Properties

Label 6004.2.a.g.1.7
Level 6004
Weight 2
Character 6004.1
Self dual Yes
Analytic conductor 47.942
Analytic rank 1
Dimension 27
CM No

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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 1.7
Character \(\chi\) = 6004.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.94547 q^{3} -1.68966 q^{5} -1.54452 q^{7} +0.784840 q^{9} +O(q^{10})\) \(q-1.94547 q^{3} -1.68966 q^{5} -1.54452 q^{7} +0.784840 q^{9} -2.23286 q^{11} -1.94704 q^{13} +3.28718 q^{15} -2.28556 q^{17} +1.00000 q^{19} +3.00481 q^{21} +0.628320 q^{23} -2.14505 q^{25} +4.30952 q^{27} +9.85349 q^{29} +8.81551 q^{31} +4.34395 q^{33} +2.60971 q^{35} -2.52622 q^{37} +3.78791 q^{39} +8.82145 q^{41} -2.39479 q^{43} -1.32611 q^{45} -1.22440 q^{47} -4.61447 q^{49} +4.44649 q^{51} +5.98586 q^{53} +3.77277 q^{55} -1.94547 q^{57} -8.90536 q^{59} -0.227978 q^{61} -1.21220 q^{63} +3.28984 q^{65} +10.6449 q^{67} -1.22238 q^{69} -11.5083 q^{71} +10.5499 q^{73} +4.17311 q^{75} +3.44869 q^{77} -1.00000 q^{79} -10.7385 q^{81} +11.1289 q^{83} +3.86183 q^{85} -19.1696 q^{87} +0.0896524 q^{89} +3.00724 q^{91} -17.1503 q^{93} -1.68966 q^{95} -6.86913 q^{97} -1.75244 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 27q - 4q^{3} - 10q^{5} - 8q^{7} + 19q^{9} + O(q^{10}) \) \( 27q - 4q^{3} - 10q^{5} - 8q^{7} + 19q^{9} + 3q^{11} - 5q^{13} - 11q^{15} - 17q^{17} + 27q^{19} - 28q^{21} - 11q^{23} + 13q^{25} - 7q^{27} - 39q^{29} - 27q^{31} - 18q^{33} - 5q^{35} - q^{37} - 22q^{39} - 36q^{41} - 2q^{43} - 18q^{45} - 12q^{47} + 15q^{49} + 4q^{51} - 28q^{53} + 5q^{55} - 4q^{57} - 30q^{59} - 6q^{61} - 4q^{63} - 32q^{65} + 13q^{67} - 27q^{69} - 59q^{71} - 30q^{73} - 21q^{75} - 39q^{77} - 27q^{79} - 5q^{81} + 4q^{83} - 3q^{85} + 22q^{87} - 56q^{89} - 8q^{91} - 38q^{93} - 10q^{95} - 30q^{97} + 31q^{99} + O(q^{100}) \)

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
\(3\) −1.94547 −1.12322 −0.561608 0.827404i \(-0.689817\pi\)
−0.561608 + 0.827404i \(0.689817\pi\)
\(4\) 0 0
\(5\) −1.68966 −0.755639 −0.377820 0.925879i \(-0.623326\pi\)
−0.377820 + 0.925879i \(0.623326\pi\)
\(6\) 0 0
\(7\) −1.54452 −0.583773 −0.291886 0.956453i \(-0.594283\pi\)
−0.291886 + 0.956453i \(0.594283\pi\)
\(8\) 0 0
\(9\) 0.784840 0.261613
\(10\) 0 0
\(11\) −2.23286 −0.673232 −0.336616 0.941642i \(-0.609282\pi\)
−0.336616 + 0.941642i \(0.609282\pi\)
\(12\) 0 0
\(13\) −1.94704 −0.540012 −0.270006 0.962859i \(-0.587026\pi\)
−0.270006 + 0.962859i \(0.587026\pi\)
\(14\) 0 0
\(15\) 3.28718 0.848746
\(16\) 0 0
\(17\) −2.28556 −0.554331 −0.277165 0.960822i \(-0.589395\pi\)
−0.277165 + 0.960822i \(0.589395\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) 3.00481 0.655702
\(22\) 0 0
\(23\) 0.628320 0.131014 0.0655069 0.997852i \(-0.479134\pi\)
0.0655069 + 0.997852i \(0.479134\pi\)
\(24\) 0 0
\(25\) −2.14505 −0.429009
\(26\) 0 0
\(27\) 4.30952 0.829367
\(28\) 0 0
\(29\) 9.85349 1.82975 0.914874 0.403740i \(-0.132290\pi\)
0.914874 + 0.403740i \(0.132290\pi\)
\(30\) 0 0
\(31\) 8.81551 1.58331 0.791656 0.610967i \(-0.209219\pi\)
0.791656 + 0.610967i \(0.209219\pi\)
\(32\) 0 0
\(33\) 4.34395 0.756185
\(34\) 0 0
\(35\) 2.60971 0.441122
\(36\) 0 0
\(37\) −2.52622 −0.415309 −0.207654 0.978202i \(-0.566583\pi\)
−0.207654 + 0.978202i \(0.566583\pi\)
\(38\) 0 0
\(39\) 3.78791 0.606550
\(40\) 0 0
\(41\) 8.82145 1.37768 0.688840 0.724914i \(-0.258120\pi\)
0.688840 + 0.724914i \(0.258120\pi\)
\(42\) 0 0
\(43\) −2.39479 −0.365203 −0.182601 0.983187i \(-0.558452\pi\)
−0.182601 + 0.983187i \(0.558452\pi\)
\(44\) 0 0
\(45\) −1.32611 −0.197685
\(46\) 0 0
\(47\) −1.22440 −0.178597 −0.0892986 0.996005i \(-0.528463\pi\)
−0.0892986 + 0.996005i \(0.528463\pi\)
\(48\) 0 0
\(49\) −4.61447 −0.659210
\(50\) 0 0
\(51\) 4.44649 0.622633
\(52\) 0 0
\(53\) 5.98586 0.822221 0.411111 0.911585i \(-0.365141\pi\)
0.411111 + 0.911585i \(0.365141\pi\)
\(54\) 0 0
\(55\) 3.77277 0.508721
\(56\) 0 0
\(57\) −1.94547 −0.257683
\(58\) 0 0
\(59\) −8.90536 −1.15938 −0.579690 0.814837i \(-0.696826\pi\)
−0.579690 + 0.814837i \(0.696826\pi\)
\(60\) 0 0
\(61\) −0.227978 −0.0291896 −0.0145948 0.999893i \(-0.504646\pi\)
−0.0145948 + 0.999893i \(0.504646\pi\)
