Properties

Label 4014.2.a.q.1.4
Level 4014
Weight 2
Character 4014.1
Self dual Yes
Analytic conductor 32.052
Analytic rank 1
Dimension 4
CM No
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 4014 = 2 \cdot 3^{2} \cdot 223 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4014.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0519513713\)
Analytic rank: \(1\)
Dimension: \(4\)
Coefficient field: 4.4.10273.1
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(3.35017\)
Character \(\chi\) = 4014.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(+1.00000 q^{4}\) \(+2.35017 q^{5}\) \(-1.22988 q^{7}\) \(+1.00000 q^{8}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(+1.00000 q^{4}\) \(+2.35017 q^{5}\) \(-1.22988 q^{7}\) \(+1.00000 q^{8}\) \(+2.35017 q^{10}\) \(-5.87349 q^{11}\) \(-3.29344 q^{13}\) \(-1.22988 q^{14}\) \(+1.00000 q^{16}\) \(+1.69645 q^{17}\) \(-0.613919 q^{19}\) \(+2.35017 q^{20}\) \(-5.87349 q^{22}\) \(-5.52721 q^{23}\) \(+0.523313 q^{25}\) \(-3.29344 q^{26}\) \(-1.22988 q^{28}\) \(-6.27650 q^{29}\) \(-1.38608 q^{31}\) \(+1.00000 q^{32}\) \(+1.69645 q^{34}\) \(-2.89042 q^{35}\) \(+2.93022 q^{37}\) \(-0.613919 q^{38}\) \(+2.35017 q^{40}\) \(+2.48944 q^{41}\) \(-3.47669 q^{43}\) \(-5.87349 q^{44}\) \(-5.52721 q^{46}\) \(+0.843795 q^{47}\) \(-5.48741 q^{49}\) \(+0.523313 q^{50}\) \(-3.29344 q^{52}\) \(+3.77402 q^{53}\) \(-13.8037 q^{55}\) \(-1.22988 q^{56}\) \(-6.27650 q^{58}\) \(+4.43067 q^{59}\) \(-7.93022 q^{61}\) \(-1.38608 q^{62}\) \(+1.00000 q^{64}\) \(-7.74015 q^{65}\) \(-8.35017 q^{67}\) \(+1.69645 q^{68}\) \(-2.89042 q^{70}\) \(-7.83758 q^{71}\) \(-6.71932 q^{73}\) \(+2.93022 q^{74}\) \(-0.613919 q^{76}\) \(+7.22366 q^{77}\) \(+0.124190 q^{79}\) \(+2.35017 q^{80}\) \(+2.48944 q^{82}\) \(+0.936439 q^{83}\) \(+3.98696 q^{85}\) \(-3.47669 q^{86}\) \(-5.87349 q^{88}\) \(+9.09032 q^{89}\) \(+4.05052 q^{91}\) \(-5.52721 q^{92}\) \(+0.843795 q^{94}\) \(-1.44282 q^{95}\) \(+1.28039 q^{97}\) \(-5.48741 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(4q \) \(\mathstrut +\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 4q^{4} \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 4q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(4q \) \(\mathstrut +\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 4q^{4} \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 4q^{8} \) \(\mathstrut -\mathstrut 2q^{10} \) \(\mathstrut -\mathstrut 4q^{11} \) \(\mathstrut -\mathstrut 5q^{13} \) \(\mathstrut -\mathstrut 5q^{14} \) \(\mathstrut +\mathstrut 4q^{16} \) \(\mathstrut +\mathstrut 2q^{17} \) \(\mathstrut -\mathstrut 7q^{19} \) \(\mathstrut -\mathstrut 2q^{20} \) \(\mathstrut -\mathstrut 4q^{22} \) \(\mathstrut +\mathstrut 4q^{23} \) \(\mathstrut -\mathstrut 6q^{25} \) \(\mathstrut -\mathstrut 5q^{26} \) \(\mathstrut -\mathstrut 5q^{28} \) \(\mathstrut -\mathstrut 9q^{29} \) \(\mathstrut -\mathstrut q^{31} \) \(\mathstrut +\mathstrut 4q^{32} \) \(\mathstrut +\mathstrut 2q^{34} \) \(\mathstrut -\mathstrut 11q^{37} \) \(\mathstrut -\mathstrut 7q^{38} \) \(\mathstrut -\mathstrut 2q^{40} \) \(\mathstrut -\mathstrut 14q^{41} \) \(\mathstrut -\mathstrut 22q^{43} \) \(\mathstrut -\mathstrut 4q^{44} \) \(\mathstrut +\mathstrut 4q^{46} \) \(\mathstrut +\mathstrut 8q^{47} \) \(\mathstrut -\mathstrut 7q^{49} \) \(\mathstrut -\mathstrut 6q^{50} \) \(\mathstrut -\mathstrut 5q^{52} \) \(\mathstrut -\mathstrut 3q^{53} \) \(\mathstrut -\mathstrut 13q^{55} \) \(\mathstrut -\mathstrut 5q^{56} \) \(\mathstrut -\mathstrut 9q^{58} \) \(\mathstrut +\mathstrut 6q^{59} \) \(\mathstrut -\mathstrut 9q^{61} \) \(\mathstrut -\mathstrut q^{62} \) \(\mathstrut +\mathstrut 4q^{64} \) \(\mathstrut +\mathstrut 3q^{65} \) \(\mathstrut -\mathstrut 22q^{67} \) \(\mathstrut +\mathstrut 2q^{68} \) \(\mathstrut -\mathstrut 5q^{71} \) \(\mathstrut -\mathstrut 3q^{73} \) \(\mathstrut -\mathstrut 11q^{74} \) \(\mathstrut -\mathstrut 7q^{76} \) \(\mathstrut -\mathstrut 2q^{77} \) \(\mathstrut -\mathstrut 29q^{79} \) \(\mathstrut -\mathstrut 2q^{80} \) \(\mathstrut -\mathstrut 14q^{82} \) \(\mathstrut +\mathstrut 12q^{83} \) \(\mathstrut -\mathstrut 10q^{85} \) \(\mathstrut -\mathstrut 22q^{86} \) \(\mathstrut -\mathstrut 4q^{88} \) \(\mathstrut -\mathstrut 9q^{89} \) \(\mathstrut -\mathstrut 18q^{91} \) \(\mathstrut +\mathstrut 4q^{92} \) \(\mathstrut +\mathstrut 8q^{94} \) \(\mathstrut +\mathstrut 2q^{95} \) \(\mathstrut -\mathstrut 29q^{97} \) \(\mathstrut -\mathstrut 7q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 0 0
\(4\) 1.00000 0.500000
\(5\) 2.35017 1.05103 0.525515 0.850785i \(-0.323873\pi\)
0.525515 + 0.850785i \(0.323873\pi\)
\(6\) 0 0
\(7\) −1.22988 −0.464849 −0.232425 0.972614i \(-0.574666\pi\)
−0.232425 + 0.972614i \(0.574666\pi\)
