Properties

Label 6027.2.a.m.1.2
Level 6027
Weight 2
Character 6027.1
Self dual Yes
Analytic conductor 48.126
Analytic rank 1
Dimension 2
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6027.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.1258372982\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{8})^+\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(1.41421\)
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.41421 q^{2} -1.00000 q^{3} -0.585786 q^{5} -1.41421 q^{6} -2.82843 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.41421 q^{2} -1.00000 q^{3} -0.585786 q^{5} -1.41421 q^{6} -2.82843 q^{8} +1.00000 q^{9} -0.828427 q^{10} -0.414214 q^{11} +2.24264 q^{13} +0.585786 q^{15} -4.00000 q^{16} -2.41421 q^{17} +1.41421 q^{18} +2.58579 q^{19} -0.585786 q^{22} +1.41421 q^{23} +2.82843 q^{24} -4.65685 q^{25} +3.17157 q^{26} -1.00000 q^{27} +8.07107 q^{29} +0.828427 q^{30} +3.00000 q^{31} +0.414214 q^{33} -3.41421 q^{34} +7.48528 q^{37} +3.65685 q^{38} -2.24264 q^{39} +1.65685 q^{40} +1.00000 q^{41} -5.00000 q^{43} -0.585786 q^{45} +2.00000 q^{46} -7.58579 q^{47} +4.00000 q^{48} -6.58579 q^{50} +2.41421 q^{51} +1.17157 q^{53} -1.41421 q^{54} +0.242641 q^{55} -2.58579 q^{57} +11.4142 q^{58} -8.48528 q^{59} -6.65685 q^{61} +4.24264 q^{62} +8.00000 q^{64} -1.31371 q^{65} +0.585786 q^{66} -6.48528 q^{67} -1.41421 q^{69} -4.07107 q^{71} -2.82843 q^{72} -12.3137 q^{73} +10.5858 q^{74} +4.65685 q^{75} -3.17157 q^{78} +3.65685 q^{79} +2.34315 q^{80} +1.00000 q^{81} +1.41421 q^{82} +13.0711 q^{83} +1.41421 q^{85} -7.07107 q^{86} -8.07107 q^{87} +1.17157 q^{88} +0.343146 q^{89} -0.828427 q^{90} -3.00000 q^{93} -10.7279 q^{94} -1.51472 q^{95} -16.2426 q^{97} -0.414214 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 2q^{3} - 4q^{5} + 2q^{9} + O(q^{10}) \) \( 2q - 2q^{3} - 4q^{5} + 2q^{9} + 4q^{10} + 2q^{11} - 4q^{13} + 4q^{15} - 8q^{16} - 2q^{17} + 8q^{19} - 4q^{22} + 2q^{25} + 12q^{26} - 2q^{27} + 2q^{29} - 4q^{30} + 6q^{31} - 2q^{33} - 4q^{34} - 2q^{37} - 4q^{38} + 4q^{39} - 8q^{40} + 2q^{41} - 10q^{43} - 4q^{45} + 4q^{46} - 18q^{47} + 8q^{48} - 16q^{50} + 2q^{51} + 8q^{53} - 8q^{55} - 8q^{57} + 20q^{58} - 2q^{61} + 16q^{64} + 20q^{65} + 4q^{66} + 4q^{67} + 6q^{71} - 2q^{73} + 24q^{74} - 2q^{75} - 12q^{78} - 4q^{79} + 16q^{80} + 2q^{81} + 12q^{83} - 2q^{87} + 8q^{88} + 12q^{89} + 4q^{90} - 6q^{93} + 4q^{94} - 20q^{95} - 24q^{97} + 2q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.41421 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(3\) −1.00000 −0.577350
\(4\) 0 0
\(5\) −0.585786 −0.261972 −0.130986 0.991384i \(-0.541814\pi\)
−0.130986 + 0.991384i \(0.541814\pi\)
\(6\) −1.41421 −0.577350
\(7\) 0 0
\(8\) −2.82843 −1.00000
\(9\) 1.00000 0.333333
\(10\) −0.828427 −0.261972
\(11\) −0.414214 −0.124890 −0.0624450 0.998048i \(-0.519890\pi\)
−0.0624450 + 0.998048i \(0.519890\pi\)
\(12\) 0 0
\(13\) 2.24264 0.621997 0.310998 0.950410i \(-0.399337\pi\)
0.310998 + 0.950410i \(0.399337\pi\)
\(14\) 0 0
\(15\) 0.585786 0.151249
\(16\) −4.00000 −1.00000
\(17\) −2.41421 −0.585533 −0.292766 0.956184i \(-0.594576\pi\)
−0.292766 + 0.956184i \(0.594576\pi\)
\(18\) 1.41421 0.333333
\(19\) 2.58579 0.593220 0.296610 0.954999i \(-0.404144\pi\)
0.296610 + 0.954999i \(0.404144\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −0.585786 −0.124890
\(23\) 1.41421 0.294884 0.147442 0.989071i \(-0.452896\pi\)
0.147442 + 0.989071i \(0.452896\pi\)
\(24\) 2.82843 0.577350
\(25\) −4.65685 −0.931371
\(26\) 3.17157 0.621997
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 8.07107 1.49876 0.749380 0.662140i \(-0.230352\pi\)
0.749380 + 0.662140i \(0.230352\pi\)
\(30\) 0.828427 0.151249
\(31\) 3.00000 0.538816 0.269408 0.963026i \(-0.413172\pi\)
0.269408 + 0.963026i \(0.413172\pi\)
\(32\) 0 0
\(33\) 0.414214 0.0721053
\(34\) −3.41421 −0.585533
\(35\) 0 0
\(36\) 0 0
\(37\) 7.48528 1.23057 0.615286 0.788304i \(-0.289040\pi\)
0.615286 + 0.788304i \(0.289040\pi\)
\(38\) 3.65685 0.593220
\(39\) −2.24264 −0.359110
\(40\) 1.65685 0.261972
\(41\) 1.00000 0.156174
\(42\) 0 0
\(43\) −5.00000 −0.762493 −0.381246 0.924473i \(-0.624505\pi\)
−0.381246 + 0.924473i \(0.624505\pi\)
\(44\) 0 0
\(45\) −0.585786 −0.0873239
\(46\) 2.00000 0.294884
\(47\) −7.58579 −1.10650 −0.553250 0.833015i \(-0.686613\pi\)
−0.553250 + 0.833015i \(0.686613\pi\)
\(48\) 4.00000 0.577350
\(49\) 0 0
\(50\) −6.58579 −0.931371
\(51\) 2.41421 0.338058
\(52\) 0 0
\(53\) 1.17157 0.160928 0.0804640 0.996758i \(-0.474360\pi\)
0.0804640 + 0.996758i \(0.474360\pi\)
\(54\) −1.41421 −0.192450
\(55\) 0.242641 0.0327177
\(56\) 0 0
\(57\) −2.58579 −0.342496
\(58\) 11.4142 1.49876
