Properties

Label 6027.2.a.bm.1.15
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 1.15
Root \(-2.11474\)
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.11474 q^{2} +1.00000 q^{3} +2.47212 q^{4} -0.285010 q^{5} +2.11474 q^{6} +0.998417 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+2.11474 q^{2} +1.00000 q^{3} +2.47212 q^{4} -0.285010 q^{5} +2.11474 q^{6} +0.998417 q^{8} +1.00000 q^{9} -0.602721 q^{10} -3.38810 q^{11} +2.47212 q^{12} +0.720106 q^{13} -0.285010 q^{15} -2.83285 q^{16} -4.26834 q^{17} +2.11474 q^{18} -6.19369 q^{19} -0.704579 q^{20} -7.16495 q^{22} -3.13345 q^{23} +0.998417 q^{24} -4.91877 q^{25} +1.52284 q^{26} +1.00000 q^{27} +0.696665 q^{29} -0.602721 q^{30} +9.88002 q^{31} -7.98758 q^{32} -3.38810 q^{33} -9.02642 q^{34} +2.47212 q^{36} +0.244950 q^{37} -13.0980 q^{38} +0.720106 q^{39} -0.284558 q^{40} +1.00000 q^{41} -2.01718 q^{43} -8.37580 q^{44} -0.285010 q^{45} -6.62643 q^{46} -8.72811 q^{47} -2.83285 q^{48} -10.4019 q^{50} -4.26834 q^{51} +1.78019 q^{52} -14.1567 q^{53} +2.11474 q^{54} +0.965642 q^{55} -6.19369 q^{57} +1.47327 q^{58} +9.03275 q^{59} -0.704579 q^{60} +3.37394 q^{61} +20.8937 q^{62} -11.2259 q^{64} -0.205237 q^{65} -7.16495 q^{66} +10.3436 q^{67} -10.5519 q^{68} -3.13345 q^{69} +2.17761 q^{71} +0.998417 q^{72} -11.9292 q^{73} +0.518005 q^{74} -4.91877 q^{75} -15.3116 q^{76} +1.52284 q^{78} -11.8004 q^{79} +0.807391 q^{80} +1.00000 q^{81} +2.11474 q^{82} -7.48655 q^{83} +1.21652 q^{85} -4.26581 q^{86} +0.696665 q^{87} -3.38274 q^{88} +5.06017 q^{89} -0.602721 q^{90} -7.74628 q^{92} +9.88002 q^{93} -18.4577 q^{94} +1.76526 q^{95} -7.98758 q^{96} +15.2586 q^{97} -3.38810 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 4q^{2} + 16q^{3} + 12q^{4} - 12q^{5} - 4q^{6} - 12q^{8} + 16q^{9} + O(q^{10}) \) \( 16q - 4q^{2} + 16q^{3} + 12q^{4} - 12q^{5} - 4q^{6} - 12q^{8} + 16q^{9} - 4q^{10} - 4q^{11} + 12q^{12} - 12q^{15} - 8q^{17} - 4q^{18} + 4q^{19} - 20q^{20} - 16q^{22} - 12q^{23} - 12q^{24} - 8q^{25} - 8q^{26} + 16q^{27} - 16q^{29} - 4q^{30} - 4q^{31} - 48q^{32} - 4q^{33} + 16q^{34} + 12q^{36} - 48q^{37} - 4q^{38} + 56q^{40} + 16q^{41} - 16q^{43} - 12q^{45} - 4q^{46} - 36q^{47} - 8q^{50} - 8q^{51} - 60q^{53} - 4q^{54} + 8q^{55} + 4q^{57} - 36q^{58} - 36q^{59} - 20q^{60} - 4q^{61} - 12q^{62} + 52q^{64} - 36q^{65} - 16q^{66} - 52q^{67} - 8q^{68} - 12q^{69} - 12q^{71} - 12q^{72} - 16q^{73} + 4q^{74} - 8q^{75} + 16q^{76} - 8q^{78} - 36q^{79} - 68q^{80} + 16q^{81} - 4q^{82} - 32q^{83} - 28q^{85} - 8q^{86} - 16q^{87} - 36q^{88} - 12q^{89} - 4q^{90} - 36q^{92} - 4q^{93} + 24q^{94} - 20q^{95} - 48q^{96} + 48q^{97} - 4q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.11474 1.49535 0.747673 0.664067i \(-0.231171\pi\)
0.747673 + 0.664067i \(0.231171\pi\)
\(3\) 1.00000 0.577350
\(4\) 2.47212 1.23606
\(5\) −0.285010 −0.127460 −0.0637301 0.997967i \(-0.520300\pi\)
−0.0637301 + 0.997967i \(0.520300\pi\)
\(6\) 2.11474 0.863339
\(7\) 0 0
\(8\) 0.998417 0.352994
\(9\) 1.00000 0.333333
\(10\) −0.602721 −0.190597
\(11\) −3.38810 −1.02155 −0.510776 0.859714i \(-0.670642\pi\)
−0.510776 + 0.859714i \(0.670642\pi\)
\(12\) 2.47212 0.713640
\(13\) 0.720106 0.199721 0.0998607 0.995001i \(-0.468160\pi\)
0.0998607 + 0.995001i \(0.468160\pi\)
\(14\) 0 0
\(15\) −0.285010 −0.0735892
\(16\) −2.83285 −0.708214
\(17\) −4.26834 −1.03522 −0.517612 0.855616i \(-0.673179\pi\)
−0.517612 + 0.855616i \(0.673179\pi\)
\(18\) 2.11474 0.498449
\(19\) −6.19369 −1.42093 −0.710465 0.703733i \(-0.751515\pi\)
−0.710465 + 0.703733i \(0.751515\pi\)
\(20\) −0.704579 −0.157549
\(21\) 0 0
\(22\) −7.16495 −1.52757
\(23\) −3.13345 −0.653370 −0.326685 0.945133i \(-0.605932\pi\)
−0.326685 + 0.945133i \(0.605932\pi\)
\(24\) 0.998417 0.203801
\(25\) −4.91877 −0.983754
\(26\) 1.52284 0.298653
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 0.696665 0.129368 0.0646838 0.997906i \(-0.479396\pi\)
0.0646838 + 0.997906i \(0.479396\pi\)
\(30\) −0.602721 −0.110041
\(31\) 9.88002 1.77450 0.887252 0.461285i \(-0.152612\pi\)
0.887252 + 0.461285i \(0.152612\pi\)
\(32\) −7.98758 −1.41202
\(33\) −3.38810 −0.589793
\(34\) −9.02642 −1.54802
\(35\) 0 0
\(36\) 2.47212 0.412020
\(37\) 0.244950 0.0402695 0.0201348 0.999797i \(-0.493590\pi\)
0.0201348 + 0.999797i \(0.493590\pi\)
\(38\) −13.0980 −2.12478
\(39\) 0.720106 0.115309
\(40\) −0.284558 −0.0449926
\(41\) 1.00000 0.156174
\(42\) 0 0
\(43\) −2.01718 −0.307617 −0.153809 0.988101i \(-0.549154\pi\)
−0.153809 + 0.988101i \(0.549154\pi\)
\(44\) −8.37580 −1.26270
\(45\) −0.285010 −0.0424867
\(46\) −6.62643 −0.977014
\(47\) −8.72811 −1.27313 −0.636563 0.771225i \(-0.719644\pi\)
−0.636563 + 0.771225i \(0.719644\pi\)
\(48\) −2.83285 −0.408887
\(49\) 0 0
\(50\) −10.4019 −1.47105
\(51\) −4.26834 −0.597687
\(52\) 1.78019 0.246868
\(53\) −14.1567 −1.94457 −0.972283 0.233805i \(-0.924882\pi\)
−0.972283 + 0.233805i \(0.924882\pi\)
\(54\) 2.11474 0.287780
