Properties

Label 6008.2.a.e.1.27
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 1.27
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.343448 q^{3} -0.515640 q^{5} -3.09823 q^{7} -2.88204 q^{9} +O(q^{10})\) \(q+0.343448 q^{3} -0.515640 q^{5} -3.09823 q^{7} -2.88204 q^{9} +3.36617 q^{11} +6.89124 q^{13} -0.177095 q^{15} -2.74330 q^{17} +5.90448 q^{19} -1.06408 q^{21} +0.434326 q^{23} -4.73412 q^{25} -2.02018 q^{27} +0.715207 q^{29} -0.476381 q^{31} +1.15611 q^{33} +1.59757 q^{35} -10.3893 q^{37} +2.36678 q^{39} +5.09378 q^{41} -2.97309 q^{43} +1.48610 q^{45} +5.04407 q^{47} +2.59903 q^{49} -0.942183 q^{51} +8.94342 q^{53} -1.73573 q^{55} +2.02788 q^{57} -9.71744 q^{59} -9.74340 q^{61} +8.92924 q^{63} -3.55340 q^{65} +7.35306 q^{67} +0.149168 q^{69} -1.40295 q^{71} +16.7996 q^{73} -1.62592 q^{75} -10.4292 q^{77} -5.53188 q^{79} +7.95230 q^{81} -12.9852 q^{83} +1.41456 q^{85} +0.245636 q^{87} +0.906320 q^{89} -21.3506 q^{91} -0.163612 q^{93} -3.04458 q^{95} +0.281398 q^{97} -9.70146 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} + O(q^{10}) \) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} - 5q^{11} + 36q^{13} + 5q^{15} + 14q^{17} + 9q^{19} + 30q^{21} + 3q^{23} + 71q^{25} + 24q^{27} + 61q^{29} + 27q^{31} + 24q^{33} - 7q^{35} + 56q^{37} - 2q^{39} + 10q^{41} + 19q^{43} + 76q^{45} + 3q^{47} + 82q^{49} - q^{51} + 56q^{53} + 7q^{55} + 35q^{57} - q^{59} + 67q^{61} + 25q^{63} + 27q^{65} + 46q^{67} + 68q^{69} + 4q^{71} + 62q^{73} + 27q^{75} + 71q^{77} + 7q^{79} + 74q^{81} - q^{83} + 72q^{85} + 25q^{87} + 19q^{89} + 45q^{91} + 72q^{93} - 24q^{95} + 81q^{97} + 16q^{99} + O(q^{100}) \)

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
\(3\) 0.343448 0.198290 0.0991449 0.995073i \(-0.468389\pi\)
0.0991449 + 0.995073i \(0.468389\pi\)
\(4\) 0 0
\(5\) −0.515640 −0.230601 −0.115301 0.993331i \(-0.536783\pi\)
−0.115301 + 0.993331i \(0.536783\pi\)
\(6\) 0 0
\(7\) −3.09823 −1.17102 −0.585511 0.810665i \(-0.699106\pi\)
−0.585511 + 0.810665i \(0.699106\pi\)
\(8\) 0 0
\(9\) −2.88204 −0.960681
\(10\) 0 0
\(11\) 3.36617 1.01494 0.507470 0.861670i \(-0.330581\pi\)
0.507470 + 0.861670i \(0.330581\pi\)
\(12\) 0 0
\(13\) 6.89124 1.91128 0.955642 0.294529i \(-0.0951629\pi\)
0.955642 + 0.294529i \(0.0951629\pi\)
\(14\) 0 0
\(15\) −0.177095 −0.0457259
\(16\) 0 0
\(17\) −2.74330 −0.665349 −0.332675 0.943042i \(-0.607951\pi\)
−0.332675 + 0.943042i \(0.607951\pi\)
\(18\) 0 0
\(19\) 5.90448 1.35458 0.677290 0.735716i \(-0.263154\pi\)
0.677290 + 0.735716i \(0.263154\pi\)
\(20\) 0 0
\(21\) −1.06408 −0.232202
\(22\) 0 0
\(23\) 0.434326 0.0905631 0.0452816 0.998974i \(-0.485581\pi\)
0.0452816 + 0.998974i \(0.485581\pi\)
\(24\) 0 0
\(25\) −4.73412 −0.946823
\(26\) 0 0
\(27\) −2.02018 −0.388783
\(28\) 0 0
\(29\) 0.715207 0.132811 0.0664053 0.997793i \(-0.478847\pi\)
0.0664053 + 0.997793i \(0.478847\pi\)
\(30\) 0 0
\(31\) −0.476381 −0.0855606 −0.0427803 0.999085i \(-0.513622\pi\)
−0.0427803 + 0.999085i \(0.513622\pi\)
\(32\) 0 0
\(33\) 1.15611 0.201252
\(34\) 0 0
\(35\) 1.59757 0.270039
\(36\) 0 0
\(37\) −10.3893 −1.70799 −0.853995 0.520281i \(-0.825827\pi\)
−0.853995 + 0.520281i \(0.825827\pi\)
\(38\) 0 0
\(39\) 2.36678 0.378988
\(40\) 0 0
\(41\) 5.09378 0.795516 0.397758 0.917490i \(-0.369788\pi\)
0.397758 + 0.917490i \(0.369788\pi\)
\(42\) 0 0
\(43\) −2.97309 −0.453392 −0.226696 0.973966i \(-0.572792\pi\)
−0.226696 + 0.973966i \(0.572792\pi\)
\(44\) 0 0
\(45\) 1.48610 0.221534
\(46\) 0 0
\(47\) 5.04407 0.735753 0.367877 0.929875i \(-0.380085\pi\)
0.367877 + 0.929875i \(0.380085\pi\)
\(48\) 0 0
\(49\) 2.59903 0.371291
\(50\) 0 0
\(51\) −0.942183 −0.131932
\(52\) 0 0
\(53\) 8.94342 1.22847 0.614237 0.789122i \(-0.289464\pi\)
0.614237 + 0.789122i \(0.289464\pi\)
\(54\) 0 0
\(55\) −1.73573 −0.234046
\(56\) 0 0
\(57\) 2.02788 0.268600
\(58\) 0 0
\(59\) −9.71744 −1.26510 −0.632552 0.774518i \(-0.717992\pi\)
−0.632552 + 0.774518i \(0.717992\pi\)
\(60\) 0 0
\(61\) −9.74340 −1.24751 −0.623757 0.781618i \(-0.714395\pi\)
−0.623757 + 0.781618i \(0.714395\pi\)
\(62\) 0 0
\(63\) 8.92924 1.12498
\(64\) 0 0
\(65\) −3.55340 −0.440744
\(66\) 0 0
