Properties

Label 19.2.a.a.1.1
Level 19
Weight 2
Character 19.1
Self dual Yes
Analytic conductor 0.152
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 19 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 19.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(0.15171576384\)
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 \(\chi\) = 19.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.00000 q^{3} -2.00000 q^{4} +3.00000 q^{5} -1.00000 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q-2.00000 q^{3} -2.00000 q^{4} +3.00000 q^{5} -1.00000 q^{7} +1.00000 q^{9} +3.00000 q^{11} +4.00000 q^{12} -4.00000 q^{13} -6.00000 q^{15} +4.00000 q^{16} -3.00000 q^{17} +1.00000 q^{19} -6.00000 q^{20} +2.00000 q^{21} +4.00000 q^{25} +4.00000 q^{27} +2.00000 q^{28} +6.00000 q^{29} -4.00000 q^{31} -6.00000 q^{33} -3.00000 q^{35} -2.00000 q^{36} +2.00000 q^{37} +8.00000 q^{39} -6.00000 q^{41} -1.00000 q^{43} -6.00000 q^{44} +3.00000 q^{45} -3.00000 q^{47} -8.00000 q^{48} -6.00000 q^{49} +6.00000 q^{51} +8.00000 q^{52} +12.0000 q^{53} +9.00000 q^{55} -2.00000 q^{57} -6.00000 q^{59} +12.0000 q^{60} -1.00000 q^{61} -1.00000 q^{63} -8.00000 q^{64} -12.0000 q^{65} -4.00000 q^{67} +6.00000 q^{68} +6.00000 q^{71} -7.00000 q^{73} -8.00000 q^{75} -2.00000 q^{76} -3.00000 q^{77} +8.00000 q^{79} +12.0000 q^{80} -11.0000 q^{81} +12.0000 q^{83} -4.00000 q^{84} -9.00000 q^{85} -12.0000 q^{87} +12.0000 q^{89} +4.00000 q^{91} +8.00000 q^{93} +3.00000 q^{95} +8.00000 q^{97} +3.00000 q^{99} +O(q^{100})\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(3\) −2.00000 −1.15470 −0.577350 0.816497i \(-0.695913\pi\)
−0.577350 + 0.816497i \(0.695913\pi\)
\(4\) −2.00000 −1.00000
\(5\) 3.00000 1.34164 0.670820 0.741620i \(-0.265942\pi\)
0.670820 + 0.741620i \(0.265942\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964 −0.188982 0.981981i \(-0.560519\pi\)
−0.188982 + 0.981981i \(0.560519\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 3.00000 0.904534 0.452267 0.891883i \(-0.350615\pi\)
0.452267 + 0.891883i \(0.350615\pi\)
\(12\) 4.00000 1.15470
\(13\) −4.00000 −1.10940 −0.554700 0.832050i \(-0.687167\pi\)
−0.554700 + 0.832050i \(0.687167\pi\)
\(14\) 0 0
\(15\) −6.00000 −1.54919
\(16\) 4.00000 1.00000
\(17\) −3.00000 −0.727607 −0.363803 0.931476i \(-0.618522\pi\)
−0.363803 + 0.931476i \(0.618522\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) −6.00000 −1.34164
\(21\) 2.00000 0.436436
\(22\) 0 0
\(23\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) 0 0
\(25\) 4.00000 0.800000
\(26\) 0 0
\(27\) 4.00000 0.769800
\(28\) 2.00000 0.377964
\(29\) 6.00000 1.11417 0.557086 0.830455i \(-0.311919\pi\)
0.557086 + 0.830455i \(0.311919\pi\)
\(30\) 0 0
\(31\) −4.00000 −0.718421 −0.359211 0.933257i \(-0.616954\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) 0 0
\(33\) −6.00000 −1.04447
\(34\) 0 0
\(35\) −3.00000 −0.507093
\(36\) −2.00000 −0.333333
\(37\) 2.00000 0.328798 0.164399 0.986394i \(-0.447432\pi\)
0.164399 + 0.986394i \(0.447432\pi\)
\(38\) 0 0
\(39\) 8.00000 1.28103
\(40\) 0 0
\(41\) −6.00000 −0.937043 −0.468521 0.883452i \(-0.655213\pi\)
−0.468521 + 0.883452i \(0.655213\pi\)
\(42\) 0 0
\(43\) −1.00000 −0.152499 −0.0762493 0.997089i \(-0.524294\pi\)
−0.0762493 + 0.997089i \(0.524294\pi\)
\(44\) −6.00000 −0.904534
\(45\) 3.00000 0.447214
\(46\) 0 0
\(47\) −3.00000 −0.437595 −0.218797 0.975770i \(-0.570213\pi\)
−0.218797 + 0.975770i \(0.570213\pi\)
\(48\) −8.00000 −1.15470
\(49\) −6.00000 −0.857143
\(50\) 0 0
\(51\) 6.00000 0.840168
\(52\) 8.00000 1.10940
\(53\) 12.0000 1.64833 0.824163 0.566352i \(-0.191646\pi\)
0.824163 + 0.566352i \(0.191646\pi\)
\(54\) 0 0
\(55\) 9.00000 1.21356
\(56\) 0 0
\(57\) −2.00000 −0.264906
\(58\) 0 0
\(59\) −6.00000 −0.781133 −0.390567 0.920575i \(-0.627721\pi\)
−0.390567 + 0.920575i \(0.627721\pi\)
\(60\) 12.0000 1.54919
\(61\) −1.00000 −0.128037 −0.0640184 0.997949i \(-0.520392\pi\)
−0.0640184 + 0.997949i \(0.520392\pi\)
\(62\) 0 0
\(63\) −1.00000 −0.125988
\(64\) −8.00000 −1.00000
\(65\) −12.0000 −1.48842
\(66\) 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
\(71\) 6.00000 0.712069 0.356034 0.934473i \(-0.384129\pi\)
0.356034 + 0.934473i \(0.384129\pi\)
\(72\) 0 0
\(73\) −7.00000 −0.819288 −0.409644 0.912245i \(-0.634347\pi\)
