Properties

Label 6027.2.a.n.1.2
Level 6027
Weight 2
Character 6027.1
Self dual Yes
Analytic conductor 48.126
Analytic rank 0
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: \(0\)
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 1.2
Root \(-1.73205\)
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{3} -2.00000 q^{4} +3.46410 q^{5} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{3} -2.00000 q^{4} +3.46410 q^{5} +1.00000 q^{9} +5.73205 q^{11} -2.00000 q^{12} -5.46410 q^{13} +3.46410 q^{15} +4.00000 q^{16} -5.00000 q^{17} -0.535898 q^{19} -6.92820 q^{20} +5.46410 q^{23} +7.00000 q^{25} +1.00000 q^{27} -5.19615 q^{29} -5.73205 q^{31} +5.73205 q^{33} -2.00000 q^{36} -1.00000 q^{37} -5.46410 q^{39} +1.00000 q^{41} +9.92820 q^{43} -11.4641 q^{44} +3.46410 q^{45} +11.9282 q^{47} +4.00000 q^{48} -5.00000 q^{51} +10.9282 q^{52} +10.9282 q^{53} +19.8564 q^{55} -0.535898 q^{57} +6.92820 q^{59} -6.92820 q^{60} +1.73205 q^{61} -8.00000 q^{64} -18.9282 q^{65} +7.46410 q^{67} +10.0000 q^{68} +5.46410 q^{69} +13.1962 q^{71} +9.19615 q^{73} +7.00000 q^{75} +1.07180 q^{76} +0.928203 q^{79} +13.8564 q^{80} +1.00000 q^{81} -10.0000 q^{83} -17.3205 q^{85} -5.19615 q^{87} -8.92820 q^{89} -10.9282 q^{92} -5.73205 q^{93} -1.85641 q^{95} -2.39230 q^{97} +5.73205 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 2q^{3} - 4q^{4} + 2q^{9} + O(q^{10}) \) \( 2q + 2q^{3} - 4q^{4} + 2q^{9} + 8q^{11} - 4q^{12} - 4q^{13} + 8q^{16} - 10q^{17} - 8q^{19} + 4q^{23} + 14q^{25} + 2q^{27} - 8q^{31} + 8q^{33} - 4q^{36} - 2q^{37} - 4q^{39} + 2q^{41} + 6q^{43} - 16q^{44} + 10q^{47} + 8q^{48} - 10q^{51} + 8q^{52} + 8q^{53} + 12q^{55} - 8q^{57} - 16q^{64} - 24q^{65} + 8q^{67} + 20q^{68} + 4q^{69} + 16q^{71} + 8q^{73} + 14q^{75} + 16q^{76} - 12q^{79} + 2q^{81} - 20q^{83} - 4q^{89} - 8q^{92} - 8q^{93} + 24q^{95} + 16q^{97} + 8q^{99} + O(q^{100}) \)

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 \(-0.217953\pi\)
0.774597 + 0.632456i \(0.217953\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 5.73205 1.72828 0.864139 0.503253i \(-0.167864\pi\)
0.864139 + 0.503253i \(0.167864\pi\)
\(12\) −2.00000 −0.577350
\(13\) −5.46410 −1.51547 −0.757735 0.652563i \(-0.773694\pi\)
−0.757735 + 0.652563i \(0.773694\pi\)
\(14\) 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
\(19\) −0.535898 −0.122944 −0.0614718 0.998109i \(-0.519579\pi\)
−0.0614718 + 0.998109i \(0.519579\pi\)
\(20\) −6.92820 −1.54919
\(21\) 0 0
\(22\) 0 0
\(23\) 5.46410 1.13934 0.569672 0.821872i \(-0.307070\pi\)
0.569672 + 0.821872i \(0.307070\pi\)
\(24\) 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 \(-0.660253\pi\)
−0.482451 + 0.875923i \(0.660253\pi\)
\(30\) 0 0
\(31\) −5.73205 −1.02951 −0.514753 0.857338i \(-0.672117\pi\)
−0.514753 + 0.857338i \(0.672117\pi\)
\(32\) 0 0
\(33\) 5.73205 0.997822
\(34\) 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
\(39\) −5.46410 −0.874957
\(40\) 0 0
\(41\) 1.00000 0.156174
\(42\) 0 0
\(43\) 9.92820 1.51404 0.757018 0.653394i \(-0.226655\pi\)
0.757018 + 0.653394i \(0.226655\pi\)
\(44\) −11.4641 −1.72828
\(45\) 3.46410 0.516398
\(46\) 0 0
\(47\) 11.9282 1.73991 0.869954 0.493134i \(-0.164149\pi\)
0.869954 + 0.493134i \(0.164149\pi\)
\(48\) 4.00000 0.577350
\(49\) 0 0
\(50\) 0 0
\(51\) −5.00000 −0.700140
\(52\) 10.9282 1.51547
\(53\) 10.9282 1.50110 0.750552 0.660811i \(-0.229788\pi\)
0.750552 + 0.660811i \(0.229788\pi\)
\(54\) 0 0
\(55\) 19.8564 2.67744
\(56\) 0 0
\(57\) −0.535898 −0.0709815
\(58\) 0 0
\(59\) 6.92820 0.901975 0.450988 0.892530i \(-0.351072\pi\)
0.450988 + 0.892530i \(0.351072\pi\)
\(60\) −6.92820 −0.894427
\(61\) 1.73205 0.221766 0.110883 0.993833i \(-0.464632\pi\)
0.110883 + 0.993833i \(0.464632\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −8.00000 −1.00000
\(65\) −18.9282 −2.34775
\(66\) 0 0
\(67\) 7.46410 0.911885 0.455943 0.890009i \(-0.349302\pi\)
0.455943 + 0.890009i \(0.349302\pi\)
\(68\) 10.0000 1.21268
\(69\) 5.46410 0.657801
\(70\) 0 0
\(71\) 13.1962 1.56610 0.783048 0.621962i \(-0.213664\pi\)
0.783048 + 0.621962i \(0.213664\pi\)
\(72\) 0 0
\(73\) 9.19615 1.07633 0.538164 0.842840i \(-0.319118\pi\)
