Properties

Label 6004.2.a.g.1.11
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 1.11
Character \(\chi\) = 6004.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.907672 q^{3} +1.31635 q^{5} -2.29510 q^{7} -2.17613 q^{9} +O(q^{10})\) \(q-0.907672 q^{3} +1.31635 q^{5} -2.29510 q^{7} -2.17613 q^{9} +0.212653 q^{11} +6.06499 q^{13} -1.19481 q^{15} +0.799701 q^{17} +1.00000 q^{19} +2.08320 q^{21} +0.602634 q^{23} -3.26723 q^{25} +4.69823 q^{27} -7.49105 q^{29} -1.42670 q^{31} -0.193019 q^{33} -3.02116 q^{35} -8.32189 q^{37} -5.50502 q^{39} +0.745533 q^{41} +8.77416 q^{43} -2.86455 q^{45} -9.64327 q^{47} -1.73250 q^{49} -0.725867 q^{51} -9.32363 q^{53} +0.279925 q^{55} -0.907672 q^{57} +10.5563 q^{59} +4.47197 q^{61} +4.99445 q^{63} +7.98364 q^{65} +2.17038 q^{67} -0.546994 q^{69} +10.3644 q^{71} +6.30094 q^{73} +2.96557 q^{75} -0.488060 q^{77} -1.00000 q^{79} +2.26394 q^{81} +8.03828 q^{83} +1.05269 q^{85} +6.79942 q^{87} +10.3703 q^{89} -13.9198 q^{91} +1.29497 q^{93} +1.31635 q^{95} +7.60934 q^{97} -0.462760 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 27q - 4q^{3} - 10q^{5} - 8q^{7} + 19q^{9} + O(q^{10}) \) \( 27q - 4q^{3} - 10q^{5} - 8q^{7} + 19q^{9} + 3q^{11} - 5q^{13} - 11q^{15} - 17q^{17} + 27q^{19} - 28q^{21} - 11q^{23} + 13q^{25} - 7q^{27} - 39q^{29} - 27q^{31} - 18q^{33} - 5q^{35} - q^{37} - 22q^{39} - 36q^{41} - 2q^{43} - 18q^{45} - 12q^{47} + 15q^{49} + 4q^{51} - 28q^{53} + 5q^{55} - 4q^{57} - 30q^{59} - 6q^{61} - 4q^{63} - 32q^{65} + 13q^{67} - 27q^{69} - 59q^{71} - 30q^{73} - 21q^{75} - 39q^{77} - 27q^{79} - 5q^{81} + 4q^{83} - 3q^{85} + 22q^{87} - 56q^{89} - 8q^{91} - 38q^{93} - 10q^{95} - 30q^{97} + 31q^{99} + O(q^{100}) \)

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
\(3\) −0.907672 −0.524045 −0.262022 0.965062i \(-0.584389\pi\)
−0.262022 + 0.965062i \(0.584389\pi\)
\(4\) 0 0
\(5\) 1.31635 0.588689 0.294344 0.955699i \(-0.404899\pi\)
0.294344 + 0.955699i \(0.404899\pi\)
\(6\) 0 0
\(7\) −2.29510 −0.867468 −0.433734 0.901041i \(-0.642804\pi\)
−0.433734 + 0.901041i \(0.642804\pi\)
\(8\) 0 0
\(9\) −2.17613 −0.725377
\(10\) 0 0
\(11\) 0.212653 0.0641172 0.0320586 0.999486i \(-0.489794\pi\)
0.0320586 + 0.999486i \(0.489794\pi\)
\(12\) 0 0
\(13\) 6.06499 1.68213 0.841063 0.540937i \(-0.181930\pi\)
0.841063 + 0.540937i \(0.181930\pi\)
\(14\) 0 0
\(15\) −1.19481 −0.308499
\(16\) 0 0
\(17\) 0.799701 0.193956 0.0969780 0.995287i \(-0.469082\pi\)
0.0969780 + 0.995287i \(0.469082\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) 2.08320 0.454592
\(22\) 0 0
\(23\) 0.602634 0.125658 0.0628289 0.998024i \(-0.479988\pi\)
0.0628289 + 0.998024i \(0.479988\pi\)
\(24\) 0 0
\(25\) −3.26723 −0.653446
\(26\) 0 0
\(27\) 4.69823 0.904175
\(28\) 0 0
\(29\) −7.49105 −1.39105 −0.695526 0.718501i \(-0.744829\pi\)
−0.695526 + 0.718501i \(0.744829\pi\)
\(30\) 0 0
\(31\) −1.42670 −0.256242 −0.128121 0.991759i \(-0.540895\pi\)
−0.128121 + 0.991759i \(0.540895\pi\)
\(32\) 0 0
\(33\) −0.193019 −0.0336003
\(34\) 0 0
\(35\) −3.02116 −0.510668
\(36\) 0 0
\(37\) −8.32189 −1.36811 −0.684055 0.729431i \(-0.739785\pi\)
−0.684055 + 0.729431i \(0.739785\pi\)
\(38\) 0 0
\(39\) −5.50502 −0.881509
\(40\) 0 0
\(41\) 0.745533 0.116433 0.0582164 0.998304i \(-0.481459\pi\)
0.0582164 + 0.998304i \(0.481459\pi\)
\(42\) 0 0
\(43\) 8.77416 1.33805 0.669023 0.743242i \(-0.266713\pi\)
0.669023 + 0.743242i \(0.266713\pi\)
\(44\) 0 0
\(45\) −2.86455 −0.427021
\(46\) 0 0
\(47\) −9.64327 −1.40662 −0.703308 0.710885i \(-0.748294\pi\)
−0.703308 + 0.710885i \(0.748294\pi\)
\(48\) 0 0
\(49\) −1.73250 −0.247500
\(50\) 0 0
\(51\) −0.725867 −0.101642
\(52\) 0 0
\(53\) −9.32363 −1.28070 −0.640350 0.768083i \(-0.721211\pi\)
−0.640350 + 0.768083i \(0.721211\pi\)
\(54\) 0 0
\(55\) 0.279925 0.0377451
\(56\) 0 0
\(57\) −0.907672 −0.120224
\(58\) 0 0
\(59\) 10.5563 1.37431 0.687157 0.726509i \(-0.258858\pi\)
0.687157 + 0.726509i \(0.258858\pi\)
\(60\) 0 0
\(61\) 4.47197 0.572577 0.286289 0.958143i \(-0.407578\pi\)
0.286289 + 0.958143i \(0.407578\pi\)
\(62\) 0 0
\(63\) 4.99445 0.629241
\(64\) 0 0
\(65\) 7.98364 0.990249
\(66\) 0 0
\(67\) 2.17038 0.265155 0.132577 0.991173i \(-0.457675\pi\)