\(67\) 7.35306 0.898319 0.449160 0.893452i \(-0.351723\pi\)
0.449160 + 0.893452i \(0.351723\pi\)
\(68\) 0 0
\(69\) 0.149168 0.0179578
\(70\) 0 0
\(71\) −1.40295 −0.166500 −0.0832499 0.996529i \(-0.526530\pi\)
−0.0832499 + 0.996529i \(0.526530\pi\)
\(72\) 0 0
\(73\) 16.7996 1.96625 0.983124 0.182939i \(-0.0585612\pi\)
0.983124 + 0.182939i \(0.0585612\pi\)
\(74\) 0 0
\(75\) −1.62592 −0.187745
\(76\) 0 0
\(77\) −10.4292 −1.18852
\(78\) 0 0
\(79\) −5.53188 −0.622385 −0.311192 0.950347i \(-0.600728\pi\)
−0.311192 + 0.950347i \(0.600728\pi\)
\(80\) 0 0
\(81\) 7.95230 0.883589
\(82\) 0 0
\(83\) −12.9852 −1.42531 −0.712657 0.701512i \(-0.752509\pi\)
−0.712657 + 0.701512i \(0.752509\pi\)
\(84\) 0 0
\(85\) 1.41456 0.153430
\(86\) 0 0
\(87\) 0.245636 0.0263350
\(88\) 0 0
\(89\) 0.906320 0.0960697 0.0480349 0.998846i \(-0.484704\pi\)
0.0480349 + 0.998846i \(0.484704\pi\)
\(90\) 0 0
\(91\) −21.3506 −2.23816
\(92\) 0 0
\(93\) −0.163612 −0.0169658
\(94\) 0 0
\(95\) −3.04458 −0.312368
\(96\) 0 0
\(97\) 0.281398 0.0285716 0.0142858 0.999898i \(-0.495453\pi\)
0.0142858 + 0.999898i \(0.495453\pi\)
\(98\) 0 0
\(99\) −9.70146 −0.975033
\(100\) 0 0
\(101\) 18.4146 1.83232 0.916161 0.400810i \(-0.131271\pi\)
0.916161 + 0.400810i \(0.131271\pi\)
\(102\) 0 0
\(103\) 10.3375 1.01858 0.509291 0.860595i \(-0.329908\pi\)
0.509291 + 0.860595i \(0.329908\pi\)
\(104\) 0 0
\(105\) 0.548683 0.0535459
\(106\) 0 0
\(107\) 7.19350 0.695422 0.347711 0.937602i \(-0.386959\pi\)
0.347711 + 0.937602i \(0.386959\pi\)
\(108\) 0 0
\(109\) 8.15842 0.781435 0.390717 0.920511i \(-0.372227\pi\)
0.390717 + 0.920511i \(0.372227\pi\)
\(110\) 0 0
\(111\) −3.56819 −0.338677
\(112\) 0 0
\(113\) −3.72132 −0.350073 −0.175036 0.984562i \(-0.556004\pi\)
−0.175036 + 0.984562i \(0.556004\pi\)
\(114\) 0 0
\(115\) −0.223956 −0.0208840
\(116\) 0 0
\(117\) −19.8608 −1.83614
\(118\) 0 0
\(119\) 8.49939 0.779138
\(120\) 0 0
\(121\) 0.331129 0.0301026
\(122\) 0 0
\(123\) 1.74945 0.157743
\(124\) 0 0
\(125\) 5.01930 0.448940
\(126\) 0 0
\(127\) −4.16513 −0.369596 −0.184798 0.982777i \(-0.559163\pi\)
−0.184798 + 0.982777i \(0.559163\pi\)
\(128\) 0 0
\(129\) −1.02110 −0.0899030
\(130\) 0 0
\(131\) −8.44647 −0.737972 −0.368986 0.929435i \(-0.620295\pi\)
−0.368986 + 0.929435i \(0.620295\pi\)
\(132\) 0 0
\(133\) −18.2934 −1.58624
\(134\) 0 0
\(135\) 1.04168 0.0896538
\(136\) 0 0
\(137\) 8.24979 0.704827 0.352413 0.935844i \(-0.385361\pi\)
0.352413 + 0.935844i \(0.385361\pi\)
\(138\) 0 0
\(139\) 19.5669 1.65964 0.829822 0.558029i \(-0.188442\pi\)
0.829822 + 0.558029i \(0.188442\pi\)
\(140\) 0 0
\(141\) 1.73238 0.145892
\(142\) 0 0
\(143\) 23.1971 1.93984
\(144\) 0 0
\(145\) −0.368789 −0.0306263
\(146\) 0 0
\(147\) 0.892633 0.0736231
\(148\) 0 0
\(149\) 5.72499 0.469009 0.234505 0.972115i \(-0.424653\pi\)
0.234505 + 0.972115i \(0.424653\pi\)
\(150\) 0 0
\(151\) 11.2188 0.912977 0.456488 0.889729i \(-0.349107\pi\)
0.456488 + 0.889729i \(0.349107\pi\)
\(152\) 0 0
\(153\) 7.90632 0.639188
\(154\) 0 0
\(155\) 0.245641 0.0197304
\(156\) 0 0
\(157\) 11.0698 0.883467 0.441733 0.897146i \(-0.354364\pi\)
0.441733 + 0.897146i \(0.354364\pi\)
\(158\) 0 0
\(159\) 3.07160 0.243594
\(160\) 0 0
\(161\) −1.34564 −0.106051
\(162\) 0 0
\(163\) −2.14185 −0.167763 −0.0838813 0.996476i \(-0.526732\pi\)
−0.0838813 + 0.996476i \(0.526732\pi\)
\(164\) 0 0
\(165\) −0.596134 −0.0464090
\(166\) 0 0
\(167\) −13.1466 −1.01731 −0.508657 0.860970i \(-0.669858\pi\)
−0.508657 + 0.860970i \(0.669858\pi\)
\(168\) 0 0
\(169\) 34.4891 2.65301
\(170\) 0 0
\(171\) −17.0170 −1.30132
\(172\) 0 0
\(173\) −5.61280 −0.426733 −0.213367 0.976972i \(-0.568443\pi\)
−0.213367 + 0.976972i \(0.568443\pi\)
\(174\) 0 0
\(175\) 14.6674 1.10875
\(176\) 0 0
\(177\) −3.33744 −0.250857
\(178\) 0 0
\(179\) 4.12561 0.308363 0.154181 0.988043i \(-0.450726\pi\)
0.154181 + 0.988043i \(0.450726\pi\)
\(180\) 0 0
\(181\) 12.6748 0.942111 0.471056 0.882104i \(-0.343873\pi\)
0.471056 + 0.882104i \(0.343873\pi\)
\(182\) 0 0
\(183\) −3.34635 −0.247369
\(184\) 0 0
\(185\) 5.35714 0.393865
\(186\) 0 0
\(187\) −9.23444 −0.675289
\(188\) 0 0
\(189\) 6.25897 0.455273
\(190\) 0 0
\(191\) 14.2870 1.03377 0.516885 0.856055i \(-0.327091\pi\)
