Properties

Label 6027.2.a.n.1.1
Level 6027
Weight 2
Character 6027.1
Self dual Yes
Analytic conductor 48.126
Analytic rank 0
Dimension 2
CM No
Inner twists 1

Related objects

Downloads

Learn more about

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: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{12})^+\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(1.73205\)
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{3} -2.00000 q^{4} -3.46410 q^{5} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{3} -2.00000 q^{4} -3.46410 q^{5} +1.00000 q^{9} +2.26795 q^{11} -2.00000 q^{12} +1.46410 q^{13} -3.46410 q^{15} +4.00000 q^{16} -5.00000 q^{17} -7.46410 q^{19} +6.92820 q^{20} -1.46410 q^{23} +7.00000 q^{25} +1.00000 q^{27} +5.19615 q^{29} -2.26795 q^{31} +2.26795 q^{33} -2.00000 q^{36} -1.00000 q^{37} +1.46410 q^{39} +1.00000 q^{41} -3.92820 q^{43} -4.53590 q^{44} -3.46410 q^{45} -1.92820 q^{47} +4.00000 q^{48} -5.00000 q^{51} -2.92820 q^{52} -2.92820 q^{53} -7.85641 q^{55} -7.46410 q^{57} -6.92820 q^{59} +6.92820 q^{60} -1.73205 q^{61} -8.00000 q^{64} -5.07180 q^{65} +0.535898 q^{67} +10.0000 q^{68} -1.46410 q^{69} +2.80385 q^{71} -1.19615 q^{73} +7.00000 q^{75} +14.9282 q^{76} -12.9282 q^{79} -13.8564 q^{80} +1.00000 q^{81} -10.0000 q^{83} +17.3205 q^{85} +5.19615 q^{87} +4.92820 q^{89} +2.92820 q^{92} -2.26795 q^{93} +25.8564 q^{95} +18.3923 q^{97} +2.26795 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 2q^{3} - 4q^{4} + 2q^{9} + O(q^{10}) \) \( 2q + 2q^{3} - 4q^{4} + 2q^{9} + 8q^{11} - 4q^{12} - 4q^{13} + 8q^{16} - 10q^{17} - 8q^{19} + 4q^{23} + 14q^{25} + 2q^{27} - 8q^{31} + 8q^{33} - 4q^{36} - 2q^{37} - 4q^{39} + 2q^{41} + 6q^{43} - 16q^{44} + 10q^{47} + 8q^{48} - 10q^{51} + 8q^{52} + 8q^{53} + 12q^{55} - 8q^{57} - 16q^{64} - 24q^{65} + 8q^{67} + 20q^{68} + 4q^{69} + 16q^{71} + 8q^{73} + 14q^{75} + 16q^{76} - 12q^{79} + 2q^{81} - 20q^{83} - 4q^{89} - 8q^{92} - 8q^{93} + 24q^{95} + 16q^{97} + 8q^{99} + O(q^{100}) \)

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
\(4\) −2.00000 −1.00000
\(5\) −3.46410 −1.54919 −0.774597 0.632456i \(-0.782047\pi\)
−0.774597 + 0.632456i \(0.782047\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 2.26795 0.683812 0.341906 0.939734i \(-0.388927\pi\)
0.341906 + 0.939734i \(0.388927\pi\)
\(12\) −2.00000 −0.577350
\(13\) 1.46410 0.406069 0.203034 0.979172i \(-0.434920\pi\)
0.203034 + 0.979172i \(0.434920\pi\)
\(14\) 0 0
\(15\) −3.46410 −0.894427
\(16\) 4.00000 1.00000
\(17\) −5.00000 −1.21268 −0.606339 0.795206i \(-0.707363\pi\)
−0.606339 + 0.795206i \(0.707363\pi\)
\(18\) 0 0
\(19\) −7.46410 −1.71238 −0.856191 0.516659i \(-0.827175\pi\)
−0.856191 + 0.516659i \(0.827175\pi\)
\(20\) 6.92820 1.54919
\(21\) 0 0
\(22\) 0 0
\(23\) −1.46410 −0.305286 −0.152643 0.988281i \(-0.548779\pi\)
−0.152643 + 0.988281i \(0.548779\pi\)
\(24\) 0 0
\(25\) 7.00000 1.40000
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 5.19615 0.964901 0.482451 0.875923i \(-0.339747\pi\)
0.482451 + 0.875923i \(0.339747\pi\)
\(30\) 0 0
\(31\) −2.26795 −0.407336 −0.203668 0.979040i \(-0.565286\pi\)
−0.203668 + 0.979040i \(0.565286\pi\)
\(32\) 0 0
\(33\) 2.26795 0.394799
\(34\) 0 0
\(35\) 0 0
\(36\) −2.00000 −0.333333
\(37\) −1.00000 −0.164399 −0.0821995 0.996616i \(-0.526194\pi\)
−0.0821995 + 0.996616i \(0.526194\pi\)
\(38\) 0 0
\(39\) 1.46410 0.234444
\(40\) 0 0
\(41\) 1.00000 0.156174
\(42\) 0 0
\(43\) −3.92820 −0.599045 −0.299523 0.954089i \(-0.596827\pi\)
−0.299523 + 0.954089i \(0.596827\pi\)
\(44\) −4.53590 −0.683812
\(45\) −3.46410 −0.516398
\(46\) 0 0
\(47\) −1.92820 −0.281257 −0.140629 0.990062i \(-0.544912\pi\)
−0.140629 + 0.990062i \(0.544912\pi\)
\(48\) 4.00000 0.577350
\(49\) 0 0
\(50\) 0 0
\(51\) −5.00000 −0.700140
\(52\) −2.92820 −0.406069
\(53\) −2.92820 −0.402220 −0.201110 0.979569i \(-0.564455\pi\)
−0.201110 + 0.979569i \(0.564455\pi\)
\(54\) 0 0
\(55\) −7.85641 −1.05936
\(56\) 0 0
\(57\) −7.46410 −0.988644
\(58\) 0 0
\(59\) −6.92820 −0.901975 −0.450988 0.892530i \(-0.648928\pi\)
−0.450988 + 0.892530i \(0.648928\pi\)
\(60\) 6.92820 0.894427
\(61\) −1.73205 −0.221766 −0.110883 0.993833i \(-0.535368\pi\)
−0.110883 + 0.993833i \(0.535368\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −8.00000 −1.00000
\(65\) −5.07180 −0.629079
\(66\) 0 0