0.132577 + 0.991173i \(0.457675\pi\)
\(68\) 0 0
\(69\) −0.546994 −0.0658503
\(70\) 0 0
\(71\) 10.3644 1.23002 0.615012 0.788518i \(-0.289151\pi\)
0.615012 + 0.788518i \(0.289151\pi\)
\(72\) 0 0
\(73\) 6.30094 0.737469 0.368735 0.929535i \(-0.379791\pi\)
0.368735 + 0.929535i \(0.379791\pi\)
\(74\) 0 0
\(75\) 2.96557 0.342435
\(76\) 0 0
\(77\) −0.488060 −0.0556196
\(78\) 0 0
\(79\) −1.00000 −0.112509
\(80\) 0 0
\(81\) 2.26394 0.251549
\(82\) 0 0
\(83\) 8.03828 0.882316 0.441158 0.897430i \(-0.354568\pi\)
0.441158 + 0.897430i \(0.354568\pi\)
\(84\) 0 0
\(85\) 1.05269 0.114180
\(86\) 0 0
\(87\) 6.79942 0.728974
\(88\) 0 0
\(89\) 10.3703 1.09925 0.549626 0.835411i \(-0.314770\pi\)
0.549626 + 0.835411i \(0.314770\pi\)
\(90\) 0 0
\(91\) −13.9198 −1.45919
\(92\) 0 0
\(93\) 1.29497 0.134283
\(94\) 0 0
\(95\) 1.31635 0.135054
\(96\) 0 0
\(97\) 7.60934 0.772612 0.386306 0.922371i \(-0.373751\pi\)
0.386306 + 0.922371i \(0.373751\pi\)
\(98\) 0 0
\(99\) −0.462760 −0.0465091
\(100\) 0 0
\(101\) −8.90950 −0.886528 −0.443264 0.896391i \(-0.646180\pi\)
−0.443264 + 0.896391i \(0.646180\pi\)
\(102\) 0 0
\(103\) −12.4376 −1.22551 −0.612756 0.790272i \(-0.709939\pi\)
−0.612756 + 0.790272i \(0.709939\pi\)
\(104\) 0 0
\(105\) 2.74222 0.267613
\(106\) 0 0
\(107\) −4.09598 −0.395973 −0.197986 0.980205i \(-0.563440\pi\)
−0.197986 + 0.980205i \(0.563440\pi\)
\(108\) 0 0
\(109\) −6.21166 −0.594969 −0.297484 0.954727i \(-0.596148\pi\)
−0.297484 + 0.954727i \(0.596148\pi\)
\(110\) 0 0
\(111\) 7.55355 0.716951
\(112\) 0 0
\(113\) −11.0711 −1.04148 −0.520740 0.853716i \(-0.674344\pi\)
−0.520740 + 0.853716i \(0.674344\pi\)
\(114\) 0 0
\(115\) 0.793276 0.0739733
\(116\) 0 0
\(117\) −13.1982 −1.22018
\(118\) 0 0
\(119\) −1.83540 −0.168251
\(120\) 0 0
\(121\) −10.9548 −0.995889
\(122\) 0 0
\(123\) −0.676700 −0.0610160
\(124\) 0 0
\(125\) −10.8825 −0.973365
\(126\) 0 0
\(127\) 11.9148 1.05727 0.528633 0.848850i \(-0.322705\pi\)
0.528633 + 0.848850i \(0.322705\pi\)
\(128\) 0 0
\(129\) −7.96406 −0.701196
\(130\) 0 0
\(131\) −2.73112 −0.238619 −0.119309 0.992857i \(-0.538068\pi\)
−0.119309 + 0.992857i \(0.538068\pi\)
\(132\) 0 0
\(133\) −2.29510 −0.199011
\(134\) 0 0
\(135\) 6.18451 0.532278
\(136\) 0 0
\(137\) −21.3863 −1.82715 −0.913577 0.406666i \(-0.866691\pi\)
−0.913577 + 0.406666i \(0.866691\pi\)
\(138\) 0 0
\(139\) −5.13598 −0.435628 −0.217814 0.975990i \(-0.569893\pi\)
−0.217814 + 0.975990i \(0.569893\pi\)
\(140\) 0 0
\(141\) 8.75293 0.737130
\(142\) 0 0
\(143\) 1.28974 0.107853
\(144\) 0 0
\(145\) −9.86083 −0.818897
\(146\) 0 0
\(147\) 1.57254 0.129701
\(148\) 0 0
\(149\) −16.3694 −1.34103 −0.670515 0.741896i \(-0.733927\pi\)
−0.670515 + 0.741896i \(0.733927\pi\)
\(150\) 0 0
\(151\) 18.7389 1.52495 0.762475 0.647017i \(-0.223984\pi\)
0.762475 + 0.647017i \(0.223984\pi\)
\(152\) 0 0
\(153\) −1.74026 −0.140691
\(154\) 0 0
\(155\) −1.87803 −0.150847
\(156\) 0 0
\(157\) −22.2865 −1.77866 −0.889328 0.457270i \(-0.848827\pi\)
−0.889328 + 0.457270i \(0.848827\pi\)
\(158\) 0 0
\(159\) 8.46280 0.671144
\(160\) 0 0
\(161\) −1.38311 −0.109004
\(162\) 0 0
\(163\) 6.68612 0.523697 0.261849 0.965109i \(-0.415668\pi\)
0.261849 + 0.965109i \(0.415668\pi\)
\(164\) 0 0
\(165\) −0.254080 −0.0197801
\(166\) 0 0
\(167\) −7.87917 −0.609709 −0.304854 0.952399i \(-0.598608\pi\)
−0.304854 + 0.952399i \(0.598608\pi\)
\(168\) 0 0
\(169\) 23.7841 1.82955
\(170\) 0 0
\(171\) −2.17613 −0.166413
\(172\) 0 0
\(173\) −11.4446 −0.870115 −0.435058 0.900403i \(-0.643272\pi\)
−0.435058 + 0.900403i \(0.643272\pi\)
\(174\) 0 0
\(175\) 7.49863 0.566843
\(176\) 0 0
\(177\) −9.58167 −0.720202
\(178\) 0 0
\(179\) −3.16670 −0.236690 −0.118345 0.992973i \(-0.537759\pi\)
−0.118345 + 0.992973i \(0.537759\pi\)
\(180\) 0 0
\(181\) −14.7792 −1.09853 −0.549264 0.835649i \(-0.685092\pi\)
−0.549264 + 0.835649i \(0.685092\pi\)
\(182\) 0 0
\(183\) −4.05909 −0.300056
\(184\) 0 0
\(185\) −10.9545 −0.805391
\(186\) 0 0
\(187\) 0.170059 0.0124359
\(188\) 0 0
\(189\) −10.7829 −0.784343
\(190\) 0 0
\(191\) −5.50227 −0.398131 −0.199065 0.979986i \(-0.563791\pi\)
−0.199065 + 0.979986i \(0.563791\pi\)
\(192\) 0 0