0.538164 + 0.842840i \(0.319118\pi\)
\(74\) 0 0
\(75\) 7.00000 0.808290
\(76\) 1.07180 0.122944
\(77\) 0 0
\(78\) 0 0
\(79\) 0.928203 0.104431 0.0522155 0.998636i \(-0.483372\pi\)
0.0522155 + 0.998636i \(0.483372\pi\)
\(80\) 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
\(89\) −8.92820 −0.946388 −0.473194 0.880958i \(-0.656899\pi\)
−0.473194 + 0.880958i \(0.656899\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −10.9282 −1.13934
\(93\) −5.73205 −0.594386
\(94\) 0 0
\(95\) −1.85641 −0.190463
\(96\) 0 0
\(97\) −2.39230 −0.242902 −0.121451 0.992597i \(-0.538755\pi\)
−0.121451 + 0.992597i \(0.538755\pi\)
\(98\) 0 0
\(99\) 5.73205 0.576093
\(100\) −14.0000 −1.40000
\(101\) −18.8564 −1.87628 −0.938141 0.346253i \(-0.887454\pi\)
−0.938141 + 0.346253i \(0.887454\pi\)
\(102\) 0 0
\(103\) 1.19615 0.117860 0.0589302 0.998262i \(-0.481231\pi\)
0.0589302 + 0.998262i \(0.481231\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −3.46410 −0.334887 −0.167444 0.985882i \(-0.553551\pi\)
−0.167444 + 0.985882i \(0.553551\pi\)
\(108\) −2.00000 −0.192450
\(109\) 2.53590 0.242895 0.121448 0.992598i \(-0.461246\pi\)
0.121448 + 0.992598i \(0.461246\pi\)
\(110\) 0 0
\(111\) −1.00000 −0.0949158
\(112\) 0 0
\(113\) −17.3205 −1.62938 −0.814688 0.579899i \(-0.803092\pi\)
−0.814688 + 0.579899i \(0.803092\pi\)
\(114\) 0 0
\(115\) 18.9282 1.76506
\(116\) 10.3923 0.964901
\(117\) −5.46410 −0.505156
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 21.8564 1.98695
\(122\) 0 0
\(123\) 1.00000 0.0901670
\(124\) 11.4641 1.02951
\(125\) 6.92820 0.619677
\(126\) 0 0
\(127\) 17.8564 1.58450 0.792250 0.610197i \(-0.208910\pi\)
0.792250 + 0.610197i \(0.208910\pi\)
\(128\) 0 0
\(129\) 9.92820 0.874130
\(130\) 0 0
\(131\) 10.5359 0.920526 0.460263 0.887783i \(-0.347755\pi\)
0.460263 + 0.887783i \(0.347755\pi\)
\(132\) −11.4641 −0.997822
\(133\) 0 0
\(134\) 0 0
\(135\) 3.46410 0.298142
\(136\) 0 0
\(137\) 2.80385 0.239549 0.119774 0.992801i \(-0.461783\pi\)
0.119774 + 0.992801i \(0.461783\pi\)
\(138\) 0 0
\(139\) 11.4641 0.972372 0.486186 0.873855i \(-0.338388\pi\)
0.486186 + 0.873855i \(0.338388\pi\)
\(140\) 0 0
\(141\) 11.9282 1.00454
\(142\) 0 0
\(143\) −31.3205 −2.61915
\(144\) 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 \(-0.692120\pi\)
−0.567581 + 0.823318i \(0.692120\pi\)
\(150\) 0 0
\(151\) 20.3923 1.65950 0.829751 0.558134i \(-0.188482\pi\)
0.829751 + 0.558134i \(0.188482\pi\)
\(152\) 0 0
\(153\) −5.00000 −0.404226
\(154\) 0 0
\(155\) −19.8564 −1.59490
\(156\) 10.9282 0.874957
\(157\) 10.0000 0.798087 0.399043 0.916932i \(-0.369342\pi\)
0.399043 + 0.916932i \(0.369342\pi\)
\(158\) 0 0
\(159\) 10.9282 0.866663
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −17.9282 −1.40425 −0.702123 0.712056i \(-0.747764\pi\)
−0.702123 + 0.712056i \(0.747764\pi\)
\(164\) −2.00000 −0.156174
\(165\) 19.8564 1.54582
\(166\) 0 0
\(167\) 18.9282 1.46471 0.732354 0.680924i \(-0.238422\pi\)
0.732354 + 0.680924i \(0.238422\pi\)
\(168\) 0 0
\(169\) 16.8564 1.29665
\(170\) 0 0
\(171\) −0.535898 −0.0409812
\(172\) −19.8564 −1.51404
\(173\) −7.07180 −0.537659 −0.268829 0.963188i \(-0.586637\pi\)
−0.268829 + 0.963188i \(0.586637\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 22.9282 1.72828
\(177\) 6.92820 0.520756
\(178\) 0 0
\(179\) 15.5885 1.16514 0.582568 0.812782i \(-0.302048\pi\)
0.582568 + 0.812782i \(0.302048\pi\)
\(180\) −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
\(187\) −28.6603 −2.09585
\(188\) −23.8564 −1.73991
\(189\) 0 0
\(190\) 0 0
\(191\) −10.3923 −0.751961 −0.375980 0.926628i \(-0.622694\pi\)
−0.375980 + 0.926628i \(0.622694\pi\)
\(192\) −8.00000 −0.577350
\(193\) −7.32051 −0.526942 −0.263471 0.964667i \(-0.584867\pi\)
−0.263471 + 0.964667i \(0.584867\pi\)
\(194\) 0 0
\(195\) −18.9282 −1.35548
\(196\) 0 0
\(197\) 0.535898 0.0381812 0.0190906 0.999818i \(-0.493923\pi\)
0.0190906 + 0.999818i \(0.493923\pi\)
\(198\) 0 0
\(199\) −25.3205 −1.79492 −0.897462 0.441093i \(-0.854591\pi\)
−0.897462 + 0.441093i \(0.854591\pi\)
\(200\) 0 0
\(201\) 7.46410 0.526477
\(202\) 0 0
\(203\) 0 0
