Properties

Label 53.2.a.a.1.1
Level 53
Weight 2
Character 53.1
Self dual Yes
Analytic conductor 0.423
Analytic rank 1
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 53 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 53.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(0.423207130713\)
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 \(\chi\) = 53.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(-3.00000 q^{3}\) \(-1.00000 q^{4}\) \(+3.00000 q^{6}\) \(-4.00000 q^{7}\) \(+3.00000 q^{8}\) \(+6.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(-3.00000 q^{3}\) \(-1.00000 q^{4}\) \(+3.00000 q^{6}\) \(-4.00000 q^{7}\) \(+3.00000 q^{8}\) \(+6.00000 q^{9}\) \(+3.00000 q^{12}\) \(-3.00000 q^{13}\) \(+4.00000 q^{14}\) \(-1.00000 q^{16}\) \(-3.00000 q^{17}\) \(-6.00000 q^{18}\) \(-5.00000 q^{19}\) \(+12.0000 q^{21}\) \(+7.00000 q^{23}\) \(-9.00000 q^{24}\) \(-5.00000 q^{25}\) \(+3.00000 q^{26}\) \(-9.00000 q^{27}\) \(+4.00000 q^{28}\) \(-7.00000 q^{29}\) \(+4.00000 q^{31}\) \(-5.00000 q^{32}\) \(+3.00000 q^{34}\) \(-6.00000 q^{36}\) \(+5.00000 q^{37}\) \(+5.00000 q^{38}\) \(+9.00000 q^{39}\) \(+6.00000 q^{41}\) \(-12.0000 q^{42}\) \(-2.00000 q^{43}\) \(-7.00000 q^{46}\) \(-2.00000 q^{47}\) \(+3.00000 q^{48}\) \(+9.00000 q^{49}\) \(+5.00000 q^{50}\) \(+9.00000 q^{51}\) \(+3.00000 q^{52}\) \(-1.00000 q^{53}\) \(+9.00000 q^{54}\) \(-12.0000 q^{56}\) \(+15.0000 q^{57}\) \(+7.00000 q^{58}\) \(-2.00000 q^{59}\) \(-8.00000 q^{61}\) \(-4.00000 q^{62}\) \(-24.0000 q^{63}\) \(+7.00000 q^{64}\) \(-12.0000 q^{67}\) \(+3.00000 q^{68}\) \(-21.0000 q^{69}\) \(+1.00000 q^{71}\) \(+18.0000 q^{72}\) \(-4.00000 q^{73}\) \(-5.00000 q^{74}\) \(+15.0000 q^{75}\) \(+5.00000 q^{76}\) \(-9.00000 q^{78}\) \(-1.00000 q^{79}\) \(+9.00000 q^{81}\) \(-6.00000 q^{82}\) \(-1.00000 q^{83}\) \(-12.0000 q^{84}\) \(+2.00000 q^{86}\) \(+21.0000 q^{87}\) \(-14.0000 q^{89}\) \(+12.0000 q^{91}\) \(-7.00000 q^{92}\) \(-12.0000 q^{93}\) \(+2.00000 q^{94}\) \(+15.0000 q^{96}\) \(+1.00000 q^{97}\) \(-9.00000 q^{98}\) \(+O(q^{100})\)

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 −0.353553 0.935414i \(-0.615027\pi\)
−0.353553 + 0.935414i \(0.615027\pi\)
\(3\) −3.00000 −1.73205 −0.866025 0.500000i \(-0.833333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(4\) −1.00000 −0.500000
\(5\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(6\) 3.00000 1.22474
\(7\) −4.00000 −1.51186 −0.755929 0.654654i \(-0.772814\pi\)
−0.755929 + 0.654654i \(0.772814\pi\)
\(8\) 3.00000 1.06066
\(9\) 6.00000 2.00000
\(10\) 0 0
\(11\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) 3.00000 0.866025
\(13\) −3.00000 −0.832050 −0.416025 0.909353i \(-0.636577\pi\)
−0.416025 + 0.909353i \(0.636577\pi\)
\(14\) 4.00000 1.06904
\(15\) 0 0
\(16\) −1.00000 −0.250000
\(17\) −3.00000 −0.727607 −0.363803 0.931476i \(-0.618522\pi\)
−0.363803 + 0.931476i \(0.618522\pi\)
\(18\) −6.00000 −1.41421
\(19\) −5.00000 −1.14708 −0.573539 0.819178i \(-0.694430\pi\)
−0.573539 + 0.819178i \(0.694430\pi\)
\(20\) 0 0
\(21\) 12.0000 2.61861
\(22\) 0 0
\(23\) 7.00000 1.45960 0.729800 0.683660i \(-0.239613\pi\)
0.729800 + 0.683660i \(0.239613\pi\)
\(24\) −9.00000 −1.83712
\(25\) −5.00000 −1.00000
\(26\) 3.00000 0.588348
\(27\) −9.00000 −1.73205
\(28\) 4.00000 0.755929
\(29\) −7.00000 −1.29987 −0.649934 0.759991i \(-0.725203\pi\)
−0.649934 + 0.759991i \(0.725203\pi\)
\(30\) 0 0
\(31\) 4.00000 0.718421 0.359211 0.933257i \(-0.383046\pi\)
0.359211 + 0.933257i \(0.383046\pi\)
\(32\) −5.00000 −0.883883
\(33\) 0 0
\(34\) 3.00000 0.514496
\(35\) 0 0
\(36\) −6.00000 −1.00000
\(37\) 5.00000 0.821995 0.410997 0.911636i \(-0.365181\pi\)
0.410997 + 0.911636i \(0.365181\pi\)
\(38\) 5.00000 0.811107
\(39\) 9.00000 1.44115
\(40\) 0 0
\(41\) 6.00000 0.937043 0.468521 0.883452i \(-0.344787\pi\)
0.468521 + 0.883452i \(0.344787\pi\)
\(42\) −12.0000 −1.85164
\(43\) −2.00000 −0.304997 −0.152499 0.988304i \(-0.548732\pi\)
−0.152499 + 0.988304i \(0.548732\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) −7.00000 −1.03209
\(47\) −2.00000 −0.291730 −0.145865 0.989305i \(-0.546597\pi\)
−0.145865 + 0.989305i \(0.546597\pi\)
\(48\) 3.00000 0.433013
\(49\) 9.00000 1.28571
\(50\) 5.00000 0.707107
\(51\) 9.00000 1.26025
\(52\) 3.00000 0.416025
\(53\) −1.00000 −0.137361
\(54\) 9.00000 1.22474
\(55\) 0 0
\(56\) −12.0000 −1.60357
\(57\) 15.0000 1.98680
\(58\) 7.00000 0.919145
\(59\) −2.00000 −0.260378 −0.130189 0.991489i \(-0.541558\pi\)
−0.130189 + 0.991489i \(0.541558\pi\)
\(60\) 0 0
\(61\) −8.00000 −1.02430 −0.512148 0.858898i \(-0.671150\pi\)
−0.512148 + 0.858898i \(0.671150\pi\)