\(193\) 15.2497 1.09769 0.548847 0.835923i \(-0.315067\pi\)
0.548847 + 0.835923i \(0.315067\pi\)
\(194\) 0 0
\(195\) −7.24653 −0.518935
\(196\) 0 0
\(197\) 3.14603 0.224146 0.112073 0.993700i \(-0.464251\pi\)
0.112073 + 0.993700i \(0.464251\pi\)
\(198\) 0 0
\(199\) −15.7138 −1.11392 −0.556962 0.830538i \(-0.688033\pi\)
−0.556962 + 0.830538i \(0.688033\pi\)
\(200\) 0 0
\(201\) −1.97000 −0.138953
\(202\) 0 0
\(203\) 17.1927 1.20669
\(204\) 0 0
\(205\) 0.981381 0.0685426
\(206\) 0 0
\(207\) −1.31141 −0.0911493
\(208\) 0 0
\(209\) 0.212653 0.0147095
\(210\) 0 0
\(211\) 7.51341 0.517245 0.258622 0.965979i \(-0.416731\pi\)
0.258622 + 0.965979i \(0.416731\pi\)
\(212\) 0 0
\(213\) −9.40745 −0.644588
\(214\) 0 0
\(215\) 11.5498 0.787693
\(216\) 0 0
\(217\) 3.27442 0.222282
\(218\) 0 0
\(219\) −5.71919 −0.386467
\(220\) 0 0
\(221\) 4.85018 0.326259
\(222\) 0 0
\(223\) −6.84169 −0.458153 −0.229077 0.973408i \(-0.573571\pi\)
−0.229077 + 0.973408i \(0.573571\pi\)
\(224\) 0 0
\(225\) 7.10991 0.473994
\(226\) 0 0
\(227\) −28.8344 −1.91380 −0.956902 0.290410i \(-0.906208\pi\)
−0.956902 + 0.290410i \(0.906208\pi\)
\(228\) 0 0
\(229\) −22.7678 −1.50454 −0.752271 0.658854i \(-0.771041\pi\)
−0.752271 + 0.658854i \(0.771041\pi\)
\(230\) 0 0
\(231\) 0.442998 0.0291471
\(232\) 0 0
\(233\) 7.41156 0.485547 0.242774 0.970083i \(-0.421943\pi\)
0.242774 + 0.970083i \(0.421943\pi\)
\(234\) 0 0
\(235\) −12.6939 −0.828059
\(236\) 0 0
\(237\) 0.907672 0.0589597
\(238\) 0 0
\(239\) −9.06663 −0.586472 −0.293236 0.956040i \(-0.594732\pi\)
−0.293236 + 0.956040i \(0.594732\pi\)
\(240\) 0 0
\(241\) 0.888982 0.0572644 0.0286322 0.999590i \(-0.490885\pi\)
0.0286322 + 0.999590i \(0.490885\pi\)
\(242\) 0 0
\(243\) −16.1496 −1.03600
\(244\) 0 0
\(245\) −2.28057 −0.145700
\(246\) 0 0
\(247\) 6.06499 0.385906
\(248\) 0 0
\(249\) −7.29612 −0.462373
\(250\) 0 0
\(251\) 8.90246 0.561919 0.280959 0.959720i \(-0.409347\pi\)
0.280959 + 0.959720i \(0.409347\pi\)
\(252\) 0 0
\(253\) 0.128152 0.00805682
\(254\) 0 0
\(255\) −0.955494 −0.0598353
\(256\) 0 0
\(257\) −7.73303 −0.482373 −0.241187 0.970479i \(-0.577537\pi\)
−0.241187 + 0.970479i \(0.577537\pi\)
\(258\) 0 0
\(259\) 19.0996 1.18679
\(260\) 0 0
\(261\) 16.3015 1.00904
\(262\) 0 0
\(263\) 13.0240 0.803095 0.401548 0.915838i \(-0.368472\pi\)
0.401548 + 0.915838i \(0.368472\pi\)
\(264\) 0 0
\(265\) −12.2731 −0.753933
\(266\) 0 0
\(267\) −9.41285 −0.576057
\(268\) 0 0
\(269\) 9.05414 0.552041 0.276020 0.961152i \(-0.410984\pi\)
0.276020 + 0.961152i \(0.410984\pi\)
\(270\) 0 0
\(271\) −17.4755 −1.06156 −0.530780 0.847510i \(-0.678101\pi\)
−0.530780 + 0.847510i \(0.678101\pi\)
\(272\) 0 0
\(273\) 12.6346 0.764681
\(274\) 0 0
\(275\) −0.694784 −0.0418971
\(276\) 0 0
\(277\) 17.1324 1.02938 0.514692 0.857375i \(-0.327906\pi\)
0.514692 + 0.857375i \(0.327906\pi\)
\(278\) 0 0
\(279\) 3.10468 0.185872
\(280\) 0 0
\(281\) −6.99487 −0.417279 −0.208639 0.977993i \(-0.566904\pi\)
−0.208639 + 0.977993i \(0.566904\pi\)
\(282\) 0 0
\(283\) −15.6513 −0.930371 −0.465185 0.885213i \(-0.654012\pi\)
−0.465185 + 0.885213i \(0.654012\pi\)
\(284\) 0 0
\(285\) −1.19481 −0.0707746
\(286\) 0 0
\(287\) −1.71108 −0.101002
\(288\) 0 0
\(289\) −16.3605 −0.962381
\(290\) 0 0
\(291\) −6.90679 −0.404883
\(292\) 0 0
\(293\) 0.782121 0.0456920 0.0228460 0.999739i \(-0.492727\pi\)
0.0228460 + 0.999739i \(0.492727\pi\)
\(294\) 0 0
\(295\) 13.8958 0.809043
\(296\) 0 0
\(297\) 0.999091 0.0579731
\(298\) 0 0
\(299\) 3.65497 0.211372
\(300\) 0 0
\(301\) −20.1376 −1.16071
\(302\) 0 0
\(303\) 8.08691 0.464581
\(304\) 0 0
\(305\) 5.88667 0.337070
\(306\) 0 0
\(307\) −32.1179 −1.83307 −0.916533 0.399959i \(-0.869024\pi\)
−0.916533 + 0.399959i \(0.869024\pi\)
\(308\) 0 0
\(309\) 11.2893 0.642223
\(310\) 0 0
\(311\) 13.5891 0.770569 0.385285 0.922798i \(-0.374103\pi\)
0.385285 + 0.922798i \(0.374103\pi\)
\(312\) 0 0
\(313\) −33.1834 −1.87563 −0.937817 0.347130i \(-0.887156\pi\)
−0.937817 + 0.347130i \(0.887156\pi\)
\(314\) 0 0
\(315\) 6.57443 0.370427
\(316\) 0 0
\(317\) 1.60751 0.0902869 0.0451434 0.998981i \(-0.485626\pi\)
0.0451434 + 0.998981i \(0.485626\pi\)
\(318\) 0 0
\(319\) −1.59299 −0.0891903
