Properties

Label 8002.2.a.e.1.13
Level 8002
Weight 2
Character 8002.1
Self dual Yes
Analytic conductor 63.896
Analytic rank 0
Dimension 77
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 8002 = 2 \cdot 4001 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8002.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.8962916974\)
Analytic rank: \(0\)
Dimension: \(77\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Character \(\chi\) = 8002.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -2.19428 q^{3} +1.00000 q^{4} +0.0495220 q^{5} +2.19428 q^{6} +1.71879 q^{7} -1.00000 q^{8} +1.81487 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -2.19428 q^{3} +1.00000 q^{4} +0.0495220 q^{5} +2.19428 q^{6} +1.71879 q^{7} -1.00000 q^{8} +1.81487 q^{9} -0.0495220 q^{10} -4.48853 q^{11} -2.19428 q^{12} +0.149594 q^{13} -1.71879 q^{14} -0.108665 q^{15} +1.00000 q^{16} -0.611407 q^{17} -1.81487 q^{18} -6.46347 q^{19} +0.0495220 q^{20} -3.77151 q^{21} +4.48853 q^{22} -3.90677 q^{23} +2.19428 q^{24} -4.99755 q^{25} -0.149594 q^{26} +2.60050 q^{27} +1.71879 q^{28} -4.90060 q^{29} +0.108665 q^{30} -6.63863 q^{31} -1.00000 q^{32} +9.84910 q^{33} +0.611407 q^{34} +0.0851178 q^{35} +1.81487 q^{36} -8.78763 q^{37} +6.46347 q^{38} -0.328251 q^{39} -0.0495220 q^{40} +6.85972 q^{41} +3.77151 q^{42} +2.76613 q^{43} -4.48853 q^{44} +0.0898762 q^{45} +3.90677 q^{46} -6.87998 q^{47} -2.19428 q^{48} -4.04577 q^{49} +4.99755 q^{50} +1.34160 q^{51} +0.149594 q^{52} -9.77518 q^{53} -2.60050 q^{54} -0.222281 q^{55} -1.71879 q^{56} +14.1827 q^{57} +4.90060 q^{58} +1.30319 q^{59} -0.108665 q^{60} -2.05964 q^{61} +6.63863 q^{62} +3.11938 q^{63} +1.00000 q^{64} +0.00740819 q^{65} -9.84910 q^{66} -6.84709 q^{67} -0.611407 q^{68} +8.57257 q^{69} -0.0851178 q^{70} +15.9726 q^{71} -1.81487 q^{72} -12.9027 q^{73} +8.78763 q^{74} +10.9660 q^{75} -6.46347 q^{76} -7.71483 q^{77} +0.328251 q^{78} +11.9686 q^{79} +0.0495220 q^{80} -11.1509 q^{81} -6.85972 q^{82} +4.22776 q^{83} -3.77151 q^{84} -0.0302781 q^{85} -2.76613 q^{86} +10.7533 q^{87} +4.48853 q^{88} +5.68357 q^{89} -0.0898762 q^{90} +0.257120 q^{91} -3.90677 q^{92} +14.5670 q^{93} +6.87998 q^{94} -0.320084 q^{95} +2.19428 q^{96} +1.41020 q^{97} +4.04577 q^{98} -8.14612 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 77q - 77q^{2} + 10q^{3} + 77q^{4} + 18q^{5} - 10q^{6} + 21q^{7} - 77q^{8} + 71q^{9} + O(q^{10}) \) \( 77q - 77q^{2} + 10q^{3} + 77q^{4} + 18q^{5} - 10q^{6} + 21q^{7} - 77q^{8} + 71q^{9} - 18q^{10} + 30q^{11} + 10q^{12} - 2q^{13} - 21q^{14} + 21q^{15} + 77q^{16} + 60q^{17} - 71q^{18} - 3q^{19} + 18q^{20} + 10q^{21} - 30q^{22} + 53q^{23} - 10q^{24} + 59q^{25} + 2q^{26} + 43q^{27} + 21q^{28} + 30q^{29} - 21q^{30} + 22q^{31} - 77q^{32} + 31q^{33} - 60q^{34} + 41q^{35} + 71q^{36} - 3q^{37} + 3q^{38} + 44q^{39} - 18q^{40} + 48q^{41} - 10q^{42} + 21q^{43} + 30q^{44} + 33q^{45} - 53q^{46} + 107q^{47} + 10q^{48} + 24q^{49} - 59q^{50} + 18q^{51} - 2q^{52} + 42q^{53} - 43q^{54} + 49q^{55} - 21q^{56} + 32q^{57} - 30q^{58} + 42q^{59} + 21q^{60} - 31q^{61} - 22q^{62} + 109q^{63} + 77q^{64} + 39q^{65} - 31q^{66} - q^{67} + 60q^{68} - 33q^{69} - 41q^{70} + 58q^{71} - 71q^{72} + 35q^{73} + 3q^{74} + 34q^{75} - 3q^{76} + 86q^{77} - 44q^{78} + 25q^{79} + 18q^{80} + 53q^{81} - 48q^{82} + 107q^{83} + 10q^{84} + 21q^{85} - 21q^{86} + 100q^{87} - 30q^{88} + 34q^{89} - 33q^{90} - 51q^{91} + 53q^{92} + 48q^{93} - 107q^{94} + 118q^{95} - 10q^{96} - 13q^{97} - 24q^{98} + 63q^{99} + O(q^{100}) \)

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
\(3\) −2.19428 −1.26687 −0.633435 0.773796i \(-0.718355\pi\)
−0.633435 + 0.773796i \(0.718355\pi\)
\(4\) 1.00000 0.500000
\(5\) 0.0495220 0.0221469 0.0110735 0.999939i \(-0.496475\pi\)
0.0110735 + 0.999939i \(0.496475\pi\)
\(6\) 2.19428 0.895812
\(7\) 1.71879 0.649641 0.324820 0.945776i \(-0.394696\pi\)
0.324820 + 0.945776i \(0.394696\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.81487 0.604958
\(10\) −0.0495220 −0.0156602
\(11\) −4.48853 −1.35334 −0.676671 0.736285i \(-0.736578\pi\)
−0.676671 + 0.736285i \(0.736578\pi\)
\(12\) −2.19428 −0.633435
\(13\) 0.149594 0.0414899 0.0207449 0.999785i \(-0.493396\pi\)
0.0207449 + 0.999785i \(0.493396\pi\)
\(14\) −1.71879 −0.459365
\(15\) −0.108665 −0.0280572
\(16\) 1.00000 0.250000
\(17\) −0.611407 −0.148288 −0.0741440 0.997248i \(-0.523622\pi\)
−0.0741440 + 0.997248i \(0.523622\pi\)
\(18\) −1.81487 −0.427770
\(19\) −6.46347 −1.48282 −0.741411 0.671052i \(-0.765843\pi\)
−0.741411 + 0.671052i \(0.765843\pi\)
\(20\) 0.0495220 0.0110735
\(21\) −3.77151 −0.823010
\(22\) 4.48853 0.956958
\(23\) −3.90677 −0.814619 −0.407309 0.913290i \(-0.633533\pi\)
−0.407309 + 0.913290i \(0.633533\pi\)
\(24\) 2.19428 0.447906
\(25\) −4.99755 −0.999510
\(26\) −0.149594 −0.0293378
\(27\) 2.60050 0.500467
\(28\) 1.71879 0.324820
\(29\) −4.90060 −0.910018 −0.455009 0.890487i \(-0.650364\pi\)
−0.455009 + 0.890487i \(0.650364\pi\)
\(30\) 0.108665 0.0198395
\(31\) −6.63863 −1.19233 −0.596167 0.802861i \(-0.703310\pi\)
−0.596167 + 0.802861i \(0.703310\pi\)
\(32\) −1.00000 −0.176777
\(33\) 9.84910 1.71451
\(34\) 0.611407 0.104855
\(35\) 0.0851178 0.0143875
\(36\) 1.81487 0.302479
\(37\) −8.78763 −1.44468 −0.722339 0.691539i \(-0.756933\pi\)
−0.722339 + 0.691539i \(0.756933\pi\)
\(38\) 6.46347 1.04851
\(39\) −0.328251 −0.0525622
