Properties

Label 4017.2.a.j.1.16
Level 4017
Weight 2
Character 4017.1
Self dual Yes
Analytic conductor 32.076
Analytic rank 0
Dimension 25
CM No

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Newspace parameters

Level: \( N \) = \( 4017 = 3 \cdot 13 \cdot 103 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4017.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0759064919\)
Analytic rank: \(0\)
Dimension: \(25\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Character \(\chi\) = 4017.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.30548 q^{2} -1.00000 q^{3} -0.295718 q^{4} +2.71388 q^{5} -1.30548 q^{6} +2.93494 q^{7} -2.99702 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.30548 q^{2} -1.00000 q^{3} -0.295718 q^{4} +2.71388 q^{5} -1.30548 q^{6} +2.93494 q^{7} -2.99702 q^{8} +1.00000 q^{9} +3.54292 q^{10} +4.39855 q^{11} +0.295718 q^{12} +1.00000 q^{13} +3.83151 q^{14} -2.71388 q^{15} -3.32111 q^{16} +7.00308 q^{17} +1.30548 q^{18} +2.39267 q^{19} -0.802544 q^{20} -2.93494 q^{21} +5.74223 q^{22} -3.41270 q^{23} +2.99702 q^{24} +2.36516 q^{25} +1.30548 q^{26} -1.00000 q^{27} -0.867916 q^{28} +4.65913 q^{29} -3.54292 q^{30} -2.86740 q^{31} +1.65838 q^{32} -4.39855 q^{33} +9.14239 q^{34} +7.96509 q^{35} -0.295718 q^{36} +4.87509 q^{37} +3.12358 q^{38} -1.00000 q^{39} -8.13355 q^{40} -9.26951 q^{41} -3.83151 q^{42} -0.300510 q^{43} -1.30073 q^{44} +2.71388 q^{45} -4.45522 q^{46} -6.75031 q^{47} +3.32111 q^{48} +1.61389 q^{49} +3.08767 q^{50} -7.00308 q^{51} -0.295718 q^{52} -9.66362 q^{53} -1.30548 q^{54} +11.9372 q^{55} -8.79608 q^{56} -2.39267 q^{57} +6.08240 q^{58} +0.569872 q^{59} +0.802544 q^{60} -5.37556 q^{61} -3.74333 q^{62} +2.93494 q^{63} +8.80722 q^{64} +2.71388 q^{65} -5.74223 q^{66} +10.6429 q^{67} -2.07094 q^{68} +3.41270 q^{69} +10.3983 q^{70} +5.14090 q^{71} -2.99702 q^{72} -9.70296 q^{73} +6.36434 q^{74} -2.36516 q^{75} -0.707555 q^{76} +12.9095 q^{77} -1.30548 q^{78} +11.5440 q^{79} -9.01311 q^{80} +1.00000 q^{81} -12.1012 q^{82} +6.57810 q^{83} +0.867916 q^{84} +19.0055 q^{85} -0.392310 q^{86} -4.65913 q^{87} -13.1825 q^{88} +10.8369 q^{89} +3.54292 q^{90} +2.93494 q^{91} +1.00920 q^{92} +2.86740 q^{93} -8.81241 q^{94} +6.49342 q^{95} -1.65838 q^{96} +1.43594 q^{97} +2.10691 q^{98} +4.39855 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 25q + 6q^{2} - 25q^{3} + 28q^{4} + 7q^{5} - 6q^{6} + 17q^{7} + 21q^{8} + 25q^{9} + O(q^{10}) \) \( 25q + 6q^{2} - 25q^{3} + 28q^{4} + 7q^{5} - 6q^{6} + 17q^{7} + 21q^{8} + 25q^{9} - 6q^{10} + 21q^{11} - 28q^{12} + 25q^{13} + 10q^{14} - 7q^{15} + 30q^{16} + 14q^{17} + 6q^{18} + 12q^{19} + 24q^{20} - 17q^{21} + 3q^{22} + 41q^{23} - 21q^{24} + 30q^{25} + 6q^{26} - 25q^{27} + 14q^{28} + 22q^{29} + 6q^{30} + 14q^{31} + 28q^{32} - 21q^{33} - 11q^{34} + 14q^{35} + 28q^{36} - 6q^{37} + 16q^{38} - 25q^{39} - 34q^{40} + 33q^{41} - 10q^{42} + 35q^{43} + 45q^{44} + 7q^{45} + 3q^{46} + 48q^{47} - 30q^{48} - 4q^{49} + 7q^{50} - 14q^{51} + 28q^{52} + 18q^{53} - 6q^{54} + 10q^{55} + 32q^{56} - 12q^{57} + 33q^{58} + 46q^{59} - 24q^{60} - 19q^{61} + 5q^{62} + 17q^{63} + 29q^{64} + 7q^{65} - 3q^{66} + 16q^{67} + 20q^{68} - 41q^{69} - 43q^{70} + 60q^{71} + 21q^{72} - 14q^{73} - 50q^{74} - 30q^{75} + 59q^{77} - 6q^{78} + 7q^{79} + 32q^{80} + 25q^{81} + 18q^{82} + 23q^{83} - 14q^{84} - 9q^{85} - 9q^{86} - 22q^{87} + 23q^{88} + 10q^{89} - 6q^{90} + 17q^{91} + 69q^{92} - 14q^{93} - 30q^{94} + 81q^{95} - 28q^{96} - 10q^{97} + 55q^{98} + 21q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.30548 0.923115 0.461557 0.887110i \(-0.347291\pi\)
0.461557 + 0.887110i \(0.347291\pi\)
\(3\) −1.00000 −0.577350
\(4\) −0.295718 −0.147859
\(5\) 2.71388 1.21369 0.606843 0.794822i \(-0.292436\pi\)
0.606843 + 0.794822i \(0.292436\pi\)
\(6\) −1.30548 −0.532961
\(7\) 2.93494 1.10930 0.554652 0.832082i \(-0.312851\pi\)
0.554652 + 0.832082i \(0.312851\pi\)
\(8\) −2.99702 −1.05961
\(9\) 1.00000 0.333333
\(10\) 3.54292 1.12037
\(11\) 4.39855 1.32621 0.663107 0.748525i \(-0.269237\pi\)
0.663107 + 0.748525i \(0.269237\pi\)
\(12\) 0.295718 0.0853665
\(13\) 1.00000 0.277350
\(14\) 3.83151 1.02402
\(15\) −2.71388 −0.700721
\(16\) −3.32111 −0.830279
\(17\) 7.00308 1.69850 0.849248 0.527994i \(-0.177056\pi\)
0.849248 + 0.527994i \(0.177056\pi\)
\(18\) 1.30548 0.307705
\(19\) 2.39267 0.548916 0.274458 0.961599i \(-0.411502\pi\)
0.274458 + 0.961599i \(0.411502\pi\)
\(20\) −0.802544 −0.179454
\(21\) −2.93494 −0.640457
\(22\) 5.74223 1.22425
\(23\) −3.41270 −0.711598 −0.355799 0.934562i \(-0.615791\pi\)
−0.355799 + 0.934562i \(0.615791\pi\)
\(24\) 2.99702 0.611764
\(25\) 2.36516 0.473031
\(26\) 1.30548 0.256026
\(27\) −1.00000 −0.192450
\(28\) −0.867916 −0.164021
\(29\) 4.65913 0.865178 0.432589 0.901591i \(-0.357600\pi\)
0.432589 + 0.901591i \(0.357600\pi\)
\(30\) −3.54292 −0.646846
\(31\) −2.86740 −0.515000 −0.257500 0.966278i \(-0.582899\pi\)
−0.257500 + 0.966278i \(0.582899\pi\)
\(32\) 1.65838 0.293163
\(33\) −4.39855 −0.765690
\(34\) 9.14239 1.56791
\(35\) 7.96509 1.34635
\(36\) −0.295718 −0.0492864
\(37\) 4.87509 0.801460 0.400730 0.916196i \(-0.368757\pi\)
0.400730 + 0.916196i \(0.368757\pi\)
\(38\) 3.12358 0.506712
\(39\) −1.00000 −0.160128
\(40\) −8.13355 −1.28603