\(67\) 0.535898 0.0654704 0.0327352 0.999464i \(-0.489578\pi\)
0.0327352 + 0.999464i \(0.489578\pi\)
\(68\) 10.0000 1.21268
\(69\) −1.46410 −0.176257
\(70\) 0 0
\(71\) 2.80385 0.332755 0.166378 0.986062i \(-0.446793\pi\)
0.166378 + 0.986062i \(0.446793\pi\)
\(72\) 0 0
\(73\) −1.19615 −0.139999 −0.0699995 0.997547i \(-0.522300\pi\)
−0.0699995 + 0.997547i \(0.522300\pi\)
\(74\) 0 0
\(75\) 7.00000 0.808290
\(76\) 14.9282 1.71238
\(77\) 0 0
\(78\) 0 0
\(79\) −12.9282 −1.45454 −0.727268 0.686353i \(-0.759210\pi\)
−0.727268 + 0.686353i \(0.759210\pi\)
\(80\) −13.8564 −1.54919
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −10.0000 −1.09764 −0.548821 0.835940i \(-0.684923\pi\)
−0.548821 + 0.835940i \(0.684923\pi\)
\(84\) 0 0
\(85\) 17.3205 1.87867
\(86\) 0 0
\(87\) 5.19615 0.557086
\(88\) 0 0
\(89\) 4.92820 0.522388 0.261194 0.965286i \(-0.415884\pi\)
0.261194 + 0.965286i \(0.415884\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 2.92820 0.305286
\(93\) −2.26795 −0.235175
\(94\) 0 0
\(95\) 25.8564 2.65281
\(96\) 0 0
\(97\) 18.3923 1.86746 0.933728 0.357984i \(-0.116536\pi\)
0.933728 + 0.357984i \(0.116536\pi\)
\(98\) 0 0
\(99\) 2.26795 0.227937
\(100\) −14.0000 −1.40000
\(101\) 8.85641 0.881245 0.440623 0.897692i \(-0.354758\pi\)
0.440623 + 0.897692i \(0.354758\pi\)
\(102\) 0 0
\(103\) −9.19615 −0.906124 −0.453062 0.891479i \(-0.649668\pi\)
−0.453062 + 0.891479i \(0.649668\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 3.46410 0.334887 0.167444 0.985882i \(-0.446449\pi\)
0.167444 + 0.985882i \(0.446449\pi\)
\(108\) −2.00000 −0.192450
\(109\) 9.46410 0.906497 0.453248 0.891384i \(-0.350265\pi\)
0.453248 + 0.891384i \(0.350265\pi\)
\(110\) 0 0
\(111\) −1.00000 −0.0949158
\(112\) 0 0
\(113\) 17.3205 1.62938 0.814688 0.579899i \(-0.196908\pi\)
0.814688 + 0.579899i \(0.196908\pi\)
\(114\) 0 0
\(115\) 5.07180 0.472947
\(116\) −10.3923 −0.964901
\(117\) 1.46410 0.135356
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −5.85641 −0.532401
\(122\) 0 0
\(123\) 1.00000 0.0901670
\(124\) 4.53590 0.407336
\(125\) −6.92820 −0.619677
\(126\) 0 0
\(127\) −9.85641 −0.874615 −0.437307 0.899312i \(-0.644068\pi\)
−0.437307 + 0.899312i \(0.644068\pi\)
\(128\) 0 0
\(129\) −3.92820 −0.345859
\(130\) 0 0
\(131\) 17.4641 1.52585 0.762923 0.646490i \(-0.223764\pi\)
0.762923 + 0.646490i \(0.223764\pi\)
\(132\) −4.53590 −0.394799
\(133\) 0 0
\(134\) 0 0
\(135\) −3.46410 −0.298142
\(136\) 0 0
\(137\) 13.1962 1.12742 0.563712 0.825972i \(-0.309373\pi\)
0.563712 + 0.825972i \(0.309373\pi\)
\(138\) 0 0
\(139\) 4.53590 0.384730 0.192365 0.981323i \(-0.438384\pi\)
0.192365 + 0.981323i \(0.438384\pi\)
\(140\) 0 0
\(141\) −1.92820 −0.162384
\(142\) 0 0
\(143\) 3.32051 0.277675
\(144\) 4.00000 0.333333
\(145\) −18.0000 −1.49482
\(146\) 0 0
\(147\) 0 0
\(148\) 2.00000 0.164399
\(149\) 13.8564 1.13516 0.567581 0.823318i \(-0.307880\pi\)
0.567581 + 0.823318i \(0.307880\pi\)
\(150\) 0 0
\(151\) −0.392305 −0.0319253 −0.0159627 0.999873i \(-0.505081\pi\)
−0.0159627 + 0.999873i \(0.505081\pi\)
\(152\) 0 0
\(153\) −5.00000 −0.404226
\(154\) 0 0
\(155\) 7.85641 0.631042
\(156\) −2.92820 −0.234444
\(157\) 10.0000 0.798087 0.399043 0.916932i \(-0.369342\pi\)
0.399043 + 0.916932i \(0.369342\pi\)
\(158\) 0 0
\(159\) −2.92820 −0.232222
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −4.07180 −0.318928 −0.159464 0.987204i \(-0.550977\pi\)
−0.159464 + 0.987204i \(0.550977\pi\)
\(164\) −2.00000 −0.156174
\(165\) −7.85641 −0.611620
\(166\) 0 0
\(167\) 5.07180 0.392467 0.196234 0.980557i \(-0.437129\pi\)
0.196234 + 0.980557i \(0.437129\pi\)
\(168\) 0 0
\(169\) −10.8564 −0.835108
\(170\) 0 0
\(171\) −7.46410 −0.570794
\(172\) 7.85641 0.599045
\(173\) −20.9282 −1.59114 −0.795571 0.605860i \(-0.792829\pi\)
−0.795571 + 0.605860i \(0.792829\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 9.07180 0.683812
\(177\) −6.92820 −0.520756
\(178\) 0 0
\(179\) −15.5885 −1.16514 −0.582568 0.812782i \(-0.697952\pi\)
−0.582568 + 0.812782i \(0.697952\pi\)
\(180\) 6.92820 0.516398
\(181\) 20.0000 1.48659 0.743294 0.668965i \(-0.233262\pi\)
0.743294 + 0.668965i \(0.233262\pi\)
\(182\) 0 0
\(183\) −1.73205 −0.128037
\(184\) 0 0
\(185\) 3.46410 0.254686
\(186\) 0 0
\(187\) −11.3397 −0.829244
\(188\) 3.85641 0.281257
\(189\) 0 0
\(190\) 0 0
\(191\) 10.3923 0.751961 0.375980 0.926628i \(-0.377306\pi\)