\(40\) −0.0495220 −0.00783012
\(41\) 6.85972 1.07131 0.535654 0.844437i \(-0.320065\pi\)
0.535654 + 0.844437i \(0.320065\pi\)
\(42\) 3.77151 0.581956
\(43\) 2.76613 0.421832 0.210916 0.977504i \(-0.432355\pi\)
0.210916 + 0.977504i \(0.432355\pi\)
\(44\) −4.48853 −0.676671
\(45\) 0.0898762 0.0133980
\(46\) 3.90677 0.576022
\(47\) −6.87998 −1.00355 −0.501774 0.864999i \(-0.667319\pi\)
−0.501774 + 0.864999i \(0.667319\pi\)
\(48\) −2.19428 −0.316717
\(49\) −4.04577 −0.577967
\(50\) 4.99755 0.706760
\(51\) 1.34160 0.187862
\(52\) 0.149594 0.0207449
\(53\) −9.77518 −1.34272 −0.671362 0.741129i \(-0.734290\pi\)
−0.671362 + 0.741129i \(0.734290\pi\)
\(54\) −2.60050 −0.353883
\(55\) −0.222281 −0.0299724
\(56\) −1.71879 −0.229683
\(57\) 14.1827 1.87854
\(58\) 4.90060 0.643480
\(59\) 1.30319 0.169661 0.0848303 0.996395i \(-0.472965\pi\)
0.0848303 + 0.996395i \(0.472965\pi\)
\(60\) −0.108665 −0.0140286
\(61\) −2.05964 −0.263709 −0.131855 0.991269i \(-0.542093\pi\)
−0.131855 + 0.991269i \(0.542093\pi\)
\(62\) 6.63863 0.843107
\(63\) 3.11938 0.393005
\(64\) 1.00000 0.125000
\(65\) 0.00740819 0.000918872 0
\(66\) −9.84910 −1.21234
\(67\) −6.84709 −0.836506 −0.418253 0.908331i \(-0.637357\pi\)
−0.418253 + 0.908331i \(0.637357\pi\)
\(68\) −0.611407 −0.0741440
\(69\) 8.57257 1.03202
\(70\) −0.0851178 −0.0101735
\(71\) 15.9726 1.89560 0.947800 0.318864i \(-0.103301\pi\)
0.947800 + 0.318864i \(0.103301\pi\)
\(72\) −1.81487 −0.213885
\(73\) −12.9027 −1.51015 −0.755075 0.655639i \(-0.772400\pi\)
−0.755075 + 0.655639i \(0.772400\pi\)
\(74\) 8.78763 1.02154
\(75\) 10.9660 1.26625
\(76\) −6.46347 −0.741411
\(77\) −7.71483 −0.879187
\(78\) 0.328251 0.0371671
\(79\) 11.9686 1.34657 0.673285 0.739383i \(-0.264883\pi\)
0.673285 + 0.739383i \(0.264883\pi\)
\(80\) 0.0495220 0.00553673
\(81\) −11.1509 −1.23898
\(82\) −6.85972 −0.757530
\(83\) 4.22776 0.464057 0.232029 0.972709i \(-0.425464\pi\)
0.232029 + 0.972709i \(0.425464\pi\)
\(84\) −3.77151 −0.411505
\(85\) −0.0302781 −0.00328412
\(86\) −2.76613 −0.298280
\(87\) 10.7533 1.15287
\(88\) 4.48853 0.478479
\(89\) 5.68357 0.602457 0.301229 0.953552i \(-0.402603\pi\)
0.301229 + 0.953552i \(0.402603\pi\)
\(90\) −0.0898762 −0.00947378
\(91\) 0.257120 0.0269535
\(92\) −3.90677 −0.407309
\(93\) 14.5670 1.51053
\(94\) 6.87998 0.709616
\(95\) −0.320084 −0.0328399
\(96\) 2.19428 0.223953
\(97\) 1.41020 0.143184 0.0715922 0.997434i \(-0.477192\pi\)
0.0715922 + 0.997434i \(0.477192\pi\)
\(98\) 4.04577 0.408684
\(99\) −8.14612 −0.818716
\(100\) −4.99755 −0.499755
\(101\) −12.7606 −1.26973 −0.634864 0.772624i \(-0.718944\pi\)
−0.634864 + 0.772624i \(0.718944\pi\)
\(102\) −1.34160 −0.132838
\(103\) 11.7694 1.15967 0.579836 0.814733i \(-0.303117\pi\)
0.579836 + 0.814733i \(0.303117\pi\)
\(104\) −0.149594 −0.0146689
\(105\) −0.186772 −0.0182271
\(106\) 9.77518 0.949450
\(107\) −7.35234 −0.710778 −0.355389 0.934719i \(-0.615652\pi\)
−0.355389 + 0.934719i \(0.615652\pi\)
\(108\) 2.60050 0.250233
\(109\) −0.814455 −0.0780106 −0.0390053 0.999239i \(-0.512419\pi\)
−0.0390053 + 0.999239i \(0.512419\pi\)
\(110\) 0.222281 0.0211937
\(111\) 19.2825 1.83022
\(112\) 1.71879 0.162410
\(113\) 10.1353 0.953447 0.476724 0.879053i \(-0.341824\pi\)
0.476724 + 0.879053i \(0.341824\pi\)
\(114\) −14.1827 −1.32833
\(115\) −0.193471 −0.0180413
\(116\) −4.90060 −0.455009
\(117\) 0.271494 0.0250996
\(118\) −1.30319 −0.119968
\(119\) −1.05088 −0.0963340
\(120\) 0.108665 0.00991973
\(121\) 9.14690 0.831536
\(122\) 2.05964 0.186471
\(123\) −15.0522 −1.35721
\(124\) −6.63863 −0.596167
\(125\) −0.495099 −0.0442830
\(126\) −3.11938 −0.277897
\(127\) 4.88085 0.433106 0.216553 0.976271i \(-0.430519\pi\)
0.216553 + 0.976271i \(0.430519\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −6.06968 −0.534405
\(130\) −0.00740819 −0.000649741 0
\(131\) −0.0816734 −0.00713584 −0.00356792 0.999994i \(-0.501136\pi\)
−0.00356792 + 0.999994i \(0.501136\pi\)
\(132\) 9.84910 0.857254
\(133\) −11.1093 −0.963301
\(134\) 6.84709 0.591499
\(135\) 0.128782 0.0110838
\(136\) 0.611407 0.0524277
\(137\) 4.22433 0.360909 0.180454 0.983583i \(-0.442243\pi\)
0.180454 + 0.983583i \(0.442243\pi\)
\(138\) −8.57257 −0.729745
\(139\) 2.90677 0.246549 0.123274 0.992373i \(-0.460660\pi\)
0.123274 + 0.992373i \(0.460660\pi\)
\(140\) 0.0851178 0.00719377
\(141\) 15.0966 1.27136
\(142\) −15.9726 −1.34039
\(143\) −0.671456 −0.0561500
\(144\) 1.81487 0.151240
\(145\) −0.242687 −0.0201541
\(146\) 12.9027 1.06784
\(147\) 8.87756 0.732209
\(148\) −8.78763 −0.722339
\(149\) 16.1227 1.32082 0.660410 0.750905i \(-0.270383\pi\)
0.660410 + 0.750905i \(0.270383\pi\)
\(150\) −10.9660 −0.895373
\(151\) −9.26507 −0.753981 −0.376991 0.926217i \(-0.623041\pi\)
−0.376991 + 0.926217i \(0.623041\pi\)
\(152\) 6.46347 0.524256
\(153\) −1.10963 −0.0897080
\(154\) 7.71483 0.621679
\(155\) −0.328758 −0.0264065
\(156\) −0.328251 −0.0262811
\(157\) −9.73885 −0.777245 −0.388622 0.921397i \(-0.627049\pi\)
−0.388622 + 0.921397i \(0.627049\pi\)
\(158\) −11.9686 −0.952168
\(159\) 21.4495 1.70106
\(160\) −0.0495220 −0.00391506
\(161\) −6.71492 −0.529210
\(162\) 11.1509 0.876094
\(163\) 2.70166 0.211610 0.105805 0.994387i \(-0.466258\pi\)
0.105805 + 0.994387i \(0.466258\pi\)
\(164\) 6.85972 0.535654
\(165\) 0.487747 0.0379711
\(166\) −4.22776 −0.328138
\(167\) 20.6077 1.59467 0.797335 0.603538i \(-0.206243\pi\)
