Properties

Label 143.2.a.a.1.1
Level 143
Weight 2
Character 143.1
Self dual Yes
Analytic conductor 1.142
Analytic rank 1
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 143 = 11 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 143.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(1.1418607489\)
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 \(\chi\) = 143.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{3}\) \(-2.00000 q^{4}\) \(-1.00000 q^{5}\) \(-2.00000 q^{7}\) \(-2.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{3}\) \(-2.00000 q^{4}\) \(-1.00000 q^{5}\) \(-2.00000 q^{7}\) \(-2.00000 q^{9}\) \(-1.00000 q^{11}\) \(+2.00000 q^{12}\) \(-1.00000 q^{13}\) \(+1.00000 q^{15}\) \(+4.00000 q^{16}\) \(-4.00000 q^{17}\) \(+2.00000 q^{19}\) \(+2.00000 q^{20}\) \(+2.00000 q^{21}\) \(+7.00000 q^{23}\) \(-4.00000 q^{25}\) \(+5.00000 q^{27}\) \(+4.00000 q^{28}\) \(-2.00000 q^{29}\) \(-3.00000 q^{31}\) \(+1.00000 q^{33}\) \(+2.00000 q^{35}\) \(+4.00000 q^{36}\) \(-11.0000 q^{37}\) \(+1.00000 q^{39}\) \(+10.0000 q^{41}\) \(-4.00000 q^{43}\) \(+2.00000 q^{44}\) \(+2.00000 q^{45}\) \(-4.00000 q^{47}\) \(-4.00000 q^{48}\) \(-3.00000 q^{49}\) \(+4.00000 q^{51}\) \(+2.00000 q^{52}\) \(+2.00000 q^{53}\) \(+1.00000 q^{55}\) \(-2.00000 q^{57}\) \(-1.00000 q^{59}\) \(-2.00000 q^{60}\) \(-2.00000 q^{61}\) \(+4.00000 q^{63}\) \(-8.00000 q^{64}\) \(+1.00000 q^{65}\) \(-1.00000 q^{67}\) \(+8.00000 q^{68}\) \(-7.00000 q^{69}\) \(-9.00000 q^{71}\) \(-16.0000 q^{73}\) \(+4.00000 q^{75}\) \(-4.00000 q^{76}\) \(+2.00000 q^{77}\) \(+8.00000 q^{79}\) \(-4.00000 q^{80}\) \(+1.00000 q^{81}\) \(-4.00000 q^{84}\) \(+4.00000 q^{85}\) \(+2.00000 q^{87}\) \(-7.00000 q^{89}\) \(+2.00000 q^{91}\) \(-14.0000 q^{92}\) \(+3.00000 q^{93}\) \(-2.00000 q^{95}\) \(-13.0000 q^{97}\) \(+2.00000 q^{99}\) \(+O(q^{100})\)

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 \(0.5\pi\)
\(3\) −1.00000 −0.577350 −0.288675 0.957427i \(-0.593215\pi\)
−0.288675 + 0.957427i \(0.593215\pi\)
\(4\) −2.00000 −1.00000
\(5\) −1.00000 −0.447214 −0.223607 0.974679i \(-0.571783\pi\)
−0.223607 + 0.974679i \(0.571783\pi\)
\(6\) 0 0
\(7\) −2.00000 −0.755929 −0.377964 0.925820i \(-0.623376\pi\)
−0.377964 + 0.925820i \(0.623376\pi\)
\(8\) 0 0
\(9\) −2.00000 −0.666667
\(10\) 0 0
\(11\) −1.00000 −0.301511
\(12\) 2.00000 0.577350
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) 1.00000 0.258199
\(16\) 4.00000 1.00000
\(17\) −4.00000 −0.970143 −0.485071 0.874475i \(-0.661206\pi\)
−0.485071 + 0.874475i \(0.661206\pi\)
\(18\) 0 0
\(19\) 2.00000 0.458831 0.229416 0.973329i \(-0.426318\pi\)
0.229416 + 0.973329i \(0.426318\pi\)
\(20\) 2.00000 0.447214
\(21\) 2.00000 0.436436
\(22\) 0 0
\(23\) 7.00000 1.45960 0.729800 0.683660i \(-0.239613\pi\)
0.729800 + 0.683660i \(0.239613\pi\)
\(24\) 0 0
\(25\) −4.00000 −0.800000
\(26\) 0 0
\(27\) 5.00000 0.962250
\(28\) 4.00000 0.755929
\(29\) −2.00000 −0.371391 −0.185695 0.982607i \(-0.559454\pi\)
−0.185695 + 0.982607i \(0.559454\pi\)
\(30\) 0 0
\(31\) −3.00000 −0.538816 −0.269408 0.963026i \(-0.586828\pi\)
−0.269408 + 0.963026i \(0.586828\pi\)
\(32\) 0 0
\(33\) 1.00000 0.174078
\(34\) 0 0
\(35\) 2.00000 0.338062
\(36\) 4.00000 0.666667
\(37\) −11.0000 −1.80839 −0.904194 0.427121i \(-0.859528\pi\)
−0.904194 + 0.427121i \(0.859528\pi\)
\(38\) 0 0
\(39\) 1.00000 0.160128
\(40\) 0 0
\(41\) 10.0000 1.56174 0.780869 0.624695i \(-0.214777\pi\)
0.780869 + 0.624695i \(0.214777\pi\)
\(42\) 0 0
\(43\) −4.00000 −0.609994 −0.304997 0.952353i \(-0.598656\pi\)
−0.304997 + 0.952353i \(0.598656\pi\)
\(44\) 2.00000 0.301511
\(45\) 2.00000 0.298142
\(46\) 0 0
\(47\) −4.00000 −0.583460 −0.291730 0.956501i \(-0.594231\pi\)
−0.291730 + 0.956501i \(0.594231\pi\)
\(48\) −4.00000 −0.577350
\(49\) −3.00000 −0.428571
\(50\) 0 0
\(51\) 4.00000 0.560112
\(52\) 2.00000 0.277350
\(53\) 2.00000 0.274721 0.137361 0.990521i \(-0.456138\pi\)
0.137361 + 0.990521i \(0.456138\pi\)
\(54\) 0 0
\(55\) 1.00000 0.134840
\(56\) 0 0
\(57\) −2.00000 −0.264906
\(58\) 0 0
\(59\) −1.00000 −0.130189 −0.0650945 0.997879i \(-0.520735\pi\)
−0.0650945 + 0.997879i \(0.520735\pi\)
\(60\) −2.00000 −0.258199
\(61\) −2.00000 −0.256074 −0.128037 0.991769i \(-0.540868\pi\)
−0.128037 + 0.991769i \(0.540868\pi\)
\(62\) 0 0
\(63\) 4.00000 0.503953
\(64\) −8.00000 −1.00000
\(65\) 1.00000 0.124035
\(66\) 0 0
\(67\) −1.00000 −0.122169 −0.0610847 0.998133i \(-0.519456\pi\)
