Properties

Label 6027.2.a.bm.1.6
Level 6027
Weight 2
Character 6027.1
Self dual Yes
Analytic conductor 48.126
Analytic rank 1
Dimension 16
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6027.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.1258372982\)
Analytic rank: \(1\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(1.44011\)
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.44011 q^{2} +1.00000 q^{3} +0.0739309 q^{4} +3.20961 q^{5} -1.44011 q^{6} +2.77376 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.44011 q^{2} +1.00000 q^{3} +0.0739309 q^{4} +3.20961 q^{5} -1.44011 q^{6} +2.77376 q^{8} +1.00000 q^{9} -4.62221 q^{10} -3.71531 q^{11} +0.0739309 q^{12} +1.13302 q^{13} +3.20961 q^{15} -4.14240 q^{16} -5.67373 q^{17} -1.44011 q^{18} +3.14749 q^{19} +0.237290 q^{20} +5.35047 q^{22} -4.86181 q^{23} +2.77376 q^{24} +5.30163 q^{25} -1.63167 q^{26} +1.00000 q^{27} +2.25032 q^{29} -4.62221 q^{30} -1.73959 q^{31} +0.418005 q^{32} -3.71531 q^{33} +8.17082 q^{34} +0.0739309 q^{36} -4.53215 q^{37} -4.53274 q^{38} +1.13302 q^{39} +8.90270 q^{40} +1.00000 q^{41} -6.99210 q^{43} -0.274676 q^{44} +3.20961 q^{45} +7.00157 q^{46} -6.44011 q^{47} -4.14240 q^{48} -7.63495 q^{50} -5.67373 q^{51} +0.0837649 q^{52} +3.39697 q^{53} -1.44011 q^{54} -11.9247 q^{55} +3.14749 q^{57} -3.24072 q^{58} -3.87745 q^{59} +0.237290 q^{60} +8.17051 q^{61} +2.50520 q^{62} +7.68282 q^{64} +3.63655 q^{65} +5.35047 q^{66} -4.36043 q^{67} -0.419464 q^{68} -4.86181 q^{69} +7.54065 q^{71} +2.77376 q^{72} -9.11677 q^{73} +6.52682 q^{74} +5.30163 q^{75} +0.232697 q^{76} -1.63167 q^{78} +0.0474074 q^{79} -13.2955 q^{80} +1.00000 q^{81} -1.44011 q^{82} -8.03200 q^{83} -18.2105 q^{85} +10.0694 q^{86} +2.25032 q^{87} -10.3054 q^{88} -9.30187 q^{89} -4.62221 q^{90} -0.359438 q^{92} -1.73959 q^{93} +9.27450 q^{94} +10.1022 q^{95} +0.418005 q^{96} -17.8996 q^{97} -3.71531 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 4q^{2} + 16q^{3} + 12q^{4} - 12q^{5} - 4q^{6} - 12q^{8} + 16q^{9} + O(q^{10}) \) \( 16q - 4q^{2} + 16q^{3} + 12q^{4} - 12q^{5} - 4q^{6} - 12q^{8} + 16q^{9} - 4q^{10} - 4q^{11} + 12q^{12} - 12q^{15} - 8q^{17} - 4q^{18} + 4q^{19} - 20q^{20} - 16q^{22} - 12q^{23} - 12q^{24} - 8q^{25} - 8q^{26} + 16q^{27} - 16q^{29} - 4q^{30} - 4q^{31} - 48q^{32} - 4q^{33} + 16q^{34} + 12q^{36} - 48q^{37} - 4q^{38} + 56q^{40} + 16q^{41} - 16q^{43} - 12q^{45} - 4q^{46} - 36q^{47} - 8q^{50} - 8q^{51} - 60q^{53} - 4q^{54} + 8q^{55} + 4q^{57} - 36q^{58} - 36q^{59} - 20q^{60} - 4q^{61} - 12q^{62} + 52q^{64} - 36q^{65} - 16q^{66} - 52q^{67} - 8q^{68} - 12q^{69} - 12q^{71} - 12q^{72} - 16q^{73} + 4q^{74} - 8q^{75} + 16q^{76} - 8q^{78} - 36q^{79} - 68q^{80} + 16q^{81} - 4q^{82} - 32q^{83} - 28q^{85} - 8q^{86} - 16q^{87} - 36q^{88} - 12q^{89} - 4q^{90} - 36q^{92} - 4q^{93} + 24q^{94} - 20q^{95} - 48q^{96} + 48q^{97} - 4q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.44011 −1.01832 −0.509158 0.860673i \(-0.670043\pi\)
−0.509158 + 0.860673i \(0.670043\pi\)
\(3\) 1.00000 0.577350
\(4\) 0.0739309 0.0369655
\(5\) 3.20961 1.43538 0.717692 0.696361i \(-0.245199\pi\)
0.717692 + 0.696361i \(0.245199\pi\)
\(6\) −1.44011 −0.587924
\(7\) 0 0
\(8\) 2.77376 0.980673
\(9\) 1.00000 0.333333
\(10\) −4.62221 −1.46167
\(11\) −3.71531 −1.12021 −0.560103 0.828423i \(-0.689239\pi\)
−0.560103 + 0.828423i \(0.689239\pi\)
\(12\) 0.0739309 0.0213420
\(13\) 1.13302 0.314242 0.157121 0.987579i \(-0.449779\pi\)
0.157121 + 0.987579i \(0.449779\pi\)
\(14\) 0 0
\(15\) 3.20961 0.828719
\(16\) −4.14240 −1.03560
\(17\) −5.67373 −1.37608 −0.688041 0.725672i \(-0.741529\pi\)
−0.688041 + 0.725672i \(0.741529\pi\)
\(18\) −1.44011 −0.339438
\(19\) 3.14749 0.722083 0.361041 0.932550i \(-0.382421\pi\)
0.361041 + 0.932550i \(0.382421\pi\)
\(20\) 0.237290 0.0530596
\(21\) 0 0
\(22\) 5.35047 1.14072
\(23\) −4.86181 −1.01376 −0.506879 0.862017i \(-0.669201\pi\)
−0.506879 + 0.862017i \(0.669201\pi\)
\(24\) 2.77376 0.566192
\(25\) 5.30163 1.06033
\(26\) −1.63167 −0.319998
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 2.25032 0.417874 0.208937 0.977929i \(-0.433000\pi\)
0.208937 + 0.977929i \(0.433000\pi\)
\(30\) −4.62221 −0.843897
\(31\) −1.73959 −0.312439 −0.156219 0.987722i \(-0.549931\pi\)
−0.156219 + 0.987722i \(0.549931\pi\)
\(32\) 0.418005 0.0738935
\(33\) −3.71531 −0.646752
\(34\) 8.17082 1.40128
\(35\) 0 0
\(36\) 0.0739309 0.0123218
\(37\) −4.53215 −0.745081 −0.372540 0.928016i \(-0.621513\pi\)
−0.372540 + 0.928016i \(0.621513\pi\)
\(38\) −4.53274 −0.735308
\(39\) 1.13302 0.181428
\(40\) 8.90270 1.40764
\(41\) 1.00000 0.156174
\(42\) 0 0
\(43\) −6.99210 −1.06629 −0.533143 0.846025i \(-0.678989\pi\)
−0.533143 + 0.846025i \(0.678989\pi\)
\(44\) −0.274676 −0.0414090
\(45\) 3.20961 0.478461
\(46\) 7.00157 1.03232
\(47\) −6.44011 −0.939387 −0.469694 0.882830i \(-0.655636\pi\)
−0.469694 + 0.882830i \(0.655636\pi\)
\(48\) −4.14240 −0.597903
\(49\) 0 0
\(50\) −7.63495 −1.07975