\(320\) 0 0
\(321\) 3.71780 0.207508
\(322\) 0 0
\(323\) 0.799701 0.0444966
\(324\) 0 0
\(325\) −19.8157 −1.09918
\(326\) 0 0
\(327\) 5.63815 0.311790
\(328\) 0 0
\(329\) 22.1323 1.22019
\(330\) 0 0
\(331\) −17.2000 −0.945398 −0.472699 0.881224i \(-0.656720\pi\)
−0.472699 + 0.881224i \(0.656720\pi\)
\(332\) 0 0
\(333\) 18.1095 0.992395
\(334\) 0 0
\(335\) 2.85698 0.156094
\(336\) 0 0
\(337\) 5.43131 0.295863 0.147931 0.988998i \(-0.452739\pi\)
0.147931 + 0.988998i \(0.452739\pi\)
\(338\) 0 0
\(339\) 10.0489 0.545782
\(340\) 0 0
\(341\) −0.303391 −0.0164295
\(342\) 0 0
\(343\) 20.0420 1.08217
\(344\) 0 0
\(345\) −0.720035 −0.0387654
\(346\) 0 0
\(347\) −8.39695 −0.450772 −0.225386 0.974270i \(-0.572364\pi\)
−0.225386 + 0.974270i \(0.572364\pi\)
\(348\) 0 0
\(349\) −15.2473 −0.816168 −0.408084 0.912944i \(-0.633803\pi\)
−0.408084 + 0.912944i \(0.633803\pi\)
\(350\) 0 0
\(351\) 28.4947 1.52094
\(352\) 0 0
\(353\) 9.60997 0.511487 0.255744 0.966745i \(-0.417680\pi\)
0.255744 + 0.966745i \(0.417680\pi\)
\(354\) 0 0
\(355\) 13.6431 0.724101
\(356\) 0 0
\(357\) 1.66594 0.0881709
\(358\) 0 0
\(359\) 6.27060 0.330950 0.165475 0.986214i \(-0.447084\pi\)
0.165475 + 0.986214i \(0.447084\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 9.94335 0.521891
\(364\) 0 0
\(365\) 8.29423 0.434140
\(366\) 0 0
\(367\) −36.9952 −1.93113 −0.965566 0.260158i \(-0.916225\pi\)
−0.965566 + 0.260158i \(0.916225\pi\)
\(368\) 0 0
\(369\) −1.62238 −0.0844576
\(370\) 0 0
\(371\) 21.3987 1.11097
\(372\) 0 0
\(373\) 10.8082 0.559629 0.279815 0.960054i \(-0.409727\pi\)
0.279815 + 0.960054i \(0.409727\pi\)
\(374\) 0 0
\(375\) 9.87779 0.510087
\(376\) 0 0
\(377\) −45.4331 −2.33993
\(378\) 0 0
\(379\) 8.00285 0.411079 0.205539 0.978649i \(-0.434105\pi\)
0.205539 + 0.978649i \(0.434105\pi\)
\(380\) 0 0
\(381\) −10.8147 −0.554055
\(382\) 0 0
\(383\) −6.55079 −0.334730 −0.167365 0.985895i \(-0.553526\pi\)
−0.167365 + 0.985895i \(0.553526\pi\)
\(384\) 0 0
\(385\) −0.642456 −0.0327426
\(386\) 0 0
\(387\) −19.0937 −0.970588
\(388\) 0 0
\(389\) −17.8079 −0.902895 −0.451448 0.892298i \(-0.649092\pi\)
−0.451448 + 0.892298i \(0.649092\pi\)
\(390\) 0 0
\(391\) 0.481927 0.0243721
\(392\) 0 0
\(393\) 2.47896 0.125047
\(394\) 0 0
\(395\) −1.31635 −0.0662327
\(396\) 0 0
\(397\) 33.3653 1.67456 0.837279 0.546776i \(-0.184145\pi\)
0.837279 + 0.546776i \(0.184145\pi\)
\(398\) 0 0
\(399\) 2.08320 0.104291
\(400\) 0 0
\(401\) −22.9966 −1.14839 −0.574197 0.818717i \(-0.694686\pi\)
−0.574197 + 0.818717i \(0.694686\pi\)
\(402\) 0 0
\(403\) −8.65291 −0.431032
\(404\) 0 0
\(405\) 2.98013 0.148084
\(406\) 0 0
\(407\) −1.76967 −0.0877193
\(408\) 0 0
\(409\) 5.76368 0.284996 0.142498 0.989795i \(-0.454487\pi\)
0.142498 + 0.989795i \(0.454487\pi\)
\(410\) 0 0
\(411\) 19.4117 0.957511
\(412\) 0 0
\(413\) −24.2278 −1.19217
\(414\) 0 0
\(415\) 10.5812 0.519409
\(416\) 0 0
\(417\) 4.66179 0.228289
\(418\) 0 0
\(419\) −29.2053 −1.42677 −0.713386 0.700771i \(-0.752840\pi\)
−0.713386 + 0.700771i \(0.752840\pi\)
\(420\) 0 0
\(421\) −9.41774 −0.458992 −0.229496 0.973310i \(-0.573708\pi\)
−0.229496 + 0.973310i \(0.573708\pi\)
\(422\) 0 0
\(423\) 20.9850 1.02033
\(424\) 0 0
\(425\) −2.61281 −0.126740
\(426\) 0 0
\(427\) −10.2636 −0.496692
\(428\) 0 0
\(429\) −1.17066 −0.0565199
\(430\) 0 0
\(431\) 18.6086 0.896345 0.448173 0.893947i \(-0.352075\pi\)
0.448173 + 0.893947i \(0.352075\pi\)
\(432\) 0 0
\(433\) −0.0750803 −0.00360813 −0.00180406 0.999998i \(-0.500574\pi\)
−0.00180406 + 0.999998i \(0.500574\pi\)
\(434\) 0 0
\(435\) 8.95040 0.429139
\(436\) 0 0
\(437\) 0.602634 0.0288279
\(438\) 0 0
\(439\) −18.2730 −0.872125 −0.436062 0.899916i \(-0.643627\pi\)
−0.436062 + 0.899916i \(0.643627\pi\)
\(440\) 0 0
\(441\) 3.77014 0.179531
\(442\) 0 0
\(443\) −14.7909 −0.702738 −0.351369 0.936237i \(-0.614284\pi\)
−0.351369 + 0.936237i \(0.614284\pi\)
\(444\) 0 0
\(445\) 13.6509 0.647117
\(446\) 0 0
\(447\) 14.8580 0.702760
\(448\) 0 0
\(449\) 5.82066 0.274694 0.137347 0.990523i \(-0.456143\pi\)
0.137347 + 0.990523i \(0.456143\pi\)
\(450\) 0 0
\(451\) 0.158540 0.00746534
\(452\) 0 0
\(453\) −17.0088 −0.799143
\(454\) 0 0