−0.409644 + 0.912245i \(0.634347\pi\)
\(74\) 0 0
\(75\) −8.00000 −0.923760
\(76\) −2.00000 −0.229416
\(77\) −3.00000 −0.341882
\(78\) 0 0
\(79\) 8.00000 0.900070 0.450035 0.893011i \(-0.351411\pi\)
0.450035 + 0.893011i \(0.351411\pi\)
\(80\) 12.0000 1.34164
\(81\) −11.0000 −1.22222
\(82\) 0 0
\(83\) 12.0000 1.31717 0.658586 0.752506i \(-0.271155\pi\)
0.658586 + 0.752506i \(0.271155\pi\)
\(84\) −4.00000 −0.436436
\(85\) −9.00000 −0.976187
\(86\) 0 0
\(87\) −12.0000 −1.28654
\(88\) 0 0
\(89\) 12.0000 1.27200 0.635999 0.771690i \(-0.280588\pi\)
0.635999 + 0.771690i \(0.280588\pi\)
\(90\) 0 0
\(91\) 4.00000 0.419314
\(92\) 0 0
\(93\) 8.00000 0.829561
\(94\) 0 0
\(95\) 3.00000 0.307794
\(96\) 0 0
\(97\) 8.00000 0.812277 0.406138 0.913812i \(-0.366875\pi\)
0.406138 + 0.913812i \(0.366875\pi\)
\(98\) 0 0
\(99\) 3.00000 0.301511
\(100\) −8.00000 −0.800000
\(101\) 6.00000 0.597022 0.298511 0.954406i \(-0.403510\pi\)
0.298511 + 0.954406i \(0.403510\pi\)
\(102\) 0 0
\(103\) 14.0000 1.37946 0.689730 0.724066i \(-0.257729\pi\)
0.689730 + 0.724066i \(0.257729\pi\)
\(104\) 0 0
\(105\) 6.00000 0.585540
\(106\) 0 0
\(107\) −18.0000 −1.74013 −0.870063 0.492941i \(-0.835922\pi\)
−0.870063 + 0.492941i \(0.835922\pi\)
\(108\) −8.00000 −0.769800
\(109\) −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
\(112\) −4.00000 −0.377964
\(113\) 6.00000 0.564433 0.282216 0.959351i \(-0.408930\pi\)
0.282216 + 0.959351i \(0.408930\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −12.0000 −1.11417
\(117\) −4.00000 −0.369800
\(118\) 0 0
\(119\) 3.00000 0.275010
\(120\) 0 0
\(121\) −2.00000 −0.181818
\(122\) 0 0
\(123\) 12.0000 1.08200
\(124\) 8.00000 0.718421
\(125\) −3.00000 −0.268328
\(126\) 0 0
\(127\) 2.00000 0.177471 0.0887357 0.996055i \(-0.471717\pi\)
0.0887357 + 0.996055i \(0.471717\pi\)
\(128\) 0 0
\(129\) 2.00000 0.176090
\(130\) 0 0
\(131\) −15.0000 −1.31056 −0.655278 0.755388i \(-0.727449\pi\)
−0.655278 + 0.755388i \(0.727449\pi\)
\(132\) 12.0000 1.04447
\(133\) −1.00000 −0.0867110
\(134\) 0 0
\(135\) 12.0000 1.03280
\(136\) 0 0
\(137\) −3.00000 −0.256307 −0.128154 0.991754i \(-0.540905\pi\)
−0.128154 + 0.991754i \(0.540905\pi\)
\(138\) 0 0
\(139\) −13.0000 −1.10265 −0.551323 0.834292i \(-0.685877\pi\)
−0.551323 + 0.834292i \(0.685877\pi\)
\(140\) 6.00000 0.507093
\(141\) 6.00000 0.505291
\(142\) 0 0
\(143\) −12.0000 −1.00349
\(144\) 4.00000 0.333333
\(145\) 18.0000 1.49482
\(146\) 0 0
\(147\) 12.0000 0.989743
\(148\) −4.00000 −0.328798
\(149\) 21.0000 1.72039 0.860194 0.509968i \(-0.170343\pi\)
0.860194 + 0.509968i \(0.170343\pi\)
\(150\) 0 0
\(151\) −10.0000 −0.813788 −0.406894 0.913475i \(-0.633388\pi\)
−0.406894 + 0.913475i \(0.633388\pi\)
\(152\) 0 0
\(153\) −3.00000 −0.242536
\(154\) 0 0
\(155\) −12.0000 −0.963863
\(156\) −16.0000 −1.28103
\(157\) 14.0000 1.11732 0.558661 0.829396i \(-0.311315\pi\)
0.558661 + 0.829396i \(0.311315\pi\)
\(158\) 0 0
\(159\) −24.0000 −1.90332
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 20.0000 1.56652 0.783260 0.621694i \(-0.213555\pi\)
0.783260 + 0.621694i \(0.213555\pi\)
\(164\) 12.0000 0.937043
\(165\) −18.0000 −1.40130
\(166\) 0 0
\(167\) −18.0000 −1.39288 −0.696441 0.717614i \(-0.745234\pi\)
−0.696441 + 0.717614i \(0.745234\pi\)
\(168\) 0 0
\(169\) 3.00000 0.230769
\(170\) 0 0
\(171\) 1.00000 0.0764719
\(172\) 2.00000 0.152499
\(173\) −18.0000 −1.36851 −0.684257 0.729241i \(-0.739873\pi\)
−0.684257 + 0.729241i \(0.739873\pi\)
\(174\) 0 0
\(175\) −4.00000 −0.302372
\(176\) 12.0000 0.904534
\(177\) 12.0000 0.901975
\(178\) 0 0
\(179\) −18.0000 −1.34538 −0.672692 0.739923i \(-0.734862\pi\)
−0.672692 + 0.739923i \(0.734862\pi\)
\(180\) −6.00000 −0.447214
\(181\) 2.00000 0.148659 0.0743294 0.997234i \(-0.476318\pi\)
0.0743294 + 0.997234i \(0.476318\pi\)
\(182\) 0 0
\(183\) 2.00000 0.147844
\(184\) 0 0
\(185\) 6.00000 0.441129
\(186\) 0 0
\(187\) −9.00000 −0.658145
\(188\) 6.00000 0.437595
\(189\) −4.00000 −0.290957
\(190\) 0 0
\(191\) 3.00000 0.217072 0.108536 0.994092i \(-0.465384\pi\)
0.108536 + 0.994092i \(0.465384\pi\)
\(192\) 16.0000 1.15470
\(193\) −4.00000 −0.287926 −0.143963 0.989583i \(-0.545985\pi\)
−0.143963 + 0.989583i \(0.545985\pi\)
\(194\) 0 0
\(195\) 24.0000 1.71868
\(196\) 12.0000 0.857143
\(197\) 18.0000 1.28245 0.641223 0.767354i \(-0.278427\pi\)