\(51\) −5.67373 −0.794481
\(52\) 0.0837649 0.0116161
\(53\) 3.39697 0.466610 0.233305 0.972404i \(-0.425046\pi\)
0.233305 + 0.972404i \(0.425046\pi\)
\(54\) −1.44011 −0.195975
\(55\) −11.9247 −1.60793
\(56\) 0 0
\(57\) 3.14749 0.416895
\(58\) −3.24072 −0.425528
\(59\) −3.87745 −0.504800 −0.252400 0.967623i \(-0.581220\pi\)
−0.252400 + 0.967623i \(0.581220\pi\)
\(60\) 0.237290 0.0306340
\(61\) 8.17051 1.04613 0.523063 0.852294i \(-0.324789\pi\)
0.523063 + 0.852294i \(0.324789\pi\)
\(62\) 2.50520 0.318161
\(63\) 0 0
\(64\) 7.68282 0.960352
\(65\) 3.63655 0.451058
\(66\) 5.35047 0.658597
\(67\) −4.36043 −0.532712 −0.266356 0.963875i \(-0.585820\pi\)
−0.266356 + 0.963875i \(0.585820\pi\)
\(68\) −0.419464 −0.0508675
\(69\) −4.86181 −0.585293
\(70\) 0 0
\(71\) 7.54065 0.894910 0.447455 0.894306i \(-0.352330\pi\)
0.447455 + 0.894306i \(0.352330\pi\)
\(72\) 2.77376 0.326891
\(73\) −9.11677 −1.06704 −0.533519 0.845788i \(-0.679131\pi\)
−0.533519 + 0.845788i \(0.679131\pi\)
\(74\) 6.52682 0.758727
\(75\) 5.30163 0.612179
\(76\) 0.232697 0.0266921
\(77\) 0 0
\(78\) −1.63167 −0.184751
\(79\) 0.0474074 0.00533375 0.00266688 0.999996i \(-0.499151\pi\)
0.00266688 + 0.999996i \(0.499151\pi\)
\(80\) −13.2955 −1.48648
\(81\) 1.00000 0.111111
\(82\) −1.44011 −0.159034
\(83\) −8.03200 −0.881626 −0.440813 0.897599i \(-0.645310\pi\)
−0.440813 + 0.897599i \(0.645310\pi\)
\(84\) 0 0
\(85\) −18.2105 −1.97520
\(86\) 10.0694 1.08581
\(87\) 2.25032 0.241260
\(88\) −10.3054 −1.09856
\(89\) −9.30187 −0.985996 −0.492998 0.870030i \(-0.664099\pi\)
−0.492998 + 0.870030i \(0.664099\pi\)
\(90\) −4.62221 −0.487224
\(91\) 0 0
\(92\) −0.359438 −0.0374740
\(93\) −1.73959 −0.180387
\(94\) 9.27450 0.956592
\(95\) 10.1022 1.03647
\(96\) 0.418005 0.0426624
\(97\) −17.8996 −1.81743 −0.908714 0.417420i \(-0.862934\pi\)
−0.908714 + 0.417420i \(0.862934\pi\)
\(98\) 0 0
\(99\) −3.71531 −0.373402
\(100\) 0.391954 0.0391954
\(101\) −3.11847 −0.310300 −0.155150 0.987891i \(-0.549586\pi\)
−0.155150 + 0.987891i \(0.549586\pi\)
\(102\) 8.17082 0.809032
\(103\) 2.85378 0.281192 0.140596 0.990067i \(-0.455098\pi\)
0.140596 + 0.990067i \(0.455098\pi\)
\(104\) 3.14272 0.308169
\(105\) 0 0
\(106\) −4.89203 −0.475156
\(107\) 12.8370 1.24100 0.620500 0.784206i \(-0.286930\pi\)
0.620500 + 0.784206i \(0.286930\pi\)
\(108\) 0.0739309 0.00711401
\(109\) −19.4326 −1.86131 −0.930655 0.365899i \(-0.880762\pi\)
−0.930655 + 0.365899i \(0.880762\pi\)
\(110\) 17.1729 1.63738
\(111\) −4.53215 −0.430173
\(112\) 0 0
\(113\) −8.96160 −0.843037 −0.421518 0.906820i \(-0.638503\pi\)
−0.421518 + 0.906820i \(0.638503\pi\)
\(114\) −4.53274 −0.424530
\(115\) −15.6045 −1.45513
\(116\) 0.166368 0.0154469
\(117\) 1.13302 0.104747
\(118\) 5.58397 0.514046
\(119\) 0 0
\(120\) 8.90270 0.812702
\(121\) 2.80350 0.254863
\(122\) −11.7665 −1.06529
\(123\) 1.00000 0.0901670
\(124\) −0.128609 −0.0115495
\(125\) 0.968108 0.0865902
\(126\) 0 0
\(127\) 15.5846 1.38291 0.691455 0.722420i \(-0.256970\pi\)
0.691455 + 0.722420i \(0.256970\pi\)
\(128\) −11.9001 −1.05183
\(129\) −6.99210 −0.615620
\(130\) −5.23704 −0.459319
\(131\) 11.1927 0.977913 0.488957 0.872308i \(-0.337378\pi\)
0.488957 + 0.872308i \(0.337378\pi\)
\(132\) −0.274676 −0.0239075
\(133\) 0 0
\(134\) 6.27953 0.542468
\(135\) 3.20961 0.276240
\(136\) −15.7376 −1.34949
\(137\) −9.63284 −0.822989 −0.411494 0.911412i \(-0.634993\pi\)
−0.411494 + 0.911412i \(0.634993\pi\)
\(138\) 7.00157 0.596013
\(139\) −12.4957 −1.05987 −0.529935 0.848039i \(-0.677784\pi\)
−0.529935 + 0.848039i \(0.677784\pi\)
\(140\) 0 0
\(141\) −6.44011 −0.542355
\(142\) −10.8594 −0.911301
\(143\) −4.20950 −0.352016
\(144\) −4.14240 −0.345200
\(145\) 7.22267 0.599810
\(146\) 13.1292 1.08658
\(147\) 0 0
\(148\) −0.335066 −0.0275423
\(149\) −13.7960 −1.13021 −0.565105 0.825019i \(-0.691165\pi\)
−0.565105 + 0.825019i \(0.691165\pi\)
\(150\) −7.63495 −0.623391
\(151\) 15.3274 1.24733 0.623663 0.781694i \(-0.285644\pi\)
0.623663 + 0.781694i \(0.285644\pi\)
\(152\) 8.73037 0.708127
\(153\) −5.67373 −0.458694
\(154\) 0 0
\(155\) −5.58340 −0.448470
\(156\) 0.0837649 0.00670656
\(157\) −5.91126 −0.471770 −0.235885 0.971781i \(-0.575799\pi\)
−0.235885 + 0.971781i \(0.575799\pi\)
\(158\) −0.0682721 −0.00543144
\(159\) 3.39697 0.269398
\(160\) 1.34163 0.106066
\(161\) 0 0
\(162\) −1.44011 −0.113146
\(163\) 9.18322 0.719285 0.359643 0.933090i \(-0.382899\pi\)
0.359643 + 0.933090i \(0.382899\pi\)
\(164\) 0.0739309 0.00577304
\(165\) −11.9247 −0.928337
\(166\) 11.5670 0.897773
\(167\) −20.1802 −1.56159 −0.780795 0.624787i \(-0.785186\pi\)
−0.780795 + 0.624787i \(0.785186\pi\)
\(168\) 0 0
\(169\) −11.7163 −0.901252
\(170\) 26.2252 2.01138
\(171\) 3.14749 0.240694
\(172\) −0.516932 −0.0394157
\(173\) −22.8081 −1.73407 −0.867033 0.498250i \(-0.833976\pi\)
−0.867033 + 0.498250i \(0.833976\pi\)
\(174\) −3.24072 −0.245679
\(175\) 0 0
\(176\) 15.3903 1.16009
\(177\) −3.87745 −0.291447