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) 2.35017 0.743190
\(11\) −5.87349 −1.77092 −0.885461 0.464713i \(-0.846157\pi\)
−0.885461 + 0.464713i \(0.846157\pi\)
\(12\) 0 0
\(13\) −3.29344 −0.913435 −0.456718 0.889612i \(-0.650975\pi\)
−0.456718 + 0.889612i \(0.650975\pi\)
\(14\) −1.22988 −0.328698
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 1.69645 0.411450 0.205725 0.978610i \(-0.434045\pi\)
0.205725 + 0.978610i \(0.434045\pi\)
\(18\) 0 0
\(19\) −0.613919 −0.140843 −0.0704214 0.997517i \(-0.522434\pi\)
−0.0704214 + 0.997517i \(0.522434\pi\)
\(20\) 2.35017 0.525515
\(21\) 0 0
\(22\) −5.87349 −1.25223
\(23\) −5.52721 −1.15250 −0.576251 0.817273i \(-0.695485\pi\)
−0.576251 + 0.817273i \(0.695485\pi\)
\(24\) 0 0
\(25\) 0.523313 0.104663
\(26\) −3.29344 −0.645896
\(27\) 0 0
\(28\) −1.22988 −0.232425
\(29\) −6.27650 −1.16552 −0.582759 0.812645i \(-0.698027\pi\)
−0.582759 + 0.812645i \(0.698027\pi\)
\(30\) 0 0
\(31\) −1.38608 −0.248947 −0.124474 0.992223i \(-0.539724\pi\)
−0.124474 + 0.992223i \(0.539724\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) 1.69645 0.290939
\(35\) −2.89042 −0.488570
\(36\) 0 0
\(37\) 2.93022 0.481726 0.240863 0.970559i \(-0.422570\pi\)
0.240863 + 0.970559i \(0.422570\pi\)
\(38\) −0.613919 −0.0995909
\(39\) 0 0
\(40\) 2.35017 0.371595
\(41\) 2.48944 0.388786 0.194393 0.980924i \(-0.437726\pi\)
0.194393 + 0.980924i \(0.437726\pi\)
\(42\) 0 0
\(43\) −3.47669 −0.530190 −0.265095 0.964222i \(-0.585403\pi\)
−0.265095 + 0.964222i \(0.585403\pi\)
\(44\) −5.87349 −0.885461
\(45\) 0 0
\(46\) −5.52721 −0.814942
\(47\) 0.843795 0.123080 0.0615401 0.998105i \(-0.480399\pi\)
0.0615401 + 0.998105i \(0.480399\pi\)
\(48\) 0 0
\(49\) −5.48741 −0.783915
\(50\) 0.523313 0.0740076
\(51\) 0 0
\(52\) −3.29344 −0.456718
\(53\) 3.77402 0.518401 0.259201 0.965824i \(-0.416541\pi\)
0.259201 + 0.965824i \(0.416541\pi\)
\(54\) 0 0
\(55\) −13.8037 −1.86129
\(56\) −1.22988 −0.164349
\(57\) 0 0
\(58\) −6.27650 −0.824145
\(59\) 4.43067 0.576824 0.288412 0.957506i \(-0.406873\pi\)
0.288412 + 0.957506i \(0.406873\pi\)
\(60\) 0 0
\(61\) −7.93022 −1.01536 −0.507680 0.861545i \(-0.669497\pi\)
−0.507680 + 0.861545i \(0.669497\pi\)
\(62\) −1.38608 −0.176032
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −7.74015 −0.960047
\(66\) 0 0
\(67\) −8.35017 −1.02014 −0.510068 0.860134i \(-0.670380\pi\)
−0.510068 + 0.860134i \(0.670380\pi\)
\(68\) 1.69645 0.205725
\(69\) 0 0
\(70\) −2.89042 −0.345471
\(71\) −7.83758 −0.930149 −0.465075 0.885271i \(-0.653973\pi\)
−0.465075 + 0.885271i \(0.653973\pi\)
\(72\) 0 0
\(73\) −6.71932 −0.786437 −0.393218 0.919445i \(-0.628638\pi\)
−0.393218 + 0.919445i \(0.628638\pi\)
\(74\) 2.93022 0.340631
\(75\) 0 0
\(76\) −0.613919 −0.0704214
\(77\) 7.22366 0.823212
\(78\) 0 0
\(79\) 0.124190 0.0139725 0.00698624 0.999976i \(-0.497776\pi\)
0.00698624 + 0.999976i \(0.497776\pi\)
\(80\) 2.35017 0.262757
\(81\) 0 0
\(82\) 2.48944 0.274913
\(83\) 0.936439 0.102788 0.0513938 0.998678i \(-0.483634\pi\)
0.0513938 + 0.998678i \(0.483634\pi\)
\(84\) 0 0
\(85\) 3.98696 0.432446
\(86\) −3.47669 −0.374901
\(87\) 0 0
\(88\) −5.87349 −0.626116
\(89\) 9.09032 0.963572 0.481786 0.876289i \(-0.339988\pi\)
0.481786 + 0.876289i \(0.339988\pi\)
\(90\) 0 0
\(91\) 4.05052 0.424610
\(92\) −5.52721 −0.576251
\(93\) 0 0
\(94\) 0.843795 0.0870308
\(95\) −1.44282 −0.148030
\(96\) 0 0
\(97\) 1.28039 0.130004 0.0650022 0.997885i \(-0.479295\pi\)
0.0650022 + 0.997885i \(0.479295\pi\)
\(98\) −5.48741 −0.554312
\(99\) 0 0
\(100\) 0.523313 0.0523313
\(101\) 3.15806 0.314239 0.157119 0.987580i \(-0.449779\pi\)
0.157119 + 0.987580i \(0.449779\pi\)
\(102\) 0 0
\(103\) −16.9511 −1.67024 −0.835118 0.550070i \(-0.814601\pi\)
−0.835118 + 0.550070i \(0.814601\pi\)
\(104\) −3.29344 −0.322948
\(105\) 0 0
\(106\) 3.77402 0.366565
\(107\) 18.4405 1.78271 0.891355 0.453306i \(-0.149756\pi\)
0.891355 + 0.453306i \(0.149756\pi\)
\(108\) 0 0
\(109\) 6.56994 0.629286 0.314643 0.949210i \(-0.398115\pi\)
0.314643 + 0.949210i \(0.398115\pi\)
\(110\) −13.8037 −1.31613
\(111\) 0 0
\(112\) −1.22988 −0.116212
\(113\) 5.19601 0.488799 0.244400 0.969675i \(-0.421409\pi\)
0.244400 + 0.969675i \(0.421409\pi\)
\(114\) 0 0
\(115\) −12.9899 −1.21131
\(116\) −6.27650 −0.582759
\(117\) 0 0
\(118\) 4.43067 0.407876
\(119\) −2.08643 −0.191262
\(120\) 0 0
\(121\) 23.4978 2.13617
\(122\) −7.93022 −0.717969
\(123\) 0 0
\(124\) −1.38608 −0.124474
\(125\) −10.5210 −0.941026
\(126\) 0 0
\(127\) 8.97063 0.796015 0.398007 0.917382i \(-0.369702\pi\)
0.398007 + 0.917382i \(0.369702\pi\)
\(128\) 1.00000 0.0883883
\(129\) 0 0
\(130\) −7.74015 −0.678856
\(131\) −1.11347 −0.0972845 −0.0486422 0.998816i \(-0.515489\pi\)
−0.0486422 + 0.998816i \(0.515489\pi\)
\(132\) 0 0
\(133\) 0.755045 0.0654707
\(134\) −8.35017 −0.721345
\(135\) 0 0