−0.0610847 + 0.998133i \(0.519456\pi\)
\(68\) 8.00000 0.970143
\(69\) −7.00000 −0.842701
\(70\) 0 0
\(71\) −9.00000 −1.06810 −0.534052 0.845452i \(-0.679331\pi\)
−0.534052 + 0.845452i \(0.679331\pi\)
\(72\) 0 0
\(73\) −16.0000 −1.87266 −0.936329 0.351123i \(-0.885800\pi\)
−0.936329 + 0.351123i \(0.885800\pi\)
\(74\) 0 0
\(75\) 4.00000 0.461880
\(76\) −4.00000 −0.458831
\(77\) 2.00000 0.227921
\(78\) 0 0
\(79\) 8.00000 0.900070 0.450035 0.893011i \(-0.351411\pi\)
0.450035 + 0.893011i \(0.351411\pi\)
\(80\) −4.00000 −0.447214
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) −4.00000 −0.436436
\(85\) 4.00000 0.433861
\(86\) 0 0
\(87\) 2.00000 0.214423
\(88\) 0 0
\(89\) −7.00000 −0.741999 −0.370999 0.928633i \(-0.620985\pi\)
−0.370999 + 0.928633i \(0.620985\pi\)
\(90\) 0 0
\(91\) 2.00000 0.209657
\(92\) −14.0000 −1.45960
\(93\) 3.00000 0.311086
\(94\) 0 0
\(95\) −2.00000 −0.205196
\(96\) 0 0
\(97\) −13.0000 −1.31995 −0.659975 0.751288i \(-0.729433\pi\)
−0.659975 + 0.751288i \(0.729433\pi\)
\(98\) 0 0
\(99\) 2.00000 0.201008
\(100\) 8.00000 0.800000
\(101\) 18.0000 1.79107 0.895533 0.444994i \(-0.146794\pi\)
0.895533 + 0.444994i \(0.146794\pi\)
\(102\) 0 0
\(103\) 8.00000 0.788263 0.394132 0.919054i \(-0.371045\pi\)
0.394132 + 0.919054i \(0.371045\pi\)
\(104\) 0 0
\(105\) −2.00000 −0.195180
\(106\) 0 0
\(107\) 8.00000 0.773389 0.386695 0.922208i \(-0.373617\pi\)
0.386695 + 0.922208i \(0.373617\pi\)
\(108\) −10.0000 −0.962250
\(109\) 4.00000 0.383131 0.191565 0.981480i \(-0.438644\pi\)
0.191565 + 0.981480i \(0.438644\pi\)
\(110\) 0 0
\(111\) 11.0000 1.04407
\(112\) −8.00000 −0.755929
\(113\) 1.00000 0.0940721 0.0470360 0.998893i \(-0.485022\pi\)
0.0470360 + 0.998893i \(0.485022\pi\)
\(114\) 0 0
\(115\) −7.00000 −0.652753
\(116\) 4.00000 0.371391
\(117\) 2.00000 0.184900
\(118\) 0 0
\(119\) 8.00000 0.733359
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) −10.0000 −0.901670
\(124\) 6.00000 0.538816
\(125\) 9.00000 0.804984
\(126\) 0 0
\(127\) −8.00000 −0.709885 −0.354943 0.934888i \(-0.615500\pi\)
−0.354943 + 0.934888i \(0.615500\pi\)
\(128\) 0 0
\(129\) 4.00000 0.352180
\(130\) 0 0
\(131\) 18.0000 1.57267 0.786334 0.617802i \(-0.211977\pi\)
0.786334 + 0.617802i \(0.211977\pi\)
\(132\) −2.00000 −0.174078
\(133\) −4.00000 −0.346844
\(134\) 0 0
\(135\) −5.00000 −0.430331
\(136\) 0 0
\(137\) −17.0000 −1.45241 −0.726204 0.687479i \(-0.758717\pi\)
−0.726204 + 0.687479i \(0.758717\pi\)
\(138\) 0 0
\(139\) 18.0000 1.52674 0.763370 0.645961i \(-0.223543\pi\)
0.763370 + 0.645961i \(0.223543\pi\)
\(140\) −4.00000 −0.338062
\(141\) 4.00000 0.336861
\(142\) 0 0
\(143\) 1.00000 0.0836242
\(144\) −8.00000 −0.666667
\(145\) 2.00000 0.166091
\(146\) 0 0
\(147\) 3.00000 0.247436
\(148\) 22.0000 1.80839
\(149\) 14.0000 1.14692 0.573462 0.819232i \(-0.305600\pi\)
0.573462 + 0.819232i \(0.305600\pi\)
\(150\) 0 0
\(151\) 4.00000 0.325515 0.162758 0.986666i \(-0.447961\pi\)
0.162758 + 0.986666i \(0.447961\pi\)
\(152\) 0 0
\(153\) 8.00000 0.646762
\(154\) 0 0
\(155\) 3.00000 0.240966
\(156\) −2.00000 −0.160128
\(157\) 5.00000 0.399043 0.199522 0.979893i \(-0.436061\pi\)
0.199522 + 0.979893i \(0.436061\pi\)
\(158\) 0 0
\(159\) −2.00000 −0.158610
\(160\) 0 0
\(161\) −14.0000 −1.10335
\(162\) 0 0
\(163\) −4.00000 −0.313304 −0.156652 0.987654i \(-0.550070\pi\)
−0.156652 + 0.987654i \(0.550070\pi\)
\(164\) −20.0000 −1.56174
\(165\) −1.00000 −0.0778499
\(166\) 0 0
\(167\) 4.00000 0.309529 0.154765 0.987951i \(-0.450538\pi\)
0.154765 + 0.987951i \(0.450538\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) −4.00000 −0.305888
\(172\) 8.00000 0.609994
\(173\) −8.00000 −0.608229 −0.304114 0.952636i \(-0.598361\pi\)
−0.304114 + 0.952636i \(0.598361\pi\)
\(174\) 0 0
\(175\) 8.00000 0.604743
\(176\) −4.00000 −0.301511
\(177\) 1.00000 0.0751646
\(178\) 0 0
\(179\) −15.0000 −1.12115 −0.560576 0.828103i \(-0.689420\pi\)
−0.560576 + 0.828103i \(0.689420\pi\)
\(180\) −4.00000 −0.298142
\(181\) 7.00000 0.520306 0.260153 0.965567i \(-0.416227\pi\)
0.260153 + 0.965567i \(0.416227\pi\)
\(182\) 0 0
\(183\) 2.00000 0.147844
\(184\) 0 0
\(185\) 11.0000 0.808736
\(186\) 0 0
\(187\) 4.00000 0.292509
\(188\) 8.00000 0.583460
\(189\) −10.0000 −0.727393
\(190\) 0 0
\(191\) −15.0000 −1.08536 −0.542681 0.839939i \(-0.682591\pi\)
−0.542681 + 0.839939i \(0.682591\pi\)
\(192\) 8.00000 0.577350
