Properties

Label 8018.2.a.d.1.6
Level 8018
Weight 2
Character 8018.1
Self dual Yes
Analytic conductor 64.024
Analytic rank 1
Dimension 30
CM No

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Newspace parameters

Level: \( N \) = \( 8018 = 2 \cdot 19 \cdot 211 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8018.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0240523407\)
Analytic rank: \(1\)
Dimension: \(30\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Character \(\chi\) = 8018.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -2.43818 q^{3} +1.00000 q^{4} +3.21483 q^{5} -2.43818 q^{6} -0.555600 q^{7} +1.00000 q^{8} +2.94471 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -2.43818 q^{3} +1.00000 q^{4} +3.21483 q^{5} -2.43818 q^{6} -0.555600 q^{7} +1.00000 q^{8} +2.94471 q^{9} +3.21483 q^{10} +2.38226 q^{11} -2.43818 q^{12} -3.53467 q^{13} -0.555600 q^{14} -7.83832 q^{15} +1.00000 q^{16} -2.52293 q^{17} +2.94471 q^{18} +1.00000 q^{19} +3.21483 q^{20} +1.35465 q^{21} +2.38226 q^{22} -5.51596 q^{23} -2.43818 q^{24} +5.33512 q^{25} -3.53467 q^{26} +0.134814 q^{27} -0.555600 q^{28} -4.31652 q^{29} -7.83832 q^{30} +3.40000 q^{31} +1.00000 q^{32} -5.80837 q^{33} -2.52293 q^{34} -1.78616 q^{35} +2.94471 q^{36} +3.58396 q^{37} +1.00000 q^{38} +8.61814 q^{39} +3.21483 q^{40} -0.595664 q^{41} +1.35465 q^{42} -6.33007 q^{43} +2.38226 q^{44} +9.46673 q^{45} -5.51596 q^{46} -4.42185 q^{47} -2.43818 q^{48} -6.69131 q^{49} +5.33512 q^{50} +6.15135 q^{51} -3.53467 q^{52} -8.35764 q^{53} +0.134814 q^{54} +7.65855 q^{55} -0.555600 q^{56} -2.43818 q^{57} -4.31652 q^{58} +2.18069 q^{59} -7.83832 q^{60} -3.16510 q^{61} +3.40000 q^{62} -1.63608 q^{63} +1.00000 q^{64} -11.3633 q^{65} -5.80837 q^{66} -10.2588 q^{67} -2.52293 q^{68} +13.4489 q^{69} -1.78616 q^{70} +5.55633 q^{71} +2.94471 q^{72} -1.24252 q^{73} +3.58396 q^{74} -13.0080 q^{75} +1.00000 q^{76} -1.32358 q^{77} +8.61814 q^{78} -1.74139 q^{79} +3.21483 q^{80} -9.16282 q^{81} -0.595664 q^{82} -3.53175 q^{83} +1.35465 q^{84} -8.11078 q^{85} -6.33007 q^{86} +10.5244 q^{87} +2.38226 q^{88} +11.4856 q^{89} +9.46673 q^{90} +1.96386 q^{91} -5.51596 q^{92} -8.28981 q^{93} -4.42185 q^{94} +3.21483 q^{95} -2.43818 q^{96} -18.3341 q^{97} -6.69131 q^{98} +7.01505 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30q + 30q^{2} - 10q^{3} + 30q^{4} - 12q^{5} - 10q^{6} - 15q^{7} + 30q^{8} + 10q^{9} + O(q^{10}) \) \( 30q + 30q^{2} - 10q^{3} + 30q^{4} - 12q^{5} - 10q^{6} - 15q^{7} + 30q^{8} + 10q^{9} - 12q^{10} - 17q^{11} - 10q^{12} - 19q^{13} - 15q^{14} - 8q^{15} + 30q^{16} - 18q^{17} + 10q^{18} + 30q^{19} - 12q^{20} - 14q^{21} - 17q^{22} - 15q^{23} - 10q^{24} - 4q^{25} - 19q^{26} - 37q^{27} - 15q^{28} - 37q^{29} - 8q^{30} - 11q^{31} + 30q^{32} + 6q^{33} - 18q^{34} - 4q^{35} + 10q^{36} - 46q^{37} + 30q^{38} - 12q^{40} - 28q^{41} - 14q^{42} - 61q^{43} - 17q^{44} - 14q^{45} - 15q^{46} - 4q^{47} - 10q^{48} - q^{49} - 4q^{50} - 8q^{51} - 19q^{52} - 19q^{53} - 37q^{54} - 17q^{55} - 15q^{56} - 10q^{57} - 37q^{58} - 6q^{59} - 8q^{60} - 32q^{61} - 11q^{62} - 24q^{63} + 30q^{64} - 24q^{65} + 6q^{66} - 44q^{67} - 18q^{68} - 2q^{69} - 4q^{70} + 10q^{71} + 10q^{72} - 58q^{73} - 46q^{74} - 42q^{75} + 30q^{76} - 32q^{77} - 42q^{79} - 12q^{80} - 38q^{81} - 28q^{82} - 25q^{83} - 14q^{84} - 48q^{85} - 61q^{86} - 15q^{87} - 17q^{88} - 39q^{89} - 14q^{90} - 21q^{91} - 15q^{92} - 45q^{93} - 4q^{94} - 12q^{95} - 10q^{96} - 33q^{97} - q^{98} - 38q^{99} + O(q^{100}) \)

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
\(3\) −2.43818 −1.40768 −0.703841 0.710357i \(-0.748533\pi\)
−0.703841 + 0.710357i \(0.748533\pi\)
\(4\) 1.00000 0.500000
\(5\) 3.21483 1.43771 0.718857 0.695158i \(-0.244665\pi\)
0.718857 + 0.695158i \(0.244665\pi\)
\(6\) −2.43818 −0.995382
\(7\) −0.555600 −0.209997 −0.104999 0.994472i \(-0.533484\pi\)
−0.104999 + 0.994472i \(0.533484\pi\)
\(8\) 1.00000 0.353553
\(9\) 2.94471 0.981569
\(10\) 3.21483 1.01662
\(11\) 2.38226 0.718278 0.359139 0.933284i \(-0.383070\pi\)
0.359139 + 0.933284i \(0.383070\pi\)
\(12\) −2.43818 −0.703841
\(13\) −3.53467 −0.980340 −0.490170 0.871627i \(-0.663065\pi\)
−0.490170 + 0.871627i \(0.663065\pi\)
\(14\) −0.555600 −0.148490
\(15\) −7.83832 −2.02385
\(16\) 1.00000 0.250000
\(17\) −2.52293 −0.611900 −0.305950 0.952048i \(-0.598974\pi\)
−0.305950 + 0.952048i \(0.598974\pi\)
\(18\) 2.94471 0.694074
\(19\) 1.00000 0.229416
\(20\) 3.21483 0.718857
\(21\) 1.35465 0.295609
\(22\) 2.38226 0.507899
\(23\) −5.51596 −1.15016 −0.575079 0.818098i \(-0.695029\pi\)
−0.575079 + 0.818098i \(0.695029\pi\)
\(24\) −2.43818 −0.497691
\(25\) 5.33512 1.06702
\(26\) −3.53467 −0.693205
\(27\) 0.134814 0.0259450
\(28\) −0.555600 −0.104999
\(29\) −4.31652 −0.801557 −0.400779 0.916175i \(-0.631260\pi\)
−0.400779 + 0.916175i \(0.631260\pi\)
\(30\) −7.83832 −1.43107
\(31\) 3.40000 0.610658 0.305329 0.952247i \(-0.401233\pi\)
0.305329 + 0.952247i \(0.401233\pi\)
\(32\) 1.00000 0.176777
\(33\) −5.80837 −1.01111
\(34\) −2.52293 −0.432679
\(35\) −1.78616 −0.301916
\(36\) 2.94471 0.490784
\(37\) 3.58396 0.589199 0.294599 0.955621i \(-0.404814\pi\)
0.294599 + 0.955621i \(0.404814\pi\)
\(38\) 1.00000 0.162221
\(39\) 8.61814 1.38001
\(40\) 3.21483 0.508309