0.375980 + 0.926628i \(0.377306\pi\)
\(192\) −8.00000 −0.577350
\(193\) 27.3205 1.96657 0.983287 0.182064i \(-0.0582779\pi\)
0.983287 + 0.182064i \(0.0582779\pi\)
\(194\) 0 0
\(195\) −5.07180 −0.363199
\(196\) 0 0
\(197\) 7.46410 0.531795 0.265898 0.964001i \(-0.414332\pi\)
0.265898 + 0.964001i \(0.414332\pi\)
\(198\) 0 0
\(199\) 9.32051 0.660713 0.330357 0.943856i \(-0.392831\pi\)
0.330357 + 0.943856i \(0.392831\pi\)
\(200\) 0 0
\(201\) 0.535898 0.0377994
\(202\) 0 0
\(203\) 0 0
\(204\) 10.0000 0.700140
\(205\) −3.46410 −0.241943
\(206\) 0 0
\(207\) −1.46410 −0.101762
\(208\) 5.85641 0.406069
\(209\) −16.9282 −1.17095
\(210\) 0 0
\(211\) 1.07180 0.0737855 0.0368928 0.999319i \(-0.488254\pi\)
0.0368928 + 0.999319i \(0.488254\pi\)
\(212\) 5.85641 0.402220
\(213\) 2.80385 0.192116
\(214\) 0 0
\(215\) 13.6077 0.928037
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −1.19615 −0.0808285
\(220\) 15.7128 1.05936
\(221\) −7.32051 −0.492431
\(222\) 0 0
\(223\) −15.4641 −1.03555 −0.517776 0.855516i \(-0.673240\pi\)
−0.517776 + 0.855516i \(0.673240\pi\)
\(224\) 0 0
\(225\) 7.00000 0.466667
\(226\) 0 0
\(227\) 13.9282 0.924447 0.462224 0.886763i \(-0.347052\pi\)
0.462224 + 0.886763i \(0.347052\pi\)
\(228\) 14.9282 0.988644
\(229\) 4.92820 0.325665 0.162832 0.986654i \(-0.447937\pi\)
0.162832 + 0.986654i \(0.447937\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 13.8564 0.907763 0.453882 0.891062i \(-0.350039\pi\)
0.453882 + 0.891062i \(0.350039\pi\)
\(234\) 0 0
\(235\) 6.67949 0.435722
\(236\) 13.8564 0.901975
\(237\) −12.9282 −0.839777
\(238\) 0 0
\(239\) −8.53590 −0.552141 −0.276071 0.961137i \(-0.589032\pi\)
−0.276071 + 0.961137i \(0.589032\pi\)
\(240\) −13.8564 −0.894427
\(241\) −5.19615 −0.334714 −0.167357 0.985896i \(-0.553523\pi\)
−0.167357 + 0.985896i \(0.553523\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 3.46410 0.221766
\(245\) 0 0
\(246\) 0 0
\(247\) −10.9282 −0.695345
\(248\) 0 0
\(249\) −10.0000 −0.633724
\(250\) 0 0
\(251\) 0.535898 0.0338256 0.0169128 0.999857i \(-0.494616\pi\)
0.0169128 + 0.999857i \(0.494616\pi\)
\(252\) 0 0
\(253\) −3.32051 −0.208759
\(254\) 0 0
\(255\) 17.3205 1.08465
\(256\) 16.0000 1.00000
\(257\) 3.00000 0.187135 0.0935674 0.995613i \(-0.470173\pi\)
0.0935674 + 0.995613i \(0.470173\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 10.1436 0.629079
\(261\) 5.19615 0.321634
\(262\) 0 0
\(263\) 4.12436 0.254319 0.127159 0.991882i \(-0.459414\pi\)
0.127159 + 0.991882i \(0.459414\pi\)
\(264\) 0 0
\(265\) 10.1436 0.623116
\(266\) 0 0
\(267\) 4.92820 0.301601
\(268\) −1.07180 −0.0654704
\(269\) 10.5359 0.642385 0.321193 0.947014i \(-0.395916\pi\)
0.321193 + 0.947014i \(0.395916\pi\)
\(270\) 0 0
\(271\) 19.5885 1.18991 0.594957 0.803758i \(-0.297169\pi\)
0.594957 + 0.803758i \(0.297169\pi\)
\(272\) −20.0000 −1.21268
\(273\) 0 0
\(274\) 0 0
\(275\) 15.8756 0.957337
\(276\) 2.92820 0.176257
\(277\) −8.07180 −0.484987 −0.242494 0.970153i \(-0.577965\pi\)
−0.242494 + 0.970153i \(0.577965\pi\)
\(278\) 0 0
\(279\) −2.26795 −0.135779
\(280\) 0 0
\(281\) 24.1244 1.43914 0.719569 0.694421i \(-0.244339\pi\)
0.719569 + 0.694421i \(0.244339\pi\)
\(282\) 0 0
\(283\) −12.6603 −0.752574 −0.376287 0.926503i \(-0.622799\pi\)
−0.376287 + 0.926503i \(0.622799\pi\)
\(284\) −5.60770 −0.332755
\(285\) 25.8564 1.53160
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 8.00000 0.470588
\(290\) 0 0
\(291\) 18.3923 1.07818
\(292\) 2.39230 0.139999
\(293\) −9.00000 −0.525786 −0.262893 0.964825i \(-0.584677\pi\)
−0.262893 + 0.964825i \(0.584677\pi\)
\(294\) 0 0
\(295\) 24.0000 1.39733
\(296\) 0 0
\(297\) 2.26795 0.131600
\(298\) 0 0
\(299\) −2.14359 −0.123967
\(300\) −14.0000 −0.808290
\(301\) 0 0
\(302\) 0 0
\(303\) 8.85641 0.508787
\(304\) −29.8564 −1.71238
\(305\) 6.00000 0.343559
\(306\) 0 0
\(307\) 17.7321 1.01202 0.506011 0.862527i \(-0.331120\pi\)
0.506011 + 0.862527i \(0.331120\pi\)
\(308\) 0 0
\(309\) −9.19615 −0.523151
\(310\) 0 0
\(311\) −1.85641 −0.105267 −0.0526336 0.998614i \(-0.516762\pi\)
−0.0526336 + 0.998614i \(0.516762\pi\)
\(312\) 0 0
\(313\) −10.9282 −0.617699 −0.308849 0.951111i \(-0.599944\pi\)
−0.308849 + 0.951111i \(0.599944\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 25.8564 1.45454
\(317\) 33.1962 1.86448 0.932241 0.361838i \(-0.117851\pi\)
