Properties

Label 6027.2.a.bn.1.8
Level 6027
Weight 2
Character 6027.1
Self dual Yes
Analytic conductor 48.126
Analytic rank 0
Dimension 24
CM No

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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: \(0\)
Dimension: \(24\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.844195 q^{2} -1.00000 q^{3} -1.28734 q^{4} +1.91229 q^{5} +0.844195 q^{6} +2.77515 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-0.844195 q^{2} -1.00000 q^{3} -1.28734 q^{4} +1.91229 q^{5} +0.844195 q^{6} +2.77515 q^{8} +1.00000 q^{9} -1.61434 q^{10} +2.68119 q^{11} +1.28734 q^{12} -1.87964 q^{13} -1.91229 q^{15} +0.231902 q^{16} -6.09325 q^{17} -0.844195 q^{18} -7.23586 q^{19} -2.46175 q^{20} -2.26345 q^{22} -3.42494 q^{23} -2.77515 q^{24} -1.34316 q^{25} +1.58678 q^{26} -1.00000 q^{27} +10.5168 q^{29} +1.61434 q^{30} -7.41515 q^{31} -5.74607 q^{32} -2.68119 q^{33} +5.14389 q^{34} -1.28734 q^{36} +1.51750 q^{37} +6.10847 q^{38} +1.87964 q^{39} +5.30689 q^{40} +1.00000 q^{41} -4.03715 q^{43} -3.45159 q^{44} +1.91229 q^{45} +2.89131 q^{46} +12.2199 q^{47} -0.231902 q^{48} +1.13389 q^{50} +6.09325 q^{51} +2.41973 q^{52} +11.8762 q^{53} +0.844195 q^{54} +5.12720 q^{55} +7.23586 q^{57} -8.87821 q^{58} -1.76036 q^{59} +2.46175 q^{60} +10.2265 q^{61} +6.25983 q^{62} +4.38700 q^{64} -3.59441 q^{65} +2.26345 q^{66} -3.15832 q^{67} +7.84405 q^{68} +3.42494 q^{69} -4.62953 q^{71} +2.77515 q^{72} -4.04568 q^{73} -1.28107 q^{74} +1.34316 q^{75} +9.31497 q^{76} -1.58678 q^{78} +1.99326 q^{79} +0.443463 q^{80} +1.00000 q^{81} -0.844195 q^{82} +7.18385 q^{83} -11.6520 q^{85} +3.40814 q^{86} -10.5168 q^{87} +7.44070 q^{88} -4.71625 q^{89} -1.61434 q^{90} +4.40904 q^{92} +7.41515 q^{93} -10.3159 q^{94} -13.8370 q^{95} +5.74607 q^{96} +4.66151 q^{97} +2.68119 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 8q^{2} - 24q^{3} + 32q^{4} - 4q^{5} - 8q^{6} + 24q^{8} + 24q^{9} + O(q^{10}) \) \( 24q + 8q^{2} - 24q^{3} + 32q^{4} - 4q^{5} - 8q^{6} + 24q^{8} + 24q^{9} + 4q^{10} + 12q^{11} - 32q^{12} + 4q^{15} + 44q^{16} - 8q^{17} + 8q^{18} + 4q^{19} - 28q^{20} + 16q^{22} + 20q^{23} - 24q^{24} + 48q^{25} - 32q^{26} - 24q^{27} + 24q^{29} - 4q^{30} + 4q^{31} + 36q^{32} - 12q^{33} - 16q^{34} + 32q^{36} + 64q^{37} - 20q^{38} + 48q^{40} + 24q^{41} + 20q^{43} + 48q^{44} - 4q^{45} + 28q^{46} - 32q^{47} - 44q^{48} - 20q^{50} + 8q^{51} + 76q^{53} - 8q^{54} + 24q^{55} - 4q^{57} + 28q^{58} - 28q^{59} + 28q^{60} + 28q^{61} + 4q^{62} + 48q^{64} + 28q^{65} - 16q^{66} + 44q^{67} + 32q^{68} - 20q^{69} + 20q^{71} + 24q^{72} + 16q^{73} + 44q^{74} - 48q^{75} + 16q^{76} + 32q^{78} + 4q^{79} - 44q^{80} + 24q^{81} + 8q^{82} - 8q^{83} + 28q^{85} + 56q^{86} - 24q^{87} + 60q^{88} - 60q^{89} + 4q^{90} + 60q^{92} - 4q^{93} - 24q^{94} + 28q^{95} - 36q^{96} + 48q^{97} + 12q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.844195 −0.596936 −0.298468 0.954420i \(-0.596476\pi\)
−0.298468 + 0.954420i \(0.596476\pi\)
\(3\) −1.00000 −0.577350
\(4\) −1.28734 −0.643668
\(5\) 1.91229 0.855201 0.427600 0.903968i \(-0.359359\pi\)
0.427600 + 0.903968i \(0.359359\pi\)
\(6\) 0.844195 0.344641
\(7\) 0 0
\(8\) 2.77515 0.981164
\(9\) 1.00000 0.333333
\(10\) −1.61434 −0.510500
\(11\) 2.68119 0.808409 0.404204 0.914669i \(-0.367548\pi\)
0.404204 + 0.914669i \(0.367548\pi\)
\(12\) 1.28734 0.371622
\(13\) −1.87964 −0.521319 −0.260659 0.965431i \(-0.583940\pi\)
−0.260659 + 0.965431i \(0.583940\pi\)
\(14\) 0 0
\(15\) −1.91229 −0.493750
\(16\) 0.231902 0.0579755
\(17\) −6.09325 −1.47783 −0.738915 0.673799i \(-0.764661\pi\)
−0.738915 + 0.673799i \(0.764661\pi\)
\(18\) −0.844195 −0.198979
\(19\) −7.23586 −1.66002 −0.830010 0.557749i \(-0.811665\pi\)
−0.830010 + 0.557749i \(0.811665\pi\)
\(20\) −2.46175 −0.550465
\(21\) 0 0
\(22\) −2.26345 −0.482568
\(23\) −3.42494 −0.714149 −0.357074 0.934076i \(-0.616226\pi\)
−0.357074 + 0.934076i \(0.616226\pi\)
\(24\) −2.77515 −0.566475
\(25\) −1.34316 −0.268631
\(26\) 1.58678 0.311194
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 10.5168 1.95292 0.976458 0.215705i \(-0.0692051\pi\)
0.976458 + 0.215705i \(0.0692051\pi\)
\(30\) 1.61434 0.294737
\(31\) −7.41515 −1.33180 −0.665900 0.746041i \(-0.731952\pi\)
−0.665900 + 0.746041i \(0.731952\pi\)
\(32\) −5.74607 −1.01577
\(33\) −2.68119 −0.466735
\(34\) 5.14389 0.882170
\(35\) 0 0
\(36\) −1.28734 −0.214556
\(37\) 1.51750 0.249476 0.124738 0.992190i \(-0.460191\pi\)
0.124738 + 0.992190i \(0.460191\pi\)
\(38\) 6.10847 0.990925
\(39\) 1.87964 0.300984
\(40\) 5.30689 0.839092
\(41\) 1.00000 0.156174
\(42\) 0 0
\(43\) −4.03715 −0.615660 −0.307830 0.951441i \(-0.599603\pi\)
−0.307830 + 0.951441i \(0.599603\pi\)
\(44\) −3.45159 −0.520346
\(45\) 1.91229 0.285067
\(46\) 2.89131 0.426301
\(47\) 12.2199 1.78245 0.891225 0.453561i \(-0.149846\pi\)
0.891225 + 0.453561i \(0.149846\pi\)
\(48\) −0.231902 −0.0334721
\(49\) 0 0
\(50\) 1.13389 0.160356
