Properties

Label 14.2.a.a.1.1
Level 14
Weight 2
Character 14.1
Self dual Yes
Analytic conductor 0.112
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 14 = 2 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 14.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(0.11179056283\)
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 \(\chi\) = 14.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(-2.00000 q^{3}\) \(+1.00000 q^{4}\) \(+2.00000 q^{6}\) \(+1.00000 q^{7}\) \(-1.00000 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(-2.00000 q^{3}\) \(+1.00000 q^{4}\) \(+2.00000 q^{6}\) \(+1.00000 q^{7}\) \(-1.00000 q^{8}\) \(+1.00000 q^{9}\) \(-2.00000 q^{12}\) \(-4.00000 q^{13}\) \(-1.00000 q^{14}\) \(+1.00000 q^{16}\) \(+6.00000 q^{17}\) \(-1.00000 q^{18}\) \(+2.00000 q^{19}\) \(-2.00000 q^{21}\) \(+2.00000 q^{24}\) \(-5.00000 q^{25}\) \(+4.00000 q^{26}\) \(+4.00000 q^{27}\) \(+1.00000 q^{28}\) \(-6.00000 q^{29}\) \(-4.00000 q^{31}\) \(-1.00000 q^{32}\) \(-6.00000 q^{34}\) \(+1.00000 q^{36}\) \(+2.00000 q^{37}\) \(-2.00000 q^{38}\) \(+8.00000 q^{39}\) \(+6.00000 q^{41}\) \(+2.00000 q^{42}\) \(+8.00000 q^{43}\) \(-12.0000 q^{47}\) \(-2.00000 q^{48}\) \(+1.00000 q^{49}\) \(+5.00000 q^{50}\) \(-12.0000 q^{51}\) \(-4.00000 q^{52}\) \(+6.00000 q^{53}\) \(-4.00000 q^{54}\) \(-1.00000 q^{56}\) \(-4.00000 q^{57}\) \(+6.00000 q^{58}\) \(-6.00000 q^{59}\) \(+8.00000 q^{61}\) \(+4.00000 q^{62}\) \(+1.00000 q^{63}\) \(+1.00000 q^{64}\) \(-4.00000 q^{67}\) \(+6.00000 q^{68}\) \(-1.00000 q^{72}\) \(+2.00000 q^{73}\) \(-2.00000 q^{74}\) \(+10.0000 q^{75}\) \(+2.00000 q^{76}\) \(-8.00000 q^{78}\) \(+8.00000 q^{79}\) \(-11.0000 q^{81}\) \(-6.00000 q^{82}\) \(-6.00000 q^{83}\) \(-2.00000 q^{84}\) \(-8.00000 q^{86}\) \(+12.0000 q^{87}\) \(-6.00000 q^{89}\) \(-4.00000 q^{91}\) \(+8.00000 q^{93}\) \(+12.0000 q^{94}\) \(+2.00000 q^{96}\) \(-10.0000 q^{97}\) \(-1.00000 q^{98}\) \(+O(q^{100})\)

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
\(3\) −2.00000 −1.15470 −0.577350 0.816497i \(-0.695913\pi\)
−0.577350 + 0.816497i \(0.695913\pi\)
\(4\) 1.00000 0.500000
\(5\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(6\) 2.00000 0.816497
\(7\) 1.00000 0.377964
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) −2.00000 −0.577350
\(13\) −4.00000 −1.10940 −0.554700 0.832050i \(-0.687167\pi\)
−0.554700 + 0.832050i \(0.687167\pi\)
\(14\) −1.00000 −0.267261
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 6.00000 1.45521 0.727607 0.685994i \(-0.240633\pi\)
0.727607 + 0.685994i \(0.240633\pi\)
\(18\) −1.00000 −0.235702
\(19\) 2.00000 0.458831 0.229416 0.973329i \(-0.426318\pi\)
0.229416 + 0.973329i \(0.426318\pi\)
\(20\) 0 0
\(21\) −2.00000 −0.436436
\(22\) 0 0
\(23\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) 2.00000 0.408248
\(25\) −5.00000 −1.00000
\(26\) 4.00000 0.784465
\(27\) 4.00000 0.769800
\(28\) 1.00000 0.188982
\(29\) −6.00000 −1.11417 −0.557086 0.830455i \(-0.688081\pi\)
−0.557086 + 0.830455i \(0.688081\pi\)
\(30\) 0 0
\(31\) −4.00000 −0.718421 −0.359211 0.933257i \(-0.616954\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) −6.00000 −1.02899
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) 2.00000 0.328798 0.164399 0.986394i \(-0.447432\pi\)
0.164399 + 0.986394i \(0.447432\pi\)
\(38\) −2.00000 −0.324443
\(39\) 8.00000 1.28103
\(40\) 0 0
\(41\) 6.00000 0.937043 0.468521 0.883452i \(-0.344787\pi\)
0.468521 + 0.883452i \(0.344787\pi\)
\(42\) 2.00000 0.308607
\(43\) 8.00000 1.21999 0.609994 0.792406i \(-0.291172\pi\)
0.609994 + 0.792406i \(0.291172\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −12.0000 −1.75038 −0.875190 0.483779i \(-0.839264\pi\)
−0.875190 + 0.483779i \(0.839264\pi\)
\(48\) −2.00000 −0.288675
\(49\) 1.00000 0.142857
\(50\) 5.00000 0.707107
\(51\) −12.0000 −1.68034
\(52\) −4.00000 −0.554700
\(53\) 6.00000 0.824163 0.412082 0.911147i \(-0.364802\pi\)
0.412082 + 0.911147i \(0.364802\pi\)
\(54\) −4.00000 −0.544331
\(55\) 0 0
\(56\) −1.00000 −0.133631
\(57\) −4.00000 −0.529813
\(58\) 6.00000 0.787839
\(59\) −6.00000 −0.781133 −0.390567 0.920575i \(-0.627721\pi\)
−0.390567 + 0.920575i \(0.627721\pi\)
\(60\) 0 0
\(61\) 8.00000 1.02430 0.512148 0.858898i \(-0.328850\pi\)
0.512148 + 0.858898i \(0.328850\pi\)
\(62\) 4.00000 0.508001
\(63\) 1.00000 0.125988
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) −4.00000 −0.488678 −0.244339 0.969690i \(-0.578571\pi\)
−0.244339 + 0.969690i \(0.578571\pi\)