0.516885 + 0.856055i \(0.327091\pi\)
\(192\) 0 0
\(193\) 26.1431 1.88182 0.940911 0.338654i \(-0.109972\pi\)
0.940911 + 0.338654i \(0.109972\pi\)
\(194\) 0 0
\(195\) −1.22041 −0.0873951
\(196\) 0 0
\(197\) 13.8668 0.987966 0.493983 0.869472i \(-0.335541\pi\)
0.493983 + 0.869472i \(0.335541\pi\)
\(198\) 0 0
\(199\) 24.3548 1.72647 0.863234 0.504804i \(-0.168435\pi\)
0.863234 + 0.504804i \(0.168435\pi\)
\(200\) 0 0
\(201\) 2.52539 0.178128
\(202\) 0 0
\(203\) −2.21588 −0.155524
\(204\) 0 0
\(205\) −2.62656 −0.183447
\(206\) 0 0
\(207\) −1.25175 −0.0870023
\(208\) 0 0
\(209\) 19.8755 1.37482
\(210\) 0 0
\(211\) −8.23438 −0.566878 −0.283439 0.958990i \(-0.591475\pi\)
−0.283439 + 0.958990i \(0.591475\pi\)
\(212\) 0 0
\(213\) −0.481841 −0.0330152
\(214\) 0 0
\(215\) 1.53304 0.104553
\(216\) 0 0
\(217\) 1.47594 0.100193
\(218\) 0 0
\(219\) 5.76980 0.389887
\(220\) 0 0
\(221\) −18.9048 −1.27167
\(222\) 0 0
\(223\) −10.4987 −0.703044 −0.351522 0.936180i \(-0.614336\pi\)
−0.351522 + 0.936180i \(0.614336\pi\)
\(224\) 0 0
\(225\) 13.6439 0.909595
\(226\) 0 0
\(227\) 4.26952 0.283378 0.141689 0.989911i \(-0.454747\pi\)
0.141689 + 0.989911i \(0.454747\pi\)
\(228\) 0 0
\(229\) −14.6811 −0.970156 −0.485078 0.874471i \(-0.661209\pi\)
−0.485078 + 0.874471i \(0.661209\pi\)
\(230\) 0 0
\(231\) −3.58188 −0.235671
\(232\) 0 0
\(233\) 25.7022 1.68380 0.841902 0.539630i \(-0.181436\pi\)
0.841902 + 0.539630i \(0.181436\pi\)
\(234\) 0 0
\(235\) −2.60092 −0.169665
\(236\) 0 0
\(237\) −1.89991 −0.123413
\(238\) 0 0
\(239\) −1.27590 −0.0825314 −0.0412657 0.999148i \(-0.513139\pi\)
−0.0412657 + 0.999148i \(0.513139\pi\)
\(240\) 0 0
\(241\) 7.09166 0.456814 0.228407 0.973566i \(-0.426648\pi\)
0.228407 + 0.973566i \(0.426648\pi\)
\(242\) 0 0
\(243\) 8.79173 0.563990
\(244\) 0 0
\(245\) −1.34017 −0.0856200
\(246\) 0 0
\(247\) 40.6892 2.58899
\(248\) 0 0
\(249\) −4.45975 −0.282625
\(250\) 0 0
\(251\) −0.986908 −0.0622931 −0.0311465 0.999515i \(-0.509916\pi\)
−0.0311465 + 0.999515i \(0.509916\pi\)
\(252\) 0 0
\(253\) 1.46202 0.0919161
\(254\) 0 0
\(255\) 0.485827 0.0304237
\(256\) 0 0
\(257\) −16.2595 −1.01424 −0.507120 0.861875i \(-0.669290\pi\)
−0.507120 + 0.861875i \(0.669290\pi\)
\(258\) 0 0
\(259\) 32.1885 2.00009
\(260\) 0 0
\(261\) −2.06126 −0.127589
\(262\) 0 0
\(263\) 26.6080 1.64072 0.820360 0.571848i \(-0.193773\pi\)
0.820360 + 0.571848i \(0.193773\pi\)
\(264\) 0 0
\(265\) −4.61158 −0.283287
\(266\) 0 0
\(267\) 0.311274 0.0190496
\(268\) 0 0
\(269\) −7.21445 −0.439873 −0.219936 0.975514i \(-0.570585\pi\)
−0.219936 + 0.975514i \(0.570585\pi\)
\(270\) 0 0
\(271\) −8.37271 −0.508606 −0.254303 0.967125i \(-0.581846\pi\)
−0.254303 + 0.967125i \(0.581846\pi\)
\(272\) 0 0
\(273\) −7.33284 −0.443803
\(274\) 0 0
\(275\) −15.9359 −0.960968
\(276\) 0 0
\(277\) −2.26449 −0.136060 −0.0680301 0.997683i \(-0.521671\pi\)
−0.0680301 + 0.997683i \(0.521671\pi\)
\(278\) 0 0
\(279\) 1.37295 0.0821965
\(280\) 0 0
\(281\) 9.68208 0.577584 0.288792 0.957392i \(-0.406746\pi\)
0.288792 + 0.957392i \(0.406746\pi\)
\(282\) 0 0
\(283\) −3.63538 −0.216101 −0.108051 0.994145i \(-0.534461\pi\)
−0.108051 + 0.994145i \(0.534461\pi\)
\(284\) 0 0
\(285\) −1.04566 −0.0619394
\(286\) 0 0
\(287\) −15.7817 −0.931566
\(288\) 0 0
\(289\) −9.47428 −0.557311
\(290\) 0 0
\(291\) 0.0966455 0.00566546
\(292\) 0 0
\(293\) 26.6553 1.55722 0.778610 0.627508i \(-0.215925\pi\)
0.778610 + 0.627508i \(0.215925\pi\)
\(294\) 0 0
\(295\) 5.01070 0.291734
\(296\) 0 0
\(297\) −6.80027 −0.394591
\(298\) 0 0
\(299\) 2.99304 0.173092
\(300\) 0 0
\(301\) 9.21132 0.530931
\(302\) 0 0
\(303\) 6.32446 0.363331
\(304\) 0 0
\(305\) 5.02408 0.287678
\(306\) 0 0
\(307\) 13.2265 0.754878 0.377439 0.926034i \(-0.376805\pi\)
0.377439 + 0.926034i \(0.376805\pi\)
\(308\) 0 0
\(309\) 3.55038 0.201974
\(310\) 0 0
\(311\) −4.48783 −0.254481 −0.127241 0.991872i \(-0.540612\pi\)
−0.127241 + 0.991872i \(0.540612\pi\)
\(312\) 0 0
\(313\) 1.55093 0.0876638 0.0438319 0.999039i \(-0.486043\pi\)
0.0438319 + 0.999039i \(0.486043\pi\)
\(314\) 0 0
\(315\) −4.60427 −0.259421
\(316\) 0 0
\(317\) 25.0826 1.40878 0.704388 0.709815i \(-0.251221\pi\)