\(51\) 6.09325 0.853226
\(52\) 2.41973 0.335556
\(53\) 11.8762 1.63132 0.815659 0.578533i \(-0.196374\pi\)
0.815659 + 0.578533i \(0.196374\pi\)
\(54\) 0.844195 0.114880
\(55\) 5.12720 0.691352
\(56\) 0 0
\(57\) 7.23586 0.958412
\(58\) −8.87821 −1.16577
\(59\) −1.76036 −0.229179 −0.114590 0.993413i \(-0.536555\pi\)
−0.114590 + 0.993413i \(0.536555\pi\)
\(60\) 2.46175 0.317811
\(61\) 10.2265 1.30937 0.654686 0.755901i \(-0.272801\pi\)
0.654686 + 0.755901i \(0.272801\pi\)
\(62\) 6.25983 0.794999
\(63\) 0 0
\(64\) 4.38700 0.548375
\(65\) −3.59441 −0.445832
\(66\) 2.26345 0.278611
\(67\) −3.15832 −0.385850 −0.192925 0.981214i \(-0.561797\pi\)
−0.192925 + 0.981214i \(0.561797\pi\)
\(68\) 7.84405 0.951231
\(69\) 3.42494 0.412314
\(70\) 0 0
\(71\) −4.62953 −0.549424 −0.274712 0.961527i \(-0.588583\pi\)
−0.274712 + 0.961527i \(0.588583\pi\)
\(72\) 2.77515 0.327055
\(73\) −4.04568 −0.473511 −0.236755 0.971569i \(-0.576084\pi\)
−0.236755 + 0.971569i \(0.576084\pi\)
\(74\) −1.28107 −0.148921
\(75\) 1.34316 0.155094
\(76\) 9.31497 1.06850
\(77\) 0 0
\(78\) −1.58678 −0.179668
\(79\) 1.99326 0.224260 0.112130 0.993694i \(-0.464233\pi\)
0.112130 + 0.993694i \(0.464233\pi\)
\(80\) 0.443463 0.0495807
\(81\) 1.00000 0.111111
\(82\) −0.844195 −0.0932257
\(83\) 7.18385 0.788529 0.394265 0.918997i \(-0.370999\pi\)
0.394265 + 0.918997i \(0.370999\pi\)
\(84\) 0 0
\(85\) −11.6520 −1.26384
\(86\) 3.40814 0.367509
\(87\) −10.5168 −1.12752
\(88\) 7.44070 0.793182
\(89\) −4.71625 −0.499921 −0.249961 0.968256i \(-0.580418\pi\)
−0.249961 + 0.968256i \(0.580418\pi\)
\(90\) −1.61434 −0.170167
\(91\) 0 0
\(92\) 4.40904 0.459675
\(93\) 7.41515 0.768915
\(94\) −10.3159 −1.06401
\(95\) −13.8370 −1.41965
\(96\) 5.74607 0.586456
\(97\) 4.66151 0.473304 0.236652 0.971594i \(-0.423950\pi\)
0.236652 + 0.971594i \(0.423950\pi\)
\(98\) 0 0
\(99\) 2.68119 0.269470
\(100\) 1.72909 0.172909
\(101\) −4.23382 −0.421281 −0.210641 0.977564i \(-0.567555\pi\)
−0.210641 + 0.977564i \(0.567555\pi\)
\(102\) −5.14389 −0.509321
\(103\) −9.73645 −0.959361 −0.479680 0.877443i \(-0.659247\pi\)
−0.479680 + 0.877443i \(0.659247\pi\)
\(104\) −5.21629 −0.511499
\(105\) 0 0
\(106\) −10.0258 −0.973793
\(107\) 2.13975 0.206858 0.103429 0.994637i \(-0.467019\pi\)
0.103429 + 0.994637i \(0.467019\pi\)
\(108\) 1.28734 0.123874
\(109\) −8.76924 −0.839941 −0.419970 0.907538i \(-0.637960\pi\)
−0.419970 + 0.907538i \(0.637960\pi\)
\(110\) −4.32836 −0.412693
\(111\) −1.51750 −0.144035
\(112\) 0 0
\(113\) 1.79145 0.168526 0.0842628 0.996444i \(-0.473146\pi\)
0.0842628 + 0.996444i \(0.473146\pi\)
\(114\) −6.10847 −0.572111
\(115\) −6.54947 −0.610741
\(116\) −13.5386 −1.25703
\(117\) −1.87964 −0.173773
\(118\) 1.48608 0.136805
\(119\) 0 0
\(120\) −5.30689 −0.484450
\(121\) −3.81123 −0.346476
\(122\) −8.63317 −0.781611
\(123\) −1.00000 −0.0901670
\(124\) 9.54578 0.857237
\(125\) −12.1299 −1.08493
\(126\) 0 0
\(127\) 13.5946 1.20632 0.603162 0.797619i \(-0.293907\pi\)
0.603162 + 0.797619i \(0.293907\pi\)
\(128\) 7.78866 0.688427
\(129\) 4.03715 0.355451
\(130\) 3.03439 0.266133
\(131\) 18.4781 1.61444 0.807219 0.590252i \(-0.200972\pi\)
0.807219 + 0.590252i \(0.200972\pi\)
\(132\) 3.45159 0.300422
\(133\) 0 0
\(134\) 2.66624 0.230328
\(135\) −1.91229 −0.164583
\(136\) −16.9097 −1.44999
\(137\) 10.6875 0.913097 0.456548 0.889699i \(-0.349085\pi\)
0.456548 + 0.889699i \(0.349085\pi\)
\(138\) −2.89131 −0.246125
\(139\) 3.38677 0.287262 0.143631 0.989631i \(-0.454122\pi\)
0.143631 + 0.989631i \(0.454122\pi\)
\(140\) 0 0
\(141\) −12.2199 −1.02910
\(142\) 3.90823 0.327971
\(143\) −5.03967 −0.421439
\(144\) 0.231902 0.0193252
\(145\) 20.1111 1.67014
\(146\) 3.41534 0.282655
\(147\) 0 0
\(148\) −1.95353 −0.160579
\(149\) 7.62042 0.624289 0.312145 0.950035i \(-0.398953\pi\)
0.312145 + 0.950035i \(0.398953\pi\)
\(150\) −1.13389 −0.0925814
\(151\) 7.06209 0.574705 0.287352 0.957825i \(-0.407225\pi\)
0.287352 + 0.957825i \(0.407225\pi\)
\(152\) −20.0806 −1.62875
\(153\) −6.09325 −0.492610
\(154\) 0 0
\(155\) −14.1799 −1.13896
\(156\) −2.41973 −0.193733
\(157\) −10.5957 −0.845625 −0.422813 0.906217i \(-0.638957\pi\)
−0.422813 + 0.906217i \(0.638957\pi\)
\(158\) −1.68270 −0.133869
\(159\) −11.8762 −0.941842
\(160\) −10.9881 −0.868689
\(161\) 0 0
\(162\) −0.844195 −0.0663262
\(163\) −21.4964 −1.68373 −0.841865 0.539688i \(-0.818542\pi\)
−0.841865 + 0.539688i \(0.818542\pi\)
\(164\) −1.28734 −0.100524
\(165\) −5.12720 −0.399152
\(166\) −6.06456 −0.470702
\(167\) −5.80772 −0.449415 −0.224707 0.974426i \(-0.572143\pi\)
−0.224707 + 0.974426i \(0.572143\pi\)
\(168\) 0 0
\(169\) −9.46695 −0.728227
\(170\) 9.83659 0.754432
\(171\) −7.23586 −0.553340
\(172\) 5.19717 0.396280
\(173\) 21.1101 1.60497 0.802487 0.596670i \(-0.203510\pi\)
0.802487 + 0.596670i \(0.203510\pi\)
\(174\) 8.87821 0.673055
\(175\) 0 0
\(176\) 0.621772 0.0468679
\(177\) 1.76036 0.132317
\(178\) 3.98143 0.298421