\(178\) 13.3958 1.00405
\(179\) 22.3973 1.67405 0.837025 0.547165i \(-0.184293\pi\)
0.837025 + 0.547165i \(0.184293\pi\)
\(180\) 0.237290 0.0176865
\(181\) 18.9086 1.40546 0.702732 0.711455i \(-0.251963\pi\)
0.702732 + 0.711455i \(0.251963\pi\)
\(182\) 0 0
\(183\) 8.17051 0.603981
\(184\) −13.4855 −0.994165
\(185\) −14.5465 −1.06948
\(186\) 2.50520 0.183691
\(187\) 21.0796 1.54150
\(188\) −0.476124 −0.0347249
\(189\) 0 0
\(190\) −14.5484 −1.05545
\(191\) 19.3875 1.40283 0.701416 0.712752i \(-0.252552\pi\)
0.701416 + 0.712752i \(0.252552\pi\)
\(192\) 7.68282 0.554460
\(193\) −8.99357 −0.647371 −0.323686 0.946165i \(-0.604922\pi\)
−0.323686 + 0.946165i \(0.604922\pi\)
\(194\) 25.7775 1.85071
\(195\) 3.63655 0.260418
\(196\) 0 0
\(197\) −16.6318 −1.18497 −0.592484 0.805583i \(-0.701852\pi\)
−0.592484 + 0.805583i \(0.701852\pi\)
\(198\) 5.35047 0.380241
\(199\) 8.98803 0.637144 0.318572 0.947899i \(-0.396797\pi\)
0.318572 + 0.947899i \(0.396797\pi\)
\(200\) 14.7054 1.03983
\(201\) −4.36043 −0.307561
\(202\) 4.49096 0.315983
\(203\) 0 0
\(204\) −0.419464 −0.0293684
\(205\) 3.20961 0.224169
\(206\) −4.10978 −0.286342
\(207\) −4.86181 −0.337919
\(208\) −4.69340 −0.325429
\(209\) −11.6939 −0.808882
\(210\) 0 0
\(211\) 25.8993 1.78298 0.891490 0.453040i \(-0.149661\pi\)
0.891490 + 0.453040i \(0.149661\pi\)
\(212\) 0.251141 0.0172485
\(213\) 7.54065 0.516677
\(214\) −18.4868 −1.26373
\(215\) −22.4419 −1.53053
\(216\) 2.77376 0.188731
\(217\) 0 0
\(218\) 27.9852 1.89540
\(219\) −9.11677 −0.616054
\(220\) −0.881604 −0.0594377
\(221\) −6.42843 −0.432423
\(222\) 6.52682 0.438051
\(223\) 18.1127 1.21292 0.606458 0.795115i \(-0.292590\pi\)
0.606458 + 0.795115i \(0.292590\pi\)
\(224\) 0 0
\(225\) 5.30163 0.353442
\(226\) 12.9057 0.858477
\(227\) −12.9994 −0.862802 −0.431401 0.902160i \(-0.641981\pi\)
−0.431401 + 0.902160i \(0.641981\pi\)
\(228\) 0.232697 0.0154107
\(229\) 5.48370 0.362373 0.181187 0.983449i \(-0.442006\pi\)
0.181187 + 0.983449i \(0.442006\pi\)
\(230\) 22.4723 1.48178
\(231\) 0 0
\(232\) 6.24186 0.409798
\(233\) 9.19946 0.602676 0.301338 0.953517i \(-0.402567\pi\)
0.301338 + 0.953517i \(0.402567\pi\)
\(234\) −1.63167 −0.106666
\(235\) −20.6703 −1.34838
\(236\) −0.286663 −0.0186602
\(237\) 0.0474074 0.00307944
\(238\) 0 0
\(239\) 0.823059 0.0532393 0.0266196 0.999646i \(-0.491526\pi\)
0.0266196 + 0.999646i \(0.491526\pi\)
\(240\) −13.2955 −0.858221
\(241\) 6.48256 0.417578 0.208789 0.977961i \(-0.433048\pi\)
0.208789 + 0.977961i \(0.433048\pi\)
\(242\) −4.03736 −0.259531
\(243\) 1.00000 0.0641500
\(244\) 0.604053 0.0386706
\(245\) 0 0
\(246\) −1.44011 −0.0918184
\(247\) 3.56615 0.226909
\(248\) −4.82520 −0.306400
\(249\) −8.03200 −0.509007
\(250\) −1.39419 −0.0881761
\(251\) 11.0992 0.700575 0.350287 0.936642i \(-0.386084\pi\)
0.350287 + 0.936642i \(0.386084\pi\)
\(252\) 0 0
\(253\) 18.0631 1.13562
\(254\) −22.4436 −1.40824
\(255\) −18.2105 −1.14039
\(256\) 1.77195 0.110747
\(257\) −9.44160 −0.588951 −0.294475 0.955659i \(-0.595145\pi\)
−0.294475 + 0.955659i \(0.595145\pi\)
\(258\) 10.0694 0.626895
\(259\) 0 0
\(260\) 0.268853 0.0166736
\(261\) 2.25032 0.139291
\(262\) −16.1188 −0.995824
\(263\) −12.5414 −0.773333 −0.386666 0.922220i \(-0.626374\pi\)
−0.386666 + 0.922220i \(0.626374\pi\)
\(264\) −10.3054 −0.634252
\(265\) 10.9030 0.669765
\(266\) 0 0
\(267\) −9.30187 −0.569265
\(268\) −0.322371 −0.0196919
\(269\) 2.28195 0.139133 0.0695666 0.997577i \(-0.477838\pi\)
0.0695666 + 0.997577i \(0.477838\pi\)
\(270\) −4.62221 −0.281299
\(271\) −12.2113 −0.741781 −0.370891 0.928677i \(-0.620948\pi\)
−0.370891 + 0.928677i \(0.620948\pi\)
\(272\) 23.5028 1.42507
\(273\) 0 0
\(274\) 13.8724 0.838062
\(275\) −19.6972 −1.18778
\(276\) −0.359438 −0.0216356
\(277\) −24.7287 −1.48580 −0.742901 0.669401i \(-0.766551\pi\)
−0.742901 + 0.669401i \(0.766551\pi\)
\(278\) 17.9952 1.07928
\(279\) −1.73959 −0.104146
\(280\) 0 0
\(281\) −4.87088 −0.290572 −0.145286 0.989390i \(-0.546410\pi\)
−0.145286 + 0.989390i \(0.546410\pi\)
\(282\) 9.27450 0.552289
\(283\) 4.43504 0.263636 0.131818 0.991274i \(-0.457919\pi\)
0.131818 + 0.991274i \(0.457919\pi\)
\(284\) 0.557487 0.0330808
\(285\) 10.1022 0.598404
\(286\) 6.06217 0.358463
\(287\) 0 0
\(288\) 0.418005 0.0246312
\(289\) 15.1912 0.893601
\(290\) −10.4015 −0.610795
\(291\) −17.8996 −1.04929
\(292\) −0.674011 −0.0394435
\(293\) 10.4636 0.611289 0.305644 0.952146i \(-0.401128\pi\)
0.305644 + 0.952146i \(0.401128\pi\)
\(294\) 0 0
\(295\) −12.4451 −0.724582
\(296\) −12.5711 −0.730680
\(297\) −3.71531 −0.215584
\(298\) 19.8678 1.15091
\(299\) −5.50851 −0.318566
\(300\) 0.391954 0.0226295
\(301\) 0 0
\(302\) −22.0732 −1.27017
\(303\) −3.11847 −0.179152
\(304\) −13.0381 −0.747788
\(305\) 26.2242 1.50159
\(306\) 8.17082 0.467095
\(307\) −4.63816 −0.264714 −0.132357 0.991202i \(-0.542254\pi\)
−0.132357 + 0.991202i \(0.542254\pi\)
\(308\) 0 0
\(309\) 2.85378 0.162346
\(310\) 8.04074 0.456683