\(136\) 1.69645 0.145470
\(137\) 1.61392 0.137886 0.0689432 0.997621i \(-0.478037\pi\)
0.0689432 + 0.997621i \(0.478037\pi\)
\(138\) 0 0
\(139\) −11.6626 −0.989207 −0.494604 0.869119i \(-0.664687\pi\)
−0.494604 + 0.869119i \(0.664687\pi\)
\(140\) −2.89042 −0.244285
\(141\) 0 0
\(142\) −7.83758 −0.657715
\(143\) 19.3440 1.61762
\(144\) 0 0
\(145\) −14.7509 −1.22499
\(146\) −6.71932 −0.556095
\(147\) 0 0
\(148\) 2.93022 0.240863
\(149\) 10.0485 0.823204 0.411602 0.911364i \(-0.364969\pi\)
0.411602 + 0.911364i \(0.364969\pi\)
\(150\) 0 0
\(151\) −12.3371 −1.00398 −0.501991 0.864873i \(-0.667399\pi\)
−0.501991 + 0.864873i \(0.667399\pi\)
\(152\) −0.613919 −0.0497954
\(153\) 0 0
\(154\) 7.22366 0.582099
\(155\) −3.25753 −0.261651
\(156\) 0 0
\(157\) −15.2742 −1.21901 −0.609506 0.792781i \(-0.708632\pi\)
−0.609506 + 0.792781i \(0.708632\pi\)
\(158\) 0.124190 0.00988003
\(159\) 0 0
\(160\) 2.35017 0.185797
\(161\) 6.79778 0.535740
\(162\) 0 0
\(163\) −23.8503 −1.86810 −0.934051 0.357139i \(-0.883752\pi\)
−0.934051 + 0.357139i \(0.883752\pi\)
\(164\) 2.48944 0.194393
\(165\) 0 0
\(166\) 0.936439 0.0726818
\(167\) 4.06356 0.314448 0.157224 0.987563i \(-0.449746\pi\)
0.157224 + 0.987563i \(0.449746\pi\)
\(168\) 0 0
\(169\) −2.15327 −0.165636
\(170\) 3.98696 0.305786
\(171\) 0 0
\(172\) −3.47669 −0.265095
\(173\) −13.9269 −1.05885 −0.529423 0.848358i \(-0.677591\pi\)
−0.529423 + 0.848358i \(0.677591\pi\)
\(174\) 0 0
\(175\) −0.643610 −0.0486523
\(176\) −5.87349 −0.442731
\(177\) 0 0
\(178\) 9.09032 0.681348
\(179\) 20.8194 1.55611 0.778057 0.628193i \(-0.216205\pi\)
0.778057 + 0.628193i \(0.216205\pi\)
\(180\) 0 0
\(181\) 24.7297 1.83815 0.919074 0.394085i \(-0.128939\pi\)
0.919074 + 0.394085i \(0.128939\pi\)
\(182\) 4.05052 0.300244
\(183\) 0 0
\(184\) −5.52721 −0.407471
\(185\) 6.88653 0.506308
\(186\) 0 0
\(187\) −9.96409 −0.728647
\(188\) 0.843795 0.0615401
\(189\) 0 0
\(190\) −1.44282 −0.104673
\(191\) −4.64779 −0.336302 −0.168151 0.985761i \(-0.553780\pi\)
−0.168151 + 0.985761i \(0.553780\pi\)
\(192\) 0 0
\(193\) 19.1419 1.37787 0.688933 0.724825i \(-0.258080\pi\)
0.688933 + 0.724825i \(0.258080\pi\)
\(194\) 1.28039 0.0919270
\(195\) 0 0
\(196\) −5.48741 −0.391958
\(197\) 20.5697 1.46553 0.732764 0.680483i \(-0.238230\pi\)
0.732764 + 0.680483i \(0.238230\pi\)
\(198\) 0 0
\(199\) 6.35203 0.450283 0.225142 0.974326i \(-0.427715\pi\)
0.225142 + 0.974326i \(0.427715\pi\)
\(200\) 0.523313 0.0370038
\(201\) 0 0
\(202\) 3.15806 0.222200
\(203\) 7.71932 0.541790
\(204\) 0 0
\(205\) 5.85062 0.408625
\(206\) −16.9511 −1.18104
\(207\) 0 0
\(208\) −3.29344 −0.228359
\(209\) 3.60585 0.249422
\(210\) 0 0
\(211\) 5.17518 0.356274 0.178137 0.984006i \(-0.442993\pi\)
0.178137 + 0.984006i \(0.442993\pi\)
\(212\) 3.77402 0.259201
\(213\) 0 0
\(214\) 18.4405 1.26057
\(215\) −8.17082 −0.557245
\(216\) 0 0
\(217\) 1.70471 0.115723
\(218\) 6.56994 0.444972
\(219\) 0 0
\(220\) −13.8037 −0.930646
\(221\) −5.58716 −0.375833
\(222\) 0 0
\(223\) −1.00000 −0.0669650
\(224\) −1.22988 −0.0821745
\(225\) 0 0
\(226\) 5.19601 0.345633
\(227\) −7.53732 −0.500269 −0.250135 0.968211i \(-0.580475\pi\)
−0.250135 + 0.968211i \(0.580475\pi\)
\(228\) 0 0
\(229\) −4.91389 −0.324719 −0.162360 0.986732i \(-0.551910\pi\)
−0.162360 + 0.986732i \(0.551910\pi\)
\(230\) −12.9899 −0.856528
\(231\) 0 0
\(232\) −6.27650 −0.412073
\(233\) −1.10815 −0.0725973 −0.0362987 0.999341i \(-0.511557\pi\)
−0.0362987 + 0.999341i \(0.511557\pi\)
\(234\) 0 0
\(235\) 1.98306 0.129361
\(236\) 4.43067 0.288412
\(237\) 0 0
\(238\) −2.08643 −0.135243
\(239\) −4.22509 −0.273298 −0.136649 0.990620i \(-0.543633\pi\)
−0.136649 + 0.990620i \(0.543633\pi\)
\(240\) 0 0
\(241\) 15.9748 1.02903 0.514514 0.857482i \(-0.327972\pi\)
0.514514 + 0.857482i \(0.327972\pi\)
\(242\) 23.4978 1.51050
\(243\) 0 0
\(244\) −7.93022 −0.507680
\(245\) −12.8964 −0.823918
\(246\) 0 0
\(247\) 2.02190 0.128651
\(248\) −1.38608 −0.0880162
\(249\) 0 0
\(250\) −10.5210 −0.665406
\(251\) 16.7746 1.05880 0.529402 0.848371i \(-0.322416\pi\)
0.529402 + 0.848371i \(0.322416\pi\)
\(252\) 0 0
\(253\) 32.4640 2.04099
\(254\) 8.97063 0.562867
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −4.17907 −0.260683 −0.130342 0.991469i \(-0.541607\pi\)
−0.130342 + 0.991469i \(0.541607\pi\)
\(258\) 0 0
\(259\) −3.60381 −0.223930
\(260\) −7.74015 −0.480024
\(261\) 0 0
\(262\) −1.11347 −0.0687905
\(263\) −12.0157 −0.740919 −0.370460 0.928849i \(-0.620800\pi\)
−0.370460 + 0.928849i \(0.620800\pi\)
\(264\) 0 0
\(265\) 8.86959 0.544855
\(266\) 0.755045 0.0462948
\(267\) 0 0
\(268\) −8.35017 −0.510068
\(269\) −10.4075 −0.634558 −0.317279 0.948332i \(-0.602769\pi\)
−0.317279 + 0.948332i \(0.602769\pi\)
\(270\) 0 0
\(271\) 2.26081 0.137335 0.0686673 0.997640i \(-0.478125\pi\)
0.0686673 + 0.997640i \(0.478125\pi\)