\(41\) −9.26951 −1.44765 −0.723827 0.689981i \(-0.757619\pi\)
−0.723827 + 0.689981i \(0.757619\pi\)
\(42\) −3.83151 −0.591216
\(43\) −0.300510 −0.0458273 −0.0229136 0.999737i \(-0.507294\pi\)
−0.0229136 + 0.999737i \(0.507294\pi\)
\(44\) −1.30073 −0.196093
\(45\) 2.71388 0.404562
\(46\) −4.45522 −0.656887
\(47\) −6.75031 −0.984634 −0.492317 0.870416i \(-0.663850\pi\)
−0.492317 + 0.870416i \(0.663850\pi\)
\(48\) 3.32111 0.479362
\(49\) 1.61389 0.230556
\(50\) 3.08767 0.436662
\(51\) −7.00308 −0.980627
\(52\) −0.295718 −0.0410087
\(53\) −9.66362 −1.32740 −0.663700 0.747999i \(-0.731015\pi\)
−0.663700 + 0.747999i \(0.731015\pi\)
\(54\) −1.30548 −0.177654
\(55\) 11.9372 1.60961
\(56\) −8.79608 −1.17543
\(57\) −2.39267 −0.316917
\(58\) 6.08240 0.798659
\(59\) 0.569872 0.0741911 0.0370955 0.999312i \(-0.488189\pi\)
0.0370955 + 0.999312i \(0.488189\pi\)
\(60\) 0.802544 0.103608
\(61\) −5.37556 −0.688270 −0.344135 0.938920i \(-0.611828\pi\)
−0.344135 + 0.938920i \(0.611828\pi\)
\(62\) −3.74333 −0.475404
\(63\) 2.93494 0.369768
\(64\) 8.80722 1.10090
\(65\) 2.71388 0.336616
\(66\) −5.74223 −0.706820
\(67\) 10.6429 1.30023 0.650117 0.759834i \(-0.274720\pi\)
0.650117 + 0.759834i \(0.274720\pi\)
\(68\) −2.07094 −0.251138
\(69\) 3.41270 0.410841
\(70\) 10.3983 1.24283
\(71\) 5.14090 0.610113 0.305056 0.952334i \(-0.401325\pi\)
0.305056 + 0.952334i \(0.401325\pi\)
\(72\) −2.99702 −0.353202
\(73\) −9.70296 −1.13565 −0.567823 0.823151i \(-0.692214\pi\)
−0.567823 + 0.823151i \(0.692214\pi\)
\(74\) 6.36434 0.739839
\(75\) −2.36516 −0.273105
\(76\) −0.707555 −0.0811622
\(77\) 12.9095 1.47117
\(78\) −1.30548 −0.147817
\(79\) 11.5440 1.29880 0.649398 0.760449i \(-0.275021\pi\)
0.649398 + 0.760449i \(0.275021\pi\)
\(80\) −9.01311 −1.00770
\(81\) 1.00000 0.111111
\(82\) −12.1012 −1.33635
\(83\) 6.57810 0.722041 0.361020 0.932558i \(-0.382429\pi\)
0.361020 + 0.932558i \(0.382429\pi\)
\(84\) 0.867916 0.0946974
\(85\) 19.0055 2.06144
\(86\) −0.392310 −0.0423038
\(87\) −4.65913 −0.499511
\(88\) −13.1825 −1.40526
\(89\) 10.8369 1.14871 0.574355 0.818606i \(-0.305253\pi\)
0.574355 + 0.818606i \(0.305253\pi\)
\(90\) 3.54292 0.373457
\(91\) 2.93494 0.307666
\(92\) 1.00920 0.105216
\(93\) 2.86740 0.297335
\(94\) −8.81241 −0.908931
\(95\) 6.49342 0.666211
\(96\) −1.65838 −0.169258
\(97\) 1.43594 0.145798 0.0728988 0.997339i \(-0.476775\pi\)
0.0728988 + 0.997339i \(0.476775\pi\)
\(98\) 2.10691 0.212830
\(99\) 4.39855 0.442071
\(100\) −0.699420 −0.0699420
\(101\) −1.63848 −0.163035 −0.0815175 0.996672i \(-0.525977\pi\)
−0.0815175 + 0.996672i \(0.525977\pi\)
\(102\) −9.14239 −0.905232
\(103\) −1.00000 −0.0985329
\(104\) −2.99702 −0.293882
\(105\) −7.96509 −0.777313
\(106\) −12.6157 −1.22534
\(107\) 8.71561 0.842570 0.421285 0.906928i \(-0.361579\pi\)
0.421285 + 0.906928i \(0.361579\pi\)
\(108\) 0.295718 0.0284555
\(109\) −2.63094 −0.251998 −0.125999 0.992030i \(-0.540214\pi\)
−0.125999 + 0.992030i \(0.540214\pi\)
\(110\) 15.5837 1.48585
\(111\) −4.87509 −0.462723
\(112\) −9.74728 −0.921032
\(113\) 3.01548 0.283673 0.141836 0.989890i \(-0.454699\pi\)
0.141836 + 0.989890i \(0.454699\pi\)
\(114\) −3.12358 −0.292550
\(115\) −9.26168 −0.863656
\(116\) −1.37779 −0.127924
\(117\) 1.00000 0.0924500
\(118\) 0.743958 0.0684869
\(119\) 20.5536 1.88415
\(120\) 8.13355 0.742488
\(121\) 8.34727 0.758843
\(122\) −7.01770 −0.635352
\(123\) 9.26951 0.835803
\(124\) 0.847941 0.0761474
\(125\) −7.15065 −0.639574
\(126\) 3.83151 0.341338
\(127\) −14.7603 −1.30977 −0.654883 0.755730i \(-0.727282\pi\)
−0.654883 + 0.755730i \(0.727282\pi\)
\(128\) 8.18089 0.723096
\(129\) 0.300510 0.0264584
\(130\) 3.54292 0.310735
\(131\) −6.60429 −0.577019 −0.288510 0.957477i \(-0.593160\pi\)
−0.288510 + 0.957477i \(0.593160\pi\)
\(132\) 1.30073 0.113214
\(133\) 7.02235 0.608915
\(134\) 13.8941 1.20026
\(135\) −2.71388 −0.233574
\(136\) −20.9884 −1.79974
\(137\) −10.9548 −0.935931 −0.467965 0.883747i \(-0.655013\pi\)
−0.467965 + 0.883747i \(0.655013\pi\)
\(138\) 4.45522 0.379254
\(139\) −11.5276 −0.977755 −0.488878 0.872352i \(-0.662594\pi\)
−0.488878 + 0.872352i \(0.662594\pi\)
\(140\) −2.35542 −0.199069
\(141\) 6.75031 0.568479
\(142\) 6.71135 0.563204
\(143\) 4.39855 0.367825
\(144\) −3.32111 −0.276760
\(145\) 12.6443 1.05005
\(146\) −12.6670 −1.04833
\(147\) −1.61389 −0.133112
\(148\) −1.44165 −0.118503
\(149\) −9.95077 −0.815199 −0.407600 0.913161i \(-0.633634\pi\)
−0.407600 + 0.913161i \(0.633634\pi\)
\(150\) −3.08767 −0.252107
\(151\) 6.14232 0.499855 0.249928 0.968265i \(-0.419593\pi\)
0.249928 + 0.968265i \(0.419593\pi\)
\(152\) −7.17087 −0.581634
\(153\) 7.00308 0.566166
\(154\) 16.8531 1.35806
\(155\) −7.78178 −0.625047
\(156\) 0.295718 0.0236764
\(157\) 5.17014 0.412622 0.206311 0.978486i \(-0.433854\pi\)
0.206311 + 0.978486i \(0.433854\pi\)
\(158\) 15.0704 1.19894
\(159\) 9.66362 0.766375
\(160\) 4.50065 0.355808
\(161\) −10.0161 −0.789379
\(162\) 1.30548 0.102568
\(163\) 22.6872 1.77700 0.888501 0.458876i \(-0.151748\pi\)
0.888501 + 0.458876i \(0.151748\pi\)
\(164\) 2.74116 0.214049
\(165\) −11.9372 −0.929306
\(166\) 8.58759 0.666526
\(167\) −0.389107 −0.0301100 −0.0150550 0.999887i \(-0.504792\pi\)
−0.0150550 + 0.999887i \(0.504792\pi\)
\(168\) 8.79608 0.678632
\(169\) 1.00000 0.0769231
