Properties

Label 6008.2.a.e.1.38
Level 6008
Weight 2
Character 6008.1
Self dual Yes
Analytic conductor 47.974
Analytic rank 0
Dimension 50
CM No

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Newspace parameters

Level: \( N \) = \( 6008 = 2^{3} \cdot 751 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6008.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9741215344\)
Analytic rank: \(0\)
Dimension: \(50\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.38
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.13238 q^{3} +3.35698 q^{5} +0.313319 q^{7} +1.54704 q^{9} +O(q^{10})\) \(q+2.13238 q^{3} +3.35698 q^{5} +0.313319 q^{7} +1.54704 q^{9} +2.50247 q^{11} -6.16150 q^{13} +7.15836 q^{15} +5.24751 q^{17} +7.03909 q^{19} +0.668115 q^{21} +1.85469 q^{23} +6.26934 q^{25} -3.09826 q^{27} -7.13470 q^{29} +8.61037 q^{31} +5.33621 q^{33} +1.05181 q^{35} +11.0889 q^{37} -13.1386 q^{39} -5.42641 q^{41} -4.95676 q^{43} +5.19339 q^{45} +2.99818 q^{47} -6.90183 q^{49} +11.1897 q^{51} +6.00096 q^{53} +8.40074 q^{55} +15.0100 q^{57} +10.4199 q^{59} -12.3401 q^{61} +0.484718 q^{63} -20.6840 q^{65} -7.81203 q^{67} +3.95490 q^{69} -2.57760 q^{71} -4.30939 q^{73} +13.3686 q^{75} +0.784070 q^{77} +2.00325 q^{79} -11.2478 q^{81} -12.5725 q^{83} +17.6158 q^{85} -15.2139 q^{87} +3.54250 q^{89} -1.93052 q^{91} +18.3606 q^{93} +23.6301 q^{95} +9.22478 q^{97} +3.87142 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} + O(q^{10}) \) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} - 5q^{11} + 36q^{13} + 5q^{15} + 14q^{17} + 9q^{19} + 30q^{21} + 3q^{23} + 71q^{25} + 24q^{27} + 61q^{29} + 27q^{31} + 24q^{33} - 7q^{35} + 56q^{37} - 2q^{39} + 10q^{41} + 19q^{43} + 76q^{45} + 3q^{47} + 82q^{49} - q^{51} + 56q^{53} + 7q^{55} + 35q^{57} - q^{59} + 67q^{61} + 25q^{63} + 27q^{65} + 46q^{67} + 68q^{69} + 4q^{71} + 62q^{73} + 27q^{75} + 71q^{77} + 7q^{79} + 74q^{81} - q^{83} + 72q^{85} + 25q^{87} + 19q^{89} + 45q^{91} + 72q^{93} - 24q^{95} + 81q^{97} + 16q^{99} + O(q^{100}) \)

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
\(3\) 2.13238 1.23113 0.615565 0.788086i \(-0.288928\pi\)
0.615565 + 0.788086i \(0.288928\pi\)
\(4\) 0 0
\(5\) 3.35698 1.50129 0.750644 0.660706i \(-0.229743\pi\)
0.750644 + 0.660706i \(0.229743\pi\)
\(6\) 0 0
\(7\) 0.313319 0.118424 0.0592118 0.998245i \(-0.481141\pi\)
0.0592118 + 0.998245i \(0.481141\pi\)
\(8\) 0 0
\(9\) 1.54704 0.515681
\(10\) 0 0
\(11\) 2.50247 0.754522 0.377261 0.926107i \(-0.376866\pi\)
0.377261 + 0.926107i \(0.376866\pi\)
\(12\) 0 0
\(13\) −6.16150 −1.70889 −0.854446 0.519540i \(-0.826103\pi\)
−0.854446 + 0.519540i \(0.826103\pi\)
\(14\) 0 0
\(15\) 7.15836 1.84828
\(16\) 0 0
\(17\) 5.24751 1.27271 0.636354 0.771397i \(-0.280442\pi\)
0.636354 + 0.771397i \(0.280442\pi\)
\(18\) 0 0
\(19\) 7.03909 1.61488 0.807439 0.589951i \(-0.200853\pi\)
0.807439 + 0.589951i \(0.200853\pi\)
\(20\) 0 0
\(21\) 0.668115 0.145795
\(22\) 0 0
\(23\) 1.85469 0.386729 0.193364 0.981127i \(-0.438060\pi\)
0.193364 + 0.981127i \(0.438060\pi\)
\(24\) 0 0
\(25\) 6.26934 1.25387
\(26\) 0 0
\(27\) −3.09826 −0.596260
\(28\) 0 0
\(29\) −7.13470 −1.32488 −0.662441 0.749114i \(-0.730479\pi\)
−0.662441 + 0.749114i \(0.730479\pi\)
\(30\) 0 0
\(31\) 8.61037 1.54647 0.773234 0.634120i \(-0.218638\pi\)
0.773234 + 0.634120i \(0.218638\pi\)
\(32\) 0 0
\(33\) 5.33621 0.928914
\(34\) 0 0
\(35\) 1.05181 0.177788
\(36\) 0 0
\(37\) 11.0889 1.82301 0.911503 0.411293i \(-0.134923\pi\)
0.911503 + 0.411293i \(0.134923\pi\)
\(38\) 0 0
\(39\) −13.1386 −2.10387
\(40\) 0 0
\(41\) −5.42641 −0.847464 −0.423732 0.905788i \(-0.639280\pi\)
−0.423732 + 0.905788i \(0.639280\pi\)
\(42\) 0 0
\(43\) −4.95676 −0.755899 −0.377949 0.925826i \(-0.623371\pi\)
−0.377949 + 0.925826i \(0.623371\pi\)
\(44\) 0 0
\(45\) 5.19339 0.774186
\(46\) 0 0
\(47\) 2.99818 0.437329 0.218665 0.975800i \(-0.429830\pi\)
0.218665 + 0.975800i \(0.429830\pi\)
\(48\) 0 0
\(49\) −6.90183 −0.985976
\(50\) 0 0
\(51\) 11.1897 1.56687
\(52\) 0 0
\(53\) 6.00096 0.824295 0.412147 0.911117i \(-0.364779\pi\)
0.412147 + 0.911117i \(0.364779\pi\)
\(54\) 0 0
\(55\) 8.40074 1.13276
\(56\) 0 0
\(57\) 15.0100 1.98812
\(58\) 0 0