0.932241 + 0.361838i \(0.117851\pi\)
\(318\) 0 0
\(319\) 11.7846 0.659811
\(320\) 27.7128 1.54919
\(321\) 3.46410 0.193347
\(322\) 0 0
\(323\) 37.3205 2.07657
\(324\) −2.00000 −0.111111
\(325\) 10.2487 0.568496
\(326\) 0 0
\(327\) 9.46410 0.523366
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −32.2487 −1.77255 −0.886275 0.463160i \(-0.846716\pi\)
−0.886275 + 0.463160i \(0.846716\pi\)
\(332\) 20.0000 1.09764
\(333\) −1.00000 −0.0547997
\(334\) 0 0
\(335\) −1.85641 −0.101426
\(336\) 0 0
\(337\) 29.0000 1.57973 0.789865 0.613280i \(-0.210150\pi\)
0.789865 + 0.613280i \(0.210150\pi\)
\(338\) 0 0
\(339\) 17.3205 0.940721
\(340\) −34.6410 −1.87867
\(341\) −5.14359 −0.278541
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 5.07180 0.273056
\(346\) 0 0
\(347\) 12.6603 0.679638 0.339819 0.940491i \(-0.389634\pi\)
0.339819 + 0.940491i \(0.389634\pi\)
\(348\) −10.3923 −0.557086
\(349\) −27.5885 −1.47678 −0.738388 0.674376i \(-0.764413\pi\)
−0.738388 + 0.674376i \(0.764413\pi\)
\(350\) 0 0
\(351\) 1.46410 0.0781480
\(352\) 0 0
\(353\) −21.3205 −1.13478 −0.567388 0.823451i \(-0.692046\pi\)
−0.567388 + 0.823451i \(0.692046\pi\)
\(354\) 0 0
\(355\) −9.71281 −0.515503
\(356\) −9.85641 −0.522388
\(357\) 0 0
\(358\) 0 0
\(359\) −23.7128 −1.25151 −0.625757 0.780018i \(-0.715210\pi\)
−0.625757 + 0.780018i \(0.715210\pi\)
\(360\) 0 0
\(361\) 36.7128 1.93225
\(362\) 0 0
\(363\) −5.85641 −0.307382
\(364\) 0 0
\(365\) 4.14359 0.216886
\(366\) 0 0
\(367\) 23.0526 1.20333 0.601667 0.798747i \(-0.294503\pi\)
0.601667 + 0.798747i \(0.294503\pi\)
\(368\) −5.85641 −0.305286
\(369\) 1.00000 0.0520579
\(370\) 0 0
\(371\) 0 0
\(372\) 4.53590 0.235175
\(373\) 34.8564 1.80480 0.902398 0.430903i \(-0.141805\pi\)
0.902398 + 0.430903i \(0.141805\pi\)
\(374\) 0 0
\(375\) −6.92820 −0.357771
\(376\) 0 0
\(377\) 7.60770 0.391816
\(378\) 0 0
\(379\) −24.0000 −1.23280 −0.616399 0.787434i \(-0.711409\pi\)
−0.616399 + 0.787434i \(0.711409\pi\)
\(380\) −51.7128 −2.65281
\(381\) −9.85641 −0.504959
\(382\) 0 0
\(383\) 22.0718 1.12782 0.563908 0.825838i \(-0.309297\pi\)
0.563908 + 0.825838i \(0.309297\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −3.92820 −0.199682
\(388\) −36.7846 −1.86746
\(389\) 34.7846 1.76365 0.881825 0.471577i \(-0.156315\pi\)
0.881825 + 0.471577i \(0.156315\pi\)
\(390\) 0 0
\(391\) 7.32051 0.370214
\(392\) 0 0
\(393\) 17.4641 0.880947
\(394\) 0 0
\(395\) 44.7846 2.25336
\(396\) −4.53590 −0.227937
\(397\) −10.5359 −0.528782 −0.264391 0.964416i \(-0.585171\pi\)
−0.264391 + 0.964416i \(0.585171\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 28.0000 1.40000
\(401\) −30.9282 −1.54448 −0.772240 0.635330i \(-0.780864\pi\)
−0.772240 + 0.635330i \(0.780864\pi\)
\(402\) 0 0
\(403\) −3.32051 −0.165406
\(404\) −17.7128 −0.881245
\(405\) −3.46410 −0.172133
\(406\) 0 0
\(407\) −2.26795 −0.112418
\(408\) 0 0
\(409\) −2.26795 −0.112143 −0.0560714 0.998427i \(-0.517857\pi\)
−0.0560714 + 0.998427i \(0.517857\pi\)
\(410\) 0 0
\(411\) 13.1962 0.650918
\(412\) 18.3923 0.906124
\(413\) 0 0
\(414\) 0 0
\(415\) 34.6410 1.70046
\(416\) 0 0
\(417\) 4.53590 0.222124
\(418\) 0 0
\(419\) 23.7128 1.15845 0.579223 0.815169i \(-0.303356\pi\)
0.579223 + 0.815169i \(0.303356\pi\)
\(420\) 0 0
\(421\) 18.5359 0.903384 0.451692 0.892174i \(-0.350821\pi\)
0.451692 + 0.892174i \(0.350821\pi\)
\(422\) 0 0
\(423\) −1.92820 −0.0937524
\(424\) 0 0
\(425\) −35.0000 −1.69775
\(426\) 0 0
\(427\) 0 0
\(428\) −6.92820 −0.334887
\(429\) 3.32051 0.160316
\(430\) 0 0
\(431\) 9.46410 0.455870 0.227935 0.973676i \(-0.426803\pi\)
0.227935 + 0.973676i \(0.426803\pi\)
\(432\) 4.00000 0.192450
\(433\) −0.411543 −0.0197775 −0.00988874 0.999951i \(-0.503148\pi\)
−0.00988874 + 0.999951i \(0.503148\pi\)
\(434\) 0 0
\(435\) −18.0000 −0.863034
\(436\) −18.9282 −0.906497
\(437\) 10.9282 0.522767
\(438\) 0 0
\(439\) −35.4641 −1.69261 −0.846305 0.532699i \(-0.821178\pi\)
−0.846305 + 0.532699i \(0.821178\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 24.3923 1.15891 0.579457 0.815003i \(-0.303265\pi\)
0.579457 + 0.815003i \(0.303265\pi\)
\(444\) 2.00000 0.0949158
\(445\) −17.0718 −0.809281
\(446\) 0 0
\(447\) 13.8564 0.655386
\(448\) 0 0
\(449\) 11.3205 0.534248 0.267124 0.963662i \(-0.413927\pi\)
0.267124 + 0.963662i \(0.413927\pi\)
\(450\) 0 0
\(451\) 2.26795 0.106794