\(170\) 24.8114 1.90295
\(171\) 2.39267 0.182972
\(172\) 0.0888661 0.00677598
\(173\) 10.8648 0.826037 0.413019 0.910723i \(-0.364474\pi\)
0.413019 + 0.910723i \(0.364474\pi\)
\(174\) −6.08240 −0.461106
\(175\) 6.94160 0.524736
\(176\) −14.6081 −1.10113
\(177\) −0.569872 −0.0428342
\(178\) 14.1474 1.06039
\(179\) −5.98118 −0.447054 −0.223527 0.974698i \(-0.571757\pi\)
−0.223527 + 0.974698i \(0.571757\pi\)
\(180\) −0.802544 −0.0598181
\(181\) 0.290058 0.0215598 0.0107799 0.999942i \(-0.496569\pi\)
0.0107799 + 0.999942i \(0.496569\pi\)
\(182\) 3.83151 0.284011
\(183\) 5.37556 0.397373
\(184\) 10.2279 0.754013
\(185\) 13.2304 0.972720
\(186\) 3.74333 0.274474
\(187\) 30.8034 2.25257
\(188\) 1.99619 0.145587
\(189\) −2.93494 −0.213486
\(190\) 8.47704 0.614989
\(191\) −18.2201 −1.31836 −0.659180 0.751985i \(-0.729096\pi\)
−0.659180 + 0.751985i \(0.729096\pi\)
\(192\) −8.80722 −0.635606
\(193\) −10.9122 −0.785478 −0.392739 0.919650i \(-0.628472\pi\)
−0.392739 + 0.919650i \(0.628472\pi\)
\(194\) 1.87459 0.134588
\(195\) −2.71388 −0.194345
\(196\) −0.477258 −0.0340898
\(197\) 0.764541 0.0544713 0.0272357 0.999629i \(-0.491330\pi\)
0.0272357 + 0.999629i \(0.491330\pi\)
\(198\) 5.74223 0.408082
\(199\) −6.88046 −0.487743 −0.243871 0.969808i \(-0.578418\pi\)
−0.243871 + 0.969808i \(0.578418\pi\)
\(200\) −7.08842 −0.501227
\(201\) −10.6429 −0.750690
\(202\) −2.13901 −0.150500
\(203\) 13.6743 0.959746
\(204\) 2.07094 0.144995
\(205\) −25.1564 −1.75700
\(206\) −1.30548 −0.0909572
\(207\) −3.41270 −0.237199
\(208\) −3.32111 −0.230278
\(209\) 10.5243 0.727980
\(210\) −10.3983 −0.717549
\(211\) −0.915251 −0.0630085 −0.0315042 0.999504i \(-0.510030\pi\)
−0.0315042 + 0.999504i \(0.510030\pi\)
\(212\) 2.85771 0.196268
\(213\) −5.14090 −0.352249
\(214\) 11.3781 0.777789
\(215\) −0.815548 −0.0556199
\(216\) 2.99702 0.203921
\(217\) −8.41565 −0.571291
\(218\) −3.43464 −0.232623
\(219\) 9.70296 0.655666
\(220\) −3.53003 −0.237995
\(221\) 7.00308 0.471078
\(222\) −6.36434 −0.427146
\(223\) 13.7316 0.919538 0.459769 0.888039i \(-0.347932\pi\)
0.459769 + 0.888039i \(0.347932\pi\)
\(224\) 4.86726 0.325207
\(225\) 2.36516 0.157677
\(226\) 3.93665 0.261862
\(227\) 21.4823 1.42583 0.712915 0.701251i \(-0.247375\pi\)
0.712915 + 0.701251i \(0.247375\pi\)
\(228\) 0.707555 0.0468590
\(229\) 16.1117 1.06469 0.532345 0.846528i \(-0.321311\pi\)
0.532345 + 0.846528i \(0.321311\pi\)
\(230\) −12.0909 −0.797254
\(231\) −12.9095 −0.849383
\(232\) −13.9635 −0.916747
\(233\) −6.44479 −0.422213 −0.211106 0.977463i \(-0.567707\pi\)
−0.211106 + 0.977463i \(0.567707\pi\)
\(234\) 1.30548 0.0853420
\(235\) −18.3196 −1.19504
\(236\) −0.168522 −0.0109698
\(237\) −11.5440 −0.749860
\(238\) 26.8324 1.73929
\(239\) 4.50706 0.291537 0.145769 0.989319i \(-0.453434\pi\)
0.145769 + 0.989319i \(0.453434\pi\)
\(240\) 9.01311 0.581794
\(241\) 7.64725 0.492603 0.246301 0.969193i \(-0.420785\pi\)
0.246301 + 0.969193i \(0.420785\pi\)
\(242\) 10.8972 0.700499
\(243\) −1.00000 −0.0641500
\(244\) 1.58965 0.101767
\(245\) 4.37992 0.279823
\(246\) 12.1012 0.771543
\(247\) 2.39267 0.152242
\(248\) 8.59364 0.545696
\(249\) −6.57810 −0.416870
\(250\) −9.33505 −0.590400
\(251\) 28.1674 1.77791 0.888955 0.457995i \(-0.151432\pi\)
0.888955 + 0.457995i \(0.151432\pi\)
\(252\) −0.867916 −0.0546736
\(253\) −15.0110 −0.943731
\(254\) −19.2693 −1.20906
\(255\) −19.0055 −1.19017
\(256\) −6.93443 −0.433402
\(257\) −1.66440 −0.103822 −0.0519112 0.998652i \(-0.516531\pi\)
−0.0519112 + 0.998652i \(0.516531\pi\)
\(258\) 0.392310 0.0244241
\(259\) 14.3081 0.889063
\(260\) −0.802544 −0.0497717
\(261\) 4.65913 0.288393
\(262\) −8.62177 −0.532655
\(263\) −11.9122 −0.734539 −0.367269 0.930115i \(-0.619707\pi\)
−0.367269 + 0.930115i \(0.619707\pi\)
\(264\) 13.1825 0.811329
\(265\) −26.2259 −1.61105
\(266\) 9.16754 0.562098
\(267\) −10.8369 −0.663208
\(268\) −3.14729 −0.192251
\(269\) 10.8140 0.659344 0.329672 0.944096i \(-0.393062\pi\)
0.329672 + 0.944096i \(0.393062\pi\)
\(270\) −3.54292 −0.215615
\(271\) 31.2042 1.89552 0.947760 0.318983i \(-0.103341\pi\)
0.947760 + 0.318983i \(0.103341\pi\)
\(272\) −23.2580 −1.41023
\(273\) −2.93494 −0.177631
\(274\) −14.3013 −0.863971
\(275\) 10.4033 0.627341
\(276\) −1.00920 −0.0607466
\(277\) 20.6938 1.24337 0.621686 0.783267i \(-0.286448\pi\)
0.621686 + 0.783267i \(0.286448\pi\)
\(278\) −15.0490 −0.902580
\(279\) −2.86740 −0.171667
\(280\) −23.8715 −1.42660
\(281\) 3.99731 0.238459 0.119230 0.992867i \(-0.461958\pi\)
0.119230 + 0.992867i \(0.461958\pi\)
\(282\) 8.81241 0.524771
\(283\) 14.0429 0.834766 0.417383 0.908731i \(-0.362947\pi\)
0.417383 + 0.908731i \(0.362947\pi\)
\(284\) −1.52026 −0.0902107
\(285\) −6.49342 −0.384637
\(286\) 5.74223 0.339545
\(287\) −27.2055 −1.60589
\(288\) 1.65838 0.0977211
\(289\) 32.0431 1.88489
\(290\) 16.5069 0.969320
\(291\) −1.43594 −0.0841763
\(292\) 2.86934 0.167916
\(293\) −23.5561 −1.37616 −0.688080 0.725635i \(-0.741546\pi\)
−0.688080 + 0.725635i \(0.741546\pi\)
\(294\) −2.10691 −0.122877
\(295\) 1.54657 0.0900446
\(296\) −14.6107 −0.849231
\(297\) −4.39855 −0.255230
\(298\) −12.9906 −0.752522
\(299\) −3.41270 −0.197362
\(300\) 0.699420 0.0403810
\(301\) −0.881979 −0.0508364
\(302\) 8.01869 0.461424
\(303\) 1.63848 0.0941283