\(193\) −24.0000 −1.72756 −0.863779 0.503871i \(-0.831909\pi\)
−0.863779 + 0.503871i \(0.831909\pi\)
\(194\) 0 0
\(195\) −1.00000 −0.0716115
\(196\) 6.00000 0.428571
\(197\) −10.0000 −0.712470 −0.356235 0.934396i \(-0.615940\pi\)
−0.356235 + 0.934396i \(0.615940\pi\)
\(198\) 0 0
\(199\) −4.00000 −0.283552 −0.141776 0.989899i \(-0.545281\pi\)
−0.141776 + 0.989899i \(0.545281\pi\)
\(200\) 0 0
\(201\) 1.00000 0.0705346
\(202\) 0 0
\(203\) 4.00000 0.280745
\(204\) −8.00000 −0.560112
\(205\) −10.0000 −0.698430
\(206\) 0 0
\(207\) −14.0000 −0.973067
\(208\) −4.00000 −0.277350
\(209\) −2.00000 −0.138343
\(210\) 0 0
\(211\) −24.0000 −1.65223 −0.826114 0.563503i \(-0.809453\pi\)
−0.826114 + 0.563503i \(0.809453\pi\)
\(212\) −4.00000 −0.274721
\(213\) 9.00000 0.616670
\(214\) 0 0
\(215\) 4.00000 0.272798
\(216\) 0 0
\(217\) 6.00000 0.407307
\(218\) 0 0
\(219\) 16.0000 1.08118
\(220\) −2.00000 −0.134840
\(221\) 4.00000 0.269069
\(222\) 0 0
\(223\) 5.00000 0.334825 0.167412 0.985887i \(-0.446459\pi\)
0.167412 + 0.985887i \(0.446459\pi\)
\(224\) 0 0
\(225\) 8.00000 0.533333
\(226\) 0 0
\(227\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(228\) 4.00000 0.264906
\(229\) 9.00000 0.594737 0.297368 0.954763i \(-0.403891\pi\)
0.297368 + 0.954763i \(0.403891\pi\)
\(230\) 0 0
\(231\) −2.00000 −0.131590
\(232\) 0 0
\(233\) −16.0000 −1.04819 −0.524097 0.851658i \(-0.675597\pi\)
−0.524097 + 0.851658i \(0.675597\pi\)
\(234\) 0 0
\(235\) 4.00000 0.260931
\(236\) 2.00000 0.130189
\(237\) −8.00000 −0.519656
\(238\) 0 0
\(239\) −30.0000 −1.94054 −0.970269 0.242028i \(-0.922188\pi\)
−0.970269 + 0.242028i \(0.922188\pi\)
\(240\) 4.00000 0.258199
\(241\) −10.0000 −0.644157 −0.322078 0.946713i \(-0.604381\pi\)
−0.322078 + 0.946713i \(0.604381\pi\)
\(242\) 0 0
\(243\) −16.0000 −1.02640
\(244\) 4.00000 0.256074
\(245\) 3.00000 0.191663
\(246\) 0 0
\(247\) −2.00000 −0.127257
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 21.0000 1.32551 0.662754 0.748837i \(-0.269387\pi\)
0.662754 + 0.748837i \(0.269387\pi\)
\(252\) −8.00000 −0.503953
\(253\) −7.00000 −0.440086
\(254\) 0 0
\(255\) −4.00000 −0.250490
\(256\) 16.0000 1.00000
\(257\) 18.0000 1.12281 0.561405 0.827541i \(-0.310261\pi\)
0.561405 + 0.827541i \(0.310261\pi\)
\(258\) 0 0
\(259\) 22.0000 1.36701
\(260\) −2.00000 −0.124035
\(261\) 4.00000 0.247594
\(262\) 0 0
\(263\) −18.0000 −1.10993 −0.554964 0.831875i \(-0.687268\pi\)
−0.554964 + 0.831875i \(0.687268\pi\)
\(264\) 0 0
\(265\) −2.00000 −0.122859
\(266\) 0 0
\(267\) 7.00000 0.428393
\(268\) 2.00000 0.122169
\(269\) −30.0000 −1.82913 −0.914566 0.404436i \(-0.867468\pi\)
−0.914566 + 0.404436i \(0.867468\pi\)
\(270\) 0 0
\(271\) 28.0000 1.70088 0.850439 0.526073i \(-0.176336\pi\)
0.850439 + 0.526073i \(0.176336\pi\)
\(272\) −16.0000 −0.970143
\(273\) −2.00000 −0.121046
\(274\) 0 0
\(275\) 4.00000 0.241209
\(276\) 14.0000 0.842701
\(277\) 26.0000 1.56219 0.781094 0.624413i \(-0.214662\pi\)
0.781094 + 0.624413i \(0.214662\pi\)
\(278\) 0 0
\(279\) 6.00000 0.359211
\(280\) 0 0
\(281\) 18.0000 1.07379 0.536895 0.843649i \(-0.319597\pi\)
0.536895 + 0.843649i \(0.319597\pi\)
\(282\) 0 0
\(283\) −30.0000 −1.78331 −0.891657 0.452711i \(-0.850457\pi\)
−0.891657 + 0.452711i \(0.850457\pi\)
\(284\) 18.0000 1.06810
\(285\) 2.00000 0.118470
\(286\) 0 0
\(287\) −20.0000 −1.18056
\(288\) 0 0
\(289\) −1.00000 −0.0588235
\(290\) 0 0
\(291\) 13.0000 0.762073
\(292\) 32.0000 1.87266
\(293\) 14.0000 0.817889 0.408944 0.912559i \(-0.365897\pi\)
0.408944 + 0.912559i \(0.365897\pi\)
\(294\) 0 0
\(295\) 1.00000 0.0582223
\(296\) 0 0
\(297\) −5.00000 −0.290129
\(298\) 0 0
\(299\) −7.00000 −0.404820
\(300\) −8.00000 −0.461880
\(301\) 8.00000 0.461112
\(302\) 0 0
\(303\) −18.0000 −1.03407
\(304\) 8.00000 0.458831
\(305\) 2.00000 0.114520
\(306\) 0 0
\(307\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(308\) −4.00000 −0.227921
\(309\) −8.00000 −0.455104
\(310\) 0 0
\(311\) 8.00000 0.453638 0.226819 0.973937i \(-0.427167\pi\)
0.226819 + 0.973937i \(0.427167\pi\)
\(312\) 0 0
\(313\) 3.00000 0.169570 0.0847850 0.996399i \(-0.472980\pi\)
0.0847850 + 0.996399i \(0.472980\pi\)
\(314\) 0 0
\(315\) −4.00000 −0.225374
\(316\) −16.0000 −0.900070
\(317\) −1.00000 −0.0561656 −0.0280828 0.999606i \(-0.508940\pi\)
−0.0280828 + 0.999606i \(0.508940\pi\)
\(318\) 0 0
\(319\) 2.00000 0.111979
\(320\) 8.00000 0.447214
\(321\) −8.00000 −0.446516
\(322\) 0 0