\(68\) 6.00000 0.727607
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) −1.00000 −0.117851
\(73\) 2.00000 0.234082 0.117041 0.993127i \(-0.462659\pi\)
0.117041 + 0.993127i \(0.462659\pi\)
\(74\) −2.00000 −0.232495
\(75\) 10.0000 1.15470
\(76\) 2.00000 0.229416
\(77\) 0 0
\(78\) −8.00000 −0.905822
\(79\) 8.00000 0.900070 0.450035 0.893011i \(-0.351411\pi\)
0.450035 + 0.893011i \(0.351411\pi\)
\(80\) 0 0
\(81\) −11.0000 −1.22222
\(82\) −6.00000 −0.662589
\(83\) −6.00000 −0.658586 −0.329293 0.944228i \(-0.606810\pi\)
−0.329293 + 0.944228i \(0.606810\pi\)
\(84\) −2.00000 −0.218218
\(85\) 0 0
\(86\) −8.00000 −0.862662
\(87\) 12.0000 1.28654
\(88\) 0 0
\(89\) −6.00000 −0.635999 −0.317999 0.948091i \(-0.603011\pi\)
−0.317999 + 0.948091i \(0.603011\pi\)
\(90\) 0 0
\(91\) −4.00000 −0.419314
\(92\) 0 0
\(93\) 8.00000 0.829561
\(94\) 12.0000 1.23771
\(95\) 0 0
\(96\) 2.00000 0.204124
\(97\) −10.0000 −1.01535 −0.507673 0.861550i \(-0.669494\pi\)
−0.507673 + 0.861550i \(0.669494\pi\)
\(98\) −1.00000 −0.101015
\(99\) 0 0
\(100\) −5.00000 −0.500000
\(101\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(102\) 12.0000 1.18818
\(103\) −4.00000 −0.394132 −0.197066 0.980390i \(-0.563141\pi\)
−0.197066 + 0.980390i \(0.563141\pi\)
\(104\) 4.00000 0.392232
\(105\) 0 0
\(106\) −6.00000 −0.582772
\(107\) 12.0000 1.16008 0.580042 0.814587i \(-0.303036\pi\)
0.580042 + 0.814587i \(0.303036\pi\)
\(108\) 4.00000 0.384900
\(109\) 2.00000 0.191565 0.0957826 0.995402i \(-0.469465\pi\)
0.0957826 + 0.995402i \(0.469465\pi\)
\(110\) 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 \(0.408930\pi\)
\(114\) 4.00000 0.374634
\(115\) 0 0
\(116\) −6.00000 −0.557086
\(117\) −4.00000 −0.369800
\(118\) 6.00000 0.552345
\(119\) 6.00000 0.550019
\(120\) 0 0
\(121\) −11.0000 −1.00000
\(122\) −8.00000 −0.724286
\(123\) −12.0000 −1.08200
\(124\) −4.00000 −0.359211
\(125\) 0 0
\(126\) −1.00000 −0.0890871
\(127\) −16.0000 −1.41977 −0.709885 0.704317i \(-0.751253\pi\)
−0.709885 + 0.704317i \(0.751253\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −16.0000 −1.40872
\(130\) 0 0
\(131\) 18.0000 1.57267 0.786334 0.617802i \(-0.211977\pi\)
0.786334 + 0.617802i \(0.211977\pi\)
\(132\) 0 0
\(133\) 2.00000 0.173422
\(134\) 4.00000 0.345547
\(135\) 0 0
\(136\) −6.00000 −0.514496
\(137\) 18.0000 1.53784 0.768922 0.639343i \(-0.220793\pi\)
0.768922 + 0.639343i \(0.220793\pi\)
\(138\) 0 0
\(139\) 14.0000 1.18746 0.593732 0.804663i \(-0.297654\pi\)
0.593732 + 0.804663i \(0.297654\pi\)
\(140\) 0 0
\(141\) 24.0000 2.02116
\(142\) 0 0
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) 0 0
\(146\) −2.00000 −0.165521
\(147\) −2.00000 −0.164957
\(148\) 2.00000 0.164399
\(149\) −18.0000 −1.47462 −0.737309 0.675556i \(-0.763904\pi\)
−0.737309 + 0.675556i \(0.763904\pi\)
\(150\) −10.0000 −0.816497
\(151\) 8.00000 0.651031 0.325515 0.945537i \(-0.394462\pi\)
0.325515 + 0.945537i \(0.394462\pi\)
\(152\) −2.00000 −0.162221
\(153\) 6.00000 0.485071
\(154\) 0 0
\(155\) 0 0
\(156\) 8.00000 0.640513
\(157\) −4.00000 −0.319235 −0.159617 0.987179i \(-0.551026\pi\)
−0.159617 + 0.987179i \(0.551026\pi\)
\(158\) −8.00000 −0.636446
\(159\) −12.0000 −0.951662
\(160\) 0 0
\(161\) 0 0
\(162\) 11.0000 0.864242
\(163\) −16.0000 −1.25322 −0.626608 0.779334i \(-0.715557\pi\)
−0.626608 + 0.779334i \(0.715557\pi\)
\(164\) 6.00000 0.468521
\(165\) 0 0
\(166\) 6.00000 0.465690
\(167\) −12.0000 −0.928588 −0.464294 0.885681i \(-0.653692\pi\)
−0.464294 + 0.885681i \(0.653692\pi\)
\(168\) 2.00000 0.154303
\(169\) 3.00000 0.230769
\(170\) 0 0
\(171\) 2.00000 0.152944
\(172\) 8.00000 0.609994
\(173\) −12.0000 −0.912343 −0.456172 0.889892i \(-0.650780\pi\)
−0.456172 + 0.889892i \(0.650780\pi\)
\(174\) −12.0000 −0.909718
\(175\) −5.00000 −0.377964
\(176\) 0 0
\(177\) 12.0000 0.901975
\(178\) 6.00000 0.449719
\(179\) −12.0000 −0.896922 −0.448461 0.893802i \(-0.648028\pi\)
−0.448461 + 0.893802i \(0.648028\pi\)
\(180\) 0 0
\(181\) 20.0000 1.48659 0.743294 0.668965i \(-0.233262\pi\)
0.743294 + 0.668965i \(0.233262\pi\)
\(182\) 4.00000 0.296500
\(183\) −16.0000 −1.18275
\(184\) 0 0
\(185\) 0 0
\(186\) −8.00000 −0.586588
\(187\) 0 0
\(188\) −12.0000 −0.875190
\(189\) 4.00000 0.290957
\(190\) 0 0
\(191\) 24.0000 1.73658 0.868290 0.496058i \(-0.165220\pi\)
0.868290 + 0.496058i \(0.165220\pi\)
\(192\) −2.00000 −0.144338
\(193\) 14.0000 1.00774 0.503871 0.863779i \(-0.331909\pi\)
0.503871 + 0.863779i \(0.331909\pi\)
\(194\) 10.0000 0.717958