\(55\) 0.965642 0.130207
\(56\) 0 0
\(57\) −6.19369 −0.820374
\(58\) 1.47327 0.193449
\(59\) 9.03275 1.17596 0.587982 0.808874i \(-0.299923\pi\)
0.587982 + 0.808874i \(0.299923\pi\)
\(60\) −0.704579 −0.0909607
\(61\) 3.37394 0.431988 0.215994 0.976395i \(-0.430701\pi\)
0.215994 + 0.976395i \(0.430701\pi\)
\(62\) 20.8937 2.65350
\(63\) 0 0
\(64\) −11.2259 −1.40324
\(65\) −0.205237 −0.0254565
\(66\) −7.16495 −0.881945
\(67\) 10.3436 1.26367 0.631837 0.775101i \(-0.282301\pi\)
0.631837 + 0.775101i \(0.282301\pi\)
\(68\) −10.5519 −1.27960
\(69\) −3.13345 −0.377223
\(70\) 0 0
\(71\) 2.17761 0.258435 0.129217 0.991616i \(-0.458754\pi\)
0.129217 + 0.991616i \(0.458754\pi\)
\(72\) 0.998417 0.117665
\(73\) −11.9292 −1.39621 −0.698106 0.715994i \(-0.745974\pi\)
−0.698106 + 0.715994i \(0.745974\pi\)
\(74\) 0.518005 0.0602169
\(75\) −4.91877 −0.567971
\(76\) −15.3116 −1.75636
\(77\) 0 0
\(78\) 1.52284 0.172427
\(79\) −11.8004 −1.32764 −0.663822 0.747891i \(-0.731067\pi\)
−0.663822 + 0.747891i \(0.731067\pi\)
\(80\) 0.807391 0.0902690
\(81\) 1.00000 0.111111
\(82\) 2.11474 0.233534
\(83\) −7.48655 −0.821756 −0.410878 0.911690i \(-0.634778\pi\)
−0.410878 + 0.911690i \(0.634778\pi\)
\(84\) 0 0
\(85\) 1.21652 0.131950
\(86\) −4.26581 −0.459995
\(87\) 0.696665 0.0746904
\(88\) −3.38274 −0.360601
\(89\) 5.06017 0.536377 0.268188 0.963367i \(-0.413575\pi\)
0.268188 + 0.963367i \(0.413575\pi\)
\(90\) −0.602721 −0.0635324
\(91\) 0 0
\(92\) −7.74628 −0.807605
\(93\) 9.88002 1.02451
\(94\) −18.4577 −1.90376
\(95\) 1.76526 0.181112
\(96\) −7.98758 −0.815229
\(97\) 15.2586 1.54928 0.774639 0.632404i \(-0.217932\pi\)
0.774639 + 0.632404i \(0.217932\pi\)
\(98\) 0 0
\(99\) −3.38810 −0.340517
\(100\) −12.1598 −1.21598
\(101\) 16.7781 1.66948 0.834741 0.550642i \(-0.185617\pi\)
0.834741 + 0.550642i \(0.185617\pi\)
\(102\) −9.02642 −0.893749
\(103\) 7.17037 0.706518 0.353259 0.935526i \(-0.385073\pi\)
0.353259 + 0.935526i \(0.385073\pi\)
\(104\) 0.718966 0.0705004
\(105\) 0 0
\(106\) −29.9376 −2.90780
\(107\) −2.30396 −0.222733 −0.111366 0.993779i \(-0.535523\pi\)
−0.111366 + 0.993779i \(0.535523\pi\)
\(108\) 2.47212 0.237880
\(109\) −5.22043 −0.500026 −0.250013 0.968242i \(-0.580435\pi\)
−0.250013 + 0.968242i \(0.580435\pi\)
\(110\) 2.04208 0.194705
\(111\) 0.244950 0.0232496
\(112\) 0 0
\(113\) −10.1900 −0.958591 −0.479295 0.877654i \(-0.659108\pi\)
−0.479295 + 0.877654i \(0.659108\pi\)
\(114\) −13.0980 −1.22674
\(115\) 0.893064 0.0832786
\(116\) 1.72224 0.159906
\(117\) 0.720106 0.0665738
\(118\) 19.1019 1.75847
\(119\) 0 0
\(120\) −0.284558 −0.0259765
\(121\) 0.479235 0.0435668
\(122\) 7.13500 0.645972
\(123\) 1.00000 0.0901670
\(124\) 24.4246 2.19340
\(125\) 2.82694 0.252850
\(126\) 0 0
\(127\) −19.7843 −1.75557 −0.877785 0.479054i \(-0.840980\pi\)
−0.877785 + 0.479054i \(0.840980\pi\)
\(128\) −7.76479 −0.686317
\(129\) −2.01718 −0.177603
\(130\) −0.434023 −0.0380663
\(131\) −11.9961 −1.04811 −0.524054 0.851685i \(-0.675581\pi\)
−0.524054 + 0.851685i \(0.675581\pi\)
\(132\) −8.37580 −0.729020
\(133\) 0 0
\(134\) 21.8741 1.88963
\(135\) −0.285010 −0.0245297
\(136\) −4.26158 −0.365427
\(137\) −7.01086 −0.598978 −0.299489 0.954100i \(-0.596816\pi\)
−0.299489 + 0.954100i \(0.596816\pi\)
\(138\) −6.62643 −0.564079
\(139\) −8.32435 −0.706062 −0.353031 0.935612i \(-0.614849\pi\)
−0.353031 + 0.935612i \(0.614849\pi\)
\(140\) 0 0
\(141\) −8.72811 −0.735039
\(142\) 4.60507 0.386449
\(143\) −2.43979 −0.204026
\(144\) −2.83285 −0.236071
\(145\) −0.198556 −0.0164892
\(146\) −25.2272 −2.08782
\(147\) 0 0
\(148\) 0.605546 0.0497756
\(149\) 17.2597 1.41397 0.706987 0.707227i \(-0.250054\pi\)
0.706987 + 0.707227i \(0.250054\pi\)
\(150\) −10.4019 −0.849313
\(151\) 17.2443 1.40332 0.701661 0.712511i \(-0.252442\pi\)
0.701661 + 0.712511i \(0.252442\pi\)
\(152\) −6.18388 −0.501579
\(153\) −4.26834 −0.345075
\(154\) 0 0
\(155\) −2.81590 −0.226179
\(156\) 1.78019 0.142529
\(157\) 11.2308 0.896319 0.448160 0.893954i \(-0.352080\pi\)
0.448160 + 0.893954i \(0.352080\pi\)
\(158\) −24.9547 −1.98529
\(159\) −14.1567 −1.12270
\(160\) 2.27654 0.179976
\(161\) 0 0
\(162\) 2.11474 0.166150
\(163\) 5.68152 0.445011 0.222506 0.974931i \(-0.428576\pi\)
0.222506 + 0.974931i \(0.428576\pi\)
\(164\) 2.47212 0.193040
\(165\) 0.965642 0.0751751
\(166\) −15.8321 −1.22881
\(167\) 15.7473 1.21856 0.609281 0.792954i \(-0.291458\pi\)
0.609281 + 0.792954i \(0.291458\pi\)
\(168\) 0 0
\(169\) −12.4814 −0.960111
\(170\) 2.57262 0.197311
\(171\) −6.19369 −0.473643
\(172\) −4.98672 −0.380234
\(173\) −13.6448 −1.03739 −0.518696 0.854959i \(-0.673582\pi\)
−0.518696 + 0.854959i \(0.673582\pi\)
\(174\) 1.47327 0.111688
\(175\) 0 0
\(176\) 9.59800 0.723476
\(177\) 9.03275 0.678943
\(178\) 10.7009 0.802069
\(179\) −9.11935 −0.681612 −0.340806 0.940134i \(-0.610700\pi\)
−0.340806 + 0.940134i \(0.610700\pi\)
\(180\) −0.704579 −0.0525162