0.641223 + 0.767354i \(0.278427\pi\)
\(198\) 0 0
\(199\) 11.0000 0.779769 0.389885 0.920864i \(-0.372515\pi\)
0.389885 + 0.920864i \(0.372515\pi\)
\(200\) 0 0
\(201\) 8.00000 0.564276
\(202\) 0 0
\(203\) −6.00000 −0.421117
\(204\) −12.0000 −0.840168
\(205\) −18.0000 −1.25717
\(206\) 0 0
\(207\) 0 0
\(208\) −16.0000 −1.10940
\(209\) 3.00000 0.207514
\(210\) 0 0
\(211\) 14.0000 0.963800 0.481900 0.876226i \(-0.339947\pi\)
0.481900 + 0.876226i \(0.339947\pi\)
\(212\) −24.0000 −1.64833
\(213\) −12.0000 −0.822226
\(214\) 0 0
\(215\) −3.00000 −0.204598
\(216\) 0 0
\(217\) 4.00000 0.271538
\(218\) 0 0
\(219\) 14.0000 0.946032
\(220\) −18.0000 −1.21356
\(221\) 12.0000 0.807207
\(222\) 0 0
\(223\) −10.0000 −0.669650 −0.334825 0.942280i \(-0.608677\pi\)
−0.334825 + 0.942280i \(0.608677\pi\)
\(224\) 0 0
\(225\) 4.00000 0.266667
\(226\) 0 0
\(227\) 12.0000 0.796468 0.398234 0.917284i \(-0.369623\pi\)
0.398234 + 0.917284i \(0.369623\pi\)
\(228\) 4.00000 0.264906
\(229\) 5.00000 0.330409 0.165205 0.986259i \(-0.447172\pi\)
0.165205 + 0.986259i \(0.447172\pi\)
\(230\) 0 0
\(231\) 6.00000 0.394771
\(232\) 0 0
\(233\) −21.0000 −1.37576 −0.687878 0.725826i \(-0.741458\pi\)
−0.687878 + 0.725826i \(0.741458\pi\)
\(234\) 0 0
\(235\) −9.00000 −0.587095
\(236\) 12.0000 0.781133
\(237\) −16.0000 −1.03931
\(238\) 0 0
\(239\) 15.0000 0.970269 0.485135 0.874439i \(-0.338771\pi\)
0.485135 + 0.874439i \(0.338771\pi\)
\(240\) −24.0000 −1.54919
\(241\) −10.0000 −0.644157 −0.322078 0.946713i \(-0.604381\pi\)
−0.322078 + 0.946713i \(0.604381\pi\)
\(242\) 0 0
\(243\) 10.0000 0.641500
\(244\) 2.00000 0.128037
\(245\) −18.0000 −1.14998
\(246\) 0 0
\(247\) −4.00000 −0.254514
\(248\) 0 0
\(249\) −24.0000 −1.52094
\(250\) 0 0
\(251\) 21.0000 1.32551 0.662754 0.748837i \(-0.269387\pi\)
0.662754 + 0.748837i \(0.269387\pi\)
\(252\) 2.00000 0.125988
\(253\) 0 0
\(254\) 0 0
\(255\) 18.0000 1.12720
\(256\) 16.0000 1.00000
\(257\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(258\) 0 0
\(259\) −2.00000 −0.124274
\(260\) 24.0000 1.48842
\(261\) 6.00000 0.371391
\(262\) 0 0
\(263\) 9.00000 0.554964 0.277482 0.960731i \(-0.410500\pi\)
0.277482 + 0.960731i \(0.410500\pi\)
\(264\) 0 0
\(265\) 36.0000 2.21146
\(266\) 0 0
\(267\) −24.0000 −1.46878
\(268\) 8.00000 0.488678
\(269\) 24.0000 1.46331 0.731653 0.681677i \(-0.238749\pi\)
0.731653 + 0.681677i \(0.238749\pi\)
\(270\) 0 0
\(271\) −16.0000 −0.971931 −0.485965 0.873978i \(-0.661532\pi\)
−0.485965 + 0.873978i \(0.661532\pi\)
\(272\) −12.0000 −0.727607
\(273\) −8.00000 −0.484182
\(274\) 0 0
\(275\) 12.0000 0.723627
\(276\) 0 0
\(277\) −19.0000 −1.14160 −0.570800 0.821089i \(-0.693367\pi\)
−0.570800 + 0.821089i \(0.693367\pi\)
\(278\) 0 0
\(279\) −4.00000 −0.239474
\(280\) 0 0
\(281\) 6.00000 0.357930 0.178965 0.983855i \(-0.442725\pi\)
0.178965 + 0.983855i \(0.442725\pi\)
\(282\) 0 0
\(283\) −13.0000 −0.772770 −0.386385 0.922338i \(-0.626276\pi\)
−0.386385 + 0.922338i \(0.626276\pi\)
\(284\) −12.0000 −0.712069
\(285\) −6.00000 −0.355409
\(286\) 0 0
\(287\) 6.00000 0.354169
\(288\) 0 0
\(289\) −8.00000 −0.470588
\(290\) 0 0
\(291\) −16.0000 −0.937937
\(292\) 14.0000 0.819288
\(293\) −12.0000 −0.701047 −0.350524 0.936554i \(-0.613996\pi\)
−0.350524 + 0.936554i \(0.613996\pi\)
\(294\) 0 0
\(295\) −18.0000 −1.04800
\(296\) 0 0
\(297\) 12.0000 0.696311
\(298\) 0 0
\(299\) 0 0
\(300\) 16.0000 0.923760
\(301\) 1.00000 0.0576390
\(302\) 0 0
\(303\) −12.0000 −0.689382
\(304\) 4.00000 0.229416
\(305\) −3.00000 −0.171780
\(306\) 0 0
\(307\) 20.0000 1.14146 0.570730 0.821138i \(-0.306660\pi\)
0.570730 + 0.821138i \(0.306660\pi\)
\(308\) 6.00000 0.341882
\(309\) −28.0000 −1.59286
\(310\) 0 0
\(311\) −3.00000 −0.170114 −0.0850572 0.996376i \(-0.527107\pi\)
−0.0850572 + 0.996376i \(0.527107\pi\)
\(312\) 0 0
\(313\) −10.0000 −0.565233 −0.282617 0.959233i \(-0.591202\pi\)
−0.282617 + 0.959233i \(0.591202\pi\)
\(314\) 0 0
\(315\) −3.00000 −0.169031
\(316\) −16.0000 −0.900070
\(317\) 6.00000 0.336994 0.168497 0.985702i \(-0.446109\pi\)
0.168497 + 0.985702i \(0.446109\pi\)
\(318\) 0 0
\(319\) 18.0000 1.00781
\(320\) −24.0000 −1.34164
\(321\) 36.0000 2.00932
\(322\) 0 0
\(323\) −3.00000 −0.166924
\(324\) 22.0000 1.22222
\(325\) −16.0000 −0.887520
\(326\) 0 0
\(327\) 32.0000 1.76960
\(328\) 0 0