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) −18.0000 −1.28245 −0.641223 0.767354i \(-0.721573\pi\)
−0.641223 + 0.767354i \(0.721573\pi\)
\(198\) 0 0
\(199\) 20.0000 1.41776 0.708881 0.705328i \(-0.249200\pi\)
0.708881 + 0.705328i \(0.249200\pi\)
\(200\) 5.00000 0.353553
\(201\) 8.00000 0.564276
\(202\) 0 0
\(203\) −6.00000 −0.421117
\(204\) −12.0000 −0.840168
\(205\) 0 0
\(206\) 4.00000 0.278693
\(207\) 0 0
\(208\) −4.00000 −0.277350
\(209\) 0 0
\(210\) 0 0
\(211\) −4.00000 −0.275371 −0.137686 0.990476i \(-0.543966\pi\)
−0.137686 + 0.990476i \(0.543966\pi\)
\(212\) 6.00000 0.412082
\(213\) 0 0
\(214\) −12.0000 −0.820303
\(215\) 0 0
\(216\) −4.00000 −0.272166
\(217\) −4.00000 −0.271538
\(218\) −2.00000 −0.135457
\(219\) −4.00000 −0.270295
\(220\) 0 0
\(221\) −24.0000 −1.61441
\(222\) 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
\(225\) −5.00000 −0.333333
\(226\) −6.00000 −0.399114
\(227\) 18.0000 1.19470 0.597351 0.801980i \(-0.296220\pi\)
0.597351 + 0.801980i \(0.296220\pi\)
\(228\) −4.00000 −0.264906
\(229\) −4.00000 −0.264327 −0.132164 0.991228i \(-0.542192\pi\)
−0.132164 + 0.991228i \(0.542192\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 6.00000 0.393919
\(233\) −6.00000 −0.393073 −0.196537 0.980497i \(-0.562969\pi\)
−0.196537 + 0.980497i \(0.562969\pi\)
\(234\) 4.00000 0.261488
\(235\) 0 0
\(236\) −6.00000 −0.390567
\(237\) −16.0000 −1.03931
\(238\) −6.00000 −0.388922
\(239\) 24.0000 1.55243 0.776215 0.630468i \(-0.217137\pi\)
0.776215 + 0.630468i \(0.217137\pi\)
\(240\) 0 0
\(241\) −10.0000 −0.644157 −0.322078 0.946713i \(-0.604381\pi\)
−0.322078 + 0.946713i \(0.604381\pi\)
\(242\) 11.0000 0.707107
\(243\) 10.0000 0.641500
\(244\) 8.00000 0.512148
\(245\) 0 0
\(246\) 12.0000 0.765092
\(247\) −8.00000 −0.509028
\(248\) 4.00000 0.254000
\(249\) 12.0000 0.760469
\(250\) 0 0
\(251\) −18.0000 −1.13615 −0.568075 0.822977i \(-0.692312\pi\)
−0.568075 + 0.822977i \(0.692312\pi\)
\(252\) 1.00000 0.0629941
\(253\) 0 0
\(254\) 16.0000 1.00393
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 18.0000 1.12281 0.561405 0.827541i \(-0.310261\pi\)
0.561405 + 0.827541i \(0.310261\pi\)
\(258\) 16.0000 0.996116
\(259\) 2.00000 0.124274
\(260\) 0 0
\(261\) −6.00000 −0.371391
\(262\) −18.0000 −1.11204
\(263\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −2.00000 −0.122628
\(267\) 12.0000 0.734388
\(268\) −4.00000 −0.244339
\(269\) −12.0000 −0.731653 −0.365826 0.930683i \(-0.619214\pi\)
−0.365826 + 0.930683i \(0.619214\pi\)
\(270\) 0 0
\(271\) −16.0000 −0.971931 −0.485965 0.873978i \(-0.661532\pi\)
−0.485965 + 0.873978i \(0.661532\pi\)
\(272\) 6.00000 0.363803
\(273\) 8.00000 0.484182
\(274\) −18.0000 −1.08742
\(275\) 0 0
\(276\) 0 0
\(277\) −10.0000 −0.600842 −0.300421 0.953807i \(-0.597127\pi\)
−0.300421 + 0.953807i \(0.597127\pi\)
\(278\) −14.0000 −0.839664
\(279\) −4.00000 −0.239474
\(280\) 0 0
\(281\) −6.00000 −0.357930 −0.178965 0.983855i \(-0.557275\pi\)
−0.178965 + 0.983855i \(0.557275\pi\)
\(282\) −24.0000 −1.42918
\(283\) −22.0000 −1.30776 −0.653882 0.756596i \(-0.726861\pi\)
−0.653882 + 0.756596i \(0.726861\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 6.00000 0.354169
\(288\) −1.00000 −0.0589256
\(289\) 19.0000 1.11765
\(290\) 0 0
\(291\) 20.0000 1.17242
\(292\) 2.00000 0.117041
\(293\) 24.0000 1.40209 0.701047 0.713115i \(-0.252716\pi\)
0.701047 + 0.713115i \(0.252716\pi\)
\(294\) 2.00000 0.116642
\(295\) 0 0
\(296\) −2.00000 −0.116248
\(297\) 0 0
\(298\) 18.0000 1.04271
\(299\) 0 0
\(300\) 10.0000 0.577350
\(301\) 8.00000 0.461112
\(302\) −8.00000 −0.460348
\(303\) 0 0
\(304\) 2.00000 0.114708
\(305\) 0 0
\(306\) −6.00000 −0.342997
\(307\) 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
\(311\) −24.0000 −1.36092 −0.680458 0.732787i \(-0.738219\pi\)
−0.680458 + 0.732787i \(0.738219\pi\)
\(312\) −8.00000 −0.452911
\(313\) −10.0000 −0.565233 −0.282617 0.959233i \(-0.591202\pi\)
−0.282617 + 0.959233i \(0.591202\pi\)
\(314\) 4.00000 0.225733
\(315\) 0 0
\(316\) 8.00000 0.450035
\(317\) 6.00000 0.336994 0.168497 0.985702i \(-0.446109\pi\)
0.168497 + 0.985702i \(0.446109\pi\)
\(318\) 12.0000 0.672927
\(319\) 0 0
\(320\) 0 0
\(321\) −24.0000 −1.33955
\(322\) 0 0
\(323\) 12.0000 0.667698
\(324\) −11.0000 −0.611111
\(325\) 20.0000 1.10940
\(326\) 16.0000 0.886158
\(327\) −4.00000 −0.221201
\(328\) −6.00000 −0.331295
\(329\) −12.0000 −0.661581
\(330\) 0 0
\(331\) 8.00000 0.439720 0.219860 0.975531i \(-0.429440\pi\)