0.797335 + 0.603538i \(0.206243\pi\)
\(168\) 3.77151 0.290978
\(169\) −12.9776 −0.998279
\(170\) 0.0302781 0.00232222
\(171\) −11.7304 −0.897045
\(172\) 2.76613 0.210916
\(173\) −19.6845 −1.49659 −0.748294 0.663368i \(-0.769127\pi\)
−0.748294 + 0.663368i \(0.769127\pi\)
\(174\) −10.7533 −0.815205
\(175\) −8.58972 −0.649322
\(176\) −4.48853 −0.338336
\(177\) −2.85956 −0.214938
\(178\) −5.68357 −0.426002
\(179\) −11.0404 −0.825200 −0.412600 0.910912i \(-0.635379\pi\)
−0.412600 + 0.910912i \(0.635379\pi\)
\(180\) 0.0898762 0.00669898
\(181\) −7.43443 −0.552597 −0.276298 0.961072i \(-0.589108\pi\)
−0.276298 + 0.961072i \(0.589108\pi\)
\(182\) −0.257120 −0.0190590
\(183\) 4.51942 0.334085
\(184\) 3.90677 0.288011
\(185\) −0.435181 −0.0319951
\(186\) −14.5670 −1.06811
\(187\) 2.74432 0.200685
\(188\) −6.87998 −0.501774
\(189\) 4.46971 0.325123
\(190\) 0.320084 0.0232213
\(191\) 9.96951 0.721368 0.360684 0.932688i \(-0.382543\pi\)
0.360684 + 0.932688i \(0.382543\pi\)
\(192\) −2.19428 −0.158359
\(193\) −1.90500 −0.137125 −0.0685623 0.997647i \(-0.521841\pi\)
−0.0685623 + 0.997647i \(0.521841\pi\)
\(194\) −1.41020 −0.101247
\(195\) −0.0162556 −0.00116409
\(196\) −4.04577 −0.288983
\(197\) −8.29086 −0.590699 −0.295350 0.955389i \(-0.595436\pi\)
−0.295350 + 0.955389i \(0.595436\pi\)
\(198\) 8.14612 0.578919
\(199\) −10.6771 −0.756877 −0.378439 0.925626i \(-0.623539\pi\)
−0.378439 + 0.925626i \(0.623539\pi\)
\(200\) 4.99755 0.353380
\(201\) 15.0245 1.05974
\(202\) 12.7606 0.897834
\(203\) −8.42309 −0.591185
\(204\) 1.34160 0.0939308
\(205\) 0.339707 0.0237262
\(206\) −11.7694 −0.820012
\(207\) −7.09030 −0.492810
\(208\) 0.149594 0.0103725
\(209\) 29.0115 2.00677
\(210\) 0.186772 0.0128885
\(211\) 10.3373 0.711649 0.355825 0.934553i \(-0.384200\pi\)
0.355825 + 0.934553i \(0.384200\pi\)
\(212\) −9.77518 −0.671362
\(213\) −35.0484 −2.40148
\(214\) 7.35234 0.502596
\(215\) 0.136985 0.00934227
\(216\) −2.60050 −0.176942
\(217\) −11.4104 −0.774588
\(218\) 0.814455 0.0551619
\(219\) 28.3122 1.91316
\(220\) −0.222281 −0.0149862
\(221\) −0.0914627 −0.00615245
\(222\) −19.2825 −1.29416
\(223\) −26.1261 −1.74954 −0.874768 0.484543i \(-0.838986\pi\)
−0.874768 + 0.484543i \(0.838986\pi\)
\(224\) −1.71879 −0.114841
\(225\) −9.06992 −0.604661
\(226\) −10.1353 −0.674189
\(227\) 4.18780 0.277954 0.138977 0.990296i \(-0.455619\pi\)
0.138977 + 0.990296i \(0.455619\pi\)
\(228\) 14.1827 0.939270
\(229\) −5.14274 −0.339842 −0.169921 0.985458i \(-0.554351\pi\)
−0.169921 + 0.985458i \(0.554351\pi\)
\(230\) 0.193471 0.0127571
\(231\) 16.9285 1.11381
\(232\) 4.90060 0.321740
\(233\) −17.6336 −1.15522 −0.577609 0.816313i \(-0.696014\pi\)
−0.577609 + 0.816313i \(0.696014\pi\)
\(234\) −0.271494 −0.0177481
\(235\) −0.340710 −0.0222255
\(236\) 1.30319 0.0848303
\(237\) −26.2624 −1.70593
\(238\) 1.05088 0.0681184
\(239\) 2.86053 0.185032 0.0925160 0.995711i \(-0.470509\pi\)
0.0925160 + 0.995711i \(0.470509\pi\)
\(240\) −0.108665 −0.00701431
\(241\) −8.97528 −0.578149 −0.289074 0.957307i \(-0.593347\pi\)
−0.289074 + 0.957307i \(0.593347\pi\)
\(242\) −9.14690 −0.587985
\(243\) 16.6666 1.06916
\(244\) −2.05964 −0.131855
\(245\) −0.200355 −0.0128002
\(246\) 15.0522 0.959691
\(247\) −0.966895 −0.0615220
\(248\) 6.63863 0.421554
\(249\) −9.27691 −0.587900
\(250\) 0.495099 0.0313128
\(251\) 11.6234 0.733665 0.366833 0.930287i \(-0.380442\pi\)
0.366833 + 0.930287i \(0.380442\pi\)
\(252\) 3.11938 0.196503
\(253\) 17.5357 1.10246
\(254\) −4.88085 −0.306252
\(255\) 0.0664387 0.00416055
\(256\) 1.00000 0.0625000
\(257\) −6.10648 −0.380912 −0.190456 0.981696i \(-0.560997\pi\)
−0.190456 + 0.981696i \(0.560997\pi\)
\(258\) 6.06968 0.377882
\(259\) −15.1041 −0.938521
\(260\) 0.00740819 0.000459436 0
\(261\) −8.89397 −0.550523
\(262\) 0.0816734 0.00504580
\(263\) 8.75820 0.540054 0.270027 0.962853i \(-0.412967\pi\)
0.270027 + 0.962853i \(0.412967\pi\)
\(264\) −9.84910 −0.606170
\(265\) −0.484086 −0.0297372
\(266\) 11.1093 0.681157
\(267\) −12.4714 −0.763235
\(268\) −6.84709 −0.418253
\(269\) −8.49852 −0.518164 −0.259082 0.965855i \(-0.583420\pi\)
−0.259082 + 0.965855i \(0.583420\pi\)
\(270\) −0.128782 −0.00783742
\(271\) −7.03183 −0.427153 −0.213577 0.976926i \(-0.568511\pi\)
−0.213577 + 0.976926i \(0.568511\pi\)
\(272\) −0.611407 −0.0370720
\(273\) −0.564194 −0.0341466
\(274\) −4.22433 −0.255201
\(275\) 22.4316 1.35268
\(276\) 8.57257 0.516008
\(277\) 27.0919 1.62779 0.813897 0.581009i \(-0.197342\pi\)
0.813897 + 0.581009i \(0.197342\pi\)
\(278\) −2.90677 −0.174336
\(279\) −12.0483 −0.721312
\(280\) −0.0851178 −0.00508676
\(281\) 0.666362 0.0397518 0.0198759 0.999802i \(-0.493673\pi\)
0.0198759 + 0.999802i \(0.493673\pi\)
\(282\) −15.0966 −0.898991
\(283\) −8.42508 −0.500819 −0.250409 0.968140i \(-0.580565\pi\)
−0.250409 + 0.968140i \(0.580565\pi\)
\(284\) 15.9726 0.947800
\(285\) 0.702354 0.0416039
\(286\) 0.671456 0.0397040
\(287\) 11.7904 0.695966
\(288\) −1.81487 −0.106942
\(289\) −16.6262 −0.978011
\(290\) 0.242687 0.0142511
\(291\) −3.09438 −0.181396
\(292\) −12.9027 −0.755075
\(293\) 20.1777 1.17879 0.589397 0.807844i \(-0.299365\pi\)
0.589397 + 0.807844i \(0.299365\pi\)
\(294\) −8.87756 −0.517750
\(295\) 0.0645364 0.00375746
\(296\) 8.78763 0.510771
\(297\) −11.6724 −0.677303
\(298\) −16.1227 −0.933961
\(299\) −0.584429 −0.0337984
