
\(583\) 0 0
\(584\) −1.00000 −0.0413803
\(585\) 0 0
\(586\) −18.0000 −0.743573
\(587\) 12.0000 0.495293 0.247647 0.968850i \(-0.420343\pi\)
0.247647 + 0.968850i \(0.420343\pi\)
\(588\) −6.00000 −0.247436
\(589\) −5.00000 −0.206021
\(590\) 0 0
\(591\) 21.0000 0.863825
\(592\) −4.00000 −0.164399
\(593\) 9.00000 0.369586 0.184793 0.982777i \(-0.440839\pi\)
0.184793 + 0.982777i \(0.440839\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −15.0000 −0.614424
\(597\) 8.00000 0.327418
\(598\) −3.00000 −0.122679
\(599\) 9.00000 0.367730 0.183865 0.982952i \(-0.441139\pi\)
0.183865 + 0.982952i \(0.441139\pi\)
\(600\) −5.00000 −0.204124
\(601\) −28.0000 −1.14214 −0.571072 0.820900i \(-0.693472\pi\)
−0.571072 + 0.820900i \(0.693472\pi\)
\(602\) 1.00000 0.0407570
\(603\) −16.0000 −0.651570
\(604\) −16.0000 −0.651031
\(605\) 0 0
\(606\) 12.0000 0.487467
\(607\) 20.0000 0.811775 0.405887 0.913923i \(-0.366962\pi\)
0.405887 + 0.913923i \(0.366962\pi\)
\(608\) −1.00000 −0.0405554
\(609\) 0 0
\(610\) 0 0
\(611\) −9.00000 −0.364101
\(612\) 0 0
\(613\) −22.0000 −0.888572 −0.444286 0.895885i \(-0.646543\pi\)
−0.444286 + 0.895885i \(0.646543\pi\)
\(614\) 2.00000 0.0807134
\(615\) 0 0
\(616\) 0 0
\(617\) 39.0000 1.57008 0.785040 0.619445i \(-0.212642\pi\)
0.785040 + 0.619445i \(0.212642\pi\)
\(618\) 8.00000 0.321807
\(619\) 8.00000 0.321547 0.160774 0.986991i \(-0.448601\pi\)
0.160774 + 0.986991i \(0.448601\pi\)
\(620\) 0 0
\(621\) −15.0000 −0.601929
\(622\) −12.0000 −0.481156
\(623\) 3.00000 0.120192
\(624\) −1.00000 −0.0400320
\(625\) 25.0000 1.00000
\(626\) −1.00000 −0.0399680
\(627\) 0 0
\(628\) 14.0000 0.558661
\(629\) 0 0
\(630\) 0 0
\(631\) −40.0000 −1.59237 −0.796187 0.605050i \(-0.793153\pi\)
−0.796187 + 0.605050i \(0.793153\pi\)
\(632\) 8.00000 0.318223
\(633\) 14.0000 0.556450
\(634\) 18.0000 0.714871
\(635\) 0 0
\(636\) 6.00000 0.237915
\(637\) 6.00000 0.237729
\(638\) 0 0
\(639\) 2.00000 0.0791188
\(640\) 0 0
\(641\) 45.0000 1.77739 0.888697 0.458496i \(-0.151612\pi\)
0.888697 + 0.458496i \(0.151612\pi\)
\(642\) −3.00000 −0.118401
\(643\) −31.0000 −1.22252 −0.611260 0.791430i \(-0.709337\pi\)
−0.611260 + 0.791430i \(0.709337\pi\)
\(644\) −3.00000 −0.118217
\(645\) 0 0
\(646\) 0 0
\(647\) 18.0000 0.707653 0.353827 0.935311i \(-0.384880\pi\)
0.353827 + 0.935311i \(0.384880\pi\)
\(648\) 1.00000 0.0392837
\(649\) 0 0
\(650\) 5.00000 0.196116
\(651\) −5.00000 −0.195965
\(652\) −4.00000 −0.156652
\(653\) −6.00000 −0.234798 −0.117399 0.993085i \(-0.537456\pi\)
−0.117399 + 0.993085i \(0.537456\pi\)
\(654\) −16.0000 −0.625650
\(655\) 0 0
\(656\) 0 0
\(657\) 2.00000 0.0780274
\(658\) −9.00000 −0.350857
\(659\) 27.0000 1.05177 0.525885 0.850555i \(-0.323734\pi\)
0.525885 + 0.850555i \(0.323734\pi\)