\(311\) 4.98755 0.282818 0.141409 0.989951i \(-0.454837\pi\)
0.141409 + 0.989951i \(0.454837\pi\)
\(312\) 3.14272 0.177921
\(313\) 12.0497 0.681087 0.340544 0.940229i \(-0.389389\pi\)
0.340544 + 0.940229i \(0.389389\pi\)
\(314\) 8.51289 0.480410
\(315\) 0 0
\(316\) 0.00350487 0.000197165 0
\(317\) 17.2675 0.969840 0.484920 0.874559i \(-0.338849\pi\)
0.484920 + 0.874559i \(0.338849\pi\)
\(318\) −4.89203 −0.274332
\(319\) −8.36064 −0.468106
\(320\) 24.6589 1.37847
\(321\) 12.8370 0.716492
\(322\) 0 0
\(323\) −17.8580 −0.993645
\(324\) 0.0739309 0.00410727
\(325\) 6.00683 0.333199
\(326\) −13.2249 −0.732459
\(327\) −19.4326 −1.07463
\(328\) 2.77376 0.153155
\(329\) 0 0
\(330\) 17.1729 0.945339
\(331\) −11.7004 −0.643110 −0.321555 0.946891i \(-0.604205\pi\)
−0.321555 + 0.946891i \(0.604205\pi\)
\(332\) −0.593813 −0.0325897
\(333\) −4.53215 −0.248360
\(334\) 29.0618 1.59019
\(335\) −13.9953 −0.764646
\(336\) 0 0
\(337\) 12.6186 0.687377 0.343689 0.939084i \(-0.388324\pi\)
0.343689 + 0.939084i \(0.388324\pi\)
\(338\) 16.8728 0.917758
\(339\) −8.96160 −0.486728
\(340\) −1.34632 −0.0730144
\(341\) 6.46310 0.349996
\(342\) −4.53274 −0.245103
\(343\) 0 0
\(344\) −19.3944 −1.04568
\(345\) −15.6045 −0.840120
\(346\) 32.8463 1.76583
\(347\) −22.2243 −1.19306 −0.596530 0.802591i \(-0.703454\pi\)
−0.596530 + 0.802591i \(0.703454\pi\)
\(348\) 0.166368 0.00891828
\(349\) 27.5451 1.47445 0.737227 0.675645i \(-0.236135\pi\)
0.737227 + 0.675645i \(0.236135\pi\)
\(350\) 0 0
\(351\) 1.13302 0.0604759
\(352\) −1.55302 −0.0827760
\(353\) −8.11789 −0.432072 −0.216036 0.976385i \(-0.569313\pi\)
−0.216036 + 0.976385i \(0.569313\pi\)
\(354\) 5.58397 0.296785
\(355\) 24.2026 1.28454
\(356\) −0.687696 −0.0364478
\(357\) 0 0
\(358\) −32.2546 −1.70471
\(359\) −16.6316 −0.877782 −0.438891 0.898540i \(-0.644629\pi\)
−0.438891 + 0.898540i \(0.644629\pi\)
\(360\) 8.90270 0.469214
\(361\) −9.09334 −0.478597
\(362\) −27.2305 −1.43121
\(363\) 2.80350 0.147145
\(364\) 0 0
\(365\) −29.2613 −1.53161
\(366\) −11.7665 −0.615043
\(367\) 23.5211 1.22779 0.613897 0.789386i \(-0.289601\pi\)
0.613897 + 0.789386i \(0.289601\pi\)
\(368\) 20.1396 1.04985
\(369\) 1.00000 0.0520579
\(370\) 20.9486 1.08906
\(371\) 0 0
\(372\) −0.128609 −0.00666808
\(373\) 14.4062 0.745923 0.372962 0.927847i \(-0.378342\pi\)
0.372962 + 0.927847i \(0.378342\pi\)
\(374\) −30.3571 −1.56973
\(375\) 0.968108 0.0499929
\(376\) −17.8633 −0.921231
\(377\) 2.54965 0.131314
\(378\) 0 0
\(379\) 4.88799 0.251079 0.125540 0.992089i \(-0.459934\pi\)
0.125540 + 0.992089i \(0.459934\pi\)
\(380\) 0.746866 0.0383134
\(381\) 15.5846 0.798423
\(382\) −27.9203 −1.42852
\(383\) 22.8952 1.16989 0.584944 0.811074i \(-0.301116\pi\)
0.584944 + 0.811074i \(0.301116\pi\)
\(384\) −11.9001 −0.607277
\(385\) 0 0
\(386\) 12.9518 0.659228
\(387\) −6.99210 −0.355428
\(388\) −1.32333 −0.0671821
\(389\) 13.6469 0.691925 0.345962 0.938248i \(-0.387553\pi\)
0.345962 + 0.938248i \(0.387553\pi\)
\(390\) −5.23704 −0.265188
\(391\) 27.5846 1.39501
\(392\) 0 0
\(393\) 11.1927 0.564599
\(394\) 23.9517 1.20667
\(395\) 0.152160 0.00765598
\(396\) −0.274676 −0.0138030
\(397\) 7.08009 0.355339 0.177670 0.984090i \(-0.443144\pi\)
0.177670 + 0.984090i \(0.443144\pi\)
\(398\) −12.9438 −0.648814
\(399\) 0 0
\(400\) −21.9614 −1.09807
\(401\) −29.9703 −1.49665 −0.748323 0.663335i \(-0.769141\pi\)
−0.748323 + 0.663335i \(0.769141\pi\)
\(402\) 6.27953 0.313194
\(403\) −1.97098 −0.0981815
\(404\) −0.230552 −0.0114704
\(405\) 3.20961 0.159487
\(406\) 0 0
\(407\) 16.8383 0.834645
\(408\) −15.7376 −0.779126
\(409\) −13.3731 −0.661258 −0.330629 0.943761i \(-0.607261\pi\)
−0.330629 + 0.943761i \(0.607261\pi\)
\(410\) −4.62221 −0.228275
\(411\) −9.63284 −0.475153
\(412\) 0.210983 0.0103944
\(413\) 0 0
\(414\) 7.00157 0.344108
\(415\) −25.7796 −1.26547
\(416\) 0.473606 0.0232205
\(417\) −12.4957 −0.611916
\(418\) 16.8405 0.823697
\(419\) −24.2251 −1.18348 −0.591738 0.806131i \(-0.701558\pi\)
−0.591738 + 0.806131i \(0.701558\pi\)
\(420\) 0 0
\(421\) −13.2818 −0.647314 −0.323657 0.946174i \(-0.604912\pi\)
−0.323657 + 0.946174i \(0.604912\pi\)
\(422\) −37.2979 −1.81564
\(423\) −6.44011 −0.313129
\(424\) 9.42239 0.457592
\(425\) −30.0800 −1.45909
\(426\) −10.8594 −0.526140
\(427\) 0 0
\(428\) 0.949052 0.0458742
\(429\) −4.20950 −0.203237
\(430\) 32.3190 1.55856
\(431\) 16.2256 0.781562 0.390781 0.920484i \(-0.372205\pi\)
0.390781 + 0.920484i \(0.372205\pi\)
\(432\) −4.14240 −0.199301
\(433\) −1.61340 −0.0775351 −0.0387675 0.999248i \(-0.512343\pi\)
−0.0387675 + 0.999248i \(0.512343\pi\)
\(434\) 0 0
\(435\) 7.22267 0.346300
\(436\) −1.43667 −0.0688042
\(437\) −15.3025 −0.732017
\(438\) 13.1292 0.627337
\(439\) −15.4861 −0.739113 −0.369556 0.929208i \(-0.620490\pi\)
−0.369556 + 0.929208i \(0.620490\pi\)
\(440\) −33.0763 −1.57685
\(441\) 0 0
\(442\) 9.25768 0.440343
\(443\) −12.9825 −0.616817 −0.308409 0.951254i \(-0.599796\pi\)
−0.308409 + 0.951254i \(0.599796\pi\)