\(62\) 0 0
\(63\) −1.21220 −0.152723
\(64\) 0 0
\(65\) 3.28984 0.408055
\(66\) 0 0
\(67\) 10.6449 1.30048 0.650239 0.759729i \(-0.274669\pi\)
0.650239 + 0.759729i \(0.274669\pi\)
\(68\) 0 0
\(69\) −1.22238 −0.147157
\(70\) 0 0
\(71\) −11.5083 −1.36579 −0.682894 0.730517i \(-0.739279\pi\)
−0.682894 + 0.730517i \(0.739279\pi\)
\(72\) 0 0
\(73\) 10.5499 1.23477 0.617384 0.786662i \(-0.288192\pi\)
0.617384 + 0.786662i \(0.288192\pi\)
\(74\) 0 0
\(75\) 4.17311 0.481870
\(76\) 0 0
\(77\) 3.44869 0.393014
\(78\) 0 0
\(79\) −1.00000 −0.112509
\(80\) 0 0
\(81\) −10.7385 −1.19317
\(82\) 0 0
\(83\) 11.1289 1.22155 0.610777 0.791802i \(-0.290857\pi\)
0.610777 + 0.791802i \(0.290857\pi\)
\(84\) 0 0
\(85\) 3.86183 0.418874
\(86\) 0 0
\(87\) −19.1696 −2.05520
\(88\) 0 0
\(89\) 0.0896524 0.00950313 0.00475157 0.999989i \(-0.498488\pi\)
0.00475157 + 0.999989i \(0.498488\pi\)
\(90\) 0 0
\(91\) 3.00724 0.315244
\(92\) 0 0
\(93\) −17.1503 −1.77840
\(94\) 0 0
\(95\) −1.68966 −0.173356
\(96\) 0 0
\(97\) −6.86913 −0.697455 −0.348727 0.937224i \(-0.613386\pi\)
−0.348727 + 0.937224i \(0.613386\pi\)
\(98\) 0 0
\(99\) −1.75244 −0.176127
\(100\) 0 0
\(101\) −19.5738 −1.94767 −0.973834 0.227261i \(-0.927023\pi\)
−0.973834 + 0.227261i \(0.927023\pi\)
\(102\) 0 0
\(103\) −2.97112 −0.292753 −0.146377 0.989229i \(-0.546761\pi\)
−0.146377 + 0.989229i \(0.546761\pi\)
\(104\) 0 0
\(105\) −5.07710 −0.495475
\(106\) 0 0
\(107\) 4.77671 0.461782 0.230891 0.972980i \(-0.425836\pi\)
0.230891 + 0.972980i \(0.425836\pi\)
\(108\) 0 0
\(109\) 9.04370 0.866230 0.433115 0.901339i \(-0.357414\pi\)
0.433115 + 0.901339i \(0.357414\pi\)
\(110\) 0 0
\(111\) 4.91469 0.466481
\(112\) 0 0
\(113\) 9.42838 0.886947 0.443474 0.896287i \(-0.353746\pi\)
0.443474 + 0.896287i \(0.353746\pi\)
\(114\) 0 0
\(115\) −1.06165 −0.0989992
\(116\) 0 0
\(117\) −1.52812 −0.141274
\(118\) 0 0
\(119\) 3.53009 0.323603
\(120\) 0 0
\(121\) −6.01434 −0.546759
\(122\) 0 0
\(123\) −17.1618 −1.54743
\(124\) 0 0
\(125\) 12.0727 1.07982
\(126\) 0 0
\(127\) 10.2289 0.907667 0.453834 0.891086i \(-0.350056\pi\)
0.453834 + 0.891086i \(0.350056\pi\)
\(128\) 0 0
\(129\) 4.65899 0.410201
\(130\) 0 0
\(131\) −1.42246 −0.124281 −0.0621406 0.998067i \(-0.519793\pi\)
−0.0621406 + 0.998067i \(0.519793\pi\)
\(132\) 0 0
\(133\) −1.54452 −0.133927
\(134\) 0 0
\(135\) −7.28163 −0.626703
\(136\) 0 0
\(137\) −6.43714 −0.549962 −0.274981 0.961450i \(-0.588672\pi\)
−0.274981 + 0.961450i \(0.588672\pi\)
\(138\) 0 0
\(139\) −18.9811 −1.60996 −0.804978 0.593304i \(-0.797823\pi\)
−0.804978 + 0.593304i \(0.797823\pi\)
\(140\) 0 0
\(141\) 2.38203 0.200603
\(142\) 0 0
\(143\) 4.34747 0.363554
\(144\) 0 0
\(145\) −16.6491 −1.38263
\(146\) 0 0
\(147\) 8.97729 0.740435
\(148\) 0 0
\(149\) −18.7653 −1.53731 −0.768657 0.639661i \(-0.779075\pi\)
−0.768657 + 0.639661i \(0.779075\pi\)
\(150\) 0 0
\(151\) 1.69858 0.138228 0.0691141 0.997609i \(-0.477983\pi\)
0.0691141 + 0.997609i \(0.477983\pi\)
\(152\) 0 0
\(153\) −1.79380 −0.145020
\(154\) 0 0
\(155\) −14.8952 −1.19641
\(156\) 0 0
\(157\) −1.35957 −0.108506 −0.0542529 0.998527i \(-0.517278\pi\)
−0.0542529 + 0.998527i \(0.517278\pi\)
\(158\) 0 0
\(159\) −11.6453 −0.923532
\(160\) 0 0
\(161\) −0.970451 −0.0764823
\(162\) 0 0
\(163\) 10.2339 0.801583 0.400791 0.916169i \(-0.368735\pi\)
0.400791 + 0.916169i \(0.368735\pi\)
\(164\) 0 0
\(165\) −7.33981 −0.571403
\(166\) 0 0
\(167\) 23.7932 1.84117 0.920587 0.390538i \(-0.127711\pi\)
0.920587 + 0.390538i \(0.127711\pi\)
\(168\) 0 0
\(169\) −9.20903 −0.708387
\(170\) 0 0
\(171\) 0.784840 0.0600182
\(172\) 0 0
\(173\) 4.59167 0.349098 0.174549 0.984648i \(-0.444153\pi\)
0.174549 + 0.984648i \(0.444153\pi\)
\(174\) 0 0
\(175\) 3.31306 0.250444
\(176\) 0 0
\(177\) 17.3251 1.30223
\(178\) 0 0
\(179\) 18.5661 1.38770 0.693849 0.720120i \(-0.255913\pi\)
0.693849 + 0.720120i \(0.255913\pi\)
\(180\) 0 0
\(181\) −5.19440 −0.386096 −0.193048 0.981189i \(-0.561837\pi\)
−0.193048 + 0.981189i \(0.561837\pi\)
\(182\) 0 0
\(183\) 0.443524 0.0327863
\(184\) 0 0
\(185\) 4.26846 0.313824
\(186\) 0 0
\(187\) 5.10334 0.373193
\(188\) 0 0
\(189\) −6.65613 −0.484162
\(190\) 0 0