\(304\) −7.94633 −0.455753
\(305\) −14.5886 −0.835343
\(306\) 9.14239 0.522636
\(307\) −28.8999 −1.64941 −0.824703 0.565566i \(-0.808658\pi\)
−0.824703 + 0.565566i \(0.808658\pi\)
\(308\) −3.81757 −0.217527
\(309\) 1.00000 0.0568880
\(310\) −10.1590 −0.576990
\(311\) 10.2465 0.581028 0.290514 0.956871i \(-0.406174\pi\)
0.290514 + 0.956871i \(0.406174\pi\)
\(312\) 2.99702 0.169673
\(313\) 2.36100 0.133452 0.0667258 0.997771i \(-0.478745\pi\)
0.0667258 + 0.997771i \(0.478745\pi\)
\(314\) 6.74952 0.380898
\(315\) 7.96509 0.448782
\(316\) −3.41376 −0.192039
\(317\) 19.8278 1.11364 0.556820 0.830633i \(-0.312021\pi\)
0.556820 + 0.830633i \(0.312021\pi\)
\(318\) 12.6157 0.707452
\(319\) 20.4934 1.14741
\(320\) 23.9017 1.33615
\(321\) −8.71561 −0.486458
\(322\) −13.0758 −0.728687
\(323\) 16.7561 0.932332
\(324\) −0.295718 −0.0164288
\(325\) 2.36516 0.131195
\(326\) 29.6178 1.64038
\(327\) 2.63094 0.145491
\(328\) 27.7809 1.53394
\(329\) −19.8118 −1.09226
\(330\) −15.5837 −0.857856
\(331\) −16.4923 −0.906498 −0.453249 0.891384i \(-0.649735\pi\)
−0.453249 + 0.891384i \(0.649735\pi\)
\(332\) −1.94526 −0.106760
\(333\) 4.87509 0.267153
\(334\) −0.507973 −0.0277950
\(335\) 28.8835 1.57807
\(336\) 9.74728 0.531758
\(337\) −8.15646 −0.444311 −0.222155 0.975011i \(-0.571309\pi\)
−0.222155 + 0.975011i \(0.571309\pi\)
\(338\) 1.30548 0.0710088
\(339\) −3.01548 −0.163778
\(340\) −5.62028 −0.304803
\(341\) −12.6124 −0.682999
\(342\) 3.12358 0.168904
\(343\) −15.8079 −0.853547
\(344\) 0.900633 0.0485589
\(345\) 9.26168 0.498632
\(346\) 14.1838 0.762527
\(347\) −19.9683 −1.07195 −0.535977 0.844233i \(-0.680057\pi\)
−0.535977 + 0.844233i \(0.680057\pi\)
\(348\) 1.37779 0.0738572
\(349\) 18.2338 0.976035 0.488018 0.872834i \(-0.337720\pi\)
0.488018 + 0.872834i \(0.337720\pi\)
\(350\) 9.06213 0.484391
\(351\) −1.00000 −0.0533761
\(352\) 7.29448 0.388797
\(353\) −23.2179 −1.23576 −0.617881 0.786272i \(-0.712009\pi\)
−0.617881 + 0.786272i \(0.712009\pi\)
\(354\) −0.743958 −0.0395409
\(355\) 13.9518 0.740485
\(356\) −3.20467 −0.169847
\(357\) −20.5536 −1.08781
\(358\) −7.80832 −0.412682
\(359\) 15.4908 0.817573 0.408786 0.912630i \(-0.365952\pi\)
0.408786 + 0.912630i \(0.365952\pi\)
\(360\) −8.13355 −0.428676
\(361\) −13.2751 −0.698691
\(362\) 0.378665 0.0199022
\(363\) −8.34727 −0.438118
\(364\) −0.867916 −0.0454912
\(365\) −26.3327 −1.37832
\(366\) 7.01770 0.366821
\(367\) 8.73335 0.455877 0.227939 0.973675i \(-0.426801\pi\)
0.227939 + 0.973675i \(0.426801\pi\)
\(368\) 11.3340 0.590825
\(369\) −9.26951 −0.482551
\(370\) 17.2721 0.897932
\(371\) −28.3622 −1.47249
\(372\) −0.847941 −0.0439637
\(373\) −5.97453 −0.309350 −0.154675 0.987965i \(-0.549433\pi\)
−0.154675 + 0.987965i \(0.549433\pi\)
\(374\) 40.2133 2.07938
\(375\) 7.15065 0.369258
\(376\) 20.2308 1.04332
\(377\) 4.65913 0.239957
\(378\) −3.83151 −0.197072
\(379\) −16.4914 −0.847106 −0.423553 0.905871i \(-0.639217\pi\)
−0.423553 + 0.905871i \(0.639217\pi\)
\(380\) −1.92022 −0.0985053
\(381\) 14.7603 0.756194
\(382\) −23.7860 −1.21700
\(383\) −23.3867 −1.19500 −0.597502 0.801868i \(-0.703840\pi\)
−0.597502 + 0.801868i \(0.703840\pi\)
\(384\) −8.18089 −0.417479
\(385\) 35.0349 1.78554
\(386\) −14.2457 −0.725086
\(387\) −0.300510 −0.0152758
\(388\) −0.424634 −0.0215575
\(389\) −21.5187 −1.09104 −0.545520 0.838098i \(-0.683668\pi\)
−0.545520 + 0.838098i \(0.683668\pi\)
\(390\) −3.54292 −0.179403
\(391\) −23.8994 −1.20865
\(392\) −4.83687 −0.244299
\(393\) 6.60429 0.333142
\(394\) 0.998095 0.0502833
\(395\) 31.3289 1.57633
\(396\) −1.30073 −0.0653642
\(397\) −16.5792 −0.832086 −0.416043 0.909345i \(-0.636583\pi\)
−0.416043 + 0.909345i \(0.636583\pi\)
\(398\) −8.98231 −0.450243
\(399\) −7.02235 −0.351557
\(400\) −7.85496 −0.392748
\(401\) −2.97880 −0.148754 −0.0743772 0.997230i \(-0.523697\pi\)
−0.0743772 + 0.997230i \(0.523697\pi\)
\(402\) −13.8941 −0.692973
\(403\) −2.86740 −0.142835
\(404\) 0.484528 0.0241062
\(405\) 2.71388 0.134854
\(406\) 17.8515 0.885955
\(407\) 21.4433 1.06291
\(408\) 20.9884 1.03908
\(409\) −14.9045 −0.736982 −0.368491 0.929631i \(-0.620125\pi\)
−0.368491 + 0.929631i \(0.620125\pi\)
\(410\) −32.8412 −1.62191
\(411\) 10.9548 0.540360
\(412\) 0.295718 0.0145690
\(413\) 1.67254 0.0823005
\(414\) −4.45522 −0.218962
\(415\) 17.8522 0.876330
\(416\) 1.65838 0.0813088
\(417\) 11.5276 0.564507
\(418\) 13.7393 0.672009
\(419\) −22.9263 −1.12002 −0.560011 0.828485i \(-0.689203\pi\)
−0.560011 + 0.828485i \(0.689203\pi\)
\(420\) 2.35542 0.114933
\(421\) −29.9384 −1.45911 −0.729553 0.683924i \(-0.760272\pi\)
−0.729553 + 0.683924i \(0.760272\pi\)
\(422\) −1.19484 −0.0581641
\(423\) −6.75031 −0.328211
\(424\) 28.9620 1.40652
\(425\) 16.5634 0.803442
\(426\) −6.71135 −0.325166
\(427\) −15.7770 −0.763501
\(428\) −2.57736 −0.124582
\(429\) −4.39855 −0.212364
\(430\) −1.06468 −0.0513435
\(431\) −15.0439 −0.724640 −0.362320 0.932054i \(-0.618015\pi\)
−0.362320 + 0.932054i \(0.618015\pi\)
\(432\) 3.32111 0.159787
\(433\) −28.9634 −1.39189 −0.695947 0.718093i \(-0.745015\pi\)
−0.695947 + 0.718093i \(0.745015\pi\)
\(434\) −10.9865 −0.527367
\(435\) −12.6443 −0.606249
\(436\) 0.778016 0.0372602
\(437\) −8.16547 −0.390607
\(438\) 12.6670 0.605255
\(439\) −13.4199 −0.640495 −0.320247 0.947334i \(-0.603766\pi\)