\(300\) 10.9660 0.633124
\(301\) 4.75440 0.274039
\(302\) 9.26507 0.533145
\(303\) 28.0004 1.60858
\(304\) −6.46347 −0.370705
\(305\) −0.101997 −0.00584035
\(306\) 1.10963 0.0634332
\(307\) −3.01484 −0.172066 −0.0860331 0.996292i \(-0.527419\pi\)
−0.0860331 + 0.996292i \(0.527419\pi\)
\(308\) −7.71483 −0.439593
\(309\) −25.8254 −1.46915
\(310\) 0.328758 0.0186722
\(311\) 18.4919 1.04858 0.524290 0.851540i \(-0.324331\pi\)
0.524290 + 0.851540i \(0.324331\pi\)
\(312\) 0.328251 0.0185836
\(313\) 10.2506 0.579401 0.289700 0.957117i \(-0.406444\pi\)
0.289700 + 0.957117i \(0.406444\pi\)
\(314\) 9.73885 0.549595
\(315\) 0.154478 0.00870386
\(316\) 11.9686 0.673285
\(317\) −22.4731 −1.26222 −0.631108 0.775695i \(-0.717399\pi\)
−0.631108 + 0.775695i \(0.717399\pi\)
\(318\) −21.4495 −1.20283
\(319\) 21.9965 1.23157
\(320\) 0.0495220 0.00276836
\(321\) 16.1331 0.900463
\(322\) 6.71492 0.374208
\(323\) 3.95181 0.219885
\(324\) −11.1509 −0.619492
\(325\) −0.747602 −0.0414695
\(326\) −2.70166 −0.149631
\(327\) 1.78714 0.0988293
\(328\) −6.85972 −0.378765
\(329\) −11.8252 −0.651946
\(330\) −0.487747 −0.0268496
\(331\) −20.6999 −1.13777 −0.568883 0.822418i \(-0.692624\pi\)
−0.568883 + 0.822418i \(0.692624\pi\)
\(332\) 4.22776 0.232029
\(333\) −15.9484 −0.873969
\(334\) −20.6077 −1.12760
\(335\) −0.339082 −0.0185260
\(336\) −3.77151 −0.205753
\(337\) −0.659518 −0.0359263 −0.0179631 0.999839i \(-0.505718\pi\)
−0.0179631 + 0.999839i \(0.505718\pi\)
\(338\) 12.9776 0.705890
\(339\) −22.2397 −1.20789
\(340\) −0.0302781 −0.00164206
\(341\) 29.7977 1.61364
\(342\) 11.7304 0.634306
\(343\) −18.9853 −1.02511
\(344\) −2.76613 −0.149140
\(345\) 0.424531 0.0228560
\(346\) 19.6845 1.05825
\(347\) −26.6562 −1.43098 −0.715491 0.698622i \(-0.753797\pi\)
−0.715491 + 0.698622i \(0.753797\pi\)
\(348\) 10.7533 0.576437
\(349\) −35.1290 −1.88041 −0.940206 0.340606i \(-0.889368\pi\)
−0.940206 + 0.340606i \(0.889368\pi\)
\(350\) 8.58972 0.459140
\(351\) 0.389019 0.0207643
\(352\) 4.48853 0.239239
\(353\) 9.85262 0.524402 0.262201 0.965013i \(-0.415552\pi\)
0.262201 + 0.965013i \(0.415552\pi\)
\(354\) 2.85956 0.151984
\(355\) 0.790996 0.0419817
\(356\) 5.68357 0.301229
\(357\) 2.30593 0.122043
\(358\) 11.0404 0.583505
\(359\) 24.5956 1.29810 0.649052 0.760744i \(-0.275166\pi\)
0.649052 + 0.760744i \(0.275166\pi\)
\(360\) −0.0898762 −0.00473689
\(361\) 22.7764 1.19876
\(362\) 7.43443 0.390745
\(363\) −20.0709 −1.05345
\(364\) 0.257120 0.0134768
\(365\) −0.638969 −0.0334452
\(366\) −4.51942 −0.236234
\(367\) −20.3170 −1.06054 −0.530268 0.847830i \(-0.677909\pi\)
−0.530268 + 0.847830i \(0.677909\pi\)
\(368\) −3.90677 −0.203655
\(369\) 12.4495 0.648097
\(370\) 0.435181 0.0226240
\(371\) −16.8015 −0.872289
\(372\) 14.5670 0.755265
\(373\) 32.0593 1.65997 0.829984 0.557787i \(-0.188349\pi\)
0.829984 + 0.557787i \(0.188349\pi\)
\(374\) −2.74432 −0.141905
\(375\) 1.08639 0.0561007
\(376\) 6.87998 0.354808
\(377\) −0.733099 −0.0377565
\(378\) −4.46971 −0.229897
\(379\) 16.0863 0.826296 0.413148 0.910664i \(-0.364429\pi\)
0.413148 + 0.910664i \(0.364429\pi\)
\(380\) −0.320084 −0.0164200
\(381\) −10.7100 −0.548689
\(382\) −9.96951 −0.510084
\(383\) 23.8546 1.21891 0.609456 0.792820i \(-0.291388\pi\)
0.609456 + 0.792820i \(0.291388\pi\)
\(384\) 2.19428 0.111976
\(385\) −0.382054 −0.0194713
\(386\) 1.90500 0.0969617
\(387\) 5.02019 0.255190
\(388\) 1.41020 0.0715922
\(389\) 26.6943 1.35346 0.676728 0.736233i \(-0.263397\pi\)
0.676728 + 0.736233i \(0.263397\pi\)
\(390\) 0.0162556 0.000823137 0
\(391\) 2.38863 0.120798
\(392\) 4.04577 0.204342
\(393\) 0.179214 0.00904017
\(394\) 8.29086 0.417687
\(395\) 0.592707 0.0298223
\(396\) −8.14612 −0.409358
\(397\) 33.2828 1.67042 0.835209 0.549933i \(-0.185347\pi\)
0.835209 + 0.549933i \(0.185347\pi\)
\(398\) 10.6771 0.535193
\(399\) 24.3770 1.22038
\(400\) −4.99755 −0.249877
\(401\) −17.2486 −0.861355 −0.430678 0.902506i \(-0.641725\pi\)
−0.430678 + 0.902506i \(0.641725\pi\)
\(402\) −15.0245 −0.749352
\(403\) −0.993098 −0.0494697
\(404\) −12.7606 −0.634864
\(405\) −0.552213 −0.0274397
\(406\) 8.42309 0.418031
\(407\) 39.4435 1.95514
\(408\) −1.34160 −0.0664191
\(409\) −17.6415 −0.872316 −0.436158 0.899870i \(-0.643661\pi\)
−0.436158 + 0.899870i \(0.643661\pi\)
\(410\) −0.339707 −0.0167769
\(411\) −9.26938 −0.457225
\(412\) 11.7694 0.579836
\(413\) 2.23990 0.110218
\(414\) 7.09030 0.348469
\(415\) 0.209367 0.0102774
\(416\) −0.149594 −0.00733444
\(417\) −6.37827 −0.312345
\(418\) −29.0115 −1.41900
\(419\) −25.6130 −1.25128 −0.625638 0.780113i \(-0.715161\pi\)
−0.625638 + 0.780113i \(0.715161\pi\)
\(420\) −0.186772 −0.00911356
\(421\) −1.23490 −0.0601851 −0.0300926 0.999547i \(-0.509580\pi\)
−0.0300926 + 0.999547i \(0.509580\pi\)
\(422\) −10.3373 −0.503212
\(423\) −12.4863 −0.607105
\(424\) 9.77518 0.474725
\(425\) 3.05554 0.148215
\(426\) 35.0484 1.69810
\(427\) −3.54008 −0.171316
\(428\) −7.35234 −0.355389
\(429\) 1.47336 0.0711347
\(430\) −0.136985 −0.00660598
\(431\) 3.10156 0.149397 0.0746985 0.997206i \(-0.476201\pi\)
0.0746985 + 0.997206i \(0.476201\pi\)
\(432\) 2.60050 0.125117
\(433\) 19.4689 0.935616 0.467808 0.883830i \(-0.345044\pi\)
0.467808 + 0.883830i \(0.345044\pi\)
\(434\) 11.4104 0.547717
\(435\) 0.532525 0.0255326
\(436\) −0.814455 −0.0390053
\(437\) 25.2513 1.20793
\(438\) −28.3122 −1.35281