\(191\) 16.9035 1.22309 0.611546 0.791209i \(-0.290548\pi\)
0.611546 + 0.791209i \(0.290548\pi\)
\(192\) 0 0
\(193\) 9.36408 0.674041 0.337021 0.941497i \(-0.390581\pi\)
0.337021 + 0.941497i \(0.390581\pi\)
\(194\) 0 0
\(195\) −6.40028 −0.458333
\(196\) 0 0
\(197\) 5.78091 0.411873 0.205936 0.978565i \(-0.433976\pi\)
0.205936 + 0.978565i \(0.433976\pi\)
\(198\) 0 0
\(199\) 8.99799 0.637851 0.318925 0.947780i \(-0.396678\pi\)
0.318925 + 0.947780i \(0.396678\pi\)
\(200\) 0 0
\(201\) −20.7093 −1.46072
\(202\) 0 0
\(203\) −15.2189 −1.06816
\(204\) 0 0
\(205\) −14.9053 −1.04103
\(206\) 0 0
\(207\) 0.493131 0.0342750
\(208\) 0 0
\(209\) −2.23286 −0.154450
\(210\) 0 0
\(211\) 12.7868 0.880281 0.440141 0.897929i \(-0.354929\pi\)
0.440141 + 0.897929i \(0.354929\pi\)
\(212\) 0 0
\(213\) 22.3891 1.53408
\(214\) 0 0
\(215\) 4.04639 0.275961
\(216\) 0 0
\(217\) −13.6157 −0.924294
\(218\) 0 0
\(219\) −20.5244 −1.38691
\(220\) 0 0
\(221\) 4.45009 0.299345
\(222\) 0 0
\(223\) 16.2912 1.09094 0.545469 0.838131i \(-0.316352\pi\)
0.545469 + 0.838131i \(0.316352\pi\)
\(224\) 0 0
\(225\) −1.68352 −0.112235
\(226\) 0 0
\(227\) −15.2508 −1.01223 −0.506116 0.862465i \(-0.668919\pi\)
−0.506116 + 0.862465i \(0.668919\pi\)
\(228\) 0 0
\(229\) 6.04728 0.399616 0.199808 0.979835i \(-0.435968\pi\)
0.199808 + 0.979835i \(0.435968\pi\)
\(230\) 0 0
\(231\) −6.70931 −0.441440
\(232\) 0 0
\(233\) −25.5034 −1.67078 −0.835390 0.549657i \(-0.814758\pi\)
−0.835390 + 0.549657i \(0.814758\pi\)
\(234\) 0 0
\(235\) 2.06882 0.134955
\(236\) 0 0
\(237\) 1.94547 0.126372
\(238\) 0 0
\(239\) −27.0987 −1.75287 −0.876435 0.481520i \(-0.840085\pi\)
−0.876435 + 0.481520i \(0.840085\pi\)
\(240\) 0 0
\(241\) −20.2881 −1.30687 −0.653437 0.756981i \(-0.726673\pi\)
−0.653437 + 0.756981i \(0.726673\pi\)
\(242\) 0 0
\(243\) 7.96293 0.510822
\(244\) 0 0
\(245\) 7.79689 0.498125
\(246\) 0 0
\(247\) −1.94704 −0.123887
\(248\) 0 0
\(249\) −21.6509 −1.37207
\(250\) 0 0
\(251\) −16.6565 −1.05135 −0.525674 0.850686i \(-0.676187\pi\)
−0.525674 + 0.850686i \(0.676187\pi\)
\(252\) 0 0
\(253\) −1.40295 −0.0882027
\(254\) 0 0
\(255\) −7.51306 −0.470486
\(256\) 0 0
\(257\) −10.5528 −0.658264 −0.329132 0.944284i \(-0.606756\pi\)
−0.329132 + 0.944284i \(0.606756\pi\)
\(258\) 0 0
\(259\) 3.90180 0.242446
\(260\) 0 0
\(261\) 7.73342 0.478687
\(262\) 0 0
\(263\) −15.7219 −0.969453 −0.484727 0.874666i \(-0.661081\pi\)
−0.484727 + 0.874666i \(0.661081\pi\)
\(264\) 0 0
\(265\) −10.1141 −0.621303
\(266\) 0 0
\(267\) −0.174416 −0.0106741
\(268\) 0 0
\(269\) −15.8377 −0.965644 −0.482822 0.875719i \(-0.660388\pi\)
−0.482822 + 0.875719i \(0.660388\pi\)
\(270\) 0 0
\(271\) −19.3871 −1.17768 −0.588841 0.808249i \(-0.700416\pi\)
−0.588841 + 0.808249i \(0.700416\pi\)
\(272\) 0 0
\(273\) −5.85048 −0.354087
\(274\) 0 0
\(275\) 4.78958 0.288823
\(276\) 0 0
\(277\) −14.1338 −0.849219 −0.424610 0.905377i \(-0.639589\pi\)
−0.424610 + 0.905377i \(0.639589\pi\)
\(278\) 0 0
\(279\) 6.91877 0.414216
\(280\) 0 0
\(281\) −31.7341 −1.89310 −0.946549 0.322559i \(-0.895457\pi\)
−0.946549 + 0.322559i \(0.895457\pi\)
\(282\) 0 0
\(283\) 21.2319 1.26210 0.631052 0.775740i \(-0.282623\pi\)
0.631052 + 0.775740i \(0.282623\pi\)
\(284\) 0 0
\(285\) 3.28718 0.194716
\(286\) 0 0
\(287\) −13.6249 −0.804252
\(288\) 0 0
\(289\) −11.7762 −0.692718
\(290\) 0 0
\(291\) 13.3637 0.783392
\(292\) 0 0
\(293\) 11.2583 0.657715 0.328857 0.944380i \(-0.393336\pi\)
0.328857 + 0.944380i \(0.393336\pi\)
\(294\) 0 0
\(295\) 15.0470 0.876073
\(296\) 0 0
\(297\) −9.62255 −0.558357
\(298\) 0 0
\(299\) −1.22337 −0.0707491
\(300\) 0 0
\(301\) 3.69880 0.213195
\(302\) 0 0
\(303\) 38.0802 2.18765
\(304\) 0 0
\(305\) 0.385206 0.0220568
\(306\) 0 0
\(307\) 14.3753 0.820442 0.410221 0.911986i \(-0.365452\pi\)
0.410221 + 0.911986i \(0.365452\pi\)
\(308\) 0 0
\(309\) 5.78021 0.328825
\(310\) 0 0
\(311\) 19.5755 1.11002 0.555011 0.831843i \(-0.312714\pi\)
0.555011 + 0.831843i \(0.312714\pi\)
\(312\) 0 0
\(313\) −17.0882 −0.965883 −0.482942 0.875652i \(-0.660432\pi\)
−0.482942 + 0.875652i \(0.660432\pi\)
\(314\) 0 0
\(315\) 2.04821 0.115403
\(316\) 0 0
\(317\) −5.37892 −0.302110 −0.151055 0.988525i \(-0.548267\pi\)