\(59\) −8.48528 −1.10469 −0.552345 0.833616i \(-0.686267\pi\)
−0.552345 + 0.833616i \(0.686267\pi\)
\(60\) 0 0
\(61\) −6.65685 −0.852323 −0.426161 0.904647i \(-0.640134\pi\)
−0.426161 + 0.904647i \(0.640134\pi\)
\(62\) 4.24264 0.538816
\(63\) 0 0
\(64\) 8.00000 1.00000
\(65\) −1.31371 −0.162945
\(66\) 0.585786 0.0721053
\(67\) −6.48528 −0.792303 −0.396152 0.918185i \(-0.629655\pi\)
−0.396152 + 0.918185i \(0.629655\pi\)
\(68\) 0 0
\(69\) −1.41421 −0.170251
\(70\) 0 0
\(71\) −4.07107 −0.483147 −0.241573 0.970383i \(-0.577663\pi\)
−0.241573 + 0.970383i \(0.577663\pi\)
\(72\) −2.82843 −0.333333
\(73\) −12.3137 −1.44121 −0.720605 0.693346i \(-0.756136\pi\)
−0.720605 + 0.693346i \(0.756136\pi\)
\(74\) 10.5858 1.23057
\(75\) 4.65685 0.537727
\(76\) 0 0
\(77\) 0 0
\(78\) −3.17157 −0.359110
\(79\) 3.65685 0.411428 0.205714 0.978612i \(-0.434048\pi\)
0.205714 + 0.978612i \(0.434048\pi\)
\(80\) 2.34315 0.261972
\(81\) 1.00000 0.111111
\(82\) 1.41421 0.156174
\(83\) 13.0711 1.43474 0.717368 0.696694i \(-0.245347\pi\)
0.717368 + 0.696694i \(0.245347\pi\)
\(84\) 0 0
\(85\) 1.41421 0.153393
\(86\) −7.07107 −0.762493
\(87\) −8.07107 −0.865309
\(88\) 1.17157 0.124890
\(89\) 0.343146 0.0363734 0.0181867 0.999835i \(-0.494211\pi\)
0.0181867 + 0.999835i \(0.494211\pi\)
\(90\) −0.828427 −0.0873239
\(91\) 0 0
\(92\) 0 0
\(93\) −3.00000 −0.311086
\(94\) −10.7279 −1.10650
\(95\) −1.51472 −0.155407
\(96\) 0 0
\(97\) −16.2426 −1.64919 −0.824595 0.565723i \(-0.808597\pi\)
−0.824595 + 0.565723i \(0.808597\pi\)
\(98\) 0 0
\(99\) −0.414214 −0.0416300
\(100\) 0 0
\(101\) −2.41421 −0.240223 −0.120112 0.992760i \(-0.538325\pi\)
−0.120112 + 0.992760i \(0.538325\pi\)
\(102\) 3.41421 0.338058
\(103\) 16.3137 1.60744 0.803719 0.595009i \(-0.202852\pi\)
0.803719 + 0.595009i \(0.202852\pi\)
\(104\) −6.34315 −0.621997
\(105\) 0 0
\(106\) 1.65685 0.160928
\(107\) −11.6569 −1.12691 −0.563455 0.826147i \(-0.690528\pi\)
−0.563455 + 0.826147i \(0.690528\pi\)
\(108\) 0 0
\(109\) −11.8995 −1.13976 −0.569882 0.821726i \(-0.693011\pi\)
−0.569882 + 0.821726i \(0.693011\pi\)
\(110\) 0.343146 0.0327177
\(111\) −7.48528 −0.710471
\(112\) 0 0
\(113\) −18.7279 −1.76177 −0.880887 0.473326i \(-0.843053\pi\)
−0.880887 + 0.473326i \(0.843053\pi\)
\(114\) −3.65685 −0.342496
\(115\) −0.828427 −0.0772512
\(116\) 0 0
\(117\) 2.24264 0.207332
\(118\) −12.0000 −1.10469
\(119\) 0 0
\(120\) −1.65685 −0.151249
\(121\) −10.8284 −0.984402
\(122\) −9.41421 −0.852323
\(123\) −1.00000 −0.0901670
\(124\) 0 0
\(125\) 5.65685 0.505964
\(126\) 0 0
\(127\) −13.3137 −1.18140 −0.590700 0.806891i \(-0.701148\pi\)
−0.590700 + 0.806891i \(0.701148\pi\)
\(128\) 11.3137 1.00000
\(129\) 5.00000 0.440225
\(130\) −1.85786 −0.162945
\(131\) 13.4142 1.17201 0.586003 0.810309i \(-0.300701\pi\)
0.586003 + 0.810309i \(0.300701\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −9.17157 −0.792303
\(135\) 0.585786 0.0504165
\(136\) 6.82843 0.585533
\(137\) 18.0711 1.54392 0.771958 0.635674i \(-0.219278\pi\)
0.771958 + 0.635674i \(0.219278\pi\)
\(138\) −2.00000 −0.170251
\(139\) 7.65685 0.649446 0.324723 0.945809i \(-0.394729\pi\)
0.324723 + 0.945809i \(0.394729\pi\)
\(140\) 0 0
\(141\) 7.58579 0.638838
\(142\) −5.75736 −0.483147
\(143\) −0.928932 −0.0776812
\(144\) −4.00000 −0.333333
\(145\) −4.72792 −0.392633
\(146\) −17.4142 −1.44121
\(147\) 0 0
\(148\) 0 0
\(149\) −5.31371 −0.435316 −0.217658 0.976025i \(-0.569842\pi\)
−0.217658 + 0.976025i \(0.569842\pi\)
\(150\) 6.58579 0.537727
\(151\) −16.0000 −1.30206 −0.651031 0.759051i \(-0.725663\pi\)
−0.651031 + 0.759051i \(0.725663\pi\)
\(152\) −7.31371 −0.593220
\(153\) −2.41421 −0.195178
\(154\) 0 0
\(155\) −1.75736 −0.141154
\(156\) 0 0
\(157\) −18.0000 −1.43656 −0.718278 0.695756i \(-0.755069\pi\)
−0.718278 + 0.695756i \(0.755069\pi\)
\(158\) 5.17157 0.411428
\(159\) −1.17157 −0.0929118
\(160\) 0 0
\(161\) 0 0
\(162\) 1.41421 0.111111
\(163\) 7.48528 0.586292 0.293146 0.956068i \(-0.405298\pi\)
0.293146 + 0.956068i \(0.405298\pi\)
\(164\) 0 0
\(165\) −0.242641 −0.0188896
\(166\) 18.4853 1.43474
\(167\) −7.65685 −0.592505 −0.296253 0.955110i \(-0.595737\pi\)
−0.296253 + 0.955110i \(0.595737\pi\)
\(168\) 0 0
\(169\) −7.97056 −0.613120
\(170\) 2.00000 0.153393
\(171\) 2.58579 0.197740
\(172\) 0 0
\(173\) −5.07107 −0.385546 −0.192773 0.981243i \(-0.561748\pi\)
−0.192773 + 0.981243i \(0.561748\pi\)
\(174\) −11.4142 −0.865309
\(175\) 0 0
\(176\) 1.65685 0.124890
\(177\) 8.48528 0.637793
\(178\) 0.485281 0.0363734
\(179\) 14.8995 1.11364 0.556820 0.830633i \(-0.312021\pi\)
0.556820 + 0.830633i \(0.312021\pi\)
\(180\) 0 0
\(181\) −15.3137 −1.13826 −0.569129 0.822248i \(-0.692720\pi\)
−0.569129 + 0.822248i \(0.692720\pi\)