\(272\) 1.69645 0.102863
\(273\) 0 0
\(274\) 1.61392 0.0975004
\(275\) −3.07367 −0.185349
\(276\) 0 0
\(277\) 23.4991 1.41192 0.705962 0.708250i \(-0.250515\pi\)
0.705962 + 0.708250i \(0.250515\pi\)
\(278\) −11.6626 −0.699475
\(279\) 0 0
\(280\) −2.89042 −0.172736
\(281\) −6.98785 −0.416860 −0.208430 0.978037i \(-0.566835\pi\)
−0.208430 + 0.978037i \(0.566835\pi\)
\(282\) 0 0
\(283\) −26.0886 −1.55081 −0.775403 0.631466i \(-0.782453\pi\)
−0.775403 + 0.631466i \(0.782453\pi\)
\(284\) −7.83758 −0.465075
\(285\) 0 0
\(286\) 19.3440 1.14383
\(287\) −3.06171 −0.180727
\(288\) 0 0
\(289\) −14.1220 −0.830709
\(290\) −14.7509 −0.866201
\(291\) 0 0
\(292\) −6.71932 −0.393218
\(293\) −22.0870 −1.29034 −0.645169 0.764040i \(-0.723213\pi\)
−0.645169 + 0.764040i \(0.723213\pi\)
\(294\) 0 0
\(295\) 10.4128 0.606259
\(296\) 2.93022 0.170316
\(297\) 0 0
\(298\) 10.0485 0.582093
\(299\) 18.2035 1.05274
\(300\) 0 0
\(301\) 4.27589 0.246458
\(302\) −12.3371 −0.709922
\(303\) 0 0
\(304\) −0.613919 −0.0352107
\(305\) −18.6374 −1.06717
\(306\) 0 0
\(307\) −2.96613 −0.169286 −0.0846430 0.996411i \(-0.526975\pi\)
−0.0846430 + 0.996411i \(0.526975\pi\)
\(308\) 7.22366 0.411606
\(309\) 0 0
\(310\) −3.25753 −0.185015
\(311\) −11.3392 −0.642985 −0.321493 0.946912i \(-0.604185\pi\)
−0.321493 + 0.946912i \(0.604185\pi\)
\(312\) 0 0
\(313\) 17.2237 0.973539 0.486769 0.873531i \(-0.338175\pi\)
0.486769 + 0.873531i \(0.338175\pi\)
\(314\) −15.2742 −0.861972
\(315\) 0 0
\(316\) 0.124190 0.00698624
\(317\) −2.82686 −0.158772 −0.0793861 0.996844i \(-0.525296\pi\)
−0.0793861 + 0.996844i \(0.525296\pi\)
\(318\) 0 0
\(319\) 36.8649 2.06404
\(320\) 2.35017 0.131379
\(321\) 0 0
\(322\) 6.79778 0.378825
\(323\) −1.04149 −0.0579498
\(324\) 0 0
\(325\) −1.72350 −0.0956025
\(326\) −23.8503 −1.32095
\(327\) 0 0
\(328\) 2.48944 0.137456
\(329\) −1.03776 −0.0572138
\(330\) 0 0
\(331\) −21.7527 −1.19564 −0.597819 0.801631i \(-0.703966\pi\)
−0.597819 + 0.801631i \(0.703966\pi\)
\(332\) 0.936439 0.0513938
\(333\) 0 0
\(334\) 4.06356 0.222348
\(335\) −19.6244 −1.07219
\(336\) 0 0
\(337\) −15.6351 −0.851696 −0.425848 0.904795i \(-0.640024\pi\)
−0.425848 + 0.904795i \(0.640024\pi\)
\(338\) −2.15327 −0.117123
\(339\) 0 0
\(340\) 3.98696 0.216223
\(341\) 8.14113 0.440867
\(342\) 0 0
\(343\) 15.3580 0.829252
\(344\) −3.47669 −0.187450
\(345\) 0 0
\(346\) −13.9269 −0.748717
\(347\) −29.0779 −1.56098 −0.780491 0.625167i \(-0.785031\pi\)
−0.780491 + 0.625167i \(0.785031\pi\)
\(348\) 0 0
\(349\) −28.9882 −1.55170 −0.775851 0.630917i \(-0.782679\pi\)
−0.775851 + 0.630917i \(0.782679\pi\)
\(350\) −0.643610 −0.0344024
\(351\) 0 0
\(352\) −5.87349 −0.313058
\(353\) 1.07475 0.0572030 0.0286015 0.999591i \(-0.490895\pi\)
0.0286015 + 0.999591i \(0.490895\pi\)
\(354\) 0 0
\(355\) −18.4197 −0.977614
\(356\) 9.09032 0.481786
\(357\) 0 0
\(358\) 20.8194 1.10034
\(359\) −18.6743 −0.985590 −0.492795 0.870145i \(-0.664025\pi\)
−0.492795 + 0.870145i \(0.664025\pi\)
\(360\) 0 0
\(361\) −18.6231 −0.980163
\(362\) 24.7297 1.29977
\(363\) 0 0
\(364\) 4.05052 0.212305
\(365\) −15.7916 −0.826568
\(366\) 0 0
\(367\) 16.5536 0.864091 0.432046 0.901852i \(-0.357792\pi\)
0.432046 + 0.901852i \(0.357792\pi\)
\(368\) −5.52721 −0.288126
\(369\) 0 0
\(370\) 6.88653 0.358014
\(371\) −4.64157 −0.240978
\(372\) 0 0
\(373\) −26.2958 −1.36154 −0.680772 0.732495i \(-0.738356\pi\)
−0.680772 + 0.732495i \(0.738356\pi\)
\(374\) −9.96409 −0.515231
\(375\) 0 0
\(376\) 0.843795 0.0435154
\(377\) 20.6713 1.06462
\(378\) 0 0
\(379\) −18.5670 −0.953723 −0.476862 0.878978i \(-0.658226\pi\)
−0.476862 + 0.878978i \(0.658226\pi\)
\(380\) −1.44282 −0.0740149
\(381\) 0 0
\(382\) −4.64779 −0.237802
\(383\) −13.3320 −0.681233 −0.340616 0.940202i \(-0.610636\pi\)
−0.340616 + 0.940202i \(0.610636\pi\)
\(384\) 0 0
\(385\) 16.9768 0.865220
\(386\) 19.1419 0.974298
\(387\) 0 0
\(388\) 1.28039 0.0650022
\(389\) 21.8611 1.10840 0.554200 0.832384i \(-0.313024\pi\)
0.554200 + 0.832384i \(0.313024\pi\)
\(390\) 0 0
\(391\) −9.37664 −0.474197
\(392\) −5.48741 −0.277156
\(393\) 0 0
\(394\) 20.5697 1.03628
\(395\) 0.291868 0.0146855
\(396\) 0 0
\(397\) −17.8783 −0.897285 −0.448642 0.893711i \(-0.648092\pi\)
−0.448642 + 0.893711i \(0.648092\pi\)
\(398\) 6.35203 0.318398
\(399\) 0 0
\(400\) 0.523313 0.0261656
\(401\) 20.0193 0.999716 0.499858 0.866107i \(-0.333386\pi\)
0.499858 + 0.866107i \(0.333386\pi\)
\(402\) 0 0
\(403\) 4.56497 0.227397
\(404\) 3.15806 0.157119
\(405\) 0 0
\(406\) 7.71932 0.383103
\(407\) −17.2106 −0.853099
\(408\) 0 0
\(409\) 19.0633 0.942618 0.471309 0.881968i \(-0.343782\pi\)
0.471309 + 0.881968i \(0.343782\pi\)
\(410\) 5.85062 0.288942
\(411\) 0 0
\(412\) −16.9511 −0.835118
\(413\) −5.44917 −0.268136
\(414\) 0 0
\(415\) 2.20079 0.108033
\(416\) −3.29344 −0.161474