\(329\) 3.00000 0.165395
\(330\) 0 0
\(331\) −28.0000 −1.53902 −0.769510 0.638635i \(-0.779499\pi\)
−0.769510 + 0.638635i \(0.779499\pi\)
\(332\) −24.0000 −1.31717
\(333\) 2.00000 0.109599
\(334\) 0 0
\(335\) −12.0000 −0.655630
\(336\) 8.00000 0.436436
\(337\) 32.0000 1.74315 0.871576 0.490261i \(-0.163099\pi\)
0.871576 + 0.490261i \(0.163099\pi\)
\(338\) 0 0
\(339\) −12.0000 −0.651751
\(340\) 18.0000 0.976187
\(341\) −12.0000 −0.649836
\(342\) 0 0
\(343\) 13.0000 0.701934
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 21.0000 1.12734 0.563670 0.826000i \(-0.309389\pi\)
0.563670 + 0.826000i \(0.309389\pi\)
\(348\) 24.0000 1.28654
\(349\) 17.0000 0.909989 0.454995 0.890494i \(-0.349641\pi\)
0.454995 + 0.890494i \(0.349641\pi\)
\(350\) 0 0
\(351\) −16.0000 −0.854017
\(352\) 0 0
\(353\) −6.00000 −0.319348 −0.159674 0.987170i \(-0.551044\pi\)
−0.159674 + 0.987170i \(0.551044\pi\)
\(354\) 0 0
\(355\) 18.0000 0.955341
\(356\) −24.0000 −1.27200
\(357\) −6.00000 −0.317554
\(358\) 0 0
\(359\) 15.0000 0.791670 0.395835 0.918322i \(-0.370455\pi\)
0.395835 + 0.918322i \(0.370455\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 4.00000 0.209946
\(364\) −8.00000 −0.419314
\(365\) −21.0000 −1.09919
\(366\) 0 0
\(367\) 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
\(371\) −12.0000 −0.623009
\(372\) −16.0000 −0.829561
\(373\) −4.00000 −0.207112 −0.103556 0.994624i \(-0.533022\pi\)
−0.103556 + 0.994624i \(0.533022\pi\)
\(374\) 0 0
\(375\) 6.00000 0.309839
\(376\) 0 0
\(377\) −24.0000 −1.23606
\(378\) 0 0
\(379\) −34.0000 −1.74646 −0.873231 0.487306i \(-0.837980\pi\)
−0.873231 + 0.487306i \(0.837980\pi\)
\(380\) −6.00000 −0.307794
\(381\) −4.00000 −0.204926
\(382\) 0 0
\(383\) 12.0000 0.613171 0.306586 0.951843i \(-0.400813\pi\)
0.306586 + 0.951843i \(0.400813\pi\)
\(384\) 0 0
\(385\) −9.00000 −0.458682
\(386\) 0 0
\(387\) −1.00000 −0.0508329
\(388\) −16.0000 −0.812277
\(389\) 15.0000 0.760530 0.380265 0.924878i \(-0.375833\pi\)
0.380265 + 0.924878i \(0.375833\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 30.0000 1.51330
\(394\) 0 0
\(395\) 24.0000 1.20757
\(396\) −6.00000 −0.301511
\(397\) −7.00000 −0.351320 −0.175660 0.984451i \(-0.556206\pi\)
−0.175660 + 0.984451i \(0.556206\pi\)
\(398\) 0 0
\(399\) 2.00000 0.100125
\(400\) 16.0000 0.800000
\(401\) 12.0000 0.599251 0.299626 0.954057i \(-0.403138\pi\)
0.299626 + 0.954057i \(0.403138\pi\)
\(402\) 0 0
\(403\) 16.0000 0.797017
\(404\) −12.0000 −0.597022
\(405\) −33.0000 −1.63978
\(406\) 0 0
\(407\) 6.00000 0.297409
\(408\) 0 0
\(409\) −4.00000 −0.197787 −0.0988936 0.995098i \(-0.531530\pi\)
−0.0988936 + 0.995098i \(0.531530\pi\)
\(410\) 0 0
\(411\) 6.00000 0.295958
\(412\) −28.0000 −1.37946
\(413\) 6.00000 0.295241
\(414\) 0 0
\(415\) 36.0000 1.76717
\(416\) 0 0
\(417\) 26.0000 1.27323
\(418\) 0 0
\(419\) −12.0000 −0.586238 −0.293119 0.956076i \(-0.594693\pi\)
−0.293119 + 0.956076i \(0.594693\pi\)
\(420\) −12.0000 −0.585540
\(421\) 8.00000 0.389896 0.194948 0.980814i \(-0.437546\pi\)
0.194948 + 0.980814i \(0.437546\pi\)
\(422\) 0 0
\(423\) −3.00000 −0.145865
\(424\) 0 0
\(425\) −12.0000 −0.582086
\(426\) 0 0
\(427\) 1.00000 0.0483934
\(428\) 36.0000 1.74013
\(429\) 24.0000 1.15873
\(430\) 0 0
\(431\) −24.0000 −1.15604 −0.578020 0.816023i \(-0.696174\pi\)
−0.578020 + 0.816023i \(0.696174\pi\)
\(432\) 16.0000 0.769800
\(433\) 2.00000 0.0961139 0.0480569 0.998845i \(-0.484697\pi\)
0.0480569 + 0.998845i \(0.484697\pi\)
\(434\) 0 0
\(435\) −36.0000 −1.72607
\(436\) 32.0000 1.53252
\(437\) 0 0
\(438\) 0 0
\(439\) −10.0000 −0.477274 −0.238637 0.971109i \(-0.576701\pi\)
−0.238637 + 0.971109i \(0.576701\pi\)
\(440\) 0 0
\(441\) −6.00000 −0.285714
\(442\) 0 0
\(443\) −3.00000 −0.142534 −0.0712672 0.997457i \(-0.522704\pi\)
−0.0712672 + 0.997457i \(0.522704\pi\)
\(444\) 8.00000 0.379663
\(445\) 36.0000 1.70656
\(446\) 0 0
\(447\) −42.0000 −1.98653
\(448\) 8.00000 0.377964
\(449\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(450\) 0 0
\(451\) −18.0000 −0.847587
\(452\) −12.0000 −0.564433
\(453\) 20.0000 0.939682
\(454\) 0 0
\(455\) 12.0000 0.562569
\(456\) 0 0
\(457\) −37.0000 −1.73079 −0.865393 0.501093i \(-0.832931\pi\)
−0.865393 + 0.501093i \(0.832931\pi\)
\(458\) 0 0
\(459\) −12.0000 −0.560112
\(460\) 0 0
\(461\) 9.00000 0.419172 0.209586 0.977790i \(-0.432788\pi\)