−0.320247 + 0.947334i \(0.603766\pi\)
\(440\) −35.7759 −1.70555
\(441\) 1.61389 0.0768521
\(442\) 9.14239 0.434859
\(443\) 15.1174 0.718249 0.359124 0.933290i \(-0.383075\pi\)
0.359124 + 0.933290i \(0.383075\pi\)
\(444\) 1.44165 0.0684178
\(445\) 29.4101 1.39417
\(446\) 17.9264 0.848839
\(447\) 9.95077 0.470655
\(448\) 25.8487 1.22124
\(449\) −38.2449 −1.80489 −0.902444 0.430806i \(-0.858229\pi\)
−0.902444 + 0.430806i \(0.858229\pi\)
\(450\) 3.08767 0.145554
\(451\) −40.7724 −1.91990
\(452\) −0.891732 −0.0419436
\(453\) −6.14232 −0.288591
\(454\) 28.0447 1.31620
\(455\) 7.96509 0.373409
\(456\) 7.17087 0.335807
\(457\) −3.77691 −0.176676 −0.0883382 0.996091i \(-0.528156\pi\)
−0.0883382 + 0.996091i \(0.528156\pi\)
\(458\) 21.0335 0.982831
\(459\) −7.00308 −0.326876
\(460\) 2.73885 0.127699
\(461\) 33.2233 1.54736 0.773681 0.633575i \(-0.218413\pi\)
0.773681 + 0.633575i \(0.218413\pi\)
\(462\) −16.8531 −0.784078
\(463\) 1.48993 0.0692431 0.0346215 0.999400i \(-0.488977\pi\)
0.0346215 + 0.999400i \(0.488977\pi\)
\(464\) −15.4735 −0.718339
\(465\) 7.78178 0.360871
\(466\) −8.41356 −0.389751
\(467\) 16.0707 0.743662 0.371831 0.928300i \(-0.378730\pi\)
0.371831 + 0.928300i \(0.378730\pi\)
\(468\) −0.295718 −0.0136696
\(469\) 31.2362 1.44235
\(470\) −23.9158 −1.10316
\(471\) −5.17014 −0.238228
\(472\) −1.70792 −0.0786133
\(473\) −1.32181 −0.0607768
\(474\) −15.0704 −0.692207
\(475\) 5.65904 0.259654
\(476\) −6.07809 −0.278589
\(477\) −9.66362 −0.442467
\(478\) 5.88388 0.269122
\(479\) −21.5503 −0.984660 −0.492330 0.870409i \(-0.663855\pi\)
−0.492330 + 0.870409i \(0.663855\pi\)
\(480\) −4.50065 −0.205426
\(481\) 4.87509 0.222285
\(482\) 9.98335 0.454729
\(483\) 10.0161 0.455748
\(484\) −2.46844 −0.112202
\(485\) 3.89697 0.176952
\(486\) −1.30548 −0.0592178
\(487\) −26.7129 −1.21048 −0.605238 0.796045i \(-0.706922\pi\)
−0.605238 + 0.796045i \(0.706922\pi\)
\(488\) 16.1107 0.729295
\(489\) −22.6872 −1.02595
\(490\) 5.71790 0.258308
\(491\) −9.86244 −0.445086 −0.222543 0.974923i \(-0.571436\pi\)
−0.222543 + 0.974923i \(0.571436\pi\)
\(492\) −2.74116 −0.123581
\(493\) 32.6282 1.46950
\(494\) 3.12358 0.140537
\(495\) 11.9372 0.536535
\(496\) 9.52295 0.427593
\(497\) 15.0883 0.676801
\(498\) −8.58759 −0.384819
\(499\) 7.66767 0.343252 0.171626 0.985162i \(-0.445098\pi\)
0.171626 + 0.985162i \(0.445098\pi\)
\(500\) 2.11458 0.0945668
\(501\) 0.389107 0.0173840
\(502\) 36.7720 1.64121
\(503\) 22.8239 1.01767 0.508833 0.860865i \(-0.330077\pi\)
0.508833 + 0.860865i \(0.330077\pi\)
\(504\) −8.79608 −0.391808
\(505\) −4.44664 −0.197873
\(506\) −19.5965 −0.871172
\(507\) −1.00000 −0.0444116
\(508\) 4.36489 0.193661
\(509\) −30.0134 −1.33032 −0.665160 0.746700i \(-0.731637\pi\)
−0.665160 + 0.746700i \(0.731637\pi\)
\(510\) −24.8114 −1.09867
\(511\) −28.4777 −1.25978
\(512\) −25.4146 −1.12318
\(513\) −2.39267 −0.105639
\(514\) −2.17284 −0.0958399
\(515\) −2.71388 −0.119588
\(516\) −0.0888661 −0.00391211
\(517\) −29.6916 −1.30584
\(518\) 18.6790 0.820707
\(519\) −10.8648 −0.476913
\(520\) −8.13355 −0.356680
\(521\) 40.9397 1.79360 0.896799 0.442437i \(-0.145886\pi\)
0.896799 + 0.442437i \(0.145886\pi\)
\(522\) 6.08240 0.266220
\(523\) −19.7665 −0.864330 −0.432165 0.901795i \(-0.642250\pi\)
−0.432165 + 0.901795i \(0.642250\pi\)
\(524\) 1.95301 0.0853175
\(525\) −6.94160 −0.302956
\(526\) −15.5512 −0.678063
\(527\) −20.0806 −0.874725
\(528\) 14.6081 0.635736
\(529\) −11.3534 −0.493628
\(530\) −34.2375 −1.48718
\(531\) 0.569872 0.0247304
\(532\) −2.07664 −0.0900336
\(533\) −9.26951 −0.401507
\(534\) −14.1474 −0.612217
\(535\) 23.6531 1.02261
\(536\) −31.8969 −1.37773
\(537\) 5.98118 0.258107
\(538\) 14.1175 0.608650
\(539\) 7.09880 0.305767
\(540\) 0.802544 0.0345360
\(541\) 40.1714 1.72710 0.863551 0.504262i \(-0.168235\pi\)
0.863551 + 0.504262i \(0.168235\pi\)
\(542\) 40.7365 1.74978
\(543\) −0.290058 −0.0124476
\(544\) 11.6138 0.497937
\(545\) −7.14006 −0.305846
\(546\) −3.83151 −0.163974
\(547\) −23.1366 −0.989250 −0.494625 0.869107i \(-0.664695\pi\)
−0.494625 + 0.869107i \(0.664695\pi\)
\(548\) 3.23953 0.138386
\(549\) −5.37556 −0.229423
\(550\) 13.5813 0.579108
\(551\) 11.1477 0.474910
\(552\) −10.2279 −0.435330
\(553\) 33.8808 1.44076
\(554\) 27.0154 1.14778
\(555\) −13.2304 −0.561600
\(556\) 3.40891 0.144570
\(557\) 35.7886 1.51641 0.758206 0.652015i \(-0.226076\pi\)
0.758206 + 0.652015i \(0.226076\pi\)
\(558\) −3.74333 −0.158468
\(559\) −0.300510 −0.0127102
\(560\) −26.4530 −1.11784
\(561\) −30.8034 −1.30052
\(562\) 5.21841 0.220125
\(563\) 3.02856 0.127639 0.0638193 0.997961i \(-0.479672\pi\)
0.0638193 + 0.997961i \(0.479672\pi\)
\(564\) −1.99619 −0.0840548
\(565\) 8.18366 0.344289
\(566\) 18.3328 0.770585
\(567\) 2.93494 0.123256
\(568\) −15.4074 −0.646479
\(569\) −27.7102 −1.16167 −0.580835 0.814021i \(-0.697274\pi\)
−0.580835 + 0.814021i \(0.697274\pi\)
\(570\) −8.47704 −0.355064
\(571\) 37.2513 1.55892 0.779458 0.626454i \(-0.215494\pi\)
0.779458 + 0.626454i \(0.215494\pi\)
\(572\) −1.30073 −0.0543863
\(573\) 18.2201 0.761155
\(574\) −35.5163 −1.48242
\(575\) −8.07158 −0.336608
\(576\) 8.80722 0.366967
\(577\) −9.99418 −0.416063 −0.208032 0.978122i \(-0.566706\pi\)
−0.208032 + 0.978122i \(0.566706\pi\)
\(578\) 41.8317 1.73997