\(59\) 10.4199 1.35656 0.678280 0.734804i \(-0.262726\pi\)
0.678280 + 0.734804i \(0.262726\pi\)
\(60\) 0 0
\(61\) −12.3401 −1.57999 −0.789994 0.613115i \(-0.789916\pi\)
−0.789994 + 0.613115i \(0.789916\pi\)
\(62\) 0 0
\(63\) 0.484718 0.0610687
\(64\) 0 0
\(65\) −20.6840 −2.56554
\(66\) 0 0
\(67\) −7.81203 −0.954392 −0.477196 0.878797i \(-0.658347\pi\)
−0.477196 + 0.878797i \(0.658347\pi\)
\(68\) 0 0
\(69\) 3.95490 0.476113
\(70\) 0 0
\(71\) −2.57760 −0.305905 −0.152953 0.988234i \(-0.548878\pi\)
−0.152953 + 0.988234i \(0.548878\pi\)
\(72\) 0 0
\(73\) −4.30939 −0.504376 −0.252188 0.967678i \(-0.581150\pi\)
−0.252188 + 0.967678i \(0.581150\pi\)
\(74\) 0 0
\(75\) 13.3686 1.54367
\(76\) 0 0
\(77\) 0.784070 0.0893531
\(78\) 0 0
\(79\) 2.00325 0.225384 0.112692 0.993630i \(-0.464053\pi\)
0.112692 + 0.993630i \(0.464053\pi\)
\(80\) 0 0
\(81\) −11.2478 −1.24975
\(82\) 0 0
\(83\) −12.5725 −1.38001 −0.690006 0.723803i \(-0.742392\pi\)
−0.690006 + 0.723803i \(0.742392\pi\)
\(84\) 0 0
\(85\) 17.6158 1.91070
\(86\) 0 0
\(87\) −15.2139 −1.63110
\(88\) 0 0
\(89\) 3.54250 0.375504 0.187752 0.982216i \(-0.439880\pi\)
0.187752 + 0.982216i \(0.439880\pi\)
\(90\) 0 0
\(91\) −1.93052 −0.202373
\(92\) 0 0
\(93\) 18.3606 1.90390
\(94\) 0 0
\(95\) 23.6301 2.42440
\(96\) 0 0
\(97\) 9.22478 0.936634 0.468317 0.883560i \(-0.344861\pi\)
0.468317 + 0.883560i \(0.344861\pi\)
\(98\) 0 0
\(99\) 3.87142 0.389092
\(100\) 0 0
\(101\) 18.4902 1.83985 0.919924 0.392096i \(-0.128250\pi\)
0.919924 + 0.392096i \(0.128250\pi\)
\(102\) 0 0
\(103\) 2.21242 0.217997 0.108998 0.994042i \(-0.465236\pi\)
0.108998 + 0.994042i \(0.465236\pi\)
\(104\) 0 0
\(105\) 2.24285 0.218880
\(106\) 0 0
\(107\) −7.86881 −0.760707 −0.380353 0.924841i \(-0.624198\pi\)
−0.380353 + 0.924841i \(0.624198\pi\)
\(108\) 0 0
\(109\) 2.53430 0.242742 0.121371 0.992607i \(-0.461271\pi\)
0.121371 + 0.992607i \(0.461271\pi\)
\(110\) 0 0
\(111\) 23.6458 2.24436
\(112\) 0 0
\(113\) −12.8349 −1.20741 −0.603703 0.797209i \(-0.706309\pi\)
−0.603703 + 0.797209i \(0.706309\pi\)
\(114\) 0 0
\(115\) 6.22615 0.580592
\(116\) 0 0
\(117\) −9.53209 −0.881242
\(118\) 0 0
\(119\) 1.64414 0.150719
\(120\) 0 0
\(121\) −4.73767 −0.430697
\(122\) 0 0
\(123\) −11.5712 −1.04334
\(124\) 0 0
\(125\) 4.26116 0.381130
\(126\) 0 0
\(127\) 4.30900 0.382362 0.191181 0.981555i \(-0.438768\pi\)
0.191181 + 0.981555i \(0.438768\pi\)
\(128\) 0 0
\(129\) −10.5697 −0.930609
\(130\) 0 0
\(131\) −12.3090 −1.07544 −0.537720 0.843123i \(-0.680714\pi\)
−0.537720 + 0.843123i \(0.680714\pi\)
\(132\) 0 0
\(133\) 2.20548 0.191239
\(134\) 0 0
\(135\) −10.4008 −0.895159
\(136\) 0 0
\(137\) 6.97954 0.596302 0.298151 0.954519i \(-0.403630\pi\)
0.298151 + 0.954519i \(0.403630\pi\)
\(138\) 0 0
\(139\) −10.6268 −0.901352 −0.450676 0.892688i \(-0.648817\pi\)
−0.450676 + 0.892688i \(0.648817\pi\)
\(140\) 0 0
\(141\) 6.39325 0.538409
\(142\) 0 0
\(143\) −15.4189 −1.28940
\(144\) 0 0
\(145\) −23.9511 −1.98903
\(146\) 0 0
\(147\) −14.7173 −1.21386
\(148\) 0 0
\(149\) 14.8083 1.21314 0.606572 0.795029i \(-0.292544\pi\)
0.606572 + 0.795029i \(0.292544\pi\)
\(150\) 0 0
\(151\) −7.22480 −0.587946 −0.293973 0.955814i \(-0.594978\pi\)
−0.293973 + 0.955814i \(0.594978\pi\)
\(152\) 0 0
\(153\) 8.11811 0.656311
\(154\) 0 0
\(155\) 28.9049 2.32170
\(156\) 0 0
\(157\) 21.9819 1.75434 0.877172 0.480176i \(-0.159427\pi\)
0.877172 + 0.480176i \(0.159427\pi\)
\(158\) 0 0
\(159\) 12.7963 1.01481
\(160\) 0 0
\(161\) 0.581109 0.0457978
\(162\) 0 0
\(163\) 15.0863 1.18165 0.590827 0.806799i \(-0.298802\pi\)
0.590827 + 0.806799i \(0.298802\pi\)
\(164\) 0 0
\(165\) 17.9136 1.39457
\(166\) 0 0
\(167\) 3.15656 0.244262 0.122131 0.992514i \(-0.461027\pi\)
0.122131 + 0.992514i \(0.461027\pi\)
\(168\) 0 0
\(169\) 24.9640 1.92031
\(170\) 0 0
\(171\) 10.8898 0.832761
\(172\) 0 0
\(173\) 21.8410 1.66054 0.830270 0.557362i \(-0.188186\pi\)
0.830270 + 0.557362i \(0.188186\pi\)
\(174\) 0 0
\(175\) 1.96431 0.148488
\(176\) 0 0
\(177\) 22.2192 1.67010
\(178\) 0 0
\(179\) 21.6640 1.61924 0.809620 0.586954i \(-0.199673\pi\)
0.809620 + 0.586954i \(0.199673\pi\)
\(180\) 0 0
\(181\) 5.94327 0.441760 0.220880 0.975301i \(-0.429107\pi\)