\(182\) 0 0
\(183\) 6.65685 0.492089
\(184\) −4.00000 −0.294884
\(185\) −4.38478 −0.322375
\(186\) −4.24264 −0.311086
\(187\) 1.00000 0.0731272
\(188\) 0 0
\(189\) 0 0
\(190\) −2.14214 −0.155407
\(191\) 13.1716 0.953062 0.476531 0.879158i \(-0.341894\pi\)
0.476531 + 0.879158i \(0.341894\pi\)
\(192\) −8.00000 −0.577350
\(193\) 3.41421 0.245760 0.122880 0.992422i \(-0.460787\pi\)
0.122880 + 0.992422i \(0.460787\pi\)
\(194\) −22.9706 −1.64919
\(195\) 1.31371 0.0940766
\(196\) 0 0
\(197\) 13.7574 0.980171 0.490086 0.871674i \(-0.336965\pi\)
0.490086 + 0.871674i \(0.336965\pi\)
\(198\) −0.585786 −0.0416300
\(199\) 7.75736 0.549905 0.274952 0.961458i \(-0.411338\pi\)
0.274952 + 0.961458i \(0.411338\pi\)
\(200\) 13.1716 0.931371
\(201\) 6.48528 0.457436
\(202\) −3.41421 −0.240223
\(203\) 0 0
\(204\) 0 0
\(205\) −0.585786 −0.0409131
\(206\) 23.0711 1.60744
\(207\) 1.41421 0.0982946
\(208\) −8.97056 −0.621997
\(209\) −1.07107 −0.0740873
\(210\) 0 0
\(211\) −7.51472 −0.517335 −0.258667 0.965966i \(-0.583283\pi\)
−0.258667 + 0.965966i \(0.583283\pi\)
\(212\) 0 0
\(213\) 4.07107 0.278945
\(214\) −16.4853 −1.12691
\(215\) 2.92893 0.199752
\(216\) 2.82843 0.192450
\(217\) 0 0
\(218\) −16.8284 −1.13976
\(219\) 12.3137 0.832083
\(220\) 0 0
\(221\) −5.41421 −0.364199
\(222\) −10.5858 −0.710471
\(223\) −21.6569 −1.45025 −0.725125 0.688617i \(-0.758218\pi\)
−0.725125 + 0.688617i \(0.758218\pi\)
\(224\) 0 0
\(225\) −4.65685 −0.310457
\(226\) −26.4853 −1.76177
\(227\) −20.8995 −1.38715 −0.693574 0.720385i \(-0.743965\pi\)
−0.693574 + 0.720385i \(0.743965\pi\)
\(228\) 0 0
\(229\) −8.24264 −0.544689 −0.272345 0.962200i \(-0.587799\pi\)
−0.272345 + 0.962200i \(0.587799\pi\)
\(230\) −1.17157 −0.0772512
\(231\) 0 0
\(232\) −22.8284 −1.49876
\(233\) −18.0000 −1.17922 −0.589610 0.807688i \(-0.700718\pi\)
−0.589610 + 0.807688i \(0.700718\pi\)
\(234\) 3.17157 0.207332
\(235\) 4.44365 0.289872
\(236\) 0 0
\(237\) −3.65685 −0.237538
\(238\) 0 0
\(239\) −10.1421 −0.656040 −0.328020 0.944671i \(-0.606381\pi\)
−0.328020 + 0.944671i \(0.606381\pi\)
\(240\) −2.34315 −0.151249
\(241\) 7.48528 0.482169 0.241085 0.970504i \(-0.422497\pi\)
0.241085 + 0.970504i \(0.422497\pi\)
\(242\) −15.3137 −0.984402
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) 0 0
\(246\) −1.41421 −0.0901670
\(247\) 5.79899 0.368981
\(248\) −8.48528 −0.538816
\(249\) −13.0711 −0.828345
\(250\) 8.00000 0.505964
\(251\) −3.17157 −0.200188 −0.100094 0.994978i \(-0.531914\pi\)
−0.100094 + 0.994978i \(0.531914\pi\)
\(252\) 0 0
\(253\) −0.585786 −0.0368281
\(254\) −18.8284 −1.18140
\(255\) −1.41421 −0.0885615
\(256\) 0 0
\(257\) 24.8995 1.55319 0.776594 0.630002i \(-0.216946\pi\)
0.776594 + 0.630002i \(0.216946\pi\)
\(258\) 7.07107 0.440225
\(259\) 0 0
\(260\) 0 0
\(261\) 8.07107 0.499587
\(262\) 18.9706 1.17201
\(263\) −0.414214 −0.0255415 −0.0127708 0.999918i \(-0.504065\pi\)
−0.0127708 + 0.999918i \(0.504065\pi\)
\(264\) −1.17157 −0.0721053
\(265\) −0.686292 −0.0421586
\(266\) 0 0
\(267\) −0.343146 −0.0210002
\(268\) 0 0
\(269\) −8.48528 −0.517357 −0.258678 0.965964i \(-0.583287\pi\)
−0.258678 + 0.965964i \(0.583287\pi\)
\(270\) 0.828427 0.0504165
\(271\) 20.7990 1.26345 0.631724 0.775193i \(-0.282347\pi\)
0.631724 + 0.775193i \(0.282347\pi\)
\(272\) 9.65685 0.585533
\(273\) 0 0
\(274\) 25.5563 1.54392
\(275\) 1.92893 0.116319
\(276\) 0 0
\(277\) 29.2843 1.75952 0.879761 0.475417i \(-0.157703\pi\)
0.879761 + 0.475417i \(0.157703\pi\)
\(278\) 10.8284 0.649446
\(279\) 3.00000 0.179605
\(280\) 0 0
\(281\) −19.3848 −1.15640 −0.578199 0.815895i \(-0.696244\pi\)
−0.578199 + 0.815895i \(0.696244\pi\)
\(282\) 10.7279 0.638838
\(283\) −21.8284 −1.29757 −0.648783 0.760974i \(-0.724722\pi\)
−0.648783 + 0.760974i \(0.724722\pi\)
\(284\) 0 0
\(285\) 1.51472 0.0897242
\(286\) −1.31371 −0.0776812
\(287\) 0 0
\(288\) 0 0
\(289\) −11.1716 −0.657151
\(290\) −6.68629 −0.392633
\(291\) 16.2426 0.952160
\(292\) 0 0
\(293\) −12.4142 −0.725246 −0.362623 0.931936i \(-0.618119\pi\)
−0.362623 + 0.931936i \(0.618119\pi\)
\(294\) 0 0
\(295\) 4.97056 0.289397
\(296\) −21.1716 −1.23057
\(297\) 0.414214 0.0240351
\(298\) −7.51472 −0.435316
\(299\) 3.17157 0.183417
\(300\) 0 0
\(301\) 0 0
\(302\) −22.6274 −1.30206
\(303\) 2.41421 0.138693
\(304\) −10.3431 −0.593220
\(305\) 3.89949 0.223284
\(306\) −3.41421 −0.195178
\(307\) −22.3137 −1.27351 −0.636755 0.771066i \(-0.719724\pi\)
−0.636755 + 0.771066i \(0.719724\pi\)
\(308\) 0 0
\(309\) −16.3137 −0.928054
\(310\) −2.48528 −0.141154
\(311\) −21.1716 −1.20053 −0.600265 0.799801i \(-0.704938\pi\)
−0.600265 + 0.799801i \(0.704938\pi\)
\(312\) 6.34315 0.359110
