Properties

Label 6004.2.a.g.1.19
Level 6004
Weight 2
Character 6004.1
Self dual Yes
Analytic conductor 47.942
Analytic rank 1
Dimension 27
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 6004 = 2^{2} \cdot 19 \cdot 79 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6004.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9421813736\)
Analytic rank: \(1\)
Dimension: \(27\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.19
Character \(\chi\) = 6004.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.21945 q^{3} +1.36200 q^{5} -2.61900 q^{7} -1.51294 q^{9} +O(q^{10})\) \(q+1.21945 q^{3} +1.36200 q^{5} -2.61900 q^{7} -1.51294 q^{9} -3.78429 q^{11} +1.85777 q^{13} +1.66089 q^{15} +2.70157 q^{17} +1.00000 q^{19} -3.19374 q^{21} +7.26110 q^{23} -3.14496 q^{25} -5.50331 q^{27} +1.91435 q^{29} +5.73815 q^{31} -4.61475 q^{33} -3.56707 q^{35} -4.70501 q^{37} +2.26546 q^{39} -10.8631 q^{41} -12.3830 q^{43} -2.06062 q^{45} +8.24286 q^{47} -0.140862 q^{49} +3.29443 q^{51} +8.29716 q^{53} -5.15419 q^{55} +1.21945 q^{57} -8.48032 q^{59} -0.427688 q^{61} +3.96238 q^{63} +2.53028 q^{65} -7.29027 q^{67} +8.85456 q^{69} -0.159689 q^{71} +2.28441 q^{73} -3.83512 q^{75} +9.91103 q^{77} -1.00000 q^{79} -2.17220 q^{81} +12.6225 q^{83} +3.67954 q^{85} +2.33446 q^{87} -12.5491 q^{89} -4.86548 q^{91} +6.99740 q^{93} +1.36200 q^{95} -14.6462 q^{97} +5.72539 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 27q - 4q^{3} - 10q^{5} - 8q^{7} + 19q^{9} + O(q^{10}) \) \( 27q - 4q^{3} - 10q^{5} - 8q^{7} + 19q^{9} + 3q^{11} - 5q^{13} - 11q^{15} - 17q^{17} + 27q^{19} - 28q^{21} - 11q^{23} + 13q^{25} - 7q^{27} - 39q^{29} - 27q^{31} - 18q^{33} - 5q^{35} - q^{37} - 22q^{39} - 36q^{41} - 2q^{43} - 18q^{45} - 12q^{47} + 15q^{49} + 4q^{51} - 28q^{53} + 5q^{55} - 4q^{57} - 30q^{59} - 6q^{61} - 4q^{63} - 32q^{65} + 13q^{67} - 27q^{69} - 59q^{71} - 30q^{73} - 21q^{75} - 39q^{77} - 27q^{79} - 5q^{81} + 4q^{83} - 3q^{85} + 22q^{87} - 56q^{89} - 8q^{91} - 38q^{93} - 10q^{95} - 30q^{97} + 31q^{99} + O(q^{100}) \)

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
\(3\) 1.21945 0.704051 0.352025 0.935991i \(-0.385493\pi\)
0.352025 + 0.935991i \(0.385493\pi\)
\(4\) 0 0
\(5\) 1.36200 0.609105 0.304552 0.952496i \(-0.401493\pi\)
0.304552 + 0.952496i \(0.401493\pi\)
\(6\) 0 0
\(7\) −2.61900 −0.989887 −0.494944 0.868925i \(-0.664811\pi\)
−0.494944 + 0.868925i \(0.664811\pi\)
\(8\) 0 0
\(9\) −1.51294 −0.504313
\(10\) 0 0
\(11\) −3.78429 −1.14100 −0.570502 0.821296i \(-0.693252\pi\)
−0.570502 + 0.821296i \(0.693252\pi\)
\(12\) 0 0
\(13\) 1.85777 0.515252 0.257626 0.966245i \(-0.417060\pi\)
0.257626 + 0.966245i \(0.417060\pi\)
\(14\) 0 0
\(15\) 1.66089 0.428840
\(16\) 0 0
\(17\) 2.70157 0.655227 0.327613 0.944812i \(-0.393756\pi\)
0.327613 + 0.944812i \(0.393756\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) −3.19374 −0.696931
\(22\) 0 0
\(23\) 7.26110 1.51404 0.757022 0.653389i \(-0.226653\pi\)
0.757022 + 0.653389i \(0.226653\pi\)
\(24\) 0 0
\(25\) −3.14496 −0.628992
\(26\) 0 0
\(27\) −5.50331 −1.05911
\(28\) 0 0
\(29\) 1.91435 0.355486 0.177743 0.984077i \(-0.443120\pi\)
0.177743 + 0.984077i \(0.443120\pi\)
\(30\) 0 0
\(31\) 5.73815 1.03060 0.515301 0.857009i \(-0.327680\pi\)
0.515301 + 0.857009i \(0.327680\pi\)
\(32\) 0 0
\(33\) −4.61475 −0.803325
\(34\) 0 0
\(35\) −3.56707 −0.602945
\(36\) 0 0
\(37\) −4.70501 −0.773500 −0.386750 0.922185i \(-0.626402\pi\)
−0.386750 + 0.922185i \(0.626402\pi\)
\(38\) 0 0
\(39\) 2.26546 0.362763
\(40\) 0 0
\(41\) −10.8631 −1.69653 −0.848267 0.529569i \(-0.822354\pi\)
−0.848267 + 0.529569i \(0.822354\pi\)
\(42\) 0 0
\(43\) −12.3830 −1.88839 −0.944195 0.329386i \(-0.893158\pi\)
−0.944195 + 0.329386i \(0.893158\pi\)
\(44\) 0 0
\(45\) −2.06062 −0.307179
\(46\) 0 0
\(47\) 8.24286 1.20234 0.601172 0.799119i \(-0.294701\pi\)
0.601172 + 0.799119i \(0.294701\pi\)
\(48\) 0 0
\(49\) −0.140862 −0.0201231
\(50\) 0 0
\(51\) 3.29443 0.461313
\(52\) 0 0
\(53\) 8.29716 1.13970 0.569851 0.821748i \(-0.307001\pi\)
0.569851 + 0.821748i \(0.307001\pi\)
\(54\) 0 0
\(55\) −5.15419 −0.694991
\(56\) 0 0
\(57\) 1.21945 0.161520
\(58\) 0 0
\(59\) −8.48032 −1.10404 −0.552022 0.833829i \(-0.686144\pi\)
