Properties

Label 6026.2.a.i.1.15
Level 6026
Weight 2
Character 6026.1
Self dual Yes
Analytic conductor 48.118
Analytic rank 1
Dimension 25
CM No

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Newspace parameters

Level: \( N \) = \( 6026 = 2 \cdot 23 \cdot 131 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6026.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.117852258\)
Analytic rank: \(1\)
Dimension: \(25\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Character \(\chi\) = 6026.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +0.489389 q^{3} +1.00000 q^{4} +2.70694 q^{5} -0.489389 q^{6} +1.75684 q^{7} -1.00000 q^{8} -2.76050 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +0.489389 q^{3} +1.00000 q^{4} +2.70694 q^{5} -0.489389 q^{6} +1.75684 q^{7} -1.00000 q^{8} -2.76050 q^{9} -2.70694 q^{10} +1.86326 q^{11} +0.489389 q^{12} -5.77826 q^{13} -1.75684 q^{14} +1.32475 q^{15} +1.00000 q^{16} +0.411409 q^{17} +2.76050 q^{18} -3.30662 q^{19} +2.70694 q^{20} +0.859779 q^{21} -1.86326 q^{22} +1.00000 q^{23} -0.489389 q^{24} +2.32751 q^{25} +5.77826 q^{26} -2.81912 q^{27} +1.75684 q^{28} -8.95375 q^{29} -1.32475 q^{30} +4.04733 q^{31} -1.00000 q^{32} +0.911859 q^{33} -0.411409 q^{34} +4.75566 q^{35} -2.76050 q^{36} +8.37793 q^{37} +3.30662 q^{38} -2.82781 q^{39} -2.70694 q^{40} -9.32536 q^{41} -0.859779 q^{42} -4.95120 q^{43} +1.86326 q^{44} -7.47250 q^{45} -1.00000 q^{46} -10.3867 q^{47} +0.489389 q^{48} -3.91351 q^{49} -2.32751 q^{50} +0.201339 q^{51} -5.77826 q^{52} +8.33584 q^{53} +2.81912 q^{54} +5.04373 q^{55} -1.75684 q^{56} -1.61822 q^{57} +8.95375 q^{58} +13.2744 q^{59} +1.32475 q^{60} +9.35245 q^{61} -4.04733 q^{62} -4.84976 q^{63} +1.00000 q^{64} -15.6414 q^{65} -0.911859 q^{66} +6.28748 q^{67} +0.411409 q^{68} +0.489389 q^{69} -4.75566 q^{70} -4.46886 q^{71} +2.76050 q^{72} -13.5354 q^{73} -8.37793 q^{74} +1.13906 q^{75} -3.30662 q^{76} +3.27346 q^{77} +2.82781 q^{78} -7.13291 q^{79} +2.70694 q^{80} +6.90185 q^{81} +9.32536 q^{82} +6.71368 q^{83} +0.859779 q^{84} +1.11366 q^{85} +4.95120 q^{86} -4.38187 q^{87} -1.86326 q^{88} +3.92441 q^{89} +7.47250 q^{90} -10.1515 q^{91} +1.00000 q^{92} +1.98072 q^{93} +10.3867 q^{94} -8.95081 q^{95} -0.489389 q^{96} -9.59770 q^{97} +3.91351 q^{98} -5.14353 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 25q - 25q^{2} - 4q^{3} + 25q^{4} - 3q^{5} + 4q^{6} - 11q^{7} - 25q^{8} + 19q^{9} + O(q^{10}) \) \( 25q - 25q^{2} - 4q^{3} + 25q^{4} - 3q^{5} + 4q^{6} - 11q^{7} - 25q^{8} + 19q^{9} + 3q^{10} - 12q^{11} - 4q^{12} - 6q^{13} + 11q^{14} + 25q^{16} + 8q^{17} - 19q^{18} - 23q^{19} - 3q^{20} - 16q^{21} + 12q^{22} + 25q^{23} + 4q^{24} + 4q^{25} + 6q^{26} - 13q^{27} - 11q^{28} - 7q^{29} - 7q^{31} - 25q^{32} + 3q^{33} - 8q^{34} - 18q^{35} + 19q^{36} - 7q^{37} + 23q^{38} - 2q^{39} + 3q^{40} - 10q^{41} + 16q^{42} - 26q^{43} - 12q^{44} + 20q^{45} - 25q^{46} - 2q^{47} - 4q^{48} + 2q^{49} - 4q^{50} - 28q^{51} - 6q^{52} + 47q^{53} + 13q^{54} - 38q^{55} + 11q^{56} - 4q^{57} + 7q^{58} - 19q^{59} - 26q^{61} + 7q^{62} - 15q^{63} + 25q^{64} + 13q^{65} - 3q^{66} - 34q^{67} + 8q^{68} - 4q^{69} + 18q^{70} - 10q^{71} - 19q^{72} - 22q^{73} + 7q^{74} - 8q^{75} - 23q^{76} + 28q^{77} + 2q^{78} - 21q^{79} - 3q^{80} - 27q^{81} + 10q^{82} - 16q^{83} - 16q^{84} - 42q^{85} + 26q^{86} - 17q^{87} + 12q^{88} + 27q^{89} - 20q^{90} - 26q^{91} + 25q^{92} - 27q^{93} + 2q^{94} + 4q^{96} + 4q^{97} - 2q^{98} - 2q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 0.489389 0.282549 0.141274 0.989970i \(-0.454880\pi\)
0.141274 + 0.989970i \(0.454880\pi\)
\(4\) 1.00000 0.500000
\(5\) 2.70694 1.21058 0.605290 0.796005i \(-0.293057\pi\)
0.605290 + 0.796005i \(0.293057\pi\)
\(6\) −0.489389 −0.199792
\(7\) 1.75684 0.664024 0.332012 0.943275i \(-0.392273\pi\)
0.332012 + 0.943275i \(0.392273\pi\)
\(8\) −1.00000 −0.353553
\(9\) −2.76050 −0.920166
\(10\) −2.70694 −0.856009
\(11\) 1.86326 0.561794 0.280897 0.959738i \(-0.409368\pi\)
0.280897 + 0.959738i \(0.409368\pi\)
\(12\) 0.489389 0.141274
\(13\) −5.77826 −1.60260 −0.801300 0.598263i \(-0.795858\pi\)
−0.801300 + 0.598263i \(0.795858\pi\)
\(14\) −1.75684 −0.469536
\(15\) 1.32475 0.342048
\(16\) 1.00000 0.250000
\(17\) 0.411409 0.0997814 0.0498907 0.998755i \(-0.484113\pi\)
0.0498907 + 0.998755i \(0.484113\pi\)
\(18\) 2.76050 0.650656
\(19\) −3.30662 −0.758590 −0.379295 0.925276i \(-0.623833\pi\)
−0.379295 + 0.925276i \(0.623833\pi\)
\(20\) 2.70694 0.605290
\(21\) 0.859779 0.187619
\(22\) −1.86326 −0.397249
\(23\) 1.00000 0.208514
\(24\) −0.489389 −0.0998961
\(25\) 2.32751 0.465502
\(26\) 5.77826 1.13321
\(27\) −2.81912 −0.542541
\(28\) 1.75684 0.332012
\(29\) −8.95375 −1.66267 −0.831335 0.555772i \(-0.812423\pi\)
−0.831335 + 0.555772i \(0.812423\pi\)
\(30\) −1.32475 −0.241864
\(31\) 4.04733 0.726921 0.363461 0.931610i \(-0.381595\pi\)
0.363461 + 0.931610i \(0.381595\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0.911859 0.158734
\(34\) −0.411409 −0.0705561
\(35\) 4.75566 0.803854
\(36\) −2.76050 −0.460083
\(37\) 8.37793 1.37732 0.688662 0.725083i \(-0.258198\pi\)
0.688662 + 0.725083i \(0.258198\pi\)
\(38\) 3.30662 0.536404
\(39\) −2.82781 −0.452813
\(40\) −2.70694 −0.428004
\(41\) −9.32536 −1.45638 −0.728188 0.685377i \(-0.759637\pi\)
