Properties

Label 6026.2.a.h.1.12
Level 6026
Weight 2
Character 6026.1
Self dual Yes
Analytic conductor 48.118
Analytic rank 1
Dimension 24
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: \(24\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Character \(\chi\) = 6026.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -0.666016 q^{3} +1.00000 q^{4} +0.513693 q^{5} +0.666016 q^{6} +2.90198 q^{7} -1.00000 q^{8} -2.55642 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -0.666016 q^{3} +1.00000 q^{4} +0.513693 q^{5} +0.666016 q^{6} +2.90198 q^{7} -1.00000 q^{8} -2.55642 q^{9} -0.513693 q^{10} +0.858892 q^{11} -0.666016 q^{12} -5.16614 q^{13} -2.90198 q^{14} -0.342128 q^{15} +1.00000 q^{16} +4.36731 q^{17} +2.55642 q^{18} -1.53998 q^{19} +0.513693 q^{20} -1.93277 q^{21} -0.858892 q^{22} -1.00000 q^{23} +0.666016 q^{24} -4.73612 q^{25} +5.16614 q^{26} +3.70067 q^{27} +2.90198 q^{28} -3.13545 q^{29} +0.342128 q^{30} +9.58158 q^{31} -1.00000 q^{32} -0.572036 q^{33} -4.36731 q^{34} +1.49073 q^{35} -2.55642 q^{36} -7.80219 q^{37} +1.53998 q^{38} +3.44073 q^{39} -0.513693 q^{40} +4.19115 q^{41} +1.93277 q^{42} +11.0431 q^{43} +0.858892 q^{44} -1.31322 q^{45} +1.00000 q^{46} -1.61318 q^{47} -0.666016 q^{48} +1.42151 q^{49} +4.73612 q^{50} -2.90870 q^{51} -5.16614 q^{52} -6.05418 q^{53} -3.70067 q^{54} +0.441207 q^{55} -2.90198 q^{56} +1.02565 q^{57} +3.13545 q^{58} +3.21058 q^{59} -0.342128 q^{60} -6.32871 q^{61} -9.58158 q^{62} -7.41870 q^{63} +1.00000 q^{64} -2.65381 q^{65} +0.572036 q^{66} -3.00309 q^{67} +4.36731 q^{68} +0.666016 q^{69} -1.49073 q^{70} +2.11045 q^{71} +2.55642 q^{72} +12.7851 q^{73} +7.80219 q^{74} +3.15433 q^{75} -1.53998 q^{76} +2.49249 q^{77} -3.44073 q^{78} -2.80194 q^{79} +0.513693 q^{80} +5.20456 q^{81} -4.19115 q^{82} -16.3424 q^{83} -1.93277 q^{84} +2.24345 q^{85} -11.0431 q^{86} +2.08826 q^{87} -0.858892 q^{88} -10.3293 q^{89} +1.31322 q^{90} -14.9920 q^{91} -1.00000 q^{92} -6.38149 q^{93} +1.61318 q^{94} -0.791075 q^{95} +0.666016 q^{96} -13.5647 q^{97} -1.42151 q^{98} -2.19569 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 24q^{2} - q^{3} + 24q^{4} - q^{5} + q^{6} - 7q^{7} - 24q^{8} + 27q^{9} + O(q^{10}) \) \( 24q - 24q^{2} - q^{3} + 24q^{4} - q^{5} + q^{6} - 7q^{7} - 24q^{8} + 27q^{9} + q^{10} - 4q^{11} - q^{12} - 5q^{13} + 7q^{14} - 6q^{15} + 24q^{16} + 5q^{17} - 27q^{18} - 20q^{19} - q^{20} + 4q^{22} - 24q^{23} + q^{24} + q^{25} + 5q^{26} - q^{27} - 7q^{28} - 6q^{29} + 6q^{30} - 23q^{31} - 24q^{32} - 6q^{33} - 5q^{34} + 5q^{35} + 27q^{36} - 6q^{37} + 20q^{38} - 39q^{39} + q^{40} - q^{41} - 44q^{43} - 4q^{44} - 13q^{45} + 24q^{46} + 32q^{47} - q^{48} - 13q^{49} - q^{50} - 44q^{51} - 5q^{52} + 21q^{53} + q^{54} - 13q^{55} + 7q^{56} + 10q^{57} + 6q^{58} - 24q^{59} - 6q^{60} - 40q^{61} + 23q^{62} - 54q^{63} + 24q^{64} - 29q^{65} + 6q^{66} - 17q^{67} + 5q^{68} + q^{69} - 5q^{70} + 4q^{71} - 27q^{72} - 16q^{73} + 6q^{74} - 36q^{75} - 20q^{76} + 24q^{77} + 39q^{78} - 53q^{79} - q^{80} + 24q^{81} + q^{82} - 9q^{83} - 37q^{85} + 44q^{86} + 7q^{87} + 4q^{88} - 46q^{89} + 13q^{90} - 44q^{91} - 24q^{92} + 23q^{93} - 32q^{94} + 28q^{95} + q^{96} - 20q^{97} + 13q^{98} - 78q^{99} + O(q^{100}) \)

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
\(3\) −0.666016 −0.384525 −0.192262 0.981344i \(-0.561582\pi\)
−0.192262 + 0.981344i \(0.561582\pi\)
\(4\) 1.00000 0.500000
\(5\) 0.513693 0.229730 0.114865 0.993381i \(-0.463356\pi\)
0.114865 + 0.993381i \(0.463356\pi\)
\(6\) 0.666016 0.271900
\(7\) 2.90198 1.09685 0.548423 0.836201i \(-0.315228\pi\)
0.548423 + 0.836201i \(0.315228\pi\)
\(8\) −1.00000 −0.353553
\(9\) −2.55642 −0.852141
\(10\) −0.513693 −0.162444
\(11\) 0.858892 0.258966 0.129483 0.991582i \(-0.458668\pi\)
0.129483 + 0.991582i \(0.458668\pi\)
\(12\) −0.666016 −0.192262
\(13\) −5.16614 −1.43283 −0.716414 0.697675i \(-0.754218\pi\)
−0.716414 + 0.697675i \(0.754218\pi\)
\(14\) −2.90198 −0.775588
\(15\) −0.342128 −0.0883370
\(16\) 1.00000 0.250000
\(17\) 4.36731 1.05923 0.529614 0.848239i \(-0.322337\pi\)
0.529614 + 0.848239i \(0.322337\pi\)
\(18\) 2.55642 0.602555
\(19\) −1.53998 −0.353295 −0.176648 0.984274i \(-0.556525\pi\)
−0.176648 + 0.984274i \(0.556525\pi\)
\(20\) 0.513693 0.114865
\(21\) −1.93277 −0.421765
\(22\) −0.858892 −0.183116
\(23\) −1.00000 −0.208514
\(24\) 0.666016 0.135950
\(25\) −4.73612 −0.947224
\(26\) 5.16614 1.01316
\(27\) 3.70067 0.712194
\(28\) 2.90198 0.548423
\(29\) −3.13545 −0.582238 −0.291119 0.956687i \(-0.594028\pi\)
−0.291119 + 0.956687i \(0.594028\pi\)
\(30\) 0.342128 0.0624637
\(31\) 9.58158 1.72090 0.860451 0.509532i \(-0.170182\pi\)
0.860451 + 0.509532i \(0.170182\pi\)
\(32\) −1.00000 −0.176777
\(33\) −0.572036 −0.0995787
\(34\) −4.36731 −0.748987
\(35\) 1.49073 0.251979
\(36\) −2.55642 −0.426070
\(37\) −7.80219 −1.28267 −0.641336 0.767260i \(-0.721619\pi\)
−0.641336 + 0.767260i \(0.721619\pi\)
\(38\) 1.53998 0.249817
\(39\) 3.44073 0.550958
\(40\) −0.513693 −0.0812219
\(41\) 4.19115 0.654547 0.327274 0.944930i \(-0.393870\pi\)
0.327274 + 0.944930i \(0.393870\pi\)
\(42\) 1.93277 0.298233
\(43\) 11.0431 1.68406 0.842029 0.539432i \(-0.181361\pi\)
0.842029 + 0.539432i \(0.181361\pi\)
\(44\) 0.858892 0.129483
\(45\) −1.31322 −0.195763