\(660\) 0 0
\(661\) 5.00000 0.194477 0.0972387 0.995261i \(-0.468999\pi\)
0.0972387 + 0.995261i \(0.468999\pi\)
\(662\) 20.0000 0.777322
\(663\) 0 0
\(664\) 12.0000 0.465690
\(665\) 0 0
\(666\) 8.00000 0.309994
\(667\) 0 0
\(668\) −18.0000 −0.696441
\(669\) 8.00000 0.309298
\(670\) 0 0
\(671\) 0 0
\(672\) −1.00000 −0.0385758
\(673\) 8.00000 0.308377 0.154189 0.988041i \(-0.450724\pi\)
0.154189 + 0.988041i \(0.450724\pi\)
\(674\) 8.00000 0.308148
\(675\) 25.0000 0.962250
\(676\) −12.0000 −0.461538
\(677\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(678\) 6.00000 0.230429
\(679\) 16.0000 0.614024
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −36.0000 −1.37750 −0.688751 0.724998i \(-0.741841\pi\)
−0.688751 + 0.724998i \(0.741841\pi\)
\(684\) 2.00000 0.0764719
\(685\) 0 0
\(686\) 13.0000 0.496342
\(687\) 14.0000 0.534133
\(688\) −1.00000 −0.0381246
\(689\) −6.00000 −0.228582
\(690\) 0 0
\(691\) 44.0000 1.67384 0.836919 0.547326i \(-0.184354\pi\)
0.836919 + 0.547326i \(0.184354\pi\)
\(692\) 21.0000 0.798300
\(693\) 0 0
\(694\) −24.0000 −0.911028
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) −13.0000 −0.492057
\(699\) 15.0000 0.567352
\(700\) 5.00000 0.188982
\(701\) 9.00000 0.339925 0.169963 0.985451i \(-0.445635\pi\)
0.169963 + 0.985451i \(0.445635\pi\)
\(702\) 5.00000 0.188713
\(703\) 4.00000 0.150863
\(704\) 0 0
\(705\) 0 0
\(706\) 30.0000 1.12906
\(707\) −12.0000 −0.451306
\(708\) 6.00000 0.225494
\(709\) −13.0000 −0.488225 −0.244113 0.969747i \(-0.578497\pi\)
−0.244113 + 0.969747i \(0.578497\pi\)
\(710\) 0 0
\(711\) −16.0000 −0.600047
\(712\) −3.00000 −0.112430
\(713\) 15.0000 0.561754
\(714\) 0 0
\(715\) 0 0
\(716\) −9.00000 −0.336346
\(717\) −15.0000 −0.560185
\(718\) −24.0000 −0.895672
\(719\) 30.0000 1.11881 0.559406 0.828894i \(-0.311029\pi\)
0.559406 + 0.828894i \(0.311029\pi\)
\(720\) 0 0
\(721\) −8.00000 −0.297936
\(722\) −18.0000 −0.669891
\(723\) 14.0000 0.520666
\(724\) 11.0000 0.408812
\(725\) 0 0
\(726\) −11.0000 −0.408248
\(727\) −1.00000 −0.0370879 −0.0185440 0.999828i \(-0.505903\pi\)
−0.0185440 + 0.999828i \(0.505903\pi\)
\(728\) 1.00000 0.0370625
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) 0 0
\(732\) 2.00000 0.0739221
\(733\) −49.0000 −1.80986 −0.904928 0.425564i \(-0.860076\pi\)
−0.904928 + 0.425564i \(0.860076\pi\)
\(734\) 38.0000 1.40261
\(735\) 0 0
\(736\) 3.00000 0.110581
\(737\) 0 0
\(738\) 0 0
\(739\) 11.0000 0.404642 0.202321 0.979319i \(-0.435152\pi\)
0.202321 + 0.979319i \(0.435152\pi\)
\(740\) 0 0
\(741\) 1.00000 0.0367359
\(742\) −6.00000 −0.220267
\(743\) 21.0000 0.770415 0.385208 0.922830i \(-0.374130\pi\)
0.385208 + 0.922830i \(0.374130\pi\)
\(744\) 5.00000 0.183309
\(745\) 0 0
\(746\) 26.0000 0.951928
\(747\) −24.0000 −0.878114