\(439\) −39.9161 −1.90509 −0.952546 0.304393i \(-0.901546\pi\)
−0.952546 + 0.304393i \(0.901546\pi\)
\(440\) 0.222281 0.0105968
\(441\) −7.34256 −0.349646
\(442\) 0.0914627 0.00435044
\(443\) 31.8463 1.51306 0.756531 0.653958i \(-0.226893\pi\)
0.756531 + 0.653958i \(0.226893\pi\)
\(444\) 19.2825 0.915109
\(445\) 0.281462 0.0133426
\(446\) 26.1261 1.23711
\(447\) −35.3777 −1.67331
\(448\) 1.71879 0.0812051
\(449\) 22.1570 1.04565 0.522827 0.852439i \(-0.324877\pi\)
0.522827 + 0.852439i \(0.324877\pi\)
\(450\) 9.06992 0.427560
\(451\) −30.7901 −1.44985
\(452\) 10.1353 0.476724
\(453\) 20.3302 0.955196
\(454\) −4.18780 −0.196543
\(455\) 0.0127331 0.000596937 0
\(456\) −14.1827 −0.664164
\(457\) −34.7269 −1.62446 −0.812228 0.583340i \(-0.801745\pi\)
−0.812228 + 0.583340i \(0.801745\pi\)
\(458\) 5.14274 0.240304
\(459\) −1.58996 −0.0742132
\(460\) −0.193471 −0.00902064
\(461\) −5.36635 −0.249936 −0.124968 0.992161i \(-0.539883\pi\)
−0.124968 + 0.992161i \(0.539883\pi\)
\(462\) −16.9285 −0.787586
\(463\) −8.49012 −0.394569 −0.197285 0.980346i \(-0.563212\pi\)
−0.197285 + 0.980346i \(0.563212\pi\)
\(464\) −4.90060 −0.227505
\(465\) 0.721388 0.0334536
\(466\) 17.6336 0.816863
\(467\) 16.9438 0.784066 0.392033 0.919951i \(-0.371772\pi\)
0.392033 + 0.919951i \(0.371772\pi\)
\(468\) 0.271494 0.0125498
\(469\) −11.7687 −0.543428
\(470\) 0.340710 0.0157158
\(471\) 21.3698 0.984668
\(472\) −1.30319 −0.0599841
\(473\) −12.4159 −0.570883
\(474\) 26.2624 1.20627
\(475\) 32.3015 1.48209
\(476\) −1.05088 −0.0481670
\(477\) −17.7407 −0.812292
\(478\) −2.86053 −0.130837
\(479\) −17.2598 −0.788619 −0.394310 0.918978i \(-0.629016\pi\)
−0.394310 + 0.918978i \(0.629016\pi\)
\(480\) 0.108665 0.00495987
\(481\) −1.31458 −0.0599395
\(482\) 8.97528 0.408813
\(483\) 14.7344 0.670439
\(484\) 9.14690 0.415768
\(485\) 0.0698360 0.00317109
\(486\) −16.6666 −0.756013
\(487\) 27.6962 1.25504 0.627518 0.778602i \(-0.284071\pi\)
0.627518 + 0.778602i \(0.284071\pi\)
\(488\) 2.05964 0.0932354
\(489\) −5.92820 −0.268083
\(490\) 0.200355 0.00905109
\(491\) −15.1407 −0.683289 −0.341645 0.939829i \(-0.610984\pi\)
−0.341645 + 0.939829i \(0.610984\pi\)
\(492\) −15.0522 −0.678604
\(493\) 2.99626 0.134945
\(494\) 0.966895 0.0435027
\(495\) −0.403412 −0.0181320
\(496\) −6.63863 −0.298083
\(497\) 27.4535 1.23146
\(498\) 9.27691 0.415708
\(499\) −3.04613 −0.136364 −0.0681818 0.997673i \(-0.521720\pi\)
−0.0681818 + 0.997673i \(0.521720\pi\)
\(500\) −0.495099 −0.0221415
\(501\) −45.2190 −2.02024
\(502\) −11.6234 −0.518780
\(503\) −26.2002 −1.16821 −0.584104 0.811679i \(-0.698554\pi\)
−0.584104 + 0.811679i \(0.698554\pi\)
\(504\) −3.11938 −0.138948
\(505\) −0.631931 −0.0281206
\(506\) −17.5357 −0.779556
\(507\) 28.4766 1.26469
\(508\) 4.88085 0.216553
\(509\) −26.7347 −1.18499 −0.592496 0.805573i \(-0.701858\pi\)
−0.592496 + 0.805573i \(0.701858\pi\)
\(510\) −0.0664387 −0.00294196
\(511\) −22.1770 −0.981055
\(512\) −1.00000 −0.0441942
\(513\) −16.8082 −0.742102
\(514\) 6.10648 0.269345
\(515\) 0.582844 0.0256832
\(516\) −6.06968 −0.267203
\(517\) 30.8810 1.35814
\(518\) 15.1041 0.663635
\(519\) 43.1934 1.89598
\(520\) −0.00740819 −0.000324870 0
\(521\) 15.5473 0.681138 0.340569 0.940220i \(-0.389380\pi\)
0.340569 + 0.940220i \(0.389380\pi\)
\(522\) 8.89397 0.389278
\(523\) 22.2301 0.972055 0.486027 0.873944i \(-0.338446\pi\)
0.486027 + 0.873944i \(0.338446\pi\)
\(524\) −0.0816734 −0.00356792
\(525\) 18.8483 0.822606
\(526\) −8.75820 −0.381876
\(527\) 4.05891 0.176809
\(528\) 9.84910 0.428627
\(529\) −7.73712 −0.336396
\(530\) 0.484086 0.0210274
\(531\) 2.36512 0.102638
\(532\) −11.1093 −0.481651
\(533\) 1.02617 0.0444485
\(534\) 12.4714 0.539689
\(535\) −0.364103 −0.0157415
\(536\) 6.84709 0.295749
\(537\) 24.2258 1.04542
\(538\) 8.49852 0.366397
\(539\) 18.1595 0.782187
\(540\) 0.128782 0.00554189
\(541\) −23.8470 −1.02526 −0.512631 0.858609i \(-0.671329\pi\)
−0.512631 + 0.858609i \(0.671329\pi\)
\(542\) 7.03183 0.302043
\(543\) 16.3132 0.700068
\(544\) 0.611407 0.0262139
\(545\) −0.0403334 −0.00172769
\(546\) 0.564194 0.0241453
\(547\) −12.6750 −0.541946 −0.270973 0.962587i \(-0.587345\pi\)
−0.270973 + 0.962587i \(0.587345\pi\)
\(548\) 4.22433 0.180454
\(549\) −3.73798 −0.159533
\(550\) −22.4316 −0.956488
\(551\) 31.6749 1.34939
\(552\) −8.57257 −0.364873
\(553\) 20.5714 0.874786
\(554\) −27.0919 −1.15102
\(555\) 0.954910 0.0405337
\(556\) 2.90677 0.123274
\(557\) 34.7629 1.47295 0.736476 0.676464i \(-0.236489\pi\)
0.736476 + 0.676464i \(0.236489\pi\)
\(558\) 12.0483 0.510044
\(559\) 0.413797 0.0175017
\(560\) 0.0851178 0.00359688
\(561\) −6.02181 −0.254241
\(562\) −0.666362 −0.0281088
\(563\) 27.8562 1.17400 0.586999 0.809588i \(-0.300309\pi\)
0.586999 + 0.809588i \(0.300309\pi\)
\(564\) 15.0966 0.635682
\(565\) 0.501919 0.0211159
\(566\) 8.42508 0.354132
\(567\) −19.1660 −0.804894
\(568\) −15.9726 −0.670196
\(569\) 29.2247 1.22517 0.612583 0.790407i \(-0.290131\pi\)
0.612583 + 0.790407i \(0.290131\pi\)
\(570\) −0.702354 −0.0294184
\(571\) −2.25160 −0.0942264 −0.0471132 0.998890i \(-0.515002\pi\)
−0.0471132 + 0.998890i \(0.515002\pi\)
\(572\) −0.671456 −0.0280750
\(573\) −21.8759 −0.913879
\(574\) −11.7904 −0.492122
\(575\) 19.5243 0.814219
\(576\) 1.81487 0.0756198
\(577\) 16.4483 0.684753 0.342376 0.939563i \(-0.388768\pi\)
0.342376 + 0.939563i \(0.388768\pi\)