\(417\) 0 0
\(418\) 3.60585 0.176368
\(419\) −23.4539 −1.14580 −0.572898 0.819627i \(-0.694181\pi\)
−0.572898 + 0.819627i \(0.694181\pi\)
\(420\) 0 0
\(421\) 19.0961 0.930685 0.465343 0.885131i \(-0.345931\pi\)
0.465343 + 0.885131i \(0.345931\pi\)
\(422\) 5.17518 0.251924
\(423\) 0 0
\(424\) 3.77402 0.183282
\(425\) 0.887776 0.0430634
\(426\) 0 0
\(427\) 9.75319 0.471990
\(428\) 18.4405 0.891355
\(429\) 0 0
\(430\) −8.17082 −0.394032
\(431\) 31.9918 1.54099 0.770495 0.637446i \(-0.220009\pi\)
0.770495 + 0.637446i \(0.220009\pi\)
\(432\) 0 0
\(433\) −2.02172 −0.0971578 −0.0485789 0.998819i \(-0.515469\pi\)
−0.0485789 + 0.998819i \(0.515469\pi\)
\(434\) 1.70471 0.0818286
\(435\) 0 0
\(436\) 6.56994 0.314643
\(437\) 3.39326 0.162322
\(438\) 0 0
\(439\) −13.7628 −0.656864 −0.328432 0.944528i \(-0.606520\pi\)
−0.328432 + 0.944528i \(0.606520\pi\)
\(440\) −13.8037 −0.658066
\(441\) 0 0
\(442\) −5.58716 −0.265754
\(443\) 35.4448 1.68403 0.842017 0.539451i \(-0.181368\pi\)
0.842017 + 0.539451i \(0.181368\pi\)
\(444\) 0 0
\(445\) 21.3638 1.01274
\(446\) −1.00000 −0.0473514
\(447\) 0 0
\(448\) −1.22988 −0.0581062
\(449\) 17.2168 0.812513 0.406256 0.913759i \(-0.366834\pi\)
0.406256 + 0.913759i \(0.366834\pi\)
\(450\) 0 0
\(451\) −14.6217 −0.688509
\(452\) 5.19601 0.244400
\(453\) 0 0
\(454\) −7.53732 −0.353744
\(455\) 9.51942 0.446277
\(456\) 0 0
\(457\) 29.3191 1.37149 0.685745 0.727842i \(-0.259477\pi\)
0.685745 + 0.727842i \(0.259477\pi\)
\(458\) −4.91389 −0.229611
\(459\) 0 0
\(460\) −12.9899 −0.605657
\(461\) −19.2523 −0.896668 −0.448334 0.893866i \(-0.647982\pi\)
−0.448334 + 0.893866i \(0.647982\pi\)
\(462\) 0 0
\(463\) 9.09450 0.422657 0.211329 0.977415i \(-0.432221\pi\)
0.211329 + 0.977415i \(0.432221\pi\)
\(464\) −6.27650 −0.291379
\(465\) 0 0
\(466\) −1.10815 −0.0513340
\(467\) 19.6339 0.908546 0.454273 0.890862i \(-0.349899\pi\)
0.454273 + 0.890862i \(0.349899\pi\)
\(468\) 0 0
\(469\) 10.2697 0.474210
\(470\) 1.98306 0.0914720
\(471\) 0 0
\(472\) 4.43067 0.203938
\(473\) 20.4203 0.938925
\(474\) 0 0
\(475\) −0.321272 −0.0147410
\(476\) −2.08643 −0.0956312
\(477\) 0 0
\(478\) −4.22509 −0.193251
\(479\) −5.33449 −0.243739 −0.121869 0.992546i \(-0.538889\pi\)
−0.121869 + 0.992546i \(0.538889\pi\)
\(480\) 0 0
\(481\) −9.65050 −0.440025
\(482\) 15.9748 0.727633
\(483\) 0 0
\(484\) 23.4978 1.06808
\(485\) 3.00915 0.136638
\(486\) 0 0
\(487\) 1.69645 0.0768736 0.0384368 0.999261i \(-0.487762\pi\)
0.0384368 + 0.999261i \(0.487762\pi\)
\(488\) −7.93022 −0.358984
\(489\) 0 0
\(490\) −12.8964 −0.582598
\(491\) −20.6650 −0.932600 −0.466300 0.884627i \(-0.654413\pi\)
−0.466300 + 0.884627i \(0.654413\pi\)
\(492\) 0 0
\(493\) −10.6478 −0.479552
\(494\) 2.02190 0.0909698
\(495\) 0 0
\(496\) −1.38608 −0.0622369
\(497\) 9.63925 0.432379
\(498\) 0 0
\(499\) 2.00275 0.0896554 0.0448277 0.998995i \(-0.485726\pi\)
0.0448277 + 0.998995i \(0.485726\pi\)
\(500\) −10.5210 −0.470513
\(501\) 0 0
\(502\) 16.7746 0.748688
\(503\) 18.6915 0.833412 0.416706 0.909041i \(-0.363184\pi\)
0.416706 + 0.909041i \(0.363184\pi\)
\(504\) 0 0
\(505\) 7.42199 0.330274
\(506\) 32.4640 1.44320
\(507\) 0 0
\(508\) 8.97063 0.398007
\(509\) −22.6404 −1.00352 −0.501759 0.865008i \(-0.667314\pi\)
−0.501759 + 0.865008i \(0.667314\pi\)
\(510\) 0 0
\(511\) 8.26393 0.365575
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) −4.17907 −0.184331
\(515\) −39.8379 −1.75547
\(516\) 0 0
\(517\) −4.95602 −0.217965
\(518\) −3.60381 −0.158342
\(519\) 0 0
\(520\) −7.74015 −0.339428
\(521\) 12.1290 0.531380 0.265690 0.964058i \(-0.414400\pi\)
0.265690 + 0.964058i \(0.414400\pi\)
\(522\) 0 0
\(523\) −23.3665 −1.02174 −0.510872 0.859657i \(-0.670677\pi\)
−0.510872 + 0.859657i \(0.670677\pi\)
\(524\) −1.11347 −0.0486422
\(525\) 0 0
\(526\) −12.0157 −0.523909
\(527\) −2.35142 −0.102429
\(528\) 0 0
\(529\) 7.55001 0.328261
\(530\) 8.86959 0.385270
\(531\) 0 0
\(532\) 0.755045 0.0327353
\(533\) −8.19882 −0.355130
\(534\) 0 0
\(535\) 43.3383 1.87368
\(536\) −8.35017 −0.360673
\(537\) 0 0
\(538\) −10.4075 −0.448700
\(539\) 32.2302 1.38825
\(540\) 0 0
\(541\) 2.47997 0.106622 0.0533112 0.998578i \(-0.483022\pi\)
0.0533112 + 0.998578i \(0.483022\pi\)
\(542\) 2.26081 0.0971103
\(543\) 0 0
\(544\) 1.69645 0.0727348
\(545\) 15.4405 0.661398
\(546\) 0 0
\(547\) −0.748219 −0.0319916 −0.0159958 0.999872i \(-0.505092\pi\)
−0.0159958 + 0.999872i \(0.505092\pi\)
\(548\) 1.61392 0.0689432
\(549\) 0 0
\(550\) −3.07367 −0.131062
\(551\) 3.85327 0.164155
\(552\) 0 0
\(553\) −0.152738 −0.00649510
\(554\) 23.4991 0.998380
\(555\) 0 0
\(556\) −11.6626 −0.494604
\(557\) 5.21930 0.221149 0.110574 0.993868i \(-0.464731\pi\)
0.110574 + 0.993868i \(0.464731\pi\)
\(558\) 0 0
\(559\) 11.4502 0.484294
\(560\) −2.89042 −0.122143
\(561\) 0 0
\(562\) −6.98785 −0.294765