\(748\) 0 0
\(749\) 3.00000 0.109618
\(750\) 0 0
\(751\) 32.0000 1.16770 0.583848 0.811863i \(-0.301546\pi\)
0.583848 + 0.811863i \(0.301546\pi\)
\(752\) 9.00000 0.328196
\(753\) −15.0000 −0.546630
\(754\) 0 0
\(755\) 0 0
\(756\) 5.00000 0.181848
\(757\) 17.0000 0.617876 0.308938 0.951082i \(-0.400027\pi\)
0.308938 + 0.951082i \(0.400027\pi\)
\(758\) −4.00000 −0.145287
\(759\) 0 0
\(760\) 0 0
\(761\) −30.0000 −1.08750 −0.543750 0.839248i \(-0.682996\pi\)
−0.543750 + 0.839248i \(0.682996\pi\)
\(762\) −16.0000 −0.579619
\(763\) 16.0000 0.579239
\(764\) 6.00000 0.217072
\(765\) 0 0
\(766\) 21.0000 0.758761
\(767\) −6.00000 −0.216647
\(768\) 1.00000 0.0360844
\(769\) 20.0000 0.721218 0.360609 0.932717i \(-0.382569\pi\)
0.360609 + 0.932717i \(0.382569\pi\)
\(770\) 0 0
\(771\) 6.00000 0.216085
\(772\) −4.00000 −0.143963
\(773\) −33.0000 −1.18693 −0.593464 0.804861i \(-0.702240\pi\)
−0.593464 + 0.804861i \(0.702240\pi\)
\(774\) 2.00000 0.0718885
\(775\) −25.0000 −0.898027
\(776\) −16.0000 −0.574367
\(777\) 4.00000 0.143499
\(778\) 21.0000 0.752886
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −6.00000 −0.214286
\(785\) 0 0
\(786\) −3.00000 −0.107006
\(787\) 5.00000 0.178231 0.0891154 0.996021i \(-0.471596\pi\)
0.0891154 + 0.996021i \(0.471596\pi\)
\(788\) 21.0000 0.748094
\(789\) −12.0000 −0.427211
\(790\) 0 0
\(791\) −6.00000 −0.213335
\(792\) 0 0
\(793\) −2.00000 −0.0710221
\(794\) 2.00000 0.0709773
\(795\) 0 0
\(796\) 8.00000 0.283552
\(797\) 18.0000 0.637593 0.318796 0.947823i \(-0.396721\pi\)
0.318796 + 0.947823i \(0.396721\pi\)
\(798\) 1.00000 0.0353996
\(799\) 0 0
\(800\) −5.00000 −0.176777
\(801\) 6.00000 0.212000
\(802\) −12.0000 −0.423735
\(803\) 0 0
\(804\) 8.00000 0.282138
\(805\) 0 0
\(806\) −5.00000 −0.176117
\(807\) −27.0000 −0.950445
\(808\) 12.0000 0.422159
\(809\) 36.0000 1.26569 0.632846 0.774277i \(-0.281886\pi\)
0.632846 + 0.774277i \(0.281886\pi\)
\(810\) 0 0
\(811\) −16.0000 −0.561836 −0.280918 0.959732i \(-0.590639\pi\)
−0.280918 + 0.959732i \(0.590639\pi\)
\(812\) 0 0
\(813\) −10.0000 −0.350715
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 1.00000 0.0349856
\(818\) −7.00000 −0.244749
\(819\) −2.00000 −0.0698857
\(820\) 0 0
\(821\) −24.0000 −0.837606 −0.418803 0.908077i \(-0.637550\pi\)
−0.418803 + 0.908077i \(0.637550\pi\)
\(822\) −12.0000 −0.418548
\(823\) 5.00000 0.174289 0.0871445 0.996196i \(-0.472226\pi\)
0.0871445 + 0.996196i \(0.472226\pi\)
\(824\) 8.00000 0.278693
\(825\) 0 0
\(826\) −6.00000 −0.208767
\(827\) −30.0000 −1.04320 −0.521601 0.853189i \(-0.674665\pi\)
−0.521601 + 0.853189i \(0.674665\pi\)
\(828\) −6.00000 −0.208514
\(829\) −40.0000 −1.38926 −0.694629 0.719368i \(-0.744431\pi\)
−0.694629 + 0.719368i \(0.744431\pi\)
\(830\) 0 0