\(181\) 25.5291 1.89756 0.948782 0.315932i \(-0.102317\pi\)
0.948782 + 0.315932i \(0.102317\pi\)
\(182\) 0 0
\(183\) 3.37394 0.249409
\(184\) −3.12849 −0.230635
\(185\) −0.0698131 −0.00513276
\(186\) 20.8937 1.53200
\(187\) 14.4616 1.05753
\(188\) −21.5770 −1.57366
\(189\) 0 0
\(190\) 3.73307 0.270825
\(191\) −8.35959 −0.604879 −0.302440 0.953169i \(-0.597801\pi\)
−0.302440 + 0.953169i \(0.597801\pi\)
\(192\) −11.2259 −0.810163
\(193\) 19.4805 1.40224 0.701118 0.713045i \(-0.252685\pi\)
0.701118 + 0.713045i \(0.252685\pi\)
\(194\) 32.2680 2.31671
\(195\) −0.205237 −0.0146973
\(196\) 0 0
\(197\) 12.4743 0.888757 0.444378 0.895839i \(-0.353425\pi\)
0.444378 + 0.895839i \(0.353425\pi\)
\(198\) −7.16495 −0.509191
\(199\) 2.86737 0.203263 0.101631 0.994822i \(-0.467594\pi\)
0.101631 + 0.994822i \(0.467594\pi\)
\(200\) −4.91098 −0.347259
\(201\) 10.3436 0.729582
\(202\) 35.4813 2.49646
\(203\) 0 0
\(204\) −10.5519 −0.738777
\(205\) −0.285010 −0.0199059
\(206\) 15.1635 1.05649
\(207\) −3.13345 −0.217790
\(208\) −2.03995 −0.141445
\(209\) 20.9849 1.45155
\(210\) 0 0
\(211\) 7.31043 0.503270 0.251635 0.967822i \(-0.419032\pi\)
0.251635 + 0.967822i \(0.419032\pi\)
\(212\) −34.9970 −2.40360
\(213\) 2.17761 0.149207
\(214\) −4.87228 −0.333062
\(215\) 0.574916 0.0392090
\(216\) 0.998417 0.0679337
\(217\) 0 0
\(218\) −11.0398 −0.747713
\(219\) −11.9292 −0.806104
\(220\) 2.38718 0.160944
\(221\) −3.07365 −0.206756
\(222\) 0.518005 0.0347662
\(223\) 0.374802 0.0250986 0.0125493 0.999921i \(-0.496005\pi\)
0.0125493 + 0.999921i \(0.496005\pi\)
\(224\) 0 0
\(225\) −4.91877 −0.327918
\(226\) −21.5491 −1.43343
\(227\) −15.8874 −1.05448 −0.527240 0.849716i \(-0.676773\pi\)
−0.527240 + 0.849716i \(0.676773\pi\)
\(228\) −15.3116 −1.01403
\(229\) 19.5385 1.29114 0.645571 0.763701i \(-0.276620\pi\)
0.645571 + 0.763701i \(0.276620\pi\)
\(230\) 1.88860 0.124530
\(231\) 0 0
\(232\) 0.695562 0.0456659
\(233\) −17.0909 −1.11966 −0.559832 0.828606i \(-0.689134\pi\)
−0.559832 + 0.828606i \(0.689134\pi\)
\(234\) 1.52284 0.0995509
\(235\) 2.48760 0.162273
\(236\) 22.3301 1.45356
\(237\) −11.8004 −0.766515
\(238\) 0 0
\(239\) 15.0447 0.973162 0.486581 0.873636i \(-0.338244\pi\)
0.486581 + 0.873636i \(0.338244\pi\)
\(240\) 0.807391 0.0521168
\(241\) −0.539340 −0.0347419 −0.0173710 0.999849i \(-0.505530\pi\)
−0.0173710 + 0.999849i \(0.505530\pi\)
\(242\) 1.01346 0.0651475
\(243\) 1.00000 0.0641500
\(244\) 8.34079 0.533964
\(245\) 0 0
\(246\) 2.11474 0.134831
\(247\) −4.46011 −0.283790
\(248\) 9.86438 0.626389
\(249\) −7.48655 −0.474441
\(250\) 5.97825 0.378098
\(251\) 12.9971 0.820368 0.410184 0.912003i \(-0.365464\pi\)
0.410184 + 0.912003i \(0.365464\pi\)
\(252\) 0 0
\(253\) 10.6165 0.667451
\(254\) −41.8386 −2.62519
\(255\) 1.21652 0.0761812
\(256\) 6.03139 0.376962
\(257\) −29.5500 −1.84328 −0.921640 0.388046i \(-0.873150\pi\)
−0.921640 + 0.388046i \(0.873150\pi\)
\(258\) −4.26581 −0.265578
\(259\) 0 0
\(260\) −0.507371 −0.0314658
\(261\) 0.696665 0.0431225
\(262\) −25.3687 −1.56728
\(263\) 16.5947 1.02327 0.511637 0.859202i \(-0.329039\pi\)
0.511637 + 0.859202i \(0.329039\pi\)
\(264\) −3.38274 −0.208193
\(265\) 4.03478 0.247855
\(266\) 0 0
\(267\) 5.06017 0.309677
\(268\) 25.5707 1.56198
\(269\) −23.9750 −1.46178 −0.730891 0.682495i \(-0.760895\pi\)
−0.730891 + 0.682495i \(0.760895\pi\)
\(270\) −0.602721 −0.0366804
\(271\) −4.41087 −0.267941 −0.133971 0.990985i \(-0.542773\pi\)
−0.133971 + 0.990985i \(0.542773\pi\)
\(272\) 12.0916 0.733159
\(273\) 0 0
\(274\) −14.8261 −0.895680
\(275\) 16.6653 1.00495
\(276\) −7.74628 −0.466271
\(277\) −23.4865 −1.41117 −0.705584 0.708626i \(-0.749315\pi\)
−0.705584 + 0.708626i \(0.749315\pi\)
\(278\) −17.6038 −1.05581
\(279\) 9.88002 0.591501
\(280\) 0 0
\(281\) −23.5640 −1.40571 −0.702856 0.711332i \(-0.748092\pi\)
−0.702856 + 0.711332i \(0.748092\pi\)
\(282\) −18.4577 −1.09914
\(283\) −19.1984 −1.14123 −0.570614 0.821219i \(-0.693295\pi\)
−0.570614 + 0.821219i \(0.693295\pi\)
\(284\) 5.38331 0.319441
\(285\) 1.76526 0.104565
\(286\) −5.15952 −0.305089
\(287\) 0 0
\(288\) −7.98758 −0.470673
\(289\) 1.21870 0.0716880
\(290\) −0.419895 −0.0246571
\(291\) 15.2586 0.894476
\(292\) −29.4906 −1.72580
\(293\) 15.8156 0.923960 0.461980 0.886890i \(-0.347139\pi\)
0.461980 + 0.886890i \(0.347139\pi\)
\(294\) 0 0
\(295\) −2.57442 −0.149889
\(296\) 0.244562 0.0142149
\(297\) −3.38810 −0.196598
\(298\) 36.4999 2.11438
\(299\) −2.25642 −0.130492
\(300\) −12.1598 −0.702047
\(301\) 0 0
\(302\) 36.4672 2.09845
\(303\) 16.7781 0.963876
\(304\) 17.5458 1.00632
\(305\) −0.961604 −0.0550613
\(306\) −9.02642 −0.516006
\(307\) 1.88472 0.107567 0.0537834 0.998553i \(-0.482872\pi\)
0.0537834 + 0.998553i \(0.482872\pi\)
\(308\) 0 0
\(309\) 7.17037 0.407908
\(310\) −5.95489 −0.338215
\(311\) −5.69831 −0.323122 −0.161561 0.986863i \(-0.551653\pi\)
−0.161561 + 0.986863i \(0.551653\pi\)
\(312\) 0.718966 0.0407034