\(578\) 16.6262 0.691558
\(579\) 4.18010 0.173719
\(580\) −0.242687 −0.0100770
\(581\) 7.26663 0.301471
\(582\) 3.09438 0.128266
\(583\) 43.8762 1.81717
\(584\) 12.9027 0.533919
\(585\) 0.0134449 0.000555879 0
\(586\) −20.1777 −0.833533
\(587\) 0.383184 0.0158157 0.00790786 0.999969i \(-0.497483\pi\)
0.00790786 + 0.999969i \(0.497483\pi\)
\(588\) 8.87756 0.366104
\(589\) 42.9086 1.76802
\(590\) −0.0645364 −0.00265692
\(591\) 18.1925 0.748339
\(592\) −8.78763 −0.361169
\(593\) −5.88116 −0.241510 −0.120755 0.992682i \(-0.538532\pi\)
−0.120755 + 0.992682i \(0.538532\pi\)
\(594\) 11.6724 0.478925
\(595\) −0.0520416 −0.00213350
\(596\) 16.1227 0.660410
\(597\) 23.4285 0.958865
\(598\) 0.584429 0.0238991
\(599\) 11.2660 0.460317 0.230159 0.973153i \(-0.426076\pi\)
0.230159 + 0.973153i \(0.426076\pi\)
\(600\) −10.9660 −0.447686
\(601\) 3.99074 0.162786 0.0813929 0.996682i \(-0.474063\pi\)
0.0813929 + 0.996682i \(0.474063\pi\)
\(602\) −4.75440 −0.193775
\(603\) −12.4266 −0.506051
\(604\) −9.26507 −0.376991
\(605\) 0.452973 0.0184160
\(606\) −28.0004 −1.13744
\(607\) 15.3100 0.621416 0.310708 0.950505i \(-0.399434\pi\)
0.310708 + 0.950505i \(0.399434\pi\)
\(608\) 6.46347 0.262128
\(609\) 18.4826 0.748954
\(610\) 0.101997 0.00412975
\(611\) −1.02920 −0.0416371
\(612\) −1.10963 −0.0448540
\(613\) 41.6194 1.68099 0.840496 0.541818i \(-0.182264\pi\)
0.840496 + 0.541818i \(0.182264\pi\)
\(614\) 3.01484 0.121669
\(615\) −0.745413 −0.0300580
\(616\) 7.71483 0.310839
\(617\) −24.6308 −0.991600 −0.495800 0.868437i \(-0.665125\pi\)
−0.495800 + 0.868437i \(0.665125\pi\)
\(618\) 25.8254 1.03885
\(619\) 0.383970 0.0154331 0.00771654 0.999970i \(-0.497544\pi\)
0.00771654 + 0.999970i \(0.497544\pi\)
\(620\) −0.328758 −0.0132032
\(621\) −10.1596 −0.407689
\(622\) −18.4919 −0.741458
\(623\) 9.76886 0.391381
\(624\) −0.328251 −0.0131406
\(625\) 24.9632 0.998529
\(626\) −10.2506 −0.409698
\(627\) −63.6593 −2.54231
\(628\) −9.73885 −0.388622
\(629\) 5.37282 0.214228
\(630\) −0.154478 −0.00615456
\(631\) 11.8514 0.471795 0.235898 0.971778i \(-0.424197\pi\)
0.235898 + 0.971778i \(0.424197\pi\)
\(632\) −11.9686 −0.476084
\(633\) −22.6830 −0.901566
\(634\) 22.4731 0.892521
\(635\) 0.241710 0.00959196
\(636\) 21.4495 0.850528
\(637\) −0.605222 −0.0239798
\(638\) −21.9965 −0.870849
\(639\) 28.9883 1.14676
\(640\) −0.0495220 −0.00195753
\(641\) −39.9262 −1.57699 −0.788495 0.615041i \(-0.789140\pi\)
−0.788495 + 0.615041i \(0.789140\pi\)
\(642\) −16.1331 −0.636723
\(643\) −3.87221 −0.152705 −0.0763526 0.997081i \(-0.524327\pi\)
−0.0763526 + 0.997081i \(0.524327\pi\)
\(644\) −6.71492 −0.264605
\(645\) −0.300583 −0.0118354
\(646\) −3.95181 −0.155482
\(647\) 4.47846 0.176066 0.0880331 0.996118i \(-0.471942\pi\)
0.0880331 + 0.996118i \(0.471942\pi\)
\(648\) 11.1509 0.438047
\(649\) −5.84940 −0.229609
\(650\) 0.747602 0.0293234
\(651\) 25.0376 0.981302
\(652\) 2.70166 0.105805
\(653\) −2.35056 −0.0919844 −0.0459922 0.998942i \(-0.514645\pi\)
−0.0459922 + 0.998942i \(0.514645\pi\)
\(654\) −1.78714 −0.0698829
\(655\) −0.00404463 −0.000158037 0
\(656\) 6.85972 0.267827
\(657\) −23.4168 −0.913577
\(658\) 11.8252 0.460995
\(659\) 25.5062 0.993582 0.496791 0.867870i \(-0.334512\pi\)
0.496791 + 0.867870i \(0.334512\pi\)
\(660\) 0.487747 0.0189855
\(661\) −3.68444 −0.143308 −0.0716541 0.997430i \(-0.522828\pi\)
−0.0716541 + 0.997430i \(0.522828\pi\)
\(662\) 20.6999 0.804523
\(663\) 0.200695 0.00779435
\(664\) −4.22776 −0.164069
\(665\) −0.550156 −0.0213341
\(666\) 15.9484 0.617990
\(667\) 19.1455 0.741318
\(668\) 20.6077 0.797335
\(669\) 57.3281 2.21643
\(670\) 0.339082 0.0130999
\(671\) 9.24474 0.356889
\(672\) 3.77151 0.145489
\(673\) 7.47582 0.288172 0.144086 0.989565i \(-0.453976\pi\)
0.144086 + 0.989565i \(0.453976\pi\)
\(674\) 0.659518 0.0254037
\(675\) −12.9961 −0.500221
\(676\) −12.9776 −0.499139
\(677\) 14.1155 0.542504 0.271252 0.962508i \(-0.412562\pi\)
0.271252 + 0.962508i \(0.412562\pi\)
\(678\) 22.2397 0.854109
\(679\) 2.42384 0.0930184
\(680\) 0.0302781 0.00116111
\(681\) −9.18922 −0.352132
\(682\) −29.7977 −1.14101
\(683\) −14.3026 −0.547272 −0.273636 0.961833i \(-0.588226\pi\)
−0.273636 + 0.961833i \(0.588226\pi\)
\(684\) −11.7304 −0.448522
\(685\) 0.209197 0.00799302
\(686\) 18.9853 0.724863
\(687\) 11.2846 0.430535
\(688\) 2.76613 0.105458
\(689\) −1.46231 −0.0557095
\(690\) −0.424531 −0.0161616
\(691\) 42.6761 1.62347 0.811737 0.584023i \(-0.198522\pi\)
0.811737 + 0.584023i \(0.198522\pi\)
\(692\) −19.6845 −0.748294
\(693\) −14.0014 −0.531871
\(694\) 26.6562 1.01186
\(695\) 0.143949 0.00546030
\(696\) −10.7533 −0.407603
\(697\) −4.19408 −0.158862
\(698\) 35.1290 1.32965
\(699\) 38.6932 1.46351
\(700\) −8.58972 −0.324661
\(701\) −36.5514 −1.38053 −0.690263 0.723558i \(-0.742505\pi\)
−0.690263 + 0.723558i \(0.742505\pi\)
\(702\) −0.389019 −0.0146826
\(703\) 56.7986 2.14220
\(704\) −4.48853 −0.169168
\(705\) 0.747615 0.0281568
\(706\) −9.85262 −0.370808
\(707\) −21.9328 −0.824868
\(708\) −2.85956 −0.107469
\(709\) 25.8383 0.970376 0.485188 0.874410i \(-0.338751\pi\)
0.485188 + 0.874410i \(0.338751\pi\)
\(710\) −0.790996 −0.0296855
\(711\) 21.7214 0.814618
\(712\) −5.68357 −0.213001
\(713\) 25.9356 0.971297
\(714\) −2.30593 −0.0862971
\(715\) −0.0332519 −0.00124355
\(716\) −11.0404 −0.412600
\(717\) −6.27680 −0.234411