0.220880 + 0.975301i \(0.429107\pi\)
\(182\) 0 0
\(183\) −26.3138 −1.94517
\(184\) 0 0
\(185\) 37.2253 2.73686
\(186\) 0 0
\(187\) 13.1317 0.960286
\(188\) 0 0
\(189\) −0.970744 −0.0706112
\(190\) 0 0
\(191\) −5.91783 −0.428199 −0.214100 0.976812i \(-0.568682\pi\)
−0.214100 + 0.976812i \(0.568682\pi\)
\(192\) 0 0
\(193\) −17.8803 −1.28705 −0.643526 0.765424i \(-0.722529\pi\)
−0.643526 + 0.765424i \(0.722529\pi\)
\(194\) 0 0
\(195\) −44.1062 −3.15851
\(196\) 0 0
\(197\) 20.1986 1.43909 0.719544 0.694446i \(-0.244351\pi\)
0.719544 + 0.694446i \(0.244351\pi\)
\(198\) 0 0
\(199\) 3.53340 0.250476 0.125238 0.992127i \(-0.460031\pi\)
0.125238 + 0.992127i \(0.460031\pi\)
\(200\) 0 0
\(201\) −16.6582 −1.17498
\(202\) 0 0
\(203\) −2.23544 −0.156897
\(204\) 0 0
\(205\) −18.2164 −1.27229
\(206\) 0 0
\(207\) 2.86928 0.199429
\(208\) 0 0
\(209\) 17.6151 1.21846
\(210\) 0 0
\(211\) −20.9948 −1.44534 −0.722670 0.691193i \(-0.757085\pi\)
−0.722670 + 0.691193i \(0.757085\pi\)
\(212\) 0 0
\(213\) −5.49642 −0.376609
\(214\) 0 0
\(215\) −16.6398 −1.13482
\(216\) 0 0
\(217\) 2.69780 0.183138
\(218\) 0 0
\(219\) −9.18926 −0.620953
\(220\) 0 0
\(221\) −32.3325 −2.17492
\(222\) 0 0
\(223\) −12.7911 −0.856552 −0.428276 0.903648i \(-0.640879\pi\)
−0.428276 + 0.903648i \(0.640879\pi\)
\(224\) 0 0
\(225\) 9.69893 0.646596
\(226\) 0 0
\(227\) −21.3732 −1.41859 −0.709294 0.704912i \(-0.750986\pi\)
−0.709294 + 0.704912i \(0.750986\pi\)
\(228\) 0 0
\(229\) −12.0904 −0.798953 −0.399477 0.916743i \(-0.630808\pi\)
−0.399477 + 0.916743i \(0.630808\pi\)
\(230\) 0 0
\(231\) 1.67194 0.110005
\(232\) 0 0
\(233\) −2.42805 −0.159067 −0.0795333 0.996832i \(-0.525343\pi\)
−0.0795333 + 0.996832i \(0.525343\pi\)
\(234\) 0 0
\(235\) 10.0648 0.656557
\(236\) 0 0
\(237\) 4.27170 0.277477
\(238\) 0 0
\(239\) 11.8069 0.763723 0.381861 0.924220i \(-0.375283\pi\)
0.381861 + 0.924220i \(0.375283\pi\)
\(240\) 0 0
\(241\) 6.28094 0.404591 0.202296 0.979325i \(-0.435160\pi\)
0.202296 + 0.979325i \(0.435160\pi\)
\(242\) 0 0
\(243\) −14.6898 −0.942349
\(244\) 0 0
\(245\) −23.1693 −1.48023
\(246\) 0 0
\(247\) −43.3713 −2.75965
\(248\) 0 0
\(249\) −26.8094 −1.69897
\(250\) 0 0
\(251\) 27.9428 1.76374 0.881868 0.471496i \(-0.156286\pi\)
0.881868 + 0.471496i \(0.156286\pi\)
\(252\) 0 0
\(253\) 4.64129 0.291795
\(254\) 0 0
\(255\) 37.5636 2.35232
\(256\) 0 0
\(257\) 5.42177 0.338201 0.169100 0.985599i \(-0.445914\pi\)
0.169100 + 0.985599i \(0.445914\pi\)
\(258\) 0 0
\(259\) 3.47437 0.215887
\(260\) 0 0
\(261\) −11.0377 −0.683215
\(262\) 0 0
\(263\) −14.1366 −0.871699 −0.435849 0.900020i \(-0.643552\pi\)
−0.435849 + 0.900020i \(0.643552\pi\)
\(264\) 0 0
\(265\) 20.1451 1.23750
\(266\) 0 0
\(267\) 7.55396 0.462295
\(268\) 0 0
\(269\) −9.45961 −0.576762 −0.288381 0.957516i \(-0.593117\pi\)
−0.288381 + 0.957516i \(0.593117\pi\)
\(270\) 0 0
\(271\) −20.9128 −1.27036 −0.635180 0.772364i \(-0.719074\pi\)
−0.635180 + 0.772364i \(0.719074\pi\)
\(272\) 0 0
\(273\) −4.11659 −0.249147
\(274\) 0 0
\(275\) 15.6888 0.946071
\(276\) 0 0
\(277\) −13.3043 −0.799375 −0.399688 0.916651i \(-0.630881\pi\)
−0.399688 + 0.916651i \(0.630881\pi\)
\(278\) 0 0
\(279\) 13.3206 0.797484
\(280\) 0 0
\(281\) −23.7950 −1.41949 −0.709746 0.704458i \(-0.751190\pi\)
−0.709746 + 0.704458i \(0.751190\pi\)
\(282\) 0 0
\(283\) −12.5028 −0.743215 −0.371607 0.928390i \(-0.621193\pi\)
−0.371607 + 0.928390i \(0.621193\pi\)
\(284\) 0 0
\(285\) 50.3884 2.98475
\(286\) 0 0
\(287\) −1.70020 −0.100360
\(288\) 0 0
\(289\) 10.5363 0.619785
\(290\) 0 0
\(291\) 19.6707 1.15312
\(292\) 0 0
\(293\) −19.4231 −1.13471 −0.567356 0.823473i \(-0.692033\pi\)
−0.567356 + 0.823473i \(0.692033\pi\)
\(294\) 0 0
\(295\) 34.9795 2.03659
\(296\) 0 0
\(297\) −7.75328 −0.449891
\(298\) 0 0
\(299\) −11.4276 −0.660878
\(300\) 0 0
\(301\) −1.55305 −0.0895162
\(302\) 0 0
\(303\) 39.4282 2.26509
\(304\) 0 0
\(305\) −41.4255 −2.37202
\(306\) 0 0
\(307\) −9.75183 −0.556566 −0.278283 0.960499i \(-0.589765\pi\)
−0.278283 + 0.960499i \(0.589765\pi\)
\(308\) 0 0
\(309\) 4.71773 0.268382
\(310\) 0 0
\(311\) 8.30282 0.470810 0.235405 0.971897i \(-0.424358\pi\)
0.235405 + 0.971897i \(0.424358\pi\)