\(46\) 1.00000 0.147442
\(47\) −1.61318 −0.235306 −0.117653 0.993055i \(-0.537537\pi\)
−0.117653 + 0.993055i \(0.537537\pi\)
\(48\) −0.666016 −0.0961312
\(49\) 1.42151 0.203073
\(50\) 4.73612 0.669789
\(51\) −2.90870 −0.407299
\(52\) −5.16614 −0.716414
\(53\) −6.05418 −0.831606 −0.415803 0.909455i \(-0.636499\pi\)
−0.415803 + 0.909455i \(0.636499\pi\)
\(54\) −3.70067 −0.503597
\(55\) 0.441207 0.0594923
\(56\) −2.90198 −0.387794
\(57\) 1.02565 0.135851
\(58\) 3.13545 0.411704
\(59\) 3.21058 0.417982 0.208991 0.977918i \(-0.432982\pi\)
0.208991 + 0.977918i \(0.432982\pi\)
\(60\) −0.342128 −0.0441685
\(61\) −6.32871 −0.810309 −0.405154 0.914248i \(-0.632782\pi\)
−0.405154 + 0.914248i \(0.632782\pi\)
\(62\) −9.58158 −1.21686
\(63\) −7.41870 −0.934668
\(64\) 1.00000 0.125000
\(65\) −2.65381 −0.329164
\(66\) 0.572036 0.0704128
\(67\) −3.00309 −0.366886 −0.183443 0.983030i \(-0.558724\pi\)
−0.183443 + 0.983030i \(0.558724\pi\)
\(68\) 4.36731 0.529614
\(69\) 0.666016 0.0801789
\(70\) −1.49073 −0.178176
\(71\) 2.11045 0.250464 0.125232 0.992127i \(-0.460032\pi\)
0.125232 + 0.992127i \(0.460032\pi\)
\(72\) 2.55642 0.301277
\(73\) 12.7851 1.49638 0.748189 0.663486i \(-0.230924\pi\)
0.748189 + 0.663486i \(0.230924\pi\)
\(74\) 7.80219 0.906986
\(75\) 3.15433 0.364231
\(76\) −1.53998 −0.176648
\(77\) 2.49249 0.284046
\(78\) −3.44073 −0.389586
\(79\) −2.80194 −0.315242 −0.157621 0.987500i \(-0.550382\pi\)
−0.157621 + 0.987500i \(0.550382\pi\)
\(80\) 0.513693 0.0574326
\(81\) 5.20456 0.578285
\(82\) −4.19115 −0.462835
\(83\) −16.3424 −1.79381 −0.896907 0.442219i \(-0.854192\pi\)
−0.896907 + 0.442219i \(0.854192\pi\)
\(84\) −1.93277 −0.210882
\(85\) 2.24345 0.243337
\(86\) −11.0431 −1.19081
\(87\) 2.08826 0.223885
\(88\) −0.858892 −0.0915582
\(89\) −10.3293 −1.09490 −0.547451 0.836837i \(-0.684402\pi\)
−0.547451 + 0.836837i \(0.684402\pi\)
\(90\) 1.31322 0.138425
\(91\) −14.9920 −1.57159
\(92\) −1.00000 −0.104257
\(93\) −6.38149 −0.661730
\(94\) 1.61318 0.166386
\(95\) −0.791075 −0.0811626
\(96\) 0.666016 0.0679750
\(97\) −13.5647 −1.37729 −0.688646 0.725098i \(-0.741794\pi\)
−0.688646 + 0.725098i \(0.741794\pi\)
\(98\) −1.42151 −0.143594
\(99\) −2.19569 −0.220675
\(100\) −4.73612 −0.473612
\(101\) −12.3385 −1.22773 −0.613864 0.789411i \(-0.710386\pi\)
−0.613864 + 0.789411i \(0.710386\pi\)
\(102\) 2.90870 0.288004
\(103\) 13.5956 1.33962 0.669809 0.742533i \(-0.266376\pi\)
0.669809 + 0.742533i \(0.266376\pi\)
\(104\) 5.16614 0.506581
\(105\) −0.992849 −0.0968921
\(106\) 6.05418 0.588034
\(107\) 2.09749 0.202772 0.101386 0.994847i \(-0.467672\pi\)
0.101386 + 0.994847i \(0.467672\pi\)
\(108\) 3.70067 0.356097
\(109\) −3.35144 −0.321010 −0.160505 0.987035i \(-0.551312\pi\)
−0.160505 + 0.987035i \(0.551312\pi\)
\(110\) −0.441207 −0.0420674
\(111\) 5.19638 0.493219
\(112\) 2.90198 0.274212
\(113\) 2.60455 0.245016 0.122508 0.992468i \(-0.460906\pi\)
0.122508 + 0.992468i \(0.460906\pi\)
\(114\) −1.02565 −0.0960610
\(115\) −0.513693 −0.0479021
\(116\) −3.13545 −0.291119
\(117\) 13.2068 1.22097
\(118\) −3.21058 −0.295558
\(119\) 12.6739 1.16181
\(120\) 0.342128 0.0312318
\(121\) −10.2623 −0.932937
\(122\) 6.32871 0.572975
\(123\) −2.79137 −0.251690
\(124\) 9.58158 0.860451
\(125\) −5.00137 −0.447336
\(126\) 7.41870 0.660910
\(127\) 8.95804 0.794898 0.397449 0.917624i \(-0.369896\pi\)
0.397449 + 0.917624i \(0.369896\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −7.35489 −0.647562
\(130\) 2.65381 0.232754
\(131\) −1.00000 −0.0873704
\(132\) −0.572036 −0.0497894
\(133\) −4.46899 −0.387511
\(134\) 3.00309 0.259427
\(135\) 1.90101 0.163613
\(136\) −4.36731 −0.374494
\(137\) −6.37224 −0.544417 −0.272209 0.962238i \(-0.587754\pi\)
−0.272209 + 0.962238i \(0.587754\pi\)
\(138\) −0.666016 −0.0566951
\(139\) −3.38441 −0.287062 −0.143531 0.989646i \(-0.545846\pi\)
−0.143531 + 0.989646i \(0.545846\pi\)
\(140\) 1.49073 0.125989
\(141\) 1.07440 0.0904810
\(142\) −2.11045 −0.177105
\(143\) −4.43716 −0.371054
\(144\) −2.55642 −0.213035
\(145\) −1.61066 −0.133758
\(146\) −12.7851 −1.05810
\(147\) −0.946748 −0.0780864
\(148\) −7.80219 −0.641336
\(149\) −8.77077 −0.718529 −0.359265 0.933236i \(-0.616972\pi\)
−0.359265 + 0.933236i \(0.616972\pi\)
\(150\) −3.15433 −0.257550
\(151\) −8.39331 −0.683038 −0.341519 0.939875i \(-0.610941\pi\)
−0.341519 + 0.939875i \(0.610941\pi\)
\(152\) 1.53998 0.124909
\(153\) −11.1647 −0.902612
\(154\) −2.49249 −0.200851
\(155\) 4.92199 0.395344
\(156\) 3.44073 0.275479
\(157\) −18.6501 −1.48844 −0.744219 0.667936i \(-0.767178\pi\)
−0.744219 + 0.667936i \(0.767178\pi\)
\(158\) 2.80194 0.222910
\(159\) 4.03219 0.319773
\(160\) −0.513693 −0.0406110
\(161\) −2.90198 −0.228708
\(162\) −5.20456 −0.408909
\(163\) −14.6796 −1.14980 −0.574898 0.818225i \(-0.694958\pi\)
−0.574898 + 0.818225i \(0.694958\pi\)
\(164\) 4.19115 0.327274
\(165\) −0.293851 −0.0228763
\(166\) 16.3424 1.26842
\(167\) 18.8637 1.45972 0.729860 0.683597i \(-0.239585\pi\)
0.729860 + 0.683597i \(0.239585\pi\)
\(168\) 1.93277 0.149116
\(169\) 13.6890 1.05300
\(170\) −2.24345 −0.172065
\(171\) 3.93683 0.301057
\(172\) 11.0431 0.842029
\(173\) −4.89372 −0.372062 −0.186031 0.982544i \(-0.559563\pi\)
−0.186031 + 0.982544i \(0.559563\pi\)
\(174\) −2.08826 −0.158311