−0.728188 + 0.685377i \(0.759637\pi\)
\(42\) −0.859779 −0.132667
\(43\) −4.95120 −0.755050 −0.377525 0.925999i \(-0.623225\pi\)
−0.377525 + 0.925999i \(0.623225\pi\)
\(44\) 1.86326 0.280897
\(45\) −7.47250 −1.11393
\(46\) −1.00000 −0.147442
\(47\) −10.3867 −1.51506 −0.757529 0.652802i \(-0.773593\pi\)
−0.757529 + 0.652802i \(0.773593\pi\)
\(48\) 0.489389 0.0706372
\(49\) −3.91351 −0.559072
\(50\) −2.32751 −0.329160
\(51\) 0.201339 0.0281931
\(52\) −5.77826 −0.801300
\(53\) 8.33584 1.14502 0.572508 0.819899i \(-0.305971\pi\)
0.572508 + 0.819899i \(0.305971\pi\)
\(54\) 2.81912 0.383634
\(55\) 5.04373 0.680097
\(56\) −1.75684 −0.234768
\(57\) −1.61822 −0.214339
\(58\) 8.95375 1.17568
\(59\) 13.2744 1.72818 0.864089 0.503340i \(-0.167896\pi\)
0.864089 + 0.503340i \(0.167896\pi\)
\(60\) 1.32475 0.171024
\(61\) 9.35245 1.19746 0.598729 0.800951i \(-0.295672\pi\)
0.598729 + 0.800951i \(0.295672\pi\)
\(62\) −4.04733 −0.514011
\(63\) −4.84976 −0.611012
\(64\) 1.00000 0.125000
\(65\) −15.6414 −1.94007
\(66\) −0.911859 −0.112242
\(67\) 6.28748 0.768138 0.384069 0.923304i \(-0.374523\pi\)
0.384069 + 0.923304i \(0.374523\pi\)
\(68\) 0.411409 0.0498907
\(69\) 0.489389 0.0589155
\(70\) −4.75566 −0.568410
\(71\) −4.46886 −0.530356 −0.265178 0.964199i \(-0.585431\pi\)
−0.265178 + 0.964199i \(0.585431\pi\)
\(72\) 2.76050 0.325328
\(73\) −13.5354 −1.58420 −0.792100 0.610391i \(-0.791012\pi\)
−0.792100 + 0.610391i \(0.791012\pi\)
\(74\) −8.37793 −0.973915
\(75\) 1.13906 0.131527
\(76\) −3.30662 −0.379295
\(77\) 3.27346 0.373045
\(78\) 2.82781 0.320187
\(79\) −7.13291 −0.802515 −0.401257 0.915965i \(-0.631427\pi\)
−0.401257 + 0.915965i \(0.631427\pi\)
\(80\) 2.70694 0.302645
\(81\) 6.90185 0.766872
\(82\) 9.32536 1.02981
\(83\) 6.71368 0.736922 0.368461 0.929643i \(-0.379885\pi\)
0.368461 + 0.929643i \(0.379885\pi\)
\(84\) 0.859779 0.0938096
\(85\) 1.11366 0.120793
\(86\) 4.95120 0.533901
\(87\) −4.38187 −0.469785
\(88\) −1.86326 −0.198624
\(89\) 3.92441 0.415987 0.207993 0.978130i \(-0.433307\pi\)
0.207993 + 0.978130i \(0.433307\pi\)
\(90\) 7.47250 0.787670
\(91\) −10.1515 −1.06416
\(92\) 1.00000 0.104257
\(93\) 1.98072 0.205391
\(94\) 10.3867 1.07131
\(95\) −8.95081 −0.918333
\(96\) −0.489389 −0.0499481
\(97\) −9.59770 −0.974499 −0.487250 0.873263i \(-0.662000\pi\)
−0.487250 + 0.873263i \(0.662000\pi\)
\(98\) 3.91351 0.395324
\(99\) −5.14353 −0.516944
\(100\) 2.32751 0.232751
\(101\) −15.0579 −1.49831 −0.749156 0.662393i \(-0.769541\pi\)
−0.749156 + 0.662393i \(0.769541\pi\)
\(102\) −0.201339 −0.0199355
\(103\) −13.5851 −1.33858 −0.669288 0.743003i \(-0.733401\pi\)
−0.669288 + 0.743003i \(0.733401\pi\)
\(104\) 5.77826 0.566605
\(105\) 2.32737 0.227128
\(106\) −8.33584 −0.809648
\(107\) −3.55479 −0.343655 −0.171827 0.985127i \(-0.554967\pi\)
−0.171827 + 0.985127i \(0.554967\pi\)
\(108\) −2.81912 −0.271270
\(109\) −14.6600 −1.40418 −0.702088 0.712090i \(-0.747749\pi\)
−0.702088 + 0.712090i \(0.747749\pi\)
\(110\) −5.04373 −0.480901
\(111\) 4.10007 0.389161
\(112\) 1.75684 0.166006
\(113\) −15.2325 −1.43295 −0.716477 0.697611i \(-0.754246\pi\)
−0.716477 + 0.697611i \(0.754246\pi\)
\(114\) 1.61822 0.151560
\(115\) 2.70694 0.252423
\(116\) −8.95375 −0.831335
\(117\) 15.9509 1.47466
\(118\) −13.2744 −1.22201
\(119\) 0.722781 0.0662572
\(120\) −1.32475 −0.120932
\(121\) −7.52826 −0.684387
\(122\) −9.35245 −0.846731
\(123\) −4.56373 −0.411497
\(124\) 4.04733 0.363461
\(125\) −7.23426 −0.647052
\(126\) 4.84976 0.432051
\(127\) 10.2391 0.908571 0.454285 0.890856i \(-0.349895\pi\)
0.454285 + 0.890856i \(0.349895\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −2.42306 −0.213339
\(130\) 15.6414 1.37184
\(131\) 1.00000 0.0873704
\(132\) 0.911859 0.0793672
\(133\) −5.80920 −0.503722
\(134\) −6.28748 −0.543155
\(135\) −7.63119 −0.656789
\(136\) −0.411409 −0.0352780
\(137\) −10.9035 −0.931545 −0.465773 0.884904i \(-0.654223\pi\)
−0.465773 + 0.884904i \(0.654223\pi\)
\(138\) −0.489389 −0.0416596
\(139\) 3.79529 0.321912 0.160956 0.986962i \(-0.448542\pi\)
0.160956 + 0.986962i \(0.448542\pi\)
\(140\) 4.75566 0.401927
\(141\) −5.08314 −0.428078
\(142\) 4.46886 0.375019
\(143\) −10.7664 −0.900331
\(144\) −2.76050 −0.230042
\(145\) −24.2372 −2.01279
\(146\) 13.5354 1.12020
\(147\) −1.91523 −0.157965
\(148\) 8.37793 0.688662
\(149\) 17.9850 1.47339 0.736695 0.676225i \(-0.236385\pi\)
0.736695 + 0.676225i \(0.236385\pi\)
\(150\) −1.13906 −0.0930037
\(151\) −19.3200 −1.57224 −0.786120 0.618074i \(-0.787913\pi\)
−0.786120 + 0.618074i \(0.787913\pi\)
\(152\) 3.30662 0.268202
\(153\) −1.13569 −0.0918155
\(154\) −3.27346 −0.263783
\(155\) 10.9559 0.879996
\(156\) −2.82781 −0.226406
\(157\) −1.36425 −0.108879 −0.0544396 0.998517i \(-0.517337\pi\)
−0.0544396 + 0.998517i \(0.517337\pi\)
\(158\) 7.13291 0.567464
\(159\) 4.07947 0.323523
\(160\) −2.70694 −0.214002
\(161\) 1.75684 0.138459
\(162\) −6.90185 −0.542260
\(163\) 11.9751 0.937959 0.468979 0.883209i \(-0.344622\pi\)
0.468979 + 0.883209i \(0.344622\pi\)
\(164\) −9.32536 −0.728188
\(165\) 2.46835 0.192161
\(166\) −6.71368 −0.521083
\(167\) −8.16434 −0.631775 −0.315888 0.948797i \(-0.602302\pi\)
−0.315888 + 0.948797i \(0.602302\pi\)
\(168\) −0.859779 −0.0663334
\(169\) 20.3882 1.56833