\(313\) −29.2119 −1.65116 −0.825578 0.564289i \(-0.809150\pi\)
−0.825578 + 0.564289i \(0.809150\pi\)
\(314\) 23.7503 1.34031
\(315\) 0 0
\(316\) −29.1719 −1.64105
\(317\) −32.9071 −1.84825 −0.924123 0.382096i \(-0.875202\pi\)
−0.924123 + 0.382096i \(0.875202\pi\)
\(318\) −29.9376 −1.67882
\(319\) −2.36037 −0.132156
\(320\) 3.19950 0.178858
\(321\) −2.30396 −0.128595
\(322\) 0 0
\(323\) 26.4368 1.47098
\(324\) 2.47212 0.137340
\(325\) −3.54203 −0.196477
\(326\) 12.0149 0.665446
\(327\) −5.22043 −0.288690
\(328\) 0.998417 0.0551283
\(329\) 0 0
\(330\) 2.04208 0.112413
\(331\) −17.9603 −0.987188 −0.493594 0.869692i \(-0.664317\pi\)
−0.493594 + 0.869692i \(0.664317\pi\)
\(332\) −18.5077 −1.01574
\(333\) 0.244950 0.0134232
\(334\) 33.3014 1.82217
\(335\) −2.94803 −0.161068
\(336\) 0 0
\(337\) −1.91719 −0.104436 −0.0522180 0.998636i \(-0.516629\pi\)
−0.0522180 + 0.998636i \(0.516629\pi\)
\(338\) −26.3950 −1.43570
\(339\) −10.1900 −0.553443
\(340\) 3.00738 0.163098
\(341\) −33.4745 −1.81275
\(342\) −13.0980 −0.708261
\(343\) 0 0
\(344\) −2.01399 −0.108587
\(345\) 0.893064 0.0480809
\(346\) −28.8551 −1.55126
\(347\) 3.05347 0.163919 0.0819595 0.996636i \(-0.473882\pi\)
0.0819595 + 0.996636i \(0.473882\pi\)
\(348\) 1.72224 0.0923219
\(349\) 18.5504 0.992981 0.496491 0.868042i \(-0.334622\pi\)
0.496491 + 0.868042i \(0.334622\pi\)
\(350\) 0 0
\(351\) 0.720106 0.0384364
\(352\) 27.0627 1.44245
\(353\) −10.4653 −0.557010 −0.278505 0.960435i \(-0.589839\pi\)
−0.278505 + 0.960435i \(0.589839\pi\)
\(354\) 19.1019 1.01526
\(355\) −0.620639 −0.0329401
\(356\) 12.5094 0.662995
\(357\) 0 0
\(358\) −19.2851 −1.01925
\(359\) 23.0278 1.21536 0.607682 0.794181i \(-0.292100\pi\)
0.607682 + 0.794181i \(0.292100\pi\)
\(360\) −0.284558 −0.0149975
\(361\) 19.3618 1.01904
\(362\) 53.9874 2.83751
\(363\) 0.479235 0.0251533
\(364\) 0 0
\(365\) 3.39995 0.177961
\(366\) 7.13500 0.372952
\(367\) −23.9454 −1.24994 −0.624970 0.780648i \(-0.714889\pi\)
−0.624970 + 0.780648i \(0.714889\pi\)
\(368\) 8.87661 0.462725
\(369\) 1.00000 0.0520579
\(370\) −0.147637 −0.00767526
\(371\) 0 0
\(372\) 24.4246 1.26636
\(373\) −21.8958 −1.13372 −0.566860 0.823814i \(-0.691842\pi\)
−0.566860 + 0.823814i \(0.691842\pi\)
\(374\) 30.5824 1.58138
\(375\) 2.82694 0.145983
\(376\) −8.71429 −0.449405
\(377\) 0.501673 0.0258375
\(378\) 0 0
\(379\) 14.7773 0.759058 0.379529 0.925180i \(-0.376086\pi\)
0.379529 + 0.925180i \(0.376086\pi\)
\(380\) 4.36394 0.223866
\(381\) −19.7843 −1.01358
\(382\) −17.6784 −0.904504
\(383\) −13.4489 −0.687206 −0.343603 0.939115i \(-0.611647\pi\)
−0.343603 + 0.939115i \(0.611647\pi\)
\(384\) −7.76479 −0.396245
\(385\) 0 0
\(386\) 41.1962 2.09683
\(387\) −2.01718 −0.102539
\(388\) 37.7212 1.91500
\(389\) −10.7324 −0.544156 −0.272078 0.962275i \(-0.587711\pi\)
−0.272078 + 0.962275i \(0.587711\pi\)
\(390\) −0.434023 −0.0219776
\(391\) 13.3746 0.676384
\(392\) 0 0
\(393\) −11.9961 −0.605125
\(394\) 26.3799 1.32900
\(395\) 3.36321 0.169222
\(396\) −8.37580 −0.420900
\(397\) −21.5444 −1.08128 −0.540641 0.841253i \(-0.681818\pi\)
−0.540641 + 0.841253i \(0.681818\pi\)
\(398\) 6.06374 0.303948
\(399\) 0 0
\(400\) 13.9342 0.696708
\(401\) 28.5605 1.42625 0.713123 0.701039i \(-0.247280\pi\)
0.713123 + 0.701039i \(0.247280\pi\)
\(402\) 21.8741 1.09098
\(403\) 7.11466 0.354406
\(404\) 41.4775 2.06358
\(405\) −0.285010 −0.0141622
\(406\) 0 0
\(407\) −0.829916 −0.0411374
\(408\) −4.26158 −0.210980
\(409\) 1.61277 0.0797462 0.0398731 0.999205i \(-0.487305\pi\)
0.0398731 + 0.999205i \(0.487305\pi\)
\(410\) −0.602721 −0.0297663
\(411\) −7.01086 −0.345820
\(412\) 17.7260 0.873300
\(413\) 0 0
\(414\) −6.62643 −0.325671
\(415\) 2.13374 0.104741
\(416\) −5.75190 −0.282010
\(417\) −8.32435 −0.407645
\(418\) 44.3775 2.17057
\(419\) −0.829572 −0.0405272 −0.0202636 0.999795i \(-0.506451\pi\)
−0.0202636 + 0.999795i \(0.506451\pi\)
\(420\) 0 0
\(421\) −3.10283 −0.151223 −0.0756113 0.997137i \(-0.524091\pi\)
−0.0756113 + 0.997137i \(0.524091\pi\)
\(422\) 15.4596 0.752564
\(423\) −8.72811 −0.424375
\(424\) −14.1342 −0.686420
\(425\) 20.9950 1.01841
\(426\) 4.60507 0.223117
\(427\) 0 0
\(428\) −5.69568 −0.275311
\(429\) −2.43979 −0.117794
\(430\) 1.21580 0.0586310
\(431\) −27.8777 −1.34282 −0.671411 0.741085i \(-0.734312\pi\)
−0.671411 + 0.741085i \(0.734312\pi\)
\(432\) −2.83285 −0.136296
\(433\) −28.4561 −1.36751 −0.683755 0.729711i \(-0.739654\pi\)
−0.683755 + 0.729711i \(0.739654\pi\)
\(434\) 0 0
\(435\) −0.198556 −0.00952005
\(436\) −12.9055 −0.618063
\(437\) 19.4076 0.928393
\(438\) −25.2272 −1.20540
\(439\) 25.2640 1.20579 0.602893 0.797822i \(-0.294014\pi\)
0.602893 + 0.797822i \(0.294014\pi\)
\(440\) 0.964113 0.0459623
\(441\) 0 0
\(442\) −6.49998 −0.309172
\(443\) −25.4878 −1.21096 −0.605480 0.795860i \(-0.707019\pi\)
−0.605480 + 0.795860i \(0.707019\pi\)
\(444\) 0.605546 0.0287380
\(445\) −1.44220 −0.0683667