\(831\) 8.00000 0.277517
\(832\) −1.00000 −0.0346688
\(833\) 0 0
\(834\) −16.0000 −0.554035
\(835\) 0 0
\(836\) 0 0
\(837\) −25.0000 −0.864126
\(838\) 36.0000 1.24360
\(839\) 12.0000 0.414286 0.207143 0.978311i \(-0.433583\pi\)
0.207143 + 0.978311i \(0.433583\pi\)
\(840\) 0 0
\(841\) −29.0000 −1.00000
\(842\) 11.0000 0.379085
\(843\) −30.0000 −1.03325
\(844\) 14.0000 0.481900
\(845\) 0 0
\(846\) −18.0000 −0.618853
\(847\) 11.0000 0.377964
\(848\) 6.00000 0.206041
\(849\) 14.0000 0.480479
\(850\) 0 0
\(851\) −12.0000 −0.411355
\(852\) −1.00000 −0.0342594
\(853\) −40.0000 −1.36957 −0.684787 0.728743i \(-0.740105\pi\)
−0.684787 + 0.728743i \(0.740105\pi\)
\(854\) −2.00000 −0.0684386
\(855\) 0 0
\(856\) −3.00000 −0.102538
\(857\) −3.00000 −0.102478 −0.0512390 0.998686i \(-0.516317\pi\)
−0.0512390 + 0.998686i \(0.516317\pi\)
\(858\) 0 0
\(859\) −4.00000 −0.136478 −0.0682391 0.997669i \(-0.521738\pi\)
−0.0682391 + 0.997669i \(0.521738\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) −12.0000 −0.408722
\(863\) −3.00000 −0.102121 −0.0510606 0.998696i \(-0.516260\pi\)
−0.0510606 + 0.998696i \(0.516260\pi\)
\(864\) −5.00000 −0.170103
\(865\) 0 0
\(866\) −34.0000 −1.15537
\(867\) −17.0000 −0.577350
\(868\) −5.00000 −0.169711
\(869\) 0 0
\(870\) 0 0
\(871\) −8.00000 −0.271070
\(872\) −16.0000 −0.541828
\(873\) 32.0000 1.08304
\(874\) −3.00000 −0.101477
\(875\) 0 0
\(876\) −1.00000 −0.0337869
\(877\) 20.0000 0.675352 0.337676 0.941262i \(-0.390359\pi\)
0.337676 + 0.941262i \(0.390359\pi\)
\(878\) 8.00000 0.269987
\(879\) −18.0000 −0.607125
\(880\) 0 0
\(881\) 9.00000 0.303218 0.151609 0.988441i \(-0.451555\pi\)
0.151609 + 0.988441i \(0.451555\pi\)
\(882\) 12.0000 0.404061
\(883\) 2.00000 0.0673054 0.0336527 0.999434i \(-0.489286\pi\)
0.0336527 + 0.999434i \(0.489286\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 18.0000 0.604722
\(887\) −36.0000 −1.20876 −0.604381 0.796696i \(-0.706579\pi\)
−0.604381 + 0.796696i \(0.706579\pi\)
\(888\) −4.00000 −0.134231
\(889\) 16.0000 0.536623
\(890\) 0 0
\(891\) 0 0
\(892\) 8.00000 0.267860
\(893\) −9.00000 −0.301174
\(894\) −15.0000 −0.501675
\(895\) 0 0
\(896\) −1.00000 −0.0334077
\(897\) −3.00000 −0.100167
\(898\) −12.0000 −0.400445
\(899\) 0 0
\(900\) 10.0000 0.333333
\(901\) 0 0
\(902\) 0 0
\(903\) 1.00000 0.0332779
\(904\) 6.00000 0.199557
\(905\) 0 0
\(906\) −16.0000 −0.531564
\(907\) −52.0000 −1.72663 −0.863316 0.504664i \(-0.831616\pi\)
−0.863316 + 0.504664i \(0.831616\pi\)
\(908\) 0 0
\(909\) −24.0000 −0.796030
\(910\) 0 0
\(911\) 9.00000 0.298183 0.149092 0.988823i \(-0.452365\pi\)
0.149092 + 0.988823i \(0.452365\pi\)
\(912\) −1.00000 −0.0331133
\(913\) 0 0
\(914\) 26.0000 0.860004
\(915\) 0 0
\(916\) 14.0000 0.462573
\(917\) 3.00000 0.0990687