\(179\) −4.84198 −0.361907 −0.180953 0.983492i \(-0.557918\pi\)
−0.180953 + 0.983492i \(0.557918\pi\)
\(180\) −2.46175 −0.183488
\(181\) −24.0285 −1.78602 −0.893012 0.450032i \(-0.851413\pi\)
−0.893012 + 0.450032i \(0.851413\pi\)
\(182\) 0 0
\(183\) −10.2265 −0.755966
\(184\) −9.50472 −0.700697
\(185\) 2.90190 0.213352
\(186\) −6.25983 −0.458993
\(187\) −16.3371 −1.19469
\(188\) −15.7311 −1.14731
\(189\) 0 0
\(190\) 11.6812 0.847440
\(191\) 17.0408 1.23303 0.616516 0.787343i \(-0.288544\pi\)
0.616516 + 0.787343i \(0.288544\pi\)
\(192\) −4.38700 −0.316605
\(193\) 26.2654 1.89062 0.945311 0.326171i \(-0.105759\pi\)
0.945311 + 0.326171i \(0.105759\pi\)
\(194\) −3.93522 −0.282532
\(195\) 3.59441 0.257401
\(196\) 0 0
\(197\) 23.0071 1.63919 0.819595 0.572943i \(-0.194198\pi\)
0.819595 + 0.572943i \(0.194198\pi\)
\(198\) −2.26345 −0.160856
\(199\) 24.8226 1.75963 0.879814 0.475317i \(-0.157667\pi\)
0.879814 + 0.475317i \(0.157667\pi\)
\(200\) −3.72746 −0.263572
\(201\) 3.15832 0.222771
\(202\) 3.57417 0.251478
\(203\) 0 0
\(204\) −7.84405 −0.549194
\(205\) 1.91229 0.133560
\(206\) 8.21946 0.572677
\(207\) −3.42494 −0.238050
\(208\) −0.435892 −0.0302237
\(209\) −19.4007 −1.34197
\(210\) 0 0
\(211\) −10.6322 −0.731949 −0.365974 0.930625i \(-0.619264\pi\)
−0.365974 + 0.930625i \(0.619264\pi\)
\(212\) −15.2886 −1.05003
\(213\) 4.62953 0.317210
\(214\) −1.80637 −0.123481
\(215\) −7.72019 −0.526513
\(216\) −2.77515 −0.188825
\(217\) 0 0
\(218\) 7.40295 0.501391
\(219\) 4.04568 0.273381
\(220\) −6.60043 −0.445001
\(221\) 11.4531 0.770420
\(222\) 1.28107 0.0859796
\(223\) 15.6888 1.05060 0.525300 0.850917i \(-0.323953\pi\)
0.525300 + 0.850917i \(0.323953\pi\)
\(224\) 0 0
\(225\) −1.34316 −0.0895438
\(226\) −1.51233 −0.100599
\(227\) −14.8416 −0.985073 −0.492536 0.870292i \(-0.663930\pi\)
−0.492536 + 0.870292i \(0.663930\pi\)
\(228\) −9.31497 −0.616899
\(229\) 7.51697 0.496735 0.248368 0.968666i \(-0.420106\pi\)
0.248368 + 0.968666i \(0.420106\pi\)
\(230\) 5.52902 0.364573
\(231\) 0 0
\(232\) 29.1857 1.91613
\(233\) 17.2580 1.13061 0.565305 0.824882i \(-0.308758\pi\)
0.565305 + 0.824882i \(0.308758\pi\)
\(234\) 1.58678 0.103731
\(235\) 23.3679 1.52435
\(236\) 2.26617 0.147515
\(237\) −1.99326 −0.129476
\(238\) 0 0
\(239\) −26.4633 −1.71177 −0.855885 0.517166i \(-0.826987\pi\)
−0.855885 + 0.517166i \(0.826987\pi\)
\(240\) −0.443463 −0.0286254
\(241\) 27.6180 1.77903 0.889515 0.456906i \(-0.151043\pi\)
0.889515 + 0.456906i \(0.151043\pi\)
\(242\) 3.21742 0.206824
\(243\) −1.00000 −0.0641500
\(244\) −13.1650 −0.842800
\(245\) 0 0
\(246\) 0.844195 0.0538239
\(247\) 13.6008 0.865399
\(248\) −20.5782 −1.30671
\(249\) −7.18385 −0.455258
\(250\) 10.2400 0.647636
\(251\) 19.4790 1.22951 0.614753 0.788719i \(-0.289256\pi\)
0.614753 + 0.788719i \(0.289256\pi\)
\(252\) 0 0
\(253\) −9.18290 −0.577324
\(254\) −11.4765 −0.720098
\(255\) 11.6520 0.729679
\(256\) −15.3492 −0.959322
\(257\) 18.4487 1.15080 0.575400 0.817872i \(-0.304846\pi\)
0.575400 + 0.817872i \(0.304846\pi\)
\(258\) −3.40814 −0.212182
\(259\) 0 0
\(260\) 4.62722 0.286968
\(261\) 10.5168 0.650972
\(262\) −15.5991 −0.963716
\(263\) 29.0590 1.79185 0.895926 0.444203i \(-0.146513\pi\)
0.895926 + 0.444203i \(0.146513\pi\)
\(264\) −7.44070 −0.457944
\(265\) 22.7107 1.39510
\(266\) 0 0
\(267\) 4.71625 0.288630
\(268\) 4.06581 0.248359
\(269\) −19.1863 −1.16981 −0.584904 0.811103i \(-0.698868\pi\)
−0.584904 + 0.811103i \(0.698868\pi\)
\(270\) 1.61434 0.0982458
\(271\) −13.5358 −0.822243 −0.411121 0.911581i \(-0.634863\pi\)
−0.411121 + 0.911581i \(0.634863\pi\)
\(272\) −1.41304 −0.0856779
\(273\) 0 0
\(274\) −9.02235 −0.545060
\(275\) −3.60126 −0.217164
\(276\) −4.40904 −0.265393
\(277\) −15.0702 −0.905478 −0.452739 0.891643i \(-0.649553\pi\)
−0.452739 + 0.891643i \(0.649553\pi\)
\(278\) −2.85910 −0.171477
\(279\) −7.41515 −0.443933
\(280\) 0 0
\(281\) 10.9228 0.651602 0.325801 0.945438i \(-0.394366\pi\)
0.325801 + 0.945438i \(0.394366\pi\)
\(282\) 10.3159 0.614306
\(283\) −5.60619 −0.333253 −0.166627 0.986020i \(-0.553287\pi\)
−0.166627 + 0.986020i \(0.553287\pi\)
\(284\) 5.95976 0.353646
\(285\) 13.8370 0.819635
\(286\) 4.25447 0.251572
\(287\) 0 0
\(288\) −5.74607 −0.338591
\(289\) 20.1277 1.18398
\(290\) −16.9777 −0.996964
\(291\) −4.66151 −0.273262
\(292\) 5.20814 0.304783
\(293\) −3.69810 −0.216045 −0.108023 0.994148i \(-0.534452\pi\)
−0.108023 + 0.994148i \(0.534452\pi\)
\(294\) 0 0
\(295\) −3.36631 −0.195994
\(296\) 4.21130 0.244777
\(297\) −2.68119 −0.155578
\(298\) −6.43312 −0.372661
\(299\) 6.43766 0.372299
\(300\) −1.72909 −0.0998293
\(301\) 0 0
\(302\) −5.96178 −0.343062
\(303\) 4.23382 0.243227
\(304\) −1.67801 −0.0962404
\(305\) 19.5560 1.11978
\(306\) 5.14389 0.294057
\(307\) −2.67275 −0.152542 −0.0762709 0.997087i \(-0.524301\pi\)
−0.0762709 + 0.997087i \(0.524301\pi\)
\(308\) 0 0
\(309\) 9.73645 0.553887
\(310\) 11.9706 0.679884