\(170\) −1.11366 −0.0854138
\(171\) 9.12791 0.698029
\(172\) −4.95120 −0.377525
\(173\) −21.4495 −1.63078 −0.815389 0.578913i \(-0.803477\pi\)
−0.815389 + 0.578913i \(0.803477\pi\)
\(174\) 4.38187 0.332188
\(175\) 4.08907 0.309105
\(176\) 1.86326 0.140449
\(177\) 6.49634 0.488295
\(178\) −3.92441 −0.294147
\(179\) −9.37898 −0.701018 −0.350509 0.936559i \(-0.613991\pi\)
−0.350509 + 0.936559i \(0.613991\pi\)
\(180\) −7.47250 −0.556967
\(181\) 18.5444 1.37839 0.689197 0.724574i \(-0.257964\pi\)
0.689197 + 0.724574i \(0.257964\pi\)
\(182\) 10.1515 0.752478
\(183\) 4.57699 0.338341
\(184\) −1.00000 −0.0737210
\(185\) 22.6785 1.66736
\(186\) −1.98072 −0.145233
\(187\) 0.766563 0.0560566
\(188\) −10.3867 −0.757529
\(189\) −4.95276 −0.360260
\(190\) 8.95081 0.649360
\(191\) 6.37074 0.460971 0.230485 0.973076i \(-0.425969\pi\)
0.230485 + 0.973076i \(0.425969\pi\)
\(192\) 0.489389 0.0353186
\(193\) −7.98381 −0.574687 −0.287344 0.957828i \(-0.592772\pi\)
−0.287344 + 0.957828i \(0.592772\pi\)
\(194\) 9.59770 0.689075
\(195\) −7.65472 −0.548166
\(196\) −3.91351 −0.279536
\(197\) −18.6150 −1.32626 −0.663131 0.748503i \(-0.730773\pi\)
−0.663131 + 0.748503i \(0.730773\pi\)
\(198\) 5.14353 0.365535
\(199\) 1.98994 0.141063 0.0705316 0.997510i \(-0.477530\pi\)
0.0705316 + 0.997510i \(0.477530\pi\)
\(200\) −2.32751 −0.164580
\(201\) 3.07702 0.217036
\(202\) 15.0579 1.05947
\(203\) −15.7303 −1.10405
\(204\) 0.201339 0.0140966
\(205\) −25.2432 −1.76306
\(206\) 13.5851 0.946517
\(207\) −2.76050 −0.191868
\(208\) −5.77826 −0.400650
\(209\) −6.16109 −0.426172
\(210\) −2.32737 −0.160604
\(211\) 27.2622 1.87681 0.938404 0.345541i \(-0.112305\pi\)
0.938404 + 0.345541i \(0.112305\pi\)
\(212\) 8.33584 0.572508
\(213\) −2.18701 −0.149852
\(214\) 3.55479 0.243001
\(215\) −13.4026 −0.914048
\(216\) 2.81912 0.191817
\(217\) 7.11052 0.482693
\(218\) 14.6600 0.992902
\(219\) −6.62408 −0.447614
\(220\) 5.04373 0.340048
\(221\) −2.37723 −0.159910
\(222\) −4.10007 −0.275179
\(223\) 17.9483 1.20191 0.600955 0.799283i \(-0.294787\pi\)
0.600955 + 0.799283i \(0.294787\pi\)
\(224\) −1.75684 −0.117384
\(225\) −6.42509 −0.428340
\(226\) 15.2325 1.01325
\(227\) 18.9955 1.26078 0.630388 0.776280i \(-0.282896\pi\)
0.630388 + 0.776280i \(0.282896\pi\)
\(228\) −1.61822 −0.107169
\(229\) 21.4469 1.41725 0.708627 0.705583i \(-0.249315\pi\)
0.708627 + 0.705583i \(0.249315\pi\)
\(230\) −2.70694 −0.178490
\(231\) 1.60199 0.105403
\(232\) 8.95375 0.587842
\(233\) 6.68967 0.438255 0.219127 0.975696i \(-0.429679\pi\)
0.219127 + 0.975696i \(0.429679\pi\)
\(234\) −15.9509 −1.04274
\(235\) −28.1162 −1.83410
\(236\) 13.2744 0.864089
\(237\) −3.49077 −0.226750
\(238\) −0.722781 −0.0468509
\(239\) 9.43105 0.610044 0.305022 0.952345i \(-0.401336\pi\)
0.305022 + 0.952345i \(0.401336\pi\)
\(240\) 1.32475 0.0855120
\(241\) −20.6794 −1.33208 −0.666040 0.745916i \(-0.732012\pi\)
−0.666040 + 0.745916i \(0.732012\pi\)
\(242\) 7.52826 0.483935
\(243\) 11.8351 0.759220
\(244\) 9.35245 0.598729
\(245\) −10.5936 −0.676801
\(246\) 4.56373 0.290973
\(247\) 19.1065 1.21572
\(248\) −4.04733 −0.257006
\(249\) 3.28560 0.208217
\(250\) 7.23426 0.457535
\(251\) −20.4131 −1.28846 −0.644231 0.764831i \(-0.722822\pi\)
−0.644231 + 0.764831i \(0.722822\pi\)
\(252\) −4.84976 −0.305506
\(253\) 1.86326 0.117142
\(254\) −10.2391 −0.642457
\(255\) 0.545012 0.0341300
\(256\) 1.00000 0.0625000
\(257\) 19.8981 1.24121 0.620605 0.784123i \(-0.286887\pi\)
0.620605 + 0.784123i \(0.286887\pi\)
\(258\) 2.42306 0.150853
\(259\) 14.7187 0.914576
\(260\) −15.6414 −0.970037
\(261\) 24.7168 1.52993
\(262\) −1.00000 −0.0617802
\(263\) −23.2400 −1.43304 −0.716521 0.697566i \(-0.754266\pi\)
−0.716521 + 0.697566i \(0.754266\pi\)
\(264\) −0.911859 −0.0561211
\(265\) 22.5646 1.38613
\(266\) 5.80920 0.356185
\(267\) 1.92056 0.117537
\(268\) 6.28748 0.384069
\(269\) −14.4636 −0.881860 −0.440930 0.897542i \(-0.645351\pi\)
−0.440930 + 0.897542i \(0.645351\pi\)
\(270\) 7.63119 0.464420
\(271\) −14.5554 −0.884175 −0.442088 0.896972i \(-0.645762\pi\)
−0.442088 + 0.896972i \(0.645762\pi\)
\(272\) 0.411409 0.0249453
\(273\) −4.96802 −0.300678
\(274\) 10.9035 0.658702
\(275\) 4.33676 0.261517
\(276\) 0.489389 0.0294578
\(277\) 13.9840 0.840219 0.420110 0.907473i \(-0.361992\pi\)
0.420110 + 0.907473i \(0.361992\pi\)
\(278\) −3.79529 −0.227626
\(279\) −11.1726 −0.668889
\(280\) −4.75566 −0.284205
\(281\) 2.40661 0.143566 0.0717831 0.997420i \(-0.477131\pi\)
0.0717831 + 0.997420i \(0.477131\pi\)
\(282\) 5.08314 0.302697
\(283\) 1.01250 0.0601869 0.0300935 0.999547i \(-0.490420\pi\)
0.0300935 + 0.999547i \(0.490420\pi\)
\(284\) −4.46886 −0.265178
\(285\) −4.38043 −0.259474
\(286\) 10.7664 0.636630
\(287\) −16.3832 −0.967069
\(288\) 2.76050 0.162664
\(289\) −16.8307 −0.990044
\(290\) 24.2372 1.42326
\(291\) −4.69701 −0.275344
\(292\) −13.5354 −0.792100
\(293\) 5.73778 0.335205 0.167602 0.985855i \(-0.446397\pi\)
0.167602 + 0.985855i \(0.446397\pi\)
\(294\) 1.91523 0.111698
\(295\) 35.9329 2.09210
\(296\) −8.37793 −0.486957
\(297\) −5.25276 −0.304796
\(298\) −17.9850 −1.04184
\(299\) −5.77826 −0.334165
\(300\) 1.13906 0.0657636
\(301\) −8.69847 −0.501372
\(302\) 19.3200 1.11174
\(303\) −7.36915 −0.423346
\(304\) −3.30662 −0.189647