\(313\) −24.8701 −1.40574 −0.702869 0.711319i \(-0.748098\pi\)
−0.702869 + 0.711319i \(0.748098\pi\)
\(314\) −25.4558 −1.43656
\(315\) 0 0
\(316\) 0 0
\(317\) 2.07107 0.116323 0.0581614 0.998307i \(-0.481476\pi\)
0.0581614 + 0.998307i \(0.481476\pi\)
\(318\) −1.65685 −0.0929118
\(319\) −3.34315 −0.187180
\(320\) −4.68629 −0.261972
\(321\) 11.6569 0.650622
\(322\) 0 0
\(323\) −6.24264 −0.347350
\(324\) 0 0
\(325\) −10.4437 −0.579310
\(326\) 10.5858 0.586292
\(327\) 11.8995 0.658044
\(328\) −2.82843 −0.156174
\(329\) 0 0
\(330\) −0.343146 −0.0188896
\(331\) 7.75736 0.426383 0.213192 0.977010i \(-0.431614\pi\)
0.213192 + 0.977010i \(0.431614\pi\)
\(332\) 0 0
\(333\) 7.48528 0.410191
\(334\) −10.8284 −0.592505
\(335\) 3.79899 0.207561
\(336\) 0 0
\(337\) −13.9706 −0.761025 −0.380513 0.924776i \(-0.624252\pi\)
−0.380513 + 0.924776i \(0.624252\pi\)
\(338\) −11.2721 −0.613120
\(339\) 18.7279 1.01716
\(340\) 0 0
\(341\) −1.24264 −0.0672928
\(342\) 3.65685 0.197740
\(343\) 0 0
\(344\) 14.1421 0.762493
\(345\) 0.828427 0.0446010
\(346\) −7.17157 −0.385546
\(347\) −18.8995 −1.01458 −0.507289 0.861776i \(-0.669352\pi\)
−0.507289 + 0.861776i \(0.669352\pi\)
\(348\) 0 0
\(349\) 19.1421 1.02466 0.512328 0.858790i \(-0.328783\pi\)
0.512328 + 0.858790i \(0.328783\pi\)
\(350\) 0 0
\(351\) −2.24264 −0.119703
\(352\) 0 0
\(353\) 1.02944 0.0547914 0.0273957 0.999625i \(-0.491279\pi\)
0.0273957 + 0.999625i \(0.491279\pi\)
\(354\) 12.0000 0.637793
\(355\) 2.38478 0.126571
\(356\) 0 0
\(357\) 0 0
\(358\) 21.0711 1.11364
\(359\) 7.75736 0.409418 0.204709 0.978823i \(-0.434375\pi\)
0.204709 + 0.978823i \(0.434375\pi\)
\(360\) 1.65685 0.0873239
\(361\) −12.3137 −0.648090
\(362\) −21.6569 −1.13826
\(363\) 10.8284 0.568345
\(364\) 0 0
\(365\) 7.21320 0.377556
\(366\) 9.41421 0.492089
\(367\) −4.65685 −0.243086 −0.121543 0.992586i \(-0.538784\pi\)
−0.121543 + 0.992586i \(0.538784\pi\)
\(368\) −5.65685 −0.294884
\(369\) 1.00000 0.0520579
\(370\) −6.20101 −0.322375
\(371\) 0 0
\(372\) 0 0
\(373\) 4.85786 0.251531 0.125765 0.992060i \(-0.459861\pi\)
0.125765 + 0.992060i \(0.459861\pi\)
\(374\) 1.41421 0.0731272
\(375\) −5.65685 −0.292119
\(376\) 21.4558 1.10650
\(377\) 18.1005 0.932223
\(378\) 0 0
\(379\) −6.97056 −0.358054 −0.179027 0.983844i \(-0.557295\pi\)
−0.179027 + 0.983844i \(0.557295\pi\)
\(380\) 0 0
\(381\) 13.3137 0.682082
\(382\) 18.6274 0.953062
\(383\) −36.8995 −1.88548 −0.942738 0.333534i \(-0.891759\pi\)
−0.942738 + 0.333534i \(0.891759\pi\)
\(384\) −11.3137 −0.577350
\(385\) 0 0
\(386\) 4.82843 0.245760
\(387\) −5.00000 −0.254164
\(388\) 0 0
\(389\) −13.7574 −0.697526 −0.348763 0.937211i \(-0.613398\pi\)
−0.348763 + 0.937211i \(0.613398\pi\)
\(390\) 1.85786 0.0940766
\(391\) −3.41421 −0.172664
\(392\) 0 0
\(393\) −13.4142 −0.676658
\(394\) 19.4558 0.980171
\(395\) −2.14214 −0.107783
\(396\) 0 0
\(397\) 34.5269 1.73286 0.866428 0.499302i \(-0.166410\pi\)
0.866428 + 0.499302i \(0.166410\pi\)
\(398\) 10.9706 0.549905
\(399\) 0 0
\(400\) 18.6274 0.931371
\(401\) −34.6274 −1.72921 −0.864605 0.502452i \(-0.832432\pi\)
−0.864605 + 0.502452i \(0.832432\pi\)
\(402\) 9.17157 0.457436
\(403\) 6.72792 0.335142
\(404\) 0 0
\(405\) −0.585786 −0.0291080
\(406\) 0 0
\(407\) −3.10051 −0.153686
\(408\) −6.82843 −0.338058
\(409\) −21.8284 −1.07935 −0.539673 0.841875i \(-0.681452\pi\)
−0.539673 + 0.841875i \(0.681452\pi\)
\(410\) −0.828427 −0.0409131
\(411\) −18.0711 −0.891380
\(412\) 0 0
\(413\) 0 0
\(414\) 2.00000 0.0982946
\(415\) −7.65685 −0.375860
\(416\) 0 0
\(417\) −7.65685 −0.374958
\(418\) −1.51472 −0.0740873
\(419\) −0.928932 −0.0453813 −0.0226907 0.999743i \(-0.507223\pi\)
−0.0226907 + 0.999743i \(0.507223\pi\)
\(420\) 0 0
\(421\) 24.9706 1.21699 0.608495 0.793557i \(-0.291773\pi\)
0.608495 + 0.793557i \(0.291773\pi\)
\(422\) −10.6274 −0.517335
\(423\) −7.58579 −0.368834
\(424\) −3.31371 −0.160928
\(425\) 11.2426 0.545348
\(426\) 5.75736 0.278945
\(427\) 0 0
\(428\) 0 0
\(429\) 0.928932 0.0448493
\(430\) 4.14214 0.199752
\(431\) 39.0711 1.88199 0.940994 0.338424i \(-0.109894\pi\)
0.940994 + 0.338424i \(0.109894\pi\)
\(432\) 4.00000 0.192450
\(433\) 11.4853 0.551947 0.275974 0.961165i \(-0.411000\pi\)
0.275974 + 0.961165i \(0.411000\pi\)
\(434\) 0 0
\(435\) 4.72792 0.226687
\(436\) 0 0
\(437\) 3.65685 0.174931
\(438\) 17.4142 0.832083
\(439\) 30.9706 1.47814 0.739072 0.673626i \(-0.235264\pi\)
0.739072 + 0.673626i \(0.235264\pi\)
\(440\) −0.686292 −0.0327177
\(441\) 0 0
\(442\) −7.65685 −0.364199
\(443\) 20.2843 0.963735 0.481867 0.876244i \(-0.339959\pi\)
0.481867 + 0.876244i \(0.339959\pi\)
\(444\) 0 0
\(445\) −0.201010 −0.00952879
\(446\) −30.6274 −1.45025
\(447\) 5.31371 0.251330
\(448\) 0 0