\(579\) 10.9122 0.453496
\(580\) −3.73915 −0.155260
\(581\) 19.3064 0.800963
\(582\) −1.87459 −0.0777044
\(583\) −42.5059 −1.76042
\(584\) 29.0800 1.20334
\(585\) 2.71388 0.112205
\(586\) −30.7520 −1.27035
\(587\) 20.0870 0.829079 0.414539 0.910031i \(-0.363943\pi\)
0.414539 + 0.910031i \(0.363943\pi\)
\(588\) 0.477258 0.0196818
\(589\) −6.86073 −0.282691
\(590\) 2.01901 0.0831215
\(591\) −0.764541 −0.0314490
\(592\) −16.1907 −0.665435
\(593\) 23.5401 0.966677 0.483338 0.875434i \(-0.339424\pi\)
0.483338 + 0.875434i \(0.339424\pi\)
\(594\) −5.74223 −0.235607
\(595\) 55.7802 2.28676
\(596\) 2.94262 0.120535
\(597\) 6.88046 0.281599
\(598\) −4.45522 −0.182188
\(599\) 43.4911 1.77700 0.888498 0.458880i \(-0.151749\pi\)
0.888498 + 0.458880i \(0.151749\pi\)
\(600\) 7.08842 0.289383
\(601\) −31.5728 −1.28788 −0.643940 0.765076i \(-0.722701\pi\)
−0.643940 + 0.765076i \(0.722701\pi\)
\(602\) −1.15141 −0.0469278
\(603\) 10.6429 0.433411
\(604\) −1.81640 −0.0739081
\(605\) 22.6535 0.920996
\(606\) 2.13901 0.0868912
\(607\) −25.6016 −1.03914 −0.519569 0.854428i \(-0.673908\pi\)
−0.519569 + 0.854428i \(0.673908\pi\)
\(608\) 3.96796 0.160922
\(609\) −13.6743 −0.554109
\(610\) −19.0452 −0.771118
\(611\) −6.75031 −0.273088
\(612\) −2.07094 −0.0837127
\(613\) −0.495486 −0.0200125 −0.0100062 0.999950i \(-0.503185\pi\)
−0.0100062 + 0.999950i \(0.503185\pi\)
\(614\) −37.7283 −1.52259
\(615\) 25.1564 1.01440
\(616\) −38.6900 −1.55887
\(617\) −20.3310 −0.818497 −0.409249 0.912423i \(-0.634209\pi\)
−0.409249 + 0.912423i \(0.634209\pi\)
\(618\) 1.30548 0.0525142
\(619\) −28.8765 −1.16065 −0.580323 0.814386i \(-0.697074\pi\)
−0.580323 + 0.814386i \(0.697074\pi\)
\(620\) 2.30121 0.0924189
\(621\) 3.41270 0.136947
\(622\) 13.3767 0.536355
\(623\) 31.8057 1.27427
\(624\) 3.32111 0.132951
\(625\) −31.2318 −1.24927
\(626\) 3.08224 0.123191
\(627\) −10.5243 −0.420299
\(628\) −1.52890 −0.0610099
\(629\) 34.1406 1.36128
\(630\) 10.3983 0.414277
\(631\) −17.9091 −0.712951 −0.356475 0.934305i \(-0.616022\pi\)
−0.356475 + 0.934305i \(0.616022\pi\)
\(632\) −34.5974 −1.37621
\(633\) 0.915251 0.0363780
\(634\) 25.8848 1.02802
\(635\) −40.0578 −1.58964
\(636\) −2.85771 −0.113315
\(637\) 1.61389 0.0639448
\(638\) 26.7538 1.05919
\(639\) 5.14090 0.203371
\(640\) 22.2020 0.877610
\(641\) −17.2776 −0.682424 −0.341212 0.939986i \(-0.610837\pi\)
−0.341212 + 0.939986i \(0.610837\pi\)
\(642\) −11.3781 −0.449057
\(643\) −14.1199 −0.556835 −0.278418 0.960460i \(-0.589810\pi\)
−0.278418 + 0.960460i \(0.589810\pi\)
\(644\) 2.96194 0.116717
\(645\) 0.815548 0.0321122
\(646\) 21.8747 0.860649
\(647\) 16.5033 0.648812 0.324406 0.945918i \(-0.394836\pi\)
0.324406 + 0.945918i \(0.394836\pi\)
\(648\) −2.99702 −0.117734
\(649\) 2.50661 0.0983932
\(650\) 3.08767 0.121108
\(651\) 8.41565 0.329835
\(652\) −6.70903 −0.262746
\(653\) −9.97625 −0.390401 −0.195200 0.980763i \(-0.562536\pi\)
−0.195200 + 0.980763i \(0.562536\pi\)
\(654\) 3.43464 0.134305
\(655\) −17.9233 −0.700320
\(656\) 30.7851 1.20196
\(657\) −9.70296 −0.378549
\(658\) −25.8639 −1.00828
\(659\) −31.9738 −1.24552 −0.622761 0.782412i \(-0.713989\pi\)
−0.622761 + 0.782412i \(0.713989\pi\)
\(660\) 3.53003 0.137406
\(661\) −20.2815 −0.788858 −0.394429 0.918926i \(-0.629058\pi\)
−0.394429 + 0.918926i \(0.629058\pi\)
\(662\) −21.5304 −0.836801
\(663\) −7.00308 −0.271977
\(664\) −19.7147 −0.765078
\(665\) 19.0578 0.739031
\(666\) 6.36434 0.246613
\(667\) −15.9002 −0.615659
\(668\) 0.115066 0.00445204
\(669\) −13.7316 −0.530895
\(670\) 37.7069 1.45674
\(671\) −23.6447 −0.912793
\(672\) −4.86726 −0.187758
\(673\) 2.75171 0.106071 0.0530353 0.998593i \(-0.483110\pi\)
0.0530353 + 0.998593i \(0.483110\pi\)
\(674\) −10.6481 −0.410150
\(675\) −2.36516 −0.0910349
\(676\) −0.295718 −0.0113738
\(677\) −9.28770 −0.356955 −0.178478 0.983944i \(-0.557117\pi\)
−0.178478 + 0.983944i \(0.557117\pi\)
\(678\) −3.93665 −0.151186
\(679\) 4.21441 0.161734
\(680\) −56.9599 −2.18431
\(681\) −21.4823 −0.823203
\(682\) −16.4652 −0.630487
\(683\) 38.3720 1.46826 0.734132 0.679007i \(-0.237589\pi\)
0.734132 + 0.679007i \(0.237589\pi\)
\(684\) −0.707555 −0.0270541
\(685\) −29.7300 −1.13592
\(686\) −20.6369 −0.787922
\(687\) −16.1117 −0.614699
\(688\) 0.998027 0.0380494
\(689\) −9.66362 −0.368155
\(690\) 12.0909 0.460295
\(691\) −29.4899 −1.12185 −0.560925 0.827866i \(-0.689554\pi\)
−0.560925 + 0.827866i \(0.689554\pi\)
\(692\) −3.21293 −0.122137
\(693\) 12.9095 0.490392
\(694\) −26.0682 −0.989536
\(695\) −31.2845 −1.18669
\(696\) 13.9635 0.529284
\(697\) −64.9151 −2.45884
\(698\) 23.8039 0.900993
\(699\) 6.44479 0.243765
\(700\) −2.05276 −0.0775870
\(701\) 39.0937 1.47655 0.738275 0.674500i \(-0.235641\pi\)
0.738275 + 0.674500i \(0.235641\pi\)
\(702\) −1.30548 −0.0492722
\(703\) 11.6645 0.439934
\(704\) 38.7390 1.46003
\(705\) 18.3196 0.689954
\(706\) −30.3105 −1.14075
\(707\) −4.80885 −0.180855
\(708\) 0.168522 0.00633343
\(709\) −24.0930 −0.904831 −0.452415 0.891807i \(-0.649438\pi\)
−0.452415 + 0.891807i \(0.649438\pi\)
\(710\) 18.2138 0.683553
\(711\) 11.5440 0.432932
\(712\) −32.4784 −1.21718
\(713\) 9.78557 0.366473
\(714\) −26.8324 −1.00418
\(715\) 11.9372 0.446424
\(716\) 1.76874 0.0661010
\(717\) −4.50706 −0.168319
\(718\) 20.2229 0.754713