\(175\) −13.7441 −1.03896
\(176\) 0.858892 0.0647414
\(177\) −2.13830 −0.160724
\(178\) 10.3293 0.774213
\(179\) −6.04074 −0.451506 −0.225753 0.974185i \(-0.572484\pi\)
−0.225753 + 0.974185i \(0.572484\pi\)
\(180\) −1.31322 −0.0978813
\(181\) 10.2860 0.764550 0.382275 0.924049i \(-0.375141\pi\)
0.382275 + 0.924049i \(0.375141\pi\)
\(182\) 14.9920 1.11128
\(183\) 4.21503 0.311584
\(184\) 1.00000 0.0737210
\(185\) −4.00793 −0.294669
\(186\) 6.38149 0.467914
\(187\) 3.75105 0.274304
\(188\) −1.61318 −0.117653
\(189\) 10.7393 0.781167
\(190\) 0.791075 0.0573906
\(191\) 7.08976 0.512997 0.256498 0.966545i \(-0.417431\pi\)
0.256498 + 0.966545i \(0.417431\pi\)
\(192\) −0.666016 −0.0480656
\(193\) 0.399230 0.0287372 0.0143686 0.999897i \(-0.495426\pi\)
0.0143686 + 0.999897i \(0.495426\pi\)
\(194\) 13.5647 0.973892
\(195\) 1.76748 0.126572
\(196\) 1.42151 0.101536
\(197\) 18.7880 1.33859 0.669294 0.742998i \(-0.266597\pi\)
0.669294 + 0.742998i \(0.266597\pi\)
\(198\) 2.19569 0.156041
\(199\) −2.56488 −0.181820 −0.0909099 0.995859i \(-0.528978\pi\)
−0.0909099 + 0.995859i \(0.528978\pi\)
\(200\) 4.73612 0.334894
\(201\) 2.00011 0.141077
\(202\) 12.3385 0.868135
\(203\) −9.09902 −0.638626
\(204\) −2.90870 −0.203650
\(205\) 2.15296 0.150369
\(206\) −13.5956 −0.947253
\(207\) 2.55642 0.177684
\(208\) −5.16614 −0.358207
\(209\) −1.32268 −0.0914914
\(210\) 0.992849 0.0685131
\(211\) 11.1136 0.765089 0.382544 0.923937i \(-0.375048\pi\)
0.382544 + 0.923937i \(0.375048\pi\)
\(212\) −6.05418 −0.415803
\(213\) −1.40559 −0.0963098
\(214\) −2.09749 −0.143382
\(215\) 5.67277 0.386879
\(216\) −3.70067 −0.251799
\(217\) 27.8056 1.88757
\(218\) 3.35144 0.226988
\(219\) −8.51506 −0.575394
\(220\) 0.441207 0.0297461
\(221\) −22.5621 −1.51769
\(222\) −5.19638 −0.348759
\(223\) 4.48756 0.300509 0.150254 0.988647i \(-0.451991\pi\)
0.150254 + 0.988647i \(0.451991\pi\)
\(224\) −2.90198 −0.193897
\(225\) 12.1075 0.807168
\(226\) −2.60455 −0.173252
\(227\) −8.01551 −0.532008 −0.266004 0.963972i \(-0.585703\pi\)
−0.266004 + 0.963972i \(0.585703\pi\)
\(228\) 1.02565 0.0679254
\(229\) −15.9785 −1.05589 −0.527945 0.849278i \(-0.677037\pi\)
−0.527945 + 0.849278i \(0.677037\pi\)
\(230\) 0.513693 0.0338719
\(231\) −1.66004 −0.109223
\(232\) 3.13545 0.205852
\(233\) −7.42163 −0.486207 −0.243104 0.970000i \(-0.578166\pi\)
−0.243104 + 0.970000i \(0.578166\pi\)
\(234\) −13.2068 −0.863357
\(235\) −0.828677 −0.0540569
\(236\) 3.21058 0.208991
\(237\) 1.86613 0.121218
\(238\) −12.6739 −0.821524
\(239\) 7.94904 0.514181 0.257090 0.966387i \(-0.417236\pi\)
0.257090 + 0.966387i \(0.417236\pi\)
\(240\) −0.342128 −0.0220842
\(241\) −18.9159 −1.21848 −0.609239 0.792986i \(-0.708525\pi\)
−0.609239 + 0.792986i \(0.708525\pi\)
\(242\) 10.2623 0.659686
\(243\) −14.5683 −0.934559
\(244\) −6.32871 −0.405154
\(245\) 0.730218 0.0466519
\(246\) 2.79137 0.177971
\(247\) 7.95574 0.506212
\(248\) −9.58158 −0.608431
\(249\) 10.8843 0.689766
\(250\) 5.00137 0.316315
\(251\) 20.4684 1.29195 0.645976 0.763358i \(-0.276451\pi\)
0.645976 + 0.763358i \(0.276451\pi\)
\(252\) −7.41870 −0.467334
\(253\) −0.858892 −0.0539981
\(254\) −8.95804 −0.562077
\(255\) −1.49418 −0.0935690
\(256\) 1.00000 0.0625000
\(257\) −17.0534 −1.06376 −0.531882 0.846818i \(-0.678515\pi\)
−0.531882 + 0.846818i \(0.678515\pi\)
\(258\) 7.35489 0.457896
\(259\) −22.6418 −1.40689
\(260\) −2.65381 −0.164582
\(261\) 8.01553 0.496149
\(262\) 1.00000 0.0617802
\(263\) −12.6819 −0.781997 −0.390998 0.920391i \(-0.627870\pi\)
−0.390998 + 0.920391i \(0.627870\pi\)
\(264\) 0.572036 0.0352064
\(265\) −3.10999 −0.191045
\(266\) 4.46899 0.274011
\(267\) 6.87948 0.421017
\(268\) −3.00309 −0.183443
\(269\) −3.85121 −0.234812 −0.117406 0.993084i \(-0.537458\pi\)
−0.117406 + 0.993084i \(0.537458\pi\)
\(270\) −1.90101 −0.115692
\(271\) −18.3602 −1.11530 −0.557650 0.830076i \(-0.688297\pi\)
−0.557650 + 0.830076i \(0.688297\pi\)
\(272\) 4.36731 0.264807
\(273\) 9.98495 0.604316
\(274\) 6.37224 0.384961
\(275\) −4.06782 −0.245299
\(276\) 0.666016 0.0400895
\(277\) −8.48390 −0.509748 −0.254874 0.966974i \(-0.582034\pi\)
−0.254874 + 0.966974i \(0.582034\pi\)
\(278\) 3.38441 0.202983
\(279\) −24.4946 −1.46645
\(280\) −1.49073 −0.0890880
\(281\) 25.6835 1.53215 0.766074 0.642753i \(-0.222208\pi\)
0.766074 + 0.642753i \(0.222208\pi\)
\(282\) −1.07440 −0.0639797
\(283\) −4.17828 −0.248373 −0.124186 0.992259i \(-0.539632\pi\)
−0.124186 + 0.992259i \(0.539632\pi\)
\(284\) 2.11045 0.125232
\(285\) 0.526869 0.0312090
\(286\) 4.43716 0.262374
\(287\) 12.1626 0.717938
\(288\) 2.55642 0.150639
\(289\) 2.07339 0.121964
\(290\) 1.61066 0.0945810
\(291\) 9.03434 0.529603
\(292\) 12.7851 0.748189
\(293\) 6.81701 0.398254 0.199127 0.979974i \(-0.436189\pi\)
0.199127 + 0.979974i \(0.436189\pi\)
\(294\) 0.946748 0.0552155
\(295\) 1.64925 0.0960231
\(296\) 7.80219 0.453493
\(297\) 3.17847 0.184434
\(298\) 8.77077 0.508077
\(299\) 5.16614 0.298765
\(300\) 3.15433 0.182116
\(301\) 32.0469 1.84715
\(302\) 8.39331 0.482981
\(303\) 8.21766 0.472092
\(304\) −1.53998 −0.0883238
\(305\) −3.25101 −0.186153
\(306\) 11.1647 0.638243
\(307\) −3.01812 −0.172253 −0.0861266 0.996284i \(-0.527449\pi\)
−0.0861266 + 0.996284i \(0.527449\pi\)