\(62\) −4.00000 −0.508001
\(63\) −24.0000 −3.02372
\(64\) 7.00000 0.875000
\(65\) 0 0
\(66\) 0 0
\(67\) −12.0000 −1.46603 −0.733017 0.680211i \(-0.761888\pi\)
−0.733017 + 0.680211i \(0.761888\pi\)
\(68\) 3.00000 0.363803
\(69\) −21.0000 −2.52810
\(70\) 0 0
\(71\) 1.00000 0.118678 0.0593391 0.998238i \(-0.481101\pi\)
0.0593391 + 0.998238i \(0.481101\pi\)
\(72\) 18.0000 2.12132
\(73\) −4.00000 −0.468165 −0.234082 0.972217i \(-0.575209\pi\)
−0.234082 + 0.972217i \(0.575209\pi\)
\(74\) −5.00000 −0.581238
\(75\) 15.0000 1.73205
\(76\) 5.00000 0.573539
\(77\) 0 0
\(78\) −9.00000 −1.01905
\(79\) −1.00000 −0.112509 −0.0562544 0.998416i \(-0.517916\pi\)
−0.0562544 + 0.998416i \(0.517916\pi\)
\(80\) 0 0
\(81\) 9.00000 1.00000
\(82\) −6.00000 −0.662589
\(83\) −1.00000 −0.109764 −0.0548821 0.998493i \(-0.517478\pi\)
−0.0548821 + 0.998493i \(0.517478\pi\)
\(84\) −12.0000 −1.30931
\(85\) 0 0
\(86\) 2.00000 0.215666
\(87\) 21.0000 2.25144
\(88\) 0 0
\(89\) −14.0000 −1.48400 −0.741999 0.670402i \(-0.766122\pi\)
−0.741999 + 0.670402i \(0.766122\pi\)
\(90\) 0 0
\(91\) 12.0000 1.25794
\(92\) −7.00000 −0.729800
\(93\) −12.0000 −1.24434
\(94\) 2.00000 0.206284
\(95\) 0 0
\(96\) 15.0000 1.53093
\(97\) 1.00000 0.101535 0.0507673 0.998711i \(-0.483833\pi\)
0.0507673 + 0.998711i \(0.483833\pi\)
\(98\) −9.00000 −0.909137
\(99\) 0 0
\(100\) 5.00000 0.500000
\(101\) −2.00000 −0.199007 −0.0995037 0.995037i \(-0.531726\pi\)
−0.0995037 + 0.995037i \(0.531726\pi\)
\(102\) −9.00000 −0.891133
\(103\) −1.00000 −0.0985329 −0.0492665 0.998786i \(-0.515688\pi\)
−0.0492665 + 0.998786i \(0.515688\pi\)
\(104\) −9.00000 −0.882523
\(105\) 0 0
\(106\) 1.00000 0.0971286
\(107\) 6.00000 0.580042 0.290021 0.957020i \(-0.406338\pi\)
0.290021 + 0.957020i \(0.406338\pi\)
\(108\) 9.00000 0.866025
\(109\) 16.0000 1.53252 0.766261 0.642529i \(-0.222115\pi\)
0.766261 + 0.642529i \(0.222115\pi\)
\(110\) 0 0
\(111\) −15.0000 −1.42374
\(112\) 4.00000 0.377964
\(113\) 15.0000 1.41108 0.705541 0.708669i \(-0.250704\pi\)
0.705541 + 0.708669i \(0.250704\pi\)
\(114\) −15.0000 −1.40488
\(115\) 0 0
\(116\) 7.00000 0.649934
\(117\) −18.0000 −1.66410
\(118\) 2.00000 0.184115
\(119\) 12.0000 1.10004
\(120\) 0 0
\(121\) −11.0000 −1.00000
\(122\) 8.00000 0.724286
\(123\) −18.0000 −1.62301
\(124\) −4.00000 −0.359211
\(125\) 0 0
\(126\) 24.0000 2.13809
\(127\) 13.0000 1.15356 0.576782 0.816898i \(-0.304308\pi\)
0.576782 + 0.816898i \(0.304308\pi\)
\(128\) 3.00000 0.265165
\(129\) 6.00000 0.528271
\(130\) 0 0
\(131\) −2.00000 −0.174741 −0.0873704 0.996176i \(-0.527846\pi\)
−0.0873704 + 0.996176i \(0.527846\pi\)
\(132\) 0 0
\(133\) 20.0000 1.73422
\(134\) 12.0000 1.03664
\(135\) 0 0
\(136\) −9.00000 −0.771744
\(137\) 12.0000 1.02523 0.512615 0.858619i \(-0.328677\pi\)
0.512615 + 0.858619i \(0.328677\pi\)
\(138\) 21.0000 1.78764
\(139\) −20.0000 −1.69638 −0.848189 0.529694i \(-0.822307\pi\)
−0.848189 + 0.529694i \(0.822307\pi\)
\(140\) 0 0
\(141\) 6.00000 0.505291
\(142\) −1.00000 −0.0839181
\(143\) 0 0
\(144\) −6.00000 −0.500000
\(145\) 0 0
\(146\) 4.00000 0.331042
\(147\) −27.0000 −2.22692
\(148\) −5.00000 −0.410997
\(149\) −5.00000 −0.409616 −0.204808 0.978802i \(-0.565657\pi\)
−0.204808 + 0.978802i \(0.565657\pi\)
\(150\) −15.0000 −1.22474
\(151\) −3.00000 −0.244137 −0.122068 0.992522i \(-0.538953\pi\)
−0.122068 + 0.992522i \(0.538953\pi\)
\(152\) −15.0000 −1.21666
\(153\) −18.0000 −1.45521
\(154\) 0 0
\(155\) 0 0
\(156\) −9.00000 −0.720577
\(157\) −4.00000 −0.319235 −0.159617 0.987179i \(-0.551026\pi\)
−0.159617 + 0.987179i \(0.551026\pi\)
\(158\) 1.00000 0.0795557
\(159\) 3.00000 0.237915
\(160\) 0 0
\(161\) −28.0000 −2.20671
\(162\) −9.00000 −0.707107
\(163\) −6.00000 −0.469956 −0.234978 0.972001i \(-0.575502\pi\)
−0.234978 + 0.972001i \(0.575502\pi\)
\(164\) −6.00000 −0.468521
\(165\) 0 0
\(166\) 1.00000 0.0776151
\(167\) 21.0000 1.62503 0.812514 0.582941i \(-0.198098\pi\)
0.812514 + 0.582941i \(0.198098\pi\)
\(168\) 36.0000 2.77746
\(169\) −4.00000 −0.307692
\(170\) 0 0
\(171\) −30.0000 −2.29416
\(172\) 2.00000 0.152499
\(173\) 10.0000 0.760286 0.380143 0.924928i \(-0.375875\pi\)
0.380143 + 0.924928i \(0.375875\pi\)
\(174\) −21.0000 −1.59201
\(175\) 20.0000 1.51186
\(176\) 0 0
\(177\) 6.00000 0.450988
\(178\) 14.0000 1.04934
\(179\) 11.0000 0.822179 0.411089 0.911595i \(-0.365148\pi\)
0.411089 + 0.911595i \(0.365148\pi\)
\(180\) 0 0
\(181\) −2.00000 −0.148659 −0.0743294 0.997234i \(-0.523682\pi\)
−0.0743294 + 0.997234i \(0.523682\pi\)
\(182\) −12.0000 −0.889499
\(183\) 24.0000 1.77413
\(184\) 21.0000 1.54814
\(185\) 0 0
\(186\) 12.0000 0.879883
\(187\) 0 0
\(188\) 2.00000 0.145865
