Properties

Label 6027.2.a.bn.1.17
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 1.17
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.64420 q^{2} -1.00000 q^{3} +0.703405 q^{4} -3.28206 q^{5} -1.64420 q^{6} -2.13187 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.64420 q^{2} -1.00000 q^{3} +0.703405 q^{4} -3.28206 q^{5} -1.64420 q^{6} -2.13187 q^{8} +1.00000 q^{9} -5.39638 q^{10} -3.35789 q^{11} -0.703405 q^{12} -5.75857 q^{13} +3.28206 q^{15} -4.91203 q^{16} -6.12943 q^{17} +1.64420 q^{18} -3.14030 q^{19} -2.30862 q^{20} -5.52106 q^{22} -9.17799 q^{23} +2.13187 q^{24} +5.77193 q^{25} -9.46827 q^{26} -1.00000 q^{27} +0.986050 q^{29} +5.39638 q^{30} +4.50254 q^{31} -3.81265 q^{32} +3.35789 q^{33} -10.0780 q^{34} +0.703405 q^{36} +11.7958 q^{37} -5.16329 q^{38} +5.75857 q^{39} +6.99692 q^{40} +1.00000 q^{41} +7.67969 q^{43} -2.36196 q^{44} -3.28206 q^{45} -15.0905 q^{46} -12.0154 q^{47} +4.91203 q^{48} +9.49023 q^{50} +6.12943 q^{51} -4.05061 q^{52} -2.61317 q^{53} -1.64420 q^{54} +11.0208 q^{55} +3.14030 q^{57} +1.62127 q^{58} -11.2245 q^{59} +2.30862 q^{60} -1.80269 q^{61} +7.40309 q^{62} +3.55530 q^{64} +18.9000 q^{65} +5.52106 q^{66} -13.1550 q^{67} -4.31147 q^{68} +9.17799 q^{69} -5.92317 q^{71} -2.13187 q^{72} +9.66466 q^{73} +19.3947 q^{74} -5.77193 q^{75} -2.20890 q^{76} +9.46827 q^{78} -8.44944 q^{79} +16.1216 q^{80} +1.00000 q^{81} +1.64420 q^{82} -5.92934 q^{83} +20.1172 q^{85} +12.6270 q^{86} -0.986050 q^{87} +7.15857 q^{88} -11.3923 q^{89} -5.39638 q^{90} -6.45584 q^{92} -4.50254 q^{93} -19.7557 q^{94} +10.3067 q^{95} +3.81265 q^{96} +11.7824 q^{97} -3.35789 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 8q^{2} - 24q^{3} + 32q^{4} - 4q^{5} - 8q^{6} + 24q^{8} + 24q^{9} + O(q^{10}) \) \( 24q + 8q^{2} - 24q^{3} + 32q^{4} - 4q^{5} - 8q^{6} + 24q^{8} + 24q^{9} + 4q^{10} + 12q^{11} - 32q^{12} + 4q^{15} + 44q^{16} - 8q^{17} + 8q^{18} + 4q^{19} - 28q^{20} + 16q^{22} + 20q^{23} - 24q^{24} + 48q^{25} - 32q^{26} - 24q^{27} + 24q^{29} - 4q^{30} + 4q^{31} + 36q^{32} - 12q^{33} - 16q^{34} + 32q^{36} + 64q^{37} - 20q^{38} + 48q^{40} + 24q^{41} + 20q^{43} + 48q^{44} - 4q^{45} + 28q^{46} - 32q^{47} - 44q^{48} - 20q^{50} + 8q^{51} + 76q^{53} - 8q^{54} + 24q^{55} - 4q^{57} + 28q^{58} - 28q^{59} + 28q^{60} + 28q^{61} + 4q^{62} + 48q^{64} + 28q^{65} - 16q^{66} + 44q^{67} + 32q^{68} - 20q^{69} + 20q^{71} + 24q^{72} + 16q^{73} + 44q^{74} - 48q^{75} + 16q^{76} + 32q^{78} + 4q^{79} - 44q^{80} + 24q^{81} + 8q^{82} - 8q^{83} + 28q^{85} + 56q^{86} - 24q^{87} + 60q^{88} - 60q^{89} + 4q^{90} + 60q^{92} - 4q^{93} - 24q^{94} + 28q^{95} - 36q^{96} + 48q^{97} + 12q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.64420 1.16263 0.581314 0.813680i \(-0.302539\pi\)
