Properties

Label 6027.2.a.bo.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 \(-0.640641\pi\)
−0.427600 + 0.903968i \(0.640641\pi\)
\(6\) −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 \(-0.416060\pi\)
0.260659 + 0.965431i \(0.416060\pi\)
\(14\) 0 0
\(15\) −1.91229 −0.493750
\(16\) 0.231902 0.0579755
\(17\) 6.09325 1.47783 0.738915 0.673799i \(-0.235339\pi\)
0.738915 + 0.673799i \(0.235339\pi\)
\(18\) −0.844195 −0.198979
\(19\) 7.23586 1.66002 0.830010 0.557749i \(-0.188335\pi\)
0.830010 + 0.557749i \(0.188335\pi\)
\(20\) 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 \(-0.268048\pi\)
0.665900 + 0.746041i \(0.268048\pi\)
\(32\) −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 \(-0.850154\pi\)
−0.891225 + 0.453561i \(0.850154\pi\)
\(48\) 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 \(-0.463445\pi\)
0.114590 + 0.993413i \(0.463445\pi\)
\(60\) 2.46175 0.317811
\(61\) −10.2265 −1.30937 −0.654686 0.755901i \(-0.727199\pi\)
−0.654686 + 0.755901i \(0.727199\pi\)
\(62\) −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 \(-0.423916\pi\)
0.236755 + 0.971569i \(0.423916\pi\)
\(74\) −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 \(-0.629001\pi\)
−0.394265 + 0.918997i \(0.629001\pi\)
\(84\) 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 \(-0.419582\pi\)
0.249961 + 0.968256i \(0.419582\pi\)
\(90\) 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 \(-0.576050\pi\)
−0.236652 + 0.971594i \(0.576050\pi\)
\(98\) 0 0
\(99\) 2.68119 0.269470
\(100\) 1.72909 0.172909
\(101\) 4.23382 0.421281 0.210641 0.977564i \(-0.432445\pi\)
0.210641 + 0.977564i \(0.432445\pi\)
\(102\) −5.14389 −0.509321
\(103\) 9.73645 0.959361 0.479680 0.877443i \(-0.340753\pi\)
0.479680 + 0.877443i \(0.340753\pi\)
\(104\) 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 \(-0.799028\pi\)
−0.807219 + 0.590252i \(0.799028\pi\)
\(132\) −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 \(-0.545878\pi\)
−0.143631 + 0.989631i \(0.545878\pi\)
\(140\) 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 \(-0.361043\pi\)
0.422813 + 0.906217i \(0.361043\pi\)
\(158\) −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 \(-0.427857\pi\)
0.224707 + 0.974426i \(0.427857\pi\)
\(168\) 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 \(-0.796490\pi\)
−0.802487 + 0.596670i \(0.796490\pi\)
\(174\) −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 \(-0.148587\pi\)
0.893012 + 0.450032i \(0.148587\pi\)
\(182\) 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 \(-0.842333\pi\)
−0.879814 + 0.475317i \(0.842333\pi\)
\(200\) −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 \(-0.676047\pi\)
−0.525300 + 0.850917i \(0.676047\pi\)
\(224\) 0 0
\(225\) −1.34316 −0.0895438
\(226\) −1.51233 −0.100599
\(227\) 14.8416 0.985073 0.492536 0.870292i \(-0.336070\pi\)
0.492536 + 0.870292i \(0.336070\pi\)
\(228\) −9.31497 −0.616899
\(229\) −7.51697 −0.496735 −0.248368 0.968666i \(-0.579894\pi\)
−0.248368 + 0.968666i \(0.579894\pi\)
\(230\) −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 \(-0.848957\pi\)
−0.889515 + 0.456906i \(0.848957\pi\)
\(242\) 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 \(-0.710744\pi\)
−0.614753 + 0.788719i \(0.710744\pi\)
\(252\) 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 \(-0.695154\pi\)
−0.575400 + 0.817872i \(0.695154\pi\)
\(258\) 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 \(-0.301132\pi\)
0.584904 + 0.811103i \(0.301132\pi\)