\(449\) 20.4853 0.966760 0.483380 0.875411i \(-0.339409\pi\)
0.483380 + 0.875411i \(0.339409\pi\)
\(450\) −6.58579 −0.310457
\(451\) −0.414214 −0.0195046
\(452\) 0 0
\(453\) 16.0000 0.751746
\(454\) −29.5563 −1.38715
\(455\) 0 0
\(456\) 7.31371 0.342496
\(457\) −4.00000 −0.187112 −0.0935561 0.995614i \(-0.529823\pi\)
−0.0935561 + 0.995614i \(0.529823\pi\)
\(458\) −11.6569 −0.544689
\(459\) 2.41421 0.112686
\(460\) 0 0
\(461\) 16.6274 0.774416 0.387208 0.921992i \(-0.373440\pi\)
0.387208 + 0.921992i \(0.373440\pi\)
\(462\) 0 0
\(463\) 5.55635 0.258225 0.129113 0.991630i \(-0.458787\pi\)
0.129113 + 0.991630i \(0.458787\pi\)
\(464\) −32.2843 −1.49876
\(465\) 1.75736 0.0814956
\(466\) −25.4558 −1.17922
\(467\) −21.3137 −0.986281 −0.493140 0.869950i \(-0.664151\pi\)
−0.493140 + 0.869950i \(0.664151\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 6.28427 0.289872
\(471\) 18.0000 0.829396
\(472\) 24.0000 1.10469
\(473\) 2.07107 0.0952278
\(474\) −5.17157 −0.237538
\(475\) −12.0416 −0.552508
\(476\) 0 0
\(477\) 1.17157 0.0536426
\(478\) −14.3431 −0.656040
\(479\) 12.8995 0.589393 0.294696 0.955591i \(-0.404781\pi\)
0.294696 + 0.955591i \(0.404781\pi\)
\(480\) 0 0
\(481\) 16.7868 0.765412
\(482\) 10.5858 0.482169
\(483\) 0 0
\(484\) 0 0
\(485\) 9.51472 0.432041
\(486\) −1.41421 −0.0641500
\(487\) −31.9706 −1.44872 −0.724362 0.689420i \(-0.757866\pi\)
−0.724362 + 0.689420i \(0.757866\pi\)
\(488\) 18.8284 0.852323
\(489\) −7.48528 −0.338496
\(490\) 0 0
\(491\) 1.07107 0.0483366 0.0241683 0.999708i \(-0.492306\pi\)
0.0241683 + 0.999708i \(0.492306\pi\)
\(492\) 0 0
\(493\) −19.4853 −0.877573
\(494\) 8.20101 0.368981
\(495\) 0.242641 0.0109059
\(496\) −12.0000 −0.538816
\(497\) 0 0
\(498\) −18.4853 −0.828345
\(499\) −36.4853 −1.63331 −0.816653 0.577129i \(-0.804173\pi\)
−0.816653 + 0.577129i \(0.804173\pi\)
\(500\) 0 0
\(501\) 7.65685 0.342083
\(502\) −4.48528 −0.200188
\(503\) 35.3848 1.57773 0.788865 0.614567i \(-0.210669\pi\)
0.788865 + 0.614567i \(0.210669\pi\)
\(504\) 0 0
\(505\) 1.41421 0.0629317
\(506\) −0.828427 −0.0368281
\(507\) 7.97056 0.353985
\(508\) 0 0
\(509\) 33.8701 1.50126 0.750632 0.660721i \(-0.229749\pi\)
0.750632 + 0.660721i \(0.229749\pi\)
\(510\) −2.00000 −0.0885615
\(511\) 0 0
\(512\) −22.6274 −1.00000
\(513\) −2.58579 −0.114165
\(514\) 35.2132 1.55319
\(515\) −9.55635 −0.421103
\(516\) 0 0
\(517\) 3.14214 0.138191
\(518\) 0 0
\(519\) 5.07107 0.222595
\(520\) 3.71573 0.162945
\(521\) −22.7574 −0.997018 −0.498509 0.866885i \(-0.666119\pi\)
−0.498509 + 0.866885i \(0.666119\pi\)
\(522\) 11.4142 0.499587
\(523\) −34.0000 −1.48672 −0.743358 0.668894i \(-0.766768\pi\)
−0.743358 + 0.668894i \(0.766768\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) −0.585786 −0.0255415
\(527\) −7.24264 −0.315494
\(528\) −1.65685 −0.0721053
\(529\) −21.0000 −0.913043
\(530\) −0.970563 −0.0421586
\(531\) −8.48528 −0.368230
\(532\) 0 0
\(533\) 2.24264 0.0971396
\(534\) −0.485281 −0.0210002
\(535\) 6.82843 0.295219
\(536\) 18.3431 0.792303
\(537\) −14.8995 −0.642961
\(538\) −12.0000 −0.517357
\(539\) 0 0
\(540\) 0 0
\(541\) 18.9706 0.815608 0.407804 0.913069i \(-0.366295\pi\)
0.407804 + 0.913069i \(0.366295\pi\)
\(542\) 29.4142 1.26345
\(543\) 15.3137 0.657174
\(544\) 0 0
\(545\) 6.97056 0.298586
\(546\) 0 0
\(547\) −7.51472 −0.321306 −0.160653 0.987011i \(-0.551360\pi\)
−0.160653 + 0.987011i \(0.551360\pi\)
\(548\) 0 0
\(549\) −6.65685 −0.284108
\(550\) 2.72792 0.116319
\(551\) 20.8701 0.889094
\(552\) 4.00000 0.170251
\(553\) 0 0
\(554\) 41.4142 1.75952
\(555\) 4.38478 0.186123
\(556\) 0 0
\(557\) 39.7279 1.68333 0.841663 0.540003i \(-0.181577\pi\)
0.841663 + 0.540003i \(0.181577\pi\)
\(558\) 4.24264 0.179605
\(559\) −11.2132 −0.474268
\(560\) 0 0
\(561\) −1.00000 −0.0422200
\(562\) −27.4142 −1.15640
\(563\) 12.8995 0.543649 0.271824 0.962347i \(-0.412373\pi\)
0.271824 + 0.962347i \(0.412373\pi\)
\(564\) 0 0
\(565\) 10.9706 0.461535
\(566\) −30.8701 −1.29757
\(567\) 0 0
\(568\) 11.5147 0.483147
\(569\) −35.5563 −1.49060 −0.745300 0.666729i \(-0.767694\pi\)
−0.745300 + 0.666729i \(0.767694\pi\)
\(570\) 2.14214 0.0897242
\(571\) 42.6274 1.78390 0.891951 0.452132i \(-0.149336\pi\)
0.891951 + 0.452132i \(0.149336\pi\)
\(572\) 0 0
\(573\) −13.1716 −0.550250
\(574\) 0 0
\(575\) −6.58579 −0.274646
\(576\) 8.00000 0.333333
\(577\) 19.5147 0.812408 0.406204 0.913782i \(-0.366852\pi\)
0.406204 + 0.913782i \(0.366852\pi\)
\(578\) −15.7990 −0.657151
\(579\) −3.41421 −0.141890
\(580\) 0 0
\(581\) 0 0
\(582\) 22.9706 0.952160
\(583\) −0.485281 −0.0200983
\(584\) 34.8284 1.44121
\(585\) −1.31371 −0.0543152
\(586\) −17.5563 −0.725246