0.219860 + 0.975531i \(0.429440\pi\)
\(332\) −6.00000 −0.329293
\(333\) 2.00000 0.109599
\(334\) 12.0000 0.656611
\(335\) 0 0
\(336\) −2.00000 −0.109109
\(337\) 14.0000 0.762629 0.381314 0.924445i \(-0.375472\pi\)
0.381314 + 0.924445i \(0.375472\pi\)
\(338\) −3.00000 −0.163178
\(339\) −12.0000 −0.651751
\(340\) 0 0
\(341\) 0 0
\(342\) −2.00000 −0.108148
\(343\) 1.00000 0.0539949
\(344\) −8.00000 −0.431331
\(345\) 0 0
\(346\) 12.0000 0.645124
\(347\) −24.0000 −1.28839 −0.644194 0.764862i \(-0.722807\pi\)
−0.644194 + 0.764862i \(0.722807\pi\)
\(348\) 12.0000 0.643268
\(349\) −28.0000 −1.49881 −0.749403 0.662114i \(-0.769659\pi\)
−0.749403 + 0.662114i \(0.769659\pi\)
\(350\) 5.00000 0.267261
\(351\) −16.0000 −0.854017
\(352\) 0 0
\(353\) 18.0000 0.958043 0.479022 0.877803i \(-0.340992\pi\)
0.479022 + 0.877803i \(0.340992\pi\)
\(354\) −12.0000 −0.637793
\(355\) 0 0
\(356\) −6.00000 −0.317999
\(357\) −12.0000 −0.635107
\(358\) 12.0000 0.634220
\(359\) −24.0000 −1.26667 −0.633336 0.773877i \(-0.718315\pi\)
−0.633336 + 0.773877i \(0.718315\pi\)
\(360\) 0 0
\(361\) −15.0000 −0.789474
\(362\) −20.0000 −1.05118
\(363\) 22.0000 1.15470
\(364\) −4.00000 −0.209657
\(365\) 0 0
\(366\) 16.0000 0.836333
\(367\) 8.00000 0.417597 0.208798 0.977959i \(-0.433045\pi\)
0.208798 + 0.977959i \(0.433045\pi\)
\(368\) 0 0
\(369\) 6.00000 0.312348
\(370\) 0 0
\(371\) 6.00000 0.311504
\(372\) 8.00000 0.414781
\(373\) 14.0000 0.724893 0.362446 0.932005i \(-0.381942\pi\)
0.362446 + 0.932005i \(0.381942\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 12.0000 0.618853
\(377\) 24.0000 1.23606
\(378\) −4.00000 −0.205738
\(379\) −16.0000 −0.821865 −0.410932 0.911666i \(-0.634797\pi\)
−0.410932 + 0.911666i \(0.634797\pi\)
\(380\) 0 0
\(381\) 32.0000 1.63941
\(382\) −24.0000 −1.22795
\(383\) 36.0000 1.83951 0.919757 0.392488i \(-0.128386\pi\)
0.919757 + 0.392488i \(0.128386\pi\)
\(384\) 2.00000 0.102062
\(385\) 0 0
\(386\) −14.0000 −0.712581
\(387\) 8.00000 0.406663
\(388\) −10.0000 −0.507673
\(389\) 18.0000 0.912636 0.456318 0.889817i \(-0.349168\pi\)
0.456318 + 0.889817i \(0.349168\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −1.00000 −0.0505076
\(393\) −36.0000 −1.81596
\(394\) 18.0000 0.906827
\(395\) 0 0
\(396\) 0 0
\(397\) 20.0000 1.00377 0.501886 0.864934i \(-0.332640\pi\)
0.501886 + 0.864934i \(0.332640\pi\)
\(398\) −20.0000 −1.00251
\(399\) −4.00000 −0.200250
\(400\) −5.00000 −0.250000
\(401\) −18.0000 −0.898877 −0.449439 0.893311i \(-0.648376\pi\)
−0.449439 + 0.893311i \(0.648376\pi\)
\(402\) −8.00000 −0.399004
\(403\) 16.0000 0.797017
\(404\) 0 0
\(405\) 0 0
\(406\) 6.00000 0.297775
\(407\) 0 0
\(408\) 12.0000 0.594089
\(409\) 14.0000 0.692255 0.346128 0.938187i \(-0.387496\pi\)
0.346128 + 0.938187i \(0.387496\pi\)
\(410\) 0 0
\(411\) −36.0000 −1.77575
\(412\) −4.00000 −0.197066
\(413\) −6.00000 −0.295241
\(414\) 0 0
\(415\) 0 0
\(416\) 4.00000 0.196116
\(417\) −28.0000 −1.37117
\(418\) 0 0
\(419\) 6.00000 0.293119 0.146560 0.989202i \(-0.453180\pi\)
0.146560 + 0.989202i \(0.453180\pi\)
\(420\) 0 0
\(421\) −10.0000 −0.487370 −0.243685 0.969854i \(-0.578356\pi\)
−0.243685 + 0.969854i \(0.578356\pi\)
\(422\) 4.00000 0.194717
\(423\) −12.0000 −0.583460
\(424\) −6.00000 −0.291386
\(425\) −30.0000 −1.45521
\(426\) 0 0
\(427\) 8.00000 0.387147
\(428\) 12.0000 0.580042
\(429\) 0 0
\(430\) 0 0
\(431\) 24.0000 1.15604 0.578020 0.816023i \(-0.303826\pi\)
0.578020 + 0.816023i \(0.303826\pi\)
\(432\) 4.00000 0.192450
\(433\) −34.0000 −1.63394 −0.816968 0.576683i \(-0.804347\pi\)
−0.816968 + 0.576683i \(0.804347\pi\)
\(434\) 4.00000 0.192006
\(435\) 0 0
\(436\) 2.00000 0.0957826
\(437\) 0 0
\(438\) 4.00000 0.191127
\(439\) 8.00000 0.381819 0.190910 0.981608i \(-0.438856\pi\)
0.190910 + 0.981608i \(0.438856\pi\)
\(440\) 0 0
\(441\) 1.00000 0.0476190
\(442\) 24.0000 1.14156
\(443\) −12.0000 −0.570137 −0.285069 0.958507i \(-0.592016\pi\)
−0.285069 + 0.958507i \(0.592016\pi\)
\(444\) −4.00000 −0.189832
\(445\) 0 0
\(446\) −8.00000 −0.378811
\(447\) 36.0000 1.70274
\(448\) 1.00000 0.0472456
\(449\) 18.0000 0.849473 0.424736 0.905317i \(-0.360367\pi\)
0.424736 + 0.905317i \(0.360367\pi\)
\(450\) 5.00000 0.235702
\(451\) 0 0
\(452\) 6.00000 0.282216
\(453\) −16.0000 −0.751746
\(454\) −18.0000 −0.844782
\(455\) 0 0
\(456\) 4.00000 0.187317
\(457\) −10.0000 −0.467780 −0.233890 0.972263i \(-0.575146\pi\)
−0.233890 + 0.972263i \(0.575146\pi\)
\(458\) 4.00000 0.186908