\(41\) −0.595664 −0.0930270 −0.0465135 0.998918i \(-0.514811\pi\)
−0.0465135 + 0.998918i \(0.514811\pi\)
\(42\) 1.35465 0.209027
\(43\) −6.33007 −0.965327 −0.482664 0.875806i \(-0.660331\pi\)
−0.482664 + 0.875806i \(0.660331\pi\)
\(44\) 2.38226 0.359139
\(45\) 9.46673 1.41122
\(46\) −5.51596 −0.813284
\(47\) −4.42185 −0.644994 −0.322497 0.946571i \(-0.604522\pi\)
−0.322497 + 0.946571i \(0.604522\pi\)
\(48\) −2.43818 −0.351921
\(49\) −6.69131 −0.955901
\(50\) 5.33512 0.754500
\(51\) 6.15135 0.861361
\(52\) −3.53467 −0.490170
\(53\) −8.35764 −1.14801 −0.574005 0.818852i \(-0.694611\pi\)
−0.574005 + 0.818852i \(0.694611\pi\)
\(54\) 0.134814 0.0183459
\(55\) 7.65855 1.03268
\(56\) −0.555600 −0.0742452
\(57\) −2.43818 −0.322944
\(58\) −4.31652 −0.566786
\(59\) 2.18069 0.283902 0.141951 0.989874i \(-0.454662\pi\)
0.141951 + 0.989874i \(0.454662\pi\)
\(60\) −7.83832 −1.01192
\(61\) −3.16510 −0.405249 −0.202625 0.979256i \(-0.564947\pi\)
−0.202625 + 0.979256i \(0.564947\pi\)
\(62\) 3.40000 0.431801
\(63\) −1.63608 −0.206127
\(64\) 1.00000 0.125000
\(65\) −11.3633 −1.40945
\(66\) −5.80837 −0.714961
\(67\) −10.2588 −1.25332 −0.626659 0.779294i \(-0.715578\pi\)
−0.626659 + 0.779294i \(0.715578\pi\)
\(68\) −2.52293 −0.305950
\(69\) 13.4489 1.61906
\(70\) −1.78616 −0.213487
\(71\) 5.55633 0.659416 0.329708 0.944083i \(-0.393050\pi\)
0.329708 + 0.944083i \(0.393050\pi\)
\(72\) 2.94471 0.347037
\(73\) −1.24252 −0.145425 −0.0727127 0.997353i \(-0.523166\pi\)
−0.0727127 + 0.997353i \(0.523166\pi\)
\(74\) 3.58396 0.416627
\(75\) −13.0080 −1.50203
\(76\) 1.00000 0.114708
\(77\) −1.32358 −0.150836
\(78\) 8.61814 0.975812
\(79\) −1.74139 −0.195922 −0.0979609 0.995190i \(-0.531232\pi\)
−0.0979609 + 0.995190i \(0.531232\pi\)
\(80\) 3.21483 0.359429
\(81\) −9.16282 −1.01809
\(82\) −0.595664 −0.0657800
\(83\) −3.53175 −0.387660 −0.193830 0.981035i \(-0.562091\pi\)
−0.193830 + 0.981035i \(0.562091\pi\)
\(84\) 1.35465 0.147805
\(85\) −8.11078 −0.879738
\(86\) −6.33007 −0.682590
\(87\) 10.5244 1.12834
\(88\) 2.38226 0.253950
\(89\) 11.4856 1.21747 0.608737 0.793372i \(-0.291677\pi\)
0.608737 + 0.793372i \(0.291677\pi\)
\(90\) 9.46673 0.997881
\(91\) 1.96386 0.205868
\(92\) −5.51596 −0.575079
\(93\) −8.28981 −0.859613
\(94\) −4.42185 −0.456079
\(95\) 3.21483 0.329834
\(96\) −2.43818 −0.248845
\(97\) −18.3341 −1.86155 −0.930773 0.365598i \(-0.880865\pi\)
−0.930773 + 0.365598i \(0.880865\pi\)
\(98\) −6.69131 −0.675924
\(99\) 7.01505 0.705039
\(100\) 5.33512 0.533512
\(101\) −11.6299 −1.15722 −0.578609 0.815605i \(-0.696404\pi\)
−0.578609 + 0.815605i \(0.696404\pi\)
\(102\) 6.15135 0.609074
\(103\) 1.47339 0.145178 0.0725888 0.997362i \(-0.476874\pi\)
0.0725888 + 0.997362i \(0.476874\pi\)
\(104\) −3.53467 −0.346602
\(105\) 4.35497 0.425001
\(106\) −8.35764 −0.811766
\(107\) 7.37019 0.712503 0.356251 0.934390i \(-0.384055\pi\)
0.356251 + 0.934390i \(0.384055\pi\)
\(108\) 0.134814 0.0129725
\(109\) 18.3957 1.76199 0.880995 0.473126i \(-0.156874\pi\)
0.880995 + 0.473126i \(0.156874\pi\)
\(110\) 7.65855 0.730214
\(111\) −8.73832 −0.829405
\(112\) −0.555600 −0.0524993
\(113\) −6.02473 −0.566759 −0.283379 0.959008i \(-0.591456\pi\)
−0.283379 + 0.959008i \(0.591456\pi\)
\(114\) −2.43818 −0.228356
\(115\) −17.7329 −1.65360
\(116\) −4.31652 −0.400779
\(117\) −10.4086 −0.962271
\(118\) 2.18069 0.200749
\(119\) 1.40174 0.128497
\(120\) −7.83832 −0.715537
\(121\) −5.32484 −0.484077
\(122\) −3.16510 −0.286554
\(123\) 1.45233 0.130952
\(124\) 3.40000 0.305329
\(125\) 1.07735 0.0963609
\(126\) −1.63608 −0.145753
\(127\) −4.39807 −0.390266 −0.195133 0.980777i \(-0.562514\pi\)
−0.195133 + 0.980777i \(0.562514\pi\)
\(128\) 1.00000 0.0883883
\(129\) 15.4338 1.35887
\(130\) −11.3633 −0.996631
\(131\) 19.7290 1.72373 0.861865 0.507137i \(-0.169296\pi\)
0.861865 + 0.507137i \(0.169296\pi\)
\(132\) −5.80837 −0.505554
\(133\) −0.555600 −0.0481766
\(134\) −10.2588 −0.886229
\(135\) 0.433405 0.0373015
\(136\) −2.52293 −0.216339
\(137\) −7.15940 −0.611668 −0.305834 0.952085i \(-0.598935\pi\)
−0.305834 + 0.952085i \(0.598935\pi\)
\(138\) 13.4489 1.14485
\(139\) −8.47304 −0.718674 −0.359337 0.933208i \(-0.616997\pi\)
−0.359337 + 0.933208i \(0.616997\pi\)
\(140\) −1.78616 −0.150958
\(141\) 10.7813 0.907946
\(142\) 5.55633 0.466277
\(143\) −8.42049 −0.704157
\(144\) 2.94471 0.245392
\(145\) −13.8769 −1.15241
\(146\) −1.24252 −0.102831
\(147\) 16.3146 1.34561
\(148\) 3.58396 0.294599
\(149\) −2.47766 −0.202978 −0.101489 0.994837i \(-0.532361\pi\)
−0.101489 + 0.994837i \(0.532361\pi\)
\(150\) −13.0080 −1.06210
\(151\) −7.88120 −0.641363 −0.320681 0.947187i \(-0.603912\pi\)
−0.320681 + 0.947187i \(0.603912\pi\)
\(152\) 1.00000 0.0811107
\(153\) −7.42929 −0.600622
\(154\) −1.32358 −0.106657
\(155\) 10.9304 0.877953
\(156\) 8.61814 0.690003
\(157\) −10.2611 −0.818922 −0.409461 0.912328i \(-0.634283\pi\)
−0.409461 + 0.912328i \(0.634283\pi\)
\(158\) −1.74139 −0.138538
\(159\) 20.3774 1.61603
\(160\) 3.21483 0.254154
\(161\) 3.06467 0.241530
\(162\) −9.16282 −0.719899
\(163\) 20.9195 1.63854 0.819271 0.573407i \(-0.194379\pi\)
0.819271 + 0.573407i \(0.194379\pi\)
\(164\) −0.595664 −0.0465135
\(165\) −18.6729 −1.45368
\(166\) −3.53175 −0.274117
\(167\) 11.4320 0.884636 0.442318 0.896858i \(-0.354156\pi\)