\(312\) 0 0
\(313\) −9.78331 −0.552986 −0.276493 0.961016i \(-0.589172\pi\)
−0.276493 + 0.961016i \(0.589172\pi\)
\(314\) 0 0
\(315\) 1.62719 0.0916818
\(316\) 0 0
\(317\) −7.36431 −0.413621 −0.206810 0.978381i \(-0.566308\pi\)
−0.206810 + 0.978381i \(0.566308\pi\)
\(318\) 0 0
\(319\) −17.8543 −0.999652
\(320\) 0 0
\(321\) −16.7793 −0.936529
\(322\) 0 0
\(323\) 36.9377 2.05527
\(324\) 0 0
\(325\) −38.6285 −2.14273
\(326\) 0 0
\(327\) 5.40409 0.298847
\(328\) 0 0
\(329\) 0.939386 0.0517900
\(330\) 0 0
\(331\) −14.6384 −0.804602 −0.402301 0.915508i \(-0.631789\pi\)
−0.402301 + 0.915508i \(0.631789\pi\)
\(332\) 0 0
\(333\) 17.1550 0.940089
\(334\) 0 0
\(335\) −26.2249 −1.43282
\(336\) 0 0
\(337\) 4.36586 0.237824 0.118912 0.992905i \(-0.462059\pi\)
0.118912 + 0.992905i \(0.462059\pi\)
\(338\) 0 0
\(339\) −27.3689 −1.48647
\(340\) 0 0
\(341\) 21.5472 1.16684
\(342\) 0 0
\(343\) −4.35571 −0.235186
\(344\) 0 0
\(345\) 13.2765 0.714784
\(346\) 0 0
\(347\) 23.8023 1.27778 0.638888 0.769300i \(-0.279395\pi\)
0.638888 + 0.769300i \(0.279395\pi\)
\(348\) 0 0
\(349\) 5.40629 0.289392 0.144696 0.989476i \(-0.453780\pi\)
0.144696 + 0.989476i \(0.453780\pi\)
\(350\) 0 0
\(351\) 19.0899 1.01894
\(352\) 0 0
\(353\) −27.1508 −1.44509 −0.722545 0.691324i \(-0.757028\pi\)
−0.722545 + 0.691324i \(0.757028\pi\)
\(354\) 0 0
\(355\) −8.65297 −0.459252
\(356\) 0 0
\(357\) 3.50594 0.185554
\(358\) 0 0
\(359\) 28.1469 1.48553 0.742767 0.669550i \(-0.233513\pi\)
0.742767 + 0.669550i \(0.233513\pi\)
\(360\) 0 0
\(361\) 30.5488 1.60783
\(362\) 0 0
\(363\) −10.1025 −0.530244
\(364\) 0 0
\(365\) −14.4666 −0.757215
\(366\) 0 0
\(367\) −23.6066 −1.23225 −0.616126 0.787648i \(-0.711299\pi\)
−0.616126 + 0.787648i \(0.711299\pi\)
\(368\) 0 0
\(369\) −8.39489 −0.437021
\(370\) 0 0
\(371\) 1.88021 0.0976159
\(372\) 0 0
\(373\) 3.46416 0.179367 0.0896837 0.995970i \(-0.471414\pi\)
0.0896837 + 0.995970i \(0.471414\pi\)
\(374\) 0 0
\(375\) 9.08642 0.469220
\(376\) 0 0
\(377\) 43.9605 2.26408
\(378\) 0 0
\(379\) −24.9895 −1.28362 −0.641812 0.766862i \(-0.721817\pi\)
−0.641812 + 0.766862i \(0.721817\pi\)
\(380\) 0 0
\(381\) 9.18843 0.470737
\(382\) 0 0
\(383\) 11.5945 0.592450 0.296225 0.955118i \(-0.404272\pi\)
0.296225 + 0.955118i \(0.404272\pi\)
\(384\) 0 0
\(385\) 2.63211 0.134145
\(386\) 0 0
\(387\) −7.66831 −0.389802
\(388\) 0 0
\(389\) −13.1452 −0.666490 −0.333245 0.942840i \(-0.608144\pi\)
−0.333245 + 0.942840i \(0.608144\pi\)
\(390\) 0 0
\(391\) 9.73248 0.492193
\(392\) 0 0
\(393\) −26.2474 −1.32401
\(394\) 0 0
\(395\) 6.72489 0.338366
\(396\) 0 0
\(397\) −17.7720 −0.891953 −0.445977 0.895045i \(-0.647144\pi\)
−0.445977 + 0.895045i \(0.647144\pi\)
\(398\) 0 0
\(399\) 4.70292 0.235441
\(400\) 0 0
\(401\) 11.4734 0.572953 0.286477 0.958087i \(-0.407516\pi\)
0.286477 + 0.958087i \(0.407516\pi\)
\(402\) 0 0
\(403\) −53.0528 −2.64275
\(404\) 0 0
\(405\) −37.7586 −1.87624
\(406\) 0 0
\(407\) 27.7496 1.37550
\(408\) 0 0
\(409\) 9.21292 0.455549 0.227775 0.973714i \(-0.426855\pi\)
0.227775 + 0.973714i \(0.426855\pi\)
\(410\) 0 0
\(411\) 14.8830 0.734126
\(412\) 0 0
\(413\) 3.26476 0.160649
\(414\) 0 0
\(415\) −42.2057 −2.07180
\(416\) 0 0
\(417\) −22.6603 −1.10968
\(418\) 0 0
\(419\) −25.7212 −1.25656 −0.628281 0.777987i \(-0.716241\pi\)
−0.628281 + 0.777987i \(0.716241\pi\)
\(420\) 0 0
\(421\) 1.98970 0.0969722 0.0484861 0.998824i \(-0.484560\pi\)
0.0484861 + 0.998824i \(0.484560\pi\)
\(422\) 0 0
\(423\) 4.63831 0.225522
\(424\) 0 0
\(425\) 32.8984 1.59581
\(426\) 0 0
\(427\) −3.86639 −0.187108
\(428\) 0 0
\(429\) −32.8790 −1.58741
\(430\) 0 0
\(431\) 3.69245 0.177859 0.0889295 0.996038i \(-0.471655\pi\)
0.0889295 + 0.996038i \(0.471655\pi\)
\(432\) 0 0
\(433\) 26.8669 1.29114 0.645571 0.763700i \(-0.276620\pi\)
0.645571 + 0.763700i \(0.276620\pi\)
\(434\) 0 0
\(435\) −51.0728 −2.44875
\(436\) 0 0
\(437\) 13.0553 0.624520
\(438\) 0 0
\(439\) −0.131440 −0.00627329 −0.00313664 0.999995i \(-0.500998\pi\)
−0.00313664 + 0.999995i \(0.500998\pi\)
\(440\) 0 0
\(441\) −10.6774 −0.508449
\(442\) 0 0
\(443\) 17.6536 0.838748 0.419374 0.907814i \(-0.362250\pi\)
0.419374 + 0.907814i \(0.362250\pi\)
\(444\) 0 0