\(459\) 24.0000 1.12022
\(460\) 0 0
\(461\) 12.0000 0.558896 0.279448 0.960161i \(-0.409849\pi\)
0.279448 + 0.960161i \(0.409849\pi\)
\(462\) 0 0
\(463\) 32.0000 1.48717 0.743583 0.668644i \(-0.233125\pi\)
0.743583 + 0.668644i \(0.233125\pi\)
\(464\) −6.00000 −0.278543
\(465\) 0 0
\(466\) 6.00000 0.277945
\(467\) −6.00000 −0.277647 −0.138823 0.990317i \(-0.544332\pi\)
−0.138823 + 0.990317i \(0.544332\pi\)
\(468\) −4.00000 −0.184900
\(469\) −4.00000 −0.184703
\(470\) 0 0
\(471\) 8.00000 0.368621
\(472\) 6.00000 0.276172
\(473\) 0 0
\(474\) 16.0000 0.734904
\(475\) −10.0000 −0.458831
\(476\) 6.00000 0.275010
\(477\) 6.00000 0.274721
\(478\) −24.0000 −1.09773
\(479\) −36.0000 −1.64488 −0.822441 0.568850i \(-0.807388\pi\)
−0.822441 + 0.568850i \(0.807388\pi\)
\(480\) 0 0
\(481\) −8.00000 −0.364769
\(482\) 10.0000 0.455488
\(483\) 0 0
\(484\) −11.0000 −0.500000
\(485\) 0 0
\(486\) −10.0000 −0.453609
\(487\) −16.0000 −0.725029 −0.362515 0.931978i \(-0.618082\pi\)
−0.362515 + 0.931978i \(0.618082\pi\)
\(488\) −8.00000 −0.362143
\(489\) 32.0000 1.44709
\(490\) 0 0
\(491\) −12.0000 −0.541552 −0.270776 0.962642i \(-0.587280\pi\)
−0.270776 + 0.962642i \(0.587280\pi\)
\(492\) −12.0000 −0.541002
\(493\) −36.0000 −1.62136
\(494\) 8.00000 0.359937
\(495\) 0 0
\(496\) −4.00000 −0.179605
\(497\) 0 0
\(498\) −12.0000 −0.537733
\(499\) −4.00000 −0.179065 −0.0895323 0.995984i \(-0.528537\pi\)
−0.0895323 + 0.995984i \(0.528537\pi\)
\(500\) 0 0
\(501\) 24.0000 1.07224
\(502\) 18.0000 0.803379
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) −1.00000 −0.0445435
\(505\) 0 0
\(506\) 0 0
\(507\) −6.00000 −0.266469
\(508\) −16.0000 −0.709885
\(509\) 36.0000 1.59567 0.797836 0.602875i \(-0.205978\pi\)
0.797836 + 0.602875i \(0.205978\pi\)
\(510\) 0 0
\(511\) 2.00000 0.0884748
\(512\) −1.00000 −0.0441942
\(513\) 8.00000 0.353209
\(514\) −18.0000 −0.793946
\(515\) 0 0
\(516\) −16.0000 −0.704361
\(517\) 0 0
\(518\) −2.00000 −0.0878750
\(519\) 24.0000 1.05348
\(520\) 0 0
\(521\) 6.00000 0.262865 0.131432 0.991325i \(-0.458042\pi\)
0.131432 + 0.991325i \(0.458042\pi\)
\(522\) 6.00000 0.262613
\(523\) 2.00000 0.0874539 0.0437269 0.999044i \(-0.486077\pi\)
0.0437269 + 0.999044i \(0.486077\pi\)
\(524\) 18.0000 0.786334
\(525\) 10.0000 0.436436
\(526\) 0 0
\(527\) −24.0000 −1.04546
\(528\) 0 0
\(529\) −23.0000 −1.00000
\(530\) 0 0
\(531\) −6.00000 −0.260378
\(532\) 2.00000 0.0867110
\(533\) −24.0000 −1.03956
\(534\) −12.0000 −0.519291
\(535\) 0 0
\(536\) 4.00000 0.172774
\(537\) 24.0000 1.03568
\(538\) 12.0000 0.517357
\(539\) 0 0
\(540\) 0 0
\(541\) 38.0000 1.63375 0.816874 0.576816i \(-0.195705\pi\)
0.816874 + 0.576816i \(0.195705\pi\)
\(542\) 16.0000 0.687259
\(543\) −40.0000 −1.71656
\(544\) −6.00000 −0.257248
\(545\) 0 0
\(546\) −8.00000 −0.342368
\(547\) 8.00000 0.342055 0.171028 0.985266i \(-0.445291\pi\)
0.171028 + 0.985266i \(0.445291\pi\)
\(548\) 18.0000 0.768922
\(549\) 8.00000 0.341432
\(550\) 0 0
\(551\) −12.0000 −0.511217
\(552\) 0 0
\(553\) 8.00000 0.340195
\(554\) 10.0000 0.424859
\(555\) 0 0
\(556\) 14.0000 0.593732
\(557\) 6.00000 0.254228 0.127114 0.991888i \(-0.459429\pi\)
0.127114 + 0.991888i \(0.459429\pi\)
\(558\) 4.00000 0.169334
\(559\) −32.0000 −1.35346
\(560\) 0 0
\(561\) 0 0
\(562\) 6.00000 0.253095
\(563\) 30.0000 1.26435 0.632175 0.774826i \(-0.282163\pi\)
0.632175 + 0.774826i \(0.282163\pi\)
\(564\) 24.0000 1.01058
\(565\) 0 0
\(566\) 22.0000 0.924729
\(567\) −11.0000 −0.461957
\(568\) 0 0
\(569\) 6.00000 0.251533 0.125767 0.992060i \(-0.459861\pi\)
0.125767 + 0.992060i \(0.459861\pi\)
\(570\) 0 0
\(571\) 32.0000 1.33916 0.669579 0.742741i \(-0.266474\pi\)
0.669579 + 0.742741i \(0.266474\pi\)
\(572\) 0 0
\(573\) −48.0000 −2.00523
\(574\) −6.00000 −0.250435
\(575\) 0 0
\(576\) 1.00000 0.0416667
\(577\) 2.00000 0.0832611 0.0416305 0.999133i \(-0.486745\pi\)
0.0416305 + 0.999133i \(0.486745\pi\)
\(578\) −19.0000 −0.790296
\(579\) −28.0000 −1.16364
\(580\) 0 0
\(581\) −6.00000 −0.248922
\(582\) −20.0000 −0.829027
\(583\) 0 0
\(584\) −2.00000 −0.0827606
\(585\) 0 0
\(586\) −24.0000 −0.991431
\(587\) −42.0000 −1.73353 −0.866763 0.498721i \(-0.833803\pi\)
−0.866763 + 0.498721i \(0.833803\pi\)
\(588\) −2.00000 −0.0824786
\(589\) −8.00000 −0.329634
\(590\) 0 0
\(591\) 36.0000 1.48084
\(592\) 2.00000 0.0821995
\(593\) −6.00000 −0.246390 −0.123195 0.992382i \(-0.539314\pi\)
−0.123195 + 0.992382i \(0.539314\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −18.0000 −0.737309