−0.552022 + 0.833829i \(0.686144\pi\)
\(60\) 0 0
\(61\) −0.427688 −0.0547599 −0.0273799 0.999625i \(-0.508716\pi\)
−0.0273799 + 0.999625i \(0.508716\pi\)
\(62\) 0 0
\(63\) 3.96238 0.499213
\(64\) 0 0
\(65\) 2.53028 0.313842
\(66\) 0 0
\(67\) −7.29027 −0.890649 −0.445324 0.895369i \(-0.646912\pi\)
−0.445324 + 0.895369i \(0.646912\pi\)
\(68\) 0 0
\(69\) 8.85456 1.06596
\(70\) 0 0
\(71\) −0.159689 −0.0189516 −0.00947580 0.999955i \(-0.503016\pi\)
−0.00947580 + 0.999955i \(0.503016\pi\)
\(72\) 0 0
\(73\) 2.28441 0.267370 0.133685 0.991024i \(-0.457319\pi\)
0.133685 + 0.991024i \(0.457319\pi\)
\(74\) 0 0
\(75\) −3.83512 −0.442842
\(76\) 0 0
\(77\) 9.91103 1.12947
\(78\) 0 0
\(79\) −1.00000 −0.112509
\(80\) 0 0
\(81\) −2.17220 −0.241356
\(82\) 0 0
\(83\) 12.6225 1.38550 0.692750 0.721178i \(-0.256399\pi\)
0.692750 + 0.721178i \(0.256399\pi\)
\(84\) 0 0
\(85\) 3.67954 0.399102
\(86\) 0 0
\(87\) 2.33446 0.250280
\(88\) 0 0
\(89\) −12.5491 −1.33021 −0.665103 0.746751i \(-0.731613\pi\)
−0.665103 + 0.746751i \(0.731613\pi\)
\(90\) 0 0
\(91\) −4.86548 −0.510041
\(92\) 0 0
\(93\) 6.99740 0.725596
\(94\) 0 0
\(95\) 1.36200 0.139738
\(96\) 0 0
\(97\) −14.6462 −1.48709 −0.743547 0.668684i \(-0.766858\pi\)
−0.743547 + 0.668684i \(0.766858\pi\)
\(98\) 0 0
\(99\) 5.72539 0.575424
\(100\) 0 0
\(101\) 5.65996 0.563187 0.281593 0.959534i \(-0.409137\pi\)
0.281593 + 0.959534i \(0.409137\pi\)
\(102\) 0 0
\(103\) −13.5375 −1.33389 −0.666946 0.745106i \(-0.732399\pi\)
−0.666946 + 0.745106i \(0.732399\pi\)
\(104\) 0 0
\(105\) −4.34987 −0.424504
\(106\) 0 0
\(107\) −8.87228 −0.857715 −0.428858 0.903372i \(-0.641084\pi\)
−0.428858 + 0.903372i \(0.641084\pi\)
\(108\) 0 0
\(109\) −9.11056 −0.872634 −0.436317 0.899793i \(-0.643717\pi\)
−0.436317 + 0.899793i \(0.643717\pi\)
\(110\) 0 0
\(111\) −5.73754 −0.544583
\(112\) 0 0
\(113\) −19.9146 −1.87341 −0.936703 0.350126i \(-0.886139\pi\)
−0.936703 + 0.350126i \(0.886139\pi\)
\(114\) 0 0
\(115\) 9.88961 0.922211
\(116\) 0 0
\(117\) −2.81069 −0.259848
\(118\) 0 0
\(119\) −7.07540 −0.648601
\(120\) 0 0
\(121\) 3.32082 0.301892
\(122\) 0 0
\(123\) −13.2470 −1.19445
\(124\) 0 0
\(125\) −11.0934 −0.992226
\(126\) 0 0
\(127\) 8.55669 0.759283 0.379642 0.925134i \(-0.376047\pi\)
0.379642 + 0.925134i \(0.376047\pi\)
\(128\) 0 0
\(129\) −15.1005 −1.32952
\(130\) 0 0
\(131\) 16.2350 1.41846 0.709228 0.704980i \(-0.249044\pi\)
0.709228 + 0.704980i \(0.249044\pi\)
\(132\) 0 0
\(133\) −2.61900 −0.227096
\(134\) 0 0
\(135\) −7.49550 −0.645110
\(136\) 0 0
\(137\) −11.1743 −0.954686 −0.477343 0.878717i \(-0.658400\pi\)
−0.477343 + 0.878717i \(0.658400\pi\)
\(138\) 0 0
\(139\) −13.9349 −1.18195 −0.590973 0.806691i \(-0.701256\pi\)
−0.590973 + 0.806691i \(0.701256\pi\)
\(140\) 0 0
\(141\) 10.0518 0.846511
\(142\) 0 0
\(143\) −7.03032 −0.587905
\(144\) 0 0
\(145\) 2.60734 0.216528
\(146\) 0 0
\(147\) −0.171774 −0.0141677
\(148\) 0 0
\(149\) −21.8523 −1.79021 −0.895107 0.445852i \(-0.852901\pi\)
−0.895107 + 0.445852i \(0.852901\pi\)
\(150\) 0 0
\(151\) 5.52135 0.449321 0.224661 0.974437i \(-0.427873\pi\)
0.224661 + 0.974437i \(0.427873\pi\)
\(152\) 0 0
\(153\) −4.08731 −0.330439
\(154\) 0 0
\(155\) 7.81536 0.627745
\(156\) 0 0
\(157\) −13.8482 −1.10521 −0.552604 0.833444i \(-0.686366\pi\)
−0.552604 + 0.833444i \(0.686366\pi\)
\(158\) 0 0
\(159\) 10.1180 0.802408
\(160\) 0 0
\(161\) −19.0168 −1.49873
\(162\) 0 0
\(163\) 5.21181 0.408220 0.204110 0.978948i \(-0.434570\pi\)
0.204110 + 0.978948i \(0.434570\pi\)
\(164\) 0 0
\(165\) −6.28529 −0.489309
\(166\) 0 0
\(167\) −4.54694 −0.351853 −0.175926 0.984403i \(-0.556292\pi\)
−0.175926 + 0.984403i \(0.556292\pi\)
\(168\) 0 0
\(169\) −9.54870 −0.734516
\(170\) 0 0
\(171\) −1.51294 −0.115697
\(172\) 0 0
\(173\) −17.0432 −1.29577 −0.647885 0.761738i \(-0.724346\pi\)
−0.647885 + 0.761738i \(0.724346\pi\)
\(174\) 0 0
\(175\) 8.23663 0.622631
\(176\) 0 0
\(177\) −10.3413 −0.777303
\(178\) 0 0
\(179\) 11.7846 0.880821 0.440410 0.897797i \(-0.354833\pi\)
0.440410 + 0.897797i \(0.354833\pi\)
\(180\) 0 0
\(181\) 24.5013 1.82117 0.910583 0.413325i \(-0.135633\pi\)
0.910583 + 0.413325i \(0.135633\pi\)
\(182\) 0 0
\(183\) −0.521545 −0.0385537