\(444\) −0.335066 −0.0159015
\(445\) −29.8554 −1.41528
\(446\) −26.0844 −1.23513
\(447\) −13.7960 −0.652528
\(448\) 0 0
\(449\) −25.4508 −1.20110 −0.600549 0.799588i \(-0.705051\pi\)
−0.600549 + 0.799588i \(0.705051\pi\)
\(450\) −7.63495 −0.359915
\(451\) −3.71531 −0.174947
\(452\) −0.662540 −0.0311633
\(453\) 15.3274 0.720144
\(454\) 18.7207 0.878604
\(455\) 0 0
\(456\) 8.73037 0.408837
\(457\) 14.1521 0.662009 0.331004 0.943629i \(-0.392613\pi\)
0.331004 + 0.943629i \(0.392613\pi\)
\(458\) −7.89716 −0.369010
\(459\) −5.67373 −0.264827
\(460\) −1.15366 −0.0537896
\(461\) 1.10138 0.0512963 0.0256481 0.999671i \(-0.491835\pi\)
0.0256481 + 0.999671i \(0.491835\pi\)
\(462\) 0 0
\(463\) −18.5041 −0.859958 −0.429979 0.902839i \(-0.641479\pi\)
−0.429979 + 0.902839i \(0.641479\pi\)
\(464\) −9.32173 −0.432750
\(465\) −5.58340 −0.258924
\(466\) −13.2483 −0.613714
\(467\) 26.1402 1.20962 0.604812 0.796368i \(-0.293248\pi\)
0.604812 + 0.796368i \(0.293248\pi\)
\(468\) 0.0837649 0.00387204
\(469\) 0 0
\(470\) 29.7676 1.37308
\(471\) −5.91126 −0.272377
\(472\) −10.7551 −0.495044
\(473\) 25.9778 1.19446
\(474\) −0.0682721 −0.00313584
\(475\) 16.6868 0.765643
\(476\) 0 0
\(477\) 3.39697 0.155537
\(478\) −1.18530 −0.0542143
\(479\) −31.4816 −1.43843 −0.719216 0.694787i \(-0.755499\pi\)
−0.719216 + 0.694787i \(0.755499\pi\)
\(480\) 1.34163 0.0612369
\(481\) −5.13500 −0.234136
\(482\) −9.33563 −0.425226
\(483\) 0 0
\(484\) 0.207265 0.00942115
\(485\) −57.4508 −2.60871
\(486\) −1.44011 −0.0653249
\(487\) 14.3104 0.648468 0.324234 0.945977i \(-0.394893\pi\)
0.324234 + 0.945977i \(0.394893\pi\)
\(488\) 22.6630 1.02591
\(489\) 9.18322 0.415279
\(490\) 0 0
\(491\) −21.7811 −0.982969 −0.491485 0.870886i \(-0.663546\pi\)
−0.491485 + 0.870886i \(0.663546\pi\)
\(492\) 0.0739309 0.00333306
\(493\) −12.7677 −0.575029
\(494\) −5.13567 −0.231065
\(495\) −11.9247 −0.535975
\(496\) 7.20606 0.323561
\(497\) 0 0
\(498\) 11.5670 0.518330
\(499\) −6.73070 −0.301308 −0.150654 0.988587i \(-0.548138\pi\)
−0.150654 + 0.988587i \(0.548138\pi\)
\(500\) 0.0715731 0.00320085
\(501\) −20.1802 −0.901585
\(502\) −15.9841 −0.713406
\(503\) 14.8815 0.663535 0.331768 0.943361i \(-0.392355\pi\)
0.331768 + 0.943361i \(0.392355\pi\)
\(504\) 0 0
\(505\) −10.0091 −0.445399
\(506\) −26.0130 −1.15642
\(507\) −11.7163 −0.520338
\(508\) 1.15218 0.0511199
\(509\) 1.57147 0.0696542 0.0348271 0.999393i \(-0.488912\pi\)
0.0348271 + 0.999393i \(0.488912\pi\)
\(510\) 26.2252 1.16127
\(511\) 0 0
\(512\) 21.2485 0.939059
\(513\) 3.14749 0.138965
\(514\) 13.5970 0.599737
\(515\) 9.15954 0.403618
\(516\) −0.516932 −0.0227567
\(517\) 23.9270 1.05231
\(518\) 0 0
\(519\) −22.8081 −1.00116
\(520\) 10.0869 0.442340
\(521\) 4.01664 0.175972 0.0879861 0.996122i \(-0.471957\pi\)
0.0879861 + 0.996122i \(0.471957\pi\)
\(522\) −3.24072 −0.141843
\(523\) −8.94282 −0.391042 −0.195521 0.980699i \(-0.562640\pi\)
−0.195521 + 0.980699i \(0.562640\pi\)
\(524\) 0.827489 0.0361490
\(525\) 0 0
\(526\) 18.0610 0.787496
\(527\) 9.86995 0.429942
\(528\) 15.3903 0.669775
\(529\) 0.637219 0.0277052
\(530\) −15.7015 −0.682031
\(531\) −3.87745 −0.168267
\(532\) 0 0
\(533\) 1.13302 0.0490764
\(534\) 13.3958 0.579691
\(535\) 41.2019 1.78131
\(536\) −12.0948 −0.522416
\(537\) 22.3973 0.966513
\(538\) −3.28628 −0.141681
\(539\) 0 0
\(540\) 0.237290 0.0102113
\(541\) 22.1175 0.950907 0.475453 0.879741i \(-0.342284\pi\)
0.475453 + 0.879741i \(0.342284\pi\)
\(542\) 17.5856 0.755367
\(543\) 18.9086 0.811445
\(544\) −2.37165 −0.101683
\(545\) −62.3713 −2.67169
\(546\) 0 0
\(547\) −3.20726 −0.137133 −0.0685663 0.997647i \(-0.521842\pi\)
−0.0685663 + 0.997647i \(0.521842\pi\)
\(548\) −0.712165 −0.0304222
\(549\) 8.17051 0.348709
\(550\) 28.3662 1.20954
\(551\) 7.08286 0.301740
\(552\) −13.4855 −0.573981
\(553\) 0 0
\(554\) 35.6121 1.51302
\(555\) −14.5465 −0.617463
\(556\) −0.923817 −0.0391786
\(557\) −36.1547 −1.53192 −0.765962 0.642886i \(-0.777737\pi\)
−0.765962 + 0.642886i \(0.777737\pi\)
\(558\) 2.50520 0.106054
\(559\) −7.92216 −0.335072
\(560\) 0 0
\(561\) 21.0796 0.889983
\(562\) 7.01463 0.295894
\(563\) 37.3991 1.57619 0.788093 0.615557i \(-0.211069\pi\)
0.788093 + 0.615557i \(0.211069\pi\)
\(564\) −0.476124 −0.0200484
\(565\) −28.7633 −1.21008
\(566\) −6.38697 −0.268464
\(567\) 0 0
\(568\) 20.9160 0.877614
\(569\) −38.4021 −1.60990 −0.804950 0.593342i \(-0.797808\pi\)
−0.804950 + 0.593342i \(0.797808\pi\)
\(570\) −14.5484 −0.609363
\(571\) 35.3708 1.48022 0.740112 0.672484i \(-0.234773\pi\)
0.740112 + 0.672484i \(0.234773\pi\)
\(572\) −0.311212 −0.0130124
\(573\) 19.3875 0.809925
\(574\) 0 0
\(575\) −25.7755 −1.07491
\(576\) 7.68282 0.320117
\(577\) 7.03644 0.292931 0.146465 0.989216i \(-0.453210\pi\)
0.146465 + 0.989216i \(0.453210\pi\)
\(578\) −21.8771 −0.909967
\(579\) −8.99357 −0.373760
\(580\) 0.533979 0.0221723
\(581\) 0 0
\(582\) 25.7775 1.06851
\(583\) −12.6208 −0.522700