0.209586 + 0.977790i \(0.432788\pi\)
\(462\) 0 0
\(463\) −31.0000 −1.44069 −0.720346 0.693615i \(-0.756017\pi\)
−0.720346 + 0.693615i \(0.756017\pi\)
\(464\) 24.0000 1.11417
\(465\) 24.0000 1.11297
\(466\) 0 0
\(467\) −27.0000 −1.24941 −0.624705 0.780860i \(-0.714781\pi\)
−0.624705 + 0.780860i \(0.714781\pi\)
\(468\) 8.00000 0.369800
\(469\) 4.00000 0.184703
\(470\) 0 0
\(471\) −28.0000 −1.29017
\(472\) 0 0
\(473\) −3.00000 −0.137940
\(474\) 0 0
\(475\) 4.00000 0.183533
\(476\) −6.00000 −0.275010
\(477\) 12.0000 0.549442
\(478\) 0 0
\(479\) −12.0000 −0.548294 −0.274147 0.961688i \(-0.588395\pi\)
−0.274147 + 0.961688i \(0.588395\pi\)
\(480\) 0 0
\(481\) −8.00000 −0.364769
\(482\) 0 0
\(483\) 0 0
\(484\) 4.00000 0.181818
\(485\) 24.0000 1.08978
\(486\) 0 0
\(487\) 2.00000 0.0906287 0.0453143 0.998973i \(-0.485571\pi\)
0.0453143 + 0.998973i \(0.485571\pi\)
\(488\) 0 0
\(489\) −40.0000 −1.80886
\(490\) 0 0
\(491\) 12.0000 0.541552 0.270776 0.962642i \(-0.412720\pi\)
0.270776 + 0.962642i \(0.412720\pi\)
\(492\) −24.0000 −1.08200
\(493\) −18.0000 −0.810679
\(494\) 0 0
\(495\) 9.00000 0.404520
\(496\) −16.0000 −0.718421
\(497\) −6.00000 −0.269137
\(498\) 0 0
\(499\) 5.00000 0.223831 0.111915 0.993718i \(-0.464301\pi\)
0.111915 + 0.993718i \(0.464301\pi\)
\(500\) 6.00000 0.268328
\(501\) 36.0000 1.60836
\(502\) 0 0
\(503\) 12.0000 0.535054 0.267527 0.963550i \(-0.413794\pi\)
0.267527 + 0.963550i \(0.413794\pi\)
\(504\) 0 0
\(505\) 18.0000 0.800989
\(506\) 0 0
\(507\) −6.00000 −0.266469
\(508\) −4.00000 −0.177471
\(509\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(510\) 0 0
\(511\) 7.00000 0.309662
\(512\) 0 0
\(513\) 4.00000 0.176604
\(514\) 0 0
\(515\) 42.0000 1.85074
\(516\) −4.00000 −0.176090
\(517\) −9.00000 −0.395820
\(518\) 0 0
\(519\) 36.0000 1.58022
\(520\) 0 0
\(521\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(522\) 0 0
\(523\) 38.0000 1.66162 0.830812 0.556553i \(-0.187876\pi\)
0.830812 + 0.556553i \(0.187876\pi\)
\(524\) 30.0000 1.31056
\(525\) 8.00000 0.349149
\(526\) 0 0
\(527\) 12.0000 0.522728
\(528\) −24.0000 −1.04447
\(529\) −23.0000 −1.00000
\(530\) 0 0
\(531\) −6.00000 −0.260378
\(532\) 2.00000 0.0867110
\(533\) 24.0000 1.03956
\(534\) 0 0
\(535\) −54.0000 −2.33462
\(536\) 0 0
\(537\) 36.0000 1.55351
\(538\) 0 0
\(539\) −18.0000 −0.775315
\(540\) −24.0000 −1.03280
\(541\) −25.0000 −1.07483 −0.537417 0.843317i \(-0.680600\pi\)
−0.537417 + 0.843317i \(0.680600\pi\)
\(542\) 0 0
\(543\) −4.00000 −0.171656
\(544\) 0 0
\(545\) −48.0000 −2.05609
\(546\) 0 0
\(547\) −28.0000 −1.19719 −0.598597 0.801050i \(-0.704275\pi\)
−0.598597 + 0.801050i \(0.704275\pi\)
\(548\) 6.00000 0.256307
\(549\) −1.00000 −0.0426790
\(550\) 0 0
\(551\) 6.00000 0.255609
\(552\) 0 0
\(553\) −8.00000 −0.340195
\(554\) 0 0
\(555\) −12.0000 −0.509372
\(556\) 26.0000 1.10265
\(557\) 21.0000 0.889799 0.444899 0.895581i \(-0.353239\pi\)
0.444899 + 0.895581i \(0.353239\pi\)
\(558\) 0 0
\(559\) 4.00000 0.169182
\(560\) −12.0000 −0.507093
\(561\) 18.0000 0.759961
\(562\) 0 0
\(563\) 6.00000 0.252870 0.126435 0.991975i \(-0.459647\pi\)
0.126435 + 0.991975i \(0.459647\pi\)
\(564\) −12.0000 −0.505291
\(565\) 18.0000 0.757266
\(566\) 0 0
\(567\) 11.0000 0.461957
\(568\) 0 0
\(569\) −24.0000 −1.00613 −0.503066 0.864248i \(-0.667795\pi\)
−0.503066 + 0.864248i \(0.667795\pi\)
\(570\) 0 0
\(571\) −4.00000 −0.167395 −0.0836974 0.996491i \(-0.526673\pi\)
−0.0836974 + 0.996491i \(0.526673\pi\)
\(572\) 24.0000 1.00349
\(573\) −6.00000 −0.250654
\(574\) 0 0
\(575\) 0 0
\(576\) −8.00000 −0.333333
\(577\) 11.0000 0.457936 0.228968 0.973434i \(-0.426465\pi\)
0.228968 + 0.973434i \(0.426465\pi\)
\(578\) 0 0
\(579\) 8.00000 0.332469
\(580\) −36.0000 −1.49482
\(581\) −12.0000 −0.497844
\(582\) 0 0
\(583\) 36.0000 1.49097
\(584\) 0 0
\(585\) −12.0000 −0.496139
\(586\) 0 0
\(587\) 45.0000 1.85735 0.928674 0.370896i \(-0.120949\pi\)
0.928674 + 0.370896i \(0.120949\pi\)
\(588\) −24.0000 −0.989743
\(589\) −4.00000 −0.164817
\(590\) 0 0
\(591\) −36.0000 −1.48084
\(592\) 8.00000 0.328798
\(593\) −42.0000 −1.72473 −0.862367 0.506284i \(-0.831019\pi\)
−0.862367 + 0.506284i \(0.831019\pi\)
\(594\) 0 0
\(595\) 9.00000 0.368964
\(596\) −42.0000 −1.72039
\(597\) −22.0000 −0.900400
\(598\) 0 0