0.704388 + 0.709815i \(0.251221\pi\)
\(318\) 0 0
\(319\) 2.40751 0.134795
\(320\) 0 0
\(321\) 2.47059 0.137895
\(322\) 0 0
\(323\) −16.1978 −0.901269
\(324\) 0 0
\(325\) −32.6239 −1.80965
\(326\) 0 0
\(327\) 2.80199 0.154951
\(328\) 0 0
\(329\) −15.6277 −0.861582
\(330\) 0 0
\(331\) −9.79211 −0.538223 −0.269112 0.963109i \(-0.586730\pi\)
−0.269112 + 0.963109i \(0.586730\pi\)
\(332\) 0 0
\(333\) 29.9424 1.64083
\(334\) 0 0
\(335\) −3.79153 −0.207153
\(336\) 0 0
\(337\) −22.7208 −1.23768 −0.618842 0.785516i \(-0.712398\pi\)
−0.618842 + 0.785516i \(0.712398\pi\)
\(338\) 0 0
\(339\) −1.27808 −0.0694159
\(340\) 0 0
\(341\) −1.60358 −0.0868389
\(342\) 0 0
\(343\) 13.6352 0.736232
\(344\) 0 0
\(345\) −0.0769171 −0.00414108
\(346\) 0 0
\(347\) −14.8362 −0.796447 −0.398223 0.917288i \(-0.630373\pi\)
−0.398223 + 0.917288i \(0.630373\pi\)
\(348\) 0 0
\(349\) 3.21654 0.172177 0.0860887 0.996287i \(-0.472563\pi\)
0.0860887 + 0.996287i \(0.472563\pi\)
\(350\) 0 0
\(351\) −13.9215 −0.743075
\(352\) 0 0
\(353\) −21.8583 −1.16340 −0.581699 0.813404i \(-0.697612\pi\)
−0.581699 + 0.813404i \(0.697612\pi\)
\(354\) 0 0
\(355\) 0.723418 0.0383951
\(356\) 0 0
\(357\) 2.91910 0.154495
\(358\) 0 0
\(359\) −17.1130 −0.903191 −0.451595 0.892223i \(-0.649145\pi\)
−0.451595 + 0.892223i \(0.649145\pi\)
\(360\) 0 0
\(361\) 15.8629 0.834889
\(362\) 0 0
\(363\) 0.113726 0.00596905
\(364\) 0 0
\(365\) −8.66256 −0.453419
\(366\) 0 0
\(367\) −27.0160 −1.41023 −0.705113 0.709095i \(-0.749104\pi\)
−0.705113 + 0.709095i \(0.749104\pi\)
\(368\) 0 0
\(369\) −14.6805 −0.764237
\(370\) 0 0
\(371\) −27.7088 −1.43857
\(372\) 0 0
\(373\) 26.3165 1.36262 0.681309 0.731996i \(-0.261411\pi\)
0.681309 + 0.731996i \(0.261411\pi\)
\(374\) 0 0
\(375\) 1.72387 0.0890202
\(376\) 0 0
\(377\) 4.92866 0.253839
\(378\) 0 0
\(379\) 7.25669 0.372751 0.186376 0.982479i \(-0.440326\pi\)
0.186376 + 0.982479i \(0.440326\pi\)
\(380\) 0 0
\(381\) −1.43051 −0.0732871
\(382\) 0 0
\(383\) −6.90410 −0.352783 −0.176392 0.984320i \(-0.556442\pi\)
−0.176392 + 0.984320i \(0.556442\pi\)
\(384\) 0 0
\(385\) 5.37770 0.274073
\(386\) 0 0
\(387\) 8.56857 0.435565
\(388\) 0 0
\(389\) −3.64038 −0.184575 −0.0922873 0.995732i \(-0.529418\pi\)
−0.0922873 + 0.995732i \(0.529418\pi\)
\(390\) 0 0
\(391\) −1.19149 −0.0602561
\(392\) 0 0
\(393\) −2.90092 −0.146332
\(394\) 0 0
\(395\) 2.85246 0.143523
\(396\) 0 0
\(397\) 12.7633 0.640571 0.320286 0.947321i \(-0.396221\pi\)
0.320286 + 0.947321i \(0.396221\pi\)
\(398\) 0 0
\(399\) −6.28285 −0.314536
\(400\) 0 0
\(401\) 7.23113 0.361106 0.180553 0.983565i \(-0.442211\pi\)
0.180553 + 0.983565i \(0.442211\pi\)
\(402\) 0 0
\(403\) −3.28286 −0.163531
\(404\) 0 0
\(405\) −4.10052 −0.203757
\(406\) 0 0
\(407\) −34.9722 −1.73351
\(408\) 0 0
\(409\) −13.5958 −0.672267 −0.336134 0.941814i \(-0.609119\pi\)
−0.336134 + 0.941814i \(0.609119\pi\)
\(410\) 0 0
\(411\) 2.83337 0.139760
\(412\) 0 0
\(413\) 30.1069 1.48146
\(414\) 0 0
\(415\) 6.69570 0.328679
\(416\) 0 0
\(417\) 6.72021 0.329090
\(418\) 0 0
\(419\) −21.9840 −1.07399 −0.536995 0.843586i \(-0.680441\pi\)
−0.536995 + 0.843586i \(0.680441\pi\)
\(420\) 0 0
\(421\) 0.710762 0.0346404 0.0173202 0.999850i \(-0.494487\pi\)
0.0173202 + 0.999850i \(0.494487\pi\)
\(422\) 0 0
\(423\) −14.5372 −0.706824
\(424\) 0 0
\(425\) 12.9871 0.629968
\(426\) 0 0
\(427\) 30.1873 1.46087
\(428\) 0 0
\(429\) 7.96700 0.384650
\(430\) 0 0
\(431\) 24.9021 1.19949 0.599746 0.800190i \(-0.295268\pi\)
0.599746 + 0.800190i \(0.295268\pi\)
\(432\) 0 0
\(433\) 33.0635 1.58893 0.794465 0.607309i \(-0.207751\pi\)
0.794465 + 0.607309i \(0.207751\pi\)
\(434\) 0 0
\(435\) −0.126660 −0.00607288
\(436\) 0 0
\(437\) 2.56447 0.122675
\(438\) 0 0
\(439\) 36.2075 1.72809 0.864044 0.503416i \(-0.167924\pi\)
0.864044 + 0.503416i \(0.167924\pi\)
\(440\) 0 0
\(441\) −7.49053 −0.356692
\(442\) 0 0
\(443\) −8.82326 −0.419206 −0.209603 0.977787i \(-0.567217\pi\)
−0.209603 + 0.977787i \(0.567217\pi\)
\(444\) 0 0
\(445\) −0.467335 −0.0221538
\(446\) 0 0
\(447\) 1.96624 0.0929997
\(448\) 0 0
\(449\) −5.88516 −0.277738 −0.138869 0.990311i \(-0.544347\pi\)
−0.138869 + 0.990311i \(0.544347\pi\)