\(584\) −25.2877 −1.04641
\(585\) 3.63655 0.150353
\(586\) −15.0687 −0.622484
\(587\) −42.9014 −1.77073 −0.885365 0.464897i \(-0.846091\pi\)
−0.885365 + 0.464897i \(0.846091\pi\)
\(588\) 0 0
\(589\) −5.47532 −0.225607
\(590\) 17.9224 0.737853
\(591\) −16.6318 −0.684141
\(592\) 18.7740 0.771605
\(593\) −29.8073 −1.22404 −0.612019 0.790843i \(-0.709642\pi\)
−0.612019 + 0.790843i \(0.709642\pi\)
\(594\) 5.35047 0.219532
\(595\) 0 0
\(596\) −1.01995 −0.0417788
\(597\) 8.98803 0.367855
\(598\) 7.93289 0.324400
\(599\) −4.94543 −0.202065 −0.101032 0.994883i \(-0.532215\pi\)
−0.101032 + 0.994883i \(0.532215\pi\)
\(600\) 14.7054 0.600347
\(601\) 31.4634 1.28342 0.641709 0.766948i \(-0.278226\pi\)
0.641709 + 0.766948i \(0.278226\pi\)
\(602\) 0 0
\(603\) −4.36043 −0.177571
\(604\) 1.13317 0.0461080
\(605\) 8.99815 0.365827
\(606\) 4.49096 0.182433
\(607\) 19.3517 0.785461 0.392730 0.919654i \(-0.371531\pi\)
0.392730 + 0.919654i \(0.371531\pi\)
\(608\) 1.31566 0.0533572
\(609\) 0 0
\(610\) −37.7658 −1.52909
\(611\) −7.29675 −0.295195
\(612\) −0.419464 −0.0169558
\(613\) −24.5783 −0.992708 −0.496354 0.868120i \(-0.665328\pi\)
−0.496354 + 0.868120i \(0.665328\pi\)
\(614\) 6.67948 0.269562
\(615\) 3.20961 0.129424
\(616\) 0 0
\(617\) −41.2037 −1.65880 −0.829399 0.558657i \(-0.811317\pi\)
−0.829399 + 0.558657i \(0.811317\pi\)
\(618\) −4.10978 −0.165319
\(619\) 10.0042 0.402102 0.201051 0.979581i \(-0.435564\pi\)
0.201051 + 0.979581i \(0.435564\pi\)
\(620\) −0.412786 −0.0165779
\(621\) −4.86181 −0.195098
\(622\) −7.18264 −0.287998
\(623\) 0 0
\(624\) −4.69340 −0.187886
\(625\) −23.4009 −0.936035
\(626\) −17.3529 −0.693561
\(627\) −11.6939 −0.467008
\(628\) −0.437025 −0.0174392
\(629\) 25.7142 1.02529
\(630\) 0 0
\(631\) −20.0998 −0.800162 −0.400081 0.916480i \(-0.631018\pi\)
−0.400081 + 0.916480i \(0.631018\pi\)
\(632\) 0.131497 0.00523066
\(633\) 25.8993 1.02940
\(634\) −24.8672 −0.987603
\(635\) 50.0205 1.98500
\(636\) 0.251141 0.00995841
\(637\) 0 0
\(638\) 12.0403 0.476679
\(639\) 7.54065 0.298303
\(640\) −38.1949 −1.50979
\(641\) 11.2048 0.442564 0.221282 0.975210i \(-0.428976\pi\)
0.221282 + 0.975210i \(0.428976\pi\)
\(642\) −18.4868 −0.729615
\(643\) −11.0643 −0.436334 −0.218167 0.975911i \(-0.570008\pi\)
−0.218167 + 0.975911i \(0.570008\pi\)
\(644\) 0 0
\(645\) −22.4419 −0.883651
\(646\) 25.7175 1.01184
\(647\) −0.620088 −0.0243782 −0.0121891 0.999926i \(-0.503880\pi\)
−0.0121891 + 0.999926i \(0.503880\pi\)
\(648\) 2.77376 0.108964
\(649\) 14.4059 0.565481
\(650\) −8.65053 −0.339302
\(651\) 0 0
\(652\) 0.678924 0.0265887
\(653\) 32.5395 1.27337 0.636684 0.771125i \(-0.280306\pi\)
0.636684 + 0.771125i \(0.280306\pi\)
\(654\) 27.9852 1.09431
\(655\) 35.9244 1.40368
\(656\) −4.14240 −0.161733
\(657\) −9.11677 −0.355679
\(658\) 0 0
\(659\) −40.2250 −1.56694 −0.783472 0.621427i \(-0.786553\pi\)
−0.783472 + 0.621427i \(0.786553\pi\)
\(660\) −0.881604 −0.0343164
\(661\) 8.07046 0.313904 0.156952 0.987606i \(-0.449833\pi\)
0.156952 + 0.987606i \(0.449833\pi\)
\(662\) 16.8499 0.654888
\(663\) −6.42843 −0.249659
\(664\) −22.2788 −0.864587
\(665\) 0 0
\(666\) 6.52682 0.252909
\(667\) −10.9406 −0.423623
\(668\) −1.49194 −0.0577249
\(669\) 18.1127 0.700278
\(670\) 20.1549 0.778650
\(671\) −30.3559 −1.17188
\(672\) 0 0
\(673\) −8.65901 −0.333780 −0.166890 0.985976i \(-0.553373\pi\)
−0.166890 + 0.985976i \(0.553373\pi\)
\(674\) −18.1722 −0.699967
\(675\) 5.30163 0.204060
\(676\) −0.866195 −0.0333152
\(677\) −41.8965 −1.61021 −0.805106 0.593131i \(-0.797892\pi\)
−0.805106 + 0.593131i \(0.797892\pi\)
\(678\) 12.9057 0.495642
\(679\) 0 0
\(680\) −50.5115 −1.93703
\(681\) −12.9994 −0.498139
\(682\) −9.30760 −0.356406
\(683\) 3.33986 0.127796 0.0638981 0.997956i \(-0.479647\pi\)
0.0638981 + 0.997956i \(0.479647\pi\)
\(684\) 0.232697 0.00889737
\(685\) −30.9177 −1.18130
\(686\) 0 0
\(687\) 5.48370 0.209216
\(688\) 28.9640 1.10424
\(689\) 3.84883 0.146629
\(690\) 22.4723 0.855507
\(691\) −37.2226 −1.41602 −0.708008 0.706205i \(-0.750406\pi\)
−0.708008 + 0.706205i \(0.750406\pi\)
\(692\) −1.68622 −0.0641006
\(693\) 0 0
\(694\) 32.0055 1.21491
\(695\) −40.1063 −1.52132
\(696\) 6.24186 0.236597
\(697\) −5.67373 −0.214908
\(698\) −39.6681 −1.50146
\(699\) 9.19946 0.347955
\(700\) 0 0
\(701\) 9.14668 0.345465 0.172733 0.984969i \(-0.444740\pi\)
0.172733 + 0.984969i \(0.444740\pi\)
\(702\) −1.63167 −0.0615836
\(703\) −14.2649 −0.538010
\(704\) −28.5440 −1.07579
\(705\) −20.6703 −0.778488
\(706\) 11.6907 0.439985
\(707\) 0 0
\(708\) −0.286663 −0.0107735
\(709\) −6.00600 −0.225560 −0.112780 0.993620i \(-0.535976\pi\)
−0.112780 + 0.993620i \(0.535976\pi\)
\(710\) −34.8545 −1.30807
\(711\) 0.0474074 0.00177792
\(712\) −25.8012 −0.966939
\(713\) 8.45754 0.316737
\(714\) 0 0
\(715\) −13.5109 −0.505278
\(716\) 1.65585 0.0618820
\(717\) 0.823059 0.0307377
\(718\) 23.9514 0.893859
\(719\) −33.9920 −1.26769 −0.633844 0.773461i \(-0.718524\pi\)