\(918\) 0 0
\(919\) 11.0000 0.362857 0.181428 0.983404i \(-0.441928\pi\)
0.181428 + 0.983404i \(0.441928\pi\)
\(920\) 0 0
\(921\) 2.00000 0.0659022
\(922\) −21.0000 −0.691598
\(923\) 1.00000 0.0329154
\(924\) 0 0
\(925\) 20.0000 0.657596
\(926\) −22.0000 −0.722965
\(927\) −16.0000 −0.525509
\(928\) 0 0
\(929\) −30.0000 −0.984268 −0.492134 0.870519i \(-0.663783\pi\)
−0.492134 + 0.870519i \(0.663783\pi\)
\(930\) 0 0
\(931\) 6.00000 0.196642
\(932\) 15.0000 0.491341
\(933\) −12.0000 −0.392862
\(934\) 30.0000 0.981630
\(935\) 0 0
\(936\) 2.00000 0.0653720
\(937\) 8.00000 0.261349 0.130674 0.991425i \(-0.458286\pi\)
0.130674 + 0.991425i \(0.458286\pi\)
\(938\) −8.00000 −0.261209
\(939\) −1.00000 −0.0326338
\(940\) 0 0
\(941\) −12.0000 −0.391189 −0.195594 0.980685i \(-0.562664\pi\)
−0.195594 + 0.980685i \(0.562664\pi\)
\(942\) 14.0000 0.456145
\(943\) 0 0
\(944\) 6.00000 0.195283
\(945\) 0 0
\(946\) 0 0
\(947\) −12.0000 −0.389948 −0.194974 0.980808i \(-0.562462\pi\)
−0.194974 + 0.980808i \(0.562462\pi\)
\(948\) 8.00000 0.259828
\(949\) 1.00000 0.0324614
\(950\) 5.00000 0.162221
\(951\) 18.0000 0.583690
\(952\) 0 0
\(953\) 18.0000 0.583077 0.291539 0.956559i \(-0.405833\pi\)
0.291539 + 0.956559i \(0.405833\pi\)
\(954\) −12.0000 −0.388514
\(955\) 0 0
\(956\) −15.0000 −0.485135
\(957\) 0 0
\(958\) 15.0000 0.484628
\(959\) 12.0000 0.387500
\(960\) 0 0
\(961\) −6.00000 −0.193548
\(962\) 4.00000 0.128965
\(963\) 6.00000 0.193347
\(964\) 14.0000 0.450910
\(965\) 0 0
\(966\) −3.00000 −0.0965234
\(967\) −13.0000 −0.418052 −0.209026 0.977910i \(-0.567029\pi\)
−0.209026 + 0.977910i \(0.567029\pi\)
\(968\) −11.0000 −0.353553
\(969\) 0 0
\(970\) 0 0
\(971\) −33.0000 −1.05902 −0.529510 0.848304i \(-0.677624\pi\)
−0.529510 + 0.848304i \(0.677624\pi\)
\(972\) 16.0000 0.513200
\(973\) 16.0000 0.512936
\(974\) 8.00000 0.256337
\(975\) 5.00000 0.160128
\(976\) 2.00000 0.0640184
\(977\) 54.0000 1.72761 0.863807 0.503824i \(-0.168074\pi\)
0.863807 + 0.503824i \(0.168074\pi\)
\(978\) −4.00000 −0.127906
\(979\) 0 0
\(980\) 0 0
\(981\) 32.0000 1.02168
\(982\) −24.0000 −0.765871
\(983\) −36.0000 −1.14822 −0.574111 0.818778i \(-0.694652\pi\)
−0.574111 + 0.818778i \(0.694652\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) −9.00000 −0.286473
\(988\) 1.00000 0.0318142
\(989\) −3.00000 −0.0953945
\(990\) 0 0
\(991\) 29.0000 0.921215 0.460608 0.887604i \(-0.347632\pi\)
0.460608 + 0.887604i \(0.347632\pi\)
\(992\) 5.00000 0.158750
\(993\) 20.0000 0.634681
\(994\) 1.00000 0.0317181
\(995\) 0 0
\(996\) 12.0000 0.380235
\(997\) 44.0000 1.39349 0.696747 0.717317i \(-0.254630\pi\)
0.696747 + 0.717317i \(0.254630\pi\)
\(998\) 41.0000 1.29783
\(999\) 20.0000 0.632772
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 \(a_p\))