\(563\) −3.39805 −0.143211 −0.0716053 0.997433i \(-0.522812\pi\)
−0.0716053 + 0.997433i \(0.522812\pi\)
\(564\) 0 0
\(565\) 12.2115 0.513742
\(566\) −26.0886 −1.09659
\(567\) 0 0
\(568\) −7.83758 −0.328857
\(569\) 14.4845 0.607221 0.303610 0.952796i \(-0.401808\pi\)
0.303610 + 0.952796i \(0.401808\pi\)
\(570\) 0 0
\(571\) −16.8460 −0.704982 −0.352491 0.935815i \(-0.614665\pi\)
−0.352491 + 0.935815i \(0.614665\pi\)
\(572\) 19.3440 0.808811
\(573\) 0 0
\(574\) −3.06171 −0.127793
\(575\) −2.89246 −0.120624
\(576\) 0 0
\(577\) −0.887489 −0.0369466 −0.0184733 0.999829i \(-0.505881\pi\)
−0.0184733 + 0.999829i \(0.505881\pi\)
\(578\) −14.1220 −0.587400
\(579\) 0 0
\(580\) −14.7509 −0.612496
\(581\) −1.15170 −0.0477807
\(582\) 0 0
\(583\) −22.1666 −0.918048
\(584\) −6.71932 −0.278047
\(585\) 0 0
\(586\) −22.0870 −0.912407
\(587\) 33.0362 1.36355 0.681776 0.731561i \(-0.261208\pi\)
0.681776 + 0.731561i \(0.261208\pi\)
\(588\) 0 0
\(589\) 0.850942 0.0350624
\(590\) 10.4128 0.428690
\(591\) 0 0
\(592\) 2.93022 0.120431
\(593\) 12.6799 0.520703 0.260351 0.965514i \(-0.416162\pi\)
0.260351 + 0.965514i \(0.416162\pi\)
\(594\) 0 0
\(595\) −4.90346 −0.201022
\(596\) 10.0485 0.411602
\(597\) 0 0
\(598\) 18.2035 0.744397
\(599\) 20.3036 0.829582 0.414791 0.909917i \(-0.363855\pi\)
0.414791 + 0.909917i \(0.363855\pi\)
\(600\) 0 0
\(601\) 29.5976 1.20731 0.603655 0.797245i \(-0.293710\pi\)
0.603655 + 0.797245i \(0.293710\pi\)
\(602\) 4.27589 0.174272
\(603\) 0 0
\(604\) −12.3371 −0.501991
\(605\) 55.2240 2.24517
\(606\) 0 0
\(607\) 10.3987 0.422068 0.211034 0.977479i \(-0.432317\pi\)
0.211034 + 0.977479i \(0.432317\pi\)
\(608\) −0.613919 −0.0248977
\(609\) 0 0
\(610\) −18.6374 −0.754606
\(611\) −2.77899 −0.112426
\(612\) 0 0
\(613\) 2.74787 0.110985 0.0554926 0.998459i \(-0.482327\pi\)
0.0554926 + 0.998459i \(0.482327\pi\)
\(614\) −2.96613 −0.119703
\(615\) 0 0
\(616\) 7.22366 0.291050
\(617\) −46.2786 −1.86311 −0.931553 0.363607i \(-0.881545\pi\)
−0.931553 + 0.363607i \(0.881545\pi\)
\(618\) 0 0
\(619\) −23.0901 −0.928071 −0.464036 0.885817i \(-0.653599\pi\)
−0.464036 + 0.885817i \(0.653599\pi\)
\(620\) −3.25753 −0.130826
\(621\) 0 0
\(622\) −11.3392 −0.454659
\(623\) −11.1800 −0.447916
\(624\) 0 0
\(625\) −27.3427 −1.09371
\(626\) 17.2237 0.688396
\(627\) 0 0
\(628\) −15.2742 −0.609506
\(629\) 4.97098 0.198206
\(630\) 0 0
\(631\) −48.9725 −1.94956 −0.974782 0.223159i \(-0.928363\pi\)
−0.974782 + 0.223159i \(0.928363\pi\)
\(632\) 0.124190 0.00494001
\(633\) 0 0
\(634\) −2.82686 −0.112269
\(635\) 21.0825 0.836635
\(636\) 0 0
\(637\) 18.0724 0.716055
\(638\) 36.8649 1.45950
\(639\) 0 0
\(640\) 2.35017 0.0928987
\(641\) −35.1814 −1.38958 −0.694790 0.719213i \(-0.744503\pi\)
−0.694790 + 0.719213i \(0.744503\pi\)
\(642\) 0 0
\(643\) 17.4912 0.689785 0.344893 0.938642i \(-0.387915\pi\)
0.344893 + 0.938642i \(0.387915\pi\)
\(644\) 6.79778 0.267870
\(645\) 0 0
\(646\) −1.04149 −0.0409767
\(647\) 41.5940 1.63523 0.817615 0.575766i \(-0.195296\pi\)
0.817615 + 0.575766i \(0.195296\pi\)
\(648\) 0 0
\(649\) −26.0235 −1.02151
\(650\) −1.72350 −0.0676012
\(651\) 0 0
\(652\) −23.8503 −0.934051
\(653\) 14.0577 0.550120 0.275060 0.961427i \(-0.411302\pi\)
0.275060 + 0.961427i \(0.411302\pi\)
\(654\) 0 0
\(655\) −2.61685 −0.102249
\(656\) 2.48944 0.0971964
\(657\) 0 0
\(658\) −1.03776 −0.0404562
\(659\) 22.8293 0.889304 0.444652 0.895703i \(-0.353327\pi\)
0.444652 + 0.895703i \(0.353327\pi\)
\(660\) 0 0
\(661\) 11.1420 0.433374 0.216687 0.976241i \(-0.430475\pi\)
0.216687 + 0.976241i \(0.430475\pi\)
\(662\) −21.7527 −0.845443
\(663\) 0 0
\(664\) 0.936439 0.0363409
\(665\) 1.77449 0.0688116
\(666\) 0 0
\(667\) 34.6915 1.34326
\(668\) 4.06356 0.157224
\(669\) 0 0
\(670\) −19.6244 −0.758155
\(671\) 46.5780 1.79813
\(672\) 0 0
\(673\) 3.67298 0.141583 0.0707915 0.997491i \(-0.477448\pi\)
0.0707915 + 0.997491i \(0.477448\pi\)
\(674\) −15.6351 −0.602240
\(675\) 0 0
\(676\) −2.15327 −0.0828182
\(677\) 11.9860 0.460659 0.230330 0.973113i \(-0.426020\pi\)
0.230330 + 0.973113i \(0.426020\pi\)
\(678\) 0 0
\(679\) −1.57473 −0.0604325
\(680\) 3.98696 0.152893
\(681\) 0 0
\(682\) 8.14113 0.311740
\(683\) −28.3794 −1.08591 −0.542954 0.839763i \(-0.682694\pi\)
−0.542954 + 0.839763i \(0.682694\pi\)
\(684\) 0 0
\(685\) 3.79299 0.144923
\(686\) 15.3580 0.586370
\(687\) 0 0
\(688\) −3.47669 −0.132547
\(689\) −12.4295 −0.473526
\(690\) 0 0
\(691\) 10.6173 0.403903 0.201951 0.979396i \(-0.435272\pi\)
0.201951 + 0.979396i \(0.435272\pi\)
\(692\) −13.9269 −0.529423
\(693\) 0 0
\(694\) −29.0779 −1.10378
\(695\) −27.4091 −1.03969
\(696\) 0 0
\(697\) 4.22322 0.159966
\(698\) −28.9882 −1.09722
\(699\) 0 0
\(700\) −0.643610 −0.0243262
\(701\) 4.18060 0.157899 0.0789496 0.996879i \(-0.474843\pi\)
0.0789496 + 0.996879i \(0.474843\pi\)