\(455\) −18.3233 −0.859009
\(456\) 0 0
\(457\) 7.45912 0.348923 0.174461 0.984664i \(-0.444182\pi\)
0.174461 + 0.984664i \(0.444182\pi\)
\(458\) 0 0
\(459\) 3.75718 0.175370
\(460\) 0 0
\(461\) 31.0021 1.44391 0.721957 0.691938i \(-0.243243\pi\)
0.721957 + 0.691938i \(0.243243\pi\)
\(462\) 0 0
\(463\) 4.65186 0.216190 0.108095 0.994141i \(-0.465525\pi\)
0.108095 + 0.994141i \(0.465525\pi\)
\(464\) 0 0
\(465\) 1.70464 0.0790506
\(466\) 0 0
\(467\) −15.1669 −0.701842 −0.350921 0.936405i \(-0.614131\pi\)
−0.350921 + 0.936405i \(0.614131\pi\)
\(468\) 0 0
\(469\) −4.98125 −0.230013
\(470\) 0 0
\(471\) 20.2288 0.932096
\(472\) 0 0
\(473\) 1.86585 0.0857917
\(474\) 0 0
\(475\) −3.26723 −0.149911
\(476\) 0 0
\(477\) 20.2894 0.928990
\(478\) 0 0
\(479\) −12.1452 −0.554930 −0.277465 0.960736i \(-0.589494\pi\)
−0.277465 + 0.960736i \(0.589494\pi\)
\(480\) 0 0
\(481\) −50.4722 −2.30133
\(482\) 0 0
\(483\) 1.25541 0.0571230
\(484\) 0 0
\(485\) 10.0165 0.454828
\(486\) 0 0
\(487\) −16.1953 −0.733880 −0.366940 0.930245i \(-0.619595\pi\)
−0.366940 + 0.930245i \(0.619595\pi\)
\(488\) 0 0
\(489\) −6.06880 −0.274441
\(490\) 0 0
\(491\) −27.3465 −1.23413 −0.617064 0.786913i \(-0.711678\pi\)
−0.617064 + 0.786913i \(0.711678\pi\)
\(492\) 0 0
\(493\) −5.99060 −0.269803
\(494\) 0 0
\(495\) −0.609153 −0.0273794
\(496\) 0 0
\(497\) −23.7873 −1.06701
\(498\) 0 0
\(499\) −0.743094 −0.0332655 −0.0166327 0.999862i \(-0.505295\pi\)
−0.0166327 + 0.999862i \(0.505295\pi\)
\(500\) 0 0
\(501\) 7.15171 0.319515
\(502\) 0 0
\(503\) 27.5285 1.22743 0.613717 0.789526i \(-0.289674\pi\)
0.613717 + 0.789526i \(0.289674\pi\)
\(504\) 0 0
\(505\) −11.7280 −0.521889
\(506\) 0 0
\(507\) −21.5882 −0.958765
\(508\) 0 0
\(509\) 30.9392 1.37136 0.685678 0.727905i \(-0.259506\pi\)
0.685678 + 0.727905i \(0.259506\pi\)
\(510\) 0 0
\(511\) −14.4613 −0.639731
\(512\) 0 0
\(513\) 4.69823 0.207432
\(514\) 0 0
\(515\) −16.3722 −0.721445
\(516\) 0 0
\(517\) −2.05067 −0.0901882
\(518\) 0 0
\(519\) 10.3879 0.455980
\(520\) 0 0
\(521\) 16.5475 0.724961 0.362481 0.931991i \(-0.381930\pi\)
0.362481 + 0.931991i \(0.381930\pi\)
\(522\) 0 0
\(523\) 25.6976 1.12368 0.561838 0.827247i \(-0.310095\pi\)
0.561838 + 0.827247i \(0.310095\pi\)
\(524\) 0 0
\(525\) −6.80630 −0.297051
\(526\) 0 0
\(527\) −1.14093 −0.0496998
\(528\) 0 0
\(529\) −22.6368 −0.984210
\(530\) 0 0
\(531\) −22.9719 −0.996896
\(532\) 0 0
\(533\) 4.52165 0.195855
\(534\) 0 0
\(535\) −5.39173 −0.233105
\(536\) 0 0
\(537\) 2.87432 0.124036
\(538\) 0 0
\(539\) −0.368420 −0.0158690
\(540\) 0 0
\(541\) 36.0660 1.55060 0.775298 0.631595i \(-0.217600\pi\)
0.775298 + 0.631595i \(0.217600\pi\)
\(542\) 0 0
\(543\) 13.4147 0.575678
\(544\) 0 0
\(545\) −8.17670 −0.350251
\(546\) 0 0
\(547\) −20.8682 −0.892260 −0.446130 0.894968i \(-0.647198\pi\)
−0.446130 + 0.894968i \(0.647198\pi\)
\(548\) 0 0
\(549\) −9.73160 −0.415334
\(550\) 0 0
\(551\) −7.49105 −0.319129
\(552\) 0 0
\(553\) 2.29510 0.0975977
\(554\) 0 0
\(555\) 9.94310 0.422061
\(556\) 0 0
\(557\) 1.68520 0.0714043 0.0357021 0.999362i \(-0.488633\pi\)
0.0357021 + 0.999362i \(0.488633\pi\)
\(558\) 0 0
\(559\) 53.2152 2.25076
\(560\) 0 0
\(561\) −0.154357 −0.00651698
\(562\) 0 0
\(563\) −22.2814 −0.939049 −0.469524 0.882920i \(-0.655575\pi\)
−0.469524 + 0.882920i \(0.655575\pi\)
\(564\) 0 0
\(565\) −14.5734 −0.613107
\(566\) 0 0
\(567\) −5.19597 −0.218210
\(568\) 0 0
\(569\) 18.6477 0.781753 0.390877 0.920443i \(-0.372172\pi\)
0.390877 + 0.920443i \(0.372172\pi\)
\(570\) 0 0
\(571\) 27.1853 1.13767 0.568835 0.822452i \(-0.307394\pi\)
0.568835 + 0.822452i \(0.307394\pi\)
\(572\) 0 0
\(573\) 4.99426 0.208638
\(574\) 0 0
\(575\) −1.96894 −0.0821105
\(576\) 0 0
\(577\) 33.9785 1.41454 0.707272 0.706941i \(-0.249925\pi\)
0.707272 + 0.706941i \(0.249925\pi\)
\(578\) 0 0
\(579\) −13.8417 −0.575241
\(580\) 0 0
\(581\) −18.4487 −0.765380
\(582\) 0 0
\(583\) −1.98269 −0.0821148
\(584\) 0 0
\(585\) −17.3734 −0.718303
\(586\) 0 0
\(587\) 36.5660 1.50924 0.754620 0.656163i \(-0.227821\pi\)
0.754620 + 0.656163i \(0.227821\pi\)
\(588\) 0 0
\(589\) −1.42670 −0.0587860
\(590\) 0 0
\(591\) −2.85557 −0.117462
\(592\) 0 0