\(311\) −14.9516 −0.847827 −0.423914 0.905703i \(-0.639344\pi\)
−0.423914 + 0.905703i \(0.639344\pi\)
\(312\) 5.21629 0.295314
\(313\) 17.4503 0.986349 0.493174 0.869930i \(-0.335836\pi\)
0.493174 + 0.869930i \(0.335836\pi\)
\(314\) 8.94480 0.504784
\(315\) 0 0
\(316\) −2.56600 −0.144349
\(317\) 29.2867 1.64491 0.822454 0.568832i \(-0.192605\pi\)
0.822454 + 0.568832i \(0.192605\pi\)
\(318\) 10.0258 0.562219
\(319\) 28.1975 1.57875
\(320\) 8.38921 0.468971
\(321\) −2.13975 −0.119429
\(322\) 0 0
\(323\) 44.0899 2.45323
\(324\) −1.28734 −0.0715186
\(325\) 2.52465 0.140043
\(326\) 18.1472 1.00508
\(327\) 8.76924 0.484940
\(328\) 2.77515 0.153232
\(329\) 0 0
\(330\) 4.32836 0.238268
\(331\) 9.52575 0.523583 0.261791 0.965125i \(-0.415687\pi\)
0.261791 + 0.965125i \(0.415687\pi\)
\(332\) −9.24802 −0.507551
\(333\) 1.51750 0.0831586
\(334\) 4.90285 0.268272
\(335\) −6.03961 −0.329979
\(336\) 0 0
\(337\) 26.0785 1.42059 0.710294 0.703905i \(-0.248562\pi\)
0.710294 + 0.703905i \(0.248562\pi\)
\(338\) 7.99195 0.434705
\(339\) −1.79145 −0.0972983
\(340\) 15.0001 0.813494
\(341\) −19.8814 −1.07664
\(342\) 6.10847 0.330308
\(343\) 0 0
\(344\) −11.2037 −0.604063
\(345\) 6.54947 0.352611
\(346\) −17.8211 −0.958067
\(347\) 7.69389 0.413030 0.206515 0.978443i \(-0.433788\pi\)
0.206515 + 0.978443i \(0.433788\pi\)
\(348\) 13.5386 0.725746
\(349\) 13.3724 0.715806 0.357903 0.933759i \(-0.383492\pi\)
0.357903 + 0.933759i \(0.383492\pi\)
\(350\) 0 0
\(351\) 1.87964 0.100328
\(352\) −15.4063 −0.821159
\(353\) −14.2898 −0.760572 −0.380286 0.924869i \(-0.624174\pi\)
−0.380286 + 0.924869i \(0.624174\pi\)
\(354\) −1.48608 −0.0789845
\(355\) −8.85299 −0.469868
\(356\) 6.07139 0.321783
\(357\) 0 0
\(358\) 4.08758 0.216035
\(359\) −2.49554 −0.131709 −0.0658547 0.997829i \(-0.520977\pi\)
−0.0658547 + 0.997829i \(0.520977\pi\)
\(360\) 5.30689 0.279697
\(361\) 33.3576 1.75566
\(362\) 20.2847 1.06614
\(363\) 3.81123 0.200038
\(364\) 0 0
\(365\) −7.73650 −0.404947
\(366\) 8.63317 0.451263
\(367\) 36.6391 1.91255 0.956273 0.292477i \(-0.0944793\pi\)
0.956273 + 0.292477i \(0.0944793\pi\)
\(368\) −0.794249 −0.0414031
\(369\) 1.00000 0.0520579
\(370\) −2.44977 −0.127357
\(371\) 0 0
\(372\) −9.54578 −0.494926
\(373\) −6.74704 −0.349349 −0.174674 0.984626i \(-0.555887\pi\)
−0.174674 + 0.984626i \(0.555887\pi\)
\(374\) 13.7917 0.713154
\(375\) 12.1299 0.626387
\(376\) 33.9120 1.74888
\(377\) −19.7678 −1.01809
\(378\) 0 0
\(379\) 8.45609 0.434360 0.217180 0.976132i \(-0.430314\pi\)
0.217180 + 0.976132i \(0.430314\pi\)
\(380\) 17.8129 0.913783
\(381\) −13.5946 −0.696471
\(382\) −14.3858 −0.736041
\(383\) −34.7954 −1.77796 −0.888981 0.457945i \(-0.848586\pi\)
−0.888981 + 0.457945i \(0.848586\pi\)
\(384\) −7.78866 −0.397463
\(385\) 0 0
\(386\) −22.1731 −1.12858
\(387\) −4.03715 −0.205220
\(388\) −6.00092 −0.304651
\(389\) −38.2428 −1.93899 −0.969494 0.245117i \(-0.921174\pi\)
−0.969494 + 0.245117i \(0.921174\pi\)
\(390\) −3.03439 −0.153652
\(391\) 20.8690 1.05539
\(392\) 0 0
\(393\) −18.4781 −0.932096
\(394\) −19.4225 −0.978492
\(395\) 3.81169 0.191787
\(396\) −3.45159 −0.173449
\(397\) −15.8180 −0.793883 −0.396941 0.917844i \(-0.629928\pi\)
−0.396941 + 0.917844i \(0.629928\pi\)
\(398\) −20.9551 −1.05039
\(399\) 0 0
\(400\) −0.311481 −0.0155740
\(401\) 2.58004 0.128841 0.0644205 0.997923i \(-0.479480\pi\)
0.0644205 + 0.997923i \(0.479480\pi\)
\(402\) −2.66624 −0.132980
\(403\) 13.9378 0.694293
\(404\) 5.45035 0.271165
\(405\) 1.91229 0.0950223
\(406\) 0 0
\(407\) 4.06871 0.201678
\(408\) 16.9097 0.837154
\(409\) −11.4726 −0.567283 −0.283641 0.958930i \(-0.591543\pi\)
−0.283641 + 0.958930i \(0.591543\pi\)
\(410\) −1.61434 −0.0797267
\(411\) −10.6875 −0.527177
\(412\) 12.5341 0.617510
\(413\) 0 0
\(414\) 2.89131 0.142100
\(415\) 13.7376 0.674351
\(416\) 10.8006 0.529541
\(417\) −3.38677 −0.165851
\(418\) 16.3780 0.801072
\(419\) −13.6522 −0.666953 −0.333476 0.942758i \(-0.608222\pi\)
−0.333476 + 0.942758i \(0.608222\pi\)
\(420\) 0 0
\(421\) −22.5347 −1.09828 −0.549138 0.835732i \(-0.685044\pi\)
−0.549138 + 0.835732i \(0.685044\pi\)
\(422\) 8.97562 0.436926
\(423\) 12.2199 0.594150
\(424\) 32.9582 1.60059
\(425\) 8.18419 0.396992
\(426\) −3.90823 −0.189354
\(427\) 0 0
\(428\) −2.75458 −0.133148
\(429\) 5.03967 0.243318
\(430\) 6.51735 0.314294
\(431\) −6.38263 −0.307441 −0.153720 0.988114i \(-0.549125\pi\)
−0.153720 + 0.988114i \(0.549125\pi\)
\(432\) −0.231902 −0.0111574
\(433\) 35.0047 1.68222 0.841109 0.540866i \(-0.181903\pi\)
0.841109 + 0.540866i \(0.181903\pi\)
\(434\) 0 0
\(435\) −20.1111 −0.964254
\(436\) 11.2890 0.540643
\(437\) 24.7824 1.18550
\(438\) −3.41534 −0.163191
\(439\) −8.35908 −0.398957 −0.199479 0.979902i \(-0.563925\pi\)
−0.199479 + 0.979902i \(0.563925\pi\)
\(440\) 14.2288 0.678330
\(441\) 0 0
\(442\) −9.66867 −0.459892
\(443\) −26.8933 −1.27774 −0.638869 0.769316i \(-0.720597\pi\)
−0.638869 + 0.769316i \(0.720597\pi\)