0.581314 + 0.813680i \(0.302539\pi\)
\(3\) −1.00000 −0.577350
\(4\) 0.703405 0.351702
\(5\) −3.28206 −1.46778 −0.733891 0.679267i \(-0.762298\pi\)
−0.733891 + 0.679267i \(0.762298\pi\)
\(6\) −1.64420 −0.671243
\(7\) 0 0
\(8\) −2.13187 −0.753729
\(9\) 1.00000 0.333333
\(10\) −5.39638 −1.70648
\(11\) −3.35789 −1.01244 −0.506221 0.862404i \(-0.668958\pi\)
−0.506221 + 0.862404i \(0.668958\pi\)
\(12\) −0.703405 −0.203055
\(13\) −5.75857 −1.59714 −0.798571 0.601901i \(-0.794410\pi\)
−0.798571 + 0.601901i \(0.794410\pi\)
\(14\) 0 0
\(15\) 3.28206 0.847425
\(16\) −4.91203 −1.22801
\(17\) −6.12943 −1.48661 −0.743303 0.668955i \(-0.766742\pi\)
−0.743303 + 0.668955i \(0.766742\pi\)
\(18\) 1.64420 0.387542
\(19\) −3.14030 −0.720434 −0.360217 0.932869i \(-0.617297\pi\)
−0.360217 + 0.932869i \(0.617297\pi\)
\(20\) −2.30862 −0.516223
\(21\) 0 0
\(22\) −5.52106 −1.17709
\(23\) −9.17799 −1.91374 −0.956871 0.290512i \(-0.906174\pi\)
−0.956871 + 0.290512i \(0.906174\pi\)
\(24\) 2.13187 0.435165
\(25\) 5.77193 1.15439
\(26\) −9.46827 −1.85688
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 0.986050 0.183105 0.0915524 0.995800i \(-0.470817\pi\)
0.0915524 + 0.995800i \(0.470817\pi\)
\(30\) 5.39638 0.985239
\(31\) 4.50254 0.808680 0.404340 0.914609i \(-0.367501\pi\)
0.404340 + 0.914609i \(0.367501\pi\)
\(32\) −3.81265 −0.673987
\(33\) 3.35789 0.584534
\(34\) −10.0780 −1.72837
\(35\) 0 0
\(36\) 0.703405 0.117234
\(37\) 11.7958 1.93922 0.969611 0.244651i \(-0.0786733\pi\)
0.969611 + 0.244651i \(0.0786733\pi\)
\(38\) −5.16329 −0.837596
\(39\) 5.75857 0.922110
\(40\) 6.99692 1.10631
\(41\) 1.00000 0.156174
\(42\) 0 0
\(43\) 7.67969 1.17114 0.585571 0.810621i \(-0.300870\pi\)
0.585571 + 0.810621i \(0.300870\pi\)
\(44\) −2.36196 −0.356078
\(45\) −3.28206 −0.489261
\(46\) −15.0905 −2.22497
\(47\) −12.0154 −1.75262 −0.876311 0.481746i \(-0.840003\pi\)
−0.876311 + 0.481746i \(0.840003\pi\)
\(48\) 4.91203 0.708991
\(49\) 0 0
\(50\) 9.49023 1.34212
\(51\) 6.12943 0.858292
\(52\) −4.05061 −0.561718
\(53\) −2.61317 −0.358947 −0.179473 0.983763i \(-0.557439\pi\)
−0.179473 + 0.983763i \(0.557439\pi\)
\(54\) −1.64420 −0.223748
\(55\) 11.0208 1.48605
\(56\) 0 0
\(57\) 3.14030 0.415943
\(58\) 1.62127 0.212883
\(59\) −11.2245 −1.46131 −0.730654 0.682748i \(-0.760785\pi\)
−0.730654 + 0.682748i \(0.760785\pi\)
\(60\) 2.30862 0.298041
\(61\) −1.80269 −0.230810 −0.115405 0.993319i \(-0.536817\pi\)
−0.115405 + 0.993319i \(0.536817\pi\)
\(62\) 7.40309 0.940194
\(63\) 0 0
\(64\) 3.55530 0.444412
\(65\) 18.9000 2.34426