\(445\) 11.8921 0.563741
\(446\) 0 0
\(447\) 31.5769 1.49354
\(448\) 0 0
\(449\) 19.3359 0.912518 0.456259 0.889847i \(-0.349189\pi\)
0.456259 + 0.889847i \(0.349189\pi\)
\(450\) 0 0
\(451\) −13.5794 −0.639430
\(452\) 0 0
\(453\) −15.4060 −0.723837
\(454\) 0 0
\(455\) −6.48071 −0.303820
\(456\) 0 0
\(457\) 1.94628 0.0910430 0.0455215 0.998963i \(-0.485505\pi\)
0.0455215 + 0.998963i \(0.485505\pi\)
\(458\) 0 0
\(459\) −16.2581 −0.758865
\(460\) 0 0
\(461\) 14.3829 0.669877 0.334939 0.942240i \(-0.391284\pi\)
0.334939 + 0.942240i \(0.391284\pi\)
\(462\) 0 0
\(463\) 17.2676 0.802492 0.401246 0.915970i \(-0.368577\pi\)
0.401246 + 0.915970i \(0.368577\pi\)
\(464\) 0 0
\(465\) 61.6362 2.85831
\(466\) 0 0
\(467\) −27.1021 −1.25414 −0.627069 0.778964i \(-0.715745\pi\)
−0.627069 + 0.778964i \(0.715745\pi\)
\(468\) 0 0
\(469\) −2.44766 −0.113022
\(470\) 0 0
\(471\) 46.8737 2.15983
\(472\) 0 0
\(473\) −12.4041 −0.570342
\(474\) 0 0
\(475\) 44.1305 2.02484
\(476\) 0 0
\(477\) 9.28373 0.425073
\(478\) 0 0
\(479\) −13.3602 −0.610443 −0.305222 0.952281i \(-0.598731\pi\)
−0.305222 + 0.952281i \(0.598731\pi\)
\(480\) 0 0
\(481\) −68.3243 −3.11532
\(482\) 0 0
\(483\) 1.23914 0.0563830
\(484\) 0 0
\(485\) 30.9674 1.40616
\(486\) 0 0
\(487\) −19.3904 −0.878665 −0.439332 0.898325i \(-0.644785\pi\)
−0.439332 + 0.898325i \(0.644785\pi\)
\(488\) 0 0
\(489\) 32.1698 1.45477
\(490\) 0 0
\(491\) −22.3790 −1.00995 −0.504974 0.863135i \(-0.668498\pi\)
−0.504974 + 0.863135i \(0.668498\pi\)
\(492\) 0 0
\(493\) −37.4394 −1.68619
\(494\) 0 0
\(495\) 12.9963 0.584140
\(496\) 0 0
\(497\) −0.807612 −0.0362264
\(498\) 0 0
\(499\) −3.54098 −0.158516 −0.0792581 0.996854i \(-0.525255\pi\)
−0.0792581 + 0.996854i \(0.525255\pi\)
\(500\) 0 0
\(501\) 6.73099 0.300718
\(502\) 0 0
\(503\) 21.5119 0.959167 0.479583 0.877496i \(-0.340788\pi\)
0.479583 + 0.877496i \(0.340788\pi\)
\(504\) 0 0
\(505\) 62.0715 2.76214
\(506\) 0 0
\(507\) 53.2328 2.36415
\(508\) 0 0
\(509\) −22.6017 −1.00180 −0.500902 0.865504i \(-0.666998\pi\)
−0.500902 + 0.865504i \(0.666998\pi\)
\(510\) 0 0
\(511\) −1.35022 −0.0597300
\(512\) 0 0
\(513\) −21.8089 −0.962887
\(514\) 0 0
\(515\) 7.42707 0.327276
\(516\) 0 0
\(517\) 7.50283 0.329974
\(518\) 0 0
\(519\) 46.5733 2.04434
\(520\) 0 0
\(521\) −17.2507 −0.755767 −0.377883 0.925853i \(-0.623348\pi\)
−0.377883 + 0.925853i \(0.623348\pi\)
\(522\) 0 0
\(523\) 9.86567 0.431395 0.215698 0.976460i \(-0.430797\pi\)
0.215698 + 0.976460i \(0.430797\pi\)
\(524\) 0 0
\(525\) 4.18864 0.182807
\(526\) 0 0
\(527\) 45.1830 1.96820
\(528\) 0 0
\(529\) −19.5601 −0.850441
\(530\) 0 0
\(531\) 16.1201 0.699551
\(532\) 0 0
\(533\) 33.4348 1.44822
\(534\) 0 0
\(535\) −26.4155 −1.14204
\(536\) 0 0
\(537\) 46.1958 1.99350
\(538\) 0 0
\(539\) −17.2716 −0.743940
\(540\) 0 0
\(541\) −43.0278 −1.84991 −0.924954 0.380079i \(-0.875897\pi\)
−0.924954 + 0.380079i \(0.875897\pi\)
\(542\) 0 0
\(543\) 12.6733 0.543863
\(544\) 0 0
\(545\) 8.50761 0.364426
\(546\) 0 0
\(547\) −1.38431 −0.0591887 −0.0295944 0.999562i \(-0.509422\pi\)
−0.0295944 + 0.999562i \(0.509422\pi\)
\(548\) 0 0
\(549\) −19.0906 −0.814769
\(550\) 0 0
\(551\) −50.2218 −2.13952
\(552\) 0 0
\(553\) 0.627658 0.0266907
\(554\) 0 0
\(555\) 79.3785 3.36943
\(556\) 0 0
\(557\) −40.7280 −1.72570 −0.862850 0.505460i \(-0.831323\pi\)
−0.862850 + 0.505460i \(0.831323\pi\)
\(558\) 0 0
\(559\) 30.5411 1.29175
\(560\) 0 0
\(561\) 28.0018 1.18224
\(562\) 0 0
\(563\) 16.8633 0.710701 0.355351 0.934733i \(-0.384361\pi\)
0.355351 + 0.934733i \(0.384361\pi\)
\(564\) 0 0
\(565\) −43.0865 −1.81266
\(566\) 0 0
\(567\) −3.52415 −0.148000
\(568\) 0 0
\(569\) −5.38083 −0.225576 −0.112788 0.993619i \(-0.535978\pi\)
−0.112788 + 0.993619i \(0.535978\pi\)
\(570\) 0 0
\(571\) 8.16422 0.341662 0.170831 0.985300i \(-0.445355\pi\)
0.170831 + 0.985300i \(0.445355\pi\)
\(572\) 0 0
\(573\) −12.6191 −0.527169
\(574\) 0 0
\(575\) 11.6277 0.484907
\(576\) 0 0
\(577\) 38.3390 1.59607 0.798036 0.602610i \(-0.205872\pi\)
0.798036 + 0.602610i \(0.205872\pi\)
\(578\) 0 0
\(579\) −38.1276 −1.58453
\(580\) 0 0
\(581\) −3.93921 −0.163426
\(582\) 0 0
\(583\) 15.0172 0.621948
\(584\) 0 0
\(585\) −31.9991 −1.32300