\(308\) 2.49249 0.142023
\(309\) −9.05492 −0.515116
\(310\) −4.92199 −0.279550
\(311\) 18.3068 1.03809 0.519043 0.854748i \(-0.326289\pi\)
0.519043 + 0.854748i \(0.326289\pi\)
\(312\) −3.44073 −0.194793
\(313\) −14.1283 −0.798579 −0.399289 0.916825i \(-0.630743\pi\)
−0.399289 + 0.916825i \(0.630743\pi\)
\(314\) 18.6501 1.05248
\(315\) −3.81093 −0.214722
\(316\) −2.80194 −0.157621
\(317\) 23.2730 1.30714 0.653572 0.756865i \(-0.273270\pi\)
0.653572 + 0.756865i \(0.273270\pi\)
\(318\) −4.03219 −0.226114
\(319\) −2.69301 −0.150780
\(320\) 0.513693 0.0287163
\(321\) −1.39696 −0.0779710
\(322\) 2.90198 0.161721
\(323\) −6.72556 −0.374220
\(324\) 5.20456 0.289142
\(325\) 24.4674 1.35721
\(326\) 14.6796 0.813028
\(327\) 2.23211 0.123436
\(328\) −4.19115 −0.231417
\(329\) −4.68141 −0.258095
\(330\) 0.293851 0.0161760
\(331\) −13.3253 −0.732427 −0.366213 0.930531i \(-0.619346\pi\)
−0.366213 + 0.930531i \(0.619346\pi\)
\(332\) −16.3424 −0.896907
\(333\) 19.9457 1.09302
\(334\) −18.8637 −1.03218
\(335\) −1.54267 −0.0842848
\(336\) −1.93277 −0.105441
\(337\) 19.3494 1.05403 0.527016 0.849856i \(-0.323311\pi\)
0.527016 + 0.849856i \(0.323311\pi\)
\(338\) −13.6890 −0.744582
\(339\) −1.73467 −0.0942146
\(340\) 2.24345 0.121668
\(341\) 8.22955 0.445655
\(342\) −3.93683 −0.212880
\(343\) −16.1887 −0.874107
\(344\) −11.0431 −0.595405
\(345\) 0.342128 0.0184195
\(346\) 4.89372 0.263088
\(347\) 12.7515 0.684535 0.342268 0.939602i \(-0.388805\pi\)
0.342268 + 0.939602i \(0.388805\pi\)
\(348\) 2.08826 0.111942
\(349\) 4.42521 0.236876 0.118438 0.992961i \(-0.462211\pi\)
0.118438 + 0.992961i \(0.462211\pi\)
\(350\) 13.7441 0.734655
\(351\) −19.1182 −1.02045
\(352\) −0.858892 −0.0457791
\(353\) −21.3505 −1.13637 −0.568185 0.822901i \(-0.692354\pi\)
−0.568185 + 0.822901i \(0.692354\pi\)
\(354\) 2.13830 0.113649
\(355\) 1.08412 0.0575393
\(356\) −10.3293 −0.547451
\(357\) −8.44100 −0.446745
\(358\) 6.04074 0.319263
\(359\) −6.08122 −0.320954 −0.160477 0.987040i \(-0.551303\pi\)
−0.160477 + 0.987040i \(0.551303\pi\)
\(360\) 1.31322 0.0692125
\(361\) −16.6285 −0.875182
\(362\) −10.2860 −0.540619
\(363\) 6.83486 0.358737
\(364\) −14.9920 −0.785797
\(365\) 6.56759 0.343763
\(366\) −4.21503 −0.220323
\(367\) −9.33388 −0.487225 −0.243612 0.969873i \(-0.578332\pi\)
−0.243612 + 0.969873i \(0.578332\pi\)
\(368\) −1.00000 −0.0521286
\(369\) −10.7143 −0.557767
\(370\) 4.00793 0.208362
\(371\) −17.5691 −0.912145
\(372\) −6.38149 −0.330865
\(373\) −1.57892 −0.0817533 −0.0408767 0.999164i \(-0.513015\pi\)
−0.0408767 + 0.999164i \(0.513015\pi\)
\(374\) −3.75105 −0.193962
\(375\) 3.33100 0.172012
\(376\) 1.61318 0.0831932
\(377\) 16.1982 0.834247
\(378\) −10.7393 −0.552369
\(379\) −20.0720 −1.03103 −0.515513 0.856882i \(-0.672399\pi\)
−0.515513 + 0.856882i \(0.672399\pi\)
\(380\) −0.791075 −0.0405813
\(381\) −5.96620 −0.305658
\(382\) −7.08976 −0.362743
\(383\) 1.58508 0.0809937 0.0404969 0.999180i \(-0.487106\pi\)
0.0404969 + 0.999180i \(0.487106\pi\)
\(384\) 0.666016 0.0339875
\(385\) 1.28037 0.0652539
\(386\) −0.399230 −0.0203203
\(387\) −28.2309 −1.43506
\(388\) −13.5647 −0.688646
\(389\) 21.8900 1.10987 0.554934 0.831895i \(-0.312744\pi\)
0.554934 + 0.831895i \(0.312744\pi\)
\(390\) −1.76748 −0.0894998
\(391\) −4.36731 −0.220864
\(392\) −1.42151 −0.0717970
\(393\) 0.666016 0.0335961
\(394\) −18.7880 −0.946524
\(395\) −1.43933 −0.0724207
\(396\) −2.19569 −0.110338
\(397\) −31.5986 −1.58589 −0.792944 0.609294i \(-0.791453\pi\)
−0.792944 + 0.609294i \(0.791453\pi\)
\(398\) 2.56488 0.128566
\(399\) 2.97642 0.149007
\(400\) −4.73612 −0.236806
\(401\) 38.0434 1.89980 0.949898 0.312561i \(-0.101187\pi\)
0.949898 + 0.312561i \(0.101187\pi\)
\(402\) −2.00011 −0.0997563
\(403\) −49.4998 −2.46576
\(404\) −12.3385 −0.613864
\(405\) 2.67354 0.132850
\(406\) 9.09902 0.451577
\(407\) −6.70124 −0.332168
\(408\) 2.90870 0.144002
\(409\) −9.93846 −0.491425 −0.245713 0.969343i \(-0.579022\pi\)
−0.245713 + 0.969343i \(0.579022\pi\)
\(410\) −2.15296 −0.106327
\(411\) 4.24401 0.209342
\(412\) 13.5956 0.669809
\(413\) 9.31705 0.458462
\(414\) −2.55642 −0.125641
\(415\) −8.39499 −0.412094
\(416\) 5.16614 0.253291
\(417\) 2.25407 0.110382
\(418\) 1.32268 0.0646942
\(419\) −7.55580 −0.369125 −0.184563 0.982821i \(-0.559087\pi\)
−0.184563 + 0.982821i \(0.559087\pi\)
\(420\) −0.992849 −0.0484461
\(421\) −8.23841 −0.401515 −0.200758 0.979641i \(-0.564340\pi\)
−0.200758 + 0.979641i \(0.564340\pi\)
\(422\) −11.1136 −0.540999
\(423\) 4.12396 0.200514
\(424\) 6.05418 0.294017
\(425\) −20.6841 −1.00333
\(426\) 1.40559 0.0681013
\(427\) −18.3658 −0.888785
\(428\) 2.09749 0.101386
\(429\) 2.95522 0.142679
\(430\) −5.67277 −0.273565
\(431\) 6.15658 0.296552 0.148276 0.988946i \(-0.452628\pi\)
0.148276 + 0.988946i \(0.452628\pi\)
\(432\) 3.70067 0.178048
\(433\) −32.2890 −1.55171 −0.775855 0.630912i \(-0.782681\pi\)
−0.775855 + 0.630912i \(0.782681\pi\)
\(434\) −27.8056 −1.33471
\(435\) 1.07272 0.0514331
\(436\) −3.35144 −0.160505
\(437\) 1.53998 0.0736672
\(438\) 8.51506 0.406865
\(439\) −20.6909 −0.987525 −0.493762 0.869597i \(-0.664379\pi\)
−0.493762 + 0.869597i \(0.664379\pi\)
\(440\) −0.441207 −0.0210337
\(441\) −3.63398 −0.173046
\(442\) 22.5621 1.07317