\(593\) 38.9967 1.60140 0.800701 0.599064i \(-0.204461\pi\)
0.800701 + 0.599064i \(0.204461\pi\)
\(594\) 0 0
\(595\) −2.41602 −0.0990473
\(596\) 0 0
\(597\) 14.2630 0.583746
\(598\) 0 0
\(599\) 15.2090 0.621422 0.310711 0.950504i \(-0.399433\pi\)
0.310711 + 0.950504i \(0.399433\pi\)
\(600\) 0 0
\(601\) −4.28586 −0.174824 −0.0874119 0.996172i \(-0.527860\pi\)
−0.0874119 + 0.996172i \(0.527860\pi\)
\(602\) 0 0
\(603\) −4.72304 −0.192337
\(604\) 0 0
\(605\) −14.4203 −0.586269
\(606\) 0 0
\(607\) −7.48618 −0.303855 −0.151927 0.988392i \(-0.548548\pi\)
−0.151927 + 0.988392i \(0.548548\pi\)
\(608\) 0 0
\(609\) −15.6054 −0.632361
\(610\) 0 0
\(611\) −58.4863 −2.36610
\(612\) 0 0
\(613\) 14.1938 0.573281 0.286640 0.958038i \(-0.407461\pi\)
0.286640 + 0.958038i \(0.407461\pi\)
\(614\) 0 0
\(615\) −0.890773 −0.0359194
\(616\) 0 0
\(617\) −16.2773 −0.655298 −0.327649 0.944800i \(-0.606256\pi\)
−0.327649 + 0.944800i \(0.606256\pi\)
\(618\) 0 0
\(619\) 17.3928 0.699075 0.349538 0.936922i \(-0.386339\pi\)
0.349538 + 0.936922i \(0.386339\pi\)
\(620\) 0 0
\(621\) 2.83131 0.113617
\(622\) 0 0
\(623\) −23.8009 −0.953565
\(624\) 0 0
\(625\) 2.01091 0.0804365
\(626\) 0 0
\(627\) −0.193019 −0.00770843
\(628\) 0 0
\(629\) −6.65503 −0.265353
\(630\) 0 0
\(631\) −18.1128 −0.721060 −0.360530 0.932748i \(-0.617404\pi\)
−0.360530 + 0.932748i \(0.617404\pi\)
\(632\) 0 0
\(633\) −6.81972 −0.271059
\(634\) 0 0
\(635\) 15.6840 0.622401
\(636\) 0 0
\(637\) −10.5076 −0.416326
\(638\) 0 0
\(639\) −22.5542 −0.892231
\(640\) 0 0
\(641\) −36.6608 −1.44801 −0.724007 0.689793i \(-0.757702\pi\)
−0.724007 + 0.689793i \(0.757702\pi\)
\(642\) 0 0
\(643\) 41.4423 1.63432 0.817162 0.576408i \(-0.195546\pi\)
0.817162 + 0.576408i \(0.195546\pi\)
\(644\) 0 0
\(645\) −10.4835 −0.412786
\(646\) 0 0
\(647\) 6.39252 0.251316 0.125658 0.992074i \(-0.459896\pi\)
0.125658 + 0.992074i \(0.459896\pi\)
\(648\) 0 0
\(649\) 2.24483 0.0881171
\(650\) 0 0
\(651\) −2.97210 −0.116486
\(652\) 0 0
\(653\) −43.1607 −1.68901 −0.844504 0.535549i \(-0.820105\pi\)
−0.844504 + 0.535549i \(0.820105\pi\)
\(654\) 0 0
\(655\) −3.59510 −0.140472
\(656\) 0 0
\(657\) −13.7117 −0.534943
\(658\) 0 0
\(659\) 7.63245 0.297318 0.148659 0.988889i \(-0.452504\pi\)
0.148659 + 0.988889i \(0.452504\pi\)
\(660\) 0 0
\(661\) 17.4839 0.680046 0.340023 0.940417i \(-0.389565\pi\)
0.340023 + 0.940417i \(0.389565\pi\)
\(662\) 0 0
\(663\) −4.40238 −0.170974
\(664\) 0 0
\(665\) −3.02116 −0.117155
\(666\) 0 0
\(667\) −4.51436 −0.174797
\(668\) 0 0
\(669\) 6.21001 0.240093
\(670\) 0 0
\(671\) 0.950976 0.0367120
\(672\) 0 0
\(673\) −4.76960 −0.183855 −0.0919273 0.995766i \(-0.529303\pi\)
−0.0919273 + 0.995766i \(0.529303\pi\)
\(674\) 0 0
\(675\) −15.3502 −0.590829
\(676\) 0 0
\(677\) −37.3659 −1.43609 −0.718044 0.695997i \(-0.754962\pi\)
−0.718044 + 0.695997i \(0.754962\pi\)
\(678\) 0 0
\(679\) −17.4642 −0.670216
\(680\) 0 0
\(681\) 26.1722 1.00292
\(682\) 0 0
\(683\) −1.07054 −0.0409630 −0.0204815 0.999790i \(-0.506520\pi\)
−0.0204815 + 0.999790i \(0.506520\pi\)
\(684\) 0 0
\(685\) −28.1518 −1.07563
\(686\) 0 0
\(687\) 20.6657 0.788447
\(688\) 0 0
\(689\) −56.5477 −2.15430
\(690\) 0 0
\(691\) −0.0167153 −0.000635881 0 −0.000317941 1.00000i \(-0.500101\pi\)
−0.000317941 1.00000i \(0.500101\pi\)
\(692\) 0 0
\(693\) 1.06208 0.0403451
\(694\) 0 0
\(695\) −6.76074 −0.256450
\(696\) 0 0
\(697\) 0.596204 0.0225828
\(698\) 0 0
\(699\) −6.72727 −0.254449
\(700\) 0 0
\(701\) −6.76635 −0.255562 −0.127781 0.991802i \(-0.540785\pi\)
−0.127781 + 0.991802i \(0.540785\pi\)
\(702\) 0 0
\(703\) −8.32189 −0.313866
\(704\) 0 0
\(705\) 11.5219 0.433940
\(706\) 0 0
\(707\) 20.4482 0.769035
\(708\) 0 0
\(709\) −14.9997 −0.563326 −0.281663 0.959513i \(-0.590886\pi\)
−0.281663 + 0.959513i \(0.590886\pi\)
\(710\) 0 0
\(711\) 2.17613 0.0816113
\(712\) 0 0
\(713\) −0.859776 −0.0321989
\(714\) 0 0
\(715\) 1.69774 0.0634919
\(716\) 0 0
\(717\) 8.22953 0.307338
\(718\) 0 0
\(719\) −2.53208 −0.0944306 −0.0472153 0.998885i \(-0.515035\pi\)
−0.0472153 + 0.998885i \(0.515035\pi\)
\(720\) 0 0
\(721\) 28.5455 1.06309
\(722\) 0 0
\(723\) −0.806905 −0.0300091
\(724\) 0 0
\(725\) 24.4750 0.908977