0.442318 + 0.896858i \(0.354156\pi\)
\(168\) 1.35465 0.104514
\(169\) −0.506142 −0.0389340
\(170\) −8.11078 −0.622069
\(171\) 2.94471 0.225187
\(172\) −6.33007 −0.482664
\(173\) −22.9979 −1.74850 −0.874249 0.485478i \(-0.838646\pi\)
−0.874249 + 0.485478i \(0.838646\pi\)
\(174\) 10.5244 0.797855
\(175\) −2.96419 −0.224072
\(176\) 2.38226 0.179570
\(177\) −5.31692 −0.399644
\(178\) 11.4856 0.860884
\(179\) 17.5294 1.31021 0.655104 0.755539i \(-0.272625\pi\)
0.655104 + 0.755539i \(0.272625\pi\)
\(180\) 9.46673 0.705608
\(181\) −5.33749 −0.396733 −0.198366 0.980128i \(-0.563564\pi\)
−0.198366 + 0.980128i \(0.563564\pi\)
\(182\) 1.96386 0.145571
\(183\) 7.71707 0.570462
\(184\) −5.51596 −0.406642
\(185\) 11.5218 0.847100
\(186\) −8.28981 −0.607838
\(187\) −6.01027 −0.439514
\(188\) −4.42185 −0.322497
\(189\) −0.0749028 −0.00544838
\(190\) 3.21483 0.233228
\(191\) −7.60800 −0.550495 −0.275248 0.961373i \(-0.588760\pi\)
−0.275248 + 0.961373i \(0.588760\pi\)
\(192\) −2.43818 −0.175960
\(193\) 24.5665 1.76834 0.884169 0.467166i \(-0.154725\pi\)
0.884169 + 0.467166i \(0.154725\pi\)
\(194\) −18.3341 −1.31631
\(195\) 27.7058 1.98406
\(196\) −6.69131 −0.477951
\(197\) 8.07966 0.575652 0.287826 0.957683i \(-0.407068\pi\)
0.287826 + 0.957683i \(0.407068\pi\)
\(198\) 7.01505 0.498538
\(199\) −17.0562 −1.20908 −0.604540 0.796575i \(-0.706643\pi\)
−0.604540 + 0.796575i \(0.706643\pi\)
\(200\) 5.33512 0.377250
\(201\) 25.0129 1.76427
\(202\) −11.6299 −0.818277
\(203\) 2.39826 0.168325
\(204\) 6.15135 0.430680
\(205\) −1.91496 −0.133746
\(206\) 1.47339 0.102656
\(207\) −16.2429 −1.12896
\(208\) −3.53467 −0.245085
\(209\) 2.38226 0.164784
\(210\) 4.35497 0.300521
\(211\) −1.00000 −0.0688428
\(212\) −8.35764 −0.574005
\(213\) −13.5473 −0.928248
\(214\) 7.37019 0.503816
\(215\) −20.3501 −1.38787
\(216\) 0.134814 0.00917295
\(217\) −1.88904 −0.128236
\(218\) 18.3957 1.24591
\(219\) 3.02947 0.204713
\(220\) 7.65855 0.516339
\(221\) 8.91771 0.599870
\(222\) −8.73832 −0.586478
\(223\) 7.63572 0.511326 0.255663 0.966766i \(-0.417706\pi\)
0.255663 + 0.966766i \(0.417706\pi\)
\(224\) −0.555600 −0.0371226
\(225\) 15.7104 1.04736
\(226\) −6.02473 −0.400759
\(227\) 1.64497 0.109180 0.0545902 0.998509i \(-0.482615\pi\)
0.0545902 + 0.998509i \(0.482615\pi\)
\(228\) −2.43818 −0.161472
\(229\) 10.5534 0.697388 0.348694 0.937237i \(-0.386625\pi\)
0.348694 + 0.937237i \(0.386625\pi\)
\(230\) −17.7329 −1.16927
\(231\) 3.22713 0.212329
\(232\) −4.31652 −0.283393
\(233\) −8.49196 −0.556327 −0.278163 0.960534i \(-0.589726\pi\)
−0.278163 + 0.960534i \(0.589726\pi\)
\(234\) −10.4086 −0.680428
\(235\) −14.2155 −0.927317
\(236\) 2.18069 0.141951
\(237\) 4.24582 0.275796
\(238\) 1.40174 0.0908612
\(239\) 18.7735 1.21436 0.607179 0.794565i \(-0.292301\pi\)
0.607179 + 0.794565i \(0.292301\pi\)
\(240\) −7.83832 −0.505961
\(241\) 13.4603 0.867054 0.433527 0.901141i \(-0.357269\pi\)
0.433527 + 0.901141i \(0.357269\pi\)
\(242\) −5.32484 −0.342294
\(243\) 21.9361 1.40720
\(244\) −3.16510 −0.202625
\(245\) −21.5114 −1.37431
\(246\) 1.45233 0.0925974
\(247\) −3.53467 −0.224905
\(248\) 3.40000 0.215900
\(249\) 8.61104 0.545703
\(250\) 1.07735 0.0681375
\(251\) −18.9434 −1.19570 −0.597848 0.801609i \(-0.703978\pi\)
−0.597848 + 0.801609i \(0.703978\pi\)
\(252\) −1.63608 −0.103063
\(253\) −13.1404 −0.826133
\(254\) −4.39807 −0.275959
\(255\) 19.7755 1.23839
\(256\) 1.00000 0.0625000
\(257\) 11.1968 0.698439 0.349219 0.937041i \(-0.386447\pi\)
0.349219 + 0.937041i \(0.386447\pi\)
\(258\) 15.4338 0.960869
\(259\) −1.99125 −0.123730
\(260\) −11.3633 −0.704724
\(261\) −12.7109 −0.786784
\(262\) 19.7290 1.21886
\(263\) −6.27255 −0.386782 −0.193391 0.981122i \(-0.561949\pi\)
−0.193391 + 0.981122i \(0.561949\pi\)
\(264\) −5.80837 −0.357480
\(265\) −26.8684 −1.65051
\(266\) −0.555600 −0.0340660
\(267\) −28.0040 −1.71382
\(268\) −10.2588 −0.626659
\(269\) 4.15129 0.253109 0.126554 0.991960i \(-0.459608\pi\)
0.126554 + 0.991960i \(0.459608\pi\)
\(270\) 0.433405 0.0263762
\(271\) −1.54101 −0.0936096 −0.0468048 0.998904i \(-0.514904\pi\)
−0.0468048 + 0.998904i \(0.514904\pi\)
\(272\) −2.52293 −0.152975
\(273\) −4.78824 −0.289797
\(274\) −7.15940 −0.432515
\(275\) 12.7096 0.766420
\(276\) 13.4489 0.809528
\(277\) −22.8290 −1.37166 −0.685830 0.727762i \(-0.740561\pi\)
−0.685830 + 0.727762i \(0.740561\pi\)
\(278\) −8.47304 −0.508179
\(279\) 10.0120 0.599403
\(280\) −1.78616 −0.106743
\(281\) −26.1261 −1.55855 −0.779275 0.626682i \(-0.784412\pi\)
−0.779275 + 0.626682i \(0.784412\pi\)
\(282\) 10.7813 0.642015
\(283\) 11.2484 0.668649 0.334325 0.942458i \(-0.391492\pi\)
0.334325 + 0.942458i \(0.391492\pi\)
\(284\) 5.55633 0.329708
\(285\) −7.83832 −0.464302
\(286\) −8.42049 −0.497914
\(287\) 0.330951 0.0195354
\(288\) 2.94471 0.173519
\(289\) −10.6348 −0.625578
\(290\) −13.8769 −0.814877
\(291\) 44.7018 2.62047
\(292\) −1.24252 −0.0727127
\(293\) −6.96211 −0.406731 −0.203366 0.979103i \(-0.565188\pi\)
−0.203366 + 0.979103i \(0.565188\pi\)
\(294\) 16.3146 0.951487
\(295\) 7.01056 0.408170
\(296\) 3.58396 0.208313
\(297\) 0.321163 0.0186357
\(298\) −2.47766 −0.143527
\(299\) 19.4971 1.12755
\(300\) −13.0080 −0.751015
\(301\) 3.51699 0.202716
\(302\) −7.88120 −0.453512
\(303\) 28.3558 1.62900