\(587\) −7.38478 −0.304802 −0.152401 0.988319i \(-0.548701\pi\)
−0.152401 + 0.988319i \(0.548701\pi\)
\(588\) 0 0
\(589\) 7.75736 0.319636
\(590\) 7.02944 0.289397
\(591\) −13.7574 −0.565902
\(592\) −29.9411 −1.23057
\(593\) −4.41421 −0.181270 −0.0906350 0.995884i \(-0.528890\pi\)
−0.0906350 + 0.995884i \(0.528890\pi\)
\(594\) 0.585786 0.0240351
\(595\) 0 0
\(596\) 0 0
\(597\) −7.75736 −0.317488
\(598\) 4.48528 0.183417
\(599\) 35.3553 1.44458 0.722290 0.691590i \(-0.243090\pi\)
0.722290 + 0.691590i \(0.243090\pi\)
\(600\) −13.1716 −0.537727
\(601\) 9.51472 0.388113 0.194057 0.980990i \(-0.437835\pi\)
0.194057 + 0.980990i \(0.437835\pi\)
\(602\) 0 0
\(603\) −6.48528 −0.264101
\(604\) 0 0
\(605\) 6.34315 0.257886
\(606\) 3.41421 0.138693
\(607\) 17.5147 0.710900 0.355450 0.934695i \(-0.384328\pi\)
0.355450 + 0.934695i \(0.384328\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 5.51472 0.223284
\(611\) −17.0122 −0.688240
\(612\) 0 0
\(613\) −3.31371 −0.133839 −0.0669197 0.997758i \(-0.521317\pi\)
−0.0669197 + 0.997758i \(0.521317\pi\)
\(614\) −31.5563 −1.27351
\(615\) 0.585786 0.0236212
\(616\) 0 0
\(617\) 27.2132 1.09556 0.547781 0.836622i \(-0.315473\pi\)
0.547781 + 0.836622i \(0.315473\pi\)
\(618\) −23.0711 −0.928054
\(619\) −12.3137 −0.494930 −0.247465 0.968897i \(-0.579597\pi\)
−0.247465 + 0.968897i \(0.579597\pi\)
\(620\) 0 0
\(621\) −1.41421 −0.0567504
\(622\) −29.9411 −1.20053
\(623\) 0 0
\(624\) 8.97056 0.359110
\(625\) 19.9706 0.798823
\(626\) −35.1716 −1.40574
\(627\) 1.07107 0.0427743
\(628\) 0 0
\(629\) −18.0711 −0.720541
\(630\) 0 0
\(631\) 22.4558 0.893953 0.446977 0.894546i \(-0.352501\pi\)
0.446977 + 0.894546i \(0.352501\pi\)
\(632\) −10.3431 −0.411428
\(633\) 7.51472 0.298683
\(634\) 2.92893 0.116323
\(635\) 7.79899 0.309493
\(636\) 0 0
\(637\) 0 0
\(638\) −4.72792 −0.187180
\(639\) −4.07107 −0.161049
\(640\) −6.62742 −0.261972
\(641\) 22.5563 0.890922 0.445461 0.895301i \(-0.353040\pi\)
0.445461 + 0.895301i \(0.353040\pi\)
\(642\) 16.4853 0.650622
\(643\) 13.4558 0.530647 0.265323 0.964159i \(-0.414521\pi\)
0.265323 + 0.964159i \(0.414521\pi\)
\(644\) 0 0
\(645\) −2.92893 −0.115327
\(646\) −8.82843 −0.347350
\(647\) −7.55635 −0.297071 −0.148535 0.988907i \(-0.547456\pi\)
−0.148535 + 0.988907i \(0.547456\pi\)
\(648\) −2.82843 −0.111111
\(649\) 3.51472 0.137965
\(650\) −14.7696 −0.579310
\(651\) 0 0
\(652\) 0 0
\(653\) 12.8995 0.504796 0.252398 0.967623i \(-0.418781\pi\)
0.252398 + 0.967623i \(0.418781\pi\)
\(654\) 16.8284 0.658044
\(655\) −7.85786 −0.307032
\(656\) −4.00000 −0.156174
\(657\) −12.3137 −0.480404
\(658\) 0 0
\(659\) −29.1716 −1.13636 −0.568182 0.822903i \(-0.692353\pi\)
−0.568182 + 0.822903i \(0.692353\pi\)
\(660\) 0 0
\(661\) 37.4558 1.45686 0.728432 0.685118i \(-0.240250\pi\)
0.728432 + 0.685118i \(0.240250\pi\)
\(662\) 10.9706 0.426383
\(663\) 5.41421 0.210271
\(664\) −36.9706 −1.43474
\(665\) 0 0
\(666\) 10.5858 0.410191
\(667\) 11.4142 0.441960
\(668\) 0 0
\(669\) 21.6569 0.837302
\(670\) 5.37258 0.207561
\(671\) 2.75736 0.106447
\(672\) 0 0
\(673\) −17.7990 −0.686101 −0.343050 0.939317i \(-0.611460\pi\)
−0.343050 + 0.939317i \(0.611460\pi\)
\(674\) −19.7574 −0.761025
\(675\) 4.65685 0.179242
\(676\) 0 0
\(677\) −2.44365 −0.0939171 −0.0469586 0.998897i \(-0.514953\pi\)
−0.0469586 + 0.998897i \(0.514953\pi\)
\(678\) 26.4853 1.01716
\(679\) 0 0
\(680\) −4.00000 −0.153393
\(681\) 20.8995 0.800870
\(682\) −1.75736 −0.0672928
\(683\) 50.2843 1.92407 0.962037 0.272919i \(-0.0879890\pi\)
0.962037 + 0.272919i \(0.0879890\pi\)
\(684\) 0 0
\(685\) −10.5858 −0.404462
\(686\) 0 0
\(687\) 8.24264 0.314476
\(688\) 20.0000 0.762493
\(689\) 2.62742 0.100097
\(690\) 1.17157 0.0446010
\(691\) 14.7279 0.560277 0.280138 0.959960i \(-0.409620\pi\)
0.280138 + 0.959960i \(0.409620\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) −26.7279 −1.01458
\(695\) −4.48528 −0.170136
\(696\) 22.8284 0.865309
\(697\) −2.41421 −0.0914449
\(698\) 27.0711 1.02466
\(699\) 18.0000 0.680823
\(700\) 0 0
\(701\) −6.20101 −0.234209 −0.117104 0.993120i \(-0.537361\pi\)
−0.117104 + 0.993120i \(0.537361\pi\)
\(702\) −3.17157 −0.119703
\(703\) 19.3553 0.730000
\(704\) −3.31371 −0.124890
\(705\) −4.44365 −0.167358
\(706\) 1.45584 0.0547914
\(707\) 0 0
\(708\) 0 0
\(709\) −13.5147 −0.507556 −0.253778 0.967263i \(-0.581673\pi\)
−0.253778 + 0.967263i \(0.581673\pi\)
\(710\) 3.37258 0.126571
\(711\) 3.65685 0.137143
\(712\) −0.970563 −0.0363734
\(713\) 4.24264 0.158888
\(714\) 0 0
\(715\) 0.544156 0.0203503
\(716\) 0 0
\(717\) 10.1421 0.378765
\(718\) 10.9706 0.409418
\(719\) −9.44365 −0.352189 −0.176094 0.984373i \(-0.556346\pi\)
−0.176094 + 0.984373i \(0.556346\pi\)