\(452\) −34.6410 −1.62938
\(453\) −0.392305 −0.0184321
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 30.6410 1.43333 0.716663 0.697419i \(-0.245669\pi\)
0.716663 + 0.697419i \(0.245669\pi\)
\(458\) 0 0
\(459\) −5.00000 −0.233380
\(460\) −10.1436 −0.472947
\(461\) 24.2487 1.12938 0.564688 0.825305i \(-0.308997\pi\)
0.564688 + 0.825305i \(0.308997\pi\)
\(462\) 0 0
\(463\) −12.3923 −0.575919 −0.287960 0.957643i \(-0.592977\pi\)
−0.287960 + 0.957643i \(0.592977\pi\)
\(464\) 20.7846 0.964901
\(465\) 7.85641 0.364332
\(466\) 0 0
\(467\) −7.46410 −0.345397 −0.172699 0.984975i \(-0.555249\pi\)
−0.172699 + 0.984975i \(0.555249\pi\)
\(468\) −2.92820 −0.135356
\(469\) 0 0
\(470\) 0 0
\(471\) 10.0000 0.460776
\(472\) 0 0
\(473\) −8.90897 −0.409635
\(474\) 0 0
\(475\) −52.2487 −2.39734
\(476\) 0 0
\(477\) −2.92820 −0.134073
\(478\) 0 0
\(479\) −14.7128 −0.672246 −0.336123 0.941818i \(-0.609116\pi\)
−0.336123 + 0.941818i \(0.609116\pi\)
\(480\) 0 0
\(481\) −1.46410 −0.0667573
\(482\) 0 0
\(483\) 0 0
\(484\) 11.7128 0.532401
\(485\) −63.7128 −2.89305
\(486\) 0 0
\(487\) 15.9282 0.721776 0.360888 0.932609i \(-0.382474\pi\)
0.360888 + 0.932609i \(0.382474\pi\)
\(488\) 0 0
\(489\) −4.07180 −0.184133
\(490\) 0 0
\(491\) −23.8564 −1.07662 −0.538312 0.842745i \(-0.680938\pi\)
−0.538312 + 0.842745i \(0.680938\pi\)
\(492\) −2.00000 −0.0901670
\(493\) −25.9808 −1.17011
\(494\) 0 0
\(495\) −7.85641 −0.353119
\(496\) −9.07180 −0.407336
\(497\) 0 0
\(498\) 0 0
\(499\) 5.46410 0.244607 0.122303 0.992493i \(-0.460972\pi\)
0.122303 + 0.992493i \(0.460972\pi\)
\(500\) 13.8564 0.619677
\(501\) 5.07180 0.226591
\(502\) 0 0
\(503\) 29.7846 1.32803 0.664015 0.747719i \(-0.268851\pi\)
0.664015 + 0.747719i \(0.268851\pi\)
\(504\) 0 0
\(505\) −30.6795 −1.36522
\(506\) 0 0
\(507\) −10.8564 −0.482150
\(508\) 19.7128 0.874615
\(509\) 21.9282 0.971951 0.485975 0.873973i \(-0.338465\pi\)
0.485975 + 0.873973i \(0.338465\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −7.46410 −0.329548
\(514\) 0 0
\(515\) 31.8564 1.40376
\(516\) 7.85641 0.345859
\(517\) −4.37307 −0.192327
\(518\) 0 0
\(519\) −20.9282 −0.918646
\(520\) 0 0
\(521\) −20.8564 −0.913736 −0.456868 0.889535i \(-0.651029\pi\)
−0.456868 + 0.889535i \(0.651029\pi\)
\(522\) 0 0
\(523\) −31.1769 −1.36327 −0.681636 0.731692i \(-0.738731\pi\)
−0.681636 + 0.731692i \(0.738731\pi\)
\(524\) −34.9282 −1.52585
\(525\) 0 0
\(526\) 0 0
\(527\) 11.3397 0.493967
\(528\) 9.07180 0.394799
\(529\) −20.8564 −0.906800
\(530\) 0 0
\(531\) −6.92820 −0.300658
\(532\) 0 0
\(533\) 1.46410 0.0634173
\(534\) 0 0
\(535\) −12.0000 −0.518805
\(536\) 0 0
\(537\) −15.5885 −0.672692
\(538\) 0 0
\(539\) 0 0
\(540\) 6.92820 0.298142
\(541\) 16.9282 0.727800 0.363900 0.931438i \(-0.381445\pi\)
0.363900 + 0.931438i \(0.381445\pi\)
\(542\) 0 0
\(543\) 20.0000 0.858282
\(544\) 0 0
\(545\) −32.7846 −1.40434
\(546\) 0 0
\(547\) −11.6077 −0.496309 −0.248155 0.968720i \(-0.579824\pi\)
−0.248155 + 0.968720i \(0.579824\pi\)
\(548\) −26.3923 −1.12742
\(549\) −1.73205 −0.0739221
\(550\) 0 0
\(551\) −38.7846 −1.65228
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 3.46410 0.147043
\(556\) −9.07180 −0.384730
\(557\) 10.5167 0.445605 0.222803 0.974864i \(-0.428479\pi\)
0.222803 + 0.974864i \(0.428479\pi\)
\(558\) 0 0
\(559\) −5.75129 −0.243254
\(560\) 0 0
\(561\) −11.3397 −0.478764
\(562\) 0 0
\(563\) −5.92820 −0.249844 −0.124922 0.992167i \(-0.539868\pi\)
−0.124922 + 0.992167i \(0.539868\pi\)
\(564\) 3.85641 0.162384
\(565\) −60.0000 −2.52422
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −26.2487 −1.10040 −0.550202 0.835032i \(-0.685449\pi\)
−0.550202 + 0.835032i \(0.685449\pi\)
\(570\) 0 0
\(571\) 34.9282 1.46170 0.730850 0.682538i \(-0.239124\pi\)
0.730850 + 0.682538i \(0.239124\pi\)
\(572\) −6.64102 −0.277675
\(573\) 10.3923 0.434145
\(574\) 0 0
\(575\) −10.2487 −0.427401
\(576\) −8.00000 −0.333333
\(577\) −35.3205 −1.47041 −0.735206 0.677844i \(-0.762915\pi\)
−0.735206 + 0.677844i \(0.762915\pi\)
\(578\) 0 0
\(579\) 27.3205 1.13540
\(580\) 36.0000 1.49482
\(581\) 0 0
\(582\) 0 0
\(583\) −6.64102 −0.275043
\(584\) 0 0
\(585\) −5.07180 −0.209693
\(586\) 0 0
\(587\) −41.9282 −1.73056 −0.865281 0.501287i \(-0.832860\pi\)
−0.865281 + 0.501287i \(0.832860\pi\)
\(588\) 0 0
\(589\) 16.9282 0.697514
\(590\) 0 0