\(305\) 25.3165 1.44962
\(306\) 1.13569 0.0649233
\(307\) 12.1385 0.692780 0.346390 0.938091i \(-0.387407\pi\)
0.346390 + 0.938091i \(0.387407\pi\)
\(308\) 3.27346 0.186522
\(309\) −6.64838 −0.378213
\(310\) −10.9559 −0.622251
\(311\) −7.46737 −0.423436 −0.211718 0.977331i \(-0.567906\pi\)
−0.211718 + 0.977331i \(0.567906\pi\)
\(312\) 2.82781 0.160093
\(313\) −16.2053 −0.915978 −0.457989 0.888958i \(-0.651430\pi\)
−0.457989 + 0.888958i \(0.651430\pi\)
\(314\) 1.36425 0.0769892
\(315\) −13.1280 −0.739679
\(316\) −7.13291 −0.401257
\(317\) 31.7233 1.78176 0.890879 0.454242i \(-0.150090\pi\)
0.890879 + 0.454242i \(0.150090\pi\)
\(318\) −4.07947 −0.228765
\(319\) −16.6832 −0.934078
\(320\) 2.70694 0.151322
\(321\) −1.73968 −0.0970993
\(322\) −1.75684 −0.0979050
\(323\) −1.36037 −0.0756932
\(324\) 6.90185 0.383436
\(325\) −13.4490 −0.746014
\(326\) −11.9751 −0.663237
\(327\) −7.17446 −0.396748
\(328\) 9.32536 0.514907
\(329\) −18.2478 −1.00603
\(330\) −2.46835 −0.135878
\(331\) 12.6481 0.695204 0.347602 0.937642i \(-0.386996\pi\)
0.347602 + 0.937642i \(0.386996\pi\)
\(332\) 6.71368 0.368461
\(333\) −23.1273 −1.26737
\(334\) 8.16434 0.446733
\(335\) 17.0198 0.929892
\(336\) 0.859779 0.0469048
\(337\) 10.0795 0.549067 0.274534 0.961578i \(-0.411477\pi\)
0.274534 + 0.961578i \(0.411477\pi\)
\(338\) −20.3882 −1.10897
\(339\) −7.45462 −0.404879
\(340\) 1.11366 0.0603966
\(341\) 7.54123 0.408380
\(342\) −9.12791 −0.493581
\(343\) −19.1733 −1.03526
\(344\) 4.95120 0.266951
\(345\) 1.32475 0.0713219
\(346\) 21.4495 1.15313
\(347\) −2.43014 −0.130457 −0.0652284 0.997870i \(-0.520778\pi\)
−0.0652284 + 0.997870i \(0.520778\pi\)
\(348\) −4.38187 −0.234893
\(349\) −11.8155 −0.632472 −0.316236 0.948681i \(-0.602419\pi\)
−0.316236 + 0.948681i \(0.602419\pi\)
\(350\) −4.08907 −0.218570
\(351\) 16.2896 0.869476
\(352\) −1.86326 −0.0993121
\(353\) −12.9583 −0.689699 −0.344849 0.938658i \(-0.612070\pi\)
−0.344849 + 0.938658i \(0.612070\pi\)
\(354\) −6.49634 −0.345276
\(355\) −12.0969 −0.642038
\(356\) 3.92441 0.207993
\(357\) 0.353721 0.0187209
\(358\) 9.37898 0.495694
\(359\) 25.4169 1.34145 0.670727 0.741704i \(-0.265982\pi\)
0.670727 + 0.741704i \(0.265982\pi\)
\(360\) 7.47250 0.393835
\(361\) −8.06628 −0.424541
\(362\) −18.5444 −0.974671
\(363\) −3.68425 −0.193373
\(364\) −10.1515 −0.532082
\(365\) −36.6395 −1.91780
\(366\) −4.57699 −0.239243
\(367\) 4.09411 0.213711 0.106855 0.994275i \(-0.465922\pi\)
0.106855 + 0.994275i \(0.465922\pi\)
\(368\) 1.00000 0.0521286
\(369\) 25.7426 1.34011
\(370\) −22.6785 −1.17900
\(371\) 14.6448 0.760318
\(372\) 1.98072 0.102695
\(373\) −14.1480 −0.732556 −0.366278 0.930505i \(-0.619368\pi\)
−0.366278 + 0.930505i \(0.619368\pi\)
\(374\) −0.766563 −0.0396380
\(375\) −3.54037 −0.182824
\(376\) 10.3867 0.535654
\(377\) 51.7370 2.66459
\(378\) 4.95276 0.254742
\(379\) −15.6164 −0.802159 −0.401080 0.916043i \(-0.631365\pi\)
−0.401080 + 0.916043i \(0.631365\pi\)
\(380\) −8.95081 −0.459167
\(381\) 5.01089 0.256716
\(382\) −6.37074 −0.325955
\(383\) 21.4338 1.09521 0.547607 0.836736i \(-0.315539\pi\)
0.547607 + 0.836736i \(0.315539\pi\)
\(384\) −0.489389 −0.0249740
\(385\) 8.86104 0.451600
\(386\) 7.98381 0.406365
\(387\) 13.6678 0.694772
\(388\) −9.59770 −0.487250
\(389\) −10.1472 −0.514485 −0.257243 0.966347i \(-0.582814\pi\)
−0.257243 + 0.966347i \(0.582814\pi\)
\(390\) 7.65472 0.387612
\(391\) 0.411409 0.0208059
\(392\) 3.91351 0.197662
\(393\) 0.489389 0.0246864
\(394\) 18.6150 0.937809
\(395\) −19.3083 −0.971508
\(396\) −5.14353 −0.258472
\(397\) 7.32012 0.367386 0.183693 0.982984i \(-0.441195\pi\)
0.183693 + 0.982984i \(0.441195\pi\)
\(398\) −1.98994 −0.0997467
\(399\) −2.84296 −0.142326
\(400\) 2.32751 0.116376
\(401\) 16.9234 0.845114 0.422557 0.906336i \(-0.361133\pi\)
0.422557 + 0.906336i \(0.361133\pi\)
\(402\) −3.07702 −0.153468
\(403\) −23.3865 −1.16496
\(404\) −15.0579 −0.749156
\(405\) 18.6829 0.928359
\(406\) 15.7303 0.780683
\(407\) 15.6103 0.773773
\(408\) −0.201339 −0.00996777
\(409\) 2.23908 0.110715 0.0553577 0.998467i \(-0.482370\pi\)
0.0553577 + 0.998467i \(0.482370\pi\)
\(410\) 25.2432 1.24667
\(411\) −5.33603 −0.263207
\(412\) −13.5851 −0.669288
\(413\) 23.3210 1.14755
\(414\) 2.76050 0.135671
\(415\) 18.1735 0.892103
\(416\) 5.77826 0.283302
\(417\) 1.85737 0.0909559
\(418\) 6.16109 0.301349
\(419\) −7.44628 −0.363775 −0.181887 0.983319i \(-0.558221\pi\)
−0.181887 + 0.983319i \(0.558221\pi\)
\(420\) 2.32737 0.113564
\(421\) 22.1005 1.07711 0.538555 0.842590i \(-0.318970\pi\)
0.538555 + 0.842590i \(0.318970\pi\)
\(422\) −27.2622 −1.32710
\(423\) 28.6725 1.39410
\(424\) −8.33584 −0.404824
\(425\) 0.957560 0.0464485
\(426\) 2.18701 0.105961
\(427\) 16.4308 0.795141
\(428\) −3.55479 −0.171827
\(429\) −5.26896 −0.254388
\(430\) 13.4026 0.646330
\(431\) −11.7617 −0.566540 −0.283270 0.959040i \(-0.591419\pi\)
−0.283270 + 0.959040i \(0.591419\pi\)
\(432\) −2.81912 −0.135635
\(433\) −17.0115 −0.817520 −0.408760 0.912642i \(-0.634039\pi\)
−0.408760 + 0.912642i \(0.634039\pi\)
\(434\) −7.11052 −0.341316
\(435\) −11.8614 −0.568712
\(436\) −14.6600 −0.702088
\(437\) −3.30662 −0.158177
\(438\) 6.62408 0.316511
\(439\) 37.3642 1.78329 0.891647 0.452731i \(-0.149550\pi\)