\(189\) 36.0000 2.61861
\(190\) 0 0
\(191\) −21.0000 −1.51951 −0.759753 0.650211i \(-0.774680\pi\)
−0.759753 + 0.650211i \(0.774680\pi\)
\(192\) −21.0000 −1.51554
\(193\) −16.0000 −1.15171 −0.575853 0.817554i \(-0.695330\pi\)
−0.575853 + 0.817554i \(0.695330\pi\)
\(194\) −1.00000 −0.0717958
\(195\) 0 0
\(196\) −9.00000 −0.642857
\(197\) −18.0000 −1.28245 −0.641223 0.767354i \(-0.721573\pi\)
−0.641223 + 0.767354i \(0.721573\pi\)
\(198\) 0 0
\(199\) 4.00000 0.283552 0.141776 0.989899i \(-0.454719\pi\)
0.141776 + 0.989899i \(0.454719\pi\)
\(200\) −15.0000 −1.06066
\(201\) 36.0000 2.53924
\(202\) 2.00000 0.140720
\(203\) 28.0000 1.96521
\(204\) −9.00000 −0.630126
\(205\) 0 0
\(206\) 1.00000 0.0696733
\(207\) 42.0000 2.91920
\(208\) 3.00000 0.208013
\(209\) 0 0
\(210\) 0 0
\(211\) −2.00000 −0.137686 −0.0688428 0.997628i \(-0.521931\pi\)
−0.0688428 + 0.997628i \(0.521931\pi\)
\(212\) 1.00000 0.0686803
\(213\) −3.00000 −0.205557
\(214\) −6.00000 −0.410152
\(215\) 0 0
\(216\) −27.0000 −1.83712
\(217\) −16.0000 −1.08615
\(218\) −16.0000 −1.08366
\(219\) 12.0000 0.810885
\(220\) 0 0
\(221\) 9.00000 0.605406
\(222\) 15.0000 1.00673
\(223\) −14.0000 −0.937509 −0.468755 0.883328i \(-0.655297\pi\)
−0.468755 + 0.883328i \(0.655297\pi\)
\(224\) 20.0000 1.33631
\(225\) −30.0000 −2.00000
\(226\) −15.0000 −0.997785
\(227\) 6.00000 0.398234 0.199117 0.979976i \(-0.436193\pi\)
0.199117 + 0.979976i \(0.436193\pi\)
\(228\) −15.0000 −0.993399
\(229\) 21.0000 1.38772 0.693860 0.720110i \(-0.255909\pi\)
0.693860 + 0.720110i \(0.255909\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −21.0000 −1.37872
\(233\) −8.00000 −0.524097 −0.262049 0.965055i \(-0.584398\pi\)
−0.262049 + 0.965055i \(0.584398\pi\)
\(234\) 18.0000 1.17670
\(235\) 0 0
\(236\) 2.00000 0.130189
\(237\) 3.00000 0.194871
\(238\) −12.0000 −0.777844
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) 0 0
\(241\) −11.0000 −0.708572 −0.354286 0.935137i \(-0.615276\pi\)
−0.354286 + 0.935137i \(0.615276\pi\)
\(242\) 11.0000 0.707107
\(243\) 0 0
\(244\) 8.00000 0.512148
\(245\) 0 0
\(246\) 18.0000 1.14764
\(247\) 15.0000 0.954427
\(248\) 12.0000 0.762001
\(249\) 3.00000 0.190117
\(250\) 0 0
\(251\) 20.0000 1.26239 0.631194 0.775625i \(-0.282565\pi\)
0.631194 + 0.775625i \(0.282565\pi\)
\(252\) 24.0000 1.51186
\(253\) 0 0
\(254\) −13.0000 −0.815693
\(255\) 0 0
\(256\) −17.0000 −1.06250
\(257\) −28.0000 −1.74659 −0.873296 0.487190i \(-0.838022\pi\)
−0.873296 + 0.487190i \(0.838022\pi\)
\(258\) −6.00000 −0.373544
\(259\) −20.0000 −1.24274
\(260\) 0 0
\(261\) −42.0000 −2.59973
\(262\) 2.00000 0.123560
\(263\) −28.0000 −1.72655 −0.863277 0.504730i \(-0.831592\pi\)
−0.863277 + 0.504730i \(0.831592\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −20.0000 −1.22628
\(267\) 42.0000 2.57036
\(268\) 12.0000 0.733017
\(269\) 9.00000 0.548740 0.274370 0.961624i \(-0.411531\pi\)
0.274370 + 0.961624i \(0.411531\pi\)
\(270\) 0 0
\(271\) −14.0000 −0.850439 −0.425220 0.905090i \(-0.639803\pi\)
−0.425220 + 0.905090i \(0.639803\pi\)
\(272\) 3.00000 0.181902
\(273\) −36.0000 −2.17882
\(274\) −12.0000 −0.724947
\(275\) 0 0
\(276\) 21.0000 1.26405
\(277\) −8.00000 −0.480673 −0.240337 0.970690i \(-0.577258\pi\)
−0.240337 + 0.970690i \(0.577258\pi\)
\(278\) 20.0000 1.19952
\(279\) 24.0000 1.43684
\(280\) 0 0
\(281\) 17.0000 1.01413 0.507067 0.861906i \(-0.330729\pi\)
0.507067 + 0.861906i \(0.330729\pi\)
\(282\) −6.00000 −0.357295
\(283\) −9.00000 −0.534994 −0.267497 0.963559i \(-0.586197\pi\)
−0.267497 + 0.963559i \(0.586197\pi\)
\(284\) −1.00000 −0.0593391
\(285\) 0 0
\(286\) 0 0
\(287\) −24.0000 −1.41668
\(288\) −30.0000 −1.76777
\(289\) −8.00000 −0.470588
\(290\) 0 0
\(291\) −3.00000 −0.175863
\(292\) 4.00000 0.234082
\(293\) 26.0000 1.51894 0.759468 0.650545i \(-0.225459\pi\)
0.759468 + 0.650545i \(0.225459\pi\)
\(294\) 27.0000 1.57467
\(295\) 0 0
\(296\) 15.0000 0.871857
\(297\) 0 0
\(298\) 5.00000 0.289642
\(299\) −21.0000 −1.21446
\(300\) −15.0000 −0.866025
\(301\) 8.00000 0.461112
\(302\) 3.00000 0.172631
\(303\) 6.00000 0.344691
\(304\) 5.00000 0.286770
\(305\) 0 0
\(306\) 18.0000 1.02899
\(307\) −16.0000 −0.913168 −0.456584 0.889680i \(-0.650927\pi\)
−0.456584 + 0.889680i \(0.650927\pi\)
\(308\) 0 0
\(309\) 3.00000 0.170664
\(310\) 0 0
\(311\) 16.0000 0.907277 0.453638 0.891186i \(-0.350126\pi\)
0.453638 + 0.891186i \(0.350126\pi\)
\(312\) 27.0000 1.52857
\(313\) −6.00000 −0.339140 −0.169570 0.985518i \(-0.554238\pi\)
−0.169570 + 0.985518i \(0.554238\pi\)
\(314\) 4.00000 0.225733
\(315\) 0 0
\(316\) 1.00000 0.0562544
\(317\) 3.00000 0.168497 0.0842484 0.996445i \(-0.473151\pi\)