\(184\) 0 0
\(185\) −6.40823 −0.471142
\(186\) 0 0
\(187\) −10.2235 −0.747617
\(188\) 0 0
\(189\) 14.4131 1.04840
\(190\) 0 0
\(191\) −3.46352 −0.250612 −0.125306 0.992118i \(-0.539991\pi\)
−0.125306 + 0.992118i \(0.539991\pi\)
\(192\) 0 0
\(193\) −13.3788 −0.963029 −0.481515 0.876438i \(-0.659913\pi\)
−0.481515 + 0.876438i \(0.659913\pi\)
\(194\) 0 0
\(195\) 3.08555 0.220961
\(196\) 0 0
\(197\) 7.98328 0.568785 0.284393 0.958708i \(-0.408208\pi\)
0.284393 + 0.958708i \(0.408208\pi\)
\(198\) 0 0
\(199\) 1.35809 0.0962722 0.0481361 0.998841i \(-0.484672\pi\)
0.0481361 + 0.998841i \(0.484672\pi\)
\(200\) 0 0
\(201\) −8.89013 −0.627062
\(202\) 0 0
\(203\) −5.01367 −0.351891
\(204\) 0 0
\(205\) −14.7956 −1.03337
\(206\) 0 0
\(207\) −10.9856 −0.763552
\(208\) 0 0
\(209\) −3.78429 −0.261764
\(210\) 0 0
\(211\) 5.30977 0.365540 0.182770 0.983156i \(-0.441494\pi\)
0.182770 + 0.983156i \(0.441494\pi\)
\(212\) 0 0
\(213\) −0.194733 −0.0133429
\(214\) 0 0
\(215\) −16.8656 −1.15023
\(216\) 0 0
\(217\) −15.0282 −1.02018
\(218\) 0 0
\(219\) 2.78573 0.188242
\(220\) 0 0
\(221\) 5.01889 0.337607
\(222\) 0 0
\(223\) 7.59874 0.508849 0.254425 0.967093i \(-0.418114\pi\)
0.254425 + 0.967093i \(0.418114\pi\)
\(224\) 0 0
\(225\) 4.75813 0.317209
\(226\) 0 0
\(227\) 13.9932 0.928764 0.464382 0.885635i \(-0.346277\pi\)
0.464382 + 0.885635i \(0.346277\pi\)
\(228\) 0 0
\(229\) 4.43286 0.292932 0.146466 0.989216i \(-0.453210\pi\)
0.146466 + 0.989216i \(0.453210\pi\)
\(230\) 0 0
\(231\) 12.0860 0.795201
\(232\) 0 0
\(233\) −14.6083 −0.957018 −0.478509 0.878083i \(-0.658823\pi\)
−0.478509 + 0.878083i \(0.658823\pi\)
\(234\) 0 0
\(235\) 11.2268 0.732354
\(236\) 0 0
\(237\) −1.21945 −0.0792119
\(238\) 0 0
\(239\) −9.23501 −0.597363 −0.298682 0.954353i \(-0.596547\pi\)
−0.298682 + 0.954353i \(0.596547\pi\)
\(240\) 0 0
\(241\) 12.7048 0.818391 0.409196 0.912447i \(-0.365809\pi\)
0.409196 + 0.912447i \(0.365809\pi\)
\(242\) 0 0
\(243\) 13.8610 0.889186
\(244\) 0 0
\(245\) −0.191854 −0.0122571
\(246\) 0 0
\(247\) 1.85777 0.118207
\(248\) 0 0
\(249\) 15.3925 0.975461
\(250\) 0 0
\(251\) −18.8283 −1.18843 −0.594217 0.804305i \(-0.702538\pi\)
−0.594217 + 0.804305i \(0.702538\pi\)
\(252\) 0 0
\(253\) −27.4781 −1.72753
\(254\) 0 0
\(255\) 4.48701 0.280988
\(256\) 0 0
\(257\) 11.4559 0.714601 0.357300 0.933989i \(-0.383697\pi\)
0.357300 + 0.933989i \(0.383697\pi\)
\(258\) 0 0
\(259\) 12.3224 0.765677
\(260\) 0 0
\(261\) −2.89629 −0.179276
\(262\) 0 0
\(263\) −14.5254 −0.895675 −0.447837 0.894115i \(-0.647806\pi\)
−0.447837 + 0.894115i \(0.647806\pi\)
\(264\) 0 0
\(265\) 11.3007 0.694198
\(266\) 0 0
\(267\) −15.3031 −0.936533
\(268\) 0 0
\(269\) 11.6789 0.712076 0.356038 0.934472i \(-0.384127\pi\)
0.356038 + 0.934472i \(0.384127\pi\)
\(270\) 0 0
\(271\) 12.1117 0.735734 0.367867 0.929878i \(-0.380088\pi\)
0.367867 + 0.929878i \(0.380088\pi\)
\(272\) 0 0
\(273\) −5.93322 −0.359095
\(274\) 0 0
\(275\) 11.9014 0.717683
\(276\) 0 0
\(277\) −5.98590 −0.359658 −0.179829 0.983698i \(-0.557554\pi\)
−0.179829 + 0.983698i \(0.557554\pi\)
\(278\) 0 0
\(279\) −8.68147 −0.519746
\(280\) 0 0
\(281\) 26.0410 1.55348 0.776739 0.629822i \(-0.216872\pi\)
0.776739 + 0.629822i \(0.216872\pi\)
\(282\) 0 0
\(283\) −3.60003 −0.213999 −0.107000 0.994259i \(-0.534124\pi\)
−0.107000 + 0.994259i \(0.534124\pi\)
\(284\) 0 0
\(285\) 1.66089 0.0983827
\(286\) 0 0
\(287\) 28.4504 1.67938
\(288\) 0 0
\(289\) −9.70152 −0.570678
\(290\) 0 0
\(291\) −17.8603 −1.04699
\(292\) 0 0
\(293\) −17.8937 −1.04536 −0.522680 0.852529i \(-0.675068\pi\)
−0.522680 + 0.852529i \(0.675068\pi\)
\(294\) 0 0
\(295\) −11.5502 −0.672478
\(296\) 0 0
\(297\) 20.8261 1.20845
\(298\) 0 0
\(299\) 13.4894 0.780114
\(300\) 0 0
\(301\) 32.4310 1.86929
\(302\) 0 0
\(303\) 6.90204 0.396512
\(304\) 0 0
\(305\) −0.582511 −0.0333545
\(306\) 0 0
\(307\) −6.87629 −0.392451 −0.196225 0.980559i \(-0.562868\pi\)
−0.196225 + 0.980559i \(0.562868\pi\)
\(308\) 0 0
\(309\) −16.5083 −0.939127
\(310\) 0 0
\(311\) 6.53075 0.370325 0.185162 0.982708i \(-0.440719\pi\)
0.185162 + 0.982708i \(0.440719\pi\)
\(312\) 0 0
\(313\) 14.5647 0.823248 0.411624 0.911354i \(-0.364962\pi\)