\(591\) 7.46410 0.307032
\(592\) −4.00000 −0.164399
\(593\) 42.7128 1.75400 0.877002 0.480486i \(-0.159540\pi\)
0.877002 + 0.480486i \(0.159540\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −27.7128 −1.13516
\(597\) 9.32051 0.381463
\(598\) 0 0
\(599\) 40.0000 1.63436 0.817178 0.576386i \(-0.195537\pi\)
0.817178 + 0.576386i \(0.195537\pi\)
\(600\) 0 0
\(601\) 40.2487 1.64178 0.820890 0.571087i \(-0.193478\pi\)
0.820890 + 0.571087i \(0.193478\pi\)
\(602\) 0 0
\(603\) 0.535898 0.0218235
\(604\) 0.784610 0.0319253
\(605\) 20.2872 0.824791
\(606\) 0 0
\(607\) −44.2487 −1.79600 −0.898000 0.439996i \(-0.854980\pi\)
−0.898000 + 0.439996i \(0.854980\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −2.82309 −0.114210
\(612\) 10.0000 0.404226
\(613\) −32.6410 −1.31836 −0.659179 0.751986i \(-0.729096\pi\)
−0.659179 + 0.751986i \(0.729096\pi\)
\(614\) 0 0
\(615\) −3.46410 −0.139686
\(616\) 0 0
\(617\) −19.8564 −0.799389 −0.399694 0.916648i \(-0.630884\pi\)
−0.399694 + 0.916648i \(0.630884\pi\)
\(618\) 0 0
\(619\) 37.1962 1.49504 0.747520 0.664240i \(-0.231245\pi\)
0.747520 + 0.664240i \(0.231245\pi\)
\(620\) −15.7128 −0.631042
\(621\) −1.46410 −0.0587524
\(622\) 0 0
\(623\) 0 0
\(624\) 5.85641 0.234444
\(625\) −11.0000 −0.440000
\(626\) 0 0
\(627\) −16.9282 −0.676047
\(628\) −20.0000 −0.798087
\(629\) 5.00000 0.199363
\(630\) 0 0
\(631\) 0.0717968 0.00285818 0.00142909 0.999999i \(-0.499545\pi\)
0.00142909 + 0.999999i \(0.499545\pi\)
\(632\) 0 0
\(633\) 1.07180 0.0426001
\(634\) 0 0
\(635\) 34.1436 1.35495
\(636\) 5.85641 0.232222
\(637\) 0 0
\(638\) 0 0
\(639\) 2.80385 0.110918
\(640\) 0 0
\(641\) 2.51666 0.0994021 0.0497011 0.998764i \(-0.484173\pi\)
0.0497011 + 0.998764i \(0.484173\pi\)
\(642\) 0 0
\(643\) 10.2487 0.404170 0.202085 0.979368i \(-0.435228\pi\)
0.202085 + 0.979368i \(0.435228\pi\)
\(644\) 0 0
\(645\) 13.6077 0.535802
\(646\) 0 0
\(647\) −10.9282 −0.429632 −0.214816 0.976655i \(-0.568915\pi\)
−0.214816 + 0.976655i \(0.568915\pi\)
\(648\) 0 0
\(649\) −15.7128 −0.616782
\(650\) 0 0
\(651\) 0 0
\(652\) 8.14359 0.318928
\(653\) 4.66025 0.182370 0.0911849 0.995834i \(-0.470935\pi\)
0.0911849 + 0.995834i \(0.470935\pi\)
\(654\) 0 0
\(655\) −60.4974 −2.36383
\(656\) 4.00000 0.156174
\(657\) −1.19615 −0.0466664
\(658\) 0 0
\(659\) −19.4641 −0.758214 −0.379107 0.925353i \(-0.623769\pi\)
−0.379107 + 0.925353i \(0.623769\pi\)
\(660\) 15.7128 0.611620
\(661\) −38.6410 −1.50296 −0.751481 0.659755i \(-0.770660\pi\)
−0.751481 + 0.659755i \(0.770660\pi\)
\(662\) 0 0
\(663\) −7.32051 −0.284305
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −7.60770 −0.294571
\(668\) −10.1436 −0.392467
\(669\) −15.4641 −0.597877
\(670\) 0 0
\(671\) −3.92820 −0.151647
\(672\) 0 0
\(673\) 8.53590 0.329035 0.164517 0.986374i \(-0.447393\pi\)
0.164517 + 0.986374i \(0.447393\pi\)
\(674\) 0 0
\(675\) 7.00000 0.269430
\(676\) 21.7128 0.835108
\(677\) 23.8564 0.916876 0.458438 0.888726i \(-0.348409\pi\)
0.458438 + 0.888726i \(0.348409\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 13.9282 0.533730
\(682\) 0 0
\(683\) 36.2487 1.38702 0.693509 0.720448i \(-0.256064\pi\)
0.693509 + 0.720448i \(0.256064\pi\)
\(684\) 14.9282 0.570794
\(685\) −45.7128 −1.74660
\(686\) 0 0
\(687\) 4.92820 0.188023
\(688\) −15.7128 −0.599045
\(689\) −4.28719 −0.163329
\(690\) 0 0
\(691\) 21.1769 0.805608 0.402804 0.915286i \(-0.368036\pi\)
0.402804 + 0.915286i \(0.368036\pi\)
\(692\) 41.8564 1.59114
\(693\) 0 0
\(694\) 0 0
\(695\) −15.7128 −0.596021
\(696\) 0 0
\(697\) −5.00000 −0.189389
\(698\) 0 0
\(699\) 13.8564 0.524097
\(700\) 0 0
\(701\) −8.53590 −0.322396 −0.161198 0.986922i \(-0.551536\pi\)
−0.161198 + 0.986922i \(0.551536\pi\)
\(702\) 0 0
\(703\) 7.46410 0.281514
\(704\) −18.1436 −0.683812
\(705\) 6.67949 0.251564
\(706\) 0 0
\(707\) 0 0
\(708\) 13.8564 0.520756
\(709\) −1.32051 −0.0495927 −0.0247964 0.999693i \(-0.507894\pi\)
−0.0247964 + 0.999693i \(0.507894\pi\)
\(710\) 0 0
\(711\) −12.9282 −0.484846
\(712\) 0 0
\(713\) 3.32051 0.124354
\(714\) 0 0
\(715\) −11.5026 −0.430172
\(716\) 31.1769 1.16514
\(717\) −8.53590 −0.318779
\(718\) 0 0
\(719\) −17.0000 −0.633993 −0.316997 0.948427i \(-0.602674\pi\)
−0.316997 + 0.948427i \(0.602674\pi\)
\(720\) −13.8564 −0.516398
\(721\) 0 0
\(722\) 0 0
\(723\) −5.19615 −0.193247
\(724\) −40.0000 −1.48659