−0.151055 + 0.988525i \(0.548267\pi\)
\(318\) 0 0
\(319\) −22.0015 −1.23184
\(320\) 0 0
\(321\) −9.29293 −0.518681
\(322\) 0 0
\(323\) −2.28556 −0.127172
\(324\) 0 0
\(325\) 4.17649 0.231670
\(326\) 0 0
\(327\) −17.5942 −0.972963
\(328\) 0 0
\(329\) 1.89111 0.104260
\(330\) 0 0
\(331\) −6.89404 −0.378931 −0.189465 0.981887i \(-0.560675\pi\)
−0.189465 + 0.981887i \(0.560675\pi\)
\(332\) 0 0
\(333\) −1.98268 −0.108650
\(334\) 0 0
\(335\) −17.9862 −0.982693
\(336\) 0 0
\(337\) 16.8477 0.917751 0.458876 0.888500i \(-0.348252\pi\)
0.458876 + 0.888500i \(0.348252\pi\)
\(338\) 0 0
\(339\) −18.3426 −0.996233
\(340\) 0 0
\(341\) −19.6838 −1.06594
\(342\) 0 0
\(343\) 17.9387 0.968601
\(344\) 0 0
\(345\) 2.06540 0.111197
\(346\) 0 0
\(347\) −0.878020 −0.0471346 −0.0235673 0.999722i \(-0.507502\pi\)
−0.0235673 + 0.999722i \(0.507502\pi\)
\(348\) 0 0
\(349\) 16.5273 0.884685 0.442342 0.896846i \(-0.354148\pi\)
0.442342 + 0.896846i \(0.354148\pi\)
\(350\) 0 0
\(351\) −8.39082 −0.447869
\(352\) 0 0
\(353\) −16.6844 −0.888020 −0.444010 0.896022i \(-0.646444\pi\)
−0.444010 + 0.896022i \(0.646444\pi\)
\(354\) 0 0
\(355\) 19.4452 1.03204
\(356\) 0 0
\(357\) −6.86768 −0.363476
\(358\) 0 0
\(359\) −22.3069 −1.17732 −0.588658 0.808382i \(-0.700343\pi\)
−0.588658 + 0.808382i \(0.700343\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 11.7007 0.614128
\(364\) 0 0
\(365\) −17.8257 −0.933040
\(366\) 0 0
\(367\) −2.87588 −0.150120 −0.0750598 0.997179i \(-0.523915\pi\)
−0.0750598 + 0.997179i \(0.523915\pi\)
\(368\) 0 0
\(369\) 6.92343 0.360420
\(370\) 0 0
\(371\) −9.24526 −0.479990
\(372\) 0 0
\(373\) −7.25843 −0.375827 −0.187914 0.982186i \(-0.560172\pi\)
−0.187914 + 0.982186i \(0.560172\pi\)
\(374\) 0 0
\(375\) −23.4870 −1.21287
\(376\) 0 0
\(377\) −19.1852 −0.988086
\(378\) 0 0
\(379\) 12.9269 0.664011 0.332005 0.943278i \(-0.392275\pi\)
0.332005 + 0.943278i \(0.392275\pi\)
\(380\) 0 0
\(381\) −19.9000 −1.01951
\(382\) 0 0
\(383\) −28.3525 −1.44874 −0.724372 0.689409i \(-0.757870\pi\)
−0.724372 + 0.689409i \(0.757870\pi\)
\(384\) 0 0
\(385\) −5.82711 −0.296977
\(386\) 0 0
\(387\) −1.87953 −0.0955419
\(388\) 0 0
\(389\) 24.0792 1.22086 0.610431 0.792069i \(-0.290996\pi\)
0.610431 + 0.792069i \(0.290996\pi\)
\(390\) 0 0
\(391\) −1.43607 −0.0726250
\(392\) 0 0
\(393\) 2.76735 0.139595
\(394\) 0 0
\(395\) 1.68966 0.0850161
\(396\) 0 0
\(397\) −8.21626 −0.412362 −0.206181 0.978514i \(-0.566104\pi\)
−0.206181 + 0.978514i \(0.566104\pi\)
\(398\) 0 0
\(399\) 3.00481 0.150428
\(400\) 0 0
\(401\) −13.3379 −0.666065 −0.333032 0.942915i \(-0.608072\pi\)
−0.333032 + 0.942915i \(0.608072\pi\)
\(402\) 0 0
\(403\) −17.1642 −0.855008
\(404\) 0 0
\(405\) 18.1445 0.901608
\(406\) 0 0
\(407\) 5.64070 0.279599
\(408\) 0 0
\(409\) 22.1978 1.09761 0.548805 0.835950i \(-0.315083\pi\)
0.548805 + 0.835950i \(0.315083\pi\)
\(410\) 0 0
\(411\) 12.5232 0.617726
\(412\) 0 0
\(413\) 13.7545 0.676814
\(414\) 0 0
\(415\) −18.8041 −0.923055
\(416\) 0 0
\(417\) 36.9271 1.80833
\(418\) 0 0
\(419\) −3.89237 −0.190155 −0.0950774 0.995470i \(-0.530310\pi\)
−0.0950774 + 0.995470i \(0.530310\pi\)
\(420\) 0 0
\(421\) 1.31264 0.0639741 0.0319870 0.999488i \(-0.489816\pi\)
0.0319870 + 0.999488i \(0.489816\pi\)
\(422\) 0 0
\(423\) −0.960959 −0.0467234
\(424\) 0 0
\(425\) 4.90264 0.237813
\(426\) 0 0
\(427\) 0.352116 0.0170401
\(428\) 0 0
\(429\) −8.45786 −0.408349
\(430\) 0 0
\(431\) −0.429092 −0.0206686 −0.0103343 0.999947i \(-0.503290\pi\)
−0.0103343 + 0.999947i \(0.503290\pi\)
\(432\) 0 0
\(433\) −21.4872 −1.03261 −0.516303 0.856406i \(-0.672692\pi\)
−0.516303 + 0.856406i \(0.672692\pi\)
\(434\) 0 0
\(435\) 32.3902 1.55299
\(436\) 0 0
\(437\) 0.628320 0.0300566
\(438\) 0 0
\(439\) 26.2766 1.25411 0.627057 0.778973i \(-0.284259\pi\)
0.627057 + 0.778973i \(0.284259\pi\)
\(440\) 0 0
\(441\) −3.62162 −0.172458
\(442\) 0 0
\(443\) 4.58447 0.217815 0.108907 0.994052i \(-0.465265\pi\)
0.108907 + 0.994052i \(0.465265\pi\)
\(444\) 0 0
\(445\) −0.151482 −0.00718094
\(446\) 0 0
\(447\) 36.5073 1.72673
\(448\) 0 0
\(449\) −39.8035 −1.87844 −0.939222 0.343310i \(-0.888452\pi\)
−0.939222 + 0.343310i \(0.888452\pi\)