\(599\) −36.0000 −1.47092 −0.735460 0.677568i \(-0.763034\pi\)
−0.735460 + 0.677568i \(0.763034\pi\)
\(600\) 0 0
\(601\) 26.0000 1.06056 0.530281 0.847822i \(-0.322086\pi\)
0.530281 + 0.847822i \(0.322086\pi\)
\(602\) 0 0
\(603\) −4.00000 −0.162893
\(604\) 20.0000 0.813788
\(605\) −6.00000 −0.243935
\(606\) 0 0
\(607\) 32.0000 1.29884 0.649420 0.760430i \(-0.275012\pi\)
0.649420 + 0.760430i \(0.275012\pi\)
\(608\) 0 0
\(609\) 12.0000 0.486265
\(610\) 0 0
\(611\) 12.0000 0.485468
\(612\) 6.00000 0.242536
\(613\) 29.0000 1.17130 0.585649 0.810564i \(-0.300840\pi\)
0.585649 + 0.810564i \(0.300840\pi\)
\(614\) 0 0
\(615\) 36.0000 1.45166
\(616\) 0 0
\(617\) 9.00000 0.362326 0.181163 0.983453i \(-0.442014\pi\)
0.181163 + 0.983453i \(0.442014\pi\)
\(618\) 0 0
\(619\) 44.0000 1.76851 0.884255 0.467005i \(-0.154667\pi\)
0.884255 + 0.467005i \(0.154667\pi\)
\(620\) 24.0000 0.963863
\(621\) 0 0
\(622\) 0 0
\(623\) −12.0000 −0.480770
\(624\) 32.0000 1.28103
\(625\) −29.0000 −1.16000
\(626\) 0 0
\(627\) −6.00000 −0.239617
\(628\) −28.0000 −1.11732
\(629\) −6.00000 −0.239236
\(630\) 0 0
\(631\) 11.0000 0.437903 0.218952 0.975736i \(-0.429736\pi\)
0.218952 + 0.975736i \(0.429736\pi\)
\(632\) 0 0
\(633\) −28.0000 −1.11290
\(634\) 0 0
\(635\) 6.00000 0.238103
\(636\) 48.0000 1.90332
\(637\) 24.0000 0.950915
\(638\) 0 0
\(639\) 6.00000 0.237356
\(640\) 0 0
\(641\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(642\) 0 0
\(643\) −13.0000 −0.512670 −0.256335 0.966588i \(-0.582515\pi\)
−0.256335 + 0.966588i \(0.582515\pi\)
\(644\) 0 0
\(645\) 6.00000 0.236250
\(646\) 0 0
\(647\) 27.0000 1.06148 0.530740 0.847535i \(-0.321914\pi\)
0.530740 + 0.847535i \(0.321914\pi\)
\(648\) 0 0
\(649\) −18.0000 −0.706562
\(650\) 0 0
\(651\) −8.00000 −0.313545
\(652\) −40.0000 −1.56652
\(653\) −39.0000 −1.52619 −0.763094 0.646288i \(-0.776321\pi\)
−0.763094 + 0.646288i \(0.776321\pi\)
\(654\) 0 0
\(655\) −45.0000 −1.75830
\(656\) −24.0000 −0.937043
\(657\) −7.00000 −0.273096
\(658\) 0 0
\(659\) −30.0000 −1.16863 −0.584317 0.811525i \(-0.698638\pi\)
−0.584317 + 0.811525i \(0.698638\pi\)
\(660\) 36.0000 1.40130
\(661\) 32.0000 1.24466 0.622328 0.782757i \(-0.286187\pi\)
0.622328 + 0.782757i \(0.286187\pi\)
\(662\) 0 0
\(663\) −24.0000 −0.932083
\(664\) 0 0
\(665\) −3.00000 −0.116335
\(666\) 0 0
\(667\) 0 0
\(668\) 36.0000 1.39288
\(669\) 20.0000 0.773245
\(670\) 0 0
\(671\) −3.00000 −0.115814
\(672\) 0 0
\(673\) −10.0000 −0.385472 −0.192736 0.981251i \(-0.561736\pi\)
−0.192736 + 0.981251i \(0.561736\pi\)
\(674\) 0 0
\(675\) 16.0000 0.615840
\(676\) −6.00000 −0.230769
\(677\) −42.0000 −1.61419 −0.807096 0.590421i \(-0.798962\pi\)
−0.807096 + 0.590421i \(0.798962\pi\)
\(678\) 0 0
\(679\) −8.00000 −0.307012
\(680\) 0 0
\(681\) −24.0000 −0.919682
\(682\) 0 0
\(683\) 36.0000 1.37750 0.688751 0.724998i \(-0.258159\pi\)
0.688751 + 0.724998i \(0.258159\pi\)
\(684\) −2.00000 −0.0764719
\(685\) −9.00000 −0.343872
\(686\) 0 0
\(687\) −10.0000 −0.381524
\(688\) −4.00000 −0.152499
\(689\) −48.0000 −1.82865
\(690\) 0 0
\(691\) 17.0000 0.646710 0.323355 0.946278i \(-0.395189\pi\)
0.323355 + 0.946278i \(0.395189\pi\)
\(692\) 36.0000 1.36851
\(693\) −3.00000 −0.113961
\(694\) 0 0
\(695\) −39.0000 −1.47935
\(696\) 0 0
\(697\) 18.0000 0.681799
\(698\) 0 0
\(699\) 42.0000 1.58859
\(700\) 8.00000 0.302372
\(701\) 6.00000 0.226617 0.113308 0.993560i \(-0.463855\pi\)
0.113308 + 0.993560i \(0.463855\pi\)
\(702\) 0 0
\(703\) 2.00000 0.0754314
\(704\) −24.0000 −0.904534
\(705\) 18.0000 0.677919
\(706\) 0 0
\(707\) −6.00000 −0.225653
\(708\) −24.0000 −0.901975
\(709\) 26.0000 0.976450 0.488225 0.872718i \(-0.337644\pi\)
0.488225 + 0.872718i \(0.337644\pi\)
\(710\) 0 0
\(711\) 8.00000 0.300023
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) −36.0000 −1.34632
\(716\) 36.0000 1.34538
\(717\) −30.0000 −1.12037
\(718\) 0 0
\(719\) 15.0000 0.559406 0.279703 0.960087i \(-0.409764\pi\)
0.279703 + 0.960087i \(0.409764\pi\)
\(720\) 12.0000 0.447214
\(721\) −14.0000 −0.521387
\(722\) 0 0
\(723\) 20.0000 0.743808
\(724\) −4.00000 −0.148659
\(725\) 24.0000 0.891338
\(726\) 0 0
\(727\) −19.0000 −0.704671 −0.352335 0.935874i \(-0.614612\pi\)
−0.352335 + 0.935874i \(0.614612\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) 3.00000 0.110959
\(732\) −4.00000 −0.147844