\(725\) 36.3731 1.35086
\(726\) 0 0
\(727\) 40.6410 1.50729 0.753646 0.657281i \(-0.228293\pi\)
0.753646 + 0.657281i \(0.228293\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 19.6410 0.726449
\(732\) 3.46410 0.128037
\(733\) 21.9808 0.811878 0.405939 0.913900i \(-0.366945\pi\)
0.405939 + 0.913900i \(0.366945\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 1.21539 0.0447695
\(738\) 0 0
\(739\) −33.7846 −1.24279 −0.621393 0.783499i \(-0.713433\pi\)
−0.621393 + 0.783499i \(0.713433\pi\)
\(740\) −6.92820 −0.254686
\(741\) −10.9282 −0.401458
\(742\) 0 0
\(743\) 20.5359 0.753389 0.376695 0.926338i \(-0.377061\pi\)
0.376695 + 0.926338i \(0.377061\pi\)
\(744\) 0 0
\(745\) −48.0000 −1.75858
\(746\) 0 0
\(747\) −10.0000 −0.365881
\(748\) 22.6795 0.829244
\(749\) 0 0
\(750\) 0 0
\(751\) 24.2487 0.884848 0.442424 0.896806i \(-0.354119\pi\)
0.442424 + 0.896806i \(0.354119\pi\)
\(752\) −7.71281 −0.281257
\(753\) 0.535898 0.0195292
\(754\) 0 0
\(755\) 1.35898 0.0494585
\(756\) 0 0
\(757\) −11.8564 −0.430928 −0.215464 0.976512i \(-0.569126\pi\)
−0.215464 + 0.976512i \(0.569126\pi\)
\(758\) 0 0
\(759\) −3.32051 −0.120527
\(760\) 0 0
\(761\) −38.2487 −1.38651 −0.693257 0.720690i \(-0.743825\pi\)
−0.693257 + 0.720690i \(0.743825\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −20.7846 −0.751961
\(765\) 17.3205 0.626224
\(766\) 0 0
\(767\) −10.1436 −0.366264
\(768\) 16.0000 0.577350
\(769\) −13.1962 −0.475865 −0.237933 0.971282i \(-0.576470\pi\)
−0.237933 + 0.971282i \(0.576470\pi\)
\(770\) 0 0
\(771\) 3.00000 0.108042
\(772\) −54.6410 −1.96657
\(773\) −30.8564 −1.10983 −0.554914 0.831908i \(-0.687249\pi\)
−0.554914 + 0.831908i \(0.687249\pi\)
\(774\) 0 0
\(775\) −15.8756 −0.570270
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −7.46410 −0.267429
\(780\) 10.1436 0.363199
\(781\) 6.35898 0.227542
\(782\) 0 0
\(783\) 5.19615 0.185695
\(784\) 0 0
\(785\) −34.6410 −1.23639
\(786\) 0 0
\(787\) 18.5167 0.660048 0.330024 0.943973i \(-0.392943\pi\)
0.330024 + 0.943973i \(0.392943\pi\)
\(788\) −14.9282 −0.531795
\(789\) 4.12436 0.146831
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −2.53590 −0.0900524
\(794\) 0 0
\(795\) 10.1436 0.359756
\(796\) −18.6410 −0.660713
\(797\) 7.85641 0.278288 0.139144 0.990272i \(-0.455565\pi\)
0.139144 + 0.990272i \(0.455565\pi\)
\(798\) 0 0
\(799\) 9.64102 0.341075
\(800\) 0 0
\(801\) 4.92820 0.174129
\(802\) 0 0
\(803\) −2.71281 −0.0957331
\(804\) −1.07180 −0.0377994
\(805\) 0 0
\(806\) 0 0
\(807\) 10.5359 0.370881
\(808\) 0 0
\(809\) −54.9282 −1.93117 −0.965586 0.260083i \(-0.916250\pi\)
−0.965586 + 0.260083i \(0.916250\pi\)
\(810\) 0 0
\(811\) 1.73205 0.0608205 0.0304103 0.999538i \(-0.490319\pi\)
0.0304103 + 0.999538i \(0.490319\pi\)
\(812\) 0 0
\(813\) 19.5885 0.686997
\(814\) 0 0
\(815\) 14.1051 0.494081
\(816\) −20.0000 −0.700140
\(817\) 29.3205 1.02579
\(818\) 0 0
\(819\) 0 0
\(820\) 6.92820 0.241943
\(821\) −43.3205 −1.51190 −0.755948 0.654632i \(-0.772824\pi\)
−0.755948 + 0.654632i \(0.772824\pi\)
\(822\) 0 0
\(823\) −43.5692 −1.51873 −0.759364 0.650666i \(-0.774490\pi\)
−0.759364 + 0.650666i \(0.774490\pi\)
\(824\) 0 0
\(825\) 15.8756 0.552719
\(826\) 0 0
\(827\) −34.8038 −1.21025 −0.605124 0.796131i \(-0.706877\pi\)
−0.605124 + 0.796131i \(0.706877\pi\)
\(828\) 2.92820 0.101762
\(829\) −23.0526 −0.800648 −0.400324 0.916374i \(-0.631102\pi\)
−0.400324 + 0.916374i \(0.631102\pi\)
\(830\) 0 0
\(831\) −8.07180 −0.280008
\(832\) −11.7128 −0.406069
\(833\) 0 0
\(834\) 0 0
\(835\) −17.5692 −0.608008
\(836\) 33.8564 1.17095
\(837\) −2.26795 −0.0783918
\(838\) 0 0
\(839\) 44.0000 1.51905 0.759524 0.650479i \(-0.225432\pi\)
0.759524 + 0.650479i \(0.225432\pi\)
\(840\) 0 0
\(841\) −2.00000 −0.0689655
\(842\) 0 0
\(843\) 24.1244 0.830887
\(844\) −2.14359 −0.0737855
\(845\) 37.6077 1.29374
\(846\) 0 0
\(847\) 0 0
\(848\) −11.7128 −0.402220
\(849\) −12.6603 −0.434499
\(850\) 0 0
\(851\) 1.46410 0.0501888
\(852\) −5.60770 −0.192116
\(853\) 3.71281 0.127124 0.0635621 0.997978i \(-0.479754\pi\)
0.0635621 + 0.997978i \(0.479754\pi\)
\(854\) 0 0
\(855\) 25.8564 0.884270
\(856\) 0 0
\(857\) −14.2487 −0.486727 −0.243363 0.969935i \(-0.578251\pi\)
−0.243363 + 0.969935i \(0.578251\pi\)
\(858\) 0 0
\(859\) 13.1962 0.450247 0.225123 0.974330i \(-0.427721\pi\)
0.225123 + 0.974330i \(0.427721\pi\)