\(323\) −8.00000 −0.445132
\(324\) −2.00000 −0.111111
\(325\) 4.00000 0.221880
\(326\) 0 0
\(327\) −4.00000 −0.221201
\(328\) 0 0
\(329\) 8.00000 0.441054
\(330\) 0 0
\(331\) −11.0000 −0.604615 −0.302307 0.953211i \(-0.597757\pi\)
−0.302307 + 0.953211i \(0.597757\pi\)
\(332\) 0 0
\(333\) 22.0000 1.20559
\(334\) 0 0
\(335\) 1.00000 0.0546358
\(336\) 8.00000 0.436436
\(337\) −20.0000 −1.08947 −0.544735 0.838608i \(-0.683370\pi\)
−0.544735 + 0.838608i \(0.683370\pi\)
\(338\) 0 0
\(339\) −1.00000 −0.0543125
\(340\) −8.00000 −0.433861
\(341\) 3.00000 0.162459
\(342\) 0 0
\(343\) 20.0000 1.07990
\(344\) 0 0
\(345\) 7.00000 0.376867
\(346\) 0 0
\(347\) 18.0000 0.966291 0.483145 0.875540i \(-0.339494\pi\)
0.483145 + 0.875540i \(0.339494\pi\)
\(348\) −4.00000 −0.214423
\(349\) 16.0000 0.856460 0.428230 0.903670i \(-0.359137\pi\)
0.428230 + 0.903670i \(0.359137\pi\)
\(350\) 0 0
\(351\) −5.00000 −0.266880
\(352\) 0 0
\(353\) −15.0000 −0.798369 −0.399185 0.916871i \(-0.630707\pi\)
−0.399185 + 0.916871i \(0.630707\pi\)
\(354\) 0 0
\(355\) 9.00000 0.477670
\(356\) 14.0000 0.741999
\(357\) −8.00000 −0.423405
\(358\) 0 0
\(359\) 22.0000 1.16112 0.580558 0.814219i \(-0.302835\pi\)
0.580558 + 0.814219i \(0.302835\pi\)
\(360\) 0 0
\(361\) −15.0000 −0.789474
\(362\) 0 0
\(363\) −1.00000 −0.0524864
\(364\) −4.00000 −0.209657
\(365\) 16.0000 0.837478
\(366\) 0 0
\(367\) 3.00000 0.156599 0.0782994 0.996930i \(-0.475051\pi\)
0.0782994 + 0.996930i \(0.475051\pi\)
\(368\) 28.0000 1.45960
\(369\) −20.0000 −1.04116
\(370\) 0 0
\(371\) −4.00000 −0.207670
\(372\) −6.00000 −0.311086
\(373\) 26.0000 1.34623 0.673114 0.739538i \(-0.264956\pi\)
0.673114 + 0.739538i \(0.264956\pi\)
\(374\) 0 0
\(375\) −9.00000 −0.464758
\(376\) 0 0
\(377\) 2.00000 0.103005
\(378\) 0 0
\(379\) −11.0000 −0.565032 −0.282516 0.959263i \(-0.591169\pi\)
−0.282516 + 0.959263i \(0.591169\pi\)
\(380\) 4.00000 0.205196
\(381\) 8.00000 0.409852
\(382\) 0 0
\(383\) −19.0000 −0.970855 −0.485427 0.874277i \(-0.661336\pi\)
−0.485427 + 0.874277i \(0.661336\pi\)
\(384\) 0 0
\(385\) −2.00000 −0.101929
\(386\) 0 0
\(387\) 8.00000 0.406663
\(388\) 26.0000 1.31995
\(389\) 9.00000 0.456318 0.228159 0.973624i \(-0.426729\pi\)
0.228159 + 0.973624i \(0.426729\pi\)
\(390\) 0 0
\(391\) −28.0000 −1.41602
\(392\) 0 0
\(393\) −18.0000 −0.907980
\(394\) 0 0
\(395\) −8.00000 −0.402524
\(396\) −4.00000 −0.201008
\(397\) −18.0000 −0.903394 −0.451697 0.892171i \(-0.649181\pi\)
−0.451697 + 0.892171i \(0.649181\pi\)
\(398\) 0 0
\(399\) 4.00000 0.200250
\(400\) −16.0000 −0.800000
\(401\) −18.0000 −0.898877 −0.449439 0.893311i \(-0.648376\pi\)
−0.449439 + 0.893311i \(0.648376\pi\)
\(402\) 0 0
\(403\) 3.00000 0.149441
\(404\) −36.0000 −1.79107
\(405\) −1.00000 −0.0496904
\(406\) 0 0
\(407\) 11.0000 0.545250
\(408\) 0 0
\(409\) −18.0000 −0.890043 −0.445021 0.895520i \(-0.646804\pi\)
−0.445021 + 0.895520i \(0.646804\pi\)
\(410\) 0 0
\(411\) 17.0000 0.838548
\(412\) −16.0000 −0.788263
\(413\) 2.00000 0.0984136
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −18.0000 −0.881464
\(418\) 0 0
\(419\) −28.0000 −1.36789 −0.683945 0.729534i \(-0.739737\pi\)
−0.683945 + 0.729534i \(0.739737\pi\)
\(420\) 4.00000 0.195180
\(421\) −22.0000 −1.07221 −0.536107 0.844150i \(-0.680106\pi\)
−0.536107 + 0.844150i \(0.680106\pi\)
\(422\) 0 0
\(423\) 8.00000 0.388973
\(424\) 0 0
\(425\) 16.0000 0.776114
\(426\) 0 0
\(427\) 4.00000 0.193574
\(428\) −16.0000 −0.773389
\(429\) −1.00000 −0.0482805
\(430\) 0 0
\(431\) −40.0000 −1.92673 −0.963366 0.268190i \(-0.913575\pi\)
−0.963366 + 0.268190i \(0.913575\pi\)
\(432\) 20.0000 0.962250
\(433\) 33.0000 1.58588 0.792939 0.609301i \(-0.208550\pi\)
0.792939 + 0.609301i \(0.208550\pi\)
\(434\) 0 0
\(435\) −2.00000 −0.0958927
\(436\) −8.00000 −0.383131
\(437\) 14.0000 0.669711
\(438\) 0 0
\(439\) 6.00000 0.286364 0.143182 0.989696i \(-0.454267\pi\)
0.143182 + 0.989696i \(0.454267\pi\)
\(440\) 0 0
\(441\) 6.00000 0.285714
\(442\) 0 0
\(443\) −23.0000 −1.09276 −0.546381 0.837536i \(-0.683995\pi\)
−0.546381 + 0.837536i \(0.683995\pi\)
\(444\) −22.0000 −1.04407
\(445\) 7.00000 0.331832
\(446\) 0 0
\(447\) −14.0000 −0.662177
\(448\) 16.0000 0.755929
\(449\) 21.0000 0.991051 0.495526 0.868593i \(-0.334975\pi\)
0.495526 + 0.868593i \(0.334975\pi\)
\(450\) 0 0
\(451\) −10.0000 −0.470882
\(452\) −2.00000 −0.0940721
\(453\) −4.00000 −0.187936
\(454\) 0 0
\(455\) −2.00000 −0.0937614