\(204\) 10.0000 0.700140
\(205\) 3.46410 0.241943
\(206\) 0 0
\(207\) 5.46410 0.379781
\(208\) −21.8564 −1.51547
\(209\) −3.07180 −0.212481
\(210\) 0 0
\(211\) 14.9282 1.02770 0.513850 0.857880i \(-0.328219\pi\)
0.513850 + 0.857880i \(0.328219\pi\)
\(212\) −21.8564 −1.50110
\(213\) 13.1962 0.904185
\(214\) 0 0
\(215\) 34.3923 2.34554
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 9.19615 0.621418
\(220\) −39.7128 −2.67744
\(221\) 27.3205 1.83778
\(222\) 0 0
\(223\) −8.53590 −0.571606 −0.285803 0.958288i \(-0.592260\pi\)
−0.285803 + 0.958288i \(0.592260\pi\)
\(224\) 0 0
\(225\) 7.00000 0.466667
\(226\) 0 0
\(227\) 0.0717968 0.00476532 0.00238266 0.999997i \(-0.499242\pi\)
0.00238266 + 0.999997i \(0.499242\pi\)
\(228\) 1.07180 0.0709815
\(229\) −8.92820 −0.589992 −0.294996 0.955498i \(-0.595318\pi\)
−0.294996 + 0.955498i \(0.595318\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −13.8564 −0.907763 −0.453882 0.891062i \(-0.649961\pi\)
−0.453882 + 0.891062i \(0.649961\pi\)
\(234\) 0 0
\(235\) 41.3205 2.69545
\(236\) −13.8564 −0.901975
\(237\) 0.928203 0.0602933
\(238\) 0 0
\(239\) −15.4641 −1.00029 −0.500145 0.865942i \(-0.666720\pi\)
−0.500145 + 0.865942i \(0.666720\pi\)
\(240\) 13.8564 0.894427
\(241\) 5.19615 0.334714 0.167357 0.985896i \(-0.446477\pi\)
0.167357 + 0.985896i \(0.446477\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) −3.46410 −0.221766
\(245\) 0 0
\(246\) 0 0
\(247\) 2.92820 0.186317
\(248\) 0 0
\(249\) −10.0000 −0.633724
\(250\) 0 0
\(251\) 7.46410 0.471130 0.235565 0.971859i \(-0.424306\pi\)
0.235565 + 0.971859i \(0.424306\pi\)
\(252\) 0 0
\(253\) 31.3205 1.96910
\(254\) 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
\(260\) 37.8564 2.34775
\(261\) −5.19615 −0.321634
\(262\) 0 0
\(263\) −20.1244 −1.24092 −0.620460 0.784238i \(-0.713054\pi\)
−0.620460 + 0.784238i \(0.713054\pi\)
\(264\) 0 0
\(265\) 37.8564 2.32550
\(266\) 0 0
\(267\) −8.92820 −0.546397
\(268\) −14.9282 −0.911885
\(269\) 17.4641 1.06481 0.532403 0.846491i \(-0.321289\pi\)
0.532403 + 0.846491i \(0.321289\pi\)
\(270\) 0 0
\(271\) −11.5885 −0.703949 −0.351974 0.936010i \(-0.614490\pi\)
−0.351974 + 0.936010i \(0.614490\pi\)
\(272\) −20.0000 −1.21268
\(273\) 0 0
\(274\) 0 0
\(275\) 40.1244 2.41959
\(276\) −10.9282 −0.657801
\(277\) −21.9282 −1.31754 −0.658769 0.752345i \(-0.728923\pi\)
−0.658769 + 0.752345i \(0.728923\pi\)
\(278\) 0 0
\(279\) −5.73205 −0.343169
\(280\) 0 0
\(281\) −0.124356 −0.00741844 −0.00370922 0.999993i \(-0.501181\pi\)
−0.00370922 + 0.999993i \(0.501181\pi\)
\(282\) 0 0
\(283\) 4.66025 0.277023 0.138512 0.990361i \(-0.455768\pi\)
0.138512 + 0.990361i \(0.455768\pi\)
\(284\) −26.3923 −1.56610
\(285\) −1.85641 −0.109964
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 8.00000 0.470588
\(290\) 0 0
\(291\) −2.39230 −0.140239
\(292\) −18.3923 −1.07633
\(293\) −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
\(297\) 5.73205 0.332607
\(298\) 0 0
\(299\) −29.8564 −1.72664
\(300\) −14.0000 −0.808290
\(301\) 0 0
\(302\) 0 0
\(303\) −18.8564 −1.08327
\(304\) −2.14359 −0.122944
\(305\) 6.00000 0.343559
\(306\) 0 0
\(307\) 14.2679 0.814315 0.407157 0.913358i \(-0.366520\pi\)
0.407157 + 0.913358i \(0.366520\pi\)
\(308\) 0 0
\(309\) 1.19615 0.0680467
\(310\) 0 0
\(311\) 25.8564 1.46618 0.733091 0.680130i \(-0.238077\pi\)
0.733091 + 0.680130i \(0.238077\pi\)
\(312\) 0 0
\(313\) 2.92820 0.165512 0.0827559 0.996570i \(-0.473628\pi\)
0.0827559 + 0.996570i \(0.473628\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) −1.85641 −0.104431
\(317\) 22.8038 1.28079 0.640396 0.768045i \(-0.278770\pi\)
0.640396 + 0.768045i \(0.278770\pi\)
\(318\) 0 0
\(319\) −29.7846 −1.66762
\(320\) −27.7128 −1.54919
\(321\) −3.46410 −0.193347
\(322\) 0 0
\(323\) 2.67949 0.149091
\(324\) −2.00000 −0.111111
\(325\) −38.2487 −2.12166
\(326\) 0 0
\(327\) 2.53590 0.140236
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 16.2487 0.893110 0.446555 0.894756i \(-0.352651\pi\)
0.446555 + 0.894756i \(0.352651\pi\)
\(332\) 20.0000 1.09764
\(333\) −1.00000 −0.0547997
\(334\) 0 0
\(335\) 25.8564 1.41269