\(66\) 5.52106 0.679595
\(67\) −13.1550 −1.60714 −0.803571 0.595209i \(-0.797069\pi\)
−0.803571 + 0.595209i \(0.797069\pi\)
\(68\) −4.31147 −0.522843
\(69\) 9.17799 1.10490
\(70\) 0 0
\(71\) −5.92317 −0.702951 −0.351475 0.936197i \(-0.614320\pi\)
−0.351475 + 0.936197i \(0.614320\pi\)
\(72\) −2.13187 −0.251243
\(73\) 9.66466 1.13116 0.565581 0.824692i \(-0.308652\pi\)
0.565581 + 0.824692i \(0.308652\pi\)
\(74\) 19.3947 2.25459
\(75\) −5.77193 −0.666485
\(76\) −2.20890 −0.253378
\(77\) 0 0
\(78\) 9.46827 1.07207
\(79\) −8.44944 −0.950637 −0.475318 0.879814i \(-0.657667\pi\)
−0.475318 + 0.879814i \(0.657667\pi\)
\(80\) 16.1216 1.80245
\(81\) 1.00000 0.111111
\(82\) 1.64420 0.181572
\(83\) −5.92934 −0.650830 −0.325415 0.945571i \(-0.605504\pi\)
−0.325415 + 0.945571i \(0.605504\pi\)
\(84\) 0 0
\(85\) 20.1172 2.18201
\(86\) 12.6270 1.36160
\(87\) −0.986050 −0.105716
\(88\) 7.15857 0.763107
\(89\) −11.3923 −1.20758 −0.603788 0.797145i \(-0.706343\pi\)
−0.603788 + 0.797145i \(0.706343\pi\)
\(90\) −5.39638 −0.568828
\(91\) 0 0
\(92\) −6.45584 −0.673068
\(93\) −4.50254 −0.466892
\(94\) −19.7557 −2.03765
\(95\) 10.3067 1.05744
\(96\) 3.81265 0.389127
\(97\) 11.7824 1.19632 0.598160 0.801377i \(-0.295899\pi\)
0.598160 + 0.801377i \(0.295899\pi\)
\(98\) 0 0
\(99\) −3.35789 −0.337481
\(100\) 4.06001 0.406001
\(101\) 4.37589 0.435417 0.217708 0.976014i \(-0.430142\pi\)
0.217708 + 0.976014i \(0.430142\pi\)
\(102\) 10.0780 0.997874
\(103\) −7.57841 −0.746723 −0.373361 0.927686i \(-0.621795\pi\)
−0.373361 + 0.927686i \(0.621795\pi\)
\(104\) 12.2765 1.20381
\(105\) 0 0
\(106\) −4.29659 −0.417321
\(107\) 20.3029 1.96276 0.981380 0.192078i \(-0.0615226\pi\)
0.981380 + 0.192078i \(0.0615226\pi\)
\(108\) −0.703405 −0.0676852
\(109\) −6.23589 −0.597290 −0.298645 0.954364i \(-0.596535\pi\)
−0.298645 + 0.954364i \(0.596535\pi\)
\(110\) 18.1204 1.72772
\(111\) −11.7958 −1.11961
\(112\) 0 0
\(113\) −3.17038 −0.298245 −0.149122 0.988819i \(-0.547645\pi\)
−0.149122 + 0.988819i \(0.547645\pi\)
\(114\) 5.16329 0.483586
\(115\) 30.1227 2.80896
\(116\) 0.693592 0.0643984
\(117\) −5.75857 −0.532380
\(118\) −18.4554 −1.69896
\(119\) 0 0
\(120\) −6.99692 −0.638728
\(121\) 0.275433 0.0250393
\(122\) −2.96398 −0.268346
\(123\) −1.00000 −0.0901670
\(124\) 3.16711 0.284415
\(125\) −2.53353 −0.226606
\(126\) 0 0
\(127\) 8.07325 0.716385 0.358193 0.933648i \(-0.383393\pi\)
0.358193 + 0.933648i \(0.383393\pi\)
\(128\) 13.4709 1.19067
\(129\) −7.67969 −0.676159
\(130\) 31.0754 2.72550
\(131\) 9.14130 0.798679 0.399340 0.916803i \(-0.369239\pi\)
0.399340 + 0.916803i \(0.369239\pi\)
\(132\) 2.36196 0.205582
\(133\) 0 0