\(270\) 1.61434 0.0982458
\(271\) 13.5358 0.822243 0.411121 0.911581i \(-0.365137\pi\)
0.411121 + 0.911581i \(0.365137\pi\)
\(272\) 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 \(-0.446713\pi\)
0.166627 + 0.986020i \(0.446713\pi\)
\(284\) 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 \(-0.465548\pi\)
0.108023 + 0.994148i \(0.465548\pi\)
\(294\) 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 \(-0.475699\pi\)
0.0762709 + 0.997087i \(0.475699\pi\)
\(308\) 0 0
\(309\) 9.73645 0.553887
\(310\) 11.9706 0.679884
\(311\) 14.9516 0.847827 0.423914 0.905703i \(-0.360656\pi\)
0.423914 + 0.905703i \(0.360656\pi\)
\(312\) 5.21629 0.295314
\(313\) −17.4503 −0.986349 −0.493174 0.869930i \(-0.664164\pi\)
−0.493174 + 0.869930i \(0.664164\pi\)
\(314\) −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 \(-0.616508\pi\)
−0.357903 + 0.933759i \(0.616508\pi\)
\(350\) 0 0
\(351\) 1.87964 0.100328
\(352\) −15.4063 −0.821159
\(353\) 14.2898 0.760572 0.380286 0.924869i \(-0.375826\pi\)
0.380286 + 0.924869i \(0.375826\pi\)
\(354\) −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 \(-0.905521\pi\)
−0.956273 + 0.292477i \(0.905521\pi\)
\(368\) −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 \(-0.151414\pi\)
0.888981 + 0.457945i \(0.151414\pi\)
\(384\) 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 \(-0.370072\pi\)
0.396941 + 0.917844i \(0.370072\pi\)
\(398\) 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 \(-0.408457\pi\)
0.283641 + 0.958930i \(0.408457\pi\)
\(410\) −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 \(-0.391778\pi\)
0.333476 + 0.942758i \(0.391778\pi\)
\(420\) 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 \(-0.818097\pi\)
−0.841109 + 0.540866i \(0.818097\pi\)
\(434\) 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 \(-0.436075\pi\)
0.199479 + 0.979902i \(0.436075\pi\)
\(440\) −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 \(-0.506241\pi\)
−0.0196039 + 0.999808i \(0.506241\pi\)
\(462\) 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 \(-0.512628\pi\)
−0.0396606 + 0.999213i \(0.512628\pi\)
\(468\) −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 \(-0.337485\pi\)
0.488663 + 0.872473i \(0.337485\pi\)
\(480\) 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 \(-0.377840\pi\)
0.374427 + 0.927257i \(0.377840\pi\)
\(504\) 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 \(-0.423673\pi\)
0.237496 + 0.971389i \(0.423673\pi\)
\(510\) 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 \(-0.722927\pi\)
−0.644482 + 0.764620i \(0.722927\pi\)
\(522\) −8.87821 −0.388589
\(523\) −19.6952 −0.861213 −0.430606 0.902540i \(-0.641700\pi\)
−0.430606 + 0.902540i \(0.641700\pi\)
\(524\) 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 \(-0.456217\pi\)
0.137117 + 0.990555i \(0.456217\pi\)
\(564\) 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 \(-0.743429\pi\)
−0.692360 + 0.721552i \(0.743429\pi\)
\(578\) −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 \(-0.732157\pi\)
−0.666379 + 0.745613i \(0.732157\pi\)
\(588\) 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 \(-0.451454\pi\)
0.151920 + 0.988393i \(0.451454\pi\)
\(594\) −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 \(-0.668632\pi\)
−0.505337 + 0.862922i \(0.668632\pi\)
\(602\) 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 \(-0.403363\pi\)
0.298951 + 0.954268i \(0.403363\pi\)
\(608\) −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 \(-0.644825\pi\)