\(702\) 0 0
\(703\) −1.79892 −0.0678475
\(704\) −5.87349 −0.221365
\(705\) 0 0
\(706\) 1.07475 0.0404487
\(707\) −3.88402 −0.146074
\(708\) 0 0
\(709\) −19.6965 −0.739716 −0.369858 0.929088i \(-0.620594\pi\)
−0.369858 + 0.929088i \(0.620594\pi\)
\(710\) −18.4197 −0.691278
\(711\) 0 0
\(712\) 9.09032 0.340674
\(713\) 7.66115 0.286912
\(714\) 0 0
\(715\) 45.4616 1.70017
\(716\) 20.8194 0.778057
\(717\) 0 0
\(718\) −18.6743 −0.696917
\(719\) 9.17225 0.342067 0.171034 0.985265i \(-0.445289\pi\)
0.171034 + 0.985265i \(0.445289\pi\)
\(720\) 0 0
\(721\) 20.8477 0.776408
\(722\) −18.6231 −0.693080
\(723\) 0 0
\(724\) 24.7297 0.919074
\(725\) −3.28457 −0.121986
\(726\) 0 0
\(727\) −22.6607 −0.840440 −0.420220 0.907422i \(-0.638047\pi\)
−0.420220 + 0.907422i \(0.638047\pi\)
\(728\) 4.05052 0.150122
\(729\) 0 0
\(730\) −15.7916 −0.584472
\(731\) −5.89804 −0.218147
\(732\) 0 0
\(733\) −22.6259 −0.835707 −0.417854 0.908514i \(-0.637218\pi\)
−0.417854 + 0.908514i \(0.637218\pi\)
\(734\) 16.5536 0.611005
\(735\) 0 0
\(736\) −5.52721 −0.203736
\(737\) 49.0446 1.80658
\(738\) 0 0
\(739\) −9.64422 −0.354768 −0.177384 0.984142i \(-0.556764\pi\)
−0.177384 + 0.984142i \(0.556764\pi\)
\(740\) 6.88653 0.253154
\(741\) 0 0
\(742\) −4.64157 −0.170397
\(743\) 24.7312 0.907299 0.453649 0.891180i \(-0.350122\pi\)
0.453649 + 0.891180i \(0.350122\pi\)
\(744\) 0 0
\(745\) 23.6157 0.865211
\(746\) −26.2958 −0.962757
\(747\) 0 0
\(748\) −9.96409 −0.364323
\(749\) −22.6795 −0.828692
\(750\) 0 0
\(751\) 44.0912 1.60891 0.804456 0.594012i \(-0.202457\pi\)
0.804456 + 0.594012i \(0.202457\pi\)
\(752\) 0.843795 0.0307700
\(753\) 0 0
\(754\) 20.6713 0.752803
\(755\) −28.9944 −1.05521
\(756\) 0 0
\(757\) −24.2296 −0.880639 −0.440320 0.897841i \(-0.645135\pi\)
−0.440320 + 0.897841i \(0.645135\pi\)
\(758\) −18.5670 −0.674384
\(759\) 0 0
\(760\) −1.44282 −0.0523365
\(761\) −44.4206 −1.61025 −0.805123 0.593108i \(-0.797901\pi\)
−0.805123 + 0.593108i \(0.797901\pi\)
\(762\) 0 0
\(763\) −8.08021 −0.292523
\(764\) −4.64779 −0.168151
\(765\) 0 0
\(766\) −13.3320 −0.481704
\(767\) −14.5921 −0.526891
\(768\) 0 0
\(769\) 29.9804 1.08112 0.540560 0.841305i \(-0.318212\pi\)
0.540560 + 0.841305i \(0.318212\pi\)
\(770\) 16.9768 0.611803
\(771\) 0 0
\(772\) 19.1419 0.688933
\(773\) −13.7064 −0.492986 −0.246493 0.969145i \(-0.579278\pi\)
−0.246493 + 0.969145i \(0.579278\pi\)
\(774\) 0 0
\(775\) −0.725354 −0.0260555
\(776\) 1.28039 0.0459635
\(777\) 0 0
\(778\) 21.8611 0.783757
\(779\) −1.52832 −0.0547576
\(780\) 0 0
\(781\) 46.0339 1.64722
\(782\) −9.37664 −0.335308
\(783\) 0 0
\(784\) −5.48741 −0.195979
\(785\) −35.8970 −1.28122
\(786\) 0 0
\(787\) 22.1364 0.789078 0.394539 0.918879i \(-0.370904\pi\)
0.394539 + 0.918879i \(0.370904\pi\)
\(788\) 20.5697 0.732764
\(789\) 0 0
\(790\) 0.291868 0.0103842
\(791\) −6.39044 −0.227218
\(792\) 0 0
\(793\) 26.1177 0.927466
\(794\) −17.8783 −0.634476
\(795\) 0 0
\(796\) 6.35203 0.225142
\(797\) 50.5494 1.79055 0.895276 0.445511i \(-0.146978\pi\)
0.895276 + 0.445511i \(0.146978\pi\)
\(798\) 0 0
\(799\) 1.43146 0.0506414
\(800\) 0.523313 0.0185019
\(801\) 0 0
\(802\) 20.0193 0.706906
\(803\) 39.4658 1.39272
\(804\) 0 0
\(805\) 15.9760 0.563078
\(806\) 4.56497 0.160794
\(807\) 0 0
\(808\) 3.15806 0.111100
\(809\) 35.1267 1.23499 0.617494 0.786576i \(-0.288148\pi\)
0.617494 + 0.786576i \(0.288148\pi\)
\(810\) 0 0
\(811\) 26.8154 0.941616 0.470808 0.882236i \(-0.343963\pi\)
0.470808 + 0.882236i \(0.343963\pi\)
\(812\) 7.71932 0.270895
\(813\) 0 0
\(814\) −17.2106 −0.603232
\(815\) −56.0524 −1.96343
\(816\) 0 0
\(817\) 2.13441 0.0746734
\(818\) 19.0633 0.666532
\(819\) 0 0
\(820\) 5.85062 0.204313
\(821\) 0.589625 0.0205780 0.0102890 0.999947i \(-0.496725\pi\)
0.0102890 + 0.999947i \(0.496725\pi\)
\(822\) 0 0
\(823\) −7.50106 −0.261470 −0.130735 0.991417i \(-0.541734\pi\)
−0.130735 + 0.991417i \(0.541734\pi\)
\(824\) −16.9511 −0.590518
\(825\) 0 0
\(826\) −5.44917 −0.189601
\(827\) 16.4319 0.571393 0.285696 0.958320i \(-0.407775\pi\)
0.285696 + 0.958320i \(0.407775\pi\)
\(828\) 0 0
\(829\) −28.0822 −0.975337 −0.487668 0.873029i \(-0.662152\pi\)
−0.487668 + 0.873029i \(0.662152\pi\)
\(830\) 2.20079 0.0763907
\(831\) 0 0
\(832\) −3.29344 −0.114179
\(833\) −9.30912 −0.322542
\(834\) 0 0
\(835\) 9.55007 0.330494
\(836\) 3.60585 0.124711
\(837\) 0 0
\(838\) −23.4539 −0.810200
\(839\) 31.8314 1.09894 0.549470 0.835513i \(-0.314830\pi\)
0.549470 + 0.835513i \(0.314830\pi\)
\(840\) 0 0
\(841\) 10.3945 0.358430
\(842\) 19.0961 0.658094
\(843\) 0 0
\(844\) 5.17518 0.178137
\(845\) −5.06056 −0.174089
\(846\) 0 0
\(847\) −28.8994 −0.992996
\(848\) 3.77402 0.129600
\(849\) 0 0
\(850\) 0.887776 0.0304505
\(851\) −16.1959 −0.555190
\(852\) 0 0
\(853\) 27.4346 0.939342 0.469671 0.882842i \(-0.344373\pi\)