\(444\) 1.95353 0.0927106
\(445\) −9.01882 −0.427533
\(446\) −13.2444 −0.627141
\(447\) −7.62042 −0.360433
\(448\) 0 0
\(449\) −0.624983 −0.0294948 −0.0147474 0.999891i \(-0.504694\pi\)
−0.0147474 + 0.999891i \(0.504694\pi\)
\(450\) 1.13389 0.0534519
\(451\) 2.68119 0.126252
\(452\) −2.30620 −0.108474
\(453\) −7.06209 −0.331806
\(454\) 12.5292 0.588025
\(455\) 0 0
\(456\) 20.0806 0.940360
\(457\) −12.4788 −0.583736 −0.291868 0.956459i \(-0.594277\pi\)
−0.291868 + 0.956459i \(0.594277\pi\)
\(458\) −6.34578 −0.296519
\(459\) 6.09325 0.284409
\(460\) 8.43136 0.393114
\(461\) 0.841829 0.0392079 0.0196039 0.999808i \(-0.493759\pi\)
0.0196039 + 0.999808i \(0.493759\pi\)
\(462\) 0 0
\(463\) 28.2428 1.31255 0.656277 0.754520i \(-0.272130\pi\)
0.656277 + 0.754520i \(0.272130\pi\)
\(464\) 2.43886 0.113221
\(465\) 14.1799 0.657577
\(466\) −14.5691 −0.674902
\(467\) 1.71415 0.0793213 0.0396606 0.999213i \(-0.487372\pi\)
0.0396606 + 0.999213i \(0.487372\pi\)
\(468\) 2.41973 0.111852
\(469\) 0 0
\(470\) −19.7271 −0.909941
\(471\) 10.5957 0.488222
\(472\) −4.88526 −0.224862
\(473\) −10.8244 −0.497705
\(474\) 1.68270 0.0772891
\(475\) 9.71889 0.445933
\(476\) 0 0
\(477\) 11.8762 0.543773
\(478\) 22.3402 1.02182
\(479\) −21.3898 −0.977326 −0.488663 0.872473i \(-0.662515\pi\)
−0.488663 + 0.872473i \(0.662515\pi\)
\(480\) 10.9881 0.501538
\(481\) −2.85236 −0.130056
\(482\) −23.3149 −1.06197
\(483\) 0 0
\(484\) 4.90633 0.223015
\(485\) 8.91414 0.404770
\(486\) 0.844195 0.0382935
\(487\) 9.09761 0.412252 0.206126 0.978525i \(-0.433914\pi\)
0.206126 + 0.978525i \(0.433914\pi\)
\(488\) 28.3801 1.28471
\(489\) 21.4964 0.972102
\(490\) 0 0
\(491\) 14.2219 0.641826 0.320913 0.947109i \(-0.396010\pi\)
0.320913 + 0.947109i \(0.396010\pi\)
\(492\) 1.28734 0.0580375
\(493\) −64.0814 −2.88608
\(494\) −11.4817 −0.516588
\(495\) 5.12720 0.230451
\(496\) −1.71959 −0.0772117
\(497\) 0 0
\(498\) 6.06456 0.271760
\(499\) −13.5848 −0.608138 −0.304069 0.952650i \(-0.598345\pi\)
−0.304069 + 0.952650i \(0.598345\pi\)
\(500\) 15.6153 0.698337
\(501\) 5.80772 0.259470
\(502\) −16.4441 −0.733937
\(503\) −16.7950 −0.748853 −0.374427 0.927257i \(-0.622160\pi\)
−0.374427 + 0.927257i \(0.622160\pi\)
\(504\) 0 0
\(505\) −8.09629 −0.360280
\(506\) 7.75216 0.344626
\(507\) 9.46695 0.420442
\(508\) −17.5008 −0.776471
\(509\) −10.7163 −0.474991 −0.237496 0.971389i \(-0.576327\pi\)
−0.237496 + 0.971389i \(0.576327\pi\)
\(510\) −9.83659 −0.435572
\(511\) 0 0
\(512\) −2.61965 −0.115773
\(513\) 7.23586 0.319471
\(514\) −15.5743 −0.686954
\(515\) −18.6189 −0.820446
\(516\) −5.19717 −0.228793
\(517\) 32.7638 1.44095
\(518\) 0 0
\(519\) −21.1101 −0.926632
\(520\) −9.97504 −0.437435
\(521\) 29.4211 1.28896 0.644482 0.764620i \(-0.277073\pi\)
0.644482 + 0.764620i \(0.277073\pi\)
\(522\) −8.87821 −0.388589
\(523\) 19.6952 0.861213 0.430606 0.902540i \(-0.358300\pi\)
0.430606 + 0.902540i \(0.358300\pi\)
\(524\) −23.7875 −1.03916
\(525\) 0 0
\(526\) −24.5314 −1.06962
\(527\) 45.1824 1.96817
\(528\) −0.621772 −0.0270592
\(529\) −11.2698 −0.489991
\(530\) −19.1722 −0.832788
\(531\) −1.76036 −0.0763930
\(532\) 0 0
\(533\) −1.87964 −0.0814163
\(534\) −3.98143 −0.172293
\(535\) 4.09183 0.176905
\(536\) −8.76481 −0.378582
\(537\) 4.84198 0.208947
\(538\) 16.1969 0.698300
\(539\) 0 0
\(540\) 2.46175 0.105937
\(541\) 14.2318 0.611874 0.305937 0.952052i \(-0.401030\pi\)
0.305937 + 0.952052i \(0.401030\pi\)
\(542\) 11.4269 0.490826
\(543\) 24.0285 1.03116
\(544\) 35.0123 1.50114
\(545\) −16.7693 −0.718318
\(546\) 0 0
\(547\) 20.5026 0.876629 0.438314 0.898822i \(-0.355576\pi\)
0.438314 + 0.898822i \(0.355576\pi\)
\(548\) −13.7584 −0.587731
\(549\) 10.2265 0.436457
\(550\) 3.04016 0.129633
\(551\) −76.0979 −3.24188
\(552\) 9.50472 0.404548
\(553\) 0 0
\(554\) 12.7222 0.540512
\(555\) −2.90190 −0.123179
\(556\) −4.35991 −0.184902
\(557\) −10.6502 −0.451265 −0.225632 0.974213i \(-0.572445\pi\)
−0.225632 + 0.974213i \(0.572445\pi\)
\(558\) 6.25983 0.265000
\(559\) 7.58840 0.320955
\(560\) 0 0
\(561\) 16.3371 0.689755
\(562\) −9.22101 −0.388965
\(563\) −6.50690 −0.274233 −0.137117 0.990555i \(-0.543783\pi\)
−0.137117 + 0.990555i \(0.543783\pi\)
\(564\) 15.7311 0.662397
\(565\) 3.42577 0.144123
\(566\) 4.73271 0.198931
\(567\) 0 0
\(568\) −12.8476 −0.539075
\(569\) 25.3805 1.06401 0.532003 0.846742i \(-0.321439\pi\)
0.532003 + 0.846742i \(0.321439\pi\)
\(570\) −11.6812 −0.489270
\(571\) −0.483855 −0.0202487 −0.0101243 0.999949i \(-0.503223\pi\)
−0.0101243 + 0.999949i \(0.503223\pi\)
\(572\) 6.48775 0.271266
\(573\) −17.0408 −0.711891
\(574\) 0 0
\(575\) 4.60023 0.191843
\(576\) 4.38700 0.182792
\(577\) 33.2621 1.38472 0.692360 0.721552i \(-0.256571\pi\)
0.692360 + 0.721552i \(0.256571\pi\)
\(578\) −16.9917 −0.706761
\(579\) −26.2654 −1.09155
\(580\) −25.8897 −1.07501
\(581\) 0 0
\(582\) 3.93522 0.163120
\(583\) 31.8423 1.31877
\(584\) −11.2274 −0.464592