0.411624 + 0.911354i \(0.364962\pi\)
\(314\) 0 0
\(315\) 5.39676 0.304073
\(316\) 0 0
\(317\) 29.5927 1.66209 0.831046 0.556203i \(-0.187742\pi\)
0.831046 + 0.556203i \(0.187742\pi\)
\(318\) 0 0
\(319\) −7.24444 −0.405611
\(320\) 0 0
\(321\) −10.8193 −0.603875
\(322\) 0 0
\(323\) 2.70157 0.150319
\(324\) 0 0
\(325\) −5.84260 −0.324089
\(326\) 0 0
\(327\) −11.1099 −0.614378
\(328\) 0 0
\(329\) −21.5880 −1.19019
\(330\) 0 0
\(331\) −3.87299 −0.212879 −0.106439 0.994319i \(-0.533945\pi\)
−0.106439 + 0.994319i \(0.533945\pi\)
\(332\) 0 0
\(333\) 7.11840 0.390086
\(334\) 0 0
\(335\) −9.92935 −0.542498
\(336\) 0 0
\(337\) −4.66535 −0.254138 −0.127069 0.991894i \(-0.540557\pi\)
−0.127069 + 0.991894i \(0.540557\pi\)
\(338\) 0 0
\(339\) −24.2849 −1.31897
\(340\) 0 0
\(341\) −21.7148 −1.17592
\(342\) 0 0
\(343\) 18.7019 1.00981
\(344\) 0 0
\(345\) 12.0599 0.649283
\(346\) 0 0
\(347\) 23.6391 1.26901 0.634507 0.772917i \(-0.281203\pi\)
0.634507 + 0.772917i \(0.281203\pi\)
\(348\) 0 0
\(349\) −33.9618 −1.81794 −0.908968 0.416866i \(-0.863129\pi\)
−0.908968 + 0.416866i \(0.863129\pi\)
\(350\) 0 0
\(351\) −10.2239 −0.545709
\(352\) 0 0
\(353\) 13.2591 0.705709 0.352854 0.935678i \(-0.385211\pi\)
0.352854 + 0.935678i \(0.385211\pi\)
\(354\) 0 0
\(355\) −0.217496 −0.0115435
\(356\) 0 0
\(357\) −8.62810 −0.456648
\(358\) 0 0
\(359\) −0.700947 −0.0369946 −0.0184973 0.999829i \(-0.505888\pi\)
−0.0184973 + 0.999829i \(0.505888\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 4.04957 0.212547
\(364\) 0 0
\(365\) 3.11137 0.162856
\(366\) 0 0
\(367\) −3.59649 −0.187735 −0.0938675 0.995585i \(-0.529923\pi\)
−0.0938675 + 0.995585i \(0.529923\pi\)
\(368\) 0 0
\(369\) 16.4352 0.855584
\(370\) 0 0
\(371\) −21.7302 −1.12818
\(372\) 0 0
\(373\) 7.36913 0.381559 0.190780 0.981633i \(-0.438898\pi\)
0.190780 + 0.981633i \(0.438898\pi\)
\(374\) 0 0
\(375\) −13.5279 −0.698577
\(376\) 0 0
\(377\) 3.55641 0.183165
\(378\) 0 0
\(379\) −23.6465 −1.21464 −0.607319 0.794458i \(-0.707755\pi\)
−0.607319 + 0.794458i \(0.707755\pi\)
\(380\) 0 0
\(381\) 10.4345 0.534574
\(382\) 0 0
\(383\) −15.7699 −0.805804 −0.402902 0.915243i \(-0.631998\pi\)
−0.402902 + 0.915243i \(0.631998\pi\)
\(384\) 0 0
\(385\) 13.4988 0.687963
\(386\) 0 0
\(387\) 18.7347 0.952340
\(388\) 0 0
\(389\) 11.6307 0.589699 0.294849 0.955544i \(-0.404731\pi\)
0.294849 + 0.955544i \(0.404731\pi\)
\(390\) 0 0
\(391\) 19.6164 0.992043
\(392\) 0 0
\(393\) 19.7977 0.998664
\(394\) 0 0
\(395\) −1.36200 −0.0685296
\(396\) 0 0
\(397\) 27.2316 1.36672 0.683358 0.730084i \(-0.260519\pi\)
0.683358 + 0.730084i \(0.260519\pi\)
\(398\) 0 0
\(399\) −3.19374 −0.159887
\(400\) 0 0
\(401\) 18.2105 0.909391 0.454695 0.890647i \(-0.349748\pi\)
0.454695 + 0.890647i \(0.349748\pi\)
\(402\) 0 0
\(403\) 10.6601 0.531020
\(404\) 0 0
\(405\) −2.95854 −0.147011
\(406\) 0 0
\(407\) 17.8051 0.882567
\(408\) 0 0
\(409\) 8.91520 0.440828 0.220414 0.975406i \(-0.429259\pi\)
0.220414 + 0.975406i \(0.429259\pi\)
\(410\) 0 0
\(411\) −13.6265 −0.672147
\(412\) 0 0
\(413\) 22.2099 1.09288
\(414\) 0 0
\(415\) 17.1918 0.843914
\(416\) 0 0
\(417\) −16.9930 −0.832150
\(418\) 0 0
\(419\) −3.03648 −0.148342 −0.0741710 0.997246i \(-0.523631\pi\)
−0.0741710 + 0.997246i \(0.523631\pi\)
\(420\) 0 0
\(421\) −16.7166 −0.814717 −0.407359 0.913268i \(-0.633550\pi\)
−0.407359 + 0.913268i \(0.633550\pi\)
\(422\) 0 0
\(423\) −12.4709 −0.606358
\(424\) 0 0
\(425\) −8.49632 −0.412132
\(426\) 0 0
\(427\) 1.12011 0.0542061
\(428\) 0 0
\(429\) −8.57313 −0.413915
\(430\) 0 0
\(431\) 6.04079 0.290974 0.145487 0.989360i \(-0.453525\pi\)
0.145487 + 0.989360i \(0.453525\pi\)
\(432\) 0 0
\(433\) −7.42407 −0.356778 −0.178389 0.983960i \(-0.557089\pi\)
−0.178389 + 0.983960i \(0.557089\pi\)
\(434\) 0 0
\(435\) 3.17953 0.152447
\(436\) 0 0
\(437\) 7.26110 0.347346
\(438\) 0 0
\(439\) 20.3642 0.971931 0.485965 0.873978i \(-0.338468\pi\)
0.485965 + 0.873978i \(0.338468\pi\)
\(440\) 0 0
\(441\) 0.213115 0.0101483
\(442\) 0 0
\(443\) −7.73863 −0.367673 −0.183837 0.982957i \(-0.558852\pi\)
−0.183837 + 0.982957i \(0.558852\pi\)
\(444\) 0 0
\(445\) −17.0919 −0.810235
\(446\) 0 0
\(447\) −26.6479 −1.26040
\(448\) 0 0