\(443\) −13.7282 −0.652246 −0.326123 0.945327i \(-0.605742\pi\)
−0.326123 + 0.945327i \(0.605742\pi\)
\(444\) 5.19638 0.246610
\(445\) −5.30608 −0.251532
\(446\) −4.48756 −0.212492
\(447\) 5.84147 0.276292
\(448\) 2.90198 0.137106
\(449\) −22.8131 −1.07662 −0.538309 0.842748i \(-0.680936\pi\)
−0.538309 + 0.842748i \(0.680936\pi\)
\(450\) −12.1075 −0.570754
\(451\) 3.59974 0.169505
\(452\) 2.60455 0.122508
\(453\) 5.59008 0.262645
\(454\) 8.01551 0.376186
\(455\) −7.70130 −0.361043
\(456\) −1.02565 −0.0480305
\(457\) −24.2316 −1.13351 −0.566753 0.823888i \(-0.691800\pi\)
−0.566753 + 0.823888i \(0.691800\pi\)
\(458\) 15.9785 0.746627
\(459\) 16.1620 0.754376
\(460\) −0.513693 −0.0239510
\(461\) −3.90091 −0.181683 −0.0908417 0.995865i \(-0.528956\pi\)
−0.0908417 + 0.995865i \(0.528956\pi\)
\(462\) 1.66004 0.0772320
\(463\) −0.835677 −0.0388372 −0.0194186 0.999811i \(-0.506182\pi\)
−0.0194186 + 0.999811i \(0.506182\pi\)
\(464\) −3.13545 −0.145559
\(465\) −3.27812 −0.152019
\(466\) 7.42163 0.343801
\(467\) −5.54999 −0.256823 −0.128411 0.991721i \(-0.540988\pi\)
−0.128411 + 0.991721i \(0.540988\pi\)
\(468\) 13.2068 0.610486
\(469\) −8.71492 −0.402418
\(470\) 0.828677 0.0382240
\(471\) 12.4212 0.572341
\(472\) −3.21058 −0.147779
\(473\) 9.48484 0.436114
\(474\) −1.86613 −0.0857144
\(475\) 7.29352 0.334650
\(476\) 12.6739 0.580905
\(477\) 15.4771 0.708646
\(478\) −7.94904 −0.363581
\(479\) −7.49287 −0.342358 −0.171179 0.985240i \(-0.554758\pi\)
−0.171179 + 0.985240i \(0.554758\pi\)
\(480\) 0.342128 0.0156159
\(481\) 40.3072 1.83785
\(482\) 18.9159 0.861594
\(483\) 1.93277 0.0879440
\(484\) −10.2623 −0.466468
\(485\) −6.96811 −0.316406
\(486\) 14.5683 0.660833
\(487\) −15.4115 −0.698361 −0.349181 0.937055i \(-0.613540\pi\)
−0.349181 + 0.937055i \(0.613540\pi\)
\(488\) 6.32871 0.286487
\(489\) 9.77685 0.442125
\(490\) −0.730218 −0.0329879
\(491\) −17.3428 −0.782670 −0.391335 0.920248i \(-0.627987\pi\)
−0.391335 + 0.920248i \(0.627987\pi\)
\(492\) −2.79137 −0.125845
\(493\) −13.6935 −0.616723
\(494\) −7.95574 −0.357946
\(495\) −1.12791 −0.0506958
\(496\) 9.58158 0.430226
\(497\) 6.12449 0.274721
\(498\) −10.8843 −0.487738
\(499\) −24.4498 −1.09452 −0.547262 0.836961i \(-0.684330\pi\)
−0.547262 + 0.836961i \(0.684330\pi\)
\(500\) −5.00137 −0.223668
\(501\) −12.5636 −0.561298
\(502\) −20.4684 −0.913548
\(503\) 20.8743 0.930740 0.465370 0.885116i \(-0.345921\pi\)
0.465370 + 0.885116i \(0.345921\pi\)
\(504\) 7.41870 0.330455
\(505\) −6.33821 −0.282047
\(506\) 0.858892 0.0381824
\(507\) −9.11708 −0.404904
\(508\) 8.95804 0.397449
\(509\) −41.7327 −1.84977 −0.924886 0.380245i \(-0.875840\pi\)
−0.924886 + 0.380245i \(0.875840\pi\)
\(510\) 1.49418 0.0661633
\(511\) 37.1020 1.64130
\(512\) −1.00000 −0.0441942
\(513\) −5.69895 −0.251615
\(514\) 17.0534 0.752195
\(515\) 6.98398 0.307751
\(516\) −7.35489 −0.323781
\(517\) −1.38555 −0.0609362
\(518\) 22.6418 0.994825
\(519\) 3.25929 0.143067
\(520\) 2.65381 0.116377
\(521\) −37.4460 −1.64054 −0.820269 0.571978i \(-0.806176\pi\)
−0.820269 + 0.571978i \(0.806176\pi\)
\(522\) −8.01553 −0.350830
\(523\) −28.7944 −1.25909 −0.629545 0.776964i \(-0.716759\pi\)
−0.629545 + 0.776964i \(0.716759\pi\)
\(524\) −1.00000 −0.0436852
\(525\) 9.15382 0.399506
\(526\) 12.6819 0.552955
\(527\) 41.8457 1.82283
\(528\) −0.572036 −0.0248947
\(529\) 1.00000 0.0434783
\(530\) 3.10999 0.135089
\(531\) −8.20760 −0.356179
\(532\) −4.46899 −0.193755
\(533\) −21.6521 −0.937854
\(534\) −6.87948 −0.297704
\(535\) 1.07747 0.0465830
\(536\) 3.00309 0.129714
\(537\) 4.02323 0.173615
\(538\) 3.85121 0.166037
\(539\) 1.22092 0.0525889
\(540\) 1.90101 0.0818063
\(541\) 22.8379 0.981879 0.490939 0.871194i \(-0.336654\pi\)
0.490939 + 0.871194i \(0.336654\pi\)
\(542\) 18.3602 0.788636
\(543\) −6.85062 −0.293988
\(544\) −4.36731 −0.187247
\(545\) −1.72161 −0.0737457
\(546\) −9.98495 −0.427316
\(547\) 9.08995 0.388658 0.194329 0.980936i \(-0.437747\pi\)
0.194329 + 0.980936i \(0.437747\pi\)
\(548\) −6.37224 −0.272209
\(549\) 16.1789 0.690497
\(550\) 4.06782 0.173452
\(551\) 4.82852 0.205702
\(552\) −0.666016 −0.0283475
\(553\) −8.13117 −0.345773
\(554\) 8.48390 0.360446
\(555\) 2.66934 0.113307
\(556\) −3.38441 −0.143531
\(557\) −28.5010 −1.20763 −0.603813 0.797126i \(-0.706353\pi\)
−0.603813 + 0.797126i \(0.706353\pi\)
\(558\) 24.4946 1.03694
\(559\) −57.0502 −2.41297
\(560\) 1.49073 0.0629947
\(561\) −2.49826 −0.105477
\(562\) −25.6835 −1.08339
\(563\) 4.56056 0.192205 0.0961024 0.995371i \(-0.469362\pi\)
0.0961024 + 0.995371i \(0.469362\pi\)
\(564\) 1.07440 0.0452405
\(565\) 1.33794 0.0562875
\(566\) 4.17828 0.175626
\(567\) 15.1036 0.634290
\(568\) −2.11045 −0.0885526
\(569\) −9.59342 −0.402177 −0.201088 0.979573i \(-0.564448\pi\)
−0.201088 + 0.979573i \(0.564448\pi\)
\(570\) −0.526869 −0.0220681
\(571\) −32.7726 −1.37149 −0.685745 0.727841i \(-0.740524\pi\)
−0.685745 + 0.727841i \(0.740524\pi\)
\(572\) −4.43716 −0.185527
\(573\) −4.72189 −0.197260
\(574\) −12.1626 −0.507659
\(575\) 4.73612 0.197510
\(576\) −2.55642 −0.106518
\(577\) −47.0143 −1.95723 −0.978616 0.205696i \(-0.934054\pi\)
−0.978616 + 0.205696i \(0.934054\pi\)
\(578\) −2.07339 −0.0862418
\(579\) −0.265894 −0.0110502
\(580\) −1.61066 −0.0668789
\(581\) −47.4255 −1.96754