\(450\) 0 0
\(451\) 17.1466 0.807400
\(452\) 0 0
\(453\) 3.85309 0.181034
\(454\) 0 0
\(455\) 11.0092 0.516121
\(456\) 0 0
\(457\) 8.79112 0.411231 0.205616 0.978633i \(-0.434080\pi\)
0.205616 + 0.978633i \(0.434080\pi\)
\(458\) 0 0
\(459\) 5.54196 0.258676
\(460\) 0 0
\(461\) −10.3747 −0.483197 −0.241599 0.970376i \(-0.577672\pi\)
−0.241599 + 0.970376i \(0.577672\pi\)
\(462\) 0 0
\(463\) −41.0615 −1.90829 −0.954146 0.299342i \(-0.903233\pi\)
−0.954146 + 0.299342i \(0.903233\pi\)
\(464\) 0 0
\(465\) 0.0843650 0.00391233
\(466\) 0 0
\(467\) −32.4988 −1.50387 −0.751933 0.659239i \(-0.770879\pi\)
−0.751933 + 0.659239i \(0.770879\pi\)
\(468\) 0 0
\(469\) −22.7815 −1.05195
\(470\) 0 0
\(471\) 3.80190 0.175182
\(472\) 0 0
\(473\) −10.0079 −0.460165
\(474\) 0 0
\(475\) −27.9525 −1.28255
\(476\) 0 0
\(477\) −25.7753 −1.18017
\(478\) 0 0
\(479\) −29.6681 −1.35557 −0.677784 0.735261i \(-0.737060\pi\)
−0.677784 + 0.735261i \(0.737060\pi\)
\(480\) 0 0
\(481\) −71.5951 −3.26446
\(482\) 0 0
\(483\) −0.462158 −0.0210289
\(484\) 0 0
\(485\) −0.145100 −0.00658864
\(486\) 0 0
\(487\) −1.70979 −0.0774781 −0.0387390 0.999249i \(-0.512334\pi\)
−0.0387390 + 0.999249i \(0.512334\pi\)
\(488\) 0 0
\(489\) −0.735614 −0.0332656
\(490\) 0 0
\(491\) −43.4862 −1.96250 −0.981252 0.192732i \(-0.938265\pi\)
−0.981252 + 0.192732i \(0.938265\pi\)
\(492\) 0 0
\(493\) −1.96203 −0.0883654
\(494\) 0 0
\(495\) 5.00246 0.224844
\(496\) 0 0
\(497\) 4.34667 0.194975
\(498\) 0 0
\(499\) −2.03095 −0.0909178 −0.0454589 0.998966i \(-0.514475\pi\)
−0.0454589 + 0.998966i \(0.514475\pi\)
\(500\) 0 0
\(501\) −4.51517 −0.201723
\(502\) 0 0
\(503\) 39.7730 1.77339 0.886696 0.462353i \(-0.152995\pi\)
0.886696 + 0.462353i \(0.152995\pi\)
\(504\) 0 0
\(505\) −9.49531 −0.422536
\(506\) 0 0
\(507\) 11.8452 0.526065
\(508\) 0 0
\(509\) −24.3853 −1.08086 −0.540430 0.841389i \(-0.681738\pi\)
−0.540430 + 0.841389i \(0.681738\pi\)
\(510\) 0 0
\(511\) −52.0491 −2.30252
\(512\) 0 0
\(513\) −11.9281 −0.526638
\(514\) 0 0
\(515\) −5.33041 −0.234886
\(516\) 0 0
\(517\) 16.9792 0.746745
\(518\) 0 0
\(519\) −1.92771 −0.0846169
\(520\) 0 0
\(521\) −5.08675 −0.222854 −0.111427 0.993773i \(-0.535542\pi\)
−0.111427 + 0.993773i \(0.535542\pi\)
\(522\) 0 0
\(523\) 20.8229 0.910522 0.455261 0.890358i \(-0.349546\pi\)
0.455261 + 0.890358i \(0.349546\pi\)
\(524\) 0 0
\(525\) 5.03748 0.219854
\(526\) 0 0
\(527\) 1.30686 0.0569277
\(528\) 0 0
\(529\) −22.8114 −0.991798
\(530\) 0 0
\(531\) 28.0061 1.21536
\(532\) 0 0
\(533\) 35.1025 1.52046
\(534\) 0 0
\(535\) −3.70926 −0.160365
\(536\) 0 0
\(537\) 1.41693 0.0611452
\(538\) 0 0
\(539\) 8.74880 0.376838
\(540\) 0 0
\(541\) 16.6226 0.714659 0.357330 0.933978i \(-0.383687\pi\)
0.357330 + 0.933978i \(0.383687\pi\)
\(542\) 0 0
\(543\) 4.35314 0.186811
\(544\) 0 0
\(545\) −4.20681 −0.180200
\(546\) 0 0
\(547\) 16.4550 0.703564 0.351782 0.936082i \(-0.385576\pi\)
0.351782 + 0.936082i \(0.385576\pi\)
\(548\) 0 0
\(549\) 28.0809 1.19846
\(550\) 0 0
\(551\) 4.22292 0.179903
\(552\) 0 0
\(553\) 17.1390 0.728826
\(554\) 0 0
\(555\) 1.83990 0.0780993
\(556\) 0 0
\(557\) 14.8187 0.627889 0.313944 0.949441i \(-0.398349\pi\)
0.313944 + 0.949441i \(0.398349\pi\)
\(558\) 0 0
\(559\) −20.4883 −0.866561
\(560\) 0 0
\(561\) −3.17155 −0.133903
\(562\) 0 0
\(563\) −16.0405 −0.676026 −0.338013 0.941141i \(-0.609755\pi\)
−0.338013 + 0.941141i \(0.609755\pi\)
\(564\) 0 0
\(565\) 1.91886 0.0807272
\(566\) 0 0
\(567\) −24.6381 −1.03470
\(568\) 0 0
\(569\) −0.969004 −0.0406228 −0.0203114 0.999794i \(-0.506466\pi\)
−0.0203114 + 0.999794i \(0.506466\pi\)
\(570\) 0 0
\(571\) −22.6264 −0.946887 −0.473444 0.880824i \(-0.656989\pi\)
−0.473444 + 0.880824i \(0.656989\pi\)
\(572\) 0 0
\(573\) 4.90684 0.204986
\(574\) 0 0
\(575\) −2.05615 −0.0857473
\(576\) 0 0
\(577\) −3.91281 −0.162893 −0.0814463 0.996678i \(-0.525954\pi\)
−0.0814463 + 0.996678i \(0.525954\pi\)
\(578\) 0 0
\(579\) 8.97880 0.373146
\(580\) 0 0
\(581\) 40.2313 1.66907
\(582\) 0 0
\(583\) 30.1051 1.24683
\(584\) 0 0
\(585\) 10.2410 0.423415
\(586\) 0 0
\(587\) −20.2990 −0.837829 −0.418915 0.908026i \(-0.637589\pi\)
−0.418915 + 0.908026i \(0.637589\pi\)