\(719\) −18.1502 −0.676889 −0.338445 0.940986i \(-0.609901\pi\)
−0.338445 + 0.940986i \(0.609901\pi\)
\(720\) −9.01311 −0.335899
\(721\) −2.93494 −0.109303
\(722\) −17.3304 −0.644972
\(723\) −7.64725 −0.284404
\(724\) −0.0857754 −0.00318782
\(725\) 11.0196 0.409256
\(726\) −10.8972 −0.404433
\(727\) 14.0622 0.521538 0.260769 0.965401i \(-0.416024\pi\)
0.260769 + 0.965401i \(0.416024\pi\)
\(728\) −8.79608 −0.326004
\(729\) 1.00000 0.0370370
\(730\) −34.3769 −1.27234
\(731\) −2.10449 −0.0778375
\(732\) −1.58965 −0.0587552
\(733\) −47.5969 −1.75803 −0.879016 0.476793i \(-0.841799\pi\)
−0.879016 + 0.476793i \(0.841799\pi\)
\(734\) 11.4012 0.420827
\(735\) −4.37992 −0.161556
\(736\) −5.65957 −0.208614
\(737\) 46.8132 1.72439
\(738\) −12.1012 −0.445450
\(739\) −1.11770 −0.0411151 −0.0205576 0.999789i \(-0.506544\pi\)
−0.0205576 + 0.999789i \(0.506544\pi\)
\(740\) −3.91247 −0.143825
\(741\) −2.39267 −0.0878969
\(742\) −37.0263 −1.35928
\(743\) 18.8094 0.690050 0.345025 0.938594i \(-0.387871\pi\)
0.345025 + 0.938594i \(0.387871\pi\)
\(744\) −8.59364 −0.315058
\(745\) −27.0052 −0.989395
\(746\) −7.79964 −0.285565
\(747\) 6.57810 0.240680
\(748\) −9.10913 −0.333063
\(749\) 25.5798 0.934667
\(750\) 9.33505 0.340868
\(751\) 51.1722 1.86730 0.933650 0.358186i \(-0.116605\pi\)
0.933650 + 0.358186i \(0.116605\pi\)
\(752\) 22.4186 0.817521
\(753\) −28.1674 −1.02648
\(754\) 6.08240 0.221508
\(755\) 16.6695 0.606667
\(756\) 0.867916 0.0315658
\(757\) 22.4845 0.817214 0.408607 0.912711i \(-0.366015\pi\)
0.408607 + 0.912711i \(0.366015\pi\)
\(758\) −21.5292 −0.781976
\(759\) 15.0110 0.544863
\(760\) −19.4609 −0.705921
\(761\) −44.7519 −1.62226 −0.811128 0.584869i \(-0.801146\pi\)
−0.811128 + 0.584869i \(0.801146\pi\)
\(762\) 19.2693 0.698054
\(763\) −7.72166 −0.279543
\(764\) 5.38801 0.194931
\(765\) 19.0055 0.687147
\(766\) −30.5309 −1.10313
\(767\) 0.569872 0.0205769
\(768\) 6.93443 0.250225
\(769\) −29.0791 −1.04862 −0.524310 0.851528i \(-0.675677\pi\)
−0.524310 + 0.851528i \(0.675677\pi\)
\(770\) 45.7374 1.64826
\(771\) 1.66440 0.0599418
\(772\) 3.22694 0.116140
\(773\) −26.9175 −0.968155 −0.484078 0.875025i \(-0.660845\pi\)
−0.484078 + 0.875025i \(0.660845\pi\)
\(774\) −0.392310 −0.0141013
\(775\) −6.78184 −0.243611
\(776\) −4.30354 −0.154488
\(777\) −14.3081 −0.513301
\(778\) −28.0922 −1.00715
\(779\) −22.1789 −0.794640
\(780\) 0.802544 0.0287357
\(781\) 22.6125 0.809140
\(782\) −31.2003 −1.11572
\(783\) −4.65913 −0.166504
\(784\) −5.35993 −0.191426
\(785\) 14.0312 0.500793
\(786\) 8.62177 0.307528
\(787\) −46.6118 −1.66153 −0.830766 0.556621i \(-0.812097\pi\)
−0.830766 + 0.556621i \(0.812097\pi\)
\(788\) −0.226089 −0.00805408
\(789\) 11.9122 0.424086
\(790\) 40.8993 1.45513
\(791\) 8.85026 0.314679
\(792\) −13.1825 −0.468421
\(793\) −5.37556 −0.190892
\(794\) −21.6438 −0.768111
\(795\) 26.2259 0.930138
\(796\) 2.03468 0.0721172
\(797\) 9.07218 0.321353 0.160677 0.987007i \(-0.448632\pi\)
0.160677 + 0.987007i \(0.448632\pi\)
\(798\) −9.16754 −0.324528
\(799\) −47.2730 −1.67240
\(800\) 3.92233 0.138675
\(801\) 10.8369 0.382903
\(802\) −3.88877 −0.137317
\(803\) −42.6790 −1.50611
\(804\) 3.14729 0.110996
\(805\) −27.1825 −0.958057
\(806\) −3.74333 −0.131853
\(807\) −10.8140 −0.380672
\(808\) 4.91056 0.172753
\(809\) −27.5336 −0.968031 −0.484015 0.875059i \(-0.660822\pi\)
−0.484015 + 0.875059i \(0.660822\pi\)
\(810\) 3.54292 0.124486
\(811\) −40.7488 −1.43088 −0.715442 0.698673i \(-0.753774\pi\)
−0.715442 + 0.698673i \(0.753774\pi\)
\(812\) −4.04373 −0.141907
\(813\) −31.2042 −1.09438
\(814\) 27.9939 0.981185
\(815\) 61.5705 2.15672
\(816\) 23.2580 0.814194
\(817\) −0.719020 −0.0251553
\(818\) −19.4576 −0.680319
\(819\) 2.93494 0.102555
\(820\) 7.43919 0.259788
\(821\) −5.80191 −0.202488 −0.101244 0.994862i \(-0.532282\pi\)
−0.101244 + 0.994862i \(0.532282\pi\)
\(822\) 14.3013 0.498814
\(823\) 33.9771 1.18437 0.592183 0.805803i \(-0.298266\pi\)
0.592183 + 0.805803i \(0.298266\pi\)
\(824\) 2.99702 0.104406
\(825\) −10.4033 −0.362195
\(826\) 2.18347 0.0759728
\(827\) 55.0980 1.91594 0.957972 0.286860i \(-0.0926116\pi\)
0.957972 + 0.286860i \(0.0926116\pi\)
\(828\) 1.00920 0.0350721
\(829\) 9.62395 0.334254 0.167127 0.985935i \(-0.446551\pi\)
0.167127 + 0.985935i \(0.446551\pi\)
\(830\) 23.3057 0.808953
\(831\) −20.6938 −0.717861
\(832\) 8.80722 0.305335
\(833\) 11.3022 0.391599
\(834\) 15.0490 0.521105
\(835\) −1.05599 −0.0365441
\(836\) −3.11222 −0.107638
\(837\) 2.86740 0.0991117
\(838\) −29.9298 −1.03391
\(839\) 42.8559 1.47955 0.739775 0.672854i \(-0.234932\pi\)
0.739775 + 0.672854i \(0.234932\pi\)
\(840\) 23.8715 0.823646
\(841\) −7.29255 −0.251467
\(842\) −39.0840 −1.34692
\(843\) −3.99731 −0.137675
\(844\) 0.270656 0.00931637
\(845\) 2.71388 0.0933604
\(846\) −8.81241 −0.302977
\(847\) 24.4988 0.841788
\(848\) 32.0940 1.10211
\(849\) −14.0429 −0.481952
\(850\) 21.6232 0.741669
\(851\) −16.6372 −0.570317
\(852\) 1.52026 0.0520832
\(853\) 42.6021 1.45867 0.729333 0.684158i \(-0.239830\pi\)
0.729333 + 0.684158i \(0.239830\pi\)
\(854\) −20.5965 −0.704799
\(855\) 6.49342 0.222070
\(856\) −26.1208 −0.892792
\(857\) 7.44858 0.254439 0.127219 0.991875i \(-0.459395\pi\)
0.127219 + 0.991875i \(0.459395\pi\)
\(858\) −5.74223 −0.196036