\(586\) 0 0
\(587\) −35.8650 −1.48031 −0.740153 0.672439i \(-0.765247\pi\)
−0.740153 + 0.672439i \(0.765247\pi\)
\(588\) 0 0
\(589\) 60.6092 2.49736
\(590\) 0 0
\(591\) 43.0710 1.77171
\(592\) 0 0
\(593\) 43.6135 1.79099 0.895495 0.445071i \(-0.146822\pi\)
0.895495 + 0.445071i \(0.146822\pi\)
\(594\) 0 0
\(595\) 5.51937 0.226272
\(596\) 0 0
\(597\) 7.53454 0.308368
\(598\) 0 0
\(599\) −17.2171 −0.703474 −0.351737 0.936099i \(-0.614409\pi\)
−0.351737 + 0.936099i \(0.614409\pi\)
\(600\) 0 0
\(601\) 16.2288 0.661988 0.330994 0.943633i \(-0.392616\pi\)
0.330994 + 0.943633i \(0.392616\pi\)
\(602\) 0 0
\(603\) −12.0855 −0.492161
\(604\) 0 0
\(605\) −15.9043 −0.646601
\(606\) 0 0
\(607\) −32.3908 −1.31470 −0.657351 0.753584i \(-0.728323\pi\)
−0.657351 + 0.753584i \(0.728323\pi\)
\(608\) 0 0
\(609\) −4.76680 −0.193161
\(610\) 0 0
\(611\) −18.4733 −0.747348
\(612\) 0 0
\(613\) 34.0607 1.37570 0.687849 0.725853i \(-0.258555\pi\)
0.687849 + 0.725853i \(0.258555\pi\)
\(614\) 0 0
\(615\) −38.8443 −1.56635
\(616\) 0 0
\(617\) −17.0616 −0.686873 −0.343437 0.939176i \(-0.611591\pi\)
−0.343437 + 0.939176i \(0.611591\pi\)
\(618\) 0 0
\(619\) −3.65747 −0.147006 −0.0735031 0.997295i \(-0.523418\pi\)
−0.0735031 + 0.997295i \(0.523418\pi\)
\(620\) 0 0
\(621\) −5.74630 −0.230591
\(622\) 0 0
\(623\) 1.10993 0.0444685
\(624\) 0 0
\(625\) −17.0421 −0.681682
\(626\) 0 0
\(627\) 37.5620 1.50008
\(628\) 0 0
\(629\) 58.1892 2.32015
\(630\) 0 0
\(631\) 2.18425 0.0869537 0.0434769 0.999054i \(-0.486157\pi\)
0.0434769 + 0.999054i \(0.486157\pi\)
\(632\) 0 0
\(633\) −44.7688 −1.77940
\(634\) 0 0
\(635\) 14.4653 0.574036
\(636\) 0 0
\(637\) 42.5256 1.68493
\(638\) 0 0
\(639\) −3.98766 −0.157749
\(640\) 0 0
\(641\) −33.4019 −1.31930 −0.659648 0.751575i \(-0.729295\pi\)
−0.659648 + 0.751575i \(0.729295\pi\)
\(642\) 0 0
\(643\) −40.4816 −1.59644 −0.798219 0.602368i \(-0.794224\pi\)
−0.798219 + 0.602368i \(0.794224\pi\)
\(644\) 0 0
\(645\) −35.4823 −1.39711
\(646\) 0 0
\(647\) 10.0519 0.395181 0.197591 0.980285i \(-0.436688\pi\)
0.197591 + 0.980285i \(0.436688\pi\)
\(648\) 0 0
\(649\) 26.0755 1.02355
\(650\) 0 0
\(651\) 5.75272 0.225467
\(652\) 0 0
\(653\) 24.4580 0.957114 0.478557 0.878056i \(-0.341160\pi\)
0.478557 + 0.878056i \(0.341160\pi\)
\(654\) 0 0
\(655\) −41.3210 −1.61455
\(656\) 0 0
\(657\) −6.66681 −0.260097
\(658\) 0 0
\(659\) 41.2636 1.60740 0.803702 0.595032i \(-0.202861\pi\)
0.803702 + 0.595032i \(0.202861\pi\)
\(660\) 0 0
\(661\) 20.5331 0.798645 0.399323 0.916811i \(-0.369245\pi\)
0.399323 + 0.916811i \(0.369245\pi\)
\(662\) 0 0
\(663\) −68.9452 −2.67761
\(664\) 0 0
\(665\) 7.40377 0.287106
\(666\) 0 0
\(667\) −13.2326 −0.512370
\(668\) 0 0
\(669\) −27.2754 −1.05453
\(670\) 0 0
\(671\) −30.8807 −1.19214
\(672\) 0 0
\(673\) 23.7108 0.913986 0.456993 0.889470i \(-0.348927\pi\)
0.456993 + 0.889470i \(0.348927\pi\)
\(674\) 0 0
\(675\) −19.4240 −0.747632
\(676\) 0 0
\(677\) 17.6801 0.679501 0.339750 0.940516i \(-0.389657\pi\)
0.339750 + 0.940516i \(0.389657\pi\)
\(678\) 0 0
\(679\) 2.89030 0.110920
\(680\) 0 0
\(681\) −45.5758 −1.74647
\(682\) 0 0
\(683\) 4.14755 0.158702 0.0793508 0.996847i \(-0.474715\pi\)
0.0793508 + 0.996847i \(0.474715\pi\)
\(684\) 0 0
\(685\) 23.4302 0.895222
\(686\) 0 0
\(687\) −25.7812 −0.983615
\(688\) 0 0
\(689\) −36.9749 −1.40863
\(690\) 0 0
\(691\) −16.5345 −0.629002 −0.314501 0.949257i \(-0.601837\pi\)
−0.314501 + 0.949257i \(0.601837\pi\)
\(692\) 0 0
\(693\) 1.21299 0.0460777
\(694\) 0 0
\(695\) −35.6740 −1.35319
\(696\) 0 0
\(697\) −28.4752 −1.07857
\(698\) 0 0
\(699\) −5.17751 −0.195832
\(700\) 0 0
\(701\) −37.2653 −1.40749 −0.703745 0.710453i \(-0.748490\pi\)
−0.703745 + 0.710453i \(0.748490\pi\)
\(702\) 0 0
\(703\) 78.0559 2.94393
\(704\) 0 0
\(705\) 21.4620 0.808307
\(706\) 0 0
\(707\) 5.79335 0.217881
\(708\) 0 0
\(709\) −43.0375 −1.61631 −0.808154 0.588972i \(-0.799533\pi\)
−0.808154 + 0.588972i \(0.799533\pi\)
\(710\) 0 0
\(711\) 3.09912 0.116226
\(712\) 0 0
\(713\) 15.9695 0.598064
\(714\) 0 0
\(715\) −51.7611 −1.93576
\(716\) 0 0
\(717\) 25.1767 0.940242
\(718\) 0 0
\(719\) −27.8865 −1.03999 −0.519995 0.854169i \(-0.674066\pi\)