\(597\) −40.0000 −1.63709
\(598\) 0 0
\(599\) −24.0000 −0.980613 −0.490307 0.871550i \(-0.663115\pi\)
−0.490307 + 0.871550i \(0.663115\pi\)
\(600\) −10.0000 −0.408248
\(601\) 26.0000 1.06056 0.530281 0.847822i \(-0.322086\pi\)
0.530281 + 0.847822i \(0.322086\pi\)
\(602\) −8.00000 −0.326056
\(603\) −4.00000 −0.162893
\(604\) 8.00000 0.325515
\(605\) 0 0
\(606\) 0 0
\(607\) 32.0000 1.29884 0.649420 0.760430i \(-0.275012\pi\)
0.649420 + 0.760430i \(0.275012\pi\)
\(608\) −2.00000 −0.0811107
\(609\) 12.0000 0.486265
\(610\) 0 0
\(611\) 48.0000 1.94187
\(612\) 6.00000 0.242536
\(613\) 2.00000 0.0807792 0.0403896 0.999184i \(-0.487140\pi\)
0.0403896 + 0.999184i \(0.487140\pi\)
\(614\) −2.00000 −0.0807134
\(615\) 0 0
\(616\) 0 0
\(617\) 6.00000 0.241551 0.120775 0.992680i \(-0.461462\pi\)
0.120775 + 0.992680i \(0.461462\pi\)
\(618\) −8.00000 −0.321807
\(619\) 26.0000 1.04503 0.522514 0.852631i \(-0.324994\pi\)
0.522514 + 0.852631i \(0.324994\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 24.0000 0.962312
\(623\) −6.00000 −0.240385
\(624\) 8.00000 0.320256
\(625\) 25.0000 1.00000
\(626\) 10.0000 0.399680
\(627\) 0 0
\(628\) −4.00000 −0.159617
\(629\) 12.0000 0.478471
\(630\) 0 0
\(631\) −16.0000 −0.636950 −0.318475 0.947931i \(-0.603171\pi\)
−0.318475 + 0.947931i \(0.603171\pi\)
\(632\) −8.00000 −0.318223
\(633\) 8.00000 0.317971
\(634\) −6.00000 −0.238290
\(635\) 0 0
\(636\) −12.0000 −0.475831
\(637\) −4.00000 −0.158486
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −18.0000 −0.710957 −0.355479 0.934684i \(-0.615682\pi\)
−0.355479 + 0.934684i \(0.615682\pi\)
\(642\) 24.0000 0.947204
\(643\) 14.0000 0.552106 0.276053 0.961142i \(-0.410973\pi\)
0.276053 + 0.961142i \(0.410973\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −12.0000 −0.472134
\(647\) −12.0000 −0.471769 −0.235884 0.971781i \(-0.575799\pi\)
−0.235884 + 0.971781i \(0.575799\pi\)
\(648\) 11.0000 0.432121
\(649\) 0 0
\(650\) −20.0000 −0.784465
\(651\) 8.00000 0.313545
\(652\) −16.0000 −0.626608
\(653\) 18.0000 0.704394 0.352197 0.935926i \(-0.385435\pi\)
0.352197 + 0.935926i \(0.385435\pi\)
\(654\) 4.00000 0.156412
\(655\) 0 0
\(656\) 6.00000 0.234261
\(657\) 2.00000 0.0780274
\(658\) 12.0000 0.467809
\(659\) −24.0000 −0.934907 −0.467454 0.884018i \(-0.654829\pi\)
−0.467454 + 0.884018i \(0.654829\pi\)
\(660\) 0 0
\(661\) −40.0000 −1.55582 −0.777910 0.628376i \(-0.783720\pi\)
−0.777910 + 0.628376i \(0.783720\pi\)
\(662\) −8.00000 −0.310929
\(663\) 48.0000 1.86417
\(664\) 6.00000 0.232845
\(665\) 0 0
\(666\) −2.00000 −0.0774984
\(667\) 0 0
\(668\) −12.0000 −0.464294
\(669\) −16.0000 −0.618596
\(670\) 0 0
\(671\) 0 0
\(672\) 2.00000 0.0771517
\(673\) 26.0000 1.00223 0.501113 0.865382i \(-0.332924\pi\)
0.501113 + 0.865382i \(0.332924\pi\)
\(674\) −14.0000 −0.539260
\(675\) −20.0000 −0.769800
\(676\) 3.00000 0.115385
\(677\) −12.0000 −0.461197 −0.230599 0.973049i \(-0.574068\pi\)
−0.230599 + 0.973049i \(0.574068\pi\)
\(678\) 12.0000 0.460857
\(679\) −10.0000 −0.383765
\(680\) 0 0
\(681\) −36.0000 −1.37952
\(682\) 0 0
\(683\) −12.0000 −0.459167 −0.229584 0.973289i \(-0.573736\pi\)
−0.229584 + 0.973289i \(0.573736\pi\)
\(684\) 2.00000 0.0764719
\(685\) 0 0
\(686\) −1.00000 −0.0381802
\(687\) 8.00000 0.305219
\(688\) 8.00000 0.304997
\(689\) −24.0000 −0.914327
\(690\) 0 0
\(691\) −46.0000 −1.74992 −0.874961 0.484193i \(-0.839113\pi\)
−0.874961 + 0.484193i \(0.839113\pi\)
\(692\) −12.0000 −0.456172
\(693\) 0 0
\(694\) 24.0000 0.911028
\(695\) 0 0
\(696\) −12.0000 −0.454859
\(697\) 36.0000 1.36360
\(698\) 28.0000 1.05982
\(699\) 12.0000 0.453882
\(700\) −5.00000 −0.188982
\(701\) 18.0000 0.679851 0.339925 0.940452i \(-0.389598\pi\)
0.339925 + 0.940452i \(0.389598\pi\)
\(702\) 16.0000 0.603881
\(703\) 4.00000 0.150863
\(704\) 0 0
\(705\) 0 0
\(706\) −18.0000 −0.677439
\(707\) 0 0
\(708\) 12.0000 0.450988
\(709\) −46.0000 −1.72757 −0.863783 0.503864i \(-0.831911\pi\)
−0.863783 + 0.503864i \(0.831911\pi\)
\(710\) 0 0
\(711\) 8.00000 0.300023
\(712\) 6.00000 0.224860
\(713\) 0 0
\(714\) 12.0000 0.449089
\(715\) 0 0
\(716\) −12.0000 −0.448461
\(717\) −48.0000 −1.79259
\(718\) 24.0000 0.895672
\(719\) 12.0000 0.447524 0.223762 0.974644i \(-0.428166\pi\)
0.223762 + 0.974644i \(0.428166\pi\)
\(720\) 0 0
\(721\) −4.00000 −0.148968
\(722\) 15.0000 0.558242
\(723\) 20.0000 0.743808
\(724\) 20.0000 0.743294
\(725\) 30.0000 1.11417
\(726\) −22.0000 −0.816497