\(585\) −3.59441 −0.148611
\(586\) 3.12192 0.128965
\(587\) 32.2902 1.33276 0.666379 0.745613i \(-0.267843\pi\)
0.666379 + 0.745613i \(0.267843\pi\)
\(588\) 0 0
\(589\) 53.6550 2.21081
\(590\) 2.84182 0.116996
\(591\) −23.0071 −0.946387
\(592\) 0.351911 0.0144635
\(593\) −7.39899 −0.303840 −0.151920 0.988393i \(-0.548546\pi\)
−0.151920 + 0.988393i \(0.548546\pi\)
\(594\) 2.26345 0.0928703
\(595\) 0 0
\(596\) −9.81003 −0.401835
\(597\) −24.8226 −1.01592
\(598\) −5.43464 −0.222239
\(599\) −42.5119 −1.73699 −0.868495 0.495698i \(-0.834912\pi\)
−0.868495 + 0.495698i \(0.834912\pi\)
\(600\) 3.72746 0.152173
\(601\) 24.7770 1.01067 0.505337 0.862922i \(-0.331368\pi\)
0.505337 + 0.862922i \(0.331368\pi\)
\(602\) 0 0
\(603\) −3.15832 −0.128617
\(604\) −9.09128 −0.369919
\(605\) −7.28817 −0.296306
\(606\) −3.57417 −0.145191
\(607\) −14.7307 −0.597902 −0.298951 0.954268i \(-0.596637\pi\)
−0.298951 + 0.954268i \(0.596637\pi\)
\(608\) 41.5778 1.68620
\(609\) 0 0
\(610\) −16.5091 −0.668434
\(611\) −22.9690 −0.929225
\(612\) 7.84405 0.317077
\(613\) 25.1379 1.01531 0.507655 0.861560i \(-0.330512\pi\)
0.507655 + 0.861560i \(0.330512\pi\)
\(614\) 2.25632 0.0910576
\(615\) −1.91229 −0.0771109
\(616\) 0 0
\(617\) 20.2465 0.815094 0.407547 0.913184i \(-0.366384\pi\)
0.407547 + 0.913184i \(0.366384\pi\)
\(618\) −8.21946 −0.330635
\(619\) 21.8666 0.878892 0.439446 0.898269i \(-0.355175\pi\)
0.439446 + 0.898269i \(0.355175\pi\)
\(620\) 18.2543 0.733110
\(621\) 3.42494 0.137438
\(622\) 12.6221 0.506099
\(623\) 0 0
\(624\) 0.435892 0.0174497
\(625\) −16.4801 −0.659206
\(626\) −14.7314 −0.588787
\(627\) 19.4007 0.774789
\(628\) 13.6402 0.544302
\(629\) −9.24652 −0.368683
\(630\) 0 0
\(631\) 25.8901 1.03067 0.515334 0.856989i \(-0.327668\pi\)
0.515334 + 0.856989i \(0.327668\pi\)
\(632\) 5.53161 0.220035
\(633\) 10.6322 0.422591
\(634\) −24.7237 −0.981904
\(635\) 25.9967 1.03165
\(636\) 15.2886 0.606233
\(637\) 0 0
\(638\) −23.8042 −0.942415
\(639\) −4.62953 −0.183141
\(640\) 14.8942 0.588743
\(641\) 23.2803 0.919516 0.459758 0.888044i \(-0.347936\pi\)
0.459758 + 0.888044i \(0.347936\pi\)
\(642\) 1.80637 0.0712917
\(643\) 35.9954 1.41952 0.709759 0.704444i \(-0.248804\pi\)
0.709759 + 0.704444i \(0.248804\pi\)
\(644\) 0 0
\(645\) 7.72019 0.303982
\(646\) −37.2204 −1.46442
\(647\) −9.20528 −0.361897 −0.180948 0.983493i \(-0.557917\pi\)
−0.180948 + 0.983493i \(0.557917\pi\)
\(648\) 2.77515 0.109018
\(649\) −4.71985 −0.185270
\(650\) −2.13130 −0.0835965
\(651\) 0 0
\(652\) 27.6731 1.08376
\(653\) −32.8249 −1.28454 −0.642269 0.766480i \(-0.722007\pi\)
−0.642269 + 0.766480i \(0.722007\pi\)
\(654\) −7.40295 −0.289478
\(655\) 35.3354 1.38067
\(656\) 0.231902 0.00905424
\(657\) −4.04568 −0.157837
\(658\) 0 0
\(659\) 21.5406 0.839102 0.419551 0.907732i \(-0.362187\pi\)
0.419551 + 0.907732i \(0.362187\pi\)
\(660\) 6.60043 0.256921
\(661\) 11.7865 0.458441 0.229220 0.973375i \(-0.426382\pi\)
0.229220 + 0.973375i \(0.426382\pi\)
\(662\) −8.04159 −0.312545
\(663\) −11.4531 −0.444802
\(664\) 19.9363 0.773677
\(665\) 0 0
\(666\) −1.28107 −0.0496403
\(667\) −36.0193 −1.39467
\(668\) 7.47648 0.289274
\(669\) −15.6888 −0.606564
\(670\) 5.09861 0.196976
\(671\) 27.4192 1.05851
\(672\) 0 0
\(673\) −34.5436 −1.33156 −0.665778 0.746150i \(-0.731900\pi\)
−0.665778 + 0.746150i \(0.731900\pi\)
\(674\) −22.0154 −0.848000
\(675\) 1.34316 0.0516981
\(676\) 12.1871 0.468736
\(677\) −27.2133 −1.04589 −0.522945 0.852366i \(-0.675167\pi\)
−0.522945 + 0.852366i \(0.675167\pi\)
\(678\) 1.51233 0.0580808
\(679\) 0 0
\(680\) −32.3362 −1.24004
\(681\) 14.8416 0.568732
\(682\) 16.7838 0.642684
\(683\) 6.92911 0.265135 0.132567 0.991174i \(-0.457678\pi\)
0.132567 + 0.991174i \(0.457678\pi\)
\(684\) 9.31497 0.356167
\(685\) 20.4376 0.780881
\(686\) 0 0
\(687\) −7.51697 −0.286790
\(688\) −0.936223 −0.0356932
\(689\) −22.3230 −0.850437
\(690\) −5.52902 −0.210486
\(691\) 37.1434 1.41300 0.706500 0.707713i \(-0.250273\pi\)
0.706500 + 0.707713i \(0.250273\pi\)
\(692\) −27.1758 −1.03307
\(693\) 0 0
\(694\) −6.49514 −0.246552
\(695\) 6.47649 0.245667
\(696\) −29.1857 −1.10628
\(697\) −6.09325 −0.230798
\(698\) −11.2889 −0.427290
\(699\) −17.2580 −0.652759
\(700\) 0 0
\(701\) 29.7764 1.12464 0.562319 0.826921i \(-0.309909\pi\)
0.562319 + 0.826921i \(0.309909\pi\)
\(702\) −1.58678 −0.0598893
\(703\) −10.9804 −0.414134
\(704\) 11.7624 0.443311
\(705\) −23.3679 −0.880086
\(706\) 12.0634 0.454013
\(707\) 0 0
\(708\) −2.26617 −0.0851679
\(709\) −27.4792 −1.03200 −0.516002 0.856587i \(-0.672580\pi\)
−0.516002 + 0.856587i \(0.672580\pi\)
\(710\) 7.47365 0.280481
\(711\) 1.99326 0.0747532
\(712\) −13.0883 −0.490505
\(713\) 25.3964 0.951104
\(714\) 0 0
\(715\) −9.63730 −0.360415
\(716\) 6.23325 0.232948
\(717\) 26.4633 0.988291
\(718\) 2.10672 0.0786221
\(719\) 4.88656 0.182238 0.0911189 0.995840i \(-0.470956\pi\)
0.0911189 + 0.995840i \(0.470956\pi\)