0.0842484 + 0.996445i \(0.473151\pi\)
\(318\) −3.00000 −0.168232
\(319\) 0 0
\(320\) 0 0
\(321\) −18.0000 −1.00466
\(322\) 28.0000 1.56038
\(323\) 15.0000 0.834622
\(324\) −9.00000 −0.500000
\(325\) 15.0000 0.832050
\(326\) 6.00000 0.332309
\(327\) −48.0000 −2.65441
\(328\) 18.0000 0.993884
\(329\) 8.00000 0.441054
\(330\) 0 0
\(331\) 28.0000 1.53902 0.769510 0.638635i \(-0.220501\pi\)
0.769510 + 0.638635i \(0.220501\pi\)
\(332\) 1.00000 0.0548821
\(333\) 30.0000 1.64399
\(334\) −21.0000 −1.14907
\(335\) 0 0
\(336\) −12.0000 −0.654654
\(337\) 10.0000 0.544735 0.272367 0.962193i \(-0.412193\pi\)
0.272367 + 0.962193i \(0.412193\pi\)
\(338\) 4.00000 0.217571
\(339\) −45.0000 −2.44406
\(340\) 0 0
\(341\) 0 0
\(342\) 30.0000 1.62221
\(343\) −8.00000 −0.431959
\(344\) −6.00000 −0.323498
\(345\) 0 0
\(346\) −10.0000 −0.537603
\(347\) −30.0000 −1.61048 −0.805242 0.592946i \(-0.797965\pi\)
−0.805242 + 0.592946i \(0.797965\pi\)
\(348\) −21.0000 −1.12572
\(349\) 24.0000 1.28469 0.642345 0.766415i \(-0.277962\pi\)
0.642345 + 0.766415i \(0.277962\pi\)
\(350\) −20.0000 −1.06904
\(351\) 27.0000 1.44115
\(352\) 0 0
\(353\) −18.0000 −0.958043 −0.479022 0.877803i \(-0.659008\pi\)
−0.479022 + 0.877803i \(0.659008\pi\)
\(354\) −6.00000 −0.318896
\(355\) 0 0
\(356\) 14.0000 0.741999
\(357\) −36.0000 −1.90532
\(358\) −11.0000 −0.581368
\(359\) 9.00000 0.475002 0.237501 0.971387i \(-0.423672\pi\)
0.237501 + 0.971387i \(0.423672\pi\)
\(360\) 0 0
\(361\) 6.00000 0.315789
\(362\) 2.00000 0.105118
\(363\) 33.0000 1.73205
\(364\) −12.0000 −0.628971
\(365\) 0 0
\(366\) −24.0000 −1.25450
\(367\) 22.0000 1.14839 0.574195 0.818718i \(-0.305315\pi\)
0.574195 + 0.818718i \(0.305315\pi\)
\(368\) −7.00000 −0.364900
\(369\) 36.0000 1.87409
\(370\) 0 0
\(371\) 4.00000 0.207670
\(372\) 12.0000 0.622171
\(373\) −10.0000 −0.517780 −0.258890 0.965907i \(-0.583357\pi\)
−0.258890 + 0.965907i \(0.583357\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −6.00000 −0.309426
\(377\) 21.0000 1.08156
\(378\) −36.0000 −1.85164
\(379\) 11.0000 0.565032 0.282516 0.959263i \(-0.408831\pi\)
0.282516 + 0.959263i \(0.408831\pi\)
\(380\) 0 0
\(381\) −39.0000 −1.99803
\(382\) 21.0000 1.07445
\(383\) 16.0000 0.817562 0.408781 0.912633i \(-0.365954\pi\)
0.408781 + 0.912633i \(0.365954\pi\)
\(384\) −9.00000 −0.459279
\(385\) 0 0
\(386\) 16.0000 0.814379
\(387\) −12.0000 −0.609994
\(388\) −1.00000 −0.0507673
\(389\) 12.0000 0.608424 0.304212 0.952604i \(-0.401607\pi\)
0.304212 + 0.952604i \(0.401607\pi\)
\(390\) 0 0
\(391\) −21.0000 −1.06202
\(392\) 27.0000 1.36371
\(393\) 6.00000 0.302660
\(394\) 18.0000 0.906827
\(395\) 0 0
\(396\) 0 0
\(397\) 18.0000 0.903394 0.451697 0.892171i \(-0.350819\pi\)
0.451697 + 0.892171i \(0.350819\pi\)
\(398\) −4.00000 −0.200502
\(399\) −60.0000 −3.00376
\(400\) 5.00000 0.250000
\(401\) −32.0000 −1.59800 −0.799002 0.601329i \(-0.794638\pi\)
−0.799002 + 0.601329i \(0.794638\pi\)
\(402\) −36.0000 −1.79552
\(403\) −12.0000 −0.597763
\(404\) 2.00000 0.0995037
\(405\) 0 0
\(406\) −28.0000 −1.38962
\(407\) 0 0
\(408\) 27.0000 1.33670
\(409\) 19.0000 0.939490 0.469745 0.882802i \(-0.344346\pi\)
0.469745 + 0.882802i \(0.344346\pi\)
\(410\) 0 0
\(411\) −36.0000 −1.77575
\(412\) 1.00000 0.0492665
\(413\) 8.00000 0.393654
\(414\) −42.0000 −2.06419
\(415\) 0 0
\(416\) 15.0000 0.735436
\(417\) 60.0000 2.93821
\(418\) 0 0
\(419\) −12.0000 −0.586238 −0.293119 0.956076i \(-0.594693\pi\)
−0.293119 + 0.956076i \(0.594693\pi\)
\(420\) 0 0
\(421\) 14.0000 0.682318 0.341159 0.940006i \(-0.389181\pi\)
0.341159 + 0.940006i \(0.389181\pi\)
\(422\) 2.00000 0.0973585
\(423\) −12.0000 −0.583460
\(424\) −3.00000 −0.145693
\(425\) 15.0000 0.727607
\(426\) 3.00000 0.145350
\(427\) 32.0000 1.54859
\(428\) −6.00000 −0.290021
\(429\) 0 0
\(430\) 0 0
\(431\) −36.0000 −1.73406 −0.867029 0.498257i \(-0.833974\pi\)
−0.867029 + 0.498257i \(0.833974\pi\)
\(432\) 9.00000 0.433013
\(433\) −7.00000 −0.336399 −0.168199 0.985753i \(-0.553795\pi\)
−0.168199 + 0.985753i \(0.553795\pi\)
\(434\) 16.0000 0.768025
\(435\) 0 0
\(436\) −16.0000 −0.766261
\(437\) −35.0000 −1.67428
\(438\) −12.0000 −0.573382
\(439\) −34.0000 −1.62273 −0.811366 0.584539i \(-0.801275\pi\)
−0.811366 + 0.584539i \(0.801275\pi\)
\(440\) 0 0
\(441\) 54.0000 2.57143
\(442\) −9.00000 −0.428086
\(443\) −33.0000 −1.56788 −0.783939 0.620838i \(-0.786792\pi\)
−0.783939 + 0.620838i \(0.786792\pi\)
\(444\) 15.0000 0.711868
\(445\) 0 0
\(446\) 14.0000 0.662919
\(447\) 15.0000 0.709476
\(448\) −28.0000 −1.32288
\(449\) −11.0000 −0.519122 −0.259561 0.965727i \(-0.583578\pi\)
−0.259561 + 0.965727i \(0.583578\pi\)