\(727\) 44.0000 1.63187 0.815935 0.578144i \(-0.196223\pi\)
0.815935 + 0.578144i \(0.196223\pi\)
\(728\) 4.00000 0.148250
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) 48.0000 1.77534
\(732\) −16.0000 −0.591377
\(733\) −40.0000 −1.47743 −0.738717 0.674016i \(-0.764568\pi\)
−0.738717 + 0.674016i \(0.764568\pi\)
\(734\) −8.00000 −0.295285
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) −6.00000 −0.220863
\(739\) −16.0000 −0.588570 −0.294285 0.955718i \(-0.595081\pi\)
−0.294285 + 0.955718i \(0.595081\pi\)
\(740\) 0 0
\(741\) 16.0000 0.587775
\(742\) −6.00000 −0.220267
\(743\) 24.0000 0.880475 0.440237 0.897881i \(-0.354894\pi\)
0.440237 + 0.897881i \(0.354894\pi\)
\(744\) −8.00000 −0.293294
\(745\) 0 0
\(746\) −14.0000 −0.512576
\(747\) −6.00000 −0.219529
\(748\) 0 0
\(749\) 12.0000 0.438470
\(750\) 0 0
\(751\) −40.0000 −1.45962 −0.729810 0.683650i \(-0.760392\pi\)
−0.729810 + 0.683650i \(0.760392\pi\)
\(752\) −12.0000 −0.437595
\(753\) 36.0000 1.31191
\(754\) −24.0000 −0.874028
\(755\) 0 0
\(756\) 4.00000 0.145479
\(757\) 2.00000 0.0726912 0.0363456 0.999339i \(-0.488428\pi\)
0.0363456 + 0.999339i \(0.488428\pi\)
\(758\) 16.0000 0.581146
\(759\) 0 0
\(760\) 0 0
\(761\) −18.0000 −0.652499 −0.326250 0.945284i \(-0.605785\pi\)
−0.326250 + 0.945284i \(0.605785\pi\)
\(762\) −32.0000 −1.15924
\(763\) 2.00000 0.0724049
\(764\) 24.0000 0.868290
\(765\) 0 0
\(766\) −36.0000 −1.30073
\(767\) 24.0000 0.866590
\(768\) −2.00000 −0.0721688
\(769\) 14.0000 0.504853 0.252426 0.967616i \(-0.418771\pi\)
0.252426 + 0.967616i \(0.418771\pi\)
\(770\) 0 0
\(771\) −36.0000 −1.29651
\(772\) 14.0000 0.503871
\(773\) 24.0000 0.863220 0.431610 0.902060i \(-0.357946\pi\)
0.431610 + 0.902060i \(0.357946\pi\)
\(774\) −8.00000 −0.287554
\(775\) 20.0000 0.718421
\(776\) 10.0000 0.358979
\(777\) −4.00000 −0.143499
\(778\) −18.0000 −0.645331
\(779\) 12.0000 0.429945
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) −24.0000 −0.857690
\(784\) 1.00000 0.0357143
\(785\) 0 0
\(786\) 36.0000 1.28408
\(787\) −22.0000 −0.784215 −0.392108 0.919919i \(-0.628254\pi\)
−0.392108 + 0.919919i \(0.628254\pi\)
\(788\) −18.0000 −0.641223
\(789\) 0 0
\(790\) 0 0
\(791\) 6.00000 0.213335
\(792\) 0 0
\(793\) −32.0000 −1.13635
\(794\) −20.0000 −0.709773
\(795\) 0 0
\(796\) 20.0000 0.708881
\(797\) −12.0000 −0.425062 −0.212531 0.977154i \(-0.568171\pi\)
−0.212531 + 0.977154i \(0.568171\pi\)
\(798\) 4.00000 0.141598
\(799\) −72.0000 −2.54718
\(800\) 5.00000 0.176777
\(801\) −6.00000 −0.212000
\(802\) 18.0000 0.635602
\(803\) 0 0
\(804\) 8.00000 0.282138
\(805\) 0 0
\(806\) −16.0000 −0.563576
\(807\) 24.0000 0.844840
\(808\) 0 0
\(809\) 6.00000 0.210949 0.105474 0.994422i \(-0.466364\pi\)
0.105474 + 0.994422i \(0.466364\pi\)
\(810\) 0 0
\(811\) 2.00000 0.0702295 0.0351147 0.999383i \(-0.488820\pi\)
0.0351147 + 0.999383i \(0.488820\pi\)
\(812\) −6.00000 −0.210559
\(813\) 32.0000 1.12229
\(814\) 0 0
\(815\) 0 0
\(816\) −12.0000 −0.420084
\(817\) 16.0000 0.559769
\(818\) −14.0000 −0.489499
\(819\) −4.00000 −0.139771
\(820\) 0 0
\(821\) 6.00000 0.209401 0.104701 0.994504i \(-0.466612\pi\)
0.104701 + 0.994504i \(0.466612\pi\)
\(822\) 36.0000 1.25564
\(823\) −40.0000 −1.39431 −0.697156 0.716919i \(-0.745552\pi\)
−0.697156 + 0.716919i \(0.745552\pi\)
\(824\) 4.00000 0.139347
\(825\) 0 0
\(826\) 6.00000 0.208767
\(827\) −36.0000 −1.25184 −0.625921 0.779886i \(-0.715277\pi\)
−0.625921 + 0.779886i \(0.715277\pi\)
\(828\) 0 0
\(829\) 56.0000 1.94496 0.972480 0.232986i \(-0.0748495\pi\)
0.972480 + 0.232986i \(0.0748495\pi\)
\(830\) 0 0
\(831\) 20.0000 0.693792
\(832\) −4.00000 −0.138675
\(833\) 6.00000 0.207888
\(834\) 28.0000 0.969561
\(835\) 0 0
\(836\) 0 0
\(837\) −16.0000 −0.553041
\(838\) −6.00000 −0.207267
\(839\) 12.0000 0.414286 0.207143 0.978311i \(-0.433583\pi\)
0.207143 + 0.978311i \(0.433583\pi\)
\(840\) 0 0
\(841\) 7.00000 0.241379
\(842\) 10.0000 0.344623
\(843\) 12.0000 0.413302
\(844\) −4.00000 −0.137686
\(845\) 0 0
\(846\) 12.0000 0.412568
\(847\) −11.0000 −0.377964
\(848\) 6.00000 0.206041
\(849\) 44.0000 1.51008
\(850\) 30.0000 1.02899
\(851\) 0 0
\(852\) 0 0
\(853\) 44.0000 1.50653 0.753266 0.657716i \(-0.228477\pi\)
0.753266 + 0.657716i \(0.228477\pi\)
\(854\) −8.00000 −0.273754
\(855\) 0 0
\(856\) −12.0000 −0.410152
\(857\) −18.0000 −0.614868 −0.307434 0.951569i \(-0.599470\pi\)
−0.307434 + 0.951569i \(0.599470\pi\)
\(858\) 0 0
\(859\) 14.0000 0.477674 0.238837 0.971060i \(-0.423234\pi\)