\(726\) 0 0
\(727\) 18.6961 0.693400 0.346700 0.937976i \(-0.387302\pi\)
0.346700 + 0.937976i \(0.387302\pi\)
\(728\) 0 0
\(729\) 7.86674 0.291361
\(730\) 0 0
\(731\) 7.01670 0.259522
\(732\) 0 0
\(733\) −44.5545 −1.64566 −0.822829 0.568289i \(-0.807606\pi\)
−0.822829 + 0.568289i \(0.807606\pi\)
\(734\) 0 0
\(735\) 2.07001 0.0763536
\(736\) 0 0
\(737\) 0.461538 0.0170010
\(738\) 0 0
\(739\) 27.5839 1.01469 0.507346 0.861743i \(-0.330627\pi\)
0.507346 + 0.861743i \(0.330627\pi\)
\(740\) 0 0
\(741\) −5.50502 −0.202232
\(742\) 0 0
\(743\) −23.1685 −0.849971 −0.424985 0.905200i \(-0.639721\pi\)
−0.424985 + 0.905200i \(0.639721\pi\)
\(744\) 0 0
\(745\) −21.5478 −0.789449
\(746\) 0 0
\(747\) −17.4923 −0.640011
\(748\) 0 0
\(749\) 9.40069 0.343494
\(750\) 0 0
\(751\) −35.1753 −1.28357 −0.641783 0.766887i \(-0.721805\pi\)
−0.641783 + 0.766887i \(0.721805\pi\)
\(752\) 0 0
\(753\) −8.08052 −0.294471
\(754\) 0 0
\(755\) 24.6669 0.897721
\(756\) 0 0
\(757\) −33.2779 −1.20950 −0.604752 0.796414i \(-0.706728\pi\)
−0.604752 + 0.796414i \(0.706728\pi\)
\(758\) 0 0
\(759\) −0.116320 −0.00422214
\(760\) 0 0
\(761\) 11.3808 0.412553 0.206277 0.978494i \(-0.433865\pi\)
0.206277 + 0.978494i \(0.433865\pi\)
\(762\) 0 0
\(763\) 14.2564 0.516116
\(764\) 0 0
\(765\) −2.29078 −0.0828234
\(766\) 0 0
\(767\) 64.0239 2.31177
\(768\) 0 0
\(769\) −28.9211 −1.04292 −0.521461 0.853275i \(-0.674613\pi\)
−0.521461 + 0.853275i \(0.674613\pi\)
\(770\) 0 0
\(771\) 7.01906 0.252785
\(772\) 0 0
\(773\) −45.0244 −1.61941 −0.809707 0.586834i \(-0.800374\pi\)
−0.809707 + 0.586834i \(0.800374\pi\)
\(774\) 0 0
\(775\) 4.66134 0.167440
\(776\) 0 0
\(777\) −17.3362 −0.621932
\(778\) 0 0
\(779\) 0.745533 0.0267115
\(780\) 0 0
\(781\) 2.20401 0.0788657
\(782\) 0 0
\(783\) −35.1947 −1.25776
\(784\) 0 0
\(785\) −29.3368 −1.04707
\(786\) 0 0
\(787\) 0.0180664 0.000643996 0 0.000321998 1.00000i \(-0.499898\pi\)
0.000321998 1.00000i \(0.499898\pi\)
\(788\) 0 0
\(789\) −11.8215 −0.420858
\(790\) 0 0
\(791\) 25.4093 0.903450
\(792\) 0 0
\(793\) 27.1225 0.963147
\(794\) 0 0
\(795\) 11.1400 0.395095
\(796\) 0 0
\(797\) −27.4973 −0.974005 −0.487002 0.873401i \(-0.661910\pi\)
−0.487002 + 0.873401i \(0.661910\pi\)
\(798\) 0 0
\(799\) −7.71174 −0.272822
\(800\) 0 0
\(801\) −22.5672 −0.797371
\(802\) 0 0
\(803\) 1.33991 0.0472844
\(804\) 0 0
\(805\) −1.82065 −0.0641695
\(806\) 0 0
\(807\) −8.21819 −0.289294
\(808\) 0 0
\(809\) 37.2070 1.30813 0.654065 0.756439i \(-0.273062\pi\)
0.654065 + 0.756439i \(0.273062\pi\)
\(810\) 0 0
\(811\) 16.6138 0.583390 0.291695 0.956511i \(-0.405781\pi\)
0.291695 + 0.956511i \(0.405781\pi\)
\(812\) 0 0
\(813\) 15.8620 0.556305
\(814\) 0 0
\(815\) 8.80126 0.308295
\(816\) 0 0
\(817\) 8.77416 0.306969
\(818\) 0 0
\(819\) 30.2913 1.05846
\(820\) 0 0
\(821\) 27.4193 0.956941 0.478470 0.878104i \(-0.341191\pi\)
0.478470 + 0.878104i \(0.341191\pi\)
\(822\) 0 0
\(823\) −19.3656 −0.675043 −0.337522 0.941318i \(-0.609589\pi\)
−0.337522 + 0.941318i \(0.609589\pi\)
\(824\) 0 0
\(825\) 0.630637 0.0219559
\(826\) 0 0
\(827\) 45.8321 1.59374 0.796869 0.604152i \(-0.206488\pi\)
0.796869 + 0.604152i \(0.206488\pi\)
\(828\) 0 0
\(829\) 12.4776 0.433366 0.216683 0.976242i \(-0.430476\pi\)
0.216683 + 0.976242i \(0.430476\pi\)
\(830\) 0 0
\(831\) −15.5506 −0.539443
\(832\) 0 0
\(833\) −1.38548 −0.0480041
\(834\) 0 0
\(835\) −10.3717 −0.358929
\(836\) 0 0
\(837\) −6.70295 −0.231688
\(838\) 0 0
\(839\) 20.7591 0.716684 0.358342 0.933590i \(-0.383342\pi\)
0.358342 + 0.933590i \(0.383342\pi\)
\(840\) 0 0
\(841\) 27.1158 0.935028
\(842\) 0 0
\(843\) 6.34905 0.218673
\(844\) 0 0
\(845\) 31.3082 1.07703
\(846\) 0 0
\(847\) 25.1424 0.863901
\(848\) 0 0
\(849\) 14.2062 0.487556
\(850\) 0 0
\(851\) −5.01505 −0.171914
\(852\) 0 0
\(853\) 16.7925 0.574964 0.287482 0.957786i \(-0.407182\pi\)
0.287482 + 0.957786i \(0.407182\pi\)
\(854\) 0 0
\(855\) −2.86455 −0.0979654
\(856\) 0 0
\(857\) 27.3214 0.933283 0.466641 0.884447i \(-0.345464\pi\)
0.466641 + 0.884447i \(0.345464\pi\)
\(858\) 0 0
\(859\) −34.6749 −1.18309 −0.591546 0.806271i \(-0.701482\pi\)
−0.591546 + 0.806271i \(0.701482\pi\)
\(860\) 0 0