\(450\) 30.0000 1.41421
\(451\) 0 0
\(452\) −15.0000 −0.705541
\(453\) 9.00000 0.422857
\(454\) −6.00000 −0.281594
\(455\) 0 0
\(456\) 45.0000 2.10732
\(457\) 38.0000 1.77757 0.888783 0.458329i \(-0.151552\pi\)
0.888783 + 0.458329i \(0.151552\pi\)
\(458\) −21.0000 −0.981266
\(459\) 27.0000 1.26025
\(460\) 0 0
\(461\) −9.00000 −0.419172 −0.209586 0.977790i \(-0.567212\pi\)
−0.209586 + 0.977790i \(0.567212\pi\)
\(462\) 0 0
\(463\) −23.0000 −1.06890 −0.534450 0.845200i \(-0.679481\pi\)
−0.534450 + 0.845200i \(0.679481\pi\)
\(464\) 7.00000 0.324967
\(465\) 0 0
\(466\) 8.00000 0.370593
\(467\) −28.0000 −1.29569 −0.647843 0.761774i \(-0.724329\pi\)
−0.647843 + 0.761774i \(0.724329\pi\)
\(468\) 18.0000 0.832050
\(469\) 48.0000 2.21643
\(470\) 0 0
\(471\) 12.0000 0.552931
\(472\) −6.00000 −0.276172
\(473\) 0 0
\(474\) −3.00000 −0.137795
\(475\) 25.0000 1.14708
\(476\) −12.0000 −0.550019
\(477\) −6.00000 −0.274721
\(478\) 0 0
\(479\) 3.00000 0.137073 0.0685367 0.997649i \(-0.478167\pi\)
0.0685367 + 0.997649i \(0.478167\pi\)
\(480\) 0 0
\(481\) −15.0000 −0.683941
\(482\) 11.0000 0.501036
\(483\) 84.0000 3.82213
\(484\) 11.0000 0.500000
\(485\) 0 0
\(486\) 0 0
\(487\) 20.0000 0.906287 0.453143 0.891438i \(-0.350303\pi\)
0.453143 + 0.891438i \(0.350303\pi\)
\(488\) −24.0000 −1.08643
\(489\) 18.0000 0.813988
\(490\) 0 0
\(491\) 27.0000 1.21849 0.609246 0.792981i \(-0.291472\pi\)
0.609246 + 0.792981i \(0.291472\pi\)
\(492\) 18.0000 0.811503
\(493\) 21.0000 0.945792
\(494\) −15.0000 −0.674882
\(495\) 0 0
\(496\) −4.00000 −0.179605
\(497\) −4.00000 −0.179425
\(498\) −3.00000 −0.134433
\(499\) −23.0000 −1.02962 −0.514811 0.857304i \(-0.672138\pi\)
−0.514811 + 0.857304i \(0.672138\pi\)
\(500\) 0 0
\(501\) −63.0000 −2.81463
\(502\) −20.0000 −0.892644
\(503\) 16.0000 0.713405 0.356702 0.934218i \(-0.383901\pi\)
0.356702 + 0.934218i \(0.383901\pi\)
\(504\) −72.0000 −3.20713
\(505\) 0 0
\(506\) 0 0
\(507\) 12.0000 0.532939
\(508\) −13.0000 −0.576782
\(509\) 2.00000 0.0886484 0.0443242 0.999017i \(-0.485887\pi\)
0.0443242 + 0.999017i \(0.485887\pi\)
\(510\) 0 0
\(511\) 16.0000 0.707798
\(512\) 11.0000 0.486136
\(513\) 45.0000 1.98680
\(514\) 28.0000 1.23503
\(515\) 0 0
\(516\) −6.00000 −0.264135
\(517\) 0 0
\(518\) 20.0000 0.878750
\(519\) −30.0000 −1.31685
\(520\) 0 0
\(521\) −45.0000 −1.97149 −0.985743 0.168259i \(-0.946186\pi\)
−0.985743 + 0.168259i \(0.946186\pi\)
\(522\) 42.0000 1.83829
\(523\) −42.0000 −1.83653 −0.918266 0.395964i \(-0.870410\pi\)
−0.918266 + 0.395964i \(0.870410\pi\)
\(524\) 2.00000 0.0873704
\(525\) −60.0000 −2.61861
\(526\) 28.0000 1.22086
\(527\) −12.0000 −0.522728
\(528\) 0 0
\(529\) 26.0000 1.13043
\(530\) 0 0
\(531\) −12.0000 −0.520756
\(532\) −20.0000 −0.867110
\(533\) −18.0000 −0.779667
\(534\) −42.0000 −1.81752
\(535\) 0 0
\(536\) −36.0000 −1.55496
\(537\) −33.0000 −1.42406
\(538\) −9.00000 −0.388018
\(539\) 0 0
\(540\) 0 0
\(541\) 22.0000 0.945854 0.472927 0.881102i \(-0.343197\pi\)
0.472927 + 0.881102i \(0.343197\pi\)
\(542\) 14.0000 0.601351
\(543\) 6.00000 0.257485
\(544\) 15.0000 0.643120
\(545\) 0 0
\(546\) 36.0000 1.54066
\(547\) −38.0000 −1.62476 −0.812381 0.583127i \(-0.801829\pi\)
−0.812381 + 0.583127i \(0.801829\pi\)
\(548\) −12.0000 −0.512615
\(549\) −48.0000 −2.04859
\(550\) 0 0
\(551\) 35.0000 1.49105
\(552\) −63.0000 −2.68146
\(553\) 4.00000 0.170097
\(554\) 8.00000 0.339887
\(555\) 0 0
\(556\) 20.0000 0.848189
\(557\) 14.0000 0.593199 0.296600 0.955002i \(-0.404147\pi\)
0.296600 + 0.955002i \(0.404147\pi\)
\(558\) −24.0000 −1.01600
\(559\) 6.00000 0.253773
\(560\) 0 0
\(561\) 0 0
\(562\) −17.0000 −0.717102
\(563\) −1.00000 −0.0421450 −0.0210725 0.999778i \(-0.506708\pi\)
−0.0210725 + 0.999778i \(0.506708\pi\)
\(564\) −6.00000 −0.252646
\(565\) 0 0
\(566\) 9.00000 0.378298
\(567\) −36.0000 −1.51186
\(568\) 3.00000 0.125877
\(569\) 24.0000 1.00613 0.503066 0.864248i \(-0.332205\pi\)
0.503066 + 0.864248i \(0.332205\pi\)
\(570\) 0 0
\(571\) −4.00000 −0.167395 −0.0836974 0.996491i \(-0.526673\pi\)
−0.0836974 + 0.996491i \(0.526673\pi\)
\(572\) 0 0
\(573\) 63.0000 2.63186
\(574\) 24.0000 1.00174
\(575\) −35.0000 −1.45960
\(576\) 42.0000 1.75000
\(577\) 10.0000 0.416305 0.208153 0.978096i \(-0.433255\pi\)
0.208153 + 0.978096i \(0.433255\pi\)
\(578\) 8.00000 0.332756
\(579\) 48.0000 1.99481
\(580\) 0 0
\(581\) 4.00000 0.165948
\(582\) 3.00000 0.124354
\(583\) 0 0
\(584\) −12.0000 −0.496564
\(585\) 0 0
\(586\) −26.0000 −1.07405
\(587\) 28.0000 1.15568 0.577842 0.816149i \(-0.303895\pi\)
0.577842 + 0.816149i \(0.303895\pi\)
\(588\) 27.0000 1.11346
\(589\) −20.0000 −0.824086
\(590\) 0 0