\(720\) 2.34315 0.0873239
\(721\) 0 0
\(722\) −17.4142 −0.648090
\(723\) −7.48528 −0.278381
\(724\) 0 0
\(725\) −37.5858 −1.39590
\(726\) 15.3137 0.568345
\(727\) 7.27208 0.269706 0.134853 0.990866i \(-0.456944\pi\)
0.134853 + 0.990866i \(0.456944\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 10.2010 0.377556
\(731\) 12.0711 0.446465
\(732\) 0 0
\(733\) 2.85786 0.105558 0.0527788 0.998606i \(-0.483192\pi\)
0.0527788 + 0.998606i \(0.483192\pi\)
\(734\) −6.58579 −0.243086
\(735\) 0 0
\(736\) 0 0
\(737\) 2.68629 0.0989508
\(738\) 1.41421 0.0520579
\(739\) 11.3431 0.417264 0.208632 0.977994i \(-0.433099\pi\)
0.208632 + 0.977994i \(0.433099\pi\)
\(740\) 0 0
\(741\) −5.79899 −0.213031
\(742\) 0 0
\(743\) −28.6274 −1.05024 −0.525119 0.851029i \(-0.675979\pi\)
−0.525119 + 0.851029i \(0.675979\pi\)
\(744\) 8.48528 0.311086
\(745\) 3.11270 0.114040
\(746\) 6.87006 0.251531
\(747\) 13.0711 0.478245
\(748\) 0 0
\(749\) 0 0
\(750\) −8.00000 −0.292119
\(751\) 1.02944 0.0375647 0.0187823 0.999824i \(-0.494021\pi\)
0.0187823 + 0.999824i \(0.494021\pi\)
\(752\) 30.3431 1.10650
\(753\) 3.17157 0.115579
\(754\) 25.5980 0.932223
\(755\) 9.37258 0.341103
\(756\) 0 0
\(757\) −0.242641 −0.00881893 −0.00440946 0.999990i \(-0.501404\pi\)
−0.00440946 + 0.999990i \(0.501404\pi\)
\(758\) −9.85786 −0.358054
\(759\) 0.585786 0.0212627
\(760\) 4.28427 0.155407
\(761\) −9.17157 −0.332469 −0.166235 0.986086i \(-0.553161\pi\)
−0.166235 + 0.986086i \(0.553161\pi\)
\(762\) 18.8284 0.682082
\(763\) 0 0
\(764\) 0 0
\(765\) 1.41421 0.0511310
\(766\) −52.1838 −1.88548
\(767\) −19.0294 −0.687113
\(768\) 0 0
\(769\) 16.5147 0.595536 0.297768 0.954638i \(-0.403758\pi\)
0.297768 + 0.954638i \(0.403758\pi\)
\(770\) 0 0
\(771\) −24.8995 −0.896733
\(772\) 0 0
\(773\) −47.5858 −1.71154 −0.855771 0.517355i \(-0.826917\pi\)
−0.855771 + 0.517355i \(0.826917\pi\)
\(774\) −7.07107 −0.254164
\(775\) −13.9706 −0.501837
\(776\) 45.9411 1.64919
\(777\) 0 0
\(778\) −19.4558 −0.697526
\(779\) 2.58579 0.0926454
\(780\) 0 0
\(781\) 1.68629 0.0603403
\(782\) −4.82843 −0.172664
\(783\) −8.07107 −0.288436
\(784\) 0 0
\(785\) 10.5442 0.376337
\(786\) −18.9706 −0.676658
\(787\) −19.9706 −0.711874 −0.355937 0.934510i \(-0.615838\pi\)
−0.355937 + 0.934510i \(0.615838\pi\)
\(788\) 0 0
\(789\) 0.414214 0.0147464
\(790\) −3.02944 −0.107783
\(791\) 0 0
\(792\) 1.17157 0.0416300
\(793\) −14.9289 −0.530142
\(794\) 48.8284 1.73286
\(795\) 0.686292 0.0243403
\(796\) 0 0
\(797\) 15.8579 0.561714 0.280857 0.959750i \(-0.409381\pi\)
0.280857 + 0.959750i \(0.409381\pi\)
\(798\) 0 0
\(799\) 18.3137 0.647892
\(800\) 0 0
\(801\) 0.343146 0.0121245
\(802\) −48.9706 −1.72921
\(803\) 5.10051 0.179993
\(804\) 0 0
\(805\) 0 0
\(806\) 9.51472 0.335142
\(807\) 8.48528 0.298696
\(808\) 6.82843 0.240223
\(809\) −37.1127 −1.30481 −0.652406 0.757869i \(-0.726240\pi\)
−0.652406 + 0.757869i \(0.726240\pi\)
\(810\) −0.828427 −0.0291080
\(811\) −15.9706 −0.560802 −0.280401 0.959883i \(-0.590467\pi\)
−0.280401 + 0.959883i \(0.590467\pi\)
\(812\) 0 0
\(813\) −20.7990 −0.729452
\(814\) −4.38478 −0.153686
\(815\) −4.38478 −0.153592
\(816\) −9.65685 −0.338058
\(817\) −12.9289 −0.452326
\(818\) −30.8701 −1.07935
\(819\) 0 0
\(820\) 0 0
\(821\) 14.8701 0.518969 0.259484 0.965747i \(-0.416447\pi\)
0.259484 + 0.965747i \(0.416447\pi\)
\(822\) −25.5563 −0.891380
\(823\) −52.4264 −1.82747 −0.913735 0.406311i \(-0.866815\pi\)
−0.913735 + 0.406311i \(0.866815\pi\)
\(824\) −46.1421 −1.60744
\(825\) −1.92893 −0.0671568
\(826\) 0 0
\(827\) 22.0711 0.767486 0.383743 0.923440i \(-0.374635\pi\)
0.383743 + 0.923440i \(0.374635\pi\)
\(828\) 0 0
\(829\) −42.9411 −1.49141 −0.745703 0.666278i \(-0.767886\pi\)
−0.745703 + 0.666278i \(0.767886\pi\)
\(830\) −10.8284 −0.375860
\(831\) −29.2843 −1.01586
\(832\) 17.9411 0.621997
\(833\) 0 0
\(834\) −10.8284 −0.374958
\(835\) 4.48528 0.155220
\(836\) 0 0
\(837\) −3.00000 −0.103695
\(838\) −1.31371 −0.0453813
\(839\) 17.1716 0.592829 0.296414 0.955059i \(-0.404209\pi\)
0.296414 + 0.955059i \(0.404209\pi\)
\(840\) 0 0
\(841\) 36.1421 1.24628
\(842\) 35.3137 1.21699
\(843\) 19.3848 0.667647
\(844\) 0 0
\(845\) 4.66905 0.160620
\(846\) −10.7279 −0.368834
\(847\) 0 0
\(848\) −4.68629 −0.160928
\(849\) 21.8284 0.749150
\(850\) 15.8995 0.545348
\(851\) 10.5858 0.362876
\(852\) 0 0
\(853\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(854\) 0 0
\(855\) −1.51472 −0.0518023
\(856\) 32.9706 1.12691
\(857\) −12.2010 −0.416779 −0.208389 0.978046i \(-0.566822\pi\)
−0.208389 + 0.978046i \(0.566822\pi\)
\(858\) 1.31371 0.0448493
\(859\) −5.34315 −0.182306 −0.0911529 0.995837i \(-0.529055\pi\)