−0.633844 + 0.773461i \(0.718524\pi\)
\(720\) −13.2955 −0.495494
\(721\) 0 0
\(722\) 13.0954 0.487362
\(723\) 6.48256 0.241089
\(724\) 1.39793 0.0519536
\(725\) 11.9304 0.443083
\(726\) −4.03736 −0.149840
\(727\) −16.9197 −0.627516 −0.313758 0.949503i \(-0.601588\pi\)
−0.313758 + 0.949503i \(0.601588\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 42.1397 1.55966
\(731\) 39.6713 1.46730
\(732\) 0.604053 0.0223265
\(733\) 41.7959 1.54377 0.771884 0.635763i \(-0.219315\pi\)
0.771884 + 0.635763i \(0.219315\pi\)
\(734\) −33.8731 −1.25028
\(735\) 0 0
\(736\) −2.03226 −0.0749101
\(737\) 16.2003 0.596747
\(738\) −1.44011 −0.0530114
\(739\) −9.12094 −0.335519 −0.167760 0.985828i \(-0.553653\pi\)
−0.167760 + 0.985828i \(0.553653\pi\)
\(740\) −1.07543 −0.0395337
\(741\) 3.56615 0.131006
\(742\) 0 0
\(743\) 31.7676 1.16544 0.582720 0.812673i \(-0.301988\pi\)
0.582720 + 0.812673i \(0.301988\pi\)
\(744\) −4.82520 −0.176900
\(745\) −44.2798 −1.62229
\(746\) −20.7465 −0.759585
\(747\) −8.03200 −0.293875
\(748\) 1.55844 0.0569821
\(749\) 0 0
\(750\) −1.39419 −0.0509085
\(751\) −2.28714 −0.0834590 −0.0417295 0.999129i \(-0.513287\pi\)
−0.0417295 + 0.999129i \(0.513287\pi\)
\(752\) 26.6775 0.972828
\(753\) 11.0992 0.404477
\(754\) −3.67179 −0.133719
\(755\) 49.1950 1.79039
\(756\) 0 0
\(757\) 34.8962 1.26832 0.634162 0.773201i \(-0.281345\pi\)
0.634162 + 0.773201i \(0.281345\pi\)
\(758\) −7.03927 −0.255678
\(759\) 18.0631 0.655650
\(760\) 28.0211 1.01643
\(761\) −21.0081 −0.761544 −0.380772 0.924669i \(-0.624342\pi\)
−0.380772 + 0.924669i \(0.624342\pi\)
\(762\) −22.4436 −0.813046
\(763\) 0 0
\(764\) 1.43334 0.0518563
\(765\) −18.2105 −0.658402
\(766\) −32.9717 −1.19131
\(767\) −4.39321 −0.158630
\(768\) 1.77195 0.0639397
\(769\) 18.4285 0.664548 0.332274 0.943183i \(-0.392184\pi\)
0.332274 + 0.943183i \(0.392184\pi\)
\(770\) 0 0
\(771\) −9.44160 −0.340031
\(772\) −0.664903 −0.0239304
\(773\) 53.0919 1.90958 0.954791 0.297277i \(-0.0960783\pi\)
0.954791 + 0.297277i \(0.0960783\pi\)
\(774\) 10.0694 0.361938
\(775\) −9.22264 −0.331287
\(776\) −49.6492 −1.78230
\(777\) 0 0
\(778\) −19.6531 −0.704597
\(779\) 3.14749 0.112770
\(780\) 0.268853 0.00962649
\(781\) −28.0158 −1.00248
\(782\) −39.7250 −1.42056
\(783\) 2.25032 0.0804200
\(784\) 0 0
\(785\) −18.9729 −0.677171
\(786\) −16.1188 −0.574939
\(787\) 23.7459 0.846451 0.423226 0.906024i \(-0.360898\pi\)
0.423226 + 0.906024i \(0.360898\pi\)
\(788\) −1.22960 −0.0438029
\(789\) −12.5414 −0.446484
\(790\) −0.219127 −0.00779620
\(791\) 0 0
\(792\) −10.3054 −0.366185
\(793\) 9.25732 0.328737
\(794\) −10.1961 −0.361847
\(795\) 10.9030 0.386689
\(796\) 0.664493 0.0235523
\(797\) 49.8669 1.76638 0.883189 0.469018i \(-0.155392\pi\)
0.883189 + 0.469018i \(0.155392\pi\)
\(798\) 0 0
\(799\) 36.5395 1.29267
\(800\) 2.21611 0.0783512
\(801\) −9.30187 −0.328665
\(802\) 43.1607 1.52406
\(803\) 33.8716 1.19530
\(804\) −0.322371 −0.0113691
\(805\) 0 0
\(806\) 2.83844 0.0999797
\(807\) 2.28195 0.0803286
\(808\) −8.64990 −0.304302
\(809\) 8.65135 0.304165 0.152083 0.988368i \(-0.451402\pi\)
0.152083 + 0.988368i \(0.451402\pi\)
\(810\) −4.62221 −0.162408
\(811\) 42.3391 1.48673 0.743363 0.668888i \(-0.233229\pi\)
0.743363 + 0.668888i \(0.233229\pi\)
\(812\) 0 0
\(813\) −12.2113 −0.428268
\(814\) −24.2491 −0.849931
\(815\) 29.4746 1.03245
\(816\) 23.5028 0.822764
\(817\) −22.0075 −0.769946
\(818\) 19.2588 0.673369
\(819\) 0 0
\(820\) 0.237290 0.00828652
\(821\) 14.9198 0.520703 0.260352 0.965514i \(-0.416162\pi\)
0.260352 + 0.965514i \(0.416162\pi\)
\(822\) 13.8724 0.483855
\(823\) −42.3059 −1.47469 −0.737346 0.675516i \(-0.763921\pi\)
−0.737346 + 0.675516i \(0.763921\pi\)
\(824\) 7.91571 0.275757
\(825\) −19.6972 −0.685767
\(826\) 0 0
\(827\) 18.8508 0.655507 0.327754 0.944763i \(-0.393708\pi\)
0.327754 + 0.944763i \(0.393708\pi\)
\(828\) −0.359438 −0.0124913
\(829\) −19.0982 −0.663307 −0.331654 0.943401i \(-0.607606\pi\)
−0.331654 + 0.943401i \(0.607606\pi\)
\(830\) 37.1256 1.28865
\(831\) −24.7287 −0.857829
\(832\) 8.70476 0.301783
\(833\) 0 0
\(834\) 17.9952 0.623123
\(835\) −64.7706 −2.24148
\(836\) −0.864539 −0.0299007
\(837\) −1.73959 −0.0601289
\(838\) 34.8870 1.20515
\(839\) −48.6318 −1.67895 −0.839477 0.543395i \(-0.817139\pi\)
−0.839477 + 0.543395i \(0.817139\pi\)
\(840\) 0 0
\(841\) −23.9360 −0.825381
\(842\) 19.1273 0.659170
\(843\) −4.87088 −0.167762
\(844\) 1.91476 0.0659087
\(845\) −37.6047 −1.29364
\(846\) 9.27450 0.318864
\(847\) 0 0
\(848\) −14.0716 −0.483221
\(849\) 4.43504 0.152210
\(850\) 43.3187 1.48582
\(851\) 22.0345 0.755332
\(852\) 0.557487 0.0190992
\(853\) −44.9375 −1.53863 −0.769316 0.638868i \(-0.779403\pi\)
−0.769316 + 0.638868i \(0.779403\pi\)
\(854\) 0 0
\(855\) 10.1022 0.345488
\(856\) 35.6068 1.21702
\(857\) −5.26810 −0.179955 −0.0899774 0.995944i \(-0.528679\pi\)
−0.0899774 + 0.995944i \(0.528679\pi\)
\(858\) 6.06217 0.206959
\(859\) −22.2259 −0.758336 −0.379168 0.925328i \(-0.623790\pi\)