\(582\) −9.03434 −0.374486
\(583\) −5.19989 −0.215358
\(584\) −12.7851 −0.529049
\(585\) 6.78425 0.280494
\(586\) −6.81701 −0.281608
\(587\) 43.3384 1.78877 0.894383 0.447302i \(-0.147615\pi\)
0.894383 + 0.447302i \(0.147615\pi\)
\(588\) −0.946748 −0.0390432
\(589\) −14.7554 −0.607987
\(590\) −1.64925 −0.0678986
\(591\) −12.5131 −0.514720
\(592\) −7.80219 −0.320668
\(593\) 18.7496 0.769955 0.384977 0.922926i \(-0.374209\pi\)
0.384977 + 0.922926i \(0.374209\pi\)
\(594\) −3.17847 −0.130414
\(595\) 6.51047 0.266903
\(596\) −8.77077 −0.359265
\(597\) 1.70825 0.0699142
\(598\) −5.16614 −0.211259
\(599\) 21.9935 0.898631 0.449315 0.893373i \(-0.351668\pi\)
0.449315 + 0.893373i \(0.351668\pi\)
\(600\) −3.15433 −0.128775
\(601\) 26.7252 1.09014 0.545071 0.838390i \(-0.316503\pi\)
0.545071 + 0.838390i \(0.316503\pi\)
\(602\) −32.0469 −1.30614
\(603\) 7.67717 0.312638
\(604\) −8.39331 −0.341519
\(605\) −5.27167 −0.214324
\(606\) −8.21766 −0.333820
\(607\) −28.6155 −1.16147 −0.580734 0.814093i \(-0.697235\pi\)
−0.580734 + 0.814093i \(0.697235\pi\)
\(608\) 1.53998 0.0624544
\(609\) 6.06009 0.245567
\(610\) 3.25101 0.131630
\(611\) 8.33389 0.337153
\(612\) −11.1647 −0.451306
\(613\) −6.18020 −0.249616 −0.124808 0.992181i \(-0.539831\pi\)
−0.124808 + 0.992181i \(0.539831\pi\)
\(614\) 3.01812 0.121801
\(615\) −1.43391 −0.0578207
\(616\) −2.49249 −0.100425
\(617\) 47.4025 1.90835 0.954176 0.299246i \(-0.0967350\pi\)
0.954176 + 0.299246i \(0.0967350\pi\)
\(618\) 9.05492 0.364242
\(619\) 5.78694 0.232597 0.116298 0.993214i \(-0.462897\pi\)
0.116298 + 0.993214i \(0.462897\pi\)
\(620\) 4.92199 0.197672
\(621\) −3.70067 −0.148503
\(622\) −18.3068 −0.734037
\(623\) −29.9754 −1.20094
\(624\) 3.44073 0.137740
\(625\) 21.1114 0.844457
\(626\) 14.1283 0.564681
\(627\) 0.880923 0.0351807
\(628\) −18.6501 −0.744219
\(629\) −34.0746 −1.35864
\(630\) 3.81093 0.151831
\(631\) −0.0535723 −0.00213268 −0.00106634 0.999999i \(-0.500339\pi\)
−0.00106634 + 0.999999i \(0.500339\pi\)
\(632\) 2.80194 0.111455
\(633\) −7.40181 −0.294195
\(634\) −23.2730 −0.924290
\(635\) 4.60168 0.182612
\(636\) 4.03219 0.159887
\(637\) −7.34371 −0.290968
\(638\) 2.69301 0.106617
\(639\) −5.39520 −0.213431
\(640\) −0.513693 −0.0203055
\(641\) −25.7287 −1.01622 −0.508112 0.861291i \(-0.669656\pi\)
−0.508112 + 0.861291i \(0.669656\pi\)
\(642\) 1.39696 0.0551338
\(643\) 21.7189 0.856510 0.428255 0.903658i \(-0.359128\pi\)
0.428255 + 0.903658i \(0.359128\pi\)
\(644\) −2.90198 −0.114354
\(645\) −3.77815 −0.148765
\(646\) 6.72556 0.264614
\(647\) 23.6323 0.929082 0.464541 0.885552i \(-0.346219\pi\)
0.464541 + 0.885552i \(0.346219\pi\)
\(648\) −5.20456 −0.204454
\(649\) 2.75754 0.108243
\(650\) −24.4674 −0.959692
\(651\) −18.5190 −0.725816
\(652\) −14.6796 −0.574898
\(653\) −42.1204 −1.64830 −0.824150 0.566372i \(-0.808347\pi\)
−0.824150 + 0.566372i \(0.808347\pi\)
\(654\) −2.23211 −0.0872826
\(655\) −0.513693 −0.0200716
\(656\) 4.19115 0.163637
\(657\) −32.6840 −1.27512
\(658\) 4.68141 0.182500
\(659\) −14.7719 −0.575433 −0.287717 0.957716i \(-0.592896\pi\)
−0.287717 + 0.957716i \(0.592896\pi\)
\(660\) −0.293851 −0.0114381
\(661\) 6.11864 0.237988 0.118994 0.992895i \(-0.462033\pi\)
0.118994 + 0.992895i \(0.462033\pi\)
\(662\) 13.3253 0.517904
\(663\) 15.0267 0.583590
\(664\) 16.3424 0.634209
\(665\) −2.29569 −0.0890230
\(666\) −19.9457 −0.772880
\(667\) 3.13545 0.121405
\(668\) 18.8637 0.729860
\(669\) −2.98878 −0.115553
\(670\) 1.54267 0.0595984
\(671\) −5.43568 −0.209842
\(672\) 1.93277 0.0745582
\(673\) 0.223478 0.00861445 0.00430722 0.999991i \(-0.498629\pi\)
0.00430722 + 0.999991i \(0.498629\pi\)
\(674\) −19.3494 −0.745313
\(675\) −17.5268 −0.674607
\(676\) 13.6890 0.526499
\(677\) −5.64093 −0.216799 −0.108399 0.994107i \(-0.534573\pi\)
−0.108399 + 0.994107i \(0.534573\pi\)
\(678\) 1.73467 0.0666198
\(679\) −39.3647 −1.51068
\(680\) −2.24345 −0.0860326
\(681\) 5.33846 0.204570
\(682\) −8.22955 −0.315126
\(683\) 31.1038 1.19015 0.595077 0.803669i \(-0.297122\pi\)
0.595077 + 0.803669i \(0.297122\pi\)
\(684\) 3.93683 0.150529
\(685\) −3.27337 −0.125069
\(686\) 16.1887 0.618087
\(687\) 10.6420 0.406016
\(688\) 11.0431 0.421015
\(689\) 31.2768 1.19155
\(690\) −0.342128 −0.0130246
\(691\) 15.1637 0.576855 0.288427 0.957502i \(-0.406868\pi\)
0.288427 + 0.957502i \(0.406868\pi\)
\(692\) −4.89372 −0.186031
\(693\) −6.37186 −0.242047
\(694\) −12.7515 −0.484040
\(695\) −1.73855 −0.0659468
\(696\) −2.08826 −0.0791553
\(697\) 18.3040 0.693315
\(698\) −4.42521 −0.167497
\(699\) 4.94293 0.186959
\(700\) −13.7441 −0.519480
\(701\) 22.8260 0.862126 0.431063 0.902322i \(-0.358139\pi\)
0.431063 + 0.902322i \(0.358139\pi\)
\(702\) 19.1182 0.721568
\(703\) 12.0152 0.453162
\(704\) 0.858892 0.0323707
\(705\) 0.551912 0.0207862
\(706\) 21.3505 0.803535
\(707\) −35.8062 −1.34663
\(708\) −2.13830 −0.0803622
\(709\) 27.0077 1.01430 0.507149 0.861859i \(-0.330700\pi\)
0.507149 + 0.861859i \(0.330700\pi\)
\(710\) −1.08412 −0.0406864
\(711\) 7.16293 0.268631
\(712\) 10.3293 0.387107
\(713\) −9.58158 −0.358833
\(714\) 8.44100 0.315896
\(715\) −2.27933 −0.0852423
\(716\) −6.04074 −0.225753
\(717\) −5.29419 −0.197715
\(718\) 6.08122 0.226949
\(719\) 30.9376 1.15378 0.576888 0.816823i \(-0.304267\pi\)