−0.439446 + 0.898269i \(0.644825\pi\)
\(620\) 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 \(-0.751196\pi\)
−0.709759 + 0.704444i \(0.751196\pi\)
\(644\) 0 0
\(645\) 7.72019 0.303982
\(646\) −37.2204 −1.46442
\(647\) 9.20528 0.361897 0.180948 0.983493i \(-0.442083\pi\)
0.180948 + 0.983493i \(0.442083\pi\)
\(648\) 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 \(-0.573618\pi\)
−0.229220 + 0.973375i \(0.573618\pi\)
\(662\) −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 \(-0.324833\pi\)
0.522945 + 0.852366i \(0.324833\pi\)
\(678\) −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 \(-0.749727\pi\)
−0.706500 + 0.707713i \(0.749727\pi\)
\(692\) 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 \(-0.529044\pi\)
−0.0911189 + 0.995840i \(0.529044\pi\)
\(720\) −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 \(-0.269413\pi\)
0.662694 + 0.748890i \(0.269413\pi\)
\(728\) 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 \(-0.615130\pi\)
−0.353858 + 0.935299i \(0.615130\pi\)
\(734\) 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 \(-0.565335\pi\)
−0.203818 + 0.979009i \(0.565335\pi\)
\(762\) −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 \(-0.311728\pi\)
0.557585 + 0.830120i \(0.311728\pi\)
\(770\) 0 0
\(771\) −18.4487 −0.664415
\(772\) −33.8123 −1.21693
\(773\) −28.6555 −1.03067 −0.515333 0.856990i \(-0.672332\pi\)
−0.515333 + 0.856990i \(0.672332\pi\)
\(774\) 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 \(-0.750181\pi\)
−0.707508 + 0.706705i \(0.750181\pi\)
\(788\) −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 \(-0.357545\pi\)
0.432744 + 0.901517i \(0.357545\pi\)
\(798\) 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 \(-0.488910\pi\)
0.0348347 + 0.999393i \(0.488910\pi\)
\(812\) 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 \(-0.780353\pi\)
−0.771220 + 0.636569i \(0.780353\pi\)
\(830\) −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 \(-0.663201\pi\)
−0.490542 + 0.871417i \(0.663201\pi\)
\(840\) 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 \(-0.205130\pi\)
0.799439 + 0.600747i \(0.205130\pi\)
\(854\) 0 0
\(855\) −13.8370 −0.473217
\(856\) 5.93814 0.202962
\(857\) 25.5591 0.873081 0.436541 0.899685i \(-0.356204\pi\)
0.436541 + 0.899685i \(0.356204\pi\)
\(858\) −4.25447 −0.145245
\(859\) 36.7538 1.25402 0.627012 0.779009i \(-0.284278\pi\)
0.627012 + 0.779009i \(0.284278\pi\)
\(860\) −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 \(-0.635036\pi\)
−0.411616 + 0.911357i \(0.635036\pi\)
\(882\) 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 \(-0.426200\pi\)
0.229779 + 0.973243i \(0.426200\pi\)
\(888\) 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 \(-0.546402\pi\)
−0.145260 + 0.989393i \(0.546402\pi\)
\(930\) 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 \(-0.418533\pi\)
0.253150 + 0.967427i \(0.418533\pi\)
\(938\) 0 0
\(939\) −17.4503 −0.569469
\(940\) −30.0823 −0.981177
\(941\) −4.30488 −0.140335 −0.0701675 0.997535i \(-0.522353\pi\)
−0.0701675 + 0.997535i \(0.522353\pi\)
\(942\) −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 \(-0.440396\pi\)
0.186159 + 0.982520i \(0.440396\pi\)
\(972\) −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 \(-0.722571\pi\)
−0.643625 + 0.765341i \(0.722571\pi\)
\(984\) −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 \(-0.246759\pi\)
0.714269 + 0.699871i \(0.246759\pi\)
\(998\) 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 \(a_p\))