\(336\) 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
\(341\) −32.8564 −1.77927
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 18.9282 1.01906
\(346\) 0 0
\(347\) −4.66025 −0.250176 −0.125088 0.992146i \(-0.539921\pi\)
−0.125088 + 0.992146i \(0.539921\pi\)
\(348\) 10.3923 0.557086
\(349\) 3.58846 0.192086 0.0960429 0.995377i \(-0.469381\pi\)
0.0960429 + 0.995377i \(0.469381\pi\)
\(350\) 0 0
\(351\) −5.46410 −0.291652
\(352\) 0 0
\(353\) 13.3205 0.708979 0.354490 0.935060i \(-0.384655\pi\)
0.354490 + 0.935060i \(0.384655\pi\)
\(354\) 0 0
\(355\) 45.7128 2.42618
\(356\) 17.8564 0.946388
\(357\) 0 0
\(358\) 0 0
\(359\) 31.7128 1.67374 0.836869 0.547403i \(-0.184384\pi\)
0.836869 + 0.547403i \(0.184384\pi\)
\(360\) 0 0
\(361\) −18.7128 −0.984885
\(362\) 0 0
\(363\) 21.8564 1.14716
\(364\) 0 0
\(365\) 31.8564 1.66744
\(366\) 0 0
\(367\) −15.0526 −0.785737 −0.392869 0.919595i \(-0.628517\pi\)
−0.392869 + 0.919595i \(0.628517\pi\)
\(368\) 21.8564 1.13934
\(369\) 1.00000 0.0520579
\(370\) 0 0
\(371\) 0 0
\(372\) 11.4641 0.594386
\(373\) 7.14359 0.369881 0.184941 0.982750i \(-0.440791\pi\)
0.184941 + 0.982750i \(0.440791\pi\)
\(374\) 0 0
\(375\) 6.92820 0.357771
\(376\) 0 0
\(377\) 28.3923 1.46228
\(378\) 0 0
\(379\) −24.0000 −1.23280 −0.616399 0.787434i \(-0.711409\pi\)
−0.616399 + 0.787434i \(0.711409\pi\)
\(380\) 3.71281 0.190463
\(381\) 17.8564 0.914811
\(382\) 0 0
\(383\) 35.9282 1.83585 0.917923 0.396759i \(-0.129865\pi\)
0.917923 + 0.396759i \(0.129865\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 9.92820 0.504679
\(388\) 4.78461 0.242902
\(389\) −6.78461 −0.343993 −0.171997 0.985098i \(-0.555022\pi\)
−0.171997 + 0.985098i \(0.555022\pi\)
\(390\) 0 0
\(391\) −27.3205 −1.38166
\(392\) 0 0
\(393\) 10.5359 0.531466
\(394\) 0 0
\(395\) 3.21539 0.161784
\(396\) −11.4641 −0.576093
\(397\) −17.4641 −0.876498 −0.438249 0.898854i \(-0.644401\pi\)
−0.438249 + 0.898854i \(0.644401\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 28.0000 1.40000
\(401\) −17.0718 −0.852525 −0.426262 0.904600i \(-0.640170\pi\)
−0.426262 + 0.904600i \(0.640170\pi\)
\(402\) 0 0
\(403\) 31.3205 1.56019
\(404\) 37.7128 1.87628
\(405\) 3.46410 0.172133
\(406\) 0 0
\(407\) −5.73205 −0.284127
\(408\) 0 0
\(409\) −5.73205 −0.283432 −0.141716 0.989907i \(-0.545262\pi\)
−0.141716 + 0.989907i \(0.545262\pi\)
\(410\) 0 0
\(411\) 2.80385 0.138304
\(412\) −2.39230 −0.117860
\(413\) 0 0
\(414\) 0 0
\(415\) −34.6410 −1.70046
\(416\) 0 0
\(417\) 11.4641 0.561399
\(418\) 0 0
\(419\) −31.7128 −1.54927 −0.774636 0.632407i \(-0.782067\pi\)
−0.774636 + 0.632407i \(0.782067\pi\)
\(420\) 0 0
\(421\) 25.4641 1.24104 0.620522 0.784189i \(-0.286921\pi\)
0.620522 + 0.784189i \(0.286921\pi\)
\(422\) 0 0
\(423\) 11.9282 0.579969
\(424\) 0 0
\(425\) −35.0000 −1.69775
\(426\) 0 0
\(427\) 0 0
\(428\) 6.92820 0.334887
\(429\) −31.3205 −1.51217
\(430\) 0 0
\(431\) 2.53590 0.122150 0.0610750 0.998133i \(-0.480547\pi\)
0.0610750 + 0.998133i \(0.480547\pi\)
\(432\) 4.00000 0.192450
\(433\) −31.5885 −1.51804 −0.759022 0.651065i \(-0.774323\pi\)
−0.759022 + 0.651065i \(0.774323\pi\)
\(434\) 0 0
\(435\) −18.0000 −0.863034
\(436\) −5.07180 −0.242895
\(437\) −2.92820 −0.140075
\(438\) 0 0
\(439\) −28.5359 −1.36194 −0.680972 0.732309i \(-0.738443\pi\)
−0.680972 + 0.732309i \(0.738443\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 3.60770 0.171407 0.0857034 0.996321i \(-0.472686\pi\)
0.0857034 + 0.996321i \(0.472686\pi\)
\(444\) 2.00000 0.0949158
\(445\) −30.9282 −1.46614
\(446\) 0 0
\(447\) −13.8564 −0.655386
\(448\) 0 0
\(449\) −23.3205 −1.10056 −0.550281 0.834979i \(-0.685480\pi\)
−0.550281 + 0.834979i \(0.685480\pi\)
\(450\) 0 0
\(451\) 5.73205 0.269912
\(452\) 34.6410 1.62938
\(453\) 20.3923 0.958114
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −38.6410 −1.80755 −0.903775 0.428007i \(-0.859216\pi\)
−0.903775 + 0.428007i \(0.859216\pi\)
\(458\) 0 0
\(459\) −5.00000 −0.233380
\(460\) −37.8564 −1.76506
\(461\) −24.2487 −1.12938 −0.564688 0.825305i \(-0.691003\pi\)
−0.564688 + 0.825305i \(0.691003\pi\)
\(462\) 0 0
\(463\) 8.39230 0.390023 0.195012 0.980801i \(-0.437526\pi\)