0.576888 + 0.816823i \(0.304267\pi\)
\(720\) −1.31322 −0.0489406
\(721\) 39.4543 1.46936
\(722\) 16.6285 0.618847
\(723\) 12.5983 0.468535
\(724\) 10.2860 0.382275
\(725\) 14.8499 0.551510
\(726\) −6.83486 −0.253666
\(727\) −19.7288 −0.731700 −0.365850 0.930674i \(-0.619222\pi\)
−0.365850 + 0.930674i \(0.619222\pi\)
\(728\) 14.9920 0.555642
\(729\) −5.91094 −0.218924
\(730\) −6.56759 −0.243077
\(731\) 48.2287 1.78380
\(732\) 4.21503 0.155792
\(733\) 13.5687 0.501172 0.250586 0.968094i \(-0.419377\pi\)
0.250586 + 0.968094i \(0.419377\pi\)
\(734\) 9.33388 0.344520
\(735\) −0.486337 −0.0179388
\(736\) 1.00000 0.0368605
\(737\) −2.57933 −0.0950109
\(738\) 10.7143 0.394401
\(739\) −7.09977 −0.261169 −0.130585 0.991437i \(-0.541685\pi\)
−0.130585 + 0.991437i \(0.541685\pi\)
\(740\) −4.00793 −0.147334
\(741\) −5.29865 −0.194651
\(742\) 17.5691 0.644984
\(743\) −11.4226 −0.419056 −0.209528 0.977803i \(-0.567193\pi\)
−0.209528 + 0.977803i \(0.567193\pi\)
\(744\) 6.38149 0.233957
\(745\) −4.50548 −0.165068
\(746\) 1.57892 0.0578083
\(747\) 41.7782 1.52858
\(748\) 3.75105 0.137152
\(749\) 6.08689 0.222410
\(750\) −3.33100 −0.121631
\(751\) −6.92083 −0.252545 −0.126272 0.991996i \(-0.540301\pi\)
−0.126272 + 0.991996i \(0.540301\pi\)
\(752\) −1.61318 −0.0588265
\(753\) −13.6323 −0.496787
\(754\) −16.1982 −0.589902
\(755\) −4.31158 −0.156915
\(756\) 10.7393 0.390584
\(757\) −17.5699 −0.638589 −0.319295 0.947656i \(-0.603446\pi\)
−0.319295 + 0.947656i \(0.603446\pi\)
\(758\) 20.0720 0.729046
\(759\) 0.572036 0.0207636
\(760\) 0.791075 0.0286953
\(761\) 16.0153 0.580553 0.290276 0.956943i \(-0.406253\pi\)
0.290276 + 0.956943i \(0.406253\pi\)
\(762\) 5.96620 0.216133
\(763\) −9.72583 −0.352099
\(764\) 7.08976 0.256498
\(765\) −5.73522 −0.207357
\(766\) −1.58508 −0.0572712
\(767\) −16.5863 −0.598897
\(768\) −0.666016 −0.0240328
\(769\) −38.5446 −1.38996 −0.694978 0.719031i \(-0.744586\pi\)
−0.694978 + 0.719031i \(0.744586\pi\)
\(770\) −1.28037 −0.0461415
\(771\) 11.3579 0.409044
\(772\) 0.399230 0.0143686
\(773\) −1.30869 −0.0470705 −0.0235352 0.999723i \(-0.507492\pi\)
−0.0235352 + 0.999723i \(0.507492\pi\)
\(774\) 28.2309 1.01474
\(775\) −45.3795 −1.63008
\(776\) 13.5647 0.486946
\(777\) 15.0798 0.540986
\(778\) −21.8900 −0.784795
\(779\) −6.45428 −0.231249
\(780\) 1.76748 0.0632859
\(781\) 1.81265 0.0648617
\(782\) 4.36731 0.156175
\(783\) −11.6032 −0.414666
\(784\) 1.42151 0.0507682
\(785\) −9.58040 −0.341939
\(786\) −0.666016 −0.0237560
\(787\) −30.3100 −1.08043 −0.540217 0.841526i \(-0.681658\pi\)
−0.540217 + 0.841526i \(0.681658\pi\)
\(788\) 18.7880 0.669294
\(789\) 8.44632 0.300697
\(790\) 1.43933 0.0512092
\(791\) 7.55837 0.268745
\(792\) 2.19569 0.0780205
\(793\) 32.6950 1.16103
\(794\) 31.5986 1.12139
\(795\) 2.07130 0.0734616
\(796\) −2.56488 −0.0909099
\(797\) 19.3895 0.686811 0.343405 0.939187i \(-0.388420\pi\)
0.343405 + 0.939187i \(0.388420\pi\)
\(798\) −2.97642 −0.105364
\(799\) −7.04524 −0.249243
\(800\) 4.73612 0.167447
\(801\) 26.4060 0.933011
\(802\) −38.0434 −1.34336
\(803\) 10.9810 0.387511
\(804\) 2.00011 0.0705383
\(805\) −1.49073 −0.0525412
\(806\) 49.4998 1.74355
\(807\) 2.56497 0.0902911
\(808\) 12.3385 0.434068
\(809\) 29.7412 1.04564 0.522822 0.852442i \(-0.324879\pi\)
0.522822 + 0.852442i \(0.324879\pi\)
\(810\) −2.67354 −0.0939388
\(811\) −19.6730 −0.690812 −0.345406 0.938453i \(-0.612259\pi\)
−0.345406 + 0.938453i \(0.612259\pi\)
\(812\) −9.09902 −0.319313
\(813\) 12.2282 0.428861
\(814\) 6.70124 0.234878
\(815\) −7.54080 −0.264143
\(816\) −2.90870 −0.101825
\(817\) −17.0062 −0.594970
\(818\) 9.93846 0.347490
\(819\) 38.3260 1.33922
\(820\) 2.15296 0.0751847
\(821\) −33.2545 −1.16059 −0.580295 0.814407i \(-0.697063\pi\)
−0.580295 + 0.814407i \(0.697063\pi\)
\(822\) −4.24401 −0.148027
\(823\) −12.4927 −0.435468 −0.217734 0.976008i \(-0.569867\pi\)
−0.217734 + 0.976008i \(0.569867\pi\)
\(824\) −13.5956 −0.473627
\(825\) 2.70923 0.0943234
\(826\) −9.31705 −0.324182
\(827\) 18.5792 0.646063 0.323031 0.946388i \(-0.395298\pi\)
0.323031 + 0.946388i \(0.395298\pi\)
\(828\) 2.55642 0.0888418
\(829\) −13.2394 −0.459823 −0.229912 0.973211i \(-0.573844\pi\)
−0.229912 + 0.973211i \(0.573844\pi\)
\(830\) 8.39499 0.291394
\(831\) 5.65042 0.196011
\(832\) −5.16614 −0.179104
\(833\) 6.20817 0.215100
\(834\) −2.25407 −0.0780521
\(835\) 9.69016 0.335342
\(836\) −1.32268 −0.0457457
\(837\) 35.4583 1.22562
\(838\) 7.55580 0.261011
\(839\) −36.1690 −1.24869 −0.624346 0.781148i \(-0.714635\pi\)
−0.624346 + 0.781148i \(0.714635\pi\)
\(840\) 0.992849 0.0342565
\(841\) −19.1690 −0.660999
\(842\) 8.23841 0.283914
\(843\) −17.1056 −0.589149
\(844\) 11.1136 0.382544
\(845\) 7.03193 0.241906
\(846\) −4.12396 −0.141785
\(847\) −29.7810 −1.02329
\(848\) −6.05418 −0.207902
\(849\) 2.78280 0.0955055
\(850\) 20.6841 0.709459
\(851\) 7.80219 0.267456
\(852\) −1.40559 −0.0481549
\(853\) −14.0142 −0.479837 −0.239919 0.970793i \(-0.577121\pi\)
−0.239919 + 0.970793i \(0.577121\pi\)
\(854\) 18.3658 0.628466
\(855\) 2.02232 0.0691620
\(856\) −2.09749 −0.0716908
\(857\) 45.7166 1.56165 0.780824 0.624751i \(-0.214800\pi\)
0.780824 + 0.624751i \(0.214800\pi\)
\(858\) −2.95522 −0.100889
\(859\) −12.3005 −0.419689 −0.209845 0.977735i \(-0.567296\pi\)