\(134\) −21.6295 −1.86851
\(135\) 3.28206 0.282475
\(136\) 13.0671 1.12050
\(137\) −6.53936 −0.558695 −0.279348 0.960190i \(-0.590118\pi\)
−0.279348 + 0.960190i \(0.590118\pi\)
\(138\) 15.0905 1.28459
\(139\) −8.98420 −0.762030 −0.381015 0.924569i \(-0.624425\pi\)
−0.381015 + 0.924569i \(0.624425\pi\)
\(140\) 0 0
\(141\) 12.0154 1.01188
\(142\) −9.73890 −0.817270
\(143\) 19.3367 1.61701
\(144\) −4.91203 −0.409336
\(145\) −3.23628 −0.268758
\(146\) 15.8907 1.31512
\(147\) 0 0
\(148\) 8.29724 0.682029
\(149\) 0.272952 0.0223611 0.0111805 0.999937i \(-0.496441\pi\)
0.0111805 + 0.999937i \(0.496441\pi\)
\(150\) −9.49023 −0.774874
\(151\) −6.62811 −0.539388 −0.269694 0.962946i \(-0.586923\pi\)
−0.269694 + 0.962946i \(0.586923\pi\)
\(152\) 6.69470 0.543011
\(153\) −6.12943 −0.495535
\(154\) 0 0
\(155\) −14.7776 −1.18697
\(156\) 4.05061 0.324308
\(157\) −23.3131 −1.86058 −0.930292 0.366819i \(-0.880447\pi\)
−0.930292 + 0.366819i \(0.880447\pi\)
\(158\) −13.8926 −1.10524
\(159\) 2.61317 0.207238
\(160\) 12.5133 0.989266
\(161\) 0 0
\(162\) 1.64420 0.129181
\(163\) −21.0309 −1.64727 −0.823634 0.567122i \(-0.808057\pi\)
−0.823634 + 0.567122i \(0.808057\pi\)
\(164\) 0.703405 0.0549267
\(165\) −11.0208 −0.857969
\(166\) −9.74905 −0.756673
\(167\) 3.40709 0.263648 0.131824 0.991273i \(-0.457917\pi\)
0.131824 + 0.991273i \(0.457917\pi\)
\(168\) 0 0
\(169\) 20.1612 1.55086
\(170\) 33.0767 2.53687
\(171\) −3.14030 −0.240145
\(172\) 5.40193 0.411893
\(173\) −4.48482 −0.340974 −0.170487 0.985360i \(-0.554534\pi\)
−0.170487 + 0.985360i \(0.554534\pi\)
\(174\) −1.62127 −0.122908
\(175\) 0 0
\(176\) 16.4941 1.24329
\(177\) 11.2245 0.843687
\(178\) −18.7312 −1.40396
\(179\) 13.9561 1.04313 0.521565 0.853211i \(-0.325348\pi\)
0.521565 + 0.853211i \(0.325348\pi\)
\(180\) −2.30862 −0.172074
\(181\) 9.21198 0.684721 0.342361 0.939569i \(-0.388774\pi\)
0.342361 + 0.939569i \(0.388774\pi\)
\(182\) 0 0
\(183\) 1.80269 0.133258
\(184\) 19.5662 1.44244
\(185\) −38.7147 −2.84636
\(186\) −7.40309 −0.542821
\(187\) 20.5820 1.50510
\(188\) −8.45167 −0.616401
\(189\) 0 0
\(190\) 16.9462 1.22941
\(191\) −18.9462 −1.37090 −0.685451 0.728119i \(-0.740395\pi\)
−0.685451 + 0.728119i \(0.740395\pi\)
\(192\) −3.55530 −0.256581
\(193\) −15.5168 −1.11692 −0.558461 0.829531i \(-0.688608\pi\)
−0.558461 + 0.829531i \(0.688608\pi\)
\(194\) 19.3726 1.39087
\(195\) −18.9000 −1.35346
\(196\) 0 0
\(197\) 3.07929 0.219390 0.109695 0.993965i \(-0.465013\pi\)
0.109695 + 0.993965i \(0.465013\pi\)
\(198\) −5.52106 −0.392364
\(199\) −5.82235 −0.412736 −0.206368 0.978474i \(-0.566164\pi\)
−0.206368 + 0.978474i \(0.566164\pi\)