\(456\) 0 0
\(457\) −16.0000 −0.748448 −0.374224 0.927338i \(-0.622091\pi\)
−0.374224 + 0.927338i \(0.622091\pi\)
\(458\) 0 0
\(459\) −20.0000 −0.933520
\(460\) 14.0000 0.652753
\(461\) 10.0000 0.465746 0.232873 0.972507i \(-0.425187\pi\)
0.232873 + 0.972507i \(0.425187\pi\)
\(462\) 0 0
\(463\) −9.00000 −0.418265 −0.209133 0.977887i \(-0.567064\pi\)
−0.209133 + 0.977887i \(0.567064\pi\)
\(464\) −8.00000 −0.371391
\(465\) −3.00000 −0.139122
\(466\) 0 0
\(467\) −23.0000 −1.06431 −0.532157 0.846646i \(-0.678618\pi\)
−0.532157 + 0.846646i \(0.678618\pi\)
\(468\) −4.00000 −0.184900
\(469\) 2.00000 0.0923514
\(470\) 0 0
\(471\) −5.00000 −0.230388
\(472\) 0 0
\(473\) 4.00000 0.183920
\(474\) 0 0
\(475\) −8.00000 −0.367065
\(476\) −16.0000 −0.733359
\(477\) −4.00000 −0.183147
\(478\) 0 0
\(479\) 36.0000 1.64488 0.822441 0.568850i \(-0.192612\pi\)
0.822441 + 0.568850i \(0.192612\pi\)
\(480\) 0 0
\(481\) 11.0000 0.501557
\(482\) 0 0
\(483\) 14.0000 0.637022
\(484\) −2.00000 −0.0909091
\(485\) 13.0000 0.590300
\(486\) 0 0
\(487\) 25.0000 1.13286 0.566429 0.824110i \(-0.308325\pi\)
0.566429 + 0.824110i \(0.308325\pi\)
\(488\) 0 0
\(489\) 4.00000 0.180886
\(490\) 0 0
\(491\) 12.0000 0.541552 0.270776 0.962642i \(-0.412720\pi\)
0.270776 + 0.962642i \(0.412720\pi\)
\(492\) 20.0000 0.901670
\(493\) 8.00000 0.360302
\(494\) 0 0
\(495\) −2.00000 −0.0898933
\(496\) −12.0000 −0.538816
\(497\) 18.0000 0.807410
\(498\) 0 0
\(499\) 28.0000 1.25345 0.626726 0.779240i \(-0.284395\pi\)
0.626726 + 0.779240i \(0.284395\pi\)
\(500\) −18.0000 −0.804984
\(501\) −4.00000 −0.178707
\(502\) 0 0
\(503\) 30.0000 1.33763 0.668817 0.743427i \(-0.266801\pi\)
0.668817 + 0.743427i \(0.266801\pi\)
\(504\) 0 0
\(505\) −18.0000 −0.800989
\(506\) 0 0
\(507\) −1.00000 −0.0444116
\(508\) 16.0000 0.709885
\(509\) 9.00000 0.398918 0.199459 0.979906i \(-0.436082\pi\)
0.199459 + 0.979906i \(0.436082\pi\)
\(510\) 0 0
\(511\) 32.0000 1.41560
\(512\) 0 0
\(513\) 10.0000 0.441511
\(514\) 0 0
\(515\) −8.00000 −0.352522
\(516\) −8.00000 −0.352180
\(517\) 4.00000 0.175920
\(518\) 0 0
\(519\) 8.00000 0.351161
\(520\) 0 0
\(521\) 5.00000 0.219054 0.109527 0.993984i \(-0.465066\pi\)
0.109527 + 0.993984i \(0.465066\pi\)
\(522\) 0 0
\(523\) −14.0000 −0.612177 −0.306089 0.952003i \(-0.599020\pi\)
−0.306089 + 0.952003i \(0.599020\pi\)
\(524\) −36.0000 −1.57267
\(525\) −8.00000 −0.349149
\(526\) 0 0
\(527\) 12.0000 0.522728
\(528\) 4.00000 0.174078
\(529\) 26.0000 1.13043
\(530\) 0 0
\(531\) 2.00000 0.0867926
\(532\) 8.00000 0.346844
\(533\) −10.0000 −0.433148
\(534\) 0 0
\(535\) −8.00000 −0.345870
\(536\) 0 0
\(537\) 15.0000 0.647298
\(538\) 0 0
\(539\) 3.00000 0.129219
\(540\) 10.0000 0.430331
\(541\) −30.0000 −1.28980 −0.644900 0.764267i \(-0.723101\pi\)
−0.644900 + 0.764267i \(0.723101\pi\)
\(542\) 0 0
\(543\) −7.00000 −0.300399
\(544\) 0 0
\(545\) −4.00000 −0.171341
\(546\) 0 0
\(547\) 8.00000 0.342055 0.171028 0.985266i \(-0.445291\pi\)
0.171028 + 0.985266i \(0.445291\pi\)
\(548\) 34.0000 1.45241
\(549\) 4.00000 0.170716
\(550\) 0 0
\(551\) −4.00000 −0.170406
\(552\) 0 0
\(553\) −16.0000 −0.680389
\(554\) 0 0
\(555\) −11.0000 −0.466924
\(556\) −36.0000 −1.52674
\(557\) 12.0000 0.508456 0.254228 0.967144i \(-0.418179\pi\)
0.254228 + 0.967144i \(0.418179\pi\)
\(558\) 0 0
\(559\) 4.00000 0.169182
\(560\) 8.00000 0.338062
\(561\) −4.00000 −0.168880
\(562\) 0 0
\(563\) 18.0000 0.758610 0.379305 0.925272i \(-0.376163\pi\)
0.379305 + 0.925272i \(0.376163\pi\)
\(564\) −8.00000 −0.336861
\(565\) −1.00000 −0.0420703
\(566\) 0 0
\(567\) −2.00000 −0.0839921
\(568\) 0 0
\(569\) −32.0000 −1.34151 −0.670755 0.741679i \(-0.734030\pi\)
−0.670755 + 0.741679i \(0.734030\pi\)
\(570\) 0 0
\(571\) 40.0000 1.67395 0.836974 0.547243i \(-0.184323\pi\)
0.836974 + 0.547243i \(0.184323\pi\)
\(572\) −2.00000 −0.0836242
\(573\) 15.0000 0.626634
\(574\) 0 0
\(575\) −28.0000 −1.16768
\(576\) 16.0000 0.666667
\(577\) 31.0000 1.29055 0.645273 0.763952i \(-0.276743\pi\)
0.645273 + 0.763952i \(0.276743\pi\)
\(578\) 0 0
\(579\) 24.0000 0.997406
\(580\) −4.00000 −0.166091
\(581\) 0 0
\(582\) 0 0
\(583\) −2.00000 −0.0828315
\(584\) 0 0
\(585\) −2.00000 −0.0826898
\(586\) 0 0
\(587\) −12.0000 −0.495293 −0.247647 0.968850i \(-0.579657\pi\)
−0.247647 + 0.968850i \(0.579657\pi\)
\(588\) −6.00000 −0.247436
\(589\) −6.00000 −0.247226
\(590\) 0 0
\(591\) 10.0000 0.411345
\(592\) −44.0000 −1.80839