−0.0911529 + 0.995837i \(0.529055\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 55.2548 1.88199
\(863\) 10.9289 0.372025 0.186013 0.982547i \(-0.440443\pi\)
0.186013 + 0.982547i \(0.440443\pi\)
\(864\) 0 0
\(865\) 2.97056 0.101002
\(866\) 16.2426 0.551947
\(867\) 11.1716 0.379407
\(868\) 0 0
\(869\) −1.51472 −0.0513833
\(870\) 6.68629 0.226687
\(871\) −14.5442 −0.492810
\(872\) 33.6569 1.13976
\(873\) −16.2426 −0.549730
\(874\) 5.17157 0.174931
\(875\) 0 0
\(876\) 0 0
\(877\) 1.14214 0.0385672 0.0192836 0.999814i \(-0.493861\pi\)
0.0192836 + 0.999814i \(0.493861\pi\)
\(878\) 43.7990 1.47814
\(879\) 12.4142 0.418721
\(880\) −0.970563 −0.0327177
\(881\) −2.62742 −0.0885199 −0.0442600 0.999020i \(-0.514093\pi\)
−0.0442600 + 0.999020i \(0.514093\pi\)
\(882\) 0 0
\(883\) −6.58579 −0.221629 −0.110815 0.993841i \(-0.535346\pi\)
−0.110815 + 0.993841i \(0.535346\pi\)
\(884\) 0 0
\(885\) −4.97056 −0.167084
\(886\) 28.6863 0.963735
\(887\) 46.0122 1.54494 0.772469 0.635052i \(-0.219021\pi\)
0.772469 + 0.635052i \(0.219021\pi\)
\(888\) 21.1716 0.710471
\(889\) 0 0
\(890\) −0.284271 −0.00952879
\(891\) −0.414214 −0.0138767
\(892\) 0 0
\(893\) −19.6152 −0.656398
\(894\) 7.51472 0.251330
\(895\) −8.72792 −0.291742
\(896\) 0 0
\(897\) −3.17157 −0.105896
\(898\) 28.9706 0.966760
\(899\) 24.2132 0.807556
\(900\) 0 0
\(901\) −2.82843 −0.0942286
\(902\) −0.585786 −0.0195046
\(903\) 0 0
\(904\) 52.9706 1.76177
\(905\) 8.97056 0.298192
\(906\) 22.6274 0.751746
\(907\) 4.34315 0.144212 0.0721059 0.997397i \(-0.477028\pi\)
0.0721059 + 0.997397i \(0.477028\pi\)
\(908\) 0 0
\(909\) −2.41421 −0.0800744
\(910\) 0 0
\(911\) 53.8995 1.78577 0.892885 0.450285i \(-0.148678\pi\)
0.892885 + 0.450285i \(0.148678\pi\)
\(912\) 10.3431 0.342496
\(913\) −5.41421 −0.179184
\(914\) −5.65685 −0.187112
\(915\) −3.89949 −0.128913
\(916\) 0 0
\(917\) 0 0
\(918\) 3.41421 0.112686
\(919\) −12.5858 −0.415167 −0.207583 0.978217i \(-0.566560\pi\)
−0.207583 + 0.978217i \(0.566560\pi\)
\(920\) 2.34315 0.0772512
\(921\) 22.3137 0.735262
\(922\) 23.5147 0.774416
\(923\) −9.12994 −0.300516
\(924\) 0 0
\(925\) −34.8579 −1.14612
\(926\) 7.85786 0.258225
\(927\) 16.3137 0.535812
\(928\) 0 0
\(929\) −45.8701 −1.50495 −0.752474 0.658622i \(-0.771140\pi\)
−0.752474 + 0.658622i \(0.771140\pi\)
\(930\) 2.48528 0.0814956
\(931\) 0 0
\(932\) 0 0
\(933\) 21.1716 0.693126
\(934\) −30.1421 −0.986281
\(935\) −0.585786 −0.0191573
\(936\) −6.34315 −0.207332
\(937\) −19.0294 −0.621665 −0.310832 0.950465i \(-0.600608\pi\)
−0.310832 + 0.950465i \(0.600608\pi\)
\(938\) 0 0
\(939\) 24.8701 0.811604
\(940\) 0 0
\(941\) 7.37258 0.240339 0.120170 0.992753i \(-0.461656\pi\)
0.120170 + 0.992753i \(0.461656\pi\)
\(942\) 25.4558 0.829396
\(943\) 1.41421 0.0460531
\(944\) 33.9411 1.10469
\(945\) 0 0
\(946\) 2.92893 0.0952278
\(947\) −57.5980 −1.87168 −0.935841 0.352421i \(-0.885358\pi\)
−0.935841 + 0.352421i \(0.885358\pi\)
\(948\) 0 0
\(949\) −27.6152 −0.896428
\(950\) −17.0294 −0.552508
\(951\) −2.07107 −0.0671590
\(952\) 0 0
\(953\) 17.6985 0.573310 0.286655 0.958034i \(-0.407457\pi\)
0.286655 + 0.958034i \(0.407457\pi\)
\(954\) 1.65685 0.0536426
\(955\) −7.71573 −0.249675
\(956\) 0 0
\(957\) 3.34315 0.108069
\(958\) 18.2426 0.589393
\(959\) 0 0
\(960\) 4.68629 0.151249
\(961\) −22.0000 −0.709677
\(962\) 23.7401 0.765412
\(963\) −11.6569 −0.375637
\(964\) 0 0
\(965\) −2.00000 −0.0643823
\(966\) 0 0
\(967\) −34.9706 −1.12458 −0.562289 0.826941i \(-0.690079\pi\)
−0.562289 + 0.826941i \(0.690079\pi\)
\(968\) 30.6274 0.984402
\(969\) 6.24264 0.200543
\(970\) 13.4558 0.432041
\(971\) −9.44365 −0.303061 −0.151531 0.988453i \(-0.548420\pi\)
−0.151531 + 0.988453i \(0.548420\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) −45.2132 −1.44872
\(975\) 10.4437 0.334465
\(976\) 26.6274 0.852323
\(977\) 10.4142 0.333180 0.166590 0.986026i \(-0.446724\pi\)
0.166590 + 0.986026i \(0.446724\pi\)
\(978\) −10.5858 −0.338496
\(979\) −0.142136 −0.00454267
\(980\) 0 0
\(981\) −11.8995 −0.379922
\(982\) 1.51472 0.0483366
\(983\) 37.0711 1.18238 0.591192 0.806531i \(-0.298658\pi\)
0.591192 + 0.806531i \(0.298658\pi\)
\(984\) 2.82843 0.0901670
\(985\) −8.05887 −0.256777
\(986\) −27.5563 −0.877573
\(987\) 0 0
\(988\) 0 0
\(989\) −7.07107 −0.224847
\(990\) 0.343146 0.0109059
\(991\) −11.5147 −0.365777 −0.182889 0.983134i \(-0.558545\pi\)
−0.182889 + 0.983134i \(0.558545\pi\)
\(992\) 0 0
\(993\) −7.75736 −0.246172
\(994\) 0 0
\(995\) −4.54416 −0.144059
\(996\) 0 0
\(997\) −12.5858 −0.398596 −0.199298 0.979939i \(-0.563866\pi\)
−0.199298 + 0.979939i \(0.563866\pi\)
\(998\) −51.5980 −1.63331
\(999\) −7.48528 −0.236824
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 \(a_p\))