\(450\) 0 0
\(451\) −19.6971 −0.927498
\(452\) 0 0
\(453\) −3.30452 −0.155260
\(454\) 0 0
\(455\) −5.08122 −0.238211
\(456\) 0 0
\(457\) −16.2471 −0.760006 −0.380003 0.924985i \(-0.624077\pi\)
−0.380003 + 0.924985i \(0.624077\pi\)
\(458\) 0 0
\(459\) −9.84968 −0.459744
\(460\) 0 0
\(461\) 5.66095 0.263657 0.131828 0.991273i \(-0.457915\pi\)
0.131828 + 0.991273i \(0.457915\pi\)
\(462\) 0 0
\(463\) −15.9993 −0.743550 −0.371775 0.928323i \(-0.621251\pi\)
−0.371775 + 0.928323i \(0.621251\pi\)
\(464\) 0 0
\(465\) 28.9782 1.34383
\(466\) 0 0
\(467\) −38.9373 −1.80180 −0.900902 0.434022i \(-0.857094\pi\)
−0.900902 + 0.434022i \(0.857094\pi\)
\(468\) 0 0
\(469\) −16.4412 −0.759184
\(470\) 0 0
\(471\) 2.64501 0.121875
\(472\) 0 0
\(473\) 5.34724 0.245866
\(474\) 0 0
\(475\) −2.14505 −0.0984214
\(476\) 0 0
\(477\) 4.69795 0.215104
\(478\) 0 0
\(479\) 21.3865 0.977175 0.488588 0.872515i \(-0.337512\pi\)
0.488588 + 0.872515i \(0.337512\pi\)
\(480\) 0 0
\(481\) 4.91867 0.224272
\(482\) 0 0
\(483\) 1.88798 0.0859061
\(484\) 0 0
\(485\) 11.6065 0.527024
\(486\) 0 0
\(487\) 15.0325 0.681185 0.340593 0.940211i \(-0.389372\pi\)
0.340593 + 0.940211i \(0.389372\pi\)
\(488\) 0 0
\(489\) −19.9098 −0.900351
\(490\) 0 0
\(491\) −4.71053 −0.212583 −0.106292 0.994335i \(-0.533898\pi\)
−0.106292 + 0.994335i \(0.533898\pi\)
\(492\) 0 0
\(493\) −22.5208 −1.01429
\(494\) 0 0
\(495\) 2.96102 0.133088
\(496\) 0 0
\(497\) 17.7748 0.797310
\(498\) 0 0
\(499\) 39.0601 1.74857 0.874286 0.485411i \(-0.161330\pi\)
0.874286 + 0.485411i \(0.161330\pi\)
\(500\) 0 0
\(501\) −46.2889 −2.06804
\(502\) 0 0
\(503\) −17.2588 −0.769533 −0.384766 0.923014i \(-0.625718\pi\)
−0.384766 + 0.923014i \(0.625718\pi\)
\(504\) 0 0
\(505\) 33.0731 1.47173
\(506\) 0 0
\(507\) 17.9159 0.795671
\(508\) 0 0
\(509\) −2.59053 −0.114823 −0.0574116 0.998351i \(-0.518285\pi\)
−0.0574116 + 0.998351i \(0.518285\pi\)
\(510\) 0 0
\(511\) −16.2945 −0.720824
\(512\) 0 0
\(513\) 4.30952 0.190270
\(514\) 0 0
\(515\) 5.02018 0.221216
\(516\) 0 0
\(517\) 2.73391 0.120237
\(518\) 0 0
\(519\) −8.93293 −0.392112
\(520\) 0 0
\(521\) 4.33931 0.190109 0.0950543 0.995472i \(-0.469698\pi\)
0.0950543 + 0.995472i \(0.469698\pi\)
\(522\) 0 0
\(523\) 44.4972 1.94573 0.972863 0.231382i \(-0.0743247\pi\)
0.972863 + 0.231382i \(0.0743247\pi\)
\(524\) 0 0
\(525\) −6.44545 −0.281302
\(526\) 0 0
\(527\) −20.1484 −0.877679
\(528\) 0 0
\(529\) −22.6052 −0.982835
\(530\) 0 0
\(531\) −6.98929 −0.303309
\(532\) 0 0
\(533\) −17.1757 −0.743964
\(534\) 0 0
\(535\) −8.07102 −0.348941
\(536\) 0 0
\(537\) −36.1198 −1.55868
\(538\) 0 0
\(539\) 10.3035 0.443801
\(540\) 0 0
\(541\) −36.8530 −1.58443 −0.792217 0.610239i \(-0.791073\pi\)
−0.792217 + 0.610239i \(0.791073\pi\)
\(542\) 0 0
\(543\) 10.1055 0.433670
\(544\) 0 0
\(545\) −15.2808 −0.654557
\(546\) 0 0
\(547\) 19.0232 0.813371 0.406686 0.913568i \(-0.366684\pi\)
0.406686 + 0.913568i \(0.366684\pi\)
\(548\) 0 0
\(549\) −0.178927 −0.00763640
\(550\) 0 0
\(551\) 9.85349 0.419773
\(552\) 0 0
\(553\) 1.54452 0.0656795
\(554\) 0 0
\(555\) −8.30415 −0.352492
\(556\) 0 0
\(557\) 5.76386 0.244223 0.122111 0.992516i \(-0.461033\pi\)
0.122111 + 0.992516i \(0.461033\pi\)
\(558\) 0 0
\(559\) 4.66276 0.197214
\(560\) 0 0
\(561\) −9.92838 −0.419176
\(562\) 0 0
\(563\) 11.1413 0.469551 0.234776 0.972050i \(-0.424564\pi\)
0.234776 + 0.972050i \(0.424564\pi\)
\(564\) 0 0
\(565\) −15.9308 −0.670212
\(566\) 0 0
\(567\) 16.5859 0.696541
\(568\) 0 0
\(569\) −9.34362 −0.391705 −0.195852 0.980633i \(-0.562747\pi\)
−0.195852 + 0.980633i \(0.562747\pi\)
\(570\) 0 0
\(571\) −24.4434 −1.02292 −0.511462 0.859306i \(-0.670896\pi\)
−0.511462 + 0.859306i \(0.670896\pi\)
\(572\) 0 0
\(573\) −32.8851 −1.37380
\(574\) 0 0
\(575\) −1.34778 −0.0562061
\(576\) 0 0
\(577\) 31.9054 1.32824 0.664119 0.747627i \(-0.268807\pi\)
0.664119 + 0.747627i \(0.268807\pi\)
\(578\) 0 0
\(579\) −18.2175 −0.757094
\(580\) 0 0
\(581\) −17.1888 −0.713110
\(582\) 0 0
\(583\) −13.3656 −0.553546
\(584\) 0 0
\(585\) 2.58200 0.106753
\(586\) 0 0
\(587\) 16.8863 0.696974 0.348487 0.937314i \(-0.386696\pi\)
0.348487 + 0.937314i \(0.386696\pi\)
\(588\) 0 0