\(446\) 0.792608 0.0375311
\(447\) 17.2597 0.816358
\(448\) 0 0
\(449\) 27.7044 1.30745 0.653726 0.756731i \(-0.273205\pi\)
0.653726 + 0.756731i \(0.273205\pi\)
\(450\) −10.4019 −0.490351
\(451\) −3.38810 −0.159539
\(452\) −25.1908 −1.18488
\(453\) 17.2443 0.810208
\(454\) −33.5976 −1.57681
\(455\) 0 0
\(456\) −6.18388 −0.289587
\(457\) −12.9935 −0.607808 −0.303904 0.952703i \(-0.598290\pi\)
−0.303904 + 0.952703i \(0.598290\pi\)
\(458\) 41.3189 1.93070
\(459\) −4.26834 −0.199229
\(460\) 2.20776 0.102937
\(461\) 5.41356 0.252135 0.126067 0.992022i \(-0.459764\pi\)
0.126067 + 0.992022i \(0.459764\pi\)
\(462\) 0 0
\(463\) 31.4718 1.46262 0.731309 0.682047i \(-0.238910\pi\)
0.731309 + 0.682047i \(0.238910\pi\)
\(464\) −1.97355 −0.0916198
\(465\) −2.81590 −0.130584
\(466\) −36.1429 −1.67429
\(467\) −22.4929 −1.04085 −0.520425 0.853908i \(-0.674226\pi\)
−0.520425 + 0.853908i \(0.674226\pi\)
\(468\) 1.78019 0.0822893
\(469\) 0 0
\(470\) 5.26062 0.242654
\(471\) 11.2308 0.517490
\(472\) 9.01845 0.415108
\(473\) 6.83442 0.314247
\(474\) −24.9547 −1.14621
\(475\) 30.4653 1.39785
\(476\) 0 0
\(477\) −14.1567 −0.648189
\(478\) 31.8157 1.45521
\(479\) 6.12855 0.280021 0.140010 0.990150i \(-0.455286\pi\)
0.140010 + 0.990150i \(0.455286\pi\)
\(480\) 2.27654 0.103909
\(481\) 0.176390 0.00804269
\(482\) −1.14056 −0.0519512
\(483\) 0 0
\(484\) 1.18473 0.0538512
\(485\) −4.34885 −0.197471
\(486\) 2.11474 0.0959265
\(487\) −29.9158 −1.35561 −0.677807 0.735240i \(-0.737069\pi\)
−0.677807 + 0.735240i \(0.737069\pi\)
\(488\) 3.36860 0.152489
\(489\) 5.68152 0.256927
\(490\) 0 0
\(491\) 20.4886 0.924639 0.462319 0.886713i \(-0.347017\pi\)
0.462319 + 0.886713i \(0.347017\pi\)
\(492\) 2.47212 0.111452
\(493\) −2.97360 −0.133924
\(494\) −9.43197 −0.424364
\(495\) 0.965642 0.0434024
\(496\) −27.9887 −1.25673
\(497\) 0 0
\(498\) −15.8321 −0.709454
\(499\) 32.9368 1.47445 0.737227 0.675645i \(-0.236135\pi\)
0.737227 + 0.675645i \(0.236135\pi\)
\(500\) 6.98855 0.312538
\(501\) 15.7473 0.703537
\(502\) 27.4854 1.22673
\(503\) 5.20938 0.232275 0.116137 0.993233i \(-0.462949\pi\)
0.116137 + 0.993233i \(0.462949\pi\)
\(504\) 0 0
\(505\) −4.78192 −0.212793
\(506\) 22.4510 0.998070
\(507\) −12.4814 −0.554321
\(508\) −48.9092 −2.16999
\(509\) 6.97305 0.309075 0.154537 0.987987i \(-0.450611\pi\)
0.154537 + 0.987987i \(0.450611\pi\)
\(510\) 2.57262 0.113917
\(511\) 0 0
\(512\) 28.2844 1.25001
\(513\) −6.19369 −0.273458
\(514\) −62.4906 −2.75634
\(515\) −2.04363 −0.0900529
\(516\) −4.98672 −0.219528
\(517\) 29.5717 1.30056
\(518\) 0 0
\(519\) −13.6448 −0.598938
\(520\) −0.204912 −0.00898599
\(521\) −21.7662 −0.953596 −0.476798 0.879013i \(-0.658203\pi\)
−0.476798 + 0.879013i \(0.658203\pi\)
\(522\) 1.47327 0.0644831
\(523\) 4.63146 0.202520 0.101260 0.994860i \(-0.467713\pi\)
0.101260 + 0.994860i \(0.467713\pi\)
\(524\) −29.6559 −1.29553
\(525\) 0 0
\(526\) 35.0935 1.53015
\(527\) −42.1712 −1.83701
\(528\) 9.59800 0.417699
\(529\) −13.1815 −0.573108
\(530\) 8.53252 0.370629
\(531\) 9.03275 0.391988
\(532\) 0 0
\(533\) 0.720106 0.0311912
\(534\) 10.7009 0.463075
\(535\) 0.656652 0.0283895
\(536\) 10.3272 0.446069
\(537\) −9.11935 −0.393529
\(538\) −50.7009 −2.18587
\(539\) 0 0
\(540\) −0.704579 −0.0303202
\(541\) 34.2767 1.47367 0.736836 0.676072i \(-0.236319\pi\)
0.736836 + 0.676072i \(0.236319\pi\)
\(542\) −9.32783 −0.400665
\(543\) 25.5291 1.09556
\(544\) 34.0937 1.46175
\(545\) 1.48787 0.0637335
\(546\) 0 0
\(547\) −27.1805 −1.16215 −0.581077 0.813848i \(-0.697369\pi\)
−0.581077 + 0.813848i \(0.697369\pi\)
\(548\) −17.3317 −0.740374
\(549\) 3.37394 0.143996
\(550\) 35.2428 1.50276
\(551\) −4.31493 −0.183822
\(552\) −3.12849 −0.133157
\(553\) 0 0
\(554\) −49.6679 −2.11019
\(555\) −0.0698131 −0.00296340
\(556\) −20.5788 −0.872736
\(557\) 14.9699 0.634295 0.317147 0.948376i \(-0.397275\pi\)
0.317147 + 0.948376i \(0.397275\pi\)
\(558\) 20.8937 0.884499
\(559\) −1.45258 −0.0614378
\(560\) 0 0
\(561\) 14.4616 0.610568
\(562\) −49.8318 −2.10203
\(563\) 22.5397 0.949936 0.474968 0.880003i \(-0.342460\pi\)
0.474968 + 0.880003i \(0.342460\pi\)
\(564\) −21.5770 −0.908554
\(565\) 2.90424 0.122182
\(566\) −40.5997 −1.70653
\(567\) 0 0
\(568\) 2.17416 0.0912257
\(569\) −14.3436 −0.601316 −0.300658 0.953732i \(-0.597206\pi\)
−0.300658 + 0.953732i \(0.597206\pi\)
\(570\) 3.73307 0.156361
\(571\) 35.6984 1.49393 0.746966 0.664862i \(-0.231510\pi\)
0.746966 + 0.664862i \(0.231510\pi\)
\(572\) −6.03146 −0.252188
\(573\) −8.35959 −0.349227
\(574\) 0 0
\(575\) 15.4127 0.642755
\(576\) −11.2259 −0.467748
\(577\) 12.4868 0.519834 0.259917 0.965631i \(-0.416305\pi\)
0.259917 + 0.965631i \(0.416305\pi\)
\(578\) 2.57723 0.107198
\(579\) 19.4805 0.809581
\(580\) −0.490856 −0.0203817
\(581\) 0 0
\(582\) 32.2680 1.33755
\(583\) 47.9642 1.98647
\(584\) −11.9104 −0.492854
\(585\) −0.205237 −0.00848551
\(586\) 33.4460 1.38164