\(588\) 0 0
\(589\) −2.81278 −0.115899
\(590\) 0 0
\(591\) 4.76251 0.195904
\(592\) 0 0
\(593\) 33.9897 1.39579 0.697894 0.716201i \(-0.254121\pi\)
0.697894 + 0.716201i \(0.254121\pi\)
\(594\) 0 0
\(595\) −4.38262 −0.179670
\(596\) 0 0
\(597\) 8.36462 0.342341
\(598\) 0 0
\(599\) 18.6637 0.762579 0.381290 0.924456i \(-0.375480\pi\)
0.381290 + 0.924456i \(0.375480\pi\)
\(600\) 0 0
\(601\) −27.5926 −1.12552 −0.562762 0.826619i \(-0.690261\pi\)
−0.562762 + 0.826619i \(0.690261\pi\)
\(602\) 0 0
\(603\) −21.1918 −0.862998
\(604\) 0 0
\(605\) −0.170743 −0.00694170
\(606\) 0 0
\(607\) 36.2459 1.47117 0.735587 0.677430i \(-0.236906\pi\)
0.735587 + 0.677430i \(0.236906\pi\)
\(608\) 0 0
\(609\) −0.761038 −0.0308388
\(610\) 0 0
\(611\) 34.7599 1.40623
\(612\) 0 0
\(613\) −11.4554 −0.462679 −0.231339 0.972873i \(-0.574311\pi\)
−0.231339 + 0.972873i \(0.574311\pi\)
\(614\) 0 0
\(615\) −0.902086 −0.0363756
\(616\) 0 0
\(617\) 14.9117 0.600324 0.300162 0.953888i \(-0.402959\pi\)
0.300162 + 0.953888i \(0.402959\pi\)
\(618\) 0 0
\(619\) 7.45267 0.299548 0.149774 0.988720i \(-0.452145\pi\)
0.149774 + 0.988720i \(0.452145\pi\)
\(620\) 0 0
\(621\) −0.877414 −0.0352094
\(622\) 0 0
\(623\) −2.80799 −0.112500
\(624\) 0 0
\(625\) 21.0824 0.843297
\(626\) 0 0
\(627\) 6.82620 0.272612
\(628\) 0 0
\(629\) 28.5010 1.13641
\(630\) 0 0
\(631\) −20.7325 −0.825348 −0.412674 0.910879i \(-0.635405\pi\)
−0.412674 + 0.910879i \(0.635405\pi\)
\(632\) 0 0
\(633\) −2.82808 −0.112406
\(634\) 0 0
\(635\) 2.14771 0.0852292
\(636\) 0 0
\(637\) 17.9106 0.709642
\(638\) 0 0
\(639\) 4.04337 0.159953
\(640\) 0 0
\(641\) −18.3496 −0.724766 −0.362383 0.932029i \(-0.618037\pi\)
−0.362383 + 0.932029i \(0.618037\pi\)
\(642\) 0 0
\(643\) −23.8401 −0.940160 −0.470080 0.882624i \(-0.655775\pi\)
−0.470080 + 0.882624i \(0.655775\pi\)
\(644\) 0 0
\(645\) 0.526521 0.0207317
\(646\) 0 0
\(647\) 15.2467 0.599411 0.299705 0.954032i \(-0.403112\pi\)
0.299705 + 0.954032i \(0.403112\pi\)
\(648\) 0 0
\(649\) −32.7106 −1.28400
\(650\) 0 0
\(651\) 0.506909 0.0198673
\(652\) 0 0
\(653\) 39.3804 1.54107 0.770536 0.637396i \(-0.219989\pi\)
0.770536 + 0.637396i \(0.219989\pi\)
\(654\) 0 0
\(655\) 4.35534 0.170177
\(656\) 0 0
\(657\) −48.4173 −1.88894
\(658\) 0 0
\(659\) 34.3768 1.33913 0.669566 0.742753i \(-0.266480\pi\)
0.669566 + 0.742753i \(0.266480\pi\)
\(660\) 0 0
\(661\) −35.8195 −1.39322 −0.696608 0.717452i \(-0.745308\pi\)
−0.696608 + 0.717452i \(0.745308\pi\)
\(662\) 0 0
\(663\) −6.49280 −0.252160
\(664\) 0 0
\(665\) 9.43283 0.365789
\(666\) 0 0
\(667\) 0.310633 0.0120277
\(668\) 0 0
\(669\) −3.60575 −0.139406
\(670\) 0 0
\(671\) −32.7980 −1.26615
\(672\) 0 0
\(673\) 38.7385 1.49326 0.746629 0.665240i \(-0.231671\pi\)
0.746629 + 0.665240i \(0.231671\pi\)
\(674\) 0 0
\(675\) 9.56375 0.368109
\(676\) 0 0
\(677\) 48.7473 1.87351 0.936756 0.349982i \(-0.113812\pi\)
0.936756 + 0.349982i \(0.113812\pi\)
\(678\) 0 0
\(679\) −0.871835 −0.0334580
\(680\) 0 0
\(681\) 1.46636 0.0561910
\(682\) 0 0
\(683\) −17.7784 −0.680273 −0.340136 0.940376i \(-0.610473\pi\)
−0.340136 + 0.940376i \(0.610473\pi\)
\(684\) 0 0
\(685\) −4.25392 −0.162534
\(686\) 0 0
\(687\) −5.04220 −0.192372
\(688\) 0 0
\(689\) 61.6312 2.34796
\(690\) 0 0
\(691\) 4.33759 0.165010 0.0825048 0.996591i \(-0.473708\pi\)
0.0825048 + 0.996591i \(0.473708\pi\)
\(692\) 0 0
\(693\) 30.0574 1.14178
\(694\) 0 0
\(695\) −10.0895 −0.382716
\(696\) 0 0
\(697\) −13.9738 −0.529295
\(698\) 0 0
\(699\) 8.82736 0.333881
\(700\) 0 0
\(701\) −4.91232 −0.185536 −0.0927679 0.995688i \(-0.529571\pi\)
−0.0927679 + 0.995688i \(0.529571\pi\)
\(702\) 0 0
\(703\) −61.3434 −2.31361
\(704\) 0 0
\(705\) −0.893282 −0.0336429
\(706\) 0 0
\(707\) −57.0527 −2.14569
\(708\) 0 0
\(709\) 13.2486 0.497560 0.248780 0.968560i \(-0.419970\pi\)
0.248780 + 0.968560i \(0.419970\pi\)
\(710\) 0 0
\(711\) 15.9431 0.597913
\(712\) 0 0
\(713\) −0.206905 −0.00774864
\(714\) 0 0
\(715\) −11.9613 −0.447329
\(716\) 0 0
\(717\) −0.438207 −0.0163651
\(718\) 0 0
\(719\) 4.93680 0.184112 0.0920558 0.995754i \(-0.470656\pi\)
0.0920558 + 0.995754i \(0.470656\pi\)
\(720\) 0 0
\(721\) −32.0279 −1.19278
\(722\) 0 0