0.891647 + 0.452731i \(0.149550\pi\)
\(440\) −5.04373 −0.240450
\(441\) 10.8032 0.514439
\(442\) 2.37723 0.113073
\(443\) 16.4430 0.781231 0.390615 0.920554i \(-0.372262\pi\)
0.390615 + 0.920554i \(0.372262\pi\)
\(444\) 4.10007 0.194581
\(445\) 10.6231 0.503585
\(446\) −17.9483 −0.849878
\(447\) 8.80167 0.416305
\(448\) 1.75684 0.0830030
\(449\) 13.3905 0.631939 0.315970 0.948769i \(-0.397670\pi\)
0.315970 + 0.948769i \(0.397670\pi\)
\(450\) 6.42509 0.302882
\(451\) −17.3756 −0.818184
\(452\) −15.2325 −0.716477
\(453\) −9.45500 −0.444235
\(454\) −18.9955 −0.891504
\(455\) −27.4794 −1.28826
\(456\) 1.61822 0.0757802
\(457\) −7.64751 −0.357736 −0.178868 0.983873i \(-0.557243\pi\)
−0.178868 + 0.983873i \(0.557243\pi\)
\(458\) −21.4469 −1.00215
\(459\) −1.15981 −0.0541355
\(460\) 2.70694 0.126212
\(461\) −26.6413 −1.24081 −0.620405 0.784282i \(-0.713032\pi\)
−0.620405 + 0.784282i \(0.713032\pi\)
\(462\) −1.60199 −0.0745315
\(463\) −10.0154 −0.465454 −0.232727 0.972542i \(-0.574765\pi\)
−0.232727 + 0.972542i \(0.574765\pi\)
\(464\) −8.95375 −0.415667
\(465\) 5.36168 0.248642
\(466\) −6.68967 −0.309893
\(467\) 13.7640 0.636920 0.318460 0.947936i \(-0.396834\pi\)
0.318460 + 0.947936i \(0.396834\pi\)
\(468\) 15.9509 0.737329
\(469\) 11.0461 0.510062
\(470\) 28.1162 1.29690
\(471\) −0.667650 −0.0307637
\(472\) −13.2744 −0.611003
\(473\) −9.22537 −0.424183
\(474\) 3.49077 0.160336
\(475\) −7.69619 −0.353125
\(476\) 0.722781 0.0331286
\(477\) −23.0111 −1.05360
\(478\) −9.43105 −0.431366
\(479\) −15.1671 −0.693004 −0.346502 0.938049i \(-0.612631\pi\)
−0.346502 + 0.938049i \(0.612631\pi\)
\(480\) −1.32475 −0.0604661
\(481\) −48.4098 −2.20730
\(482\) 20.6794 0.941923
\(483\) 0.859779 0.0391213
\(484\) −7.52826 −0.342194
\(485\) −25.9804 −1.17971
\(486\) −11.8351 −0.536849
\(487\) −31.5734 −1.43073 −0.715363 0.698753i \(-0.753739\pi\)
−0.715363 + 0.698753i \(0.753739\pi\)
\(488\) −9.35245 −0.423366
\(489\) 5.86046 0.265019
\(490\) 10.5936 0.478571
\(491\) −7.35504 −0.331928 −0.165964 0.986132i \(-0.553074\pi\)
−0.165964 + 0.986132i \(0.553074\pi\)
\(492\) −4.56373 −0.205749
\(493\) −3.68365 −0.165903
\(494\) −19.1065 −0.859641
\(495\) −13.9232 −0.625802
\(496\) 4.04733 0.181730
\(497\) −7.85109 −0.352169
\(498\) −3.28560 −0.147231
\(499\) −38.9889 −1.74538 −0.872692 0.488271i \(-0.837628\pi\)
−0.872692 + 0.488271i \(0.837628\pi\)
\(500\) −7.23426 −0.323526
\(501\) −3.99554 −0.178507
\(502\) 20.4131 0.911080
\(503\) −15.5334 −0.692598 −0.346299 0.938124i \(-0.612562\pi\)
−0.346299 + 0.938124i \(0.612562\pi\)
\(504\) 4.84976 0.216025
\(505\) −40.7607 −1.81383
\(506\) −1.86326 −0.0828321
\(507\) 9.97778 0.443129
\(508\) 10.2391 0.454285
\(509\) 8.81732 0.390821 0.195410 0.980722i \(-0.437396\pi\)
0.195410 + 0.980722i \(0.437396\pi\)
\(510\) −0.545012 −0.0241336
\(511\) −23.7796 −1.05195
\(512\) −1.00000 −0.0441942
\(513\) 9.32176 0.411566
\(514\) −19.8981 −0.877668
\(515\) −36.7739 −1.62045
\(516\) −2.42306 −0.106669
\(517\) −19.3532 −0.851151
\(518\) −14.7187 −0.646703
\(519\) −10.4972 −0.460775
\(520\) 15.6414 0.685920
\(521\) 24.7182 1.08292 0.541462 0.840725i \(-0.317871\pi\)
0.541462 + 0.840725i \(0.317871\pi\)
\(522\) −24.7168 −1.08183
\(523\) −3.27789 −0.143332 −0.0716660 0.997429i \(-0.522832\pi\)
−0.0716660 + 0.997429i \(0.522832\pi\)
\(524\) 1.00000 0.0436852
\(525\) 2.00115 0.0873372
\(526\) 23.2400 1.01331
\(527\) 1.66511 0.0725332
\(528\) 0.911859 0.0396836
\(529\) 1.00000 0.0434783
\(530\) −22.5646 −0.980143
\(531\) −36.6439 −1.59021
\(532\) −5.80920 −0.251861
\(533\) 53.8843 2.33399
\(534\) −1.92056 −0.0831109
\(535\) −9.62261 −0.416022
\(536\) −6.28748 −0.271578
\(537\) −4.58997 −0.198072
\(538\) 14.4636 0.623569
\(539\) −7.29188 −0.314084
\(540\) −7.63119 −0.328394
\(541\) −41.7473 −1.79486 −0.897428 0.441160i \(-0.854567\pi\)
−0.897428 + 0.441160i \(0.854567\pi\)
\(542\) 14.5554 0.625206
\(543\) 9.07542 0.389463
\(544\) −0.411409 −0.0176390
\(545\) −39.6838 −1.69987
\(546\) 4.96802 0.212612
\(547\) −41.8202 −1.78810 −0.894052 0.447964i \(-0.852149\pi\)
−0.894052 + 0.447964i \(0.852149\pi\)
\(548\) −10.9035 −0.465773
\(549\) −25.8174 −1.10186
\(550\) −4.33676 −0.184920
\(551\) 29.6066 1.26128
\(552\) −0.489389 −0.0208298
\(553\) −12.5314 −0.532889
\(554\) −13.9840 −0.594125
\(555\) 11.0986 0.471111
\(556\) 3.79529 0.160956
\(557\) 33.5427 1.42125 0.710624 0.703572i \(-0.248413\pi\)
0.710624 + 0.703572i \(0.248413\pi\)
\(558\) 11.1726 0.472976
\(559\) 28.6093 1.21004
\(560\) 4.75566 0.200963
\(561\) 0.375147 0.0158387
\(562\) −2.40661 −0.101517
\(563\) −43.0222 −1.81317 −0.906585 0.422024i \(-0.861320\pi\)
−0.906585 + 0.422024i \(0.861320\pi\)
\(564\) −5.08314 −0.214039
\(565\) −41.2335 −1.73470
\(566\) −1.01250 −0.0425586
\(567\) 12.1255 0.509221
\(568\) 4.46886 0.187509
\(569\) −13.1197 −0.550005 −0.275003 0.961443i \(-0.588679\pi\)
−0.275003 + 0.961443i \(0.588679\pi\)
\(570\) 4.38043 0.183476
\(571\) −9.01775 −0.377381 −0.188690 0.982037i \(-0.560424\pi\)
−0.188690 + 0.982037i \(0.560424\pi\)
\(572\) −10.7664 −0.450166
\(573\) 3.11777 0.130247
\(574\) 16.3832 0.683821
\(575\) 2.32751 0.0970640
\(576\) −2.76050 −0.115021
\(577\) 19.4321 0.808969 0.404485 0.914545i \(-0.367451\pi\)
0.404485 + 0.914545i \(0.367451\pi\)