−0.209845 + 0.977735i \(0.567296\pi\)
\(860\) 5.67277 0.193440
\(861\) −8.10052 −0.276065
\(862\) −6.15658 −0.209694
\(863\) −10.6679 −0.363140 −0.181570 0.983378i \(-0.558118\pi\)
−0.181570 + 0.983378i \(0.558118\pi\)
\(864\) −3.70067 −0.125899
\(865\) −2.51387 −0.0854740
\(866\) 32.2890 1.09722
\(867\) −1.38091 −0.0468983
\(868\) 27.8056 0.943783
\(869\) −2.40656 −0.0816370
\(870\) −1.07272 −0.0363687
\(871\) 15.5144 0.525685
\(872\) 3.35144 0.113494
\(873\) 34.6772 1.17365
\(874\) −1.53998 −0.0520905
\(875\) −14.5139 −0.490659
\(876\) −8.51506 −0.287697
\(877\) 29.8997 1.00964 0.504821 0.863224i \(-0.331558\pi\)
0.504821 + 0.863224i \(0.331558\pi\)
\(878\) 20.6909 0.698286
\(879\) −4.54024 −0.153138
\(880\) 0.441207 0.0148731
\(881\) −18.0201 −0.607112 −0.303556 0.952814i \(-0.598174\pi\)
−0.303556 + 0.952814i \(0.598174\pi\)
\(882\) 3.63398 0.122362
\(883\) −9.96290 −0.335278 −0.167639 0.985848i \(-0.553614\pi\)
−0.167639 + 0.985848i \(0.553614\pi\)
\(884\) −22.5621 −0.758846
\(885\) −1.09843 −0.0369233
\(886\) 13.7282 0.461208
\(887\) 14.7481 0.495193 0.247596 0.968863i \(-0.420359\pi\)
0.247596 + 0.968863i \(0.420359\pi\)
\(888\) −5.19638 −0.174379
\(889\) 25.9961 0.871881
\(890\) 5.30608 0.177860
\(891\) 4.47016 0.149756
\(892\) 4.48756 0.150254
\(893\) 2.48426 0.0831325
\(894\) −5.84147 −0.195368
\(895\) −3.10308 −0.103725
\(896\) −2.90198 −0.0969485
\(897\) −3.44073 −0.114883
\(898\) 22.8131 0.761283
\(899\) −30.0425 −1.00197
\(900\) 12.1075 0.403584
\(901\) −26.4405 −0.880861
\(902\) −3.59974 −0.119858
\(903\) −21.3438 −0.710276
\(904\) −2.60455 −0.0866262
\(905\) 5.28383 0.175640
\(906\) −5.59008 −0.185718
\(907\) 25.8084 0.856953 0.428477 0.903553i \(-0.359050\pi\)
0.428477 + 0.903553i \(0.359050\pi\)
\(908\) −8.01551 −0.266004
\(909\) 31.5425 1.04620
\(910\) 7.70130 0.255296
\(911\) 54.2863 1.79859 0.899293 0.437347i \(-0.144082\pi\)
0.899293 + 0.437347i \(0.144082\pi\)
\(912\) 1.02565 0.0339627
\(913\) −14.0364 −0.464537
\(914\) 24.2316 0.801509
\(915\) 2.16523 0.0715802
\(916\) −15.9785 −0.527945
\(917\) −2.90198 −0.0958319
\(918\) −16.1620 −0.533424
\(919\) 41.7515 1.37726 0.688628 0.725115i \(-0.258213\pi\)
0.688628 + 0.725115i \(0.258213\pi\)
\(920\) 0.513693 0.0169359
\(921\) 2.01012 0.0662356
\(922\) 3.90091 0.128470
\(923\) −10.9029 −0.358873
\(924\) −1.66004 −0.0546113
\(925\) 36.9521 1.21498
\(926\) 0.835677 0.0274621
\(927\) −34.7562 −1.14154
\(928\) 3.13545 0.102926
\(929\) −16.8914 −0.554190 −0.277095 0.960843i \(-0.589372\pi\)
−0.277095 + 0.960843i \(0.589372\pi\)
\(930\) 3.27812 0.107494
\(931\) −2.18909 −0.0717446
\(932\) −7.42163 −0.243104
\(933\) −12.1927 −0.399170
\(934\) 5.54999 0.181601
\(935\) 1.92689 0.0630159
\(936\) −13.2068 −0.431679
\(937\) 44.7518 1.46198 0.730989 0.682389i \(-0.239059\pi\)
0.730989 + 0.682389i \(0.239059\pi\)
\(938\) 8.71492 0.284552
\(939\) 9.40968 0.307073
\(940\) −0.828677 −0.0270285
\(941\) 57.9392 1.88876 0.944382 0.328850i \(-0.106661\pi\)
0.944382 + 0.328850i \(0.106661\pi\)
\(942\) −12.4212 −0.404706
\(943\) −4.19115 −0.136483
\(944\) 3.21058 0.104495
\(945\) 5.51669 0.179458
\(946\) −9.48484 −0.308379
\(947\) −4.25048 −0.138122 −0.0690610 0.997612i \(-0.522000\pi\)
−0.0690610 + 0.997612i \(0.522000\pi\)
\(948\) 1.86613 0.0606092
\(949\) −66.0494 −2.14405
\(950\) −7.29352 −0.236633
\(951\) −15.5002 −0.502629
\(952\) −12.6739 −0.410762
\(953\) −1.61863 −0.0524327 −0.0262163 0.999656i \(-0.508346\pi\)
−0.0262163 + 0.999656i \(0.508346\pi\)
\(954\) −15.4771 −0.501088
\(955\) 3.64196 0.117851
\(956\) 7.94904 0.257090
\(957\) 1.79359 0.0579785
\(958\) 7.49287 0.242084
\(959\) −18.4921 −0.597142
\(960\) −0.342128 −0.0110421
\(961\) 60.8067 1.96151
\(962\) −40.3072 −1.29956
\(963\) −5.36208 −0.172791
\(964\) −18.9159 −0.609239
\(965\) 0.205082 0.00660181
\(966\) −1.93277 −0.0621858
\(967\) −37.7757 −1.21478 −0.607392 0.794402i \(-0.707784\pi\)
−0.607392 + 0.794402i \(0.707784\pi\)
\(968\) 10.2623 0.329843
\(969\) 4.47933 0.143897
\(970\) 6.96811 0.223733
\(971\) −34.3508 −1.10237 −0.551185 0.834383i \(-0.685824\pi\)
−0.551185 + 0.834383i \(0.685824\pi\)
\(972\) −14.5683 −0.467279
\(973\) −9.82150 −0.314863
\(974\) 15.4115 0.493816
\(975\) −16.2957 −0.521881
\(976\) −6.32871 −0.202577
\(977\) 4.60066 0.147188 0.0735941 0.997288i \(-0.476553\pi\)
0.0735941 + 0.997288i \(0.476553\pi\)
\(978\) −9.77685 −0.312629
\(979\) −8.87175 −0.283542
\(980\) 0.730218 0.0233260
\(981\) 8.56770 0.273546
\(982\) 17.3428 0.553431
\(983\) 35.4909 1.13198 0.565991 0.824411i \(-0.308494\pi\)
0.565991 + 0.824411i \(0.308494\pi\)
\(984\) 2.79137 0.0889857
\(985\) 9.65124 0.307514
\(986\) 13.6935 0.436089
\(987\) 3.11790 0.0992438
\(988\) 7.95574 0.253106
\(989\) −11.0431 −0.351151
\(990\) 1.12791 0.0358473
\(991\) −1.36860 −0.0434749 −0.0217375 0.999764i \(-0.506920\pi\)
−0.0217375 + 0.999764i \(0.506920\pi\)
\(992\) −9.58158 −0.304216
\(993\) 8.87489 0.281636
\(994\) −6.12449 −0.194257
\(995\) −1.31756 −0.0417695
\(996\) 10.8843 0.344883
\(997\) 3.55884 0.112710 0.0563548 0.998411i \(-0.482052\pi\)
0.0563548 + 0.998411i \(0.482052\pi\)
\(998\) 24.4498 0.773945
\(999\) −28.8733 −0.913511
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 \(a_p\))