\(449\) 34.4893 1.62765 0.813826 0.581109i \(-0.197381\pi\)
0.813826 + 0.581109i \(0.197381\pi\)
\(450\) 0 0
\(451\) 41.1091 1.93575
\(452\) 0 0
\(453\) 6.73302 0.316345
\(454\) 0 0
\(455\) −6.62678 −0.310668
\(456\) 0 0
\(457\) −35.5876 −1.66472 −0.832360 0.554235i \(-0.813011\pi\)
−0.832360 + 0.554235i \(0.813011\pi\)
\(458\) 0 0
\(459\) −14.8676 −0.693959
\(460\) 0 0
\(461\) −8.84719 −0.412055 −0.206027 0.978546i \(-0.566054\pi\)
−0.206027 + 0.978546i \(0.566054\pi\)
\(462\) 0 0
\(463\) 11.8800 0.552112 0.276056 0.961142i \(-0.410972\pi\)
0.276056 + 0.961142i \(0.410972\pi\)
\(464\) 0 0
\(465\) 9.53045 0.441964
\(466\) 0 0
\(467\) 20.8715 0.965819 0.482910 0.875670i \(-0.339580\pi\)
0.482910 + 0.875670i \(0.339580\pi\)
\(468\) 0 0
\(469\) 19.0932 0.881642
\(470\) 0 0
\(471\) −16.8872 −0.778123
\(472\) 0 0
\(473\) 46.8608 2.15466
\(474\) 0 0
\(475\) −3.14496 −0.144301
\(476\) 0 0
\(477\) −12.5531 −0.574766
\(478\) 0 0
\(479\) −27.8227 −1.27125 −0.635627 0.771996i \(-0.719258\pi\)
−0.635627 + 0.771996i \(0.719258\pi\)
\(480\) 0 0
\(481\) −8.74082 −0.398547
\(482\) 0 0
\(483\) −23.1901 −1.05518
\(484\) 0 0
\(485\) −19.9481 −0.905795
\(486\) 0 0
\(487\) 14.6047 0.661803 0.330902 0.943665i \(-0.392647\pi\)
0.330902 + 0.943665i \(0.392647\pi\)
\(488\) 0 0
\(489\) 6.35555 0.287408
\(490\) 0 0
\(491\) 34.4556 1.55496 0.777479 0.628908i \(-0.216498\pi\)
0.777479 + 0.628908i \(0.216498\pi\)
\(492\) 0 0
\(493\) 5.17175 0.232924
\(494\) 0 0
\(495\) 7.79798 0.350493
\(496\) 0 0
\(497\) 0.418225 0.0187599
\(498\) 0 0
\(499\) −4.14844 −0.185710 −0.0928548 0.995680i \(-0.529599\pi\)
−0.0928548 + 0.995680i \(0.529599\pi\)
\(500\) 0 0
\(501\) −5.54477 −0.247722
\(502\) 0 0
\(503\) 0.439866 0.0196126 0.00980632 0.999952i \(-0.496879\pi\)
0.00980632 + 0.999952i \(0.496879\pi\)
\(504\) 0 0
\(505\) 7.70886 0.343040
\(506\) 0 0
\(507\) −11.6442 −0.517136
\(508\) 0 0
\(509\) −31.3792 −1.39086 −0.695429 0.718595i \(-0.744786\pi\)
−0.695429 + 0.718595i \(0.744786\pi\)
\(510\) 0 0
\(511\) −5.98286 −0.264666
\(512\) 0 0
\(513\) −5.50331 −0.242977
\(514\) 0 0
\(515\) −18.4381 −0.812479
\(516\) 0 0
\(517\) −31.1933 −1.37188
\(518\) 0 0
\(519\) −20.7833 −0.912288
\(520\) 0 0
\(521\) 17.3052 0.758153 0.379076 0.925365i \(-0.376242\pi\)
0.379076 + 0.925365i \(0.376242\pi\)
\(522\) 0 0
\(523\) 4.61804 0.201933 0.100966 0.994890i \(-0.467807\pi\)
0.100966 + 0.994890i \(0.467807\pi\)
\(524\) 0 0
\(525\) 10.0442 0.438364
\(526\) 0 0
\(527\) 15.5020 0.675279
\(528\) 0 0
\(529\) 29.7236 1.29233
\(530\) 0 0
\(531\) 12.8302 0.556784
\(532\) 0 0
\(533\) −20.1811 −0.874142
\(534\) 0 0
\(535\) −12.0840 −0.522438
\(536\) 0 0
\(537\) 14.3707 0.620142
\(538\) 0 0
\(539\) 0.533061 0.0229606
\(540\) 0 0
\(541\) 18.0702 0.776899 0.388449 0.921470i \(-0.373011\pi\)
0.388449 + 0.921470i \(0.373011\pi\)
\(542\) 0 0
\(543\) 29.8781 1.28219
\(544\) 0 0
\(545\) −12.4086 −0.531525
\(546\) 0 0
\(547\) −19.3446 −0.827114 −0.413557 0.910478i \(-0.635714\pi\)
−0.413557 + 0.910478i \(0.635714\pi\)
\(548\) 0 0
\(549\) 0.647066 0.0276161
\(550\) 0 0
\(551\) 1.91435 0.0815540
\(552\) 0 0
\(553\) 2.61900 0.111371
\(554\) 0 0
\(555\) −7.81452 −0.331708
\(556\) 0 0
\(557\) −43.4593 −1.84143 −0.920714 0.390237i \(-0.872393\pi\)
−0.920714 + 0.390237i \(0.872393\pi\)
\(558\) 0 0
\(559\) −23.0047 −0.972997
\(560\) 0 0
\(561\) −12.4671 −0.526360
\(562\) 0 0
\(563\) −3.97092 −0.167354 −0.0836771 0.996493i \(-0.526666\pi\)
−0.0836771 + 0.996493i \(0.526666\pi\)
\(564\) 0 0
\(565\) −27.1236 −1.14110
\(566\) 0 0
\(567\) 5.68898 0.238915
\(568\) 0 0
\(569\) −17.6084 −0.738184 −0.369092 0.929393i \(-0.620331\pi\)
−0.369092 + 0.929393i \(0.620331\pi\)
\(570\) 0 0
\(571\) −9.73458 −0.407380 −0.203690 0.979035i \(-0.565293\pi\)
−0.203690 + 0.979035i \(0.565293\pi\)
\(572\) 0 0
\(573\) −4.22360 −0.176443
\(574\) 0 0
\(575\) −22.8359 −0.952321
\(576\) 0 0
\(577\) −1.86715 −0.0777305 −0.0388653 0.999244i \(-0.512374\pi\)
−0.0388653 + 0.999244i \(0.512374\pi\)
\(578\) 0 0
\(579\) −16.3148 −0.678021
\(580\) 0 0
\(581\) −33.0583 −1.37149
\(582\) 0 0
\(583\) −31.3988 −1.30041
\(584\) 0 0
\(585\) −3.82815 −0.158275
\(586\) 0 0
\(587\) 9.36420 0.386502 0.193251 0.981149i \(-0.438097\pi\)