0.238837 + 0.971060i \(0.423234\pi\)
\(860\) 0 0
\(861\) −12.0000 −0.408959
\(862\) −24.0000 −0.817443
\(863\) −24.0000 −0.816970 −0.408485 0.912765i \(-0.633943\pi\)
−0.408485 + 0.912765i \(0.633943\pi\)
\(864\) −4.00000 −0.136083
\(865\) 0 0
\(866\) 34.0000 1.15537
\(867\) −38.0000 −1.29055
\(868\) −4.00000 −0.135769
\(869\) 0 0
\(870\) 0 0
\(871\) 16.0000 0.542139
\(872\) −2.00000 −0.0677285
\(873\) −10.0000 −0.338449
\(874\) 0 0
\(875\) 0 0
\(876\) −4.00000 −0.135147
\(877\) −22.0000 −0.742887 −0.371444 0.928456i \(-0.621137\pi\)
−0.371444 + 0.928456i \(0.621137\pi\)
\(878\) −8.00000 −0.269987
\(879\) −48.0000 −1.61900
\(880\) 0 0
\(881\) −54.0000 −1.81931 −0.909653 0.415369i \(-0.863653\pi\)
−0.909653 + 0.415369i \(0.863653\pi\)
\(882\) −1.00000 −0.0336718
\(883\) 20.0000 0.673054 0.336527 0.941674i \(-0.390748\pi\)
0.336527 + 0.941674i \(0.390748\pi\)
\(884\) −24.0000 −0.807207
\(885\) 0 0
\(886\) 12.0000 0.403148
\(887\) −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
\(893\) −24.0000 −0.803129
\(894\) −36.0000 −1.20402
\(895\) 0 0
\(896\) −1.00000 −0.0334077
\(897\) 0 0
\(898\) −18.0000 −0.600668
\(899\) 24.0000 0.800445
\(900\) −5.00000 −0.166667
\(901\) 36.0000 1.19933
\(902\) 0 0
\(903\) −16.0000 −0.532447
\(904\) −6.00000 −0.199557
\(905\) 0 0
\(906\) 16.0000 0.531564
\(907\) 44.0000 1.46100 0.730498 0.682915i \(-0.239288\pi\)
0.730498 + 0.682915i \(0.239288\pi\)
\(908\) 18.0000 0.597351
\(909\) 0 0
\(910\) 0 0
\(911\) 48.0000 1.59031 0.795155 0.606406i \(-0.207389\pi\)
0.795155 + 0.606406i \(0.207389\pi\)
\(912\) −4.00000 −0.132453
\(913\) 0 0
\(914\) 10.0000 0.330771
\(915\) 0 0
\(916\) −4.00000 −0.132164
\(917\) 18.0000 0.594412
\(918\) −24.0000 −0.792118
\(919\) 56.0000 1.84727 0.923635 0.383274i \(-0.125203\pi\)
0.923635 + 0.383274i \(0.125203\pi\)
\(920\) 0 0
\(921\) −4.00000 −0.131804
\(922\) −12.0000 −0.395199
\(923\) 0 0
\(924\) 0 0
\(925\) −10.0000 −0.328798
\(926\) −32.0000 −1.05159
\(927\) −4.00000 −0.131377
\(928\) 6.00000 0.196960
\(929\) 6.00000 0.196854 0.0984268 0.995144i \(-0.468619\pi\)
0.0984268 + 0.995144i \(0.468619\pi\)
\(930\) 0 0
\(931\) 2.00000 0.0655474
\(932\) −6.00000 −0.196537
\(933\) 48.0000 1.57145
\(934\) 6.00000 0.196326
\(935\) 0 0
\(936\) 4.00000 0.130744
\(937\) 2.00000 0.0653372 0.0326686 0.999466i \(-0.489599\pi\)
0.0326686 + 0.999466i \(0.489599\pi\)
\(938\) 4.00000 0.130605
\(939\) 20.0000 0.652675
\(940\) 0 0
\(941\) −24.0000 −0.782378 −0.391189 0.920310i \(-0.627936\pi\)
−0.391189 + 0.920310i \(0.627936\pi\)
\(942\) −8.00000 −0.260654
\(943\) 0 0
\(944\) −6.00000 −0.195283
\(945\) 0 0
\(946\) 0 0
\(947\) 24.0000 0.779895 0.389948 0.920837i \(-0.372493\pi\)
0.389948 + 0.920837i \(0.372493\pi\)
\(948\) −16.0000 −0.519656
\(949\) −8.00000 −0.259691
\(950\) 10.0000 0.324443
\(951\) −12.0000 −0.389127
\(952\) −6.00000 −0.194461
\(953\) −54.0000 −1.74923 −0.874616 0.484817i \(-0.838886\pi\)
−0.874616 + 0.484817i \(0.838886\pi\)
\(954\) −6.00000 −0.194257
\(955\) 0 0
\(956\) 24.0000 0.776215
\(957\) 0 0
\(958\) 36.0000 1.16311
\(959\) 18.0000 0.581250
\(960\) 0 0
\(961\) −15.0000 −0.483871
\(962\) 8.00000 0.257930
\(963\) 12.0000 0.386695
\(964\) −10.0000 −0.322078
\(965\) 0 0
\(966\) 0 0
\(967\) 32.0000 1.02905 0.514525 0.857475i \(-0.327968\pi\)
0.514525 + 0.857475i \(0.327968\pi\)
\(968\) 11.0000 0.353553
\(969\) −24.0000 −0.770991
\(970\) 0 0
\(971\) −6.00000 −0.192549 −0.0962746 0.995355i \(-0.530693\pi\)
−0.0962746 + 0.995355i \(0.530693\pi\)
\(972\) 10.0000 0.320750
\(973\) 14.0000 0.448819
\(974\) 16.0000 0.512673
\(975\) −40.0000 −1.28103
\(976\) 8.00000 0.256074
\(977\) −6.00000 −0.191957 −0.0959785 0.995383i \(-0.530598\pi\)
−0.0959785 + 0.995383i \(0.530598\pi\)
\(978\) −32.0000 −1.02325
\(979\) 0 0
\(980\) 0 0
\(981\) 2.00000 0.0638551
\(982\) 12.0000 0.382935
\(983\) −36.0000 −1.14822 −0.574111 0.818778i \(-0.694652\pi\)
−0.574111 + 0.818778i \(0.694652\pi\)
\(984\) 12.0000 0.382546
\(985\) 0 0
\(986\) 36.0000 1.14647
\(987\) 24.0000 0.763928
\(988\) −8.00000 −0.254514
\(989\) 0 0
\(990\) 0 0
\(991\) −16.0000 −0.508257 −0.254128 0.967170i \(-0.581789\pi\)
−0.254128 + 0.967170i \(0.581789\pi\)
\(992\) 4.00000 0.127000
\(993\) −16.0000 −0.507745
\(994\) 0 0
\(995\) 0 0
\(996\) 12.0000 0.380235
\(997\) 8.00000 0.253363 0.126681 0.991943i \(-0.459567\pi\)
0.126681 + 0.991943i \(0.459567\pi\)
\(998\) 4.00000 0.126618
\(999\) 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 \(a_p\))