\(578\) 16.8307 0.700067
\(579\) −3.90719 −0.162377
\(580\) −24.2372 −1.00640
\(581\) 11.7949 0.489334
\(582\) 4.69701 0.194697
\(583\) 15.5318 0.643263
\(584\) 13.5354 0.560099
\(585\) 43.1780 1.78519
\(586\) −5.73778 −0.237026
\(587\) 14.1535 0.584177 0.292089 0.956391i \(-0.405650\pi\)
0.292089 + 0.956391i \(0.405650\pi\)
\(588\) −1.91523 −0.0789826
\(589\) −13.3830 −0.551435
\(590\) −35.9329 −1.47934
\(591\) −9.10996 −0.374734
\(592\) 8.37793 0.344331
\(593\) 27.4777 1.12837 0.564186 0.825648i \(-0.309190\pi\)
0.564186 + 0.825648i \(0.309190\pi\)
\(594\) 5.25276 0.215524
\(595\) 1.95652 0.0802096
\(596\) 17.9850 0.736695
\(597\) 0.973855 0.0398572
\(598\) 5.77826 0.236290
\(599\) −5.82025 −0.237809 −0.118905 0.992906i \(-0.537938\pi\)
−0.118905 + 0.992906i \(0.537938\pi\)
\(600\) −1.13906 −0.0465019
\(601\) 28.9690 1.18167 0.590836 0.806792i \(-0.298798\pi\)
0.590836 + 0.806792i \(0.298798\pi\)
\(602\) 8.69847 0.354523
\(603\) −17.3566 −0.706814
\(604\) −19.3200 −0.786120
\(605\) −20.3785 −0.828505
\(606\) 7.36915 0.299351
\(607\) 18.7414 0.760689 0.380344 0.924845i \(-0.375805\pi\)
0.380344 + 0.924845i \(0.375805\pi\)
\(608\) 3.30662 0.134101
\(609\) −7.69825 −0.311949
\(610\) −25.3165 −1.02504
\(611\) 60.0171 2.42803
\(612\) −1.13569 −0.0459077
\(613\) −35.1711 −1.42055 −0.710274 0.703925i \(-0.751429\pi\)
−0.710274 + 0.703925i \(0.751429\pi\)
\(614\) −12.1385 −0.489869
\(615\) −12.3537 −0.498150
\(616\) −3.27346 −0.131891
\(617\) 17.9312 0.721883 0.360942 0.932588i \(-0.382455\pi\)
0.360942 + 0.932588i \(0.382455\pi\)
\(618\) 6.64838 0.267437
\(619\) 11.4249 0.459204 0.229602 0.973285i \(-0.426258\pi\)
0.229602 + 0.973285i \(0.426258\pi\)
\(620\) 10.9559 0.439998
\(621\) −2.81912 −0.113128
\(622\) 7.46737 0.299414
\(623\) 6.89457 0.276225
\(624\) −2.82781 −0.113203
\(625\) −31.2202 −1.24881
\(626\) 16.2053 0.647694
\(627\) −3.01517 −0.120414
\(628\) −1.36425 −0.0544396
\(629\) 3.44676 0.137431
\(630\) 13.1280 0.523032
\(631\) −45.0572 −1.79370 −0.896850 0.442335i \(-0.854150\pi\)
−0.896850 + 0.442335i \(0.854150\pi\)
\(632\) 7.13291 0.283732
\(633\) 13.3418 0.530290
\(634\) −31.7233 −1.25989
\(635\) 27.7165 1.09990
\(636\) 4.07947 0.161761
\(637\) 22.6132 0.895969
\(638\) 16.6832 0.660493
\(639\) 12.3363 0.488016
\(640\) −2.70694 −0.107001
\(641\) 46.7212 1.84538 0.922688 0.385547i \(-0.125987\pi\)
0.922688 + 0.385547i \(0.125987\pi\)
\(642\) 1.73968 0.0686596
\(643\) −8.38073 −0.330504 −0.165252 0.986251i \(-0.552844\pi\)
−0.165252 + 0.986251i \(0.552844\pi\)
\(644\) 1.75684 0.0692293
\(645\) −6.55908 −0.258263
\(646\) 1.36037 0.0535231
\(647\) −8.67354 −0.340992 −0.170496 0.985358i \(-0.554537\pi\)
−0.170496 + 0.985358i \(0.554537\pi\)
\(648\) −6.90185 −0.271130
\(649\) 24.7336 0.970880
\(650\) 13.4490 0.527512
\(651\) 3.47981 0.136384
\(652\) 11.9751 0.468979
\(653\) −2.16174 −0.0845954 −0.0422977 0.999105i \(-0.513468\pi\)
−0.0422977 + 0.999105i \(0.513468\pi\)
\(654\) 7.17446 0.280543
\(655\) 2.70694 0.105769
\(656\) −9.32536 −0.364094
\(657\) 37.3645 1.45773
\(658\) 18.2478 0.711374
\(659\) 9.18967 0.357979 0.178989 0.983851i \(-0.442717\pi\)
0.178989 + 0.983851i \(0.442717\pi\)
\(660\) 2.46835 0.0960803
\(661\) 24.7234 0.961627 0.480814 0.876823i \(-0.340341\pi\)
0.480814 + 0.876823i \(0.340341\pi\)
\(662\) −12.6481 −0.491583
\(663\) −1.16339 −0.0451823
\(664\) −6.71368 −0.260541
\(665\) −15.7252 −0.609795
\(666\) 23.1273 0.896164
\(667\) −8.95375 −0.346691
\(668\) −8.16434 −0.315888
\(669\) 8.78372 0.339598
\(670\) −17.0198 −0.657533
\(671\) 17.4261 0.672726
\(672\) −0.859779 −0.0331667
\(673\) 11.2109 0.432150 0.216075 0.976377i \(-0.430675\pi\)
0.216075 + 0.976377i \(0.430675\pi\)
\(674\) −10.0795 −0.388249
\(675\) −6.56155 −0.252554
\(676\) 20.3882 0.784163
\(677\) −8.34645 −0.320780 −0.160390 0.987054i \(-0.551275\pi\)
−0.160390 + 0.987054i \(0.551275\pi\)
\(678\) 7.45462 0.286293
\(679\) −16.8617 −0.647091
\(680\) −1.11366 −0.0427069
\(681\) 9.29620 0.356231
\(682\) −7.54123 −0.288769
\(683\) 23.8569 0.912859 0.456430 0.889759i \(-0.349128\pi\)
0.456430 + 0.889759i \(0.349128\pi\)
\(684\) 9.12791 0.349014
\(685\) −29.5150 −1.12771
\(686\) 19.1733 0.732040
\(687\) 10.4959 0.400444
\(688\) −4.95120 −0.188763
\(689\) −48.1666 −1.83500
\(690\) −1.32475 −0.0504322
\(691\) −18.8652 −0.717665 −0.358833 0.933402i \(-0.616825\pi\)
−0.358833 + 0.933402i \(0.616825\pi\)
\(692\) −21.4495 −0.815389
\(693\) −9.03637 −0.343263
\(694\) 2.43014 0.0922469
\(695\) 10.2736 0.389700
\(696\) 4.38187 0.166094
\(697\) −3.83654 −0.145319
\(698\) 11.8155 0.447225
\(699\) 3.27385 0.123828
\(700\) 4.08907 0.154552
\(701\) 21.2911 0.804155 0.402077 0.915606i \(-0.368288\pi\)
0.402077 + 0.915606i \(0.368288\pi\)
\(702\) −16.2896 −0.614812
\(703\) −27.7026 −1.04482
\(704\) 1.86326 0.0702243
\(705\) −13.7597 −0.518222
\(706\) 12.9583 0.487691
\(707\) −26.4543 −0.994915
\(708\) 6.49634 0.244147
\(709\) −24.8977 −0.935052 −0.467526 0.883979i \(-0.654855\pi\)
−0.467526 + 0.883979i \(0.654855\pi\)
\(710\) 12.0969 0.453990
\(711\) 19.6904 0.738447
\(712\) −3.92441 −0.147073
\(713\) 4.04733 0.151574
\(714\) −0.353721 −0.0132377
\(715\) −29.1440 −1.08992
\(716\) −9.37898 −0.350509
\(717\) 4.61545 0.172367
\(718\) −25.4169 −0.948552