0.195012 + 0.980801i \(0.437526\pi\)
\(464\) −20.7846 −0.964901
\(465\) −19.8564 −0.920819
\(466\) 0 0
\(467\) −0.535898 −0.0247984 −0.0123992 0.999923i \(-0.503947\pi\)
−0.0123992 + 0.999923i \(0.503947\pi\)
\(468\) 10.9282 0.505156
\(469\) 0 0
\(470\) 0 0
\(471\) 10.0000 0.460776
\(472\) 0 0
\(473\) 56.9090 2.61668
\(474\) 0 0
\(475\) −3.75129 −0.172121
\(476\) 0 0
\(477\) 10.9282 0.500368
\(478\) 0 0
\(479\) 40.7128 1.86022 0.930108 0.367286i \(-0.119713\pi\)
0.930108 + 0.367286i \(0.119713\pi\)
\(480\) 0 0
\(481\) 5.46410 0.249142
\(482\) 0 0
\(483\) 0 0
\(484\) −43.7128 −1.98695
\(485\) −8.28719 −0.376302
\(486\) 0 0
\(487\) 2.07180 0.0938821 0.0469410 0.998898i \(-0.485053\pi\)
0.0469410 + 0.998898i \(0.485053\pi\)
\(488\) 0 0
\(489\) −17.9282 −0.810741
\(490\) 0 0
\(491\) 3.85641 0.174037 0.0870186 0.996207i \(-0.472266\pi\)
0.0870186 + 0.996207i \(0.472266\pi\)
\(492\) −2.00000 −0.0901670
\(493\) 25.9808 1.17011
\(494\) 0 0
\(495\) 19.8564 0.892479
\(496\) −22.9282 −1.02951
\(497\) 0 0
\(498\) 0 0
\(499\) −1.46410 −0.0655422 −0.0327711 0.999463i \(-0.510433\pi\)
−0.0327711 + 0.999463i \(0.510433\pi\)
\(500\) −13.8564 −0.619677
\(501\) 18.9282 0.845650
\(502\) 0 0
\(503\) −11.7846 −0.525450 −0.262725 0.964871i \(-0.584621\pi\)
−0.262725 + 0.964871i \(0.584621\pi\)
\(504\) 0 0
\(505\) −65.3205 −2.90672
\(506\) 0 0
\(507\) 16.8564 0.748619
\(508\) −35.7128 −1.58450
\(509\) 8.07180 0.357776 0.178888 0.983869i \(-0.442750\pi\)
0.178888 + 0.983869i \(0.442750\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −0.535898 −0.0236605
\(514\) 0 0
\(515\) 4.14359 0.182589
\(516\) −19.8564 −0.874130
\(517\) 68.3731 3.00704
\(518\) 0 0
\(519\) −7.07180 −0.310417
\(520\) 0 0
\(521\) 6.85641 0.300385 0.150192 0.988657i \(-0.452011\pi\)
0.150192 + 0.988657i \(0.452011\pi\)
\(522\) 0 0
\(523\) 31.1769 1.36327 0.681636 0.731692i \(-0.261269\pi\)
0.681636 + 0.731692i \(0.261269\pi\)
\(524\) −21.0718 −0.920526
\(525\) 0 0
\(526\) 0 0
\(527\) 28.6603 1.24846
\(528\) 22.9282 0.997822
\(529\) 6.85641 0.298105
\(530\) 0 0
\(531\) 6.92820 0.300658
\(532\) 0 0
\(533\) −5.46410 −0.236677
\(534\) 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
\(541\) 3.07180 0.132067 0.0660334 0.997817i \(-0.478966\pi\)
0.0660334 + 0.997817i \(0.478966\pi\)
\(542\) 0 0
\(543\) 20.0000 0.858282
\(544\) 0 0
\(545\) 8.78461 0.376291
\(546\) 0 0
\(547\) −32.3923 −1.38499 −0.692497 0.721420i \(-0.743490\pi\)
−0.692497 + 0.721420i \(0.743490\pi\)
\(548\) −5.60770 −0.239549
\(549\) 1.73205 0.0739221
\(550\) 0 0
\(551\) 2.78461 0.118628
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −3.46410 −0.147043
\(556\) −22.9282 −0.972372
\(557\) −34.5167 −1.46252 −0.731259 0.682100i \(-0.761067\pi\)
−0.731259 + 0.682100i \(0.761067\pi\)
\(558\) 0 0
\(559\) −54.2487 −2.29448
\(560\) 0 0
\(561\) −28.6603 −1.21004
\(562\) 0 0
\(563\) 7.92820 0.334134 0.167067 0.985946i \(-0.446570\pi\)
0.167067 + 0.985946i \(0.446570\pi\)
\(564\) −23.8564 −1.00454
\(565\) −60.0000 −2.52422
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 22.2487 0.932714 0.466357 0.884596i \(-0.345566\pi\)
0.466357 + 0.884596i \(0.345566\pi\)
\(570\) 0 0
\(571\) 21.0718 0.881827 0.440914 0.897550i \(-0.354655\pi\)
0.440914 + 0.897550i \(0.354655\pi\)
\(572\) 62.6410 2.61915
\(573\) −10.3923 −0.434145
\(574\) 0 0
\(575\) 38.2487 1.59508
\(576\) −8.00000 −0.333333
\(577\) −0.679492 −0.0282876 −0.0141438 0.999900i \(-0.504502\pi\)
−0.0141438 + 0.999900i \(0.504502\pi\)
\(578\) 0 0
\(579\) −7.32051 −0.304230
\(580\) 36.0000 1.49482
\(581\) 0 0
\(582\) 0 0
\(583\) 62.6410 2.59433
\(584\) 0 0
\(585\) −18.9282 −0.782585
\(586\) 0 0
\(587\) −28.0718 −1.15865 −0.579324 0.815098i \(-0.696683\pi\)
−0.579324 + 0.815098i \(0.696683\pi\)
\(588\) 0 0
\(589\) 3.07180 0.126571
\(590\) 0 0
\(591\) 0.535898 0.0220439
\(592\) −4.00000 −0.164399
\(593\) −12.7128 −0.522053 −0.261026 0.965332i \(-0.584061\pi\)
−0.261026 + 0.965332i \(0.584061\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 27.7128 1.13516
\(597\) −25.3205 −1.03630
\(598\) 0 0
\(599\) 40.0000 1.63436 0.817178 0.576386i \(-0.195537\pi\)