\(304\) 1.00000 0.0573539
\(305\) −10.1752 −0.582633
\(306\) −7.42929 −0.424704
\(307\) −26.9643 −1.53893 −0.769467 0.638687i \(-0.779478\pi\)
−0.769467 + 0.638687i \(0.779478\pi\)
\(308\) −1.32358 −0.0754181
\(309\) −3.59239 −0.204364
\(310\) 10.9304 0.620806
\(311\) 7.80232 0.442429 0.221214 0.975225i \(-0.428998\pi\)
0.221214 + 0.975225i \(0.428998\pi\)
\(312\) 8.61814 0.487906
\(313\) −18.3534 −1.03740 −0.518699 0.854957i \(-0.673583\pi\)
−0.518699 + 0.854957i \(0.673583\pi\)
\(314\) −10.2611 −0.579065
\(315\) −5.25971 −0.296351
\(316\) −1.74139 −0.0979609
\(317\) −10.9492 −0.614967 −0.307484 0.951553i \(-0.599487\pi\)
−0.307484 + 0.951553i \(0.599487\pi\)
\(318\) 20.3774 1.14271
\(319\) −10.2831 −0.575741
\(320\) 3.21483 0.179714
\(321\) −17.9698 −1.00298
\(322\) 3.06467 0.170787
\(323\) −2.52293 −0.140380
\(324\) −9.16282 −0.509046
\(325\) −18.8579 −1.04605
\(326\) 20.9195 1.15862
\(327\) −44.8520 −2.48032
\(328\) −0.595664 −0.0328900
\(329\) 2.45678 0.135447
\(330\) −18.6729 −1.02791
\(331\) 14.3299 0.787644 0.393822 0.919187i \(-0.371153\pi\)
0.393822 + 0.919187i \(0.371153\pi\)
\(332\) −3.53175 −0.193830
\(333\) 10.5537 0.578339
\(334\) 11.4320 0.625532
\(335\) −32.9804 −1.80191
\(336\) 1.35465 0.0739023
\(337\) 10.2285 0.557184 0.278592 0.960410i \(-0.410132\pi\)
0.278592 + 0.960410i \(0.410132\pi\)
\(338\) −0.506142 −0.0275305
\(339\) 14.6894 0.797816
\(340\) −8.11078 −0.439869
\(341\) 8.09969 0.438623
\(342\) 2.94471 0.159232
\(343\) 7.60689 0.410733
\(344\) −6.33007 −0.341295
\(345\) 43.2359 2.32774
\(346\) −22.9979 −1.23637
\(347\) 10.7580 0.577520 0.288760 0.957401i \(-0.406757\pi\)
0.288760 + 0.957401i \(0.406757\pi\)
\(348\) 10.5244 0.564169
\(349\) 19.9423 1.06749 0.533745 0.845646i \(-0.320784\pi\)
0.533745 + 0.845646i \(0.320784\pi\)
\(350\) −2.96419 −0.158443
\(351\) −0.476523 −0.0254349
\(352\) 2.38226 0.126975
\(353\) −11.8768 −0.632141 −0.316070 0.948736i \(-0.602364\pi\)
−0.316070 + 0.948736i \(0.602364\pi\)
\(354\) −5.31692 −0.282591
\(355\) 17.8627 0.948052
\(356\) 11.4856 0.608737
\(357\) −3.41769 −0.180883
\(358\) 17.5294 0.926457
\(359\) −16.6375 −0.878095 −0.439047 0.898464i \(-0.644684\pi\)
−0.439047 + 0.898464i \(0.644684\pi\)
\(360\) 9.46673 0.498940
\(361\) 1.00000 0.0526316
\(362\) −5.33749 −0.280532
\(363\) 12.9829 0.681426
\(364\) 1.96386 0.102934
\(365\) −3.99447 −0.209080
\(366\) 7.71707 0.403378
\(367\) −1.75069 −0.0913851 −0.0456925 0.998956i \(-0.514549\pi\)
−0.0456925 + 0.998956i \(0.514549\pi\)
\(368\) −5.51596 −0.287539
\(369\) −1.75405 −0.0913124
\(370\) 11.5218 0.598990
\(371\) 4.64350 0.241079
\(372\) −8.28981 −0.429807
\(373\) 3.27944 0.169803 0.0849015 0.996389i \(-0.472942\pi\)
0.0849015 + 0.996389i \(0.472942\pi\)
\(374\) −6.01027 −0.310784
\(375\) −2.62677 −0.135646
\(376\) −4.42185 −0.228040
\(377\) 15.2574 0.785798
\(378\) −0.0749028 −0.00385259
\(379\) −1.41328 −0.0725952 −0.0362976 0.999341i \(-0.511556\pi\)
−0.0362976 + 0.999341i \(0.511556\pi\)
\(380\) 3.21483 0.164917
\(381\) 10.7233 0.549370
\(382\) −7.60800 −0.389259
\(383\) −15.0011 −0.766520 −0.383260 0.923641i \(-0.625199\pi\)
−0.383260 + 0.923641i \(0.625199\pi\)
\(384\) −2.43818 −0.124423
\(385\) −4.25509 −0.216859
\(386\) 24.5665 1.25040
\(387\) −18.6402 −0.947535
\(388\) −18.3341 −0.930773
\(389\) −32.4863 −1.64712 −0.823561 0.567227i \(-0.808016\pi\)
−0.823561 + 0.567227i \(0.808016\pi\)
\(390\) 27.7058 1.40294
\(391\) 13.9164 0.703782
\(392\) −6.69131 −0.337962
\(393\) −48.1028 −2.42646
\(394\) 8.07966 0.407047
\(395\) −5.59827 −0.281680
\(396\) 7.01505 0.352520
\(397\) 25.4821 1.27891 0.639456 0.768828i \(-0.279160\pi\)
0.639456 + 0.768828i \(0.279160\pi\)
\(398\) −17.0562 −0.854949
\(399\) 1.35465 0.0678174
\(400\) 5.33512 0.266756
\(401\) 7.02965 0.351044 0.175522 0.984475i \(-0.443839\pi\)
0.175522 + 0.984475i \(0.443839\pi\)
\(402\) 25.0129 1.24753
\(403\) −12.0179 −0.598653
\(404\) −11.6299 −0.578609
\(405\) −29.4569 −1.46372
\(406\) 2.39826 0.119023
\(407\) 8.53791 0.423209
\(408\) 6.15135 0.304537
\(409\) −8.18700 −0.404821 −0.202411 0.979301i \(-0.564878\pi\)
−0.202411 + 0.979301i \(0.564878\pi\)
\(410\) −1.91496 −0.0945729
\(411\) 17.4559 0.861035
\(412\) 1.47339 0.0725888
\(413\) −1.21159 −0.0596186
\(414\) −16.2429 −0.798295
\(415\) −11.3540 −0.557345
\(416\) −3.53467 −0.173301
\(417\) 20.6588 1.01166
\(418\) 2.38226 0.116520
\(419\) −18.0812 −0.883322 −0.441661 0.897182i \(-0.645611\pi\)
−0.441661 + 0.897182i \(0.645611\pi\)
\(420\) 4.35497 0.212501
\(421\) 0.702782 0.0342515 0.0171258 0.999853i \(-0.494548\pi\)
0.0171258 + 0.999853i \(0.494548\pi\)
\(422\) −1.00000 −0.0486792
\(423\) −13.0211 −0.633106
\(424\) −8.35764 −0.405883
\(425\) −13.4601 −0.652912
\(426\) −13.5473 −0.656370
\(427\) 1.75853 0.0851011
\(428\) 7.37019 0.356251
\(429\) 20.5306 0.991229
\(430\) −20.3501 −0.981369
\(431\) −11.9341 −0.574845 −0.287423 0.957804i \(-0.592798\pi\)
−0.287423 + 0.957804i \(0.592798\pi\)
\(432\) 0.134814 0.00648626
\(433\) −10.1960 −0.489988 −0.244994 0.969525i \(-0.578786\pi\)
−0.244994 + 0.969525i \(0.578786\pi\)
\(434\) −1.88904 −0.0906769
\(435\) 33.8342 1.62223
\(436\) 18.3957 0.880995
\(437\) −5.51596 −0.263864
\(438\) 3.02947 0.144754
\(439\) 35.3452 1.68693 0.843467 0.537181i \(-0.180511\pi\)