0.193251 + 0.981149i \(0.438097\pi\)
\(588\) 0 0
\(589\) 5.73815 0.236436
\(590\) 0 0
\(591\) 9.73522 0.400454
\(592\) 0 0
\(593\) 0.510412 0.0209601 0.0104801 0.999945i \(-0.496664\pi\)
0.0104801 + 0.999945i \(0.496664\pi\)
\(594\) 0 0
\(595\) −9.63669 −0.395066
\(596\) 0 0
\(597\) 1.65612 0.0677805
\(598\) 0 0
\(599\) 2.11801 0.0865396 0.0432698 0.999063i \(-0.486222\pi\)
0.0432698 + 0.999063i \(0.486222\pi\)
\(600\) 0 0
\(601\) 1.74605 0.0712228 0.0356114 0.999366i \(-0.488662\pi\)
0.0356114 + 0.999366i \(0.488662\pi\)
\(602\) 0 0
\(603\) 11.0297 0.449166
\(604\) 0 0
\(605\) 4.52295 0.183884
\(606\) 0 0
\(607\) 0.971749 0.0394421 0.0197210 0.999806i \(-0.493722\pi\)
0.0197210 + 0.999806i \(0.493722\pi\)
\(608\) 0 0
\(609\) −6.11393 −0.247749
\(610\) 0 0
\(611\) 15.3133 0.619510
\(612\) 0 0
\(613\) −1.53615 −0.0620446 −0.0310223 0.999519i \(-0.509876\pi\)
−0.0310223 + 0.999519i \(0.509876\pi\)
\(614\) 0 0
\(615\) −18.0425 −0.727542
\(616\) 0 0
\(617\) −35.3033 −1.42126 −0.710630 0.703566i \(-0.751590\pi\)
−0.710630 + 0.703566i \(0.751590\pi\)
\(618\) 0 0
\(619\) 20.4109 0.820381 0.410191 0.912000i \(-0.365462\pi\)
0.410191 + 0.912000i \(0.365462\pi\)
\(620\) 0 0
\(621\) −39.9601 −1.60354
\(622\) 0 0
\(623\) 32.8662 1.31675
\(624\) 0 0
\(625\) 0.615553 0.0246221
\(626\) 0 0
\(627\) −4.61475 −0.184295
\(628\) 0 0
\(629\) −12.7109 −0.506818
\(630\) 0 0
\(631\) 39.1700 1.55933 0.779667 0.626194i \(-0.215388\pi\)
0.779667 + 0.626194i \(0.215388\pi\)
\(632\) 0 0
\(633\) 6.47501 0.257358
\(634\) 0 0
\(635\) 11.6542 0.462483
\(636\) 0 0
\(637\) −0.261688 −0.0103685
\(638\) 0 0
\(639\) 0.241600 0.00955754
\(640\) 0 0
\(641\) 16.3103 0.644218 0.322109 0.946703i \(-0.395608\pi\)
0.322109 + 0.946703i \(0.395608\pi\)
\(642\) 0 0
\(643\) −36.1924 −1.42729 −0.713644 0.700508i \(-0.752957\pi\)
−0.713644 + 0.700508i \(0.752957\pi\)
\(644\) 0 0
\(645\) −20.5668 −0.809818
\(646\) 0 0
\(647\) −29.4837 −1.15912 −0.579561 0.814929i \(-0.696776\pi\)
−0.579561 + 0.814929i \(0.696776\pi\)
\(648\) 0 0
\(649\) 32.0920 1.25972
\(650\) 0 0
\(651\) −18.3262 −0.718259
\(652\) 0 0
\(653\) 34.0928 1.33415 0.667076 0.744989i \(-0.267546\pi\)
0.667076 + 0.744989i \(0.267546\pi\)
\(654\) 0 0
\(655\) 22.1120 0.863988
\(656\) 0 0
\(657\) −3.45617 −0.134838
\(658\) 0 0
\(659\) 0.611377 0.0238159 0.0119079 0.999929i \(-0.496209\pi\)
0.0119079 + 0.999929i \(0.496209\pi\)
\(660\) 0 0
\(661\) 4.42674 0.172180 0.0860901 0.996287i \(-0.472563\pi\)
0.0860901 + 0.996287i \(0.472563\pi\)
\(662\) 0 0
\(663\) 6.12029 0.237692
\(664\) 0 0
\(665\) −3.56707 −0.138325
\(666\) 0 0
\(667\) 13.9003 0.538221
\(668\) 0 0
\(669\) 9.26630 0.358256
\(670\) 0 0
\(671\) 1.61849 0.0624813
\(672\) 0 0
\(673\) −22.0602 −0.850359 −0.425179 0.905109i \(-0.639789\pi\)
−0.425179 + 0.905109i \(0.639789\pi\)
\(674\) 0 0
\(675\) 17.3077 0.666173
\(676\) 0 0
\(677\) −44.4958 −1.71011 −0.855056 0.518535i \(-0.826478\pi\)
−0.855056 + 0.518535i \(0.826478\pi\)
\(678\) 0 0
\(679\) 38.3583 1.47205
\(680\) 0 0
\(681\) 17.0641 0.653897
\(682\) 0 0
\(683\) −24.5295 −0.938594 −0.469297 0.883040i \(-0.655493\pi\)
−0.469297 + 0.883040i \(0.655493\pi\)
\(684\) 0 0
\(685\) −15.2194 −0.581503
\(686\) 0 0
\(687\) 5.40566 0.206239
\(688\) 0 0
\(689\) 15.4142 0.587233
\(690\) 0 0
\(691\) −5.65506 −0.215129 −0.107564 0.994198i \(-0.534305\pi\)
−0.107564 + 0.994198i \(0.534305\pi\)
\(692\) 0 0
\(693\) −14.9948 −0.569604
\(694\) 0 0
\(695\) −18.9794 −0.719929
\(696\) 0 0
\(697\) −29.3475 −1.11161
\(698\) 0 0
\(699\) −17.8140 −0.673789
\(700\) 0 0
\(701\) 30.8542 1.16535 0.582674 0.812706i \(-0.302006\pi\)
0.582674 + 0.812706i \(0.302006\pi\)
\(702\) 0 0
\(703\) −4.70501 −0.177453
\(704\) 0 0
\(705\) 13.6905 0.515614
\(706\) 0 0
\(707\) −14.8234 −0.557492
\(708\) 0 0
\(709\) 6.09169 0.228778 0.114389 0.993436i \(-0.463509\pi\)
0.114389 + 0.993436i \(0.463509\pi\)
\(710\) 0 0
\(711\) 1.51294 0.0567396
\(712\) 0 0
\(713\) 41.6653 1.56038
\(714\) 0 0
\(715\) −9.57529 −0.358095
\(716\) 0 0
\(717\) −11.2616 −0.420574
\(718\) 0 0
\(719\) 14.3430 0.534905 0.267452 0.963571i \(-0.413818\pi\)
0.267452 + 0.963571i \(0.413818\pi\)
\(720\) 0 0
\(721\) 35.4547 1.32040