\(859\) 35.1881 1.20060 0.600301 0.799774i \(-0.295047\pi\)
0.600301 + 0.799774i \(0.295047\pi\)
\(860\) 0.241172 0.00822390
\(861\) 27.2055 0.927160
\(862\) −19.6395 −0.668926
\(863\) 15.4402 0.525590 0.262795 0.964852i \(-0.415356\pi\)
0.262795 + 0.964852i \(0.415356\pi\)
\(864\) −1.65838 −0.0564193
\(865\) 29.4859 1.00255
\(866\) −37.8112 −1.28488
\(867\) −32.0431 −1.08824
\(868\) 2.48866 0.0844706
\(869\) 50.7767 1.72248
\(870\) −16.5069 −0.559637
\(871\) 10.6429 0.360620
\(872\) 7.88497 0.267019
\(873\) 1.43594 0.0485992
\(874\) −10.6599 −0.360575
\(875\) −20.9868 −0.709482
\(876\) −2.86934 −0.0969461
\(877\) −31.8697 −1.07616 −0.538081 0.842893i \(-0.680851\pi\)
−0.538081 + 0.842893i \(0.680851\pi\)
\(878\) −17.5194 −0.591250
\(879\) 23.5561 0.794527
\(880\) −39.6447 −1.33642
\(881\) 36.4299 1.22735 0.613677 0.789557i \(-0.289690\pi\)
0.613677 + 0.789557i \(0.289690\pi\)
\(882\) 2.10691 0.0709433
\(883\) −41.0163 −1.38031 −0.690154 0.723662i \(-0.742457\pi\)
−0.690154 + 0.723662i \(0.742457\pi\)
\(884\) −2.07094 −0.0696532
\(885\) −1.54657 −0.0519873
\(886\) 19.7355 0.663026
\(887\) −17.5850 −0.590447 −0.295224 0.955428i \(-0.595394\pi\)
−0.295224 + 0.955428i \(0.595394\pi\)
\(888\) 14.6107 0.490304
\(889\) −43.3207 −1.45293
\(890\) 38.3943 1.28698
\(891\) 4.39855 0.147357
\(892\) −4.06069 −0.135962
\(893\) −16.1513 −0.540481
\(894\) 12.9906 0.434469
\(895\) −16.2322 −0.542583
\(896\) 24.0105 0.802133
\(897\) 3.41270 0.113947
\(898\) −49.9280 −1.66612
\(899\) −13.3596 −0.445566
\(900\) −0.699420 −0.0233140
\(901\) −67.6751 −2.25458
\(902\) −53.2276 −1.77229
\(903\) 0.881979 0.0293504
\(904\) −9.03745 −0.300581
\(905\) 0.787183 0.0261669
\(906\) −8.01869 −0.266403
\(907\) −47.5325 −1.57829 −0.789146 0.614206i \(-0.789476\pi\)
−0.789146 + 0.614206i \(0.789476\pi\)
\(908\) −6.35270 −0.210822
\(909\) −1.63848 −0.0543450
\(910\) 10.3983 0.344700
\(911\) −37.5801 −1.24508 −0.622542 0.782586i \(-0.713900\pi\)
−0.622542 + 0.782586i \(0.713900\pi\)
\(912\) 7.94633 0.263129
\(913\) 28.9341 0.957580
\(914\) −4.93069 −0.163093
\(915\) 14.5886 0.482286
\(916\) −4.76452 −0.157424
\(917\) −19.3832 −0.640090
\(918\) −9.14239 −0.301744
\(919\) 25.2754 0.833759 0.416880 0.908962i \(-0.363124\pi\)
0.416880 + 0.908962i \(0.363124\pi\)
\(920\) 27.7574 0.915135
\(921\) 28.8999 0.952285
\(922\) 43.3724 1.42839
\(923\) 5.14090 0.169215
\(924\) 3.81757 0.125589
\(925\) 11.5304 0.379116
\(926\) 1.94508 0.0639193
\(927\) −1.00000 −0.0328443
\(928\) 7.72661 0.253638
\(929\) 31.9541 1.04838 0.524190 0.851601i \(-0.324368\pi\)
0.524190 + 0.851601i \(0.324368\pi\)
\(930\) 10.1590 0.333126
\(931\) 3.86151 0.126556
\(932\) 1.90584 0.0624280
\(933\) −10.2465 −0.335457
\(934\) 20.9800 0.686485
\(935\) 83.5969 2.73391
\(936\) −2.99702 −0.0979606
\(937\) 34.6534 1.13208 0.566038 0.824379i \(-0.308476\pi\)
0.566038 + 0.824379i \(0.308476\pi\)
\(938\) 40.7783 1.33146
\(939\) −2.36100 −0.0770483
\(940\) 5.41743 0.176697
\(941\) −34.6906 −1.13088 −0.565440 0.824789i \(-0.691294\pi\)
−0.565440 + 0.824789i \(0.691294\pi\)
\(942\) −6.74952 −0.219911
\(943\) 31.6341 1.03015
\(944\) −1.89261 −0.0615993
\(945\) −7.96509 −0.259104
\(946\) −1.72560 −0.0561039
\(947\) 51.6451 1.67824 0.839121 0.543945i \(-0.183070\pi\)
0.839121 + 0.543945i \(0.183070\pi\)
\(948\) 3.41376 0.110874
\(949\) −9.70296 −0.314972
\(950\) 7.38777 0.239691
\(951\) −19.8278 −0.642960
\(952\) −61.5996 −1.99646
\(953\) 23.9187 0.774803 0.387401 0.921911i \(-0.373373\pi\)
0.387401 + 0.921911i \(0.373373\pi\)
\(954\) −12.6157 −0.408448
\(955\) −49.4472 −1.60007
\(956\) −1.33282 −0.0431064
\(957\) −20.4934 −0.662458
\(958\) −28.1336 −0.908954
\(959\) −32.1517 −1.03823
\(960\) −23.9017 −0.771426
\(961\) −22.7780 −0.734775
\(962\) 6.36434 0.205195
\(963\) 8.71561 0.280857
\(964\) −2.26143 −0.0728358
\(965\) −29.6145 −0.953323
\(966\) 13.0758 0.420708
\(967\) −38.9073 −1.25117 −0.625587 0.780154i \(-0.715140\pi\)
−0.625587 + 0.780154i \(0.715140\pi\)
\(968\) −25.0169 −0.804074
\(969\) −16.7561 −0.538282
\(970\) 5.08743 0.163347
\(971\) 60.3481 1.93666 0.968332 0.249667i \(-0.0803210\pi\)
0.968332 + 0.249667i \(0.0803210\pi\)
\(972\) 0.295718 0.00948516
\(973\) −33.8328 −1.08463
\(974\) −34.8732 −1.11741
\(975\) −2.36516 −0.0757456
\(976\) 17.8529 0.571456
\(977\) 31.2124 0.998574 0.499287 0.866437i \(-0.333595\pi\)
0.499287 + 0.866437i \(0.333595\pi\)
\(978\) −29.6178 −0.947071
\(979\) 47.6667 1.52343
\(980\) −1.29522 −0.0413743
\(981\) −2.63094 −0.0839994
\(982\) −12.8752 −0.410865
\(983\) −37.1045 −1.18345 −0.591725 0.806140i \(-0.701553\pi\)
−0.591725 + 0.806140i \(0.701553\pi\)
\(984\) −27.7809 −0.885622
\(985\) 2.07488 0.0661110
\(986\) 42.5956 1.35652
\(987\) 19.8118 0.630616
\(988\) −0.707555 −0.0225103
\(989\) 1.02555 0.0326106
\(990\) 15.5837 0.495284
\(991\) 50.8547 1.61545 0.807727 0.589557i \(-0.200698\pi\)
0.807727 + 0.589557i \(0.200698\pi\)
\(992\) −4.75524 −0.150979
\(993\) 16.4923 0.523367
\(994\) 19.6974 0.624765
\(995\) −18.6728 −0.591966
\(996\) 1.94526 0.0616381
\(997\) 41.2907 1.30769 0.653845 0.756629i \(-0.273155\pi\)
0.653845 + 0.756629i \(0.273155\pi\)
\(998\) 10.0100 0.316861
\(999\) −4.87509 −0.154241
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 \(a_p\))