\(589\) 8.81551 0.363237
\(590\) 0 0
\(591\) −11.2466 −0.462622
\(592\) 0 0
\(593\) 27.6755 1.13650 0.568248 0.822857i \(-0.307621\pi\)
0.568248 + 0.822857i \(0.307621\pi\)
\(594\) 0 0
\(595\) −5.96466 −0.244527
\(596\) 0 0
\(597\) −17.5053 −0.716444
\(598\) 0 0
\(599\) −4.44481 −0.181610 −0.0908050 0.995869i \(-0.528944\pi\)
−0.0908050 + 0.995869i \(0.528944\pi\)
\(600\) 0 0
\(601\) −22.4815 −0.917039 −0.458519 0.888684i \(-0.651620\pi\)
−0.458519 + 0.888684i \(0.651620\pi\)
\(602\) 0 0
\(603\) 8.35453 0.340223
\(604\) 0 0
\(605\) 10.1622 0.413152
\(606\) 0 0
\(607\) −36.9989 −1.50174 −0.750869 0.660451i \(-0.770365\pi\)
−0.750869 + 0.660451i \(0.770365\pi\)
\(608\) 0 0
\(609\) 29.6078 1.19977
\(610\) 0 0
\(611\) 2.38396 0.0964447
\(612\) 0 0
\(613\) 41.5150 1.67677 0.838387 0.545075i \(-0.183499\pi\)
0.838387 + 0.545075i \(0.183499\pi\)
\(614\) 0 0
\(615\) 28.9977 1.16930
\(616\) 0 0
\(617\) 38.1286 1.53500 0.767499 0.641050i \(-0.221501\pi\)
0.767499 + 0.641050i \(0.221501\pi\)
\(618\) 0 0
\(619\) −43.5820 −1.75171 −0.875854 0.482575i \(-0.839701\pi\)
−0.875854 + 0.482575i \(0.839701\pi\)
\(620\) 0 0
\(621\) 2.70776 0.108659
\(622\) 0 0
\(623\) −0.138470 −0.00554767
\(624\) 0 0
\(625\) −9.67355 −0.386942
\(626\) 0 0
\(627\) 4.34395 0.173481
\(628\) 0 0
\(629\) 5.77385 0.230218
\(630\) 0 0
\(631\) 16.4660 0.655503 0.327751 0.944764i \(-0.393709\pi\)
0.327751 + 0.944764i \(0.393709\pi\)
\(632\) 0 0
\(633\) −24.8763 −0.988746
\(634\) 0 0
\(635\) −17.2834 −0.685869
\(636\) 0 0
\(637\) 8.98456 0.355981
\(638\) 0 0
\(639\) −9.03221 −0.357309
\(640\) 0 0
\(641\) −26.2420 −1.03650 −0.518249 0.855230i \(-0.673416\pi\)
−0.518249 + 0.855230i \(0.673416\pi\)
\(642\) 0 0
\(643\) −23.0795 −0.910169 −0.455084 0.890448i \(-0.650391\pi\)
−0.455084 + 0.890448i \(0.650391\pi\)
\(644\) 0 0
\(645\) −7.87212 −0.309964
\(646\) 0 0
\(647\) 38.9237 1.53025 0.765124 0.643883i \(-0.222677\pi\)
0.765124 + 0.643883i \(0.222677\pi\)
\(648\) 0 0
\(649\) 19.8844 0.780531
\(650\) 0 0
\(651\) 26.4889 1.03818
\(652\) 0 0
\(653\) −27.3366 −1.06976 −0.534882 0.844927i \(-0.679644\pi\)
−0.534882 + 0.844927i \(0.679644\pi\)
\(654\) 0 0
\(655\) 2.40348 0.0939118
\(656\) 0 0
\(657\) 8.27996 0.323032
\(658\) 0 0
\(659\) −14.0685 −0.548031 −0.274015 0.961725i \(-0.588352\pi\)
−0.274015 + 0.961725i \(0.588352\pi\)
\(660\) 0 0
\(661\) 0.0153979 0.000598911 0 0.000299455 1.00000i \(-0.499905\pi\)
0.000299455 1.00000i \(0.499905\pi\)
\(662\) 0 0
\(663\) −8.65750 −0.336229
\(664\) 0 0
\(665\) 2.60971 0.101200
\(666\) 0 0
\(667\) 6.19115 0.239722
\(668\) 0 0
\(669\) −31.6939 −1.22536
\(670\) 0 0
\(671\) 0.509043 0.0196514
\(672\) 0 0
\(673\) 12.6003 0.485705 0.242853 0.970063i \(-0.421917\pi\)
0.242853 + 0.970063i \(0.421917\pi\)
\(674\) 0 0
\(675\) −9.24412 −0.355806
\(676\) 0 0
\(677\) 46.5166 1.78778 0.893890 0.448287i \(-0.147966\pi\)
0.893890 + 0.448287i \(0.147966\pi\)
\(678\) 0 0
\(679\) 10.6095 0.407155
\(680\) 0 0
\(681\) 29.6699 1.13695
\(682\) 0 0
\(683\) 2.26070 0.0865034 0.0432517 0.999064i \(-0.486228\pi\)
0.0432517 + 0.999064i \(0.486228\pi\)
\(684\) 0 0
\(685\) 10.8766 0.415573
\(686\) 0 0
\(687\) −11.7648 −0.448855
\(688\) 0 0
\(689\) −11.6547 −0.444010
\(690\) 0 0
\(691\) 47.6231 1.81167 0.905834 0.423634i \(-0.139246\pi\)
0.905834 + 0.423634i \(0.139246\pi\)
\(692\) 0 0
\(693\) 2.70667 0.102818
\(694\) 0 0
\(695\) 32.0716 1.21655
\(696\) 0 0
\(697\) −20.1620 −0.763690
\(698\) 0 0
\(699\) 49.6159 1.87665
\(700\) 0 0
\(701\) −3.00884 −0.113642 −0.0568212 0.998384i \(-0.518096\pi\)
−0.0568212 + 0.998384i \(0.518096\pi\)
\(702\) 0 0
\(703\) −2.52622 −0.0952784
\(704\) 0 0
\(705\) −4.02483 −0.151584
\(706\) 0 0
\(707\) 30.2321 1.13700
\(708\) 0 0
\(709\) 44.3215 1.66453 0.832264 0.554380i \(-0.187044\pi\)
0.832264 + 0.554380i \(0.187044\pi\)
\(710\) 0 0
\(711\) −0.784840 −0.0294338
\(712\) 0 0
\(713\) 5.53896 0.207436
\(714\) 0 0
\(715\) −7.34575 −0.274715
\(716\) 0 0
\(717\) 52.7197 1.96885
\(718\) 0 0
\(719\) −34.7352 −1.29541 −0.647703 0.761893i \(-0.724270\pi\)
−0.647703 + 0.761893i \(0.724270\pi\)
\(720\) 0 0
\(721\) 4.58894 0.170901
\(722\) 0 0
\(723\) 39.4699 1.46790
\(724\) 0 0