\(861\) 1.55310 0.0529294
\(862\) 0 0
\(863\) 7.12687 0.242602 0.121301 0.992616i \(-0.461293\pi\)
0.121301 + 0.992616i \(0.461293\pi\)
\(864\) 0 0
\(865\) −15.0651 −0.512227
\(866\) 0 0
\(867\) 14.8500 0.504331
\(868\) 0 0
\(869\) −0.212653 −0.00721374
\(870\) 0 0
\(871\) 13.1634 0.446023
\(872\) 0 0
\(873\) −16.5589 −0.560435
\(874\) 0 0
\(875\) 24.9766 0.844363
\(876\) 0 0
\(877\) 1.43655 0.0485087 0.0242544 0.999706i \(-0.492279\pi\)
0.0242544 + 0.999706i \(0.492279\pi\)
\(878\) 0 0
\(879\) −0.709910 −0.0239447
\(880\) 0 0
\(881\) 19.1294 0.644486 0.322243 0.946657i \(-0.395563\pi\)
0.322243 + 0.946657i \(0.395563\pi\)
\(882\) 0 0
\(883\) 19.2884 0.649107 0.324554 0.945867i \(-0.394786\pi\)
0.324554 + 0.945867i \(0.394786\pi\)
\(884\) 0 0
\(885\) −12.6128 −0.423975
\(886\) 0 0
\(887\) 33.9315 1.13931 0.569654 0.821884i \(-0.307077\pi\)
0.569654 + 0.821884i \(0.307077\pi\)
\(888\) 0 0
\(889\) −27.3457 −0.917144
\(890\) 0 0
\(891\) 0.481432 0.0161286
\(892\) 0 0
\(893\) −9.64327 −0.322700
\(894\) 0 0
\(895\) −4.16848 −0.139337
\(896\) 0 0
\(897\) −3.31751 −0.110769
\(898\) 0 0
\(899\) 10.6875 0.356447
\(900\) 0 0
\(901\) −7.45612 −0.248399
\(902\) 0 0
\(903\) 18.2783 0.608265
\(904\) 0 0
\(905\) −19.4546 −0.646692
\(906\) 0 0
\(907\) −5.81028 −0.192927 −0.0964636 0.995337i \(-0.530753\pi\)
−0.0964636 + 0.995337i \(0.530753\pi\)
\(908\) 0 0
\(909\) 19.3882 0.643067
\(910\) 0 0
\(911\) −49.2030 −1.63017 −0.815084 0.579342i \(-0.803309\pi\)
−0.815084 + 0.579342i \(0.803309\pi\)
\(912\) 0 0
\(913\) 1.70936 0.0565716
\(914\) 0 0
\(915\) −5.34317 −0.176640
\(916\) 0 0
\(917\) 6.26820 0.206994
\(918\) 0 0
\(919\) 15.8208 0.521878 0.260939 0.965355i \(-0.415968\pi\)
0.260939 + 0.965355i \(0.415968\pi\)
\(920\) 0 0
\(921\) 29.1525 0.960609
\(922\) 0 0
\(923\) 62.8598 2.06906
\(924\) 0 0
\(925\) 27.1895 0.893985
\(926\) 0 0
\(927\) 27.0658 0.888958
\(928\) 0 0
\(929\) 31.1185 1.02096 0.510482 0.859888i \(-0.329467\pi\)
0.510482 + 0.859888i \(0.329467\pi\)
\(930\) 0 0
\(931\) −1.73250 −0.0567804
\(932\) 0 0
\(933\) −12.3345 −0.403813
\(934\) 0 0
\(935\) 0.223856 0.00732088
\(936\) 0 0
\(937\) 28.1811 0.920638 0.460319 0.887754i \(-0.347735\pi\)
0.460319 + 0.887754i \(0.347735\pi\)
\(938\) 0 0
\(939\) 30.1196 0.982916
\(940\) 0 0
\(941\) −49.1766 −1.60311 −0.801555 0.597920i \(-0.795994\pi\)
−0.801555 + 0.597920i \(0.795994\pi\)
\(942\) 0 0
\(943\) 0.449283 0.0146307
\(944\) 0 0
\(945\) −14.1941 −0.461734
\(946\) 0 0
\(947\) −45.5513 −1.48022 −0.740109 0.672487i \(-0.765226\pi\)
−0.740109 + 0.672487i \(0.765226\pi\)
\(948\) 0 0
\(949\) 38.2151 1.24052
\(950\) 0 0
\(951\) −1.45909 −0.0473144
\(952\) 0 0
\(953\) −45.4307 −1.47165 −0.735823 0.677174i \(-0.763204\pi\)
−0.735823 + 0.677174i \(0.763204\pi\)
\(954\) 0 0
\(955\) −7.24291 −0.234375
\(956\) 0 0
\(957\) 1.44591 0.0467397
\(958\) 0 0
\(959\) 49.0838 1.58500
\(960\) 0 0
\(961\) −28.9645 −0.934340
\(962\) 0 0
\(963\) 8.91338 0.287230
\(964\) 0 0
\(965\) 20.0739 0.646200
\(966\) 0 0
\(967\) −13.0778 −0.420555 −0.210277 0.977642i \(-0.567437\pi\)
−0.210277 + 0.977642i \(0.567437\pi\)
\(968\) 0 0
\(969\) −0.725867 −0.0233182
\(970\) 0 0
\(971\) −20.1513 −0.646687 −0.323344 0.946282i \(-0.604807\pi\)
−0.323344 + 0.946282i \(0.604807\pi\)
\(972\) 0 0
\(973\) 11.7876 0.377894
\(974\) 0 0
\(975\) 17.9862 0.576018
\(976\) 0 0
\(977\) −20.8525 −0.667131 −0.333565 0.942727i \(-0.608252\pi\)
−0.333565 + 0.942727i \(0.608252\pi\)
\(978\) 0 0
\(979\) 2.20527 0.0704809
\(980\) 0 0
\(981\) 13.5174 0.431577
\(982\) 0 0
\(983\) 31.3109 0.998664 0.499332 0.866411i \(-0.333579\pi\)
0.499332 + 0.866411i \(0.333579\pi\)
\(984\) 0 0
\(985\) 4.14128 0.131952
\(986\) 0 0
\(987\) −20.0889 −0.639436
\(988\) 0 0
\(989\) 5.28760 0.168136
\(990\) 0 0
\(991\) −20.7897 −0.660407 −0.330204 0.943910i \(-0.607117\pi\)
−0.330204 + 0.943910i \(0.607117\pi\)
\(992\) 0 0
\(993\) 15.6120 0.495431
\(994\) 0 0
\(995\) −20.6849 −0.655755
\(996\) 0 0
\(997\) 52.4444 1.66093 0.830465 0.557070i \(-0.188075\pi\)
0.830465 + 0.557070i \(0.188075\pi\)
\(998\) 0 0
\(999\) −39.0981 −1.23701
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 \(a_p\))