\(587\) 0.691794 0.0285534 0.0142767 0.999898i \(-0.495455\pi\)
0.0142767 + 0.999898i \(0.495455\pi\)
\(588\) 0 0
\(589\) −61.1938 −2.52145
\(590\) −5.44423 −0.224135
\(591\) 12.4743 0.513124
\(592\) −0.693908 −0.0285194
\(593\) 28.8261 1.18375 0.591873 0.806031i \(-0.298389\pi\)
0.591873 + 0.806031i \(0.298389\pi\)
\(594\) −7.16495 −0.293982
\(595\) 0 0
\(596\) 42.6682 1.74776
\(597\) 2.86737 0.117354
\(598\) −4.77173 −0.195131
\(599\) 19.2475 0.786430 0.393215 0.919447i \(-0.371363\pi\)
0.393215 + 0.919447i \(0.371363\pi\)
\(600\) −4.91098 −0.200490
\(601\) 39.9895 1.63120 0.815602 0.578613i \(-0.196406\pi\)
0.815602 + 0.578613i \(0.196406\pi\)
\(602\) 0 0
\(603\) 10.3436 0.421225
\(604\) 42.6300 1.73459
\(605\) −0.136586 −0.00555303
\(606\) 35.4813 1.44133
\(607\) 18.0747 0.733631 0.366816 0.930294i \(-0.380448\pi\)
0.366816 + 0.930294i \(0.380448\pi\)
\(608\) 49.4726 2.00638
\(609\) 0 0
\(610\) −2.03354 −0.0823357
\(611\) −6.28516 −0.254270
\(612\) −10.5519 −0.426533
\(613\) −8.41473 −0.339868 −0.169934 0.985455i \(-0.554355\pi\)
−0.169934 + 0.985455i \(0.554355\pi\)
\(614\) 3.98569 0.160850
\(615\) −0.285010 −0.0114927
\(616\) 0 0
\(617\) 25.3196 1.01933 0.509665 0.860373i \(-0.329769\pi\)
0.509665 + 0.860373i \(0.329769\pi\)
\(618\) 15.1635 0.609964
\(619\) −6.35528 −0.255440 −0.127720 0.991810i \(-0.540766\pi\)
−0.127720 + 0.991810i \(0.540766\pi\)
\(620\) −6.96125 −0.279571
\(621\) −3.13345 −0.125741
\(622\) −12.0504 −0.483179
\(623\) 0 0
\(624\) −2.03995 −0.0816635
\(625\) 23.7881 0.951526
\(626\) −61.7756 −2.46905
\(627\) 20.9849 0.838054
\(628\) 27.7640 1.10791
\(629\) −1.04553 −0.0416880
\(630\) 0 0
\(631\) 0.544315 0.0216688 0.0108344 0.999941i \(-0.496551\pi\)
0.0108344 + 0.999941i \(0.496551\pi\)
\(632\) −11.7817 −0.468650
\(633\) 7.31043 0.290563
\(634\) −69.5899 −2.76377
\(635\) 5.63871 0.223765
\(636\) −34.9970 −1.38772
\(637\) 0 0
\(638\) −4.99157 −0.197618
\(639\) 2.17761 0.0861448
\(640\) 2.21304 0.0874781
\(641\) −5.08501 −0.200846 −0.100423 0.994945i \(-0.532020\pi\)
−0.100423 + 0.994945i \(0.532020\pi\)
\(642\) −4.87228 −0.192294
\(643\) −21.2796 −0.839186 −0.419593 0.907712i \(-0.637827\pi\)
−0.419593 + 0.907712i \(0.637827\pi\)
\(644\) 0 0
\(645\) 0.574916 0.0226373
\(646\) 55.9068 2.19963
\(647\) 1.39928 0.0550115 0.0275057 0.999622i \(-0.491244\pi\)
0.0275057 + 0.999622i \(0.491244\pi\)
\(648\) 0.998417 0.0392215
\(649\) −30.6039 −1.20131
\(650\) −7.49048 −0.293801
\(651\) 0 0
\(652\) 14.0454 0.550061
\(653\) 1.68680 0.0660096 0.0330048 0.999455i \(-0.489492\pi\)
0.0330048 + 0.999455i \(0.489492\pi\)
\(654\) −11.0398 −0.431692
\(655\) 3.41901 0.133592
\(656\) −2.83285 −0.110604
\(657\) −11.9292 −0.465404
\(658\) 0 0
\(659\) −4.28966 −0.167101 −0.0835507 0.996504i \(-0.526626\pi\)
−0.0835507 + 0.996504i \(0.526626\pi\)
\(660\) 2.38718 0.0929210
\(661\) 30.5094 1.18668 0.593340 0.804952i \(-0.297809\pi\)
0.593340 + 0.804952i \(0.297809\pi\)
\(662\) −37.9814 −1.47619
\(663\) −3.07365 −0.119371
\(664\) −7.47470 −0.290075
\(665\) 0 0
\(666\) 0.518005 0.0200723
\(667\) −2.18297 −0.0845248
\(668\) 38.9292 1.50622
\(669\) 0.374802 0.0144907
\(670\) −6.23432 −0.240853
\(671\) −11.4312 −0.441298
\(672\) 0 0
\(673\) 10.9216 0.420996 0.210498 0.977594i \(-0.432492\pi\)
0.210498 + 0.977594i \(0.432492\pi\)
\(674\) −4.05436 −0.156168
\(675\) −4.91877 −0.189324
\(676\) −30.8557 −1.18676
\(677\) −37.4920 −1.44093 −0.720467 0.693490i \(-0.756072\pi\)
−0.720467 + 0.693490i \(0.756072\pi\)
\(678\) −21.5491 −0.827589
\(679\) 0 0
\(680\) 1.21459 0.0465774
\(681\) −15.8874 −0.608805
\(682\) −70.7899 −2.71068
\(683\) −36.5776 −1.39960 −0.699802 0.714337i \(-0.746728\pi\)
−0.699802 + 0.714337i \(0.746728\pi\)
\(684\) −15.3116 −0.585452
\(685\) 1.99816 0.0763459
\(686\) 0 0
\(687\) 19.5385 0.745441
\(688\) 5.71438 0.217859
\(689\) −10.1943 −0.388372
\(690\) 1.88860 0.0718977
\(691\) −15.2245 −0.579167 −0.289584 0.957153i \(-0.593517\pi\)
−0.289584 + 0.957153i \(0.593517\pi\)
\(692\) −33.7315 −1.28228
\(693\) 0 0
\(694\) 6.45730 0.245116
\(695\) 2.37252 0.0899948
\(696\) 0.695562 0.0263652
\(697\) −4.26834 −0.161675
\(698\) 39.2293 1.48485
\(699\) −17.0909 −0.646438
\(700\) 0 0
\(701\) −1.07207 −0.0404915 −0.0202457 0.999795i \(-0.506445\pi\)
−0.0202457 + 0.999795i \(0.506445\pi\)
\(702\) 1.52284 0.0574757
\(703\) −1.51714 −0.0572202
\(704\) 38.0347 1.43348
\(705\) 2.48760 0.0936883
\(706\) −22.1313 −0.832923
\(707\) 0 0
\(708\) 22.3301 0.839215
\(709\) −33.4908 −1.25777 −0.628887 0.777497i \(-0.716489\pi\)
−0.628887 + 0.777497i \(0.716489\pi\)
\(710\) −1.31249 −0.0492569
\(711\) −11.8004 −0.442548
\(712\) 5.05216 0.189338
\(713\) −30.9586 −1.15941
\(714\) 0 0
\(715\) 0.695364 0.0260051
\(716\) −22.5442 −0.842515
\(717\) 15.0447 0.561855
\(718\) 48.6979 1.81739
\(719\) −9.94539 −0.370900 −0.185450 0.982654i \(-0.559374\pi\)
−0.185450 + 0.982654i \(0.559374\pi\)
\(720\) 0.807391 0.0300897
\(721\) 0 0