0.843467 + 0.537181i \(0.180511\pi\)
\(440\) 7.65855 0.365107
\(441\) −19.7039 −0.938283
\(442\) 8.91771 0.424172
\(443\) −19.7234 −0.937087 −0.468543 0.883441i \(-0.655221\pi\)
−0.468543 + 0.883441i \(0.655221\pi\)
\(444\) −8.73832 −0.414702
\(445\) 36.9243 1.75038
\(446\) 7.63572 0.361562
\(447\) 6.04098 0.285728
\(448\) −0.555600 −0.0262496
\(449\) 0.655298 0.0309254 0.0154627 0.999880i \(-0.495078\pi\)
0.0154627 + 0.999880i \(0.495078\pi\)
\(450\) 15.7104 0.740593
\(451\) −1.41902 −0.0668193
\(452\) −6.02473 −0.283379
\(453\) 19.2158 0.902835
\(454\) 1.64497 0.0772021
\(455\) 6.31347 0.295980
\(456\) −2.43818 −0.114178
\(457\) −29.5719 −1.38332 −0.691658 0.722225i \(-0.743119\pi\)
−0.691658 + 0.722225i \(0.743119\pi\)
\(458\) 10.5534 0.493128
\(459\) −0.340127 −0.0158758
\(460\) −17.7329 −0.826799
\(461\) −41.2664 −1.92197 −0.960984 0.276602i \(-0.910791\pi\)
−0.960984 + 0.276602i \(0.910791\pi\)
\(462\) 3.22713 0.150140
\(463\) 5.45347 0.253444 0.126722 0.991938i \(-0.459554\pi\)
0.126722 + 0.991938i \(0.459554\pi\)
\(464\) −4.31652 −0.200389
\(465\) −26.6503 −1.23588
\(466\) −8.49196 −0.393382
\(467\) −4.19102 −0.193937 −0.0969686 0.995287i \(-0.530915\pi\)
−0.0969686 + 0.995287i \(0.530915\pi\)
\(468\) −10.4086 −0.481136
\(469\) 5.69981 0.263193
\(470\) −14.2155 −0.655712
\(471\) 25.0183 1.15278
\(472\) 2.18069 0.100375
\(473\) −15.0799 −0.693373
\(474\) 4.24582 0.195017
\(475\) 5.33512 0.244792
\(476\) 1.40174 0.0642486
\(477\) −24.6108 −1.12685
\(478\) 18.7735 0.858681
\(479\) 39.5495 1.80706 0.903531 0.428524i \(-0.140966\pi\)
0.903531 + 0.428524i \(0.140966\pi\)
\(480\) −7.83832 −0.357769
\(481\) −12.6681 −0.577615
\(482\) 13.4603 0.613099
\(483\) −7.47220 −0.339997
\(484\) −5.32484 −0.242038
\(485\) −58.9410 −2.67637
\(486\) 21.9361 0.995043
\(487\) −30.5964 −1.38646 −0.693228 0.720718i \(-0.743812\pi\)
−0.693228 + 0.720718i \(0.743812\pi\)
\(488\) −3.16510 −0.143277
\(489\) −51.0054 −2.30654
\(490\) −21.5114 −0.971786
\(491\) −8.24892 −0.372269 −0.186134 0.982524i \(-0.559596\pi\)
−0.186134 + 0.982524i \(0.559596\pi\)
\(492\) 1.45233 0.0654762
\(493\) 10.8903 0.490473
\(494\) −3.53467 −0.159032
\(495\) 22.5522 1.01365
\(496\) 3.40000 0.152665
\(497\) −3.08710 −0.138475
\(498\) 8.61104 0.385870
\(499\) −35.0967 −1.57115 −0.785573 0.618769i \(-0.787631\pi\)
−0.785573 + 0.618769i \(0.787631\pi\)
\(500\) 1.07735 0.0481805
\(501\) −27.8733 −1.24529
\(502\) −18.9434 −0.845485
\(503\) −12.5911 −0.561411 −0.280706 0.959794i \(-0.590568\pi\)
−0.280706 + 0.959794i \(0.590568\pi\)
\(504\) −1.63608 −0.0728767
\(505\) −37.3881 −1.66375
\(506\) −13.1404 −0.584164
\(507\) 1.23406 0.0548067
\(508\) −4.39807 −0.195133
\(509\) −4.60359 −0.204050 −0.102025 0.994782i \(-0.532532\pi\)
−0.102025 + 0.994782i \(0.532532\pi\)
\(510\) 19.7755 0.875675
\(511\) 0.690342 0.0305389
\(512\) 1.00000 0.0441942
\(513\) 0.134814 0.00595220
\(514\) 11.1968 0.493871
\(515\) 4.73670 0.208724
\(516\) 15.4338 0.679437
\(517\) −10.5340 −0.463285
\(518\) −1.99125 −0.0874903
\(519\) 56.0730 2.46133
\(520\) −11.3633 −0.498315
\(521\) 12.6991 0.556356 0.278178 0.960529i \(-0.410269\pi\)
0.278178 + 0.960529i \(0.410269\pi\)
\(522\) −12.7109 −0.556340
\(523\) 17.7516 0.776222 0.388111 0.921613i \(-0.373128\pi\)
0.388111 + 0.921613i \(0.373128\pi\)
\(524\) 19.7290 0.861865
\(525\) 7.22722 0.315422
\(526\) −6.27255 −0.273496
\(527\) −8.57796 −0.373662
\(528\) −5.80837 −0.252777
\(529\) 7.42584 0.322863
\(530\) −26.8684 −1.16709
\(531\) 6.42151 0.278670
\(532\) −0.555600 −0.0240883
\(533\) 2.10547 0.0911981
\(534\) −28.0040 −1.21185
\(535\) 23.6939 1.02438
\(536\) −10.2588 −0.443115
\(537\) −42.7397 −1.84436
\(538\) 4.15129 0.178975
\(539\) −15.9404 −0.686603
\(540\) 0.433405 0.0186508
\(541\) −28.0063 −1.20408 −0.602041 0.798465i \(-0.705646\pi\)
−0.602041 + 0.798465i \(0.705646\pi\)
\(542\) −1.54101 −0.0661920
\(543\) 13.0138 0.558474
\(544\) −2.52293 −0.108170
\(545\) 59.1390 2.53324
\(546\) −4.78824 −0.204918
\(547\) −25.6069 −1.09487 −0.547435 0.836848i \(-0.684396\pi\)
−0.547435 + 0.836848i \(0.684396\pi\)
\(548\) −7.15940 −0.305834
\(549\) −9.32028 −0.397780
\(550\) 12.7096 0.541941
\(551\) −4.31652 −0.183890
\(552\) 13.4489 0.572423
\(553\) 0.967517 0.0411430
\(554\) −22.8290 −0.969910
\(555\) −28.0922 −1.19245
\(556\) −8.47304 −0.359337
\(557\) 32.6060 1.38156 0.690781 0.723064i \(-0.257267\pi\)
0.690781 + 0.723064i \(0.257267\pi\)
\(558\) 10.0120 0.423842
\(559\) 22.3747 0.946349
\(560\) −1.78616 −0.0754789
\(561\) 14.6541 0.618697
\(562\) −26.1261 −1.10206
\(563\) −13.8333 −0.583005 −0.291502 0.956570i \(-0.594155\pi\)
−0.291502 + 0.956570i \(0.594155\pi\)
\(564\) 10.7813 0.453973
\(565\) −19.3685 −0.814838
\(566\) 11.2484 0.472806
\(567\) 5.09086 0.213796
\(568\) 5.55633 0.233139
\(569\) −42.6713 −1.78887 −0.894436 0.447195i \(-0.852423\pi\)
−0.894436 + 0.447195i \(0.852423\pi\)
\(570\) −7.83832 −0.328311
\(571\) −13.4909 −0.564575 −0.282288 0.959330i \(-0.591093\pi\)
−0.282288 + 0.959330i \(0.591093\pi\)
\(572\) −8.42049 −0.352078
\(573\) 18.5496 0.774922
\(574\) 0.330951 0.0138136
\(575\) −29.4283 −1.22725
\(576\) 2.94471 0.122696
\(577\) 43.4493 1.80882 0.904408 0.426668i \(-0.140313\pi\)
0.904408 + 0.426668i \(0.140313\pi\)