\(718\) −24.5956 −0.917899
\(719\) −1.22318 −0.0456168 −0.0228084 0.999740i \(-0.507261\pi\)
−0.0228084 + 0.999740i \(0.507261\pi\)
\(720\) 0.0898762 0.00334949
\(721\) 20.2291 0.753370
\(722\) −22.7764 −0.847650
\(723\) 19.6943 0.732439
\(724\) −7.43443 −0.276298
\(725\) 24.4910 0.909572
\(726\) 20.0709 0.744900
\(727\) −8.79628 −0.326236 −0.163118 0.986607i \(-0.552155\pi\)
−0.163118 + 0.986607i \(0.552155\pi\)
\(728\) −0.257120 −0.00952950
\(729\) −3.11870 −0.115508
\(730\) 0.638969 0.0236493
\(731\) −1.69123 −0.0625526
\(732\) 4.51942 0.167043
\(733\) 15.8151 0.584142 0.292071 0.956397i \(-0.405656\pi\)
0.292071 + 0.956397i \(0.405656\pi\)
\(734\) 20.3170 0.749913
\(735\) 0.439634 0.0162162
\(736\) 3.90677 0.144006
\(737\) 30.7334 1.13208
\(738\) −12.4495 −0.458274
\(739\) −1.33529 −0.0491196 −0.0245598 0.999698i \(-0.507818\pi\)
−0.0245598 + 0.999698i \(0.507818\pi\)
\(740\) −0.435181 −0.0159976
\(741\) 2.12164 0.0779404
\(742\) 16.8015 0.616801
\(743\) 33.0831 1.21370 0.606850 0.794816i \(-0.292433\pi\)
0.606850 + 0.794816i \(0.292433\pi\)
\(744\) −14.5670 −0.534053
\(745\) 0.798426 0.0292521
\(746\) −32.0593 −1.17377
\(747\) 7.67286 0.280735
\(748\) 2.74432 0.100342
\(749\) −12.6371 −0.461750
\(750\) −1.08639 −0.0396692
\(751\) 41.3968 1.51059 0.755296 0.655384i \(-0.227493\pi\)
0.755296 + 0.655384i \(0.227493\pi\)
\(752\) −6.87998 −0.250887
\(753\) −25.5051 −0.929458
\(754\) 0.733099 0.0266979
\(755\) −0.458825 −0.0166984
\(756\) 4.46971 0.162562
\(757\) −18.4458 −0.670423 −0.335212 0.942143i \(-0.608808\pi\)
−0.335212 + 0.942143i \(0.608808\pi\)
\(758\) −16.0863 −0.584280
\(759\) −38.4782 −1.39667
\(760\) 0.320084 0.0116107
\(761\) −0.286940 −0.0104016 −0.00520078 0.999986i \(-0.501655\pi\)
−0.00520078 + 0.999986i \(0.501655\pi\)
\(762\) 10.7100 0.387981
\(763\) −1.39988 −0.0506789
\(764\) 9.96951 0.360684
\(765\) −0.0549510 −0.00198676
\(766\) −23.8546 −0.861901
\(767\) 0.194949 0.00703919
\(768\) −2.19428 −0.0791793
\(769\) −23.2997 −0.840207 −0.420104 0.907476i \(-0.638006\pi\)
−0.420104 + 0.907476i \(0.638006\pi\)
\(770\) 0.382054 0.0137683
\(771\) 13.3993 0.482566
\(772\) −1.90500 −0.0685623
\(773\) 21.7576 0.782566 0.391283 0.920270i \(-0.372031\pi\)
0.391283 + 0.920270i \(0.372031\pi\)
\(774\) −5.02019 −0.180447
\(775\) 33.1769 1.19175
\(776\) −1.41020 −0.0506233
\(777\) 33.1426 1.18898
\(778\) −26.6943 −0.957038
\(779\) −44.3376 −1.58856
\(780\) −0.0162556 −0.000582046 0
\(781\) −71.6936 −2.56540
\(782\) −2.38863 −0.0854172
\(783\) −12.7440 −0.455434
\(784\) −4.04577 −0.144492
\(785\) −0.482287 −0.0172136
\(786\) −0.179214 −0.00639237
\(787\) 37.5681 1.33916 0.669580 0.742740i \(-0.266474\pi\)
0.669580 + 0.742740i \(0.266474\pi\)
\(788\) −8.29086 −0.295350
\(789\) −19.2180 −0.684178
\(790\) −0.592707 −0.0210876
\(791\) 17.4204 0.619398
\(792\) 8.14612 0.289460
\(793\) −0.308109 −0.0109413
\(794\) −33.2828 −1.18116
\(795\) 1.06222 0.0376731
\(796\) −10.6771 −0.378439
\(797\) −6.13569 −0.217337 −0.108669 0.994078i \(-0.534659\pi\)
−0.108669 + 0.994078i \(0.534659\pi\)
\(798\) −24.3770 −0.862937
\(799\) 4.20647 0.148814
\(800\) 4.99755 0.176690
\(801\) 10.3150 0.364462
\(802\) 17.2486 0.609070
\(803\) 57.9143 2.04375
\(804\) 15.0245 0.529872
\(805\) −0.332536 −0.0117204
\(806\) 0.993098 0.0349804
\(807\) 18.6482 0.656446
\(808\) 12.7606 0.448917
\(809\) 7.78281 0.273629 0.136814 0.990597i \(-0.456314\pi\)
0.136814 + 0.990597i \(0.456314\pi\)
\(810\) 0.552213 0.0194028
\(811\) −39.6378 −1.39187 −0.695936 0.718104i \(-0.745010\pi\)
−0.695936 + 0.718104i \(0.745010\pi\)
\(812\) −8.42309 −0.295592
\(813\) 15.4298 0.541147
\(814\) −39.4435 −1.38250
\(815\) 0.133792 0.00468651
\(816\) 1.34160 0.0469654
\(817\) −17.8788 −0.625501
\(818\) 17.6415 0.616820
\(819\) 0.466641 0.0163057
\(820\) 0.339707 0.0118631
\(821\) −5.71077 −0.199307 −0.0996537 0.995022i \(-0.531773\pi\)
−0.0996537 + 0.995022i \(0.531773\pi\)
\(822\) 9.26938 0.323307
\(823\) 28.6113 0.997326 0.498663 0.866796i \(-0.333825\pi\)
0.498663 + 0.866796i \(0.333825\pi\)
\(824\) −11.7694 −0.410006
\(825\) −49.2213 −1.71367
\(826\) −2.23990 −0.0779362
\(827\) −19.3506 −0.672887 −0.336444 0.941704i \(-0.609224\pi\)
−0.336444 + 0.941704i \(0.609224\pi\)
\(828\) −7.09030 −0.246405
\(829\) 18.0246 0.626021 0.313011 0.949750i \(-0.398662\pi\)
0.313011 + 0.949750i \(0.398662\pi\)
\(830\) −0.209367 −0.00726725
\(831\) −59.4473 −2.06220
\(832\) 0.149594 0.00518623
\(833\) 2.47361 0.0857056
\(834\) 6.37827 0.220861
\(835\) 1.02053 0.0353170
\(836\) 29.0115 1.00338
\(837\) −17.2638 −0.596723
\(838\) 25.6130 0.884786
\(839\) 30.3266 1.04699 0.523494 0.852029i \(-0.324628\pi\)
0.523494 + 0.852029i \(0.324628\pi\)
\(840\) 0.186772 0.00644426
\(841\) −4.98415 −0.171867
\(842\) 1.23490 0.0425573
\(843\) −1.46219 −0.0503604
\(844\) 10.3373 0.355825
\(845\) −0.642678 −0.0221088
\(846\) 12.4863 0.429288
\(847\) 15.7216 0.540200
\(848\) −9.77518 −0.335681
\(849\) 18.4870 0.634472
\(850\) −3.05554 −0.104804
\(851\) 34.3313 1.17686
\(852\) −35.0484 −1.20074
\(853\) 14.5564 0.498403 0.249202 0.968452i \(-0.419832\pi\)
0.249202 + 0.968452i \(0.419832\pi\)
\(854\) 3.54008 0.121139
\(855\) −0.580912 −0.0198668
\(856\) 7.35234 0.251298
\(857\) −12.0512 −0.411661 −0.205831 0.978588i \(-0.565990\pi\)
−0.205831 + 0.978588i \(0.565990\pi\)
\(858\) −1.47336 −0.0502998