\(733\) −22.0000 −0.812589 −0.406294 0.913742i \(-0.633179\pi\)
−0.406294 + 0.913742i \(0.633179\pi\)
\(734\) 0 0
\(735\) 36.0000 1.32788
\(736\) 0 0
\(737\) −12.0000 −0.442026
\(738\) 0 0
\(739\) 11.0000 0.404642 0.202321 0.979319i \(-0.435152\pi\)
0.202321 + 0.979319i \(0.435152\pi\)
\(740\) −12.0000 −0.441129
\(741\) 8.00000 0.293887
\(742\) 0 0
\(743\) −24.0000 −0.880475 −0.440237 0.897881i \(-0.645106\pi\)
−0.440237 + 0.897881i \(0.645106\pi\)
\(744\) 0 0
\(745\) 63.0000 2.30814
\(746\) 0 0
\(747\) 12.0000 0.439057
\(748\) 18.0000 0.658145
\(749\) 18.0000 0.657706
\(750\) 0 0
\(751\) 32.0000 1.16770 0.583848 0.811863i \(-0.301546\pi\)
0.583848 + 0.811863i \(0.301546\pi\)
\(752\) −12.0000 −0.437595
\(753\) −42.0000 −1.53057
\(754\) 0 0
\(755\) −30.0000 −1.09181
\(756\) 8.00000 0.290957
\(757\) −25.0000 −0.908640 −0.454320 0.890838i \(-0.650118\pi\)
−0.454320 + 0.890838i \(0.650118\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 33.0000 1.19625 0.598125 0.801403i \(-0.295913\pi\)
0.598125 + 0.801403i \(0.295913\pi\)
\(762\) 0 0
\(763\) 16.0000 0.579239
\(764\) −6.00000 −0.217072
\(765\) −9.00000 −0.325396
\(766\) 0 0
\(767\) 24.0000 0.866590
\(768\) −32.0000 −1.15470
\(769\) 23.0000 0.829401 0.414701 0.909958i \(-0.363886\pi\)
0.414701 + 0.909958i \(0.363886\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 8.00000 0.287926
\(773\) −6.00000 −0.215805 −0.107903 0.994161i \(-0.534413\pi\)
−0.107903 + 0.994161i \(0.534413\pi\)
\(774\) 0 0
\(775\) −16.0000 −0.574737
\(776\) 0 0
\(777\) 4.00000 0.143499
\(778\) 0 0
\(779\) −6.00000 −0.214972
\(780\) −48.0000 −1.71868
\(781\) 18.0000 0.644091
\(782\) 0 0
\(783\) 24.0000 0.857690
\(784\) −24.0000 −0.857143
\(785\) 42.0000 1.49904
\(786\) 0 0
\(787\) −4.00000 −0.142585 −0.0712923 0.997455i \(-0.522712\pi\)
−0.0712923 + 0.997455i \(0.522712\pi\)
\(788\) −36.0000 −1.28245
\(789\) −18.0000 −0.640817
\(790\) 0 0
\(791\) −6.00000 −0.213335
\(792\) 0 0
\(793\) 4.00000 0.142044
\(794\) 0 0
\(795\) −72.0000 −2.55358
\(796\) −22.0000 −0.779769
\(797\) −12.0000 −0.425062 −0.212531 0.977154i \(-0.568171\pi\)
−0.212531 + 0.977154i \(0.568171\pi\)
\(798\) 0 0
\(799\) 9.00000 0.318397
\(800\) 0 0
\(801\) 12.0000 0.423999
\(802\) 0 0
\(803\) −21.0000 −0.741074
\(804\) −16.0000 −0.564276
\(805\) 0 0
\(806\) 0 0
\(807\) −48.0000 −1.68968
\(808\) 0 0
\(809\) −9.00000 −0.316423 −0.158212 0.987405i \(-0.550573\pi\)
−0.158212 + 0.987405i \(0.550573\pi\)
\(810\) 0 0
\(811\) −16.0000 −0.561836 −0.280918 0.959732i \(-0.590639\pi\)
−0.280918 + 0.959732i \(0.590639\pi\)
\(812\) 12.0000 0.421117
\(813\) 32.0000 1.12229
\(814\) 0 0
\(815\) 60.0000 2.10171
\(816\) 24.0000 0.840168
\(817\) −1.00000 −0.0349856
\(818\) 0 0
\(819\) 4.00000 0.139771
\(820\) 36.0000 1.25717
\(821\) 33.0000 1.15171 0.575854 0.817553i \(-0.304670\pi\)
0.575854 + 0.817553i \(0.304670\pi\)
\(822\) 0 0
\(823\) −49.0000 −1.70803 −0.854016 0.520246i \(-0.825840\pi\)
−0.854016 + 0.520246i \(0.825840\pi\)
\(824\) 0 0
\(825\) −24.0000 −0.835573
\(826\) 0 0
\(827\) 12.0000 0.417281 0.208640 0.977992i \(-0.433096\pi\)
0.208640 + 0.977992i \(0.433096\pi\)
\(828\) 0 0
\(829\) −16.0000 −0.555703 −0.277851 0.960624i \(-0.589622\pi\)
−0.277851 + 0.960624i \(0.589622\pi\)
\(830\) 0 0
\(831\) 38.0000 1.31821
\(832\) 32.0000 1.10940
\(833\) 18.0000 0.623663
\(834\) 0 0
\(835\) −54.0000 −1.86875
\(836\) −6.00000 −0.207514
\(837\) −16.0000 −0.553041
\(838\) 0 0
\(839\) 18.0000 0.621429 0.310715 0.950503i \(-0.399432\pi\)
0.310715 + 0.950503i \(0.399432\pi\)
\(840\) 0 0
\(841\) 7.00000 0.241379
\(842\) 0 0
\(843\) −12.0000 −0.413302
\(844\) −28.0000 −0.963800
\(845\) 9.00000 0.309609
\(846\) 0 0
\(847\) 2.00000 0.0687208
\(848\) 48.0000 1.64833
\(849\) 26.0000 0.892318
\(850\) 0 0
\(851\) 0 0
\(852\) 24.0000 0.822226
\(853\) 26.0000 0.890223 0.445112 0.895475i \(-0.353164\pi\)
0.445112 + 0.895475i \(0.353164\pi\)
\(854\) 0 0
\(855\) 3.00000 0.102598
\(856\) 0 0
\(857\) 18.0000 0.614868 0.307434 0.951569i \(-0.400530\pi\)
0.307434 + 0.951569i \(0.400530\pi\)
\(858\) 0 0
\(859\) −49.0000 −1.67186 −0.835929 0.548837i \(-0.815071\pi\)
−0.835929 + 0.548837i \(0.815071\pi\)
\(860\) 6.00000 0.204598
\(861\) −12.0000 −0.408959
\(862\) 0 0
\(863\) 18.0000 0.612727 0.306364 0.951915i \(-0.400888\pi\)