\(722\) 40.9451 1.52382
\(723\) −0.539340 −0.0200583
\(724\) 63.1111 2.34550
\(725\) −3.42674 −0.127266
\(726\) 1.01346 0.0376129
\(727\) 4.95164 0.183646 0.0918231 0.995775i \(-0.470731\pi\)
0.0918231 + 0.995775i \(0.470731\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 7.19001 0.266114
\(731\) 8.61001 0.318453
\(732\) 8.34079 0.308284
\(733\) −18.1609 −0.670787 −0.335394 0.942078i \(-0.608869\pi\)
−0.335394 + 0.942078i \(0.608869\pi\)
\(734\) −50.6383 −1.86909
\(735\) 0 0
\(736\) 25.0287 0.922570
\(737\) −35.0452 −1.29091
\(738\) 2.11474 0.0778446
\(739\) 13.5342 0.497864 0.248932 0.968521i \(-0.419920\pi\)
0.248932 + 0.968521i \(0.419920\pi\)
\(740\) −0.172587 −0.00634441
\(741\) −4.46011 −0.163846
\(742\) 0 0
\(743\) 22.1427 0.812335 0.406168 0.913799i \(-0.366865\pi\)
0.406168 + 0.913799i \(0.366865\pi\)
\(744\) 9.86438 0.361646
\(745\) −4.91919 −0.180225
\(746\) −46.3038 −1.69530
\(747\) −7.48655 −0.273919
\(748\) 35.7508 1.30718
\(749\) 0 0
\(750\) 5.97825 0.218295
\(751\) 10.7043 0.390607 0.195304 0.980743i \(-0.437431\pi\)
0.195304 + 0.980743i \(0.437431\pi\)
\(752\) 24.7255 0.901645
\(753\) 12.9971 0.473640
\(754\) 1.06091 0.0386360
\(755\) −4.91479 −0.178868
\(756\) 0 0
\(757\) −17.0866 −0.621021 −0.310511 0.950570i \(-0.600500\pi\)
−0.310511 + 0.950570i \(0.600500\pi\)
\(758\) 31.2501 1.13506
\(759\) 10.6165 0.385353
\(760\) 1.76247 0.0639314
\(761\) 5.85387 0.212202 0.106101 0.994355i \(-0.466163\pi\)
0.106101 + 0.994355i \(0.466163\pi\)
\(762\) −41.8386 −1.51565
\(763\) 0 0
\(764\) −20.6659 −0.747668
\(765\) 1.21652 0.0439833
\(766\) −28.4409 −1.02761
\(767\) 6.50453 0.234865
\(768\) 6.03139 0.217639
\(769\) −16.7698 −0.604736 −0.302368 0.953191i \(-0.597777\pi\)
−0.302368 + 0.953191i \(0.597777\pi\)
\(770\) 0 0
\(771\) −29.5500 −1.06422
\(772\) 48.1582 1.73325
\(773\) −27.4347 −0.986756 −0.493378 0.869815i \(-0.664238\pi\)
−0.493378 + 0.869815i \(0.664238\pi\)
\(774\) −4.26581 −0.153332
\(775\) −48.5975 −1.74567
\(776\) 15.2345 0.546885
\(777\) 0 0
\(778\) −22.6963 −0.813702
\(779\) −6.19369 −0.221912
\(780\) −0.507371 −0.0181668
\(781\) −7.37796 −0.264004
\(782\) 28.2838 1.01143
\(783\) 0.696665 0.0248968
\(784\) 0 0
\(785\) −3.20090 −0.114245
\(786\) −25.3687 −0.904872
\(787\) 21.6137 0.770447 0.385223 0.922823i \(-0.374124\pi\)
0.385223 + 0.922823i \(0.374124\pi\)
\(788\) 30.8380 1.09856
\(789\) 16.5947 0.590787
\(790\) 7.11232 0.253045
\(791\) 0 0
\(792\) −3.38274 −0.120200
\(793\) 2.42959 0.0862773
\(794\) −45.5608 −1.61689
\(795\) 4.03478 0.143099
\(796\) 7.08849 0.251245
\(797\) 2.52312 0.0893736 0.0446868 0.999001i \(-0.485771\pi\)
0.0446868 + 0.999001i \(0.485771\pi\)
\(798\) 0 0
\(799\) 37.2545 1.31797
\(800\) 39.2891 1.38908
\(801\) 5.06017 0.178792
\(802\) 60.3981 2.13273
\(803\) 40.4175 1.42630
\(804\) 25.5707 0.901809
\(805\) 0 0
\(806\) 15.0456 0.529960
\(807\) −23.9750 −0.843960
\(808\) 16.7515 0.589317
\(809\) 15.5598 0.547052 0.273526 0.961865i \(-0.411810\pi\)
0.273526 + 0.961865i \(0.411810\pi\)
\(810\) −0.602721 −0.0211775
\(811\) −30.8517 −1.08335 −0.541674 0.840589i \(-0.682209\pi\)
−0.541674 + 0.840589i \(0.682209\pi\)
\(812\) 0 0
\(813\) −4.41087 −0.154696
\(814\) −1.75506 −0.0615146
\(815\) −1.61929 −0.0567212
\(816\) 12.0916 0.423290
\(817\) 12.4938 0.437103
\(818\) 3.41058 0.119248
\(819\) 0 0
\(820\) −0.704579 −0.0246050
\(821\) 48.8645 1.70538 0.852691 0.522415i \(-0.174969\pi\)
0.852691 + 0.522415i \(0.174969\pi\)
\(822\) −14.8261 −0.517121
\(823\) 26.1744 0.912382 0.456191 0.889882i \(-0.349213\pi\)
0.456191 + 0.889882i \(0.349213\pi\)
\(824\) 7.15902 0.249396
\(825\) 16.6653 0.580211
\(826\) 0 0
\(827\) 28.1957 0.980460 0.490230 0.871593i \(-0.336913\pi\)
0.490230 + 0.871593i \(0.336913\pi\)
\(828\) −7.74628 −0.269202
\(829\) 15.9005 0.552248 0.276124 0.961122i \(-0.410950\pi\)
0.276124 + 0.961122i \(0.410950\pi\)
\(830\) 4.51230 0.156624
\(831\) −23.4865 −0.814739
\(832\) −8.08387 −0.280258
\(833\) 0 0
\(834\) −17.6038 −0.609571
\(835\) −4.48813 −0.155318
\(836\) 51.8771 1.79421
\(837\) 9.88002 0.341503
\(838\) −1.75433 −0.0606023
\(839\) 17.9080 0.618253 0.309127 0.951021i \(-0.399963\pi\)
0.309127 + 0.951021i \(0.399963\pi\)
\(840\) 0 0
\(841\) −28.5147 −0.983264
\(842\) −6.56167 −0.226130
\(843\) −23.5640 −0.811589
\(844\) 18.0723 0.622073
\(845\) 3.55733 0.122376
\(846\) −18.4577 −0.634588
\(847\) 0 0
\(848\) 40.1038 1.37717
\(849\) −19.1984 −0.658888
\(850\) 44.3989 1.52287
\(851\) −0.767539 −0.0263109
\(852\) 5.38331 0.184429
\(853\) −0.747942 −0.0256090 −0.0128045 0.999918i \(-0.504076\pi\)
−0.0128045 + 0.999918i \(0.504076\pi\)
\(854\) 0 0
\(855\) 1.76526 0.0603707
\(856\) −2.30032 −0.0786232
\(857\) 13.6782 0.467237 0.233619 0.972328i \(-0.424943\pi\)
0.233619 + 0.972328i \(0.424943\pi\)
\(858\) −5.15952 −0.176143
\(859\) 17.7503 0.605633 0.302817 0.953049i \(-0.402073\pi\)
0.302817 + 0.953049i \(0.402073\pi\)