\(719\) −30.3358 −1.13133 −0.565667 0.824634i \(-0.691381\pi\)
−0.565667 + 0.824634i \(0.691381\pi\)
\(720\) −7.47250 −0.278484
\(721\) −23.8668 −0.888847
\(722\) 8.06628 0.300196
\(723\) −10.1203 −0.376378
\(724\) 18.5444 0.689197
\(725\) −20.8400 −0.773977
\(726\) 3.68425 0.136735
\(727\) 32.2087 1.19456 0.597278 0.802034i \(-0.296249\pi\)
0.597278 + 0.802034i \(0.296249\pi\)
\(728\) 10.1515 0.376239
\(729\) −14.9136 −0.552355
\(730\) 36.6395 1.35609
\(731\) −2.03697 −0.0753400
\(732\) 4.57699 0.169170
\(733\) 32.8486 1.21329 0.606646 0.794972i \(-0.292515\pi\)
0.606646 + 0.794972i \(0.292515\pi\)
\(734\) −4.09411 −0.151116
\(735\) −5.18440 −0.191229
\(736\) −1.00000 −0.0368605
\(737\) 11.7152 0.431535
\(738\) −25.7426 −0.947599
\(739\) −52.9357 −1.94727 −0.973636 0.228109i \(-0.926746\pi\)
−0.973636 + 0.228109i \(0.926746\pi\)
\(740\) 22.6785 0.833680
\(741\) 9.35050 0.343499
\(742\) −14.6448 −0.537626
\(743\) 35.0933 1.28745 0.643724 0.765258i \(-0.277388\pi\)
0.643724 + 0.765258i \(0.277388\pi\)
\(744\) −1.98072 −0.0726166
\(745\) 48.6843 1.78365
\(746\) 14.1480 0.517996
\(747\) −18.5331 −0.678091
\(748\) 0.766563 0.0280283
\(749\) −6.24521 −0.228195
\(750\) 3.54037 0.129276
\(751\) −44.5823 −1.62683 −0.813415 0.581684i \(-0.802394\pi\)
−0.813415 + 0.581684i \(0.802394\pi\)
\(752\) −10.3867 −0.378764
\(753\) −9.98993 −0.364053
\(754\) −51.7370 −1.88415
\(755\) −52.2981 −1.90332
\(756\) −4.95276 −0.180130
\(757\) −22.3479 −0.812248 −0.406124 0.913818i \(-0.633120\pi\)
−0.406124 + 0.913818i \(0.633120\pi\)
\(758\) 15.6164 0.567212
\(759\) 0.911859 0.0330984
\(760\) 8.95081 0.324680
\(761\) 6.77441 0.245572 0.122786 0.992433i \(-0.460817\pi\)
0.122786 + 0.992433i \(0.460817\pi\)
\(762\) −5.01089 −0.181525
\(763\) −25.7554 −0.932407
\(764\) 6.37074 0.230485
\(765\) −3.07425 −0.111150
\(766\) −21.4338 −0.774433
\(767\) −76.7028 −2.76958
\(768\) 0.489389 0.0176593
\(769\) 17.2431 0.621801 0.310901 0.950442i \(-0.399369\pi\)
0.310901 + 0.950442i \(0.399369\pi\)
\(770\) −8.86104 −0.319330
\(771\) 9.73791 0.350702
\(772\) −7.98381 −0.287344
\(773\) 35.0374 1.26021 0.630105 0.776510i \(-0.283012\pi\)
0.630105 + 0.776510i \(0.283012\pi\)
\(774\) −13.6678 −0.491278
\(775\) 9.42020 0.338384
\(776\) 9.59770 0.344537
\(777\) 7.20317 0.258412
\(778\) 10.1472 0.363796
\(779\) 30.8354 1.10479
\(780\) −7.65472 −0.274083
\(781\) −8.32666 −0.297951
\(782\) −0.411409 −0.0147120
\(783\) 25.2417 0.902066
\(784\) −3.91351 −0.139768
\(785\) −3.69294 −0.131807
\(786\) −0.489389 −0.0174559
\(787\) 14.7753 0.526684 0.263342 0.964703i \(-0.415175\pi\)
0.263342 + 0.964703i \(0.415175\pi\)
\(788\) −18.6150 −0.663131
\(789\) −11.3734 −0.404904
\(790\) 19.3083 0.686960
\(791\) −26.7611 −0.951516
\(792\) 5.14353 0.182767
\(793\) −54.0409 −1.91905
\(794\) −7.32012 −0.259781
\(795\) 11.0429 0.391650
\(796\) 1.98994 0.0705316
\(797\) −12.6253 −0.447210 −0.223605 0.974680i \(-0.571783\pi\)
−0.223605 + 0.974680i \(0.571783\pi\)
\(798\) 2.84296 0.100640
\(799\) −4.27319 −0.151175
\(800\) −2.32751 −0.0822900
\(801\) −10.8333 −0.382777
\(802\) −16.9234 −0.597586
\(803\) −25.2200 −0.889995
\(804\) 3.07702 0.108518
\(805\) 4.75566 0.167615
\(806\) 23.3865 0.823754
\(807\) −7.07832 −0.249169
\(808\) 15.0579 0.529733
\(809\) 43.6519 1.53472 0.767359 0.641217i \(-0.221570\pi\)
0.767359 + 0.641217i \(0.221570\pi\)
\(810\) −18.6829 −0.656449
\(811\) 29.0471 1.01998 0.509992 0.860179i \(-0.329649\pi\)
0.509992 + 0.860179i \(0.329649\pi\)
\(812\) −15.7303 −0.552026
\(813\) −7.12323 −0.249823
\(814\) −15.6103 −0.547140
\(815\) 32.4157 1.13547
\(816\) 0.201339 0.00704828
\(817\) 16.3717 0.572774
\(818\) −2.23908 −0.0782876
\(819\) 28.0232 0.979208
\(820\) −25.2432 −0.881529
\(821\) 26.1466 0.912524 0.456262 0.889845i \(-0.349188\pi\)
0.456262 + 0.889845i \(0.349188\pi\)
\(822\) 5.33603 0.186115
\(823\) 10.4056 0.362716 0.181358 0.983417i \(-0.441951\pi\)
0.181358 + 0.983417i \(0.441951\pi\)
\(824\) 13.5851 0.473258
\(825\) 2.12236 0.0738912
\(826\) −23.3210 −0.811441
\(827\) −9.15527 −0.318360 −0.159180 0.987250i \(-0.550885\pi\)
−0.159180 + 0.987250i \(0.550885\pi\)
\(828\) −2.76050 −0.0959340
\(829\) 49.3509 1.71403 0.857015 0.515292i \(-0.172317\pi\)
0.857015 + 0.515292i \(0.172317\pi\)
\(830\) −18.1735 −0.630812
\(831\) 6.84363 0.237403
\(832\) −5.77826 −0.200325
\(833\) −1.61005 −0.0557850
\(834\) −1.85737 −0.0643155
\(835\) −22.1004 −0.764814
\(836\) −6.16109 −0.213086
\(837\) −11.4099 −0.394385
\(838\) 7.44628 0.257227
\(839\) −44.8551 −1.54857 −0.774286 0.632836i \(-0.781891\pi\)
−0.774286 + 0.632836i \(0.781891\pi\)
\(840\) −2.32737 −0.0803019
\(841\) 51.1696 1.76447
\(842\) −22.1005 −0.761632
\(843\) 1.17777 0.0405644
\(844\) 27.2622 0.938404
\(845\) 55.1897 1.89858
\(846\) −28.6725 −0.985781
\(847\) −13.2260 −0.454449
\(848\) 8.33584 0.286254
\(849\) 0.495507 0.0170057
\(850\) −0.957560 −0.0328440
\(851\) 8.37793 0.287192
\(852\) −2.18701 −0.0749258
\(853\) 12.5232 0.428787 0.214393 0.976747i \(-0.431223\pi\)
0.214393 + 0.976747i \(0.431223\pi\)
\(854\) −16.4308 −0.562250
\(855\) 24.7087 0.845019
\(856\) 3.55479 0.121500
\(857\) 9.14815 0.312495 0.156247 0.987718i \(-0.450060\pi\)
0.156247 + 0.987718i \(0.450060\pi\)
\(858\) 5.26896 0.179879