\(723\) 2.43562 0.0905816
\(724\) 0 0
\(725\) −3.38587 −0.125748
\(726\) 0 0
\(727\) 6.18466 0.229377 0.114688 0.993402i \(-0.463413\pi\)
0.114688 + 0.993402i \(0.463413\pi\)
\(728\) 0 0
\(729\) −20.8374 −0.771756
\(730\) 0 0
\(731\) 8.15609 0.301664
\(732\) 0 0
\(733\) −6.66526 −0.246187 −0.123093 0.992395i \(-0.539282\pi\)
−0.123093 + 0.992395i \(0.539282\pi\)
\(734\) 0 0
\(735\) −0.460277 −0.0169776
\(736\) 0 0
\(737\) 24.7517 0.911740
\(738\) 0 0
\(739\) 19.2596 0.708476 0.354238 0.935155i \(-0.384740\pi\)
0.354238 + 0.935155i \(0.384740\pi\)
\(740\) 0 0
\(741\) 13.9746 0.513370
\(742\) 0 0
\(743\) −15.7832 −0.579031 −0.289515 0.957173i \(-0.593494\pi\)
−0.289515 + 0.957173i \(0.593494\pi\)
\(744\) 0 0
\(745\) −2.95203 −0.108154
\(746\) 0 0
\(747\) 37.4240 1.36927
\(748\) 0 0
\(749\) −22.2871 −0.814354
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) −0.338952 −0.0123521
\(754\) 0 0
\(755\) −5.78489 −0.210534
\(756\) 0 0
\(757\) 24.7476 0.899466 0.449733 0.893163i \(-0.351519\pi\)
0.449733 + 0.893163i \(0.351519\pi\)
\(758\) 0 0
\(759\) 0.502126 0.0182260
\(760\) 0 0
\(761\) 21.3236 0.772979 0.386490 0.922294i \(-0.373688\pi\)
0.386490 + 0.922294i \(0.373688\pi\)
\(762\) 0 0
\(763\) −25.2767 −0.915077
\(764\) 0 0
\(765\) −4.07681 −0.147398
\(766\) 0 0
\(767\) −66.9652 −2.41797
\(768\) 0 0
\(769\) 0.0881767 0.00317973 0.00158987 0.999999i \(-0.499494\pi\)
0.00158987 + 0.999999i \(0.499494\pi\)
\(770\) 0 0
\(771\) −5.58430 −0.201114
\(772\) 0 0
\(773\) 45.5142 1.63703 0.818517 0.574483i \(-0.194797\pi\)
0.818517 + 0.574483i \(0.194797\pi\)
\(774\) 0 0
\(775\) 2.25525 0.0810108
\(776\) 0 0
\(777\) 11.0551 0.396598
\(778\) 0 0
\(779\) 30.0761 1.07759
\(780\) 0 0
\(781\) −4.72258 −0.168987
\(782\) 0 0
\(783\) −1.44484 −0.0516345
\(784\) 0 0
\(785\) −5.70803 −0.203728
\(786\) 0 0
\(787\) 8.08193 0.288090 0.144045 0.989571i \(-0.453989\pi\)
0.144045 + 0.989571i \(0.453989\pi\)
\(788\) 0 0
\(789\) 9.13846 0.325338
\(790\) 0 0
\(791\) 11.5295 0.409943
\(792\) 0 0
\(793\) −67.1441 −2.38436
\(794\) 0 0
\(795\) −1.58384 −0.0561730
\(796\) 0 0
\(797\) −7.26236 −0.257246 −0.128623 0.991694i \(-0.541056\pi\)
−0.128623 + 0.991694i \(0.541056\pi\)
\(798\) 0 0
\(799\) −13.8374 −0.489533
\(800\) 0 0
\(801\) −2.61205 −0.0922924
\(802\) 0 0
\(803\) 56.5505 1.99562
\(804\) 0 0
\(805\) 0.693866 0.0244556
\(806\) 0 0
\(807\) −2.47779 −0.0872223
\(808\) 0 0
\(809\) 25.6438 0.901588 0.450794 0.892628i \(-0.351141\pi\)
0.450794 + 0.892628i \(0.351141\pi\)
\(810\) 0 0
\(811\) −8.64096 −0.303425 −0.151712 0.988425i \(-0.548479\pi\)
−0.151712 + 0.988425i \(0.548479\pi\)
\(812\) 0 0
\(813\) −2.87559 −0.100851
\(814\) 0 0
\(815\) 1.10442 0.0386862
\(816\) 0 0
\(817\) −17.5545 −0.614156
\(818\) 0 0
\(819\) 61.5335 2.15015
\(820\) 0 0
\(821\) 18.9555 0.661552 0.330776 0.943709i \(-0.392690\pi\)
0.330776 + 0.943709i \(0.392690\pi\)
\(822\) 0 0
\(823\) 25.7522 0.897666 0.448833 0.893616i \(-0.351840\pi\)
0.448833 + 0.893616i \(0.351840\pi\)
\(824\) 0 0
\(825\) −5.47314 −0.190550
\(826\) 0 0
\(827\) 1.61480 0.0561522 0.0280761 0.999606i \(-0.491062\pi\)
0.0280761 + 0.999606i \(0.491062\pi\)
\(828\) 0 0
\(829\) 14.0914 0.489413 0.244707 0.969597i \(-0.421308\pi\)
0.244707 + 0.969597i \(0.421308\pi\)
\(830\) 0 0
\(831\) −0.777736 −0.0269793
\(832\) 0 0
\(833\) −7.12994 −0.247038
\(834\) 0 0
\(835\) 6.77890 0.234594
\(836\) 0 0
\(837\) 0.962375 0.0332645
\(838\) 0 0
\(839\) 33.3762 1.15228 0.576138 0.817353i \(-0.304559\pi\)
0.576138 + 0.817353i \(0.304559\pi\)
\(840\) 0 0
\(841\) −28.4885 −0.982361
\(842\) 0 0
\(843\) 3.32529 0.114529
\(844\) 0 0
\(845\) −17.7840 −0.611787
\(846\) 0 0
\(847\) −1.02591 −0.0352508
\(848\) 0 0
\(849\) −1.24856 −0.0428506
\(850\) 0 0
\(851\) −4.51234 −0.154681
\(852\) 0 0
\(853\) 0.535872 0.0183479 0.00917396 0.999958i \(-0.497080\pi\)
0.00917396 + 0.999958i \(0.497080\pi\)
\(854\) 0 0
\(855\) 8.77463 0.300086
\(856\) 0 0
\(857\) −9.21396 −0.314743 −0.157371 0.987539i \(-0.550302\pi\)
−0.157371 + 0.987539i \(0.550302\pi\)
\(858\) 0 0
\(859\) −45.3827 −1.54844 −0.774219 0.632918i \(-0.781857\pi\)
−0.774219 + 0.632918i \(0.781857\pi\)
\(860\) 0 0