\(860\) −27.2154 −0.928037
\(861\) 0 0
\(862\) 0 0
\(863\) 49.3205 1.67889 0.839445 0.543445i \(-0.182880\pi\)
0.839445 + 0.543445i \(0.182880\pi\)
\(864\) 0 0
\(865\) 72.4974 2.46499
\(866\) 0 0
\(867\) 8.00000 0.271694
\(868\) 0 0
\(869\) −29.3205 −0.994630
\(870\) 0 0
\(871\) 0.784610 0.0265855
\(872\) 0 0
\(873\) 18.3923 0.622485
\(874\) 0 0
\(875\) 0 0
\(876\) 2.39230 0.0808285
\(877\) 41.9282 1.41581 0.707907 0.706305i \(-0.249639\pi\)
0.707907 + 0.706305i \(0.249639\pi\)
\(878\) 0 0
\(879\) −9.00000 −0.303562
\(880\) −31.4256 −1.05936
\(881\) 33.4641 1.12743 0.563717 0.825968i \(-0.309371\pi\)
0.563717 + 0.825968i \(0.309371\pi\)
\(882\) 0 0
\(883\) −43.5692 −1.46622 −0.733110 0.680110i \(-0.761932\pi\)
−0.733110 + 0.680110i \(0.761932\pi\)
\(884\) 14.6410 0.492431
\(885\) 24.0000 0.806751
\(886\) 0 0
\(887\) 6.85641 0.230216 0.115108 0.993353i \(-0.463279\pi\)
0.115108 + 0.993353i \(0.463279\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 2.26795 0.0759792
\(892\) 30.9282 1.03555
\(893\) 14.3923 0.481620
\(894\) 0 0
\(895\) 54.0000 1.80502
\(896\) 0 0
\(897\) −2.14359 −0.0715725
\(898\) 0 0
\(899\) −11.7846 −0.393039
\(900\) −14.0000 −0.466667
\(901\) 14.6410 0.487763
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −69.2820 −2.30301
\(906\) 0 0
\(907\) −21.8564 −0.725730 −0.362865 0.931842i \(-0.618201\pi\)
−0.362865 + 0.931842i \(0.618201\pi\)
\(908\) −27.8564 −0.924447
\(909\) 8.85641 0.293748
\(910\) 0 0
\(911\) 24.7846 0.821151 0.410575 0.911827i \(-0.365328\pi\)
0.410575 + 0.911827i \(0.365328\pi\)
\(912\) −29.8564 −0.988644
\(913\) −22.6795 −0.750582
\(914\) 0 0
\(915\) 6.00000 0.198354
\(916\) −9.85641 −0.325665
\(917\) 0 0
\(918\) 0 0
\(919\) −18.5359 −0.611443 −0.305721 0.952121i \(-0.598898\pi\)
−0.305721 + 0.952121i \(0.598898\pi\)
\(920\) 0 0
\(921\) 17.7321 0.584291
\(922\) 0 0
\(923\) 4.10512 0.135122
\(924\) 0 0
\(925\) −7.00000 −0.230159
\(926\) 0 0
\(927\) −9.19615 −0.302041
\(928\) 0 0
\(929\) −2.21539 −0.0726846 −0.0363423 0.999339i \(-0.511571\pi\)
−0.0363423 + 0.999339i \(0.511571\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) −27.7128 −0.907763
\(933\) −1.85641 −0.0607760
\(934\) 0 0
\(935\) 39.2820 1.28466
\(936\) 0 0
\(937\) 18.9282 0.618357 0.309179 0.951004i \(-0.399946\pi\)
0.309179 + 0.951004i \(0.399946\pi\)
\(938\) 0 0
\(939\) −10.9282 −0.356628
\(940\) −13.3590 −0.435722
\(941\) −1.32051 −0.0430473 −0.0215237 0.999768i \(-0.506852\pi\)
−0.0215237 + 0.999768i \(0.506852\pi\)
\(942\) 0 0
\(943\) −1.46410 −0.0476777
\(944\) −27.7128 −0.901975
\(945\) 0 0
\(946\) 0 0
\(947\) 36.9282 1.20001 0.600003 0.799998i \(-0.295166\pi\)
0.600003 + 0.799998i \(0.295166\pi\)
\(948\) 25.8564 0.839777
\(949\) −1.75129 −0.0568492
\(950\) 0 0
\(951\) 33.1962 1.07646
\(952\) 0 0
\(953\) −55.3205 −1.79201 −0.896004 0.444047i \(-0.853542\pi\)
−0.896004 + 0.444047i \(0.853542\pi\)
\(954\) 0 0
\(955\) −36.0000 −1.16493
\(956\) 17.0718 0.552141
\(957\) 11.7846 0.380942
\(958\) 0 0
\(959\) 0 0
\(960\) 27.7128 0.894427
\(961\) −25.8564 −0.834078
\(962\) 0 0
\(963\) 3.46410 0.111629
\(964\) 10.3923 0.334714
\(965\) −94.6410 −3.04660
\(966\) 0 0
\(967\) 12.2487 0.393892 0.196946 0.980414i \(-0.436898\pi\)
0.196946 + 0.980414i \(0.436898\pi\)
\(968\) 0 0
\(969\) 37.3205 1.19891
\(970\) 0 0
\(971\) 27.9282 0.896259 0.448129 0.893969i \(-0.352090\pi\)
0.448129 + 0.893969i \(0.352090\pi\)
\(972\) −2.00000 −0.0641500
\(973\) 0 0
\(974\) 0 0
\(975\) 10.2487 0.328221
\(976\) −6.92820 −0.221766
\(977\) −37.9808 −1.21511 −0.607556 0.794277i \(-0.707850\pi\)
−0.607556 + 0.794277i \(0.707850\pi\)
\(978\) 0 0
\(979\) 11.1769 0.357216
\(980\) 0 0
\(981\) 9.46410 0.302166
\(982\) 0 0
\(983\) 26.7846 0.854296 0.427148 0.904182i \(-0.359518\pi\)
0.427148 + 0.904182i \(0.359518\pi\)
\(984\) 0 0
\(985\) −25.8564 −0.823854
\(986\) 0 0
\(987\) 0 0
\(988\) 21.8564 0.695345
\(989\) 5.75129 0.182880
\(990\) 0 0
\(991\) 52.1051 1.65517 0.827587 0.561338i \(-0.189713\pi\)
0.827587 + 0.561338i \(0.189713\pi\)
\(992\) 0 0
\(993\) −32.2487 −1.02338
\(994\) 0 0
\(995\) −32.2872 −1.02357
\(996\) 20.0000 0.633724
\(997\) −41.1769 −1.30409 −0.652043 0.758182i \(-0.726088\pi\)
−0.652043 + 0.758182i \(0.726088\pi\)
\(998\) 0 0
\(999\) −1.00000 −0.0316386
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 \(a_p\))