\(720\) 0.443463 0.0165269
\(721\) 0 0
\(722\) −28.1603 −1.04802
\(723\) −27.6180 −1.02712
\(724\) 30.9327 1.14961
\(725\) −14.1257 −0.524615
\(726\) −3.21742 −0.119410
\(727\) −35.7363 −1.32539 −0.662694 0.748890i \(-0.730587\pi\)
−0.662694 + 0.748890i \(0.730587\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 6.53111 0.241727
\(731\) 24.5994 0.909841
\(732\) 13.1650 0.486591
\(733\) 19.1607 0.707715 0.353858 0.935299i \(-0.384870\pi\)
0.353858 + 0.935299i \(0.384870\pi\)
\(734\) −30.9305 −1.14167
\(735\) 0 0
\(736\) 19.6799 0.725412
\(737\) −8.46805 −0.311924
\(738\) −0.844195 −0.0310752
\(739\) 42.7261 1.57170 0.785852 0.618414i \(-0.212225\pi\)
0.785852 + 0.618414i \(0.212225\pi\)
\(740\) −3.73572 −0.137328
\(741\) −13.6008 −0.499638
\(742\) 0 0
\(743\) 13.5962 0.498795 0.249397 0.968401i \(-0.419767\pi\)
0.249397 + 0.968401i \(0.419767\pi\)
\(744\) 20.5782 0.754432
\(745\) 14.5724 0.533893
\(746\) 5.69582 0.208539
\(747\) 7.18385 0.262843
\(748\) 21.0314 0.768983
\(749\) 0 0
\(750\) −10.2400 −0.373913
\(751\) −44.5097 −1.62418 −0.812091 0.583531i \(-0.801671\pi\)
−0.812091 + 0.583531i \(0.801671\pi\)
\(752\) 2.83381 0.103338
\(753\) −19.4790 −0.709856
\(754\) 16.6879 0.607736
\(755\) 13.5047 0.491488
\(756\) 0 0
\(757\) 25.8209 0.938478 0.469239 0.883071i \(-0.344528\pi\)
0.469239 + 0.883071i \(0.344528\pi\)
\(758\) −7.13859 −0.259285
\(759\) 9.18290 0.333318
\(760\) −38.3999 −1.39291
\(761\) 11.2451 0.407635 0.203818 0.979009i \(-0.434665\pi\)
0.203818 + 0.979009i \(0.434665\pi\)
\(762\) 11.4765 0.415749
\(763\) 0 0
\(764\) −21.9373 −0.793662
\(765\) −11.6520 −0.421280
\(766\) 29.3741 1.06133
\(767\) 3.30884 0.119475
\(768\) 15.3492 0.553865
\(769\) −30.9246 −1.11517 −0.557585 0.830120i \(-0.688272\pi\)
−0.557585 + 0.830120i \(0.688272\pi\)
\(770\) 0 0
\(771\) −18.4487 −0.664415
\(772\) −33.8123 −1.21693
\(773\) 28.6555 1.03067 0.515333 0.856990i \(-0.327668\pi\)
0.515333 + 0.856990i \(0.327668\pi\)
\(774\) 3.40814 0.122503
\(775\) 9.95971 0.357763
\(776\) 12.9364 0.464389
\(777\) 0 0
\(778\) 32.2844 1.15745
\(779\) −7.23586 −0.259251
\(780\) −4.62722 −0.165681
\(781\) −12.4126 −0.444159
\(782\) −17.6175 −0.630001
\(783\) −10.5168 −0.375839
\(784\) 0 0
\(785\) −20.2619 −0.723179
\(786\) 15.5991 0.556402
\(787\) 39.6962 1.41502 0.707508 0.706705i \(-0.249819\pi\)
0.707508 + 0.706705i \(0.249819\pi\)
\(788\) −29.6179 −1.05509
\(789\) −29.0590 −1.03453
\(790\) −3.21781 −0.114485
\(791\) 0 0
\(792\) 7.44070 0.264394
\(793\) −19.2222 −0.682600
\(794\) 13.3535 0.473897
\(795\) −22.7107 −0.805464
\(796\) −31.9550 −1.13262
\(797\) −24.4338 −0.865488 −0.432744 0.901517i \(-0.642455\pi\)
−0.432744 + 0.901517i \(0.642455\pi\)
\(798\) 0 0
\(799\) −74.4587 −2.63416
\(800\) 7.71788 0.272868
\(801\) −4.71625 −0.166640
\(802\) −2.17805 −0.0769098
\(803\) −10.8472 −0.382790
\(804\) −4.06581 −0.143390
\(805\) 0 0
\(806\) −11.7662 −0.414448
\(807\) 19.1863 0.675389
\(808\) −11.7495 −0.413346
\(809\) 44.1172 1.55108 0.775539 0.631300i \(-0.217478\pi\)
0.775539 + 0.631300i \(0.217478\pi\)
\(810\) −1.61434 −0.0567222
\(811\) −1.98405 −0.0696693 −0.0348347 0.999393i \(-0.511090\pi\)
−0.0348347 + 0.999393i \(0.511090\pi\)
\(812\) 0 0
\(813\) 13.5358 0.474722
\(814\) −3.43478 −0.120389
\(815\) −41.1073 −1.43993
\(816\) 1.41304 0.0494661
\(817\) 29.2122 1.02201
\(818\) 9.68510 0.338631
\(819\) 0 0
\(820\) −2.46175 −0.0859682
\(821\) 20.8561 0.727883 0.363942 0.931422i \(-0.381431\pi\)
0.363942 + 0.931422i \(0.381431\pi\)
\(822\) 9.02235 0.314691
\(823\) −1.26248 −0.0440073 −0.0220036 0.999758i \(-0.507005\pi\)
−0.0220036 + 0.999758i \(0.507005\pi\)
\(824\) −27.0201 −0.941291
\(825\) 3.60126 0.125380
\(826\) 0 0
\(827\) −19.6810 −0.684376 −0.342188 0.939631i \(-0.611168\pi\)
−0.342188 + 0.939631i \(0.611168\pi\)
\(828\) 4.40904 0.153225
\(829\) 44.4105 1.54244 0.771220 0.636569i \(-0.219647\pi\)
0.771220 + 0.636569i \(0.219647\pi\)
\(830\) −11.5972 −0.402544
\(831\) 15.0702 0.522778
\(832\) −8.24599 −0.285878
\(833\) 0 0
\(834\) 2.85910 0.0990025
\(835\) −11.1060 −0.384340
\(836\) 24.9752 0.863785
\(837\) 7.41515 0.256305
\(838\) 11.5251 0.398128
\(839\) 28.4176 0.981084 0.490542 0.871417i \(-0.336799\pi\)
0.490542 + 0.871417i \(0.336799\pi\)
\(840\) 0 0
\(841\) 81.6027 2.81388
\(842\) 19.0237 0.655600
\(843\) −10.9228 −0.376203
\(844\) 13.6872 0.471132
\(845\) −18.1035 −0.622780
\(846\) −10.3159 −0.354670
\(847\) 0 0
\(848\) 2.75411 0.0945764
\(849\) 5.60619 0.192404
\(850\) −6.90905 −0.236979
\(851\) −5.19735 −0.178163
\(852\) −5.95976 −0.204178
\(853\) −46.6971 −1.59888 −0.799439 0.600747i \(-0.794870\pi\)
−0.799439 + 0.600747i \(0.794870\pi\)
\(854\) 0 0
\(855\) −13.8370 −0.473217
\(856\) 5.93814 0.202962
\(857\) −25.5591 −0.873081 −0.436541 0.899685i \(-0.643796\pi\)
−0.436541 + 0.899685i \(0.643796\pi\)
\(858\) −4.25447 −0.145245
\(859\) −36.7538 −1.25402 −0.627012 0.779009i \(-0.715722\pi\)