\(593\) 24.0000 0.985562 0.492781 0.870153i \(-0.335980\pi\)
0.492781 + 0.870153i \(0.335980\pi\)
\(594\) 0 0
\(595\) −8.00000 −0.327968
\(596\) −28.0000 −1.14692
\(597\) 4.00000 0.163709
\(598\) 0 0
\(599\) 24.0000 0.980613 0.490307 0.871550i \(-0.336885\pi\)
0.490307 + 0.871550i \(0.336885\pi\)
\(600\) 0 0
\(601\) −22.0000 −0.897399 −0.448699 0.893683i \(-0.648113\pi\)
−0.448699 + 0.893683i \(0.648113\pi\)
\(602\) 0 0
\(603\) 2.00000 0.0814463
\(604\) −8.00000 −0.325515
\(605\) −1.00000 −0.0406558
\(606\) 0 0
\(607\) −22.0000 −0.892952 −0.446476 0.894795i \(-0.647321\pi\)
−0.446476 + 0.894795i \(0.647321\pi\)
\(608\) 0 0
\(609\) −4.00000 −0.162088
\(610\) 0 0
\(611\) 4.00000 0.161823
\(612\) −16.0000 −0.646762
\(613\) −2.00000 −0.0807792 −0.0403896 0.999184i \(-0.512860\pi\)
−0.0403896 + 0.999184i \(0.512860\pi\)
\(614\) 0 0
\(615\) 10.0000 0.403239
\(616\) 0 0
\(617\) 42.0000 1.69086 0.845428 0.534089i \(-0.179345\pi\)
0.845428 + 0.534089i \(0.179345\pi\)
\(618\) 0 0
\(619\) −7.00000 −0.281354 −0.140677 0.990056i \(-0.544928\pi\)
−0.140677 + 0.990056i \(0.544928\pi\)
\(620\) −6.00000 −0.240966
\(621\) 35.0000 1.40450
\(622\) 0 0
\(623\) 14.0000 0.560898
\(624\) 4.00000 0.160128
\(625\) 11.0000 0.440000
\(626\) 0 0
\(627\) 2.00000 0.0798723
\(628\) −10.0000 −0.399043
\(629\) 44.0000 1.75439
\(630\) 0 0
\(631\) −27.0000 −1.07485 −0.537427 0.843311i \(-0.680603\pi\)
−0.537427 + 0.843311i \(0.680603\pi\)
\(632\) 0 0
\(633\) 24.0000 0.953914
\(634\) 0 0
\(635\) 8.00000 0.317470
\(636\) 4.00000 0.158610
\(637\) 3.00000 0.118864
\(638\) 0 0
\(639\) 18.0000 0.712069
\(640\) 0 0
\(641\) −33.0000 −1.30342 −0.651711 0.758468i \(-0.725948\pi\)
−0.651711 + 0.758468i \(0.725948\pi\)
\(642\) 0 0
\(643\) −49.0000 −1.93237 −0.966186 0.257847i \(-0.916987\pi\)
−0.966186 + 0.257847i \(0.916987\pi\)
\(644\) 28.0000 1.10335
\(645\) −4.00000 −0.157500
\(646\) 0 0
\(647\) −15.0000 −0.589711 −0.294855 0.955542i \(-0.595271\pi\)
−0.294855 + 0.955542i \(0.595271\pi\)
\(648\) 0 0
\(649\) 1.00000 0.0392534
\(650\) 0 0
\(651\) −6.00000 −0.235159
\(652\) 8.00000 0.313304
\(653\) −13.0000 −0.508729 −0.254365 0.967108i \(-0.581866\pi\)
−0.254365 + 0.967108i \(0.581866\pi\)
\(654\) 0 0
\(655\) −18.0000 −0.703318
\(656\) 40.0000 1.56174
\(657\) 32.0000 1.24844
\(658\) 0 0
\(659\) −44.0000 −1.71400 −0.856998 0.515319i \(-0.827673\pi\)
−0.856998 + 0.515319i \(0.827673\pi\)
\(660\) 2.00000 0.0778499
\(661\) 31.0000 1.20576 0.602880 0.797832i \(-0.294020\pi\)
0.602880 + 0.797832i \(0.294020\pi\)
\(662\) 0 0
\(663\) −4.00000 −0.155347
\(664\) 0 0
\(665\) 4.00000 0.155113
\(666\) 0 0
\(667\) −14.0000 −0.542082
\(668\) −8.00000 −0.309529
\(669\) −5.00000 −0.193311
\(670\) 0 0
\(671\) 2.00000 0.0772091
\(672\) 0 0
\(673\) 4.00000 0.154189 0.0770943 0.997024i \(-0.475436\pi\)
0.0770943 + 0.997024i \(0.475436\pi\)
\(674\) 0 0
\(675\) −20.0000 −0.769800
\(676\) −2.00000 −0.0769231
\(677\) 6.00000 0.230599 0.115299 0.993331i \(-0.463217\pi\)
0.115299 + 0.993331i \(0.463217\pi\)
\(678\) 0 0
\(679\) 26.0000 0.997788
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −4.00000 −0.153056 −0.0765279 0.997067i \(-0.524383\pi\)
−0.0765279 + 0.997067i \(0.524383\pi\)
\(684\) 8.00000 0.305888
\(685\) 17.0000 0.649537
\(686\) 0 0
\(687\) −9.00000 −0.343371
\(688\) −16.0000 −0.609994
\(689\) −2.00000 −0.0761939
\(690\) 0 0
\(691\) −45.0000 −1.71188 −0.855940 0.517075i \(-0.827021\pi\)
−0.855940 + 0.517075i \(0.827021\pi\)
\(692\) 16.0000 0.608229
\(693\) −4.00000 −0.151947
\(694\) 0 0
\(695\) −18.0000 −0.682779
\(696\) 0 0
\(697\) −40.0000 −1.51511
\(698\) 0 0
\(699\) 16.0000 0.605176
\(700\) −16.0000 −0.604743
\(701\) −10.0000 −0.377695 −0.188847 0.982006i \(-0.560475\pi\)
−0.188847 + 0.982006i \(0.560475\pi\)
\(702\) 0 0
\(703\) −22.0000 −0.829746
\(704\) 8.00000 0.301511
\(705\) −4.00000 −0.150649
\(706\) 0 0
\(707\) −36.0000 −1.35392
\(708\) −2.00000 −0.0751646
\(709\) −35.0000 −1.31445 −0.657226 0.753693i \(-0.728270\pi\)
−0.657226 + 0.753693i \(0.728270\pi\)
\(710\) 0 0
\(711\) −16.0000 −0.600047
\(712\) 0 0
\(713\) −21.0000 −0.786456
\(714\) 0 0
\(715\) −1.00000 −0.0373979
\(716\) 30.0000 1.12115
\(717\) 30.0000 1.12037
\(718\) 0 0
\(719\) −41.0000 −1.52904 −0.764521 0.644599i \(-0.777024\pi\)
−0.764521 + 0.644599i \(0.777024\pi\)
\(720\) 8.00000 0.298142
\(721\) −16.0000 −0.595871
\(722\) 0 0
\(723\) 10.0000 0.371904