\(725\) −21.1362 −0.784978
\(726\) 0 0
\(727\) −43.8591 −1.62665 −0.813323 0.581813i \(-0.802344\pi\)
−0.813323 + 0.581813i \(0.802344\pi\)
\(728\) 0 0
\(729\) 16.7240 0.619409
\(730\) 0 0
\(731\) 5.47345 0.202443
\(732\) 0 0
\(733\) −20.9794 −0.774890 −0.387445 0.921893i \(-0.626642\pi\)
−0.387445 + 0.921893i \(0.626642\pi\)
\(734\) 0 0
\(735\) −15.1686 −0.559502
\(736\) 0 0
\(737\) −23.7685 −0.875524
\(738\) 0 0
\(739\) −11.0946 −0.408121 −0.204060 0.978958i \(-0.565414\pi\)
−0.204060 + 0.978958i \(0.565414\pi\)
\(740\) 0 0
\(741\) 3.78791 0.139152
\(742\) 0 0
\(743\) −48.3365 −1.77329 −0.886646 0.462448i \(-0.846971\pi\)
−0.886646 + 0.462448i \(0.846971\pi\)
\(744\) 0 0
\(745\) 31.7070 1.16165
\(746\) 0 0
\(747\) 8.73440 0.319575
\(748\) 0 0
\(749\) −7.37771 −0.269576
\(750\) 0 0
\(751\) 5.57879 0.203573 0.101786 0.994806i \(-0.467544\pi\)
0.101786 + 0.994806i \(0.467544\pi\)
\(752\) 0 0
\(753\) 32.4047 1.18089
\(754\) 0 0
\(755\) −2.87002 −0.104451
\(756\) 0 0
\(757\) −29.6358 −1.07713 −0.538565 0.842584i \(-0.681034\pi\)
−0.538565 + 0.842584i \(0.681034\pi\)
\(758\) 0 0
\(759\) 2.72939 0.0990707
\(760\) 0 0
\(761\) 24.3976 0.884412 0.442206 0.896913i \(-0.354196\pi\)
0.442206 + 0.896913i \(0.354196\pi\)
\(762\) 0 0
\(763\) −13.9682 −0.505681
\(764\) 0 0
\(765\) 3.03092 0.109583
\(766\) 0 0
\(767\) 17.3391 0.626079
\(768\) 0 0
\(769\) −29.1113 −1.04978 −0.524891 0.851170i \(-0.675894\pi\)
−0.524891 + 0.851170i \(0.675894\pi\)
\(770\) 0 0
\(771\) 20.5301 0.739372
\(772\) 0 0
\(773\) −24.6129 −0.885266 −0.442633 0.896703i \(-0.645955\pi\)
−0.442633 + 0.896703i \(0.645955\pi\)
\(774\) 0 0
\(775\) −18.9097 −0.679256
\(776\) 0 0
\(777\) −7.59082 −0.272319
\(778\) 0 0
\(779\) 8.82145 0.316061
\(780\) 0 0
\(781\) 25.6965 0.919493
\(782\) 0 0
\(783\) 42.4638 1.51753
\(784\) 0 0
\(785\) 2.29722 0.0819913
\(786\) 0 0
\(787\) 23.2216 0.827760 0.413880 0.910331i \(-0.364173\pi\)
0.413880 + 0.910331i \(0.364173\pi\)
\(788\) 0 0
\(789\) 30.5864 1.08891
\(790\) 0 0
\(791\) −14.5623 −0.517775
\(792\) 0 0
\(793\) 0.443883 0.0157628
\(794\) 0 0
\(795\) 19.6766 0.697857
\(796\) 0 0
\(797\) −28.1051 −0.995535 −0.497768 0.867310i \(-0.665847\pi\)
−0.497768 + 0.867310i \(0.665847\pi\)
\(798\) 0 0
\(799\) 2.79845 0.0990019
\(800\) 0 0
\(801\) 0.0703628 0.00248615
\(802\) 0 0
\(803\) −23.5564 −0.831286
\(804\) 0 0
\(805\) 1.63973 0.0577930
\(806\) 0 0
\(807\) 30.8118 1.08463
\(808\) 0 0
\(809\) −2.22258 −0.0781419 −0.0390709 0.999236i \(-0.512440\pi\)
−0.0390709 + 0.999236i \(0.512440\pi\)
\(810\) 0 0
\(811\) −5.34496 −0.187687 −0.0938435 0.995587i \(-0.529915\pi\)
−0.0938435 + 0.995587i \(0.529915\pi\)
\(812\) 0 0
\(813\) 37.7169 1.32279
\(814\) 0 0
\(815\) −17.2919 −0.605708
\(816\) 0 0
\(817\) −2.39479 −0.0837832
\(818\) 0 0
\(819\) 2.36020 0.0824722
\(820\) 0 0
\(821\) −8.49136 −0.296351 −0.148175 0.988961i \(-0.547340\pi\)
−0.148175 + 0.988961i \(0.547340\pi\)
\(822\) 0 0
\(823\) −49.2158 −1.71555 −0.857777 0.514022i \(-0.828155\pi\)
−0.857777 + 0.514022i \(0.828155\pi\)
\(824\) 0 0
\(825\) −9.31797 −0.324410
\(826\) 0 0
\(827\) 32.5404 1.13154 0.565770 0.824563i \(-0.308579\pi\)
0.565770 + 0.824563i \(0.308579\pi\)
\(828\) 0 0
\(829\) −11.2391 −0.390349 −0.195175 0.980769i \(-0.562527\pi\)
−0.195175 + 0.980769i \(0.562527\pi\)
\(830\) 0 0
\(831\) 27.4969 0.953856
\(832\) 0 0
\(833\) 10.5467 0.365420
\(834\) 0 0
\(835\) −40.2025 −1.39126
\(836\) 0 0
\(837\) 37.9906 1.31315
\(838\) 0 0
\(839\) 6.38218 0.220337 0.110169 0.993913i \(-0.464861\pi\)
0.110169 + 0.993913i \(0.464861\pi\)
\(840\) 0 0
\(841\) 68.0913 2.34798
\(842\) 0 0
\(843\) 61.7377 2.12636
\(844\) 0 0
\(845\) 15.5601 0.535285
\(846\) 0 0
\(847\) 9.28926 0.319183
\(848\) 0 0
\(849\) −41.3059 −1.41762
\(850\) 0 0
\(851\) −1.58728 −0.0544112
\(852\) 0 0
\(853\) 43.2401 1.48051 0.740257 0.672324i \(-0.234704\pi\)
0.740257 + 0.672324i \(0.234704\pi\)
\(854\) 0 0
\(855\) −1.32611 −0.0453521
\(856\) 0 0
\(857\) 24.2471 0.828264 0.414132 0.910217i \(-0.364085\pi\)
0.414132 + 0.910217i \(0.364085\pi\)
\(858\) 0 0
\(859\) 36.6247 1.24962 0.624809 0.780778i \(-0.285177\pi\)
0.624809 + 0.780778i \(0.285177\pi\)
\(860\) 0 0