−0.519995 + 0.854169i \(0.674066\pi\)
\(720\) 0 0
\(721\) 0.693195 0.0258159
\(722\) 0 0
\(723\) 13.3934 0.498104
\(724\) 0 0
\(725\) −44.7299 −1.66123
\(726\) 0 0
\(727\) −35.4483 −1.31471 −0.657353 0.753583i \(-0.728324\pi\)
−0.657353 + 0.753583i \(0.728324\pi\)
\(728\) 0 0
\(729\) 2.41919 0.0895996
\(730\) 0 0
\(731\) −26.0106 −0.962038
\(732\) 0 0
\(733\) 6.68560 0.246938 0.123469 0.992348i \(-0.460598\pi\)
0.123469 + 0.992348i \(0.460598\pi\)
\(734\) 0 0
\(735\) −49.4058 −1.82236
\(736\) 0 0
\(737\) −19.5493 −0.720109
\(738\) 0 0
\(739\) −40.3367 −1.48381 −0.741905 0.670505i \(-0.766077\pi\)
−0.741905 + 0.670505i \(0.766077\pi\)
\(740\) 0 0
\(741\) −92.4841 −3.39749
\(742\) 0 0
\(743\) 44.6906 1.63954 0.819769 0.572694i \(-0.194102\pi\)
0.819769 + 0.572694i \(0.194102\pi\)
\(744\) 0 0
\(745\) 49.7112 1.82128
\(746\) 0 0
\(747\) −19.4502 −0.711646
\(748\) 0 0
\(749\) −2.46545 −0.0900856
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) 59.5847 2.17139
\(754\) 0 0
\(755\) −24.2535 −0.882676
\(756\) 0 0
\(757\) 8.74113 0.317702 0.158851 0.987303i \(-0.449221\pi\)
0.158851 + 0.987303i \(0.449221\pi\)
\(758\) 0 0
\(759\) 9.89699 0.359238
\(760\) 0 0
\(761\) −7.14722 −0.259087 −0.129543 0.991574i \(-0.541351\pi\)
−0.129543 + 0.991574i \(0.541351\pi\)
\(762\) 0 0
\(763\) 0.794045 0.0287464
\(764\) 0 0
\(765\) 27.2524 0.985312
\(766\) 0 0
\(767\) −64.2024 −2.31821
\(768\) 0 0
\(769\) −9.23824 −0.333140 −0.166570 0.986030i \(-0.553269\pi\)
−0.166570 + 0.986030i \(0.553269\pi\)
\(770\) 0 0
\(771\) 11.5613 0.416369
\(772\) 0 0
\(773\) −40.7693 −1.46637 −0.733185 0.680029i \(-0.761967\pi\)
−0.733185 + 0.680029i \(0.761967\pi\)
\(774\) 0 0
\(775\) 53.9814 1.93907
\(776\) 0 0
\(777\) 7.40867 0.265785
\(778\) 0 0
\(779\) −38.1970 −1.36855
\(780\) 0 0
\(781\) −6.45036 −0.230812
\(782\) 0 0
\(783\) 22.1052 0.789974
\(784\) 0 0
\(785\) 73.7928 2.63378
\(786\) 0 0
\(787\) 45.4381 1.61969 0.809847 0.586642i \(-0.199550\pi\)
0.809847 + 0.586642i \(0.199550\pi\)
\(788\) 0 0
\(789\) −30.1445 −1.07317
\(790\) 0 0
\(791\) −4.02142 −0.142985
\(792\) 0 0
\(793\) 76.0335 2.70003
\(794\) 0 0
\(795\) 42.9570 1.52353
\(796\) 0 0
\(797\) 39.5721 1.40172 0.700858 0.713301i \(-0.252801\pi\)
0.700858 + 0.713301i \(0.252801\pi\)
\(798\) 0 0
\(799\) 15.7330 0.556592
\(800\) 0 0
\(801\) 5.48040 0.193640
\(802\) 0 0
\(803\) −10.7841 −0.380563
\(804\) 0 0
\(805\) 1.95077 0.0687557
\(806\) 0 0
\(807\) −20.1715 −0.710069
\(808\) 0 0
\(809\) 21.7708 0.765419 0.382710 0.923869i \(-0.374991\pi\)
0.382710 + 0.923869i \(0.374991\pi\)
\(810\) 0 0
\(811\) −2.13128 −0.0748393 −0.0374197 0.999300i \(-0.511914\pi\)
−0.0374197 + 0.999300i \(0.511914\pi\)
\(812\) 0 0
\(813\) −44.5939 −1.56398
\(814\) 0 0
\(815\) 50.6446 1.77400
\(816\) 0 0
\(817\) −34.8911 −1.22068
\(818\) 0 0
\(819\) −2.98659 −0.104360
\(820\) 0 0
\(821\) 51.9223 1.81210 0.906051 0.423169i \(-0.139082\pi\)
0.906051 + 0.423169i \(0.139082\pi\)
\(822\) 0 0
\(823\) 13.3988 0.467054 0.233527 0.972350i \(-0.424973\pi\)
0.233527 + 0.972350i \(0.424973\pi\)
\(824\) 0 0
\(825\) 33.4545 1.16474
\(826\) 0 0
\(827\) 34.3066 1.19296 0.596478 0.802629i \(-0.296566\pi\)
0.596478 + 0.802629i \(0.296566\pi\)
\(828\) 0 0
\(829\) 27.8188 0.966186 0.483093 0.875569i \(-0.339513\pi\)
0.483093 + 0.875569i \(0.339513\pi\)
\(830\) 0 0
\(831\) −28.3697 −0.984135
\(832\) 0 0
\(833\) −36.2174 −1.25486
\(834\) 0 0
\(835\) 10.5965 0.366708
\(836\) 0 0
\(837\) −26.6772 −0.922098
\(838\) 0 0
\(839\) −24.7978 −0.856116 −0.428058 0.903751i \(-0.640802\pi\)
−0.428058 + 0.903751i \(0.640802\pi\)
\(840\) 0 0
\(841\) 21.9040 0.755310
\(842\) 0 0
\(843\) −50.7400 −1.74758
\(844\) 0 0
\(845\) 83.8039 2.88294
\(846\) 0 0
\(847\) −1.48440 −0.0510046
\(848\) 0 0
\(849\) −26.6607 −0.914994
\(850\) 0 0
\(851\) 20.5665 0.705009
\(852\) 0 0
\(853\) 30.7719 1.05361 0.526804 0.849987i \(-0.323390\pi\)
0.526804 + 0.849987i \(0.323390\pi\)
\(854\) 0 0
\(855\) 36.5568 1.25022
\(856\) 0 0
\(857\) −47.1993 −1.61230 −0.806149 0.591713i \(-0.798452\pi\)
−0.806149 + 0.591713i \(0.798452\pi\)
\(858\) 0 0
\(859\) −13.7918 −0.470570 −0.235285 0.971926i \(-0.575602\pi\)
−0.235285 + 0.971926i \(0.575602\pi\)