\(724\) −14.0000 −0.520306
\(725\) 8.00000 0.297113
\(726\) 0 0
\(727\) 19.0000 0.704671 0.352335 0.935874i \(-0.385388\pi\)
0.352335 + 0.935874i \(0.385388\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) 16.0000 0.591781
\(732\) −4.00000 −0.147844
\(733\) −46.0000 −1.69905 −0.849524 0.527549i \(-0.823111\pi\)
−0.849524 + 0.527549i \(0.823111\pi\)
\(734\) 0 0
\(735\) −3.00000 −0.110657
\(736\) 0 0
\(737\) 1.00000 0.0368355
\(738\) 0 0
\(739\) −2.00000 −0.0735712 −0.0367856 0.999323i \(-0.511712\pi\)
−0.0367856 + 0.999323i \(0.511712\pi\)
\(740\) −22.0000 −0.808736
\(741\) 2.00000 0.0734718
\(742\) 0 0
\(743\) 42.0000 1.54083 0.770415 0.637542i \(-0.220049\pi\)
0.770415 + 0.637542i \(0.220049\pi\)
\(744\) 0 0
\(745\) −14.0000 −0.512920
\(746\) 0 0
\(747\) 0 0
\(748\) −8.00000 −0.292509
\(749\) −16.0000 −0.584627
\(750\) 0 0
\(751\) −39.0000 −1.42313 −0.711565 0.702620i \(-0.752013\pi\)
−0.711565 + 0.702620i \(0.752013\pi\)
\(752\) −16.0000 −0.583460
\(753\) −21.0000 −0.765283
\(754\) 0 0
\(755\) −4.00000 −0.145575
\(756\) 20.0000 0.727393
\(757\) 30.0000 1.09037 0.545184 0.838316i \(-0.316460\pi\)
0.545184 + 0.838316i \(0.316460\pi\)
\(758\) 0 0
\(759\) 7.00000 0.254084
\(760\) 0 0
\(761\) −34.0000 −1.23250 −0.616250 0.787551i \(-0.711349\pi\)
−0.616250 + 0.787551i \(0.711349\pi\)
\(762\) 0 0
\(763\) −8.00000 −0.289619
\(764\) 30.0000 1.08536
\(765\) −8.00000 −0.289241
\(766\) 0 0
\(767\) 1.00000 0.0361079
\(768\) −16.0000 −0.577350
\(769\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(770\) 0 0
\(771\) −18.0000 −0.648254
\(772\) 48.0000 1.72756
\(773\) 30.0000 1.07903 0.539513 0.841978i \(-0.318609\pi\)
0.539513 + 0.841978i \(0.318609\pi\)
\(774\) 0 0
\(775\) 12.0000 0.431053
\(776\) 0 0
\(777\) −22.0000 −0.789246
\(778\) 0 0
\(779\) 20.0000 0.716574
\(780\) 2.00000 0.0716115
\(781\) 9.00000 0.322045
\(782\) 0 0
\(783\) −10.0000 −0.357371
\(784\) −12.0000 −0.428571
\(785\) −5.00000 −0.178458
\(786\) 0 0
\(787\) 12.0000 0.427754 0.213877 0.976861i \(-0.431391\pi\)
0.213877 + 0.976861i \(0.431391\pi\)
\(788\) 20.0000 0.712470
\(789\) 18.0000 0.640817
\(790\) 0 0
\(791\) −2.00000 −0.0711118
\(792\) 0 0
\(793\) 2.00000 0.0710221
\(794\) 0 0
\(795\) 2.00000 0.0709327
\(796\) 8.00000 0.283552
\(797\) 17.0000 0.602171 0.301085 0.953597i \(-0.402651\pi\)
0.301085 + 0.953597i \(0.402651\pi\)
\(798\) 0 0
\(799\) 16.0000 0.566039
\(800\) 0 0
\(801\) 14.0000 0.494666
\(802\) 0 0
\(803\) 16.0000 0.564628
\(804\) −2.00000 −0.0705346
\(805\) 14.0000 0.493435
\(806\) 0 0
\(807\) 30.0000 1.05605
\(808\) 0 0
\(809\) 24.0000 0.843795 0.421898 0.906644i \(-0.361364\pi\)
0.421898 + 0.906644i \(0.361364\pi\)
\(810\) 0 0
\(811\) −36.0000 −1.26413 −0.632065 0.774915i \(-0.717793\pi\)
−0.632065 + 0.774915i \(0.717793\pi\)
\(812\) −8.00000 −0.280745
\(813\) −28.0000 −0.982003
\(814\) 0 0
\(815\) 4.00000 0.140114
\(816\) 16.0000 0.560112
\(817\) −8.00000 −0.279885
\(818\) 0 0
\(819\) −4.00000 −0.139771
\(820\) 20.0000 0.698430
\(821\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(822\) 0 0
\(823\) −29.0000 −1.01088 −0.505438 0.862863i \(-0.668669\pi\)
−0.505438 + 0.862863i \(0.668669\pi\)
\(824\) 0 0
\(825\) −4.00000 −0.139262
\(826\) 0 0
\(827\) 50.0000 1.73867 0.869335 0.494223i \(-0.164547\pi\)
0.869335 + 0.494223i \(0.164547\pi\)
\(828\) 28.0000 0.973067
\(829\) 29.0000 1.00721 0.503606 0.863934i \(-0.332006\pi\)
0.503606 + 0.863934i \(0.332006\pi\)
\(830\) 0 0
\(831\) −26.0000 −0.901930
\(832\) 8.00000 0.277350
\(833\) 12.0000 0.415775
\(834\) 0 0
\(835\) −4.00000 −0.138426
\(836\) 4.00000 0.138343
\(837\) −15.0000 −0.518476
\(838\) 0 0
\(839\) 53.0000 1.82976 0.914882 0.403722i \(-0.132284\pi\)
0.914882 + 0.403722i \(0.132284\pi\)
\(840\) 0 0
\(841\) −25.0000 −0.862069
\(842\) 0 0
\(843\) −18.0000 −0.619953
\(844\) 48.0000 1.65223
\(845\) −1.00000 −0.0344010
\(846\) 0 0
\(847\) −2.00000 −0.0687208
\(848\) 8.00000 0.274721
\(849\) 30.0000 1.02960
\(850\) 0 0
\(851\) −77.0000 −2.63953
\(852\) −18.0000 −0.616670
\(853\) −50.0000 −1.71197 −0.855984 0.517003i \(-0.827048\pi\)
−0.855984 + 0.517003i \(0.827048\pi\)
\(854\) 0 0
\(855\) 4.00000 0.136797
\(856\) 0 0
\(857\) −32.0000 −1.09310 −0.546550 0.837427i \(-0.684059\pi\)
−0.546550 + 0.837427i \(0.684059\pi\)
\(858\) 0 0
\(859\) 13.0000 0.443554 0.221777 0.975097i \(-0.428814\pi\)
0.221777 + 0.975097i \(0.428814\pi\)
\(860\) −8.00000 −0.272798