\(860\) 1.42126 0.0484647
\(861\) 0 0
\(862\) −58.9541 −2.00798
\(863\) −26.0933 −0.888226 −0.444113 0.895971i \(-0.646481\pi\)
−0.444113 + 0.895971i \(0.646481\pi\)
\(864\) −7.98758 −0.271743
\(865\) 3.88889 0.132226
\(866\) −60.1771 −2.04490
\(867\) 1.21870 0.0413891
\(868\) 0 0
\(869\) 39.9808 1.35626
\(870\) −0.419895 −0.0142358
\(871\) 7.44850 0.252383
\(872\) −5.21216 −0.176506
\(873\) 15.2586 0.516426
\(874\) 41.0421 1.38827
\(875\) 0 0
\(876\) −29.4906 −0.996393
\(877\) −18.5476 −0.626310 −0.313155 0.949702i \(-0.601386\pi\)
−0.313155 + 0.949702i \(0.601386\pi\)
\(878\) 53.4269 1.80307
\(879\) 15.8156 0.533448
\(880\) −2.73552 −0.0922144
\(881\) −36.5564 −1.23162 −0.615808 0.787896i \(-0.711170\pi\)
−0.615808 + 0.787896i \(0.711170\pi\)
\(882\) 0 0
\(883\) −29.5247 −0.993585 −0.496792 0.867869i \(-0.665489\pi\)
−0.496792 + 0.867869i \(0.665489\pi\)
\(884\) −7.59845 −0.255563
\(885\) −2.57442 −0.0865382
\(886\) −53.9000 −1.81081
\(887\) 31.5502 1.05935 0.529677 0.848200i \(-0.322313\pi\)
0.529677 + 0.848200i \(0.322313\pi\)
\(888\) 0.244562 0.00820697
\(889\) 0 0
\(890\) −3.04987 −0.102232
\(891\) −3.38810 −0.113506
\(892\) 0.926555 0.0310234
\(893\) 54.0592 1.80902
\(894\) 36.4999 1.22074
\(895\) 2.59910 0.0868784
\(896\) 0 0
\(897\) −2.25642 −0.0753395
\(898\) 58.5876 1.95509
\(899\) 6.88307 0.229563
\(900\) −12.1598 −0.405327
\(901\) 60.4254 2.01306
\(902\) −7.16495 −0.238567
\(903\) 0 0
\(904\) −10.1738 −0.338376
\(905\) −7.27604 −0.241864
\(906\) 36.4672 1.21154
\(907\) 0.774377 0.0257128 0.0128564 0.999917i \(-0.495908\pi\)
0.0128564 + 0.999917i \(0.495908\pi\)
\(908\) −39.2755 −1.30340
\(909\) 16.7781 0.556494
\(910\) 0 0
\(911\) −32.0425 −1.06162 −0.530808 0.847492i \(-0.678112\pi\)
−0.530808 + 0.847492i \(0.678112\pi\)
\(912\) 17.5458 0.581000
\(913\) 25.3652 0.839466
\(914\) −27.4778 −0.908884
\(915\) −0.961604 −0.0317897
\(916\) 48.3016 1.59593
\(917\) 0 0
\(918\) −9.02642 −0.297916
\(919\) −18.5782 −0.612839 −0.306419 0.951897i \(-0.599131\pi\)
−0.306419 + 0.951897i \(0.599131\pi\)
\(920\) 0.891650 0.0293968
\(921\) 1.88472 0.0621037
\(922\) 11.4483 0.377029
\(923\) 1.56811 0.0516149
\(924\) 0 0
\(925\) −1.20485 −0.0396153
\(926\) 66.5546 2.18712
\(927\) 7.17037 0.235506
\(928\) −5.56467 −0.182669
\(929\) −24.1583 −0.792607 −0.396303 0.918120i \(-0.629707\pi\)
−0.396303 + 0.918120i \(0.629707\pi\)
\(930\) −5.95489 −0.195269
\(931\) 0 0
\(932\) −42.2509 −1.38397
\(933\) −5.69831 −0.186554
\(934\) −47.5667 −1.55643
\(935\) −4.12168 −0.134793
\(936\) 0.718966 0.0235001
\(937\) 28.0378 0.915955 0.457978 0.888964i \(-0.348574\pi\)
0.457978 + 0.888964i \(0.348574\pi\)
\(938\) 0 0
\(939\) −29.2119 −0.953295
\(940\) 6.14964 0.200579
\(941\) 5.15440 0.168029 0.0840143 0.996465i \(-0.473226\pi\)
0.0840143 + 0.996465i \(0.473226\pi\)
\(942\) 23.7503 0.773827
\(943\) −3.13345 −0.102039
\(944\) −25.5885 −0.832834
\(945\) 0 0
\(946\) 14.4530 0.469908
\(947\) 41.8074 1.35856 0.679279 0.733880i \(-0.262293\pi\)
0.679279 + 0.733880i \(0.262293\pi\)
\(948\) −29.1719 −0.947460
\(949\) −8.59032 −0.278853
\(950\) 64.4262 2.09026
\(951\) −32.9071 −1.06709
\(952\) 0 0
\(953\) 3.18682 0.103231 0.0516157 0.998667i \(-0.483563\pi\)
0.0516157 + 0.998667i \(0.483563\pi\)
\(954\) −29.9376 −0.969267
\(955\) 2.38256 0.0770980
\(956\) 37.1924 1.20289
\(957\) −2.36037 −0.0763000
\(958\) 12.9603 0.418728
\(959\) 0 0
\(960\) 3.19950 0.103264
\(961\) 66.6148 2.14886
\(962\) 0.373019 0.0120266
\(963\) −2.30396 −0.0742442
\(964\) −1.33331 −0.0429432
\(965\) −5.55213 −0.178729
\(966\) 0 0
\(967\) 32.6115 1.04871 0.524357 0.851498i \(-0.324306\pi\)
0.524357 + 0.851498i \(0.324306\pi\)
\(968\) 0.478476 0.0153788
\(969\) 26.4368 0.849271
\(970\) −9.19669 −0.295288
\(971\) −32.0671 −1.02908 −0.514542 0.857465i \(-0.672038\pi\)
−0.514542 + 0.857465i \(0.672038\pi\)
\(972\) 2.47212 0.0792934
\(973\) 0 0
\(974\) −63.2641 −2.02711
\(975\) −3.54203 −0.113436
\(976\) −9.55787 −0.305940
\(977\) −45.1298 −1.44383 −0.721915 0.691982i \(-0.756738\pi\)
−0.721915 + 0.691982i \(0.756738\pi\)
\(978\) 12.0149 0.384195
\(979\) −17.1444 −0.547936
\(980\) 0 0
\(981\) −5.22043 −0.166675
\(982\) 43.3281 1.38266
\(983\) −17.6207 −0.562013 −0.281007 0.959706i \(-0.590668\pi\)
−0.281007 + 0.959706i \(0.590668\pi\)
\(984\) 0.998417 0.0318284
\(985\) −3.55529 −0.113281
\(986\) −6.28839 −0.200263
\(987\) 0 0
\(988\) −11.0259 −0.350782
\(989\) 6.32074 0.200988
\(990\) 2.04208 0.0649016
\(991\) −11.1131 −0.353020 −0.176510 0.984299i \(-0.556481\pi\)
−0.176510 + 0.984299i \(0.556481\pi\)
\(992\) −78.9175 −2.50563
\(993\) −17.9603 −0.569953
\(994\) 0 0
\(995\) −0.817228 −0.0259079
\(996\) −18.5077 −0.586438
\(997\) −12.0055 −0.380219 −0.190109 0.981763i \(-0.560884\pi\)
−0.190109 + 0.981763i \(0.560884\pi\)
\(998\) 69.6528 2.20482
\(999\) 0.244950 0.00774987
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 \(a_p\))