\(722\) 0 0
\(723\) 15.4929 0.576189
\(724\) 0 0
\(725\) −6.02055 −0.223598
\(726\) 0 0
\(727\) 18.7363 0.694891 0.347446 0.937700i \(-0.387049\pi\)
0.347446 + 0.937700i \(0.387049\pi\)
\(728\) 0 0
\(729\) 23.4195 0.867387
\(730\) 0 0
\(731\) −33.4536 −1.23732
\(732\) 0 0
\(733\) 30.1935 1.11522 0.557611 0.830102i \(-0.311718\pi\)
0.557611 + 0.830102i \(0.311718\pi\)
\(734\) 0 0
\(735\) −0.233956 −0.00862961
\(736\) 0 0
\(737\) 27.5885 1.01623
\(738\) 0 0
\(739\) 2.96383 0.109026 0.0545132 0.998513i \(-0.482639\pi\)
0.0545132 + 0.998513i \(0.482639\pi\)
\(740\) 0 0
\(741\) 2.26546 0.0832236
\(742\) 0 0
\(743\) 17.6841 0.648767 0.324383 0.945926i \(-0.394843\pi\)
0.324383 + 0.945926i \(0.394843\pi\)
\(744\) 0 0
\(745\) −29.7629 −1.09043
\(746\) 0 0
\(747\) −19.0971 −0.698725
\(748\) 0 0
\(749\) 23.2365 0.849042
\(750\) 0 0
\(751\) −8.39421 −0.306309 −0.153155 0.988202i \(-0.548943\pi\)
−0.153155 + 0.988202i \(0.548943\pi\)
\(752\) 0 0
\(753\) −22.9602 −0.836717
\(754\) 0 0
\(755\) 7.52007 0.273684
\(756\) 0 0
\(757\) 37.5428 1.36451 0.682257 0.731112i \(-0.260998\pi\)
0.682257 + 0.731112i \(0.260998\pi\)
\(758\) 0 0
\(759\) −33.5082 −1.21627
\(760\) 0 0
\(761\) −22.1452 −0.802765 −0.401382 0.915911i \(-0.631470\pi\)
−0.401382 + 0.915911i \(0.631470\pi\)
\(762\) 0 0
\(763\) 23.8605 0.863809
\(764\) 0 0
\(765\) −5.56691 −0.201272
\(766\) 0 0
\(767\) −15.7545 −0.568861
\(768\) 0 0
\(769\) 51.0082 1.83940 0.919701 0.392619i \(-0.128431\pi\)
0.919701 + 0.392619i \(0.128431\pi\)
\(770\) 0 0
\(771\) 13.9699 0.503115
\(772\) 0 0
\(773\) −20.6703 −0.743460 −0.371730 0.928341i \(-0.621235\pi\)
−0.371730 + 0.928341i \(0.621235\pi\)
\(774\) 0 0
\(775\) −18.0463 −0.648240
\(776\) 0 0
\(777\) 15.0266 0.539076
\(778\) 0 0
\(779\) −10.8631 −0.389211
\(780\) 0 0
\(781\) 0.604309 0.0216239
\(782\) 0 0
\(783\) −10.5353 −0.376499
\(784\) 0 0
\(785\) −18.8613 −0.673188
\(786\) 0 0
\(787\) −9.92806 −0.353897 −0.176948 0.984220i \(-0.556623\pi\)
−0.176948 + 0.984220i \(0.556623\pi\)
\(788\) 0 0
\(789\) −17.7130 −0.630600
\(790\) 0 0
\(791\) 52.1562 1.85446
\(792\) 0 0
\(793\) −0.794545 −0.0282151
\(794\) 0 0
\(795\) 13.7807 0.488750
\(796\) 0 0
\(797\) 21.3227 0.755288 0.377644 0.925951i \(-0.376734\pi\)
0.377644 + 0.925951i \(0.376734\pi\)
\(798\) 0 0
\(799\) 22.2687 0.787809
\(800\) 0 0
\(801\) 18.9861 0.670840
\(802\) 0 0
\(803\) −8.64487 −0.305071
\(804\) 0 0
\(805\) −25.9009 −0.912885
\(806\) 0 0
\(807\) 14.2419 0.501337
\(808\) 0 0
\(809\) 25.8046 0.907242 0.453621 0.891195i \(-0.350132\pi\)
0.453621 + 0.891195i \(0.350132\pi\)
\(810\) 0 0
\(811\) 3.73107 0.131016 0.0655078 0.997852i \(-0.479133\pi\)
0.0655078 + 0.997852i \(0.479133\pi\)
\(812\) 0 0
\(813\) 14.7696 0.517994
\(814\) 0 0
\(815\) 7.09848 0.248649
\(816\) 0 0
\(817\) −12.3830 −0.433227
\(818\) 0 0
\(819\) 7.36118 0.257220
\(820\) 0 0
\(821\) 32.6861 1.14075 0.570376 0.821384i \(-0.306798\pi\)
0.570376 + 0.821384i \(0.306798\pi\)
\(822\) 0 0
\(823\) 7.20042 0.250991 0.125495 0.992094i \(-0.459948\pi\)
0.125495 + 0.992094i \(0.459948\pi\)
\(824\) 0 0
\(825\) 14.5132 0.505285
\(826\) 0 0
\(827\) 12.4961 0.434531 0.217265 0.976113i \(-0.430286\pi\)
0.217265 + 0.976113i \(0.430286\pi\)
\(828\) 0 0
\(829\) 0.797994 0.0277155 0.0138577 0.999904i \(-0.495589\pi\)
0.0138577 + 0.999904i \(0.495589\pi\)
\(830\) 0 0
\(831\) −7.29952 −0.253217
\(832\) 0 0
\(833\) −0.380548 −0.0131852
\(834\) 0 0
\(835\) −6.19292 −0.214315
\(836\) 0 0
\(837\) −31.5788 −1.09152
\(838\) 0 0
\(839\) −32.3364 −1.11638 −0.558188 0.829714i \(-0.688503\pi\)
−0.558188 + 0.829714i \(0.688503\pi\)
\(840\) 0 0
\(841\) −25.3353 −0.873630
\(842\) 0 0
\(843\) 31.7558 1.09373
\(844\) 0 0
\(845\) −13.0053 −0.447397
\(846\) 0 0
\(847\) −8.69720 −0.298839
\(848\) 0 0
\(849\) −4.39006 −0.150666
\(850\) 0 0
\(851\) −34.1636 −1.17111
\(852\) 0 0
\(853\) −33.9277 −1.16166 −0.580831 0.814024i \(-0.697272\pi\)
−0.580831 + 0.814024i \(0.697272\pi\)
\(854\) 0 0
\(855\) −2.06062 −0.0704718
\(856\) 0 0
\(857\) −15.4278 −0.527003 −0.263501 0.964659i \(-0.584877\pi\)
−0.263501 + 0.964659i \(0.584877\pi\)
\(858\) 0 0
\(859\) −47.6354 −1.62530 −0.812649 0.582754i \(-0.801975\pi\)