0.817178 + 0.576386i \(0.195537\pi\)
\(600\) 0 0
\(601\) −8.24871 −0.336472 −0.168236 0.985747i \(-0.553807\pi\)
−0.168236 + 0.985747i \(0.553807\pi\)
\(602\) 0 0
\(603\) 7.46410 0.303962
\(604\) −40.7846 −1.65950
\(605\) 75.7128 3.07816
\(606\) 0 0
\(607\) 4.24871 0.172450 0.0862249 0.996276i \(-0.472520\pi\)
0.0862249 + 0.996276i \(0.472520\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −65.1769 −2.63678
\(612\) 10.0000 0.404226
\(613\) 36.6410 1.47992 0.739958 0.672653i \(-0.234845\pi\)
0.739958 + 0.672653i \(0.234845\pi\)
\(614\) 0 0
\(615\) 3.46410 0.139686
\(616\) 0 0
\(617\) 7.85641 0.316287 0.158144 0.987416i \(-0.449449\pi\)
0.158144 + 0.987416i \(0.449449\pi\)
\(618\) 0 0
\(619\) 26.8038 1.07734 0.538669 0.842518i \(-0.318927\pi\)
0.538669 + 0.842518i \(0.318927\pi\)
\(620\) 39.7128 1.59490
\(621\) 5.46410 0.219267
\(622\) 0 0
\(623\) 0 0
\(624\) −21.8564 −0.874957
\(625\) −11.0000 −0.440000
\(626\) 0 0
\(627\) −3.07180 −0.122676
\(628\) −20.0000 −0.798087
\(629\) 5.00000 0.199363
\(630\) 0 0
\(631\) 13.9282 0.554473 0.277237 0.960802i \(-0.410581\pi\)
0.277237 + 0.960802i \(0.410581\pi\)
\(632\) 0 0
\(633\) 14.9282 0.593343
\(634\) 0 0
\(635\) 61.8564 2.45470
\(636\) −21.8564 −0.866663
\(637\) 0 0
\(638\) 0 0
\(639\) 13.1962 0.522032
\(640\) 0 0
\(641\) −42.5167 −1.67931 −0.839654 0.543122i \(-0.817242\pi\)
−0.839654 + 0.543122i \(0.817242\pi\)
\(642\) 0 0
\(643\) −38.2487 −1.50838 −0.754191 0.656655i \(-0.771971\pi\)
−0.754191 + 0.656655i \(0.771971\pi\)
\(644\) 0 0
\(645\) 34.3923 1.35420
\(646\) 0 0
\(647\) 2.92820 0.115120 0.0575598 0.998342i \(-0.481668\pi\)
0.0575598 + 0.998342i \(0.481668\pi\)
\(648\) 0 0
\(649\) 39.7128 1.55886
\(650\) 0 0
\(651\) 0 0
\(652\) 35.8564 1.40425
\(653\) −12.6603 −0.495434 −0.247717 0.968832i \(-0.579680\pi\)
−0.247717 + 0.968832i \(0.579680\pi\)
\(654\) 0 0
\(655\) 36.4974 1.42607
\(656\) 4.00000 0.156174
\(657\) 9.19615 0.358776
\(658\) 0 0
\(659\) −12.5359 −0.488329 −0.244165 0.969734i \(-0.578514\pi\)
−0.244165 + 0.969734i \(0.578514\pi\)
\(660\) −39.7128 −1.54582
\(661\) 30.6410 1.19180 0.595899 0.803060i \(-0.296796\pi\)
0.595899 + 0.803060i \(0.296796\pi\)
\(662\) 0 0
\(663\) 27.3205 1.06104
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −28.3923 −1.09935
\(668\) −37.8564 −1.46471
\(669\) −8.53590 −0.330017
\(670\) 0 0
\(671\) 9.92820 0.383274
\(672\) 0 0
\(673\) 15.4641 0.596097 0.298049 0.954551i \(-0.403664\pi\)
0.298049 + 0.954551i \(0.403664\pi\)
\(674\) 0 0
\(675\) 7.00000 0.269430
\(676\) −33.7128 −1.29665
\(677\) −3.85641 −0.148214 −0.0741069 0.997250i \(-0.523611\pi\)
−0.0741069 + 0.997250i \(0.523611\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0.0717968 0.00275126
\(682\) 0 0
\(683\) −12.2487 −0.468684 −0.234342 0.972154i \(-0.575294\pi\)
−0.234342 + 0.972154i \(0.575294\pi\)
\(684\) 1.07180 0.0409812
\(685\) 9.71281 0.371108
\(686\) 0 0
\(687\) −8.92820 −0.340632
\(688\) 39.7128 1.51404
\(689\) −59.7128 −2.27488
\(690\) 0 0
\(691\) −41.1769 −1.56644 −0.783222 0.621742i \(-0.786425\pi\)
−0.783222 + 0.621742i \(0.786425\pi\)
\(692\) 14.1436 0.537659
\(693\) 0 0
\(694\) 0 0
\(695\) 39.7128 1.50639
\(696\) 0 0
\(697\) −5.00000 −0.189389
\(698\) 0 0
\(699\) −13.8564 −0.524097
\(700\) 0 0
\(701\) −15.4641 −0.584071 −0.292036 0.956407i \(-0.594333\pi\)
−0.292036 + 0.956407i \(0.594333\pi\)
\(702\) 0 0
\(703\) 0.535898 0.0202118
\(704\) −45.8564 −1.72828
\(705\) 41.3205 1.55622
\(706\) 0 0
\(707\) 0 0
\(708\) −13.8564 −0.520756
\(709\) 33.3205 1.25138 0.625689 0.780073i \(-0.284818\pi\)
0.625689 + 0.780073i \(0.284818\pi\)
\(710\) 0 0
\(711\) 0.928203 0.0348103
\(712\) 0 0
\(713\) −31.3205 −1.17296
\(714\) 0 0
\(715\) −108.497 −4.05757
\(716\) −31.1769 −1.16514
\(717\) −15.4641 −0.577517
\(718\) 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
\(727\) −28.6410 −1.06224 −0.531118 0.847298i \(-0.678228\pi\)
−0.531118 + 0.847298i \(0.678228\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −49.6410 −1.83604
\(732\) −3.46410 −0.128037
\(733\) −29.9808 −1.10736 −0.553682 0.832728i \(-0.686778\pi\)