\(861\) −5.42020 −0.184720
\(862\) 0 0
\(863\) −18.4663 −0.628601 −0.314300 0.949324i \(-0.601770\pi\)
−0.314300 + 0.949324i \(0.601770\pi\)
\(864\) 0 0
\(865\) 2.89418 0.0984052
\(866\) 0 0
\(867\) −3.25392 −0.110509
\(868\) 0 0
\(869\) −18.6213 −0.631683
\(870\) 0 0
\(871\) 50.6717 1.71694
\(872\) 0 0
\(873\) −0.811000 −0.0274482
\(874\) 0 0
\(875\) −15.5509 −0.525718
\(876\) 0 0
\(877\) 14.0271 0.473663 0.236832 0.971551i \(-0.423891\pi\)
0.236832 + 0.971551i \(0.423891\pi\)
\(878\) 0 0
\(879\) 9.15472 0.308781
\(880\) 0 0
\(881\) −38.1317 −1.28469 −0.642345 0.766416i \(-0.722038\pi\)
−0.642345 + 0.766416i \(0.722038\pi\)
\(882\) 0 0
\(883\) 31.4041 1.05683 0.528416 0.848986i \(-0.322786\pi\)
0.528416 + 0.848986i \(0.322786\pi\)
\(884\) 0 0
\(885\) 1.72092 0.0578479
\(886\) 0 0
\(887\) −21.1972 −0.711733 −0.355866 0.934537i \(-0.615814\pi\)
−0.355866 + 0.934537i \(0.615814\pi\)
\(888\) 0 0
\(889\) 12.9045 0.432804
\(890\) 0 0
\(891\) 26.7688 0.896790
\(892\) 0 0
\(893\) 29.7826 0.996637
\(894\) 0 0
\(895\) −2.12733 −0.0711088
\(896\) 0 0
\(897\) 1.02795 0.0343224
\(898\) 0 0
\(899\) −0.340711 −0.0113634
\(900\) 0 0
\(901\) −24.5345 −0.817363
\(902\) 0 0
\(903\) 3.16361 0.105278
\(904\) 0 0
\(905\) −6.53564 −0.217252
\(906\) 0 0
\(907\) 9.36000 0.310794 0.155397 0.987852i \(-0.450334\pi\)
0.155397 + 0.987852i \(0.450334\pi\)
\(908\) 0 0
\(909\) −53.0717 −1.76028
\(910\) 0 0
\(911\) 3.56627 0.118156 0.0590778 0.998253i \(-0.481184\pi\)
0.0590778 + 0.998253i \(0.481184\pi\)
\(912\) 0 0
\(913\) −43.7106 −1.44661
\(914\) 0 0
\(915\) 1.72551 0.0570437
\(916\) 0 0
\(917\) 26.1691 0.864181
\(918\) 0 0
\(919\) 52.7064 1.73862 0.869312 0.494264i \(-0.164562\pi\)
0.869312 + 0.494264i \(0.164562\pi\)
\(920\) 0 0
\(921\) 4.54263 0.149685
\(922\) 0 0
\(923\) −9.66808 −0.318229
\(924\) 0 0
\(925\) 49.1842 1.61716
\(926\) 0 0
\(927\) −29.7930 −0.978532
\(928\) 0 0
\(929\) 51.7441 1.69767 0.848835 0.528658i \(-0.177305\pi\)
0.848835 + 0.528658i \(0.177305\pi\)
\(930\) 0 0
\(931\) 15.3459 0.502943
\(932\) 0 0
\(933\) −1.54134 −0.0504611
\(934\) 0 0
\(935\) 4.76165 0.155722
\(936\) 0 0
\(937\) −20.7051 −0.676407 −0.338204 0.941073i \(-0.609819\pi\)
−0.338204 + 0.941073i \(0.609819\pi\)
\(938\) 0 0
\(939\) 0.532664 0.0173828
\(940\) 0 0
\(941\) 18.1156 0.590551 0.295276 0.955412i \(-0.404589\pi\)
0.295276 + 0.955412i \(0.404589\pi\)
\(942\) 0 0
\(943\) 2.21236 0.0720444
\(944\) 0 0
\(945\) −3.22738 −0.104987
\(946\) 0 0
\(947\) −42.5973 −1.38423 −0.692113 0.721789i \(-0.743320\pi\)
−0.692113 + 0.721789i \(0.743320\pi\)
\(948\) 0 0
\(949\) 115.770 3.75806
\(950\) 0 0
\(951\) 8.61456 0.279346
\(952\) 0 0
\(953\) −37.6241 −1.21876 −0.609381 0.792877i \(-0.708582\pi\)
−0.609381 + 0.792877i \(0.708582\pi\)
\(954\) 0 0
\(955\) −7.36694 −0.238389
\(956\) 0 0
\(957\) 0.826855 0.0267284
\(958\) 0 0
\(959\) −25.5597 −0.825367
\(960\) 0 0
\(961\) −30.7731 −0.992679
\(962\) 0 0
\(963\) −20.7320 −0.668079
\(964\) 0 0
\(965\) −13.4804 −0.433950
\(966\) 0 0
\(967\) −47.9367 −1.54154 −0.770770 0.637114i \(-0.780128\pi\)
−0.770770 + 0.637114i \(0.780128\pi\)
\(968\) 0 0
\(969\) −5.56310 −0.178712
\(970\) 0 0
\(971\) −39.6857 −1.27357 −0.636787 0.771040i \(-0.719737\pi\)
−0.636787 + 0.771040i \(0.719737\pi\)
\(972\) 0 0
\(973\) −60.6228 −1.94348
\(974\) 0 0
\(975\) −11.2046 −0.358835
\(976\) 0 0
\(977\) 20.7512 0.663891 0.331945 0.943299i \(-0.392295\pi\)
0.331945 + 0.943299i \(0.392295\pi\)
\(978\) 0 0
\(979\) 3.05083 0.0975050
\(980\) 0 0
\(981\) −23.5129 −0.750710
\(982\) 0 0
\(983\) −41.4880 −1.32326 −0.661631 0.749830i \(-0.730135\pi\)
−0.661631 + 0.749830i \(0.730135\pi\)
\(984\) 0 0
\(985\) −7.15026 −0.227826
\(986\) 0 0
\(987\) −5.36730 −0.170843
\(988\) 0 0
\(989\) −1.29129 −0.0410606
\(990\) 0 0
\(991\) 48.7393 1.54825 0.774127 0.633030i \(-0.218189\pi\)
0.774127 + 0.633030i \(0.218189\pi\)
\(992\) 0 0
\(993\) −3.36308 −0.106724
\(994\) 0 0
\(995\) −12.5583 −0.398126
\(996\) 0 0
\(997\) 1.19412 0.0378182 0.0189091 0.999821i \(-0.493981\pi\)
0.0189091 + 0.999821i \(0.493981\pi\)
\(998\) 0 0
\(999\) 20.9882 0.664038
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 \(a_p\))