0.306364 + 0.951915i \(0.400888\pi\)
\(864\) 0 0
\(865\) −54.0000 −1.83606
\(866\) 0 0
\(867\) 16.0000 0.543388
\(868\) −8.00000 −0.271538
\(869\) 24.0000 0.814144
\(870\) 0 0
\(871\) 16.0000 0.542139
\(872\) 0 0
\(873\) 8.00000 0.270759
\(874\) 0 0
\(875\) 3.00000 0.101419
\(876\) −28.0000 −0.946032
\(877\) −22.0000 −0.742887 −0.371444 0.928456i \(-0.621137\pi\)
−0.371444 + 0.928456i \(0.621137\pi\)
\(878\) 0 0
\(879\) 24.0000 0.809500
\(880\) 36.0000 1.21356
\(881\) −27.0000 −0.909653 −0.454827 0.890580i \(-0.650299\pi\)
−0.454827 + 0.890580i \(0.650299\pi\)
\(882\) 0 0
\(883\) 47.0000 1.58168 0.790838 0.612026i \(-0.209645\pi\)
0.790838 + 0.612026i \(0.209645\pi\)
\(884\) −24.0000 −0.807207
\(885\) 36.0000 1.21013
\(886\) 0 0
\(887\) 18.0000 0.604381 0.302190 0.953248i \(-0.402282\pi\)
0.302190 + 0.953248i \(0.402282\pi\)
\(888\) 0 0
\(889\) −2.00000 −0.0670778
\(890\) 0 0
\(891\) −33.0000 −1.10554
\(892\) 20.0000 0.669650
\(893\) −3.00000 −0.100391
\(894\) 0 0
\(895\) −54.0000 −1.80502
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −24.0000 −0.800445
\(900\) −8.00000 −0.266667
\(901\) −36.0000 −1.19933
\(902\) 0 0
\(903\) −2.00000 −0.0665558
\(904\) 0 0
\(905\) 6.00000 0.199447
\(906\) 0 0
\(907\) 8.00000 0.265636 0.132818 0.991140i \(-0.457597\pi\)
0.132818 + 0.991140i \(0.457597\pi\)
\(908\) −24.0000 −0.796468
\(909\) 6.00000 0.199007
\(910\) 0 0
\(911\) −6.00000 −0.198789 −0.0993944 0.995048i \(-0.531691\pi\)
−0.0993944 + 0.995048i \(0.531691\pi\)
\(912\) −8.00000 −0.264906
\(913\) 36.0000 1.19143
\(914\) 0 0
\(915\) 6.00000 0.198354
\(916\) −10.0000 −0.330409
\(917\) 15.0000 0.495344
\(918\) 0 0
\(919\) 20.0000 0.659739 0.329870 0.944027i \(-0.392995\pi\)
0.329870 + 0.944027i \(0.392995\pi\)
\(920\) 0 0
\(921\) −40.0000 −1.31804
\(922\) 0 0
\(923\) −24.0000 −0.789970
\(924\) −12.0000 −0.394771
\(925\) 8.00000 0.263038
\(926\) 0 0
\(927\) 14.0000 0.459820
\(928\) 0 0
\(929\) −18.0000 −0.590561 −0.295280 0.955411i \(-0.595413\pi\)
−0.295280 + 0.955411i \(0.595413\pi\)
\(930\) 0 0
\(931\) −6.00000 −0.196642
\(932\) 42.0000 1.37576
\(933\) 6.00000 0.196431
\(934\) 0 0
\(935\) −27.0000 −0.882994
\(936\) 0 0
\(937\) −7.00000 −0.228680 −0.114340 0.993442i \(-0.536475\pi\)
−0.114340 + 0.993442i \(0.536475\pi\)
\(938\) 0 0
\(939\) 20.0000 0.652675
\(940\) 18.0000 0.587095
\(941\) −18.0000 −0.586783 −0.293392 0.955992i \(-0.594784\pi\)
−0.293392 + 0.955992i \(0.594784\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) −24.0000 −0.781133
\(945\) −12.0000 −0.390360
\(946\) 0 0
\(947\) −36.0000 −1.16984 −0.584921 0.811090i \(-0.698875\pi\)
−0.584921 + 0.811090i \(0.698875\pi\)
\(948\) 32.0000 1.03931
\(949\) 28.0000 0.908918
\(950\) 0 0
\(951\) −12.0000 −0.389127
\(952\) 0 0
\(953\) −48.0000 −1.55487 −0.777436 0.628962i \(-0.783480\pi\)
−0.777436 + 0.628962i \(0.783480\pi\)
\(954\) 0 0
\(955\) 9.00000 0.291233
\(956\) −30.0000 −0.970269
\(957\) −36.0000 −1.16371
\(958\) 0 0
\(959\) 3.00000 0.0968751
\(960\) 48.0000 1.54919
\(961\) −15.0000 −0.483871
\(962\) 0 0
\(963\) −18.0000 −0.580042
\(964\) 20.0000 0.644157
\(965\) −12.0000 −0.386294
\(966\) 0 0
\(967\) −40.0000 −1.28631 −0.643157 0.765735i \(-0.722376\pi\)
−0.643157 + 0.765735i \(0.722376\pi\)
\(968\) 0 0
\(969\) 6.00000 0.192748
\(970\) 0 0
\(971\) 60.0000 1.92549 0.962746 0.270408i \(-0.0871586\pi\)
0.962746 + 0.270408i \(0.0871586\pi\)
\(972\) −20.0000 −0.641500
\(973\) 13.0000 0.416761
\(974\) 0 0
\(975\) 32.0000 1.02482
\(976\) −4.00000 −0.128037
\(977\) 24.0000 0.767828 0.383914 0.923369i \(-0.374576\pi\)
0.383914 + 0.923369i \(0.374576\pi\)
\(978\) 0 0
\(979\) 36.0000 1.15056
\(980\) 36.0000 1.14998
\(981\) −16.0000 −0.510841
\(982\) 0 0
\(983\) −36.0000 −1.14822 −0.574111 0.818778i \(-0.694652\pi\)
−0.574111 + 0.818778i \(0.694652\pi\)
\(984\) 0 0
\(985\) 54.0000 1.72058
\(986\) 0 0
\(987\) −6.00000 −0.190982
\(988\) 8.00000 0.254514
\(989\) 0 0
\(990\) 0 0
\(991\) −34.0000 −1.08005 −0.540023 0.841650i \(-0.681584\pi\)
−0.540023 + 0.841650i \(0.681584\pi\)
\(992\) 0 0
\(993\) 56.0000 1.77711
\(994\) 0 0
\(995\) 33.0000 1.04617
\(996\) 48.0000 1.52094
\(997\) 17.0000 0.538395 0.269198 0.963085i \(-0.413241\pi\)
0.269198 + 0.963085i \(0.413241\pi\)
\(998\) 0 0
\(999\) 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 \(a_p\))