−0.553682 + 0.832728i \(0.686778\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 42.7846 1.57599
\(738\) 0 0
\(739\) 7.78461 0.286361 0.143181 0.989697i \(-0.454267\pi\)
0.143181 + 0.989697i \(0.454267\pi\)
\(740\) 6.92820 0.254686
\(741\) 2.92820 0.107570
\(742\) 0 0
\(743\) 27.4641 1.00756 0.503780 0.863832i \(-0.331942\pi\)
0.503780 + 0.863832i \(0.331942\pi\)
\(744\) 0 0
\(745\) −48.0000 −1.75858
\(746\) 0 0
\(747\) −10.0000 −0.365881
\(748\) 57.3205 2.09585
\(749\) 0 0
\(750\) 0 0
\(751\) −24.2487 −0.884848 −0.442424 0.896806i \(-0.645881\pi\)
−0.442424 + 0.896806i \(0.645881\pi\)
\(752\) 47.7128 1.73991
\(753\) 7.46410 0.272007
\(754\) 0 0
\(755\) 70.6410 2.57089
\(756\) 0 0
\(757\) 15.8564 0.576311 0.288155 0.957584i \(-0.406958\pi\)
0.288155 + 0.957584i \(0.406958\pi\)
\(758\) 0 0
\(759\) 31.3205 1.13686
\(760\) 0 0
\(761\) 10.2487 0.371515 0.185758 0.982596i \(-0.440526\pi\)
0.185758 + 0.982596i \(0.440526\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 20.7846 0.751961
\(765\) −17.3205 −0.626224
\(766\) 0 0
\(767\) −37.8564 −1.36692
\(768\) 16.0000 0.577350
\(769\) −2.80385 −0.101109 −0.0505547 0.998721i \(-0.516099\pi\)
−0.0505547 + 0.998721i \(0.516099\pi\)
\(770\) 0 0
\(771\) 3.00000 0.108042
\(772\) 14.6410 0.526942
\(773\) −3.14359 −0.113067 −0.0565336 0.998401i \(-0.518005\pi\)
−0.0565336 + 0.998401i \(0.518005\pi\)
\(774\) 0 0
\(775\) −40.1244 −1.44131
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −0.535898 −0.0192006
\(780\) 37.8564 1.35548
\(781\) 75.6410 2.70665
\(782\) 0 0
\(783\) −5.19615 −0.185695
\(784\) 0 0
\(785\) 34.6410 1.23639
\(786\) 0 0
\(787\) −26.5167 −0.945217 −0.472608 0.881273i \(-0.656687\pi\)
−0.472608 + 0.881273i \(0.656687\pi\)
\(788\) −1.07180 −0.0381812
\(789\) −20.1244 −0.716446
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −9.46410 −0.336080
\(794\) 0 0
\(795\) 37.8564 1.34263
\(796\) 50.6410 1.79492
\(797\) −19.8564 −0.703350 −0.351675 0.936122i \(-0.614388\pi\)
−0.351675 + 0.936122i \(0.614388\pi\)
\(798\) 0 0
\(799\) −59.6410 −2.10995
\(800\) 0 0
\(801\) −8.92820 −0.315463
\(802\) 0 0
\(803\) 52.7128 1.86019
\(804\) −14.9282 −0.526477
\(805\) 0 0
\(806\) 0 0
\(807\) 17.4641 0.614765
\(808\) 0 0
\(809\) −41.0718 −1.44401 −0.722004 0.691889i \(-0.756779\pi\)
−0.722004 + 0.691889i \(0.756779\pi\)
\(810\) 0 0
\(811\) −1.73205 −0.0608205 −0.0304103 0.999538i \(-0.509681\pi\)
−0.0304103 + 0.999538i \(0.509681\pi\)
\(812\) 0 0
\(813\) −11.5885 −0.406425
\(814\) 0 0
\(815\) −62.1051 −2.17545
\(816\) −20.0000 −0.700140
\(817\) −5.32051 −0.186141
\(818\) 0 0
\(819\) 0 0
\(820\) −6.92820 −0.241943
\(821\) −8.67949 −0.302916 −0.151458 0.988464i \(-0.548397\pi\)
−0.151458 + 0.988464i \(0.548397\pi\)
\(822\) 0 0
\(823\) 39.5692 1.37930 0.689648 0.724145i \(-0.257765\pi\)
0.689648 + 0.724145i \(0.257765\pi\)
\(824\) 0 0
\(825\) 40.1244 1.39695
\(826\) 0 0
\(827\) −45.1962 −1.57162 −0.785812 0.618465i \(-0.787755\pi\)
−0.785812 + 0.618465i \(0.787755\pi\)
\(828\) −10.9282 −0.379781
\(829\) 15.0526 0.522797 0.261398 0.965231i \(-0.415816\pi\)
0.261398 + 0.965231i \(0.415816\pi\)
\(830\) 0 0
\(831\) −21.9282 −0.760681
\(832\) 43.7128 1.51547
\(833\) 0 0
\(834\) 0 0
\(835\) 65.5692 2.26912
\(836\) 6.14359 0.212481
\(837\) −5.73205 −0.198129
\(838\) 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
\(843\) −0.124356 −0.00428304
\(844\) −29.8564 −1.02770
\(845\) 58.3923 2.00876
\(846\) 0 0
\(847\) 0 0
\(848\) 43.7128 1.50110
\(849\) 4.66025 0.159940
\(850\) 0 0
\(851\) −5.46410 −0.187307
\(852\) −26.3923 −0.904185
\(853\) −51.7128 −1.77061 −0.885306 0.465008i \(-0.846051\pi\)
−0.885306 + 0.465008i \(0.846051\pi\)
\(854\) 0 0
\(855\) −1.85641 −0.0634878
\(856\) 0 0
\(857\) 34.2487 1.16991 0.584957 0.811064i \(-0.301111\pi\)
0.584957 + 0.811064i \(0.301111\pi\)
\(858\) 0 0
\(859\) 2.80385 0.0956660 0.0478330 0.998855i \(-0.484768\pi\)
0.0478330 + 0.998855i \(0.484768\pi\)
\(860\) −68.7846 −2.34554
\(861\) 0 0
\(862\) 0 0
\(863\) 14.6795 0.499696 0.249848 0.968285i \(-0.419619\pi\)
0.249848 + 0.968285i \(0.419619\pi\)
\(864\) 0 0
\(865\) −24.4974 −0.832937