0.469671 + 0.882842i \(0.344373\pi\)
\(854\) 9.75319 0.333747
\(855\) 0 0
\(856\) 18.4405 0.630283
\(857\) −7.08110 −0.241886 −0.120943 0.992659i \(-0.538592\pi\)
−0.120943 + 0.992659i \(0.538592\pi\)
\(858\) 0 0
\(859\) −11.6040 −0.395923 −0.197962 0.980210i \(-0.563432\pi\)
−0.197962 + 0.980210i \(0.563432\pi\)
\(860\) −8.17082 −0.278623
\(861\) 0 0
\(862\) 31.9918 1.08964
\(863\) −39.9734 −1.36071 −0.680356 0.732882i \(-0.738175\pi\)
−0.680356 + 0.732882i \(0.738175\pi\)
\(864\) 0 0
\(865\) −32.7307 −1.11288
\(866\) −2.02172 −0.0687009
\(867\) 0 0
\(868\) 1.70471 0.0578615
\(869\) −0.729428 −0.0247442
\(870\) 0 0
\(871\) 27.5008 0.931828
\(872\) 6.56994 0.222486
\(873\) 0 0
\(874\) 3.39326 0.114779
\(875\) 12.9395 0.437435
\(876\) 0 0
\(877\) 31.1987 1.05350 0.526752 0.850019i \(-0.323410\pi\)
0.526752 + 0.850019i \(0.323410\pi\)
\(878\) −13.7628 −0.464473
\(879\) 0 0
\(880\) −13.8037 −0.465323
\(881\) 14.5634 0.490655 0.245327 0.969440i \(-0.421105\pi\)
0.245327 + 0.969440i \(0.421105\pi\)
\(882\) 0 0
\(883\) −10.0488 −0.338168 −0.169084 0.985602i \(-0.554081\pi\)
−0.169084 + 0.985602i \(0.554081\pi\)
\(884\) −5.58716 −0.187917
\(885\) 0 0
\(886\) 35.4448 1.19079
\(887\) −28.4399 −0.954917 −0.477458 0.878654i \(-0.658442\pi\)
−0.477458 + 0.878654i \(0.658442\pi\)
\(888\) 0 0
\(889\) −11.0328 −0.370027
\(890\) 21.3638 0.716117
\(891\) 0 0
\(892\) −1.00000 −0.0334825
\(893\) −0.518022 −0.0173350
\(894\) 0 0
\(895\) 48.9292 1.63552
\(896\) −1.22988 −0.0410873
\(897\) 0 0
\(898\) 17.2168 0.574533
\(899\) 8.69974 0.290153
\(900\) 0 0
\(901\) 6.40244 0.213296
\(902\) −14.6217 −0.486850
\(903\) 0 0
\(904\) 5.19601 0.172817
\(905\) 58.1192 1.93195
\(906\) 0 0
\(907\) 21.5378 0.715149 0.357575 0.933885i \(-0.383604\pi\)
0.357575 + 0.933885i \(0.383604\pi\)
\(908\) −7.53732 −0.250135
\(909\) 0 0
\(910\) 9.51942 0.315566
\(911\) 21.2338 0.703507 0.351754 0.936093i \(-0.385585\pi\)
0.351754 + 0.936093i \(0.385585\pi\)
\(912\) 0 0
\(913\) −5.50016 −0.182029
\(914\) 29.3191 0.969789
\(915\) 0 0
\(916\) −4.91389 −0.162360
\(917\) 1.36943 0.0452226
\(918\) 0 0
\(919\) −47.8688 −1.57905 −0.789524 0.613720i \(-0.789672\pi\)
−0.789524 + 0.613720i \(0.789672\pi\)
\(920\) −12.9899 −0.428264
\(921\) 0 0
\(922\) −19.2523 −0.634040
\(923\) 25.8126 0.849631
\(924\) 0 0
\(925\) 1.53342 0.0504186
\(926\) 9.09450 0.298864
\(927\) 0 0
\(928\) −6.27650 −0.206036
\(929\) −53.3852 −1.75151 −0.875755 0.482755i \(-0.839636\pi\)
−0.875755 + 0.482755i \(0.839636\pi\)
\(930\) 0 0
\(931\) 3.36882 0.110409
\(932\) −1.10815 −0.0362987
\(933\) 0 0
\(934\) 19.6339 0.642439
\(935\) −23.4173 −0.765829
\(936\) 0 0
\(937\) 46.0746 1.50519 0.752596 0.658483i \(-0.228801\pi\)
0.752596 + 0.658483i \(0.228801\pi\)
\(938\) 10.2697 0.335317
\(939\) 0 0
\(940\) 1.98306 0.0646804
\(941\) 57.8075 1.88447 0.942235 0.334954i \(-0.108721\pi\)
0.942235 + 0.334954i \(0.108721\pi\)
\(942\) 0 0
\(943\) −13.7597 −0.448076
\(944\) 4.43067 0.144206
\(945\) 0 0
\(946\) 20.4203 0.663920
\(947\) 49.0924 1.59529 0.797644 0.603128i \(-0.206079\pi\)
0.797644 + 0.603128i \(0.206079\pi\)
\(948\) 0 0
\(949\) 22.1297 0.718359
\(950\) −0.321272 −0.0104234
\(951\) 0 0
\(952\) −2.08643 −0.0676215
\(953\) 13.4296 0.435028 0.217514 0.976057i \(-0.430205\pi\)
0.217514 + 0.976057i \(0.430205\pi\)
\(954\) 0 0
\(955\) −10.9231 −0.353464
\(956\) −4.22509 −0.136649
\(957\) 0 0
\(958\) −5.33449 −0.172349
\(959\) −1.98492 −0.0640964
\(960\) 0 0
\(961\) −29.0788 −0.938025
\(962\) −9.65050 −0.311145
\(963\) 0 0
\(964\) 15.9748 0.514514
\(965\) 44.9868 1.44818
\(966\) 0 0
\(967\) 18.6164 0.598665 0.299332 0.954149i \(-0.403236\pi\)
0.299332 + 0.954149i \(0.403236\pi\)
\(968\) 23.4978 0.755249
\(969\) 0 0
\(970\) 3.00915 0.0966180
\(971\) 16.6628 0.534734 0.267367 0.963595i \(-0.413846\pi\)
0.267367 + 0.963595i \(0.413846\pi\)
\(972\) 0 0
\(973\) 14.3435 0.459832
\(974\) 1.69645 0.0543579
\(975\) 0 0
\(976\) −7.93022 −0.253840
\(977\) −45.0126 −1.44008 −0.720040 0.693932i \(-0.755877\pi\)
−0.720040 + 0.693932i \(0.755877\pi\)
\(978\) 0 0
\(979\) −53.3919 −1.70641
\(980\) −12.8964 −0.411959
\(981\) 0 0
\(982\) −20.6650 −0.659448
\(983\) −50.5203 −1.61135 −0.805674 0.592359i \(-0.798197\pi\)
−0.805674 + 0.592359i \(0.798197\pi\)
\(984\) 0 0
\(985\) 48.3422 1.54031
\(986\) −10.6478 −0.339095
\(987\) 0 0
\(988\) 2.02190 0.0643254
\(989\) 19.2164 0.611045
\(990\) 0 0
\(991\) 52.5979 1.67083 0.835414 0.549621i \(-0.185228\pi\)
0.835414 + 0.549621i \(0.185228\pi\)
\(992\) −1.38608 −0.0440081
\(993\) 0 0
\(994\) 9.63925 0.305738
\(995\) 14.9284 0.473261
\(996\) 0 0
\(997\) −50.7575 −1.60751 −0.803754 0.594962i \(-0.797167\pi\)
−0.803754 + 0.594962i \(0.797167\pi\)
\(998\) 2.00275 0.0633960
\(999\) 0 0
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 \(a_p\))