\(591\) 54.0000 2.22126
\(592\) −5.00000 −0.205499
\(593\) 25.0000 1.02663 0.513313 0.858201i \(-0.328418\pi\)
0.513313 + 0.858201i \(0.328418\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 5.00000 0.204808
\(597\) −12.0000 −0.491127
\(598\) 21.0000 0.858754
\(599\) −30.0000 −1.22577 −0.612883 0.790173i \(-0.709990\pi\)
−0.612883 + 0.790173i \(0.709990\pi\)
\(600\) 45.0000 1.83712
\(601\) 22.0000 0.897399 0.448699 0.893683i \(-0.351887\pi\)
0.448699 + 0.893683i \(0.351887\pi\)
\(602\) −8.00000 −0.326056
\(603\) −72.0000 −2.93207
\(604\) 3.00000 0.122068
\(605\) 0 0
\(606\) −6.00000 −0.243733
\(607\) −8.00000 −0.324710 −0.162355 0.986732i \(-0.551909\pi\)
−0.162355 + 0.986732i \(0.551909\pi\)
\(608\) 25.0000 1.01388
\(609\) −84.0000 −3.40385
\(610\) 0 0
\(611\) 6.00000 0.242734
\(612\) 18.0000 0.727607
\(613\) −16.0000 −0.646234 −0.323117 0.946359i \(-0.604731\pi\)
−0.323117 + 0.946359i \(0.604731\pi\)
\(614\) 16.0000 0.645707
\(615\) 0 0
\(616\) 0 0
\(617\) −42.0000 −1.69086 −0.845428 0.534089i \(-0.820655\pi\)
−0.845428 + 0.534089i \(0.820655\pi\)
\(618\) −3.00000 −0.120678
\(619\) 16.0000 0.643094 0.321547 0.946894i \(-0.395797\pi\)
0.321547 + 0.946894i \(0.395797\pi\)
\(620\) 0 0
\(621\) −63.0000 −2.52810
\(622\) −16.0000 −0.641542
\(623\) 56.0000 2.24359
\(624\) −9.00000 −0.360288
\(625\) 25.0000 1.00000
\(626\) 6.00000 0.239808
\(627\) 0 0
\(628\) 4.00000 0.159617
\(629\) −15.0000 −0.598089
\(630\) 0 0
\(631\) 7.00000 0.278666 0.139333 0.990246i \(-0.455504\pi\)
0.139333 + 0.990246i \(0.455504\pi\)
\(632\) −3.00000 −0.119334
\(633\) 6.00000 0.238479
\(634\) −3.00000 −0.119145
\(635\) 0 0
\(636\) −3.00000 −0.118958
\(637\) −27.0000 −1.06978
\(638\) 0 0
\(639\) 6.00000 0.237356
\(640\) 0 0
\(641\) 46.0000 1.81689 0.908445 0.418004i \(-0.137270\pi\)
0.908445 + 0.418004i \(0.137270\pi\)
\(642\) 18.0000 0.710403
\(643\) −8.00000 −0.315489 −0.157745 0.987480i \(-0.550422\pi\)
−0.157745 + 0.987480i \(0.550422\pi\)
\(644\) 28.0000 1.10335
\(645\) 0 0
\(646\) −15.0000 −0.590167
\(647\) 38.0000 1.49393 0.746967 0.664861i \(-0.231509\pi\)
0.746967 + 0.664861i \(0.231509\pi\)
\(648\) 27.0000 1.06066
\(649\) 0 0
\(650\) −15.0000 −0.588348
\(651\) 48.0000 1.88127
\(652\) 6.00000 0.234978
\(653\) −38.0000 −1.48705 −0.743527 0.668705i \(-0.766849\pi\)
−0.743527 + 0.668705i \(0.766849\pi\)
\(654\) 48.0000 1.87695
\(655\) 0 0
\(656\) −6.00000 −0.234261
\(657\) −24.0000 −0.936329
\(658\) −8.00000 −0.311872
\(659\) 12.0000 0.467454 0.233727 0.972302i \(-0.424908\pi\)
0.233727 + 0.972302i \(0.424908\pi\)
\(660\) 0 0
\(661\) −1.00000 −0.0388955 −0.0194477 0.999811i \(-0.506191\pi\)
−0.0194477 + 0.999811i \(0.506191\pi\)
\(662\) −28.0000 −1.08825
\(663\) −27.0000 −1.04859
\(664\) −3.00000 −0.116423
\(665\) 0 0
\(666\) −30.0000 −1.16248
\(667\) −49.0000 −1.89729
\(668\) −21.0000 −0.812514
\(669\) 42.0000 1.62381
\(670\) 0 0
\(671\) 0 0
\(672\) −60.0000 −2.31455
\(673\) −10.0000 −0.385472 −0.192736 0.981251i \(-0.561736\pi\)
−0.192736 + 0.981251i \(0.561736\pi\)
\(674\) −10.0000 −0.385186
\(675\) 45.0000 1.73205
\(676\) 4.00000 0.153846
\(677\) 40.0000 1.53732 0.768662 0.639655i \(-0.220923\pi\)
0.768662 + 0.639655i \(0.220923\pi\)
\(678\) 45.0000 1.72821
\(679\) −4.00000 −0.153506
\(680\) 0 0
\(681\) −18.0000 −0.689761
\(682\) 0 0
\(683\) 2.00000 0.0765279 0.0382639 0.999268i \(-0.487817\pi\)
0.0382639 + 0.999268i \(0.487817\pi\)
\(684\) 30.0000 1.14708
\(685\) 0 0
\(686\) 8.00000 0.305441
\(687\) −63.0000 −2.40360
\(688\) 2.00000 0.0762493
\(689\) 3.00000 0.114291
\(690\) 0 0
\(691\) 41.0000 1.55971 0.779857 0.625958i \(-0.215292\pi\)
0.779857 + 0.625958i \(0.215292\pi\)
\(692\) −10.0000 −0.380143
\(693\) 0 0
\(694\) 30.0000 1.13878
\(695\) 0 0
\(696\) 63.0000 2.38801
\(697\) −18.0000 −0.681799
\(698\) −24.0000 −0.908413
\(699\) 24.0000 0.907763
\(700\) −20.0000 −0.755929
\(701\) 12.0000 0.453234 0.226617 0.973984i \(-0.427233\pi\)
0.226617 + 0.973984i \(0.427233\pi\)
\(702\) −27.0000 −1.01905
\(703\) −25.0000 −0.942893
\(704\) 0 0
\(705\) 0 0
\(706\) 18.0000 0.677439
\(707\) 8.00000 0.300871
\(708\) −6.00000 −0.225494
\(709\) 6.00000 0.225335 0.112667 0.993633i \(-0.464061\pi\)
0.112667 + 0.993633i \(0.464061\pi\)
\(710\) 0 0
\(711\) −6.00000 −0.225018
\(712\) −42.0000 −1.57402
\(713\) 28.0000 1.04861
\(714\) 36.0000 1.34727
\(715\) 0 0
\(716\) −11.0000 −0.411089
\(717\) 0 0
\(718\) −9.00000 −0.335877
\(719\) 24.0000 0.895049 0.447524 0.894272i \(-0.352306\pi\)
0.447524 + 0.894272i \(0.352306\pi\)
\(720\) 0 0
\(721\) 4.00000 0.148968
\(722\) −6.00000 −0.223297
\(723\) 33.0000 1.22728
\(724\) 2.00000 0.0743294