\(861\) 26.5068 0.903348
\(862\) 0 0
\(863\) −2.93754 −0.0999951 −0.0499976 0.998749i \(-0.515921\pi\)
−0.0499976 + 0.998749i \(0.515921\pi\)
\(864\) 0 0
\(865\) −7.75836 −0.263792
\(866\) 0 0
\(867\) 22.9102 0.778071
\(868\) 0 0
\(869\) 2.23286 0.0757445
\(870\) 0 0
\(871\) −20.7260 −0.702274
\(872\) 0 0
\(873\) −5.39117 −0.182464
\(874\) 0 0
\(875\) −18.6465 −0.630367
\(876\) 0 0
\(877\) −53.4490 −1.80485 −0.902423 0.430852i \(-0.858213\pi\)
−0.902423 + 0.430852i \(0.858213\pi\)
\(878\) 0 0
\(879\) −21.9026 −0.738755
\(880\) 0 0
\(881\) −20.6903 −0.697074 −0.348537 0.937295i \(-0.613321\pi\)
−0.348537 + 0.937295i \(0.613321\pi\)
\(882\) 0 0
\(883\) −9.44494 −0.317848 −0.158924 0.987291i \(-0.550802\pi\)
−0.158924 + 0.987291i \(0.550802\pi\)
\(884\) 0 0
\(885\) −29.2735 −0.984018
\(886\) 0 0
\(887\) −17.7502 −0.595993 −0.297997 0.954567i \(-0.596318\pi\)
−0.297997 + 0.954567i \(0.596318\pi\)
\(888\) 0 0
\(889\) −15.7987 −0.529871
\(890\) 0 0
\(891\) 23.9777 0.803282
\(892\) 0 0
\(893\) −1.22440 −0.0409730
\(894\) 0 0
\(895\) −31.3705 −1.04860
\(896\) 0 0
\(897\) 2.38002 0.0794665
\(898\) 0 0
\(899\) 86.8636 2.89706
\(900\) 0 0
\(901\) −13.6811 −0.455782
\(902\) 0 0
\(903\) −7.19589 −0.239464
\(904\) 0 0
\(905\) 8.77677 0.291750
\(906\) 0 0
\(907\) −37.7606 −1.25382 −0.626911 0.779091i \(-0.715681\pi\)
−0.626911 + 0.779091i \(0.715681\pi\)
\(908\) 0 0
\(909\) −15.3623 −0.509536
\(910\) 0 0
\(911\) 41.5142 1.37543 0.687714 0.725982i \(-0.258614\pi\)
0.687714 + 0.725982i \(0.258614\pi\)
\(912\) 0 0
\(913\) −24.8492 −0.822390
\(914\) 0 0
\(915\) −0.749406 −0.0247746
\(916\) 0 0
\(917\) 2.19702 0.0725519
\(918\) 0 0
\(919\) 14.3875 0.474598 0.237299 0.971437i \(-0.423738\pi\)
0.237299 + 0.971437i \(0.423738\pi\)
\(920\) 0 0
\(921\) −27.9667 −0.921533
\(922\) 0 0
\(923\) 22.4072 0.737543
\(924\) 0 0
\(925\) 5.41887 0.178171
\(926\) 0 0
\(927\) −2.33185 −0.0765881
\(928\) 0 0
\(929\) −56.6503 −1.85864 −0.929319 0.369279i \(-0.879605\pi\)
−0.929319 + 0.369279i \(0.879605\pi\)
\(930\) 0 0
\(931\) −4.61447 −0.151233
\(932\) 0 0
\(933\) −38.0834 −1.24679
\(934\) 0 0
\(935\) −8.62292 −0.281999
\(936\) 0 0
\(937\) 48.7060 1.59116 0.795578 0.605851i \(-0.207167\pi\)
0.795578 + 0.605851i \(0.207167\pi\)
\(938\) 0 0
\(939\) 33.2446 1.08490
\(940\) 0 0
\(941\) 23.3910 0.762525 0.381263 0.924467i \(-0.375489\pi\)
0.381263 + 0.924467i \(0.375489\pi\)
\(942\) 0 0
\(943\) 5.54270 0.180495
\(944\) 0 0
\(945\) 11.2466 0.365852
\(946\) 0 0
\(947\) 27.9401 0.907932 0.453966 0.891019i \(-0.350009\pi\)
0.453966 + 0.891019i \(0.350009\pi\)
\(948\) 0 0
\(949\) −20.5410 −0.666790
\(950\) 0 0
\(951\) 10.4645 0.339335
\(952\) 0 0
\(953\) −39.6415 −1.28412 −0.642058 0.766656i \(-0.721919\pi\)
−0.642058 + 0.766656i \(0.721919\pi\)
\(954\) 0 0
\(955\) −28.5611 −0.924216
\(956\) 0 0
\(957\) 42.8031 1.38363
\(958\) 0 0
\(959\) 9.94228 0.321053
\(960\) 0 0
\(961\) 46.7132 1.50688
\(962\) 0 0
\(963\) 3.74895 0.120808
\(964\) 0 0
\(965\) −15.8221 −0.509332
\(966\) 0 0
\(967\) −13.5629 −0.436155 −0.218077 0.975931i \(-0.569979\pi\)
−0.218077 + 0.975931i \(0.569979\pi\)
\(968\) 0 0
\(969\) 4.44649 0.142842
\(970\) 0 0
\(971\) 12.6345 0.405461 0.202730 0.979235i \(-0.435019\pi\)
0.202730 + 0.979235i \(0.435019\pi\)
\(972\) 0 0
\(973\) 29.3166 0.939848
\(974\) 0 0
\(975\) −8.12523 −0.260216
\(976\) 0 0
\(977\) −29.4667 −0.942725 −0.471362 0.881940i \(-0.656238\pi\)
−0.471362 + 0.881940i \(0.656238\pi\)
\(978\) 0 0
\(979\) −0.200181 −0.00639782
\(980\) 0 0
\(981\) 7.09786 0.226617
\(982\) 0 0
\(983\) 16.8277 0.536721 0.268360 0.963319i \(-0.413518\pi\)
0.268360 + 0.963319i \(0.413518\pi\)
\(984\) 0 0
\(985\) −9.76778 −0.311227
\(986\) 0 0
\(987\) −3.67909 −0.117107
\(988\) 0 0
\(989\) −1.50470 −0.0478466
\(990\) 0 0
\(991\) −27.7334 −0.880979 −0.440490 0.897758i \(-0.645195\pi\)
−0.440490 + 0.897758i \(0.645195\pi\)
\(992\) 0 0
\(993\) 13.4121 0.425621
\(994\) 0 0
\(995\) −15.2036 −0.481985
\(996\) 0 0
\(997\) 45.5922 1.44392 0.721960 0.691935i \(-0.243241\pi\)
0.721960 + 0.691935i \(0.243241\pi\)
\(998\) 0 0
\(999\) −10.8868 −0.344444
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 \(a_p\))