−0.627012 + 0.779009i \(0.715722\pi\)
\(860\) 9.93848 0.338899
\(861\) 0 0
\(862\) 5.38819 0.183522
\(863\) 39.4980 1.34453 0.672263 0.740312i \(-0.265322\pi\)
0.672263 + 0.740312i \(0.265322\pi\)
\(864\) 5.74607 0.195485
\(865\) 40.3686 1.37258
\(866\) −29.5508 −1.00418
\(867\) −20.1277 −0.683572
\(868\) 0 0
\(869\) 5.34431 0.181293
\(870\) 16.9777 0.575598
\(871\) 5.93651 0.201151
\(872\) −24.3360 −0.824120
\(873\) 4.66151 0.157768
\(874\) −20.9211 −0.707668
\(875\) 0 0
\(876\) −5.20814 −0.175967
\(877\) 23.7836 0.803114 0.401557 0.915834i \(-0.368469\pi\)
0.401557 + 0.915834i \(0.368469\pi\)
\(878\) 7.05669 0.238152
\(879\) 3.69810 0.124734
\(880\) 1.18901 0.0400814
\(881\) 24.4349 0.823233 0.411616 0.911357i \(-0.364964\pi\)
0.411616 + 0.911357i \(0.364964\pi\)
\(882\) 0 0
\(883\) 6.20562 0.208836 0.104418 0.994534i \(-0.466702\pi\)
0.104418 + 0.994534i \(0.466702\pi\)
\(884\) −14.7440 −0.495895
\(885\) 3.36631 0.113157
\(886\) 22.7031 0.762727
\(887\) −13.6868 −0.459557 −0.229779 0.973243i \(-0.573800\pi\)
−0.229779 + 0.973243i \(0.573800\pi\)
\(888\) −4.21130 −0.141322
\(889\) 0 0
\(890\) 7.61364 0.255210
\(891\) 2.68119 0.0898232
\(892\) −20.1967 −0.676237
\(893\) −88.4212 −2.95890
\(894\) 6.43312 0.215156
\(895\) −9.25926 −0.309503
\(896\) 0 0
\(897\) −6.43766 −0.214947
\(898\) 0.527607 0.0176065
\(899\) −77.9835 −2.60090
\(900\) 1.72909 0.0576364
\(901\) −72.3645 −2.41081
\(902\) −2.26345 −0.0753645
\(903\) 0 0
\(904\) 4.97155 0.165351
\(905\) −45.9494 −1.52741
\(906\) 5.96178 0.198067
\(907\) −40.4953 −1.34462 −0.672312 0.740268i \(-0.734699\pi\)
−0.672312 + 0.740268i \(0.734699\pi\)
\(908\) 19.1061 0.634059
\(909\) −4.23382 −0.140427
\(910\) 0 0
\(911\) 42.8087 1.41832 0.709158 0.705050i \(-0.249075\pi\)
0.709158 + 0.705050i \(0.249075\pi\)
\(912\) 1.67801 0.0555644
\(913\) 19.2612 0.637454
\(914\) 10.5346 0.348453
\(915\) −19.5560 −0.646503
\(916\) −9.67685 −0.319732
\(917\) 0 0
\(918\) −5.14389 −0.169774
\(919\) −16.0982 −0.531030 −0.265515 0.964107i \(-0.585542\pi\)
−0.265515 + 0.964107i \(0.585542\pi\)
\(920\) −18.1758 −0.599237
\(921\) 2.67275 0.0880700
\(922\) −0.710668 −0.0234046
\(923\) 8.70186 0.286425
\(924\) 0 0
\(925\) −2.03824 −0.0670170
\(926\) −23.8424 −0.783511
\(927\) −9.73645 −0.319787
\(928\) −60.4302 −1.98372
\(929\) 8.85492 0.290520 0.145260 0.989393i \(-0.453598\pi\)
0.145260 + 0.989393i \(0.453598\pi\)
\(930\) −11.9706 −0.392531
\(931\) 0 0
\(932\) −22.2169 −0.727738
\(933\) 14.9516 0.489493
\(934\) −1.44707 −0.0473497
\(935\) −31.2413 −1.02170
\(936\) −5.21629 −0.170500
\(937\) −15.4981 −0.506301 −0.253150 0.967427i \(-0.581467\pi\)
−0.253150 + 0.967427i \(0.581467\pi\)
\(938\) 0 0
\(939\) −17.4503 −0.569469
\(940\) −30.0823 −0.981177
\(941\) 4.30488 0.140335 0.0701675 0.997535i \(-0.477647\pi\)
0.0701675 + 0.997535i \(0.477647\pi\)
\(942\) −8.94480 −0.291437
\(943\) −3.42494 −0.111531
\(944\) −0.408230 −0.0132868
\(945\) 0 0
\(946\) 9.13787 0.297098
\(947\) 18.6177 0.604992 0.302496 0.953151i \(-0.402180\pi\)
0.302496 + 0.953151i \(0.402180\pi\)
\(948\) 2.56600 0.0833397
\(949\) 7.60442 0.246850
\(950\) −8.20464 −0.266194
\(951\) −29.2867 −0.949688
\(952\) 0 0
\(953\) 16.2926 0.527768 0.263884 0.964554i \(-0.414996\pi\)
0.263884 + 0.964554i \(0.414996\pi\)
\(954\) −10.0258 −0.324598
\(955\) 32.5870 1.05449
\(956\) 34.0672 1.10181
\(957\) −28.1975 −0.911495
\(958\) 18.0572 0.583401
\(959\) 0 0
\(960\) −8.38921 −0.270760
\(961\) 23.9845 0.773692
\(962\) 2.40795 0.0776353
\(963\) 2.13975 0.0689526
\(964\) −35.5536 −1.14510
\(965\) 50.2269 1.61686
\(966\) 0 0
\(967\) 42.0786 1.35316 0.676578 0.736371i \(-0.263462\pi\)
0.676578 + 0.736371i \(0.263462\pi\)
\(968\) −10.5767 −0.339949
\(969\) −44.0899 −1.41637
\(970\) −7.52527 −0.241622
\(971\) −11.6017 −0.372317 −0.186159 0.982520i \(-0.559604\pi\)
−0.186159 + 0.982520i \(0.559604\pi\)
\(972\) 1.28734 0.0412913
\(973\) 0 0
\(974\) −7.68016 −0.246088
\(975\) −2.52465 −0.0808536
\(976\) 2.37155 0.0759114
\(977\) 36.0348 1.15286 0.576428 0.817148i \(-0.304446\pi\)
0.576428 + 0.817148i \(0.304446\pi\)
\(978\) −18.1472 −0.580282
\(979\) −12.6451 −0.404141
\(980\) 0 0
\(981\) −8.76924 −0.279980
\(982\) −12.0061 −0.383129
\(983\) 40.3590 1.28725 0.643625 0.765341i \(-0.277429\pi\)
0.643625 + 0.765341i \(0.277429\pi\)
\(984\) −2.77515 −0.0884686
\(985\) 43.9962 1.40184
\(986\) 54.0972 1.72280
\(987\) 0 0
\(988\) −17.5088 −0.557029
\(989\) 13.8270 0.439673
\(990\) −4.32836 −0.137564
\(991\) −24.9144 −0.791431 −0.395715 0.918373i \(-0.629503\pi\)
−0.395715 + 0.918373i \(0.629503\pi\)
\(992\) 42.6080 1.35281
\(993\) −9.52575 −0.302291
\(994\) 0 0
\(995\) 47.4680 1.50484
\(996\) 9.24802 0.293035
\(997\) −45.1066 −1.42854 −0.714269 0.699871i \(-0.753241\pi\)
−0.714269 + 0.699871i \(0.753241\pi\)
\(998\) 11.4682 0.363020
\(999\) −1.51750 −0.0480116
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 \(a_p\))