−0.379168 + 0.925328i \(0.623790\pi\)
\(860\) −1.65915 −0.0565767
\(861\) 0 0
\(862\) −23.3668 −0.795876
\(863\) −1.76373 −0.0600380 −0.0300190 0.999549i \(-0.509557\pi\)
−0.0300190 + 0.999549i \(0.509557\pi\)
\(864\) 0.418005 0.0142208
\(865\) −73.2052 −2.48905
\(866\) 2.32348 0.0789551
\(867\) 15.1912 0.515921
\(868\) 0 0
\(869\) −0.176133 −0.00597491
\(870\) −10.4015 −0.352643
\(871\) −4.94044 −0.167401
\(872\) −53.9015 −1.82533
\(873\) −17.8996 −0.605809
\(874\) 22.0373 0.745424
\(875\) 0 0
\(876\) −0.674011 −0.0227727
\(877\) 30.4164 1.02709 0.513544 0.858063i \(-0.328332\pi\)
0.513544 + 0.858063i \(0.328332\pi\)
\(878\) 22.3018 0.752649
\(879\) 10.4636 0.352928
\(880\) 49.3968 1.66517
\(881\) −30.7584 −1.03628 −0.518138 0.855297i \(-0.673375\pi\)
−0.518138 + 0.855297i \(0.673375\pi\)
\(882\) 0 0
\(883\) 40.3820 1.35896 0.679482 0.733693i \(-0.262205\pi\)
0.679482 + 0.733693i \(0.262205\pi\)
\(884\) −0.475260 −0.0159847
\(885\) −12.4451 −0.418338
\(886\) 18.6963 0.628114
\(887\) −15.3104 −0.514073 −0.257037 0.966402i \(-0.582746\pi\)
−0.257037 + 0.966402i \(0.582746\pi\)
\(888\) −12.5711 −0.421859
\(889\) 0 0
\(890\) 42.9952 1.44120
\(891\) −3.71531 −0.124467
\(892\) 1.33909 0.0448360
\(893\) −20.2702 −0.678315
\(894\) 19.8678 0.664479
\(895\) 71.8866 2.40290
\(896\) 0 0
\(897\) −5.50851 −0.183924
\(898\) 36.6521 1.22310
\(899\) −3.91463 −0.130560
\(900\) 0.391954 0.0130651
\(901\) −19.2735 −0.642094
\(902\) 5.35047 0.178151
\(903\) 0 0
\(904\) −24.8573 −0.826743
\(905\) 60.6893 2.01738
\(906\) −22.0732 −0.733333
\(907\) −37.4485 −1.24346 −0.621728 0.783233i \(-0.713569\pi\)
−0.621728 + 0.783233i \(0.713569\pi\)
\(908\) −0.961060 −0.0318939
\(909\) −3.11847 −0.103433
\(910\) 0 0
\(911\) −14.5170 −0.480969 −0.240485 0.970653i \(-0.577306\pi\)
−0.240485 + 0.970653i \(0.577306\pi\)
\(912\) −13.0381 −0.431736
\(913\) 29.8413 0.987604
\(914\) −20.3807 −0.674133
\(915\) 26.2242 0.866945
\(916\) 0.405415 0.0133953
\(917\) 0 0
\(918\) 8.17082 0.269677
\(919\) 9.79265 0.323030 0.161515 0.986870i \(-0.448362\pi\)
0.161515 + 0.986870i \(0.448362\pi\)
\(920\) −43.2833 −1.42701
\(921\) −4.63816 −0.152832
\(922\) −1.58611 −0.0522357
\(923\) 8.54368 0.281219
\(924\) 0 0
\(925\) −24.0278 −0.790028
\(926\) 26.6480 0.875708
\(927\) 2.85378 0.0937305
\(928\) 0.940645 0.0308782
\(929\) 34.6323 1.13625 0.568124 0.822943i \(-0.307669\pi\)
0.568124 + 0.822943i \(0.307669\pi\)
\(930\) 8.04074 0.263666
\(931\) 0 0
\(932\) 0.680124 0.0222782
\(933\) 4.98755 0.163285
\(934\) −37.6449 −1.23178
\(935\) 67.6575 2.21264
\(936\) 3.14272 0.102723
\(937\) 26.5941 0.868793 0.434396 0.900722i \(-0.356962\pi\)
0.434396 + 0.900722i \(0.356962\pi\)
\(938\) 0 0
\(939\) 12.0497 0.393226
\(940\) −1.52817 −0.0498435
\(941\) 48.6579 1.58620 0.793101 0.609091i \(-0.208465\pi\)
0.793101 + 0.609091i \(0.208465\pi\)
\(942\) 8.51289 0.277365
\(943\) −4.86181 −0.158322
\(944\) 16.0619 0.522771
\(945\) 0 0
\(946\) −37.4110 −1.21634
\(947\) 20.1400 0.654462 0.327231 0.944944i \(-0.393885\pi\)
0.327231 + 0.944944i \(0.393885\pi\)
\(948\) 0.00350487 0.000113833 0
\(949\) −10.3294 −0.335308
\(950\) −24.0309 −0.779665
\(951\) 17.2675 0.559937
\(952\) 0 0
\(953\) 2.71373 0.0879063 0.0439531 0.999034i \(-0.486005\pi\)
0.0439531 + 0.999034i \(0.486005\pi\)
\(954\) −4.89203 −0.158385
\(955\) 62.2265 2.01360
\(956\) 0.0608495 0.00196801
\(957\) −8.36064 −0.270261
\(958\) 45.3371 1.46478
\(959\) 0 0
\(960\) 24.6589 0.795862
\(961\) −27.9738 −0.902382
\(962\) 7.39499 0.238424
\(963\) 12.8370 0.413667
\(964\) 0.479262 0.0154360
\(965\) −28.8659 −0.929226
\(966\) 0 0
\(967\) −45.3281 −1.45765 −0.728827 0.684698i \(-0.759934\pi\)
−0.728827 + 0.684698i \(0.759934\pi\)
\(968\) 7.77623 0.249938
\(969\) −17.8580 −0.573681
\(970\) 82.7357 2.65648
\(971\) −55.2056 −1.77163 −0.885816 0.464036i \(-0.846401\pi\)
−0.885816 + 0.464036i \(0.846401\pi\)
\(972\) 0.0739309 0.00237134
\(973\) 0 0
\(974\) −20.6087 −0.660345
\(975\) 6.00683 0.192373
\(976\) −33.8455 −1.08337
\(977\) −26.8269 −0.858268 −0.429134 0.903241i \(-0.641181\pi\)
−0.429134 + 0.903241i \(0.641181\pi\)
\(978\) −13.2249 −0.422885
\(979\) 34.5593 1.10452
\(980\) 0 0
\(981\) −19.4326 −0.620436
\(982\) 31.3673 1.00097
\(983\) 19.9926 0.637664 0.318832 0.947811i \(-0.396709\pi\)
0.318832 + 0.947811i \(0.396709\pi\)
\(984\) 2.77376 0.0884243
\(985\) −53.3817 −1.70088
\(986\) 18.3870 0.585561
\(987\) 0 0
\(988\) 0.263649 0.00838779
\(989\) 33.9943 1.08095
\(990\) 17.1729 0.545792
\(991\) 11.1839 0.355267 0.177633 0.984097i \(-0.443156\pi\)
0.177633 + 0.984097i \(0.443156\pi\)
\(992\) −0.727156 −0.0230872
\(993\) −11.7004 −0.371300
\(994\) 0 0
\(995\) 28.8481 0.914546
\(996\) −0.593813 −0.0188157
\(997\) 45.4682 1.43999 0.719996 0.693979i \(-0.244144\pi\)
0.719996 + 0.693979i \(0.244144\pi\)
\(998\) 9.69298 0.306826
\(999\) −4.53215 −0.143391
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 \(a_p\))