\(725\) 35.0000 1.29987
\(726\) −33.0000 −1.22474
\(727\) −30.0000 −1.11264 −0.556319 0.830969i \(-0.687787\pi\)
−0.556319 + 0.830969i \(0.687787\pi\)
\(728\) 36.0000 1.33425
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) 6.00000 0.221918
\(732\) −24.0000 −0.887066
\(733\) 14.0000 0.517102 0.258551 0.965998i \(-0.416755\pi\)
0.258551 + 0.965998i \(0.416755\pi\)
\(734\) −22.0000 −0.812035
\(735\) 0 0
\(736\) −35.0000 −1.29012
\(737\) 0 0
\(738\) −36.0000 −1.32518
\(739\) 15.0000 0.551784 0.275892 0.961189i \(-0.411027\pi\)
0.275892 + 0.961189i \(0.411027\pi\)
\(740\) 0 0
\(741\) −45.0000 −1.65312
\(742\) −4.00000 −0.146845
\(743\) −26.0000 −0.953847 −0.476924 0.878945i \(-0.658248\pi\)
−0.476924 + 0.878945i \(0.658248\pi\)
\(744\) −36.0000 −1.31982
\(745\) 0 0
\(746\) 10.0000 0.366126
\(747\) −6.00000 −0.219529
\(748\) 0 0
\(749\) −24.0000 −0.876941
\(750\) 0 0
\(751\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(752\) 2.00000 0.0729325
\(753\) −60.0000 −2.18652
\(754\) −21.0000 −0.764775
\(755\) 0 0
\(756\) −36.0000 −1.30931
\(757\) −43.0000 −1.56286 −0.781431 0.623992i \(-0.785510\pi\)
−0.781431 + 0.623992i \(0.785510\pi\)
\(758\) −11.0000 −0.399538
\(759\) 0 0
\(760\) 0 0
\(761\) −28.0000 −1.01500 −0.507500 0.861652i \(-0.669430\pi\)
−0.507500 + 0.861652i \(0.669430\pi\)
\(762\) 39.0000 1.41282
\(763\) −64.0000 −2.31696
\(764\) 21.0000 0.759753
\(765\) 0 0
\(766\) −16.0000 −0.578103
\(767\) 6.00000 0.216647
\(768\) 51.0000 1.84030
\(769\) −2.00000 −0.0721218 −0.0360609 0.999350i \(-0.511481\pi\)
−0.0360609 + 0.999350i \(0.511481\pi\)
\(770\) 0 0
\(771\) 84.0000 3.02519
\(772\) 16.0000 0.575853
\(773\) 40.0000 1.43870 0.719350 0.694648i \(-0.244440\pi\)
0.719350 + 0.694648i \(0.244440\pi\)
\(774\) 12.0000 0.431331
\(775\) −20.0000 −0.718421
\(776\) 3.00000 0.107694
\(777\) 60.0000 2.15249
\(778\) −12.0000 −0.430221
\(779\) −30.0000 −1.07486
\(780\) 0 0
\(781\) 0 0
\(782\) 21.0000 0.750958
\(783\) 63.0000 2.25144
\(784\) −9.00000 −0.321429
\(785\) 0 0
\(786\) −6.00000 −0.214013
\(787\) −4.00000 −0.142585 −0.0712923 0.997455i \(-0.522712\pi\)
−0.0712923 + 0.997455i \(0.522712\pi\)
\(788\) 18.0000 0.641223
\(789\) 84.0000 2.99048
\(790\) 0 0
\(791\) −60.0000 −2.13335
\(792\) 0 0
\(793\) 24.0000 0.852265
\(794\) −18.0000 −0.638796
\(795\) 0 0
\(796\) −4.00000 −0.141776
\(797\) 16.0000 0.566749 0.283375 0.959009i \(-0.408546\pi\)
0.283375 + 0.959009i \(0.408546\pi\)
\(798\) 60.0000 2.12398
\(799\) 6.00000 0.212265
\(800\) 25.0000 0.883883
\(801\) −84.0000 −2.96799
\(802\) 32.0000 1.12996
\(803\) 0 0
\(804\) −36.0000 −1.26962
\(805\) 0 0
\(806\) 12.0000 0.422682
\(807\) −27.0000 −0.950445
\(808\) −6.00000 −0.211079
\(809\) −16.0000 −0.562530 −0.281265 0.959630i \(-0.590754\pi\)
−0.281265 + 0.959630i \(0.590754\pi\)
\(810\) 0 0
\(811\) 42.0000 1.47482 0.737410 0.675446i \(-0.236049\pi\)
0.737410 + 0.675446i \(0.236049\pi\)
\(812\) −28.0000 −0.982607
\(813\) 42.0000 1.47300
\(814\) 0 0
\(815\) 0 0
\(816\) −9.00000 −0.315063
\(817\) 10.0000 0.349856
\(818\) −19.0000 −0.664319
\(819\) 72.0000 2.51588
\(820\) 0 0
\(821\) −24.0000 −0.837606 −0.418803 0.908077i \(-0.637550\pi\)
−0.418803 + 0.908077i \(0.637550\pi\)
\(822\) 36.0000 1.25564
\(823\) 26.0000 0.906303 0.453152 0.891434i \(-0.350300\pi\)
0.453152 + 0.891434i \(0.350300\pi\)
\(824\) −3.00000 −0.104510
\(825\) 0 0
\(826\) −8.00000 −0.278356
\(827\) 47.0000 1.63435 0.817175 0.576390i \(-0.195539\pi\)
0.817175 + 0.576390i \(0.195539\pi\)
\(828\) −42.0000 −1.45960
\(829\) −30.0000 −1.04194 −0.520972 0.853574i \(-0.674430\pi\)
−0.520972 + 0.853574i \(0.674430\pi\)
\(830\) 0 0
\(831\) 24.0000 0.832551
\(832\) −21.0000 −0.728044
\(833\) −27.0000 −0.935495
\(834\) −60.0000 −2.07763
\(835\) 0 0
\(836\) 0 0
\(837\) −36.0000 −1.24434
\(838\) 12.0000 0.414533
\(839\) −30.0000 −1.03572 −0.517858 0.855467i \(-0.673270\pi\)
−0.517858 + 0.855467i \(0.673270\pi\)
\(840\) 0 0
\(841\) 20.0000 0.689655
\(842\) −14.0000 −0.482472
\(843\) −51.0000 −1.75653
\(844\) 2.00000 0.0688428
\(845\) 0 0
\(846\) 12.0000 0.412568
\(847\) 44.0000 1.51186
\(848\) 1.00000 0.0343401
\(849\) 27.0000 0.926638
\(850\) −15.0000 −0.514496
\(851\) 35.0000 1.19978
\(852\) 3.00000 0.102778
\(853\) −56.0000 −1.91740 −0.958702 0.284413i \(-0.908201\pi\)
−0.958702 + 0.284413i \(0.908201\pi\)
\(854\) −32.0000 −1.09502
\(855\) 0 0
\(856\) 18.0000 0.615227
\(857\) 42.0000 1.43469 0.717346 0.696717i \(-0.245357\pi\)
0.717346 + 0.696717i \(0.245357\pi\)
\(858\) 0 0
\(859\) −58.0000 −1.97893 −0.989467 0.144757i \(-0.953760\pi\)
−0.989467 + 0.144757i \(0.953760\pi\)
\(860\) 0 0
\(861\) 72.0000 2.45375