\(578\) −10.6348 −0.442351
\(579\) −59.8976 −2.48926
\(580\) −13.8769 −0.576205
\(581\) 1.96224 0.0814075
\(582\) 44.7018 1.85295
\(583\) −19.9101 −0.824590
\(584\) −1.24252 −0.0514157
\(585\) −33.4617 −1.38347
\(586\) −6.96211 −0.287602
\(587\) −29.7786 −1.22910 −0.614548 0.788879i \(-0.710662\pi\)
−0.614548 + 0.788879i \(0.710662\pi\)
\(588\) 16.3146 0.672803
\(589\) 3.40000 0.140095
\(590\) 7.01056 0.288620
\(591\) −19.6996 −0.810334
\(592\) 3.58396 0.147300
\(593\) −42.1916 −1.73260 −0.866300 0.499523i \(-0.833508\pi\)
−0.866300 + 0.499523i \(0.833508\pi\)
\(594\) 0.321163 0.0131775
\(595\) 4.50635 0.184742
\(596\) −2.47766 −0.101489
\(597\) 41.5860 1.70200
\(598\) 19.4971 0.797295
\(599\) −15.1049 −0.617171 −0.308585 0.951197i \(-0.599856\pi\)
−0.308585 + 0.951197i \(0.599856\pi\)
\(600\) −13.0080 −0.531048
\(601\) −26.9033 −1.09741 −0.548704 0.836016i \(-0.684879\pi\)
−0.548704 + 0.836016i \(0.684879\pi\)
\(602\) 3.51699 0.143342
\(603\) −30.2093 −1.23022
\(604\) −7.88120 −0.320681
\(605\) −17.1185 −0.695964
\(606\) 28.3558 1.15187
\(607\) −12.1020 −0.491204 −0.245602 0.969371i \(-0.578986\pi\)
−0.245602 + 0.969371i \(0.578986\pi\)
\(608\) 1.00000 0.0405554
\(609\) −5.84737 −0.236948
\(610\) −10.1752 −0.411984
\(611\) 15.6298 0.632313
\(612\) −7.42929 −0.300311
\(613\) 16.9790 0.685775 0.342887 0.939377i \(-0.388595\pi\)
0.342887 + 0.939377i \(0.388595\pi\)
\(614\) −26.9643 −1.08819
\(615\) 4.66900 0.188272
\(616\) −1.32358 −0.0533287
\(617\) −5.37322 −0.216318 −0.108159 0.994134i \(-0.534495\pi\)
−0.108159 + 0.994134i \(0.534495\pi\)
\(618\) −3.59239 −0.144507
\(619\) −24.5802 −0.987962 −0.493981 0.869473i \(-0.664459\pi\)
−0.493981 + 0.869473i \(0.664459\pi\)
\(620\) 10.9304 0.438976
\(621\) −0.743631 −0.0298409
\(622\) 7.80232 0.312844
\(623\) −6.38141 −0.255666
\(624\) 8.61814 0.345002
\(625\) −23.2121 −0.928484
\(626\) −18.3534 −0.733551
\(627\) −5.80837 −0.231964
\(628\) −10.2611 −0.409461
\(629\) −9.04207 −0.360531
\(630\) −5.25971 −0.209552
\(631\) −7.44407 −0.296344 −0.148172 0.988962i \(-0.547339\pi\)
−0.148172 + 0.988962i \(0.547339\pi\)
\(632\) −1.74139 −0.0692688
\(633\) 2.43818 0.0969088
\(634\) −10.9492 −0.434848
\(635\) −14.1390 −0.561091
\(636\) 20.3774 0.808016
\(637\) 23.6515 0.937108
\(638\) −10.2831 −0.407110
\(639\) 16.3618 0.647262
\(640\) 3.21483 0.127077
\(641\) −5.21626 −0.206030 −0.103015 0.994680i \(-0.532849\pi\)
−0.103015 + 0.994680i \(0.532849\pi\)
\(642\) −17.9698 −0.709212
\(643\) 23.4115 0.923259 0.461630 0.887073i \(-0.347265\pi\)
0.461630 + 0.887073i \(0.347265\pi\)
\(644\) 3.06467 0.120765
\(645\) 49.6171 1.95367
\(646\) −2.52293 −0.0992633
\(647\) −13.0262 −0.512111 −0.256056 0.966662i \(-0.582423\pi\)
−0.256056 + 0.966662i \(0.582423\pi\)
\(648\) −9.16282 −0.359950
\(649\) 5.19498 0.203921
\(650\) −18.8579 −0.739666
\(651\) 4.60582 0.180516
\(652\) 20.9195 0.819271
\(653\) 45.9427 1.79788 0.898938 0.438076i \(-0.144340\pi\)
0.898938 + 0.438076i \(0.144340\pi\)
\(654\) −44.8520 −1.75385
\(655\) 63.4253 2.47823
\(656\) −0.595664 −0.0232568
\(657\) −3.65885 −0.142745
\(658\) 2.45678 0.0957753
\(659\) 36.2374 1.41161 0.705805 0.708406i \(-0.250585\pi\)
0.705805 + 0.708406i \(0.250585\pi\)
\(660\) −18.6729 −0.726842
\(661\) 35.9845 1.39964 0.699818 0.714321i \(-0.253264\pi\)
0.699818 + 0.714321i \(0.253264\pi\)
\(662\) 14.3299 0.556948
\(663\) −21.7430 −0.844426
\(664\) −3.53175 −0.137059
\(665\) −1.78616 −0.0692642
\(666\) 10.5537 0.408948
\(667\) 23.8097 0.921917
\(668\) 11.4320 0.442318
\(669\) −18.6172 −0.719784
\(670\) −32.9804 −1.27415
\(671\) −7.54008 −0.291082
\(672\) 1.35465 0.0522568
\(673\) 17.3638 0.669327 0.334664 0.942338i \(-0.391377\pi\)
0.334664 + 0.942338i \(0.391377\pi\)
\(674\) 10.2285 0.393988
\(675\) 0.719250 0.0276840
\(676\) −0.506142 −0.0194670
\(677\) −25.3523 −0.974368 −0.487184 0.873299i \(-0.661976\pi\)
−0.487184 + 0.873299i \(0.661976\pi\)
\(678\) 14.6894 0.564141
\(679\) 10.1864 0.390919
\(680\) −8.11078 −0.311034
\(681\) −4.01072 −0.153691
\(682\) 8.09969 0.310153
\(683\) −35.4377 −1.35598 −0.677992 0.735069i \(-0.737150\pi\)
−0.677992 + 0.735069i \(0.737150\pi\)
\(684\) 2.94471 0.112594
\(685\) −23.0162 −0.879405
\(686\) 7.60689 0.290432
\(687\) −25.7311 −0.981701
\(688\) −6.33007 −0.241332
\(689\) 29.5414 1.12544
\(690\) 43.2359 1.64596
\(691\) 40.3513 1.53503 0.767517 0.641029i \(-0.221492\pi\)
0.767517 + 0.641029i \(0.221492\pi\)
\(692\) −22.9979 −0.874249
\(693\) −3.89756 −0.148056
\(694\) 10.7580 0.408368
\(695\) −27.2394 −1.03325
\(696\) 10.5244 0.398928
\(697\) 1.50282 0.0569232
\(698\) 19.9423 0.754829
\(699\) 20.7049 0.783131
\(700\) −2.96419 −0.112036
\(701\) 0.255443 0.00964796 0.00482398 0.999988i \(-0.498464\pi\)
0.00482398 + 0.999988i \(0.498464\pi\)
\(702\) −0.476523 −0.0179852
\(703\) 3.58396 0.135171
\(704\) 2.38226 0.0897848
\(705\) 34.6599 1.30537
\(706\) −11.8768 −0.446991
\(707\) 6.46157 0.243012
\(708\) −5.31692 −0.199822
\(709\) 40.6477 1.52656 0.763279 0.646070i \(-0.223588\pi\)
0.763279 + 0.646070i \(0.223588\pi\)
\(710\) 17.8627 0.670374
\(711\) −5.12789 −0.192311
\(712\) 11.4856 0.430442
\(713\) −18.7543 −0.702354
\(714\) −3.41769 −0.127904
\(715\) −27.0704 −1.01238
\(716\) 17.5294 0.655104
\(717\) −45.7731 −1.70943