\(866\) 0 0
\(867\) 8.00000 0.271694
\(868\) 0 0
\(869\) 5.32051 0.180486
\(870\) 0 0
\(871\) −40.7846 −1.38193
\(872\) 0 0
\(873\) −2.39230 −0.0809673
\(874\) 0 0
\(875\) 0 0
\(876\) −18.3923 −0.621418
\(877\) 28.0718 0.947917 0.473959 0.880547i \(-0.342825\pi\)
0.473959 + 0.880547i \(0.342825\pi\)
\(878\) 0 0
\(879\) −9.00000 −0.303562
\(880\) 79.4256 2.67744
\(881\) 26.5359 0.894017 0.447009 0.894530i \(-0.352489\pi\)
0.447009 + 0.894530i \(0.352489\pi\)
\(882\) 0 0
\(883\) 39.5692 1.33161 0.665805 0.746126i \(-0.268088\pi\)
0.665805 + 0.746126i \(0.268088\pi\)
\(884\) −54.6410 −1.83778
\(885\) 24.0000 0.806751
\(886\) 0 0
\(887\) −20.8564 −0.700290 −0.350145 0.936696i \(-0.613868\pi\)
−0.350145 + 0.936696i \(0.613868\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 5.73205 0.192031
\(892\) 17.0718 0.571606
\(893\) −6.39230 −0.213910
\(894\) 0 0
\(895\) 54.0000 1.80502
\(896\) 0 0
\(897\) −29.8564 −0.996876
\(898\) 0 0
\(899\) 29.7846 0.993372
\(900\) −14.0000 −0.466667
\(901\) −54.6410 −1.82036
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 69.2820 2.30301
\(906\) 0 0
\(907\) 5.85641 0.194459 0.0972294 0.995262i \(-0.469002\pi\)
0.0972294 + 0.995262i \(0.469002\pi\)
\(908\) −0.143594 −0.00476532
\(909\) −18.8564 −0.625428
\(910\) 0 0
\(911\) −16.7846 −0.556099 −0.278049 0.960567i \(-0.589688\pi\)
−0.278049 + 0.960567i \(0.589688\pi\)
\(912\) −2.14359 −0.0709815
\(913\) −57.3205 −1.89703
\(914\) 0 0
\(915\) 6.00000 0.198354
\(916\) 17.8564 0.589992
\(917\) 0 0
\(918\) 0 0
\(919\) −25.4641 −0.839983 −0.419992 0.907528i \(-0.637967\pi\)
−0.419992 + 0.907528i \(0.637967\pi\)
\(920\) 0 0
\(921\) 14.2679 0.470145
\(922\) 0 0
\(923\) −72.1051 −2.37337
\(924\) 0 0
\(925\) −7.00000 −0.230159
\(926\) 0 0
\(927\) 1.19615 0.0392868
\(928\) 0 0
\(929\) −43.7846 −1.43653 −0.718263 0.695771i \(-0.755063\pi\)
−0.718263 + 0.695771i \(0.755063\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 27.7128 0.907763
\(933\) 25.8564 0.846501
\(934\) 0 0
\(935\) −99.2820 −3.24687
\(936\) 0 0
\(937\) 5.07180 0.165688 0.0828442 0.996563i \(-0.473600\pi\)
0.0828442 + 0.996563i \(0.473600\pi\)
\(938\) 0 0
\(939\) 2.92820 0.0955583
\(940\) −82.6410 −2.69545
\(941\) 33.3205 1.08622 0.543109 0.839662i \(-0.317247\pi\)
0.543109 + 0.839662i \(0.317247\pi\)
\(942\) 0 0
\(943\) 5.46410 0.177936
\(944\) 27.7128 0.901975
\(945\) 0 0
\(946\) 0 0
\(947\) 23.0718 0.749733 0.374866 0.927079i \(-0.377689\pi\)
0.374866 + 0.927079i \(0.377689\pi\)
\(948\) −1.85641 −0.0602933
\(949\) −50.2487 −1.63114
\(950\) 0 0
\(951\) 22.8038 0.739465
\(952\) 0 0
\(953\) −20.6795 −0.669874 −0.334937 0.942240i \(-0.608715\pi\)
−0.334937 + 0.942240i \(0.608715\pi\)
\(954\) 0 0
\(955\) −36.0000 −1.16493
\(956\) 30.9282 1.00029
\(957\) −29.7846 −0.962800
\(958\) 0 0
\(959\) 0 0
\(960\) −27.7128 −0.894427
\(961\) 1.85641 0.0598841
\(962\) 0 0
\(963\) −3.46410 −0.111629
\(964\) −10.3923 −0.334714
\(965\) −25.3590 −0.816335
\(966\) 0 0
\(967\) −36.2487 −1.16568 −0.582840 0.812587i \(-0.698059\pi\)
−0.582840 + 0.812587i \(0.698059\pi\)
\(968\) 0 0
\(969\) 2.67949 0.0860777
\(970\) 0 0
\(971\) 14.0718 0.451585 0.225793 0.974175i \(-0.427503\pi\)
0.225793 + 0.974175i \(0.427503\pi\)
\(972\) −2.00000 −0.0641500
\(973\) 0 0
\(974\) 0 0
\(975\) −38.2487 −1.22494
\(976\) 6.92820 0.221766
\(977\) 13.9808 0.447284 0.223642 0.974671i \(-0.428205\pi\)
0.223642 + 0.974671i \(0.428205\pi\)
\(978\) 0 0
\(979\) −51.1769 −1.63562
\(980\) 0 0
\(981\) 2.53590 0.0809650
\(982\) 0 0
\(983\) −14.7846 −0.471556 −0.235778 0.971807i \(-0.575764\pi\)
−0.235778 + 0.971807i \(0.575764\pi\)
\(984\) 0 0
\(985\) 1.85641 0.0591500
\(986\) 0 0
\(987\) 0 0
\(988\) −5.85641 −0.186317
\(989\) 54.2487 1.72501
\(990\) 0 0
\(991\) −24.1051 −0.765724 −0.382862 0.923805i \(-0.625062\pi\)
−0.382862 + 0.923805i \(0.625062\pi\)
\(992\) 0 0
\(993\) 16.2487 0.515637
\(994\) 0 0
\(995\) −87.7128 −2.78068
\(996\) 20.0000 0.633724
\(997\) 21.1769 0.670680 0.335340 0.942097i \(-0.391149\pi\)
0.335340 + 0.942097i \(0.391149\pi\)
\(998\) 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 \(a_p\))