\(859\) 13.5353 0.461820 0.230910 0.972975i \(-0.425830\pi\)
0.230910 + 0.972975i \(0.425830\pi\)
\(860\) 0.136985 0.00467113
\(861\) −25.8715 −0.881698
\(862\) −3.10156 −0.105640
\(863\) −42.6120 −1.45053 −0.725265 0.688470i \(-0.758283\pi\)
−0.725265 + 0.688470i \(0.758283\pi\)
\(864\) −2.60050 −0.0884708
\(865\) −0.974817 −0.0331448
\(866\) −19.4689 −0.661581
\(867\) 36.4825 1.23901
\(868\) −11.4104 −0.387294
\(869\) −53.7213 −1.82237
\(870\) −0.532525 −0.0180543
\(871\) −1.02428 −0.0347065
\(872\) 0.814455 0.0275809
\(873\) 2.55934 0.0866205
\(874\) −25.2513 −0.854138
\(875\) −0.850969 −0.0287680
\(876\) 28.3122 0.956581
\(877\) −0.806782 −0.0272431 −0.0136216 0.999907i \(-0.504336\pi\)
−0.0136216 + 0.999907i \(0.504336\pi\)
\(878\) 39.9161 1.34710
\(879\) −44.2756 −1.49338
\(880\) −0.222281 −0.00749309
\(881\) 51.7530 1.74360 0.871802 0.489858i \(-0.162951\pi\)
0.871802 + 0.489858i \(0.162951\pi\)
\(882\) 7.34256 0.247237
\(883\) 4.21607 0.141882 0.0709410 0.997481i \(-0.477400\pi\)
0.0709410 + 0.997481i \(0.477400\pi\)
\(884\) −0.0914627 −0.00307623
\(885\) −0.141611 −0.00476021
\(886\) −31.8463 −1.06990
\(887\) −11.1549 −0.374546 −0.187273 0.982308i \(-0.559965\pi\)
−0.187273 + 0.982308i \(0.559965\pi\)
\(888\) −19.2825 −0.647080
\(889\) 8.38915 0.281363
\(890\) −0.281462 −0.00943462
\(891\) 50.0509 1.67677
\(892\) −26.1261 −0.874768
\(893\) 44.4685 1.48808
\(894\) 35.3777 1.18321
\(895\) −0.546744 −0.0182756
\(896\) −1.71879 −0.0574207
\(897\) 1.28240 0.0428182
\(898\) −22.1570 −0.739389
\(899\) 32.5333 1.08504
\(900\) −9.06992 −0.302331
\(901\) 5.97662 0.199110
\(902\) 30.7901 1.02520
\(903\) −10.4325 −0.347172
\(904\) −10.1353 −0.337095
\(905\) −0.368168 −0.0122383
\(906\) −20.3302 −0.675425
\(907\) 18.1152 0.601506 0.300753 0.953702i \(-0.402762\pi\)
0.300753 + 0.953702i \(0.402762\pi\)
\(908\) 4.18780 0.138977
\(909\) −23.1589 −0.768133
\(910\) −0.0127331 −0.000422098 0
\(911\) 46.4176 1.53788 0.768942 0.639319i \(-0.220784\pi\)
0.768942 + 0.639319i \(0.220784\pi\)
\(912\) 14.1827 0.469635
\(913\) −18.9764 −0.628029
\(914\) 34.7269 1.14866
\(915\) 0.223811 0.00739896
\(916\) −5.14274 −0.169921
\(917\) −0.140379 −0.00463573
\(918\) 1.58996 0.0524767
\(919\) −4.97111 −0.163982 −0.0819909 0.996633i \(-0.526128\pi\)
−0.0819909 + 0.996633i \(0.526128\pi\)
\(920\) 0.193471 0.00637856
\(921\) 6.61542 0.217985
\(922\) 5.36635 0.176731
\(923\) 2.38940 0.0786482
\(924\) 16.9285 0.556907
\(925\) 43.9166 1.44397
\(926\) 8.49012 0.279003
\(927\) 21.3600 0.701553
\(928\) 4.90060 0.160870
\(929\) 26.8589 0.881211 0.440606 0.897701i \(-0.354764\pi\)
0.440606 + 0.897701i \(0.354764\pi\)
\(930\) −0.721388 −0.0236553
\(931\) 26.1497 0.857022
\(932\) −17.6336 −0.577609
\(933\) −40.5765 −1.32841
\(934\) −16.9438 −0.554418
\(935\) 0.135904 0.00444454
\(936\) −0.271494 −0.00887406
\(937\) 19.1563 0.625809 0.312905 0.949785i \(-0.398698\pi\)
0.312905 + 0.949785i \(0.398698\pi\)
\(938\) 11.7687 0.384262
\(939\) −22.4928 −0.734025
\(940\) −0.340710 −0.0111127
\(941\) −29.7348 −0.969325 −0.484663 0.874701i \(-0.661058\pi\)
−0.484663 + 0.874701i \(0.661058\pi\)
\(942\) −21.3698 −0.696265
\(943\) −26.7994 −0.872708
\(944\) 1.30319 0.0424151
\(945\) 0.221349 0.00720048
\(946\) 12.4159 0.403675
\(947\) −46.5827 −1.51373 −0.756867 0.653569i \(-0.773271\pi\)
−0.756867 + 0.653569i \(0.773271\pi\)
\(948\) −26.2624 −0.852964
\(949\) −1.93017 −0.0626559
\(950\) −32.3015 −1.04800
\(951\) 49.3123 1.59906
\(952\) 1.05088 0.0340592
\(953\) 19.9156 0.645129 0.322564 0.946548i \(-0.395455\pi\)
0.322564 + 0.946548i \(0.395455\pi\)
\(954\) 17.7407 0.574377
\(955\) 0.493710 0.0159761
\(956\) 2.86053 0.0925160
\(957\) −48.2665 −1.56023
\(958\) 17.2598 0.557638
\(959\) 7.26073 0.234461
\(960\) −0.108665 −0.00350716
\(961\) 13.0714 0.421659
\(962\) 1.31458 0.0423836
\(963\) −13.3436 −0.429991
\(964\) −8.97528 −0.289074
\(965\) −0.0943392 −0.00303689
\(966\) −14.7344 −0.474072
\(967\) −46.8596 −1.50690 −0.753452 0.657503i \(-0.771613\pi\)
−0.753452 + 0.657503i \(0.771613\pi\)
\(968\) −9.14690 −0.293992
\(969\) −8.67139 −0.278565
\(970\) −0.0698360 −0.00224230
\(971\) −42.6905 −1.37000 −0.685002 0.728541i \(-0.740199\pi\)
−0.685002 + 0.728541i \(0.740199\pi\)
\(972\) 16.6666 0.534582
\(973\) 4.99612 0.160168
\(974\) −27.6962 −0.887444
\(975\) 1.64045 0.0525365
\(976\) −2.05964 −0.0659274
\(977\) 10.1283 0.324034 0.162017 0.986788i \(-0.448200\pi\)
0.162017 + 0.986788i \(0.448200\pi\)
\(978\) 5.92820 0.189563
\(979\) −25.5109 −0.815331
\(980\) −0.200355 −0.00640009
\(981\) −1.47813 −0.0471932
\(982\) 15.1407 0.483159
\(983\) 27.3605 0.872666 0.436333 0.899785i \(-0.356277\pi\)
0.436333 + 0.899785i \(0.356277\pi\)
\(984\) 15.0522 0.479846
\(985\) −0.410580 −0.0130822
\(986\) −2.99626 −0.0954204
\(987\) 25.9479 0.825930
\(988\) −0.966895 −0.0307610
\(989\) −10.8067 −0.343632
\(990\) 0.403412 0.0128213
\(991\) −43.0139 −1.36638 −0.683191 0.730239i \(-0.739409\pi\)
−0.683191 + 0.730239i \(0.739409\pi\)
\(992\) 6.63863 0.210777
\(993\) 45.4213 1.44140
\(994\) −27.4535 −0.870773
\(995\) −0.528750 −0.0167625
\(996\) −9.27691 −0.293950
\(997\) −39.7241 −1.25807 −0.629037 0.777375i \(-0.716551\pi\)
−0.629037 + 0.777375i \(0.716551\pi\)
\(998\) 3.04613 0.0964237
\(999\) −22.8522 −0.723013
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 \(a_p\))