\(860\) 0 0
\(861\) −3.62547 −0.123556
\(862\) 0 0
\(863\) −17.9383 −0.610628 −0.305314 0.952252i \(-0.598761\pi\)
−0.305314 + 0.952252i \(0.598761\pi\)
\(864\) 0 0
\(865\) 73.3199 2.49295
\(866\) 0 0
\(867\) 22.4675 0.763036
\(868\) 0 0
\(869\) 5.01307 0.170057
\(870\) 0 0
\(871\) 48.1338 1.63095
\(872\) 0 0
\(873\) 14.2711 0.483004
\(874\) 0 0
\(875\) 1.33510 0.0451348
\(876\) 0 0
\(877\) 23.6917 0.800011 0.400005 0.916513i \(-0.369008\pi\)
0.400005 + 0.916513i \(0.369008\pi\)
\(878\) 0 0
\(879\) −41.4175 −1.39698
\(880\) 0 0
\(881\) −5.25534 −0.177057 −0.0885284 0.996074i \(-0.528216\pi\)
−0.0885284 + 0.996074i \(0.528216\pi\)
\(882\) 0 0
\(883\) 22.1745 0.746232 0.373116 0.927785i \(-0.378289\pi\)
0.373116 + 0.927785i \(0.378289\pi\)
\(884\) 0 0
\(885\) 74.5897 2.50730
\(886\) 0 0
\(887\) −8.20195 −0.275394 −0.137697 0.990474i \(-0.543970\pi\)
−0.137697 + 0.990474i \(0.543970\pi\)
\(888\) 0 0
\(889\) 1.35009 0.0452807
\(890\) 0 0
\(891\) −28.1472 −0.942967
\(892\) 0 0
\(893\) 21.1044 0.706233
\(894\) 0 0
\(895\) 72.7256 2.43095
\(896\) 0 0
\(897\) −24.3681 −0.813626
\(898\) 0 0
\(899\) −61.4325 −2.04889
\(900\) 0 0
\(901\) 31.4901 1.04909
\(902\) 0 0
\(903\) −3.31169 −0.110206
\(904\) 0 0
\(905\) 19.9515 0.663209
\(906\) 0 0
\(907\) 0.0575697 0.00191157 0.000955785 1.00000i \(-0.499696\pi\)
0.000955785 1.00000i \(0.499696\pi\)
\(908\) 0 0
\(909\) 28.6052 0.948774
\(910\) 0 0
\(911\) −40.9087 −1.35537 −0.677683 0.735354i \(-0.737016\pi\)
−0.677683 + 0.735354i \(0.737016\pi\)
\(912\) 0 0
\(913\) −31.4623 −1.04125
\(914\) 0 0
\(915\) −88.3349 −2.92026
\(916\) 0 0
\(917\) −3.85664 −0.127357
\(918\) 0 0
\(919\) −23.1149 −0.762490 −0.381245 0.924474i \(-0.624504\pi\)
−0.381245 + 0.924474i \(0.624504\pi\)
\(920\) 0 0
\(921\) −20.7946 −0.685205
\(922\) 0 0
\(923\) 15.8819 0.522759
\(924\) 0 0
\(925\) 69.5202 2.28581
\(926\) 0 0
\(927\) 3.42271 0.112417
\(928\) 0 0
\(929\) −10.8963 −0.357497 −0.178748 0.983895i \(-0.557205\pi\)
−0.178748 + 0.983895i \(0.557205\pi\)
\(930\) 0 0
\(931\) −48.5826 −1.59223
\(932\) 0 0
\(933\) 17.7048 0.579628
\(934\) 0 0
\(935\) 44.0829 1.44167
\(936\) 0 0
\(937\) 3.23087 0.105548 0.0527739 0.998606i \(-0.483194\pi\)
0.0527739 + 0.998606i \(0.483194\pi\)
\(938\) 0 0
\(939\) −20.8617 −0.680797
\(940\) 0 0
\(941\) −2.70781 −0.0882721 −0.0441360 0.999026i \(-0.514054\pi\)
−0.0441360 + 0.999026i \(0.514054\pi\)
\(942\) 0 0
\(943\) −10.0643 −0.327739
\(944\) 0 0
\(945\) −3.25877 −0.106008
\(946\) 0 0
\(947\) −24.6709 −0.801698 −0.400849 0.916144i \(-0.631285\pi\)
−0.400849 + 0.916144i \(0.631285\pi\)
\(948\) 0 0
\(949\) 26.5523 0.861925
\(950\) 0 0
\(951\) −15.7035 −0.509221
\(952\) 0 0
\(953\) −6.38885 −0.206955 −0.103478 0.994632i \(-0.532997\pi\)
−0.103478 + 0.994632i \(0.532997\pi\)
\(954\) 0 0
\(955\) −19.8661 −0.642851
\(956\) 0 0
\(957\) −38.0722 −1.23070
\(958\) 0 0
\(959\) 2.18682 0.0706162
\(960\) 0 0
\(961\) 43.1385 1.39157
\(962\) 0 0
\(963\) −12.1734 −0.392282
\(964\) 0 0
\(965\) −60.0239 −1.93224
\(966\) 0 0
\(967\) −39.8299 −1.28084 −0.640422 0.768023i \(-0.721240\pi\)
−0.640422 + 0.768023i \(0.721240\pi\)
\(968\) 0 0
\(969\) 78.7651 2.53030
\(970\) 0 0
\(971\) −53.3171 −1.71103 −0.855513 0.517781i \(-0.826758\pi\)
−0.855513 + 0.517781i \(0.826758\pi\)
\(972\) 0 0
\(973\) −3.32958 −0.106741
\(974\) 0 0
\(975\) −82.3707 −2.63797
\(976\) 0 0
\(977\) 5.88120 0.188156 0.0940781 0.995565i \(-0.470010\pi\)
0.0940781 + 0.995565i \(0.470010\pi\)
\(978\) 0 0
\(979\) 8.86499 0.283326
\(980\) 0 0
\(981\) 3.92067 0.125177
\(982\) 0 0
\(983\) −37.7762 −1.20487 −0.602436 0.798167i \(-0.705803\pi\)
−0.602436 + 0.798167i \(0.705803\pi\)
\(984\) 0 0
\(985\) 67.8063 2.16049
\(986\) 0 0
\(987\) 2.00313 0.0637603
\(988\) 0 0
\(989\) −9.19323 −0.292328
\(990\) 0 0
\(991\) 25.2590 0.802380 0.401190 0.915995i \(-0.368597\pi\)
0.401190 + 0.915995i \(0.368597\pi\)
\(992\) 0 0
\(993\) −31.2147 −0.990569
\(994\) 0 0
\(995\) 11.8616 0.376036
\(996\) 0 0
\(997\) −19.3072 −0.611467 −0.305733 0.952117i \(-0.598902\pi\)
−0.305733 + 0.952117i \(0.598902\pi\)
\(998\) 0 0
\(999\) −34.3563 −1.08699
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 \(a_p\))