−0.812649 + 0.582754i \(0.801975\pi\)
\(860\) 0 0
\(861\) 34.6939 1.18237
\(862\) 0 0
\(863\) 0.806285 0.0274463 0.0137231 0.999906i \(-0.495632\pi\)
0.0137231 + 0.999906i \(0.495632\pi\)
\(864\) 0 0
\(865\) −23.2128 −0.789259
\(866\) 0 0
\(867\) −11.8305 −0.401786
\(868\) 0 0
\(869\) 3.78429 0.128373
\(870\) 0 0
\(871\) −13.5436 −0.458908
\(872\) 0 0
\(873\) 22.1588 0.749960
\(874\) 0 0
\(875\) 29.0536 0.982192
\(876\) 0 0
\(877\) −51.0019 −1.72221 −0.861106 0.508426i \(-0.830228\pi\)
−0.861106 + 0.508426i \(0.830228\pi\)
\(878\) 0 0
\(879\) −21.8205 −0.735986
\(880\) 0 0
\(881\) −39.4980 −1.33072 −0.665362 0.746521i \(-0.731723\pi\)
−0.665362 + 0.746521i \(0.731723\pi\)
\(882\) 0 0
\(883\) 33.7284 1.13505 0.567525 0.823356i \(-0.307901\pi\)
0.567525 + 0.823356i \(0.307901\pi\)
\(884\) 0 0
\(885\) −14.0849 −0.473459
\(886\) 0 0
\(887\) 0.829776 0.0278611 0.0139306 0.999903i \(-0.495566\pi\)
0.0139306 + 0.999903i \(0.495566\pi\)
\(888\) 0 0
\(889\) −22.4099 −0.751605
\(890\) 0 0
\(891\) 8.22023 0.275388
\(892\) 0 0
\(893\) 8.24286 0.275837
\(894\) 0 0
\(895\) 16.0506 0.536512
\(896\) 0 0
\(897\) 16.4497 0.549240
\(898\) 0 0
\(899\) 10.9848 0.366365
\(900\) 0 0
\(901\) 22.4153 0.746763
\(902\) 0 0
\(903\) 39.5481 1.31608
\(904\) 0 0
\(905\) 33.3707 1.10928
\(906\) 0 0
\(907\) 16.7705 0.556856 0.278428 0.960457i \(-0.410187\pi\)
0.278428 + 0.960457i \(0.410187\pi\)
\(908\) 0 0
\(909\) −8.56317 −0.284022
\(910\) 0 0
\(911\) −29.3158 −0.971275 −0.485638 0.874160i \(-0.661413\pi\)
−0.485638 + 0.874160i \(0.661413\pi\)
\(912\) 0 0
\(913\) −47.7671 −1.58086
\(914\) 0 0
\(915\) −0.710344 −0.0234832
\(916\) 0 0
\(917\) −42.5193 −1.40411
\(918\) 0 0
\(919\) 36.8420 1.21530 0.607652 0.794203i \(-0.292111\pi\)
0.607652 + 0.794203i \(0.292111\pi\)
\(920\) 0 0
\(921\) −8.38530 −0.276305
\(922\) 0 0
\(923\) −0.296665 −0.00976484
\(924\) 0 0
\(925\) 14.7971 0.486525
\(926\) 0 0
\(927\) 20.4814 0.672699
\(928\) 0 0
\(929\) −53.9870 −1.77126 −0.885628 0.464396i \(-0.846271\pi\)
−0.885628 + 0.464396i \(0.846271\pi\)
\(930\) 0 0
\(931\) −0.140862 −0.00461656
\(932\) 0 0
\(933\) 7.96393 0.260727
\(934\) 0 0
\(935\) −13.9244 −0.455377
\(936\) 0 0
\(937\) 12.8031 0.418260 0.209130 0.977888i \(-0.432937\pi\)
0.209130 + 0.977888i \(0.432937\pi\)
\(938\) 0 0
\(939\) 17.7610 0.579608
\(940\) 0 0
\(941\) 16.5443 0.539327 0.269664 0.962955i \(-0.413087\pi\)
0.269664 + 0.962955i \(0.413087\pi\)
\(942\) 0 0
\(943\) −78.8782 −2.56863
\(944\) 0 0
\(945\) 19.6307 0.638586
\(946\) 0 0
\(947\) 51.9125 1.68693 0.843465 0.537184i \(-0.180512\pi\)
0.843465 + 0.537184i \(0.180512\pi\)
\(948\) 0 0
\(949\) 4.24390 0.137763
\(950\) 0 0
\(951\) 36.0869 1.17020
\(952\) 0 0
\(953\) 19.3129 0.625605 0.312803 0.949818i \(-0.398732\pi\)
0.312803 + 0.949818i \(0.398732\pi\)
\(954\) 0 0
\(955\) −4.71732 −0.152649
\(956\) 0 0
\(957\) −8.83425 −0.285571
\(958\) 0 0
\(959\) 29.2655 0.945031
\(960\) 0 0
\(961\) 1.92640 0.0621419
\(962\) 0 0
\(963\) 13.4232 0.432557
\(964\) 0 0
\(965\) −18.2220 −0.586586
\(966\) 0 0
\(967\) −23.1426 −0.744215 −0.372107 0.928190i \(-0.621365\pi\)
−0.372107 + 0.928190i \(0.621365\pi\)
\(968\) 0 0
\(969\) 3.29443 0.105832
\(970\) 0 0
\(971\) 34.8990 1.11996 0.559981 0.828505i \(-0.310808\pi\)
0.559981 + 0.828505i \(0.310808\pi\)
\(972\) 0 0
\(973\) 36.4956 1.16999
\(974\) 0 0
\(975\) −7.12476 −0.228175
\(976\) 0 0
\(977\) 28.4296 0.909545 0.454772 0.890608i \(-0.349721\pi\)
0.454772 + 0.890608i \(0.349721\pi\)
\(978\) 0 0
\(979\) 47.4896 1.51777
\(980\) 0 0
\(981\) 13.7837 0.440080
\(982\) 0 0
\(983\) 10.6863 0.340839 0.170419 0.985372i \(-0.445488\pi\)
0.170419 + 0.985372i \(0.445488\pi\)
\(984\) 0 0
\(985\) 10.8732 0.346450
\(986\) 0 0
\(987\) −26.3255 −0.837951
\(988\) 0 0
\(989\) −89.9143 −2.85911
\(990\) 0 0
\(991\) −5.47077 −0.173785 −0.0868924 0.996218i \(-0.527694\pi\)
−0.0868924 + 0.996218i \(0.527694\pi\)
\(992\) 0 0
\(993\) −4.72293 −0.149878
\(994\) 0 0
\(995\) 1.84971 0.0586398
\(996\) 0 0
\(997\) 55.1101 1.74536 0.872678 0.488296i \(-0.162381\pi\)
0.872678 + 0.488296i \(0.162381\pi\)
\(998\) 0 0
\(999\) 25.8931 0.819223
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 \(a_p\))