\(859\) −7.95805 −0.271525 −0.135763 0.990741i \(-0.543348\pi\)
−0.135763 + 0.990741i \(0.543348\pi\)
\(860\) −13.4026 −0.457024
\(861\) −8.01775 −0.273244
\(862\) 11.7617 0.400604
\(863\) −7.31829 −0.249117 −0.124559 0.992212i \(-0.539752\pi\)
−0.124559 + 0.992212i \(0.539752\pi\)
\(864\) 2.81912 0.0959086
\(865\) −58.0626 −1.97419
\(866\) 17.0115 0.578074
\(867\) −8.23678 −0.279736
\(868\) 7.11052 0.241347
\(869\) −13.2905 −0.450848
\(870\) 11.8614 0.402140
\(871\) −36.3307 −1.23102
\(872\) 14.6600 0.496451
\(873\) 26.4944 0.896701
\(874\) 3.30662 0.111848
\(875\) −12.7095 −0.429658
\(876\) −6.62408 −0.223807
\(877\) −34.1203 −1.15216 −0.576080 0.817393i \(-0.695418\pi\)
−0.576080 + 0.817393i \(0.695418\pi\)
\(878\) −37.3642 −1.26098
\(879\) 2.80801 0.0947118
\(880\) 5.04373 0.170024
\(881\) 24.4209 0.822760 0.411380 0.911464i \(-0.365047\pi\)
0.411380 + 0.911464i \(0.365047\pi\)
\(882\) −10.8032 −0.363764
\(883\) −31.1626 −1.04870 −0.524352 0.851502i \(-0.675692\pi\)
−0.524352 + 0.851502i \(0.675692\pi\)
\(884\) −2.37723 −0.0799548
\(885\) 17.5852 0.591119
\(886\) −16.4430 −0.552414
\(887\) 56.1470 1.88523 0.942616 0.333880i \(-0.108358\pi\)
0.942616 + 0.333880i \(0.108358\pi\)
\(888\) −4.10007 −0.137589
\(889\) 17.9884 0.603313
\(890\) −10.6231 −0.356088
\(891\) 12.8599 0.430824
\(892\) 17.9483 0.600955
\(893\) 34.3449 1.14931
\(894\) −8.80167 −0.294372
\(895\) −25.3883 −0.848637
\(896\) −1.75684 −0.0586920
\(897\) −2.82781 −0.0944180
\(898\) −13.3905 −0.446848
\(899\) −36.2388 −1.20863
\(900\) −6.42509 −0.214170
\(901\) 3.42944 0.114251
\(902\) 17.3756 0.578543
\(903\) −4.25694 −0.141662
\(904\) 15.2325 0.506626
\(905\) 50.1985 1.66865
\(906\) 9.45500 0.314121
\(907\) −54.1884 −1.79930 −0.899648 0.436616i \(-0.856177\pi\)
−0.899648 + 0.436616i \(0.856177\pi\)
\(908\) 18.9955 0.630388
\(909\) 41.5672 1.37870
\(910\) 27.4794 0.910934
\(911\) −49.4517 −1.63841 −0.819203 0.573503i \(-0.805584\pi\)
−0.819203 + 0.573503i \(0.805584\pi\)
\(912\) −1.61822 −0.0535847
\(913\) 12.5093 0.413999
\(914\) 7.64751 0.252957
\(915\) 12.3896 0.409588
\(916\) 21.4469 0.708627
\(917\) 1.75684 0.0580160
\(918\) 1.15981 0.0382796
\(919\) 14.6614 0.483635 0.241818 0.970322i \(-0.422256\pi\)
0.241818 + 0.970322i \(0.422256\pi\)
\(920\) −2.70694 −0.0892451
\(921\) 5.94044 0.195744
\(922\) 26.6413 0.877385
\(923\) 25.8222 0.849949
\(924\) 1.60199 0.0527017
\(925\) 19.4997 0.641147
\(926\) 10.0154 0.329126
\(927\) 37.5016 1.23171
\(928\) 8.95375 0.293921
\(929\) 4.63009 0.151908 0.0759541 0.997111i \(-0.475800\pi\)
0.0759541 + 0.997111i \(0.475800\pi\)
\(930\) −5.36168 −0.175816
\(931\) 12.9405 0.424107
\(932\) 6.68967 0.219127
\(933\) −3.65445 −0.119641
\(934\) −13.7640 −0.450371
\(935\) 2.07504 0.0678610
\(936\) −15.9509 −0.521370
\(937\) −23.2690 −0.760165 −0.380082 0.924953i \(-0.624104\pi\)
−0.380082 + 0.924953i \(0.624104\pi\)
\(938\) −11.0461 −0.360668
\(939\) −7.93070 −0.258809
\(940\) −28.1162 −0.917049
\(941\) −27.5790 −0.899051 −0.449526 0.893267i \(-0.648407\pi\)
−0.449526 + 0.893267i \(0.648407\pi\)
\(942\) 0.667650 0.0217532
\(943\) −9.32536 −0.303675
\(944\) 13.2744 0.432044
\(945\) −13.4068 −0.436123
\(946\) 9.22537 0.299943
\(947\) −21.0274 −0.683298 −0.341649 0.939828i \(-0.610985\pi\)
−0.341649 + 0.939828i \(0.610985\pi\)
\(948\) −3.49077 −0.113375
\(949\) 78.2111 2.53884
\(950\) 7.69619 0.249697
\(951\) 15.5250 0.503433
\(952\) −0.722781 −0.0234255
\(953\) 19.9440 0.646050 0.323025 0.946390i \(-0.395300\pi\)
0.323025 + 0.946390i \(0.395300\pi\)
\(954\) 23.0111 0.745011
\(955\) 17.2452 0.558041
\(956\) 9.43105 0.305022
\(957\) −8.16456 −0.263923
\(958\) 15.1671 0.490028
\(959\) −19.1557 −0.618568
\(960\) 1.32475 0.0427560
\(961\) −14.6191 −0.471585
\(962\) 48.4098 1.56080
\(963\) 9.81300 0.316220
\(964\) −20.6794 −0.666040
\(965\) −21.6117 −0.695704
\(966\) −0.859779 −0.0276629
\(967\) 3.81629 0.122724 0.0613618 0.998116i \(-0.480456\pi\)
0.0613618 + 0.998116i \(0.480456\pi\)
\(968\) 7.52826 0.241967
\(969\) −0.665751 −0.0213870
\(970\) 25.9804 0.834180
\(971\) 5.44289 0.174671 0.0873353 0.996179i \(-0.472165\pi\)
0.0873353 + 0.996179i \(0.472165\pi\)
\(972\) 11.8351 0.379610
\(973\) 6.66772 0.213757
\(974\) 31.5734 1.01168
\(975\) −6.58177 −0.210785
\(976\) 9.35245 0.299365
\(977\) 15.7503 0.503896 0.251948 0.967741i \(-0.418929\pi\)
0.251948 + 0.967741i \(0.418929\pi\)
\(978\) −5.86046 −0.187397
\(979\) 7.31220 0.233699
\(980\) −10.5936 −0.338401
\(981\) 40.4690 1.29208
\(982\) 7.35504 0.234709
\(983\) 52.0544 1.66028 0.830140 0.557556i \(-0.188261\pi\)
0.830140 + 0.557556i \(0.188261\pi\)
\(984\) 4.56373 0.145486
\(985\) −50.3896 −1.60555
\(986\) 3.68365 0.117311
\(987\) −8.93028 −0.284254
\(988\) 19.1065 0.607858
\(989\) −4.95120 −0.157439
\(990\) 13.9232 0.442509
\(991\) −20.9966 −0.666978 −0.333489 0.942754i \(-0.608226\pi\)
−0.333489 + 0.942754i \(0.608226\pi\)
\(992\) −4.04733 −0.128503
\(993\) 6.18985 0.196429
\(994\) 7.85109 0.249021
\(995\) 5.38665 0.170768
\(996\) 3.28560 0.104108
\(997\) −21.9383 −0.694793 −0.347396 0.937718i \(-0.612934\pi\)
−0.347396 + 0.937718i \(0.612934\pi\)
\(998\) 38.9889 1.23417
\(999\) −23.6184 −0.747254
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 \(a_p\))