\(718\) −16.6375 −0.620907
\(719\) 7.40322 0.276094 0.138047 0.990426i \(-0.455918\pi\)
0.138047 + 0.990426i \(0.455918\pi\)
\(720\) 9.46673 0.352804
\(721\) −0.818617 −0.0304869
\(722\) 1.00000 0.0372161
\(723\) −32.8186 −1.22054
\(724\) −5.33749 −0.198366
\(725\) −23.0291 −0.855280
\(726\) 12.9829 0.481841
\(727\) −13.2279 −0.490595 −0.245297 0.969448i \(-0.578886\pi\)
−0.245297 + 0.969448i \(0.578886\pi\)
\(728\) 1.96386 0.0727855
\(729\) −25.9957 −0.962805
\(730\) −3.99447 −0.147842
\(731\) 15.9703 0.590684
\(732\) 7.71707 0.285231
\(733\) 15.6254 0.577137 0.288568 0.957459i \(-0.406821\pi\)
0.288568 + 0.957459i \(0.406821\pi\)
\(734\) −1.75069 −0.0646190
\(735\) 52.4486 1.93460
\(736\) −5.51596 −0.203321
\(737\) −24.4392 −0.900231
\(738\) −1.75405 −0.0645676
\(739\) 35.7517 1.31515 0.657574 0.753390i \(-0.271583\pi\)
0.657574 + 0.753390i \(0.271583\pi\)
\(740\) 11.5218 0.423550
\(741\) 8.61814 0.316595
\(742\) 4.64350 0.170468
\(743\) −16.1350 −0.591937 −0.295968 0.955198i \(-0.595642\pi\)
−0.295968 + 0.955198i \(0.595642\pi\)
\(744\) −8.28981 −0.303919
\(745\) −7.96526 −0.291824
\(746\) 3.27944 0.120069
\(747\) −10.4000 −0.380515
\(748\) −6.01027 −0.219757
\(749\) −4.09488 −0.149623
\(750\) −2.62677 −0.0959159
\(751\) 29.7556 1.08580 0.542899 0.839798i \(-0.317327\pi\)
0.542899 + 0.839798i \(0.317327\pi\)
\(752\) −4.42185 −0.161248
\(753\) 46.1874 1.68316
\(754\) 15.2574 0.555643
\(755\) −25.3367 −0.922097
\(756\) −0.0749028 −0.00272419
\(757\) −11.0996 −0.403422 −0.201711 0.979445i \(-0.564650\pi\)
−0.201711 + 0.979445i \(0.564650\pi\)
\(758\) −1.41328 −0.0513325
\(759\) 32.0387 1.16293
\(760\) 3.21483 0.116614
\(761\) 15.9252 0.577288 0.288644 0.957436i \(-0.406796\pi\)
0.288644 + 0.957436i \(0.406796\pi\)
\(762\) 10.7233 0.388463
\(763\) −10.2207 −0.370013
\(764\) −7.60800 −0.275248
\(765\) −23.8839 −0.863523
\(766\) −15.0011 −0.542011
\(767\) −7.70802 −0.278321
\(768\) −2.43818 −0.0879801
\(769\) 39.2638 1.41589 0.707945 0.706268i \(-0.249623\pi\)
0.707945 + 0.706268i \(0.249623\pi\)
\(770\) −4.25509 −0.153343
\(771\) −27.2998 −0.983180
\(772\) 24.5665 0.884169
\(773\) 54.3222 1.95383 0.976917 0.213621i \(-0.0685258\pi\)
0.976917 + 0.213621i \(0.0685258\pi\)
\(774\) −18.6402 −0.670009
\(775\) 18.1394 0.651587
\(776\) −18.3341 −0.658156
\(777\) 4.85501 0.174173
\(778\) −32.4863 −1.16469
\(779\) −0.595664 −0.0213419
\(780\) 27.7058 0.992028
\(781\) 13.2366 0.473644
\(782\) 13.9164 0.497649
\(783\) −0.581928 −0.0207964
\(784\) −6.69131 −0.238975
\(785\) −32.9875 −1.17738
\(786\) −48.1028 −1.71577
\(787\) 38.9818 1.38955 0.694775 0.719227i \(-0.255504\pi\)
0.694775 + 0.719227i \(0.255504\pi\)
\(788\) 8.07966 0.287826
\(789\) 15.2936 0.544466
\(790\) −5.59827 −0.199178
\(791\) 3.34734 0.119018
\(792\) 7.01505 0.249269
\(793\) 11.1876 0.397282
\(794\) 25.4821 0.904327
\(795\) 65.5098 2.32339
\(796\) −17.0562 −0.604540
\(797\) −11.8621 −0.420179 −0.210089 0.977682i \(-0.567375\pi\)
−0.210089 + 0.977682i \(0.567375\pi\)
\(798\) 1.35465 0.0479541
\(799\) 11.1560 0.394672
\(800\) 5.33512 0.188625
\(801\) 33.8218 1.19503
\(802\) 7.02965 0.248226
\(803\) −2.95999 −0.104456
\(804\) 25.0129 0.882136
\(805\) 9.85238 0.347251
\(806\) −12.0179 −0.423311
\(807\) −10.1216 −0.356297
\(808\) −11.6299 −0.409139
\(809\) 23.9974 0.843703 0.421852 0.906665i \(-0.361380\pi\)
0.421852 + 0.906665i \(0.361380\pi\)
\(810\) −29.4569 −1.03501
\(811\) −41.6588 −1.46284 −0.731420 0.681928i \(-0.761142\pi\)
−0.731420 + 0.681928i \(0.761142\pi\)
\(812\) 2.39826 0.0841623
\(813\) 3.75725 0.131772
\(814\) 8.53791 0.299254
\(815\) 67.2526 2.35575
\(816\) 6.15135 0.215340
\(817\) −6.33007 −0.221461
\(818\) −8.18700 −0.286252
\(819\) 5.78299 0.202074
\(820\) −1.91496 −0.0668732
\(821\) −42.8762 −1.49639 −0.748194 0.663480i \(-0.769079\pi\)
−0.748194 + 0.663480i \(0.769079\pi\)
\(822\) 17.4559 0.608843
\(823\) 32.2538 1.12430 0.562149 0.827036i \(-0.309975\pi\)
0.562149 + 0.827036i \(0.309975\pi\)
\(824\) 1.47339 0.0513281
\(825\) −30.9883 −1.07888
\(826\) −1.21159 −0.0421567
\(827\) 46.5272 1.61791 0.808954 0.587871i \(-0.200034\pi\)
0.808954 + 0.587871i \(0.200034\pi\)
\(828\) −16.2429 −0.564480
\(829\) 21.6542 0.752081 0.376041 0.926603i \(-0.377285\pi\)
0.376041 + 0.926603i \(0.377285\pi\)
\(830\) −11.3540 −0.394102
\(831\) 55.6611 1.93086
\(832\) −3.53467 −0.122542
\(833\) 16.8817 0.584916
\(834\) 20.6588 0.715355
\(835\) 36.7520 1.27185
\(836\) 2.38226 0.0823921
\(837\) 0.458369 0.0158436
\(838\) −18.0812 −0.624603
\(839\) 33.0977 1.14266 0.571330 0.820720i \(-0.306428\pi\)
0.571330 + 0.820720i \(0.306428\pi\)
\(840\) 4.35497 0.150261
\(841\) −10.3677 −0.357506
\(842\) 0.702782 0.0242195
\(843\) 63.6999 2.19394
\(844\) −1.00000 −0.0344214
\(845\) −1.62716 −0.0559760
\(846\) −13.0211 −0.447673
\(847\) 2.95848 0.101655
\(848\) −8.35764 −0.287002
\(849\) −27.4256 −0.941246
\(850\) −13.4601 −0.461678
\(851\) −19.7690 −0.677672
\(852\) −13.5473 −0.464124
\(853\) 4.84412 0.165859 0.0829297 0.996555i \(-0.473572\pi\)
0.0829297 + 0.996555i \(0.473572\pi\)
\(854\) 1.75853 0.0601756
\(855\) 9.46673 0.323755
\(856\) 7.37019 0.251908
\(857\) −34.6528 −1.18372 −0.591859 0.806042i \(-0.701606\pi\)
−0.591859 + 0.806042i \(0.701606\pi\)
\(858\) 20.5306 0.700904