\(861\) 20.0000 0.681598
\(862\) 0 0
\(863\) 48.0000 1.63394 0.816970 0.576681i \(-0.195652\pi\)
0.816970 + 0.576681i \(0.195652\pi\)
\(864\) 0 0
\(865\) 8.00000 0.272008
\(866\) 0 0
\(867\) 1.00000 0.0339618
\(868\) −12.0000 −0.407307
\(869\) −8.00000 −0.271381
\(870\) 0 0
\(871\) 1.00000 0.0338837
\(872\) 0 0
\(873\) 26.0000 0.879967
\(874\) 0 0
\(875\) −18.0000 −0.608511
\(876\) −32.0000 −1.08118
\(877\) 38.0000 1.28317 0.641584 0.767052i \(-0.278277\pi\)
0.641584 + 0.767052i \(0.278277\pi\)
\(878\) 0 0
\(879\) −14.0000 −0.472208
\(880\) 4.00000 0.134840
\(881\) 33.0000 1.11180 0.555899 0.831250i \(-0.312374\pi\)
0.555899 + 0.831250i \(0.312374\pi\)
\(882\) 0 0
\(883\) 28.0000 0.942275 0.471138 0.882060i \(-0.343844\pi\)
0.471138 + 0.882060i \(0.343844\pi\)
\(884\) −8.00000 −0.269069
\(885\) −1.00000 −0.0336146
\(886\) 0 0
\(887\) 12.0000 0.402921 0.201460 0.979497i \(-0.435431\pi\)
0.201460 + 0.979497i \(0.435431\pi\)
\(888\) 0 0
\(889\) 16.0000 0.536623
\(890\) 0 0
\(891\) −1.00000 −0.0335013
\(892\) −10.0000 −0.334825
\(893\) −8.00000 −0.267710
\(894\) 0 0
\(895\) 15.0000 0.501395
\(896\) 0 0
\(897\) 7.00000 0.233723
\(898\) 0 0
\(899\) 6.00000 0.200111
\(900\) −16.0000 −0.533333
\(901\) −8.00000 −0.266519
\(902\) 0 0
\(903\) −8.00000 −0.266223
\(904\) 0 0
\(905\) −7.00000 −0.232688
\(906\) 0 0
\(907\) 52.0000 1.72663 0.863316 0.504664i \(-0.168384\pi\)
0.863316 + 0.504664i \(0.168384\pi\)
\(908\) 0 0
\(909\) −36.0000 −1.19404
\(910\) 0 0
\(911\) −8.00000 −0.265052 −0.132526 0.991180i \(-0.542309\pi\)
−0.132526 + 0.991180i \(0.542309\pi\)
\(912\) −8.00000 −0.264906
\(913\) 0 0
\(914\) 0 0
\(915\) −2.00000 −0.0661180
\(916\) −18.0000 −0.594737
\(917\) −36.0000 −1.18882
\(918\) 0 0
\(919\) 40.0000 1.31948 0.659739 0.751495i \(-0.270667\pi\)
0.659739 + 0.751495i \(0.270667\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 9.00000 0.296239
\(924\) 4.00000 0.131590
\(925\) 44.0000 1.44671
\(926\) 0 0
\(927\) −16.0000 −0.525509
\(928\) 0 0
\(929\) −42.0000 −1.37798 −0.688988 0.724773i \(-0.741945\pi\)
−0.688988 + 0.724773i \(0.741945\pi\)
\(930\) 0 0
\(931\) −6.00000 −0.196642
\(932\) 32.0000 1.04819
\(933\) −8.00000 −0.261908
\(934\) 0 0
\(935\) −4.00000 −0.130814
\(936\) 0 0
\(937\) −12.0000 −0.392023 −0.196011 0.980602i \(-0.562799\pi\)
−0.196011 + 0.980602i \(0.562799\pi\)
\(938\) 0 0
\(939\) −3.00000 −0.0979013
\(940\) −8.00000 −0.260931
\(941\) −36.0000 −1.17357 −0.586783 0.809744i \(-0.699606\pi\)
−0.586783 + 0.809744i \(0.699606\pi\)
\(942\) 0 0
\(943\) 70.0000 2.27951
\(944\) −4.00000 −0.130189
\(945\) 10.0000 0.325300
\(946\) 0 0
\(947\) −9.00000 −0.292461 −0.146230 0.989251i \(-0.546714\pi\)
−0.146230 + 0.989251i \(0.546714\pi\)
\(948\) 16.0000 0.519656
\(949\) 16.0000 0.519382
\(950\) 0 0
\(951\) 1.00000 0.0324272
\(952\) 0 0
\(953\) −30.0000 −0.971795 −0.485898 0.874016i \(-0.661507\pi\)
−0.485898 + 0.874016i \(0.661507\pi\)
\(954\) 0 0
\(955\) 15.0000 0.485389
\(956\) 60.0000 1.94054
\(957\) −2.00000 −0.0646508
\(958\) 0 0
\(959\) 34.0000 1.09792
\(960\) −8.00000 −0.258199
\(961\) −22.0000 −0.709677
\(962\) 0 0
\(963\) −16.0000 −0.515593
\(964\) 20.0000 0.644157
\(965\) 24.0000 0.772587
\(966\) 0 0
\(967\) 28.0000 0.900419 0.450210 0.892923i \(-0.351349\pi\)
0.450210 + 0.892923i \(0.351349\pi\)
\(968\) 0 0
\(969\) 8.00000 0.256997
\(970\) 0 0
\(971\) −49.0000 −1.57248 −0.786242 0.617918i \(-0.787976\pi\)
−0.786242 + 0.617918i \(0.787976\pi\)
\(972\) 32.0000 1.02640
\(973\) −36.0000 −1.15411
\(974\) 0 0
\(975\) −4.00000 −0.128103
\(976\) −8.00000 −0.256074
\(977\) −9.00000 −0.287936 −0.143968 0.989582i \(-0.545986\pi\)
−0.143968 + 0.989582i \(0.545986\pi\)
\(978\) 0 0
\(979\) 7.00000 0.223721
\(980\) −6.00000 −0.191663
\(981\) −8.00000 −0.255420
\(982\) 0 0
\(983\) −31.0000 −0.988746 −0.494373 0.869250i \(-0.664602\pi\)
−0.494373 + 0.869250i \(0.664602\pi\)
\(984\) 0 0
\(985\) 10.0000 0.318626
\(986\) 0 0
\(987\) −8.00000 −0.254643
\(988\) 4.00000 0.127257
\(989\) −28.0000 −0.890348
\(990\) 0 0
\(991\) 32.0000 1.01651 0.508257 0.861206i \(-0.330290\pi\)
0.508257 + 0.861206i \(0.330290\pi\)
\(992\) 0 0
\(993\) 11.0000 0.349074
\(994\) 0 0
\(995\) 4.00000 0.126809
\(996\) 0 0
\(997\) −18.0000 −0.570066 −0.285033 0.958518i \(-0.592005\pi\)
−0.285033 + 0.958518i \(0.592005\pi\)
\(998\) 0 0
\(999\) −55.0000 −1.74012
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 \(a_p\))