\(862\) 36.0000 1.22616
\(863\) −30.0000 −1.02121 −0.510606 0.859815i \(-0.670579\pi\)
−0.510606 + 0.859815i \(0.670579\pi\)
\(864\) 45.0000 1.53093
\(865\) 0 0
\(866\) 7.00000 0.237870
\(867\) 24.0000 0.815083
\(868\) 16.0000 0.543075
\(869\) 0 0
\(870\) 0 0
\(871\) 36.0000 1.21981
\(872\) 48.0000 1.62549
\(873\) 6.00000 0.203069
\(874\) 35.0000 1.18389
\(875\) 0 0
\(876\) −12.0000 −0.405442
\(877\) −2.00000 −0.0675352 −0.0337676 0.999430i \(-0.510751\pi\)
−0.0337676 + 0.999430i \(0.510751\pi\)
\(878\) 34.0000 1.14744
\(879\) −78.0000 −2.63087
\(880\) 0 0
\(881\) 16.0000 0.539054 0.269527 0.962993i \(-0.413133\pi\)
0.269527 + 0.962993i \(0.413133\pi\)
\(882\) −54.0000 −1.81827
\(883\) −36.0000 −1.21150 −0.605748 0.795656i \(-0.707126\pi\)
−0.605748 + 0.795656i \(0.707126\pi\)
\(884\) −9.00000 −0.302703
\(885\) 0 0
\(886\) 33.0000 1.10866
\(887\) −7.00000 −0.235037 −0.117518 0.993071i \(-0.537494\pi\)
−0.117518 + 0.993071i \(0.537494\pi\)
\(888\) −45.0000 −1.51010
\(889\) −52.0000 −1.74402
\(890\) 0 0
\(891\) 0 0
\(892\) 14.0000 0.468755
\(893\) 10.0000 0.334637
\(894\) −15.0000 −0.501675
\(895\) 0 0
\(896\) −12.0000 −0.400892
\(897\) 63.0000 2.10351
\(898\) 11.0000 0.367075
\(899\) −28.0000 −0.933852
\(900\) 30.0000 1.00000
\(901\) 3.00000 0.0999445
\(902\) 0 0
\(903\) −24.0000 −0.798670
\(904\) 45.0000 1.49668
\(905\) 0 0
\(906\) −9.00000 −0.299005
\(907\) 46.0000 1.52740 0.763702 0.645568i \(-0.223379\pi\)
0.763702 + 0.645568i \(0.223379\pi\)
\(908\) −6.00000 −0.199117
\(909\) −12.0000 −0.398015
\(910\) 0 0
\(911\) −32.0000 −1.06021 −0.530104 0.847933i \(-0.677847\pi\)
−0.530104 + 0.847933i \(0.677847\pi\)
\(912\) −15.0000 −0.496700
\(913\) 0 0
\(914\) −38.0000 −1.25693
\(915\) 0 0
\(916\) −21.0000 −0.693860
\(917\) 8.00000 0.264183
\(918\) −27.0000 −0.891133
\(919\) 15.0000 0.494804 0.247402 0.968913i \(-0.420423\pi\)
0.247402 + 0.968913i \(0.420423\pi\)
\(920\) 0 0
\(921\) 48.0000 1.58165
\(922\) 9.00000 0.296399
\(923\) −3.00000 −0.0987462
\(924\) 0 0
\(925\) −25.0000 −0.821995
\(926\) 23.0000 0.755827
\(927\) −6.00000 −0.197066
\(928\) 35.0000 1.14893
\(929\) 38.0000 1.24674 0.623370 0.781927i \(-0.285763\pi\)
0.623370 + 0.781927i \(0.285763\pi\)
\(930\) 0 0
\(931\) −45.0000 −1.47482
\(932\) 8.00000 0.262049
\(933\) −48.0000 −1.57145
\(934\) 28.0000 0.916188
\(935\) 0 0
\(936\) −54.0000 −1.76505
\(937\) −55.0000 −1.79677 −0.898386 0.439207i \(-0.855259\pi\)
−0.898386 + 0.439207i \(0.855259\pi\)
\(938\) −48.0000 −1.56726
\(939\) 18.0000 0.587408
\(940\) 0 0
\(941\) 10.0000 0.325991 0.162995 0.986627i \(-0.447884\pi\)
0.162995 + 0.986627i \(0.447884\pi\)
\(942\) −12.0000 −0.390981
\(943\) 42.0000 1.36771
\(944\) 2.00000 0.0650945
\(945\) 0 0
\(946\) 0 0
\(947\) −12.0000 −0.389948 −0.194974 0.980808i \(-0.562462\pi\)
−0.194974 + 0.980808i \(0.562462\pi\)
\(948\) −3.00000 −0.0974355
\(949\) 12.0000 0.389536
\(950\) −25.0000 −0.811107
\(951\) −9.00000 −0.291845
\(952\) 36.0000 1.16677
\(953\) −42.0000 −1.36051 −0.680257 0.732974i \(-0.738132\pi\)
−0.680257 + 0.732974i \(0.738132\pi\)
\(954\) 6.00000 0.194257
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) −3.00000 −0.0969256
\(959\) −48.0000 −1.55000
\(960\) 0 0
\(961\) −15.0000 −0.483871
\(962\) 15.0000 0.483619
\(963\) 36.0000 1.16008
\(964\) 11.0000 0.354286
\(965\) 0 0
\(966\) −84.0000 −2.70266
\(967\) 52.0000 1.67221 0.836104 0.548572i \(-0.184828\pi\)
0.836104 + 0.548572i \(0.184828\pi\)
\(968\) −33.0000 −1.06066
\(969\) −45.0000 −1.44561
\(970\) 0 0
\(971\) 42.0000 1.34784 0.673922 0.738802i \(-0.264608\pi\)
0.673922 + 0.738802i \(0.264608\pi\)
\(972\) 0 0
\(973\) 80.0000 2.56468
\(974\) −20.0000 −0.640841
\(975\) −45.0000 −1.44115
\(976\) 8.00000 0.256074
\(977\) −20.0000 −0.639857 −0.319928 0.947442i \(-0.603659\pi\)
−0.319928 + 0.947442i \(0.603659\pi\)
\(978\) −18.0000 −0.575577
\(979\) 0 0
\(980\) 0 0
\(981\) 96.0000 3.06504
\(982\) −27.0000 −0.861605
\(983\) 46.0000 1.46717 0.733586 0.679597i \(-0.237845\pi\)
0.733586 + 0.679597i \(0.237845\pi\)
\(984\) −54.0000 −1.72146
\(985\) 0 0
\(986\) −21.0000 −0.668776
\(987\) −24.0000 −0.763928
\(988\) −15.0000 −0.477214
\(989\) −14.0000 −0.445174
\(990\) 0 0
\(991\) 34.0000 1.08005 0.540023 0.841650i \(-0.318416\pi\)
0.540023 + 0.841650i \(0.318416\pi\)
\(992\) −20.0000 −0.635001
\(993\) −84.0000 −2.66566
\(994\) 4.00000 0.126872
\(995\) 0 0
\(996\) −3.00000 −0.0950586
\(997\) −13.0000 −0.411714 −0.205857 0.978582i \(-0.565998\pi\)
−0.205857 + 0.978582i \(0.565998\pi\)
\(998\) 23.0000 0.728052
\(999\) −45.0000 −1.42374
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 \(a_p\))