\(859\) 43.9939 1.50105 0.750527 0.660840i \(-0.229800\pi\)
0.750527 + 0.660840i \(0.229800\pi\)
\(860\) −20.3501 −0.693933
\(861\) −0.806916 −0.0274996
\(862\) −11.9341 −0.406477
\(863\) 7.82514 0.266371 0.133185 0.991091i \(-0.457479\pi\)
0.133185 + 0.991091i \(0.457479\pi\)
\(864\) 0.134814 0.00458648
\(865\) −73.9343 −2.51384
\(866\) −10.1960 −0.346474
\(867\) 25.9296 0.880615
\(868\) −1.88904 −0.0641182
\(869\) −4.14845 −0.140726
\(870\) 33.8342 1.14709
\(871\) 36.2616 1.22868
\(872\) 18.3957 0.622957
\(873\) −53.9886 −1.82724
\(874\) −5.51596 −0.186580
\(875\) −0.598574 −0.0202355
\(876\) 3.02947 0.102356
\(877\) 14.8732 0.502231 0.251116 0.967957i \(-0.419203\pi\)
0.251116 + 0.967957i \(0.419203\pi\)
\(878\) 35.3452 1.19284
\(879\) 16.9749 0.572548
\(880\) 7.65855 0.258170
\(881\) 3.05226 0.102833 0.0514167 0.998677i \(-0.483626\pi\)
0.0514167 + 0.998677i \(0.483626\pi\)
\(882\) −19.7039 −0.663466
\(883\) 20.7317 0.697678 0.348839 0.937183i \(-0.386576\pi\)
0.348839 + 0.937183i \(0.386576\pi\)
\(884\) 8.91771 0.299935
\(885\) −17.0930 −0.574574
\(886\) −19.7234 −0.662620
\(887\) 36.5532 1.22734 0.613669 0.789563i \(-0.289693\pi\)
0.613669 + 0.789563i \(0.289693\pi\)
\(888\) −8.73832 −0.293239
\(889\) 2.44357 0.0819546
\(890\) 36.9243 1.23771
\(891\) −21.8282 −0.731273
\(892\) 7.63572 0.255663
\(893\) −4.42185 −0.147972
\(894\) 6.04098 0.202041
\(895\) 56.3539 1.88370
\(896\) −0.555600 −0.0185613
\(897\) −47.5373 −1.58723
\(898\) 0.655298 0.0218676
\(899\) −14.6762 −0.489478
\(900\) 15.7104 0.523679
\(901\) 21.0857 0.702467
\(902\) −1.41902 −0.0472484
\(903\) −8.57504 −0.285359
\(904\) −6.02473 −0.200380
\(905\) −17.1591 −0.570389
\(906\) 19.2158 0.638401
\(907\) −5.41768 −0.179891 −0.0899455 0.995947i \(-0.528669\pi\)
−0.0899455 + 0.995947i \(0.528669\pi\)
\(908\) 1.64497 0.0545902
\(909\) −34.2467 −1.13589
\(910\) 6.31347 0.209289
\(911\) 37.0183 1.22647 0.613236 0.789900i \(-0.289868\pi\)
0.613236 + 0.789900i \(0.289868\pi\)
\(912\) −2.43818 −0.0807361
\(913\) −8.41355 −0.278448
\(914\) −29.5719 −0.978152
\(915\) 24.8090 0.820162
\(916\) 10.5534 0.348694
\(917\) −10.9614 −0.361978
\(918\) −0.340127 −0.0112259
\(919\) −56.2467 −1.85541 −0.927704 0.373318i \(-0.878220\pi\)
−0.927704 + 0.373318i \(0.878220\pi\)
\(920\) −17.7329 −0.584635
\(921\) 65.7437 2.16633
\(922\) −41.2664 −1.35904
\(923\) −19.6398 −0.646451
\(924\) 3.22713 0.106165
\(925\) 19.1208 0.628689
\(926\) 5.45347 0.179212
\(927\) 4.33871 0.142502
\(928\) −4.31652 −0.141697
\(929\) 41.8430 1.37282 0.686412 0.727213i \(-0.259185\pi\)
0.686412 + 0.727213i \(0.259185\pi\)
\(930\) −26.6503 −0.873898
\(931\) −6.69131 −0.219299
\(932\) −8.49196 −0.278163
\(933\) −19.0234 −0.622799
\(934\) −4.19102 −0.137134
\(935\) −19.3220 −0.631896
\(936\) −10.4086 −0.340214
\(937\) −6.44950 −0.210696 −0.105348 0.994435i \(-0.533596\pi\)
−0.105348 + 0.994435i \(0.533596\pi\)
\(938\) 5.69981 0.186106
\(939\) 44.7489 1.46033
\(940\) −14.2155 −0.463658
\(941\) −8.16381 −0.266133 −0.133066 0.991107i \(-0.542482\pi\)
−0.133066 + 0.991107i \(0.542482\pi\)
\(942\) 25.0183 0.815140
\(943\) 3.28566 0.106996
\(944\) 2.18069 0.0709756
\(945\) −0.240800 −0.00783321
\(946\) −15.0799 −0.490289
\(947\) 28.3579 0.921509 0.460755 0.887528i \(-0.347579\pi\)
0.460755 + 0.887528i \(0.347579\pi\)
\(948\) 4.24582 0.137898
\(949\) 4.39188 0.142566
\(950\) 5.33512 0.173094
\(951\) 26.6960 0.865679
\(952\) 1.40174 0.0454306
\(953\) −20.8720 −0.676110 −0.338055 0.941126i \(-0.609769\pi\)
−0.338055 + 0.941126i \(0.609769\pi\)
\(954\) −24.6108 −0.796804
\(955\) −24.4584 −0.791455
\(956\) 18.7735 0.607179
\(957\) 25.0719 0.810460
\(958\) 39.5495 1.27779
\(959\) 3.97776 0.128449
\(960\) −7.83832 −0.252981
\(961\) −19.4400 −0.627096
\(962\) −12.6681 −0.408436
\(963\) 21.7030 0.699371
\(964\) 13.4603 0.433527
\(965\) 78.9772 2.54237
\(966\) −7.47220 −0.240414
\(967\) −18.4603 −0.593644 −0.296822 0.954933i \(-0.595927\pi\)
−0.296822 + 0.954933i \(0.595927\pi\)
\(968\) −5.32484 −0.171147
\(969\) 6.15135 0.197610
\(970\) −58.9410 −1.89248
\(971\) −12.4620 −0.399924 −0.199962 0.979804i \(-0.564082\pi\)
−0.199962 + 0.979804i \(0.564082\pi\)
\(972\) 21.9361 0.703602
\(973\) 4.70762 0.150919
\(974\) −30.5964 −0.980373
\(975\) 45.9788 1.47250
\(976\) −3.16510 −0.101312
\(977\) 46.1162 1.47539 0.737693 0.675136i \(-0.235915\pi\)
0.737693 + 0.675136i \(0.235915\pi\)
\(978\) −51.0054 −1.63097
\(979\) 27.3617 0.874485
\(980\) −21.5114 −0.687157
\(981\) 54.1700 1.72951
\(982\) −8.24892 −0.263234
\(983\) 23.2368 0.741138 0.370569 0.928805i \(-0.379163\pi\)
0.370569 + 0.928805i \(0.379163\pi\)
\(984\) 1.45233 0.0462987
\(985\) 25.9747 0.827623
\(986\) 10.8903 0.346817
\(987\) −5.99007 −0.190666
\(988\) −3.53467 −0.112453
\(989\) 34.9165 1.11028
\(990\) 22.5522 0.716756
\(991\) −7.61690 −0.241959 −0.120979 0.992655i \(-0.538603\pi\)
−0.120979 + 0.992655i \(0.538603\pi\)
\(992\) 3.40000 0.107950
\(993\) −34.9389 −1.10875
\(994\) −3.08710 −0.0979168
\(995\) −54.8327 −1.73831
\(996\) 8.61104 0.272851
\(997\) 33.4410 1.05909 0.529544 0.848282i \(-0.322363\pi\)
0.529544 + 0.848282i \(0.322363\pi\)
\(998\) −35.0967 −1.11097
\(999\) 0.483169 0.0152868
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 \(a_p\))