\(200\) −12.3050 −0.870094
\(201\) 13.1550 0.927884
\(202\) 7.19485 0.506228
\(203\) 0 0
\(204\) 4.31147 0.301863
\(205\) −3.28206 −0.229229
\(206\) −12.4604 −0.868160
\(207\) −9.17799 −0.637914
\(208\) 28.2863 1.96130
\(209\) 10.5448 0.729398
\(210\) 0 0
\(211\) −19.1035 −1.31514 −0.657569 0.753394i \(-0.728415\pi\)
−0.657569 + 0.753394i \(0.728415\pi\)
\(212\) −1.83812 −0.126242
\(213\) 5.92317 0.405849
\(214\) 33.3822 2.28196
\(215\) −25.2052 −1.71898
\(216\) 2.13187 0.145055
\(217\) 0 0
\(218\) −10.2531 −0.694426
\(219\) −9.66466 −0.653077
\(220\) 7.75209 0.522646
\(221\) 35.2968 2.37432
\(222\) −19.3947 −1.30169
\(223\) 27.3295 1.83012 0.915059 0.403320i \(-0.132144\pi\)
0.915059 + 0.403320i \(0.132144\pi\)
\(224\) 0 0
\(225\) 5.77193 0.384796
\(226\) −5.21275 −0.346747
\(227\) −6.27102 −0.416222 −0.208111 0.978105i \(-0.566732\pi\)
−0.208111 + 0.978105i \(0.566732\pi\)
\(228\) 2.20890 0.146288
\(229\) 7.57515 0.500580 0.250290 0.968171i \(-0.419474\pi\)
0.250290 + 0.968171i \(0.419474\pi\)
\(230\) 49.5279 3.26577
\(231\) 0 0
\(232\) −2.10213 −0.138011
\(233\) −1.10598 −0.0724553 −0.0362276 0.999344i \(-0.511534\pi\)
−0.0362276 + 0.999344i \(0.511534\pi\)
\(234\) −9.46827 −0.618960
\(235\) 39.4352 2.57247
\(236\) −7.89538 −0.513946
\(237\) 8.44944 0.548850
\(238\) 0 0
\(239\) 18.1910 1.17668 0.588339 0.808615i \(-0.299782\pi\)
0.588339 + 0.808615i \(0.299782\pi\)
\(240\) −16.1216 −1.04064
\(241\) −20.6913 −1.33284 −0.666422 0.745575i \(-0.732175\pi\)
−0.666422 + 0.745575i \(0.732175\pi\)
\(242\) 0.452867 0.0291114
\(243\) −1.00000 −0.0641500
\(244\) −1.26802 −0.0811765
\(245\) 0 0
\(246\) −1.64420 −0.104831
\(247\) 18.0836 1.15063
\(248\) −9.59882 −0.609525
\(249\) 5.92934 0.375757
\(250\) −4.16564 −0.263458
\(251\) 2.49992 0.157793 0.0788967 0.996883i \(-0.474860\pi\)
0.0788967 + 0.996883i \(0.474860\pi\)
\(252\) 0 0
\(253\) 30.8187 1.93755
\(254\) 13.2741 0.832889
\(255\) −20.1172 −1.25979
\(256\) 15.0383 0.939896
\(257\) −12.6110 −0.786650 −0.393325 0.919400i \(-0.628675\pi\)
−0.393325 + 0.919400i \(0.628675\pi\)
\(258\) −12.6270 −0.786121
\(259\) 0 0
\(260\) 13.2943 0.824481
\(261\) 0.986050 0.0610350
\(262\) 15.0302 0.928566
\(263\) −21.2852 −1.31250 −0.656250 0.754544i \(-0.727858\pi\)
−0.656250 + 0.754544i \(0.727858\pi\)
\(264\) −7.15857 −0.440580
\(265\) 8.57659 0.526856
\(266\) 0 0
\(267\) 11.3923 0.697195
\(268\) −9.25331 −0.565236
\(269\) 26.5602 1.61940 0.809701 0.586842i \(-0.199629\pi\)
0.809701 + 0.586842i \(0.199629\pi\)
\(270\) 5.39638 0.328413
\(271\) −11.8390 −0.719170 −0.359585 0.933112i \(-0.617082\pi\)
−0.359585 + 0.933112i \(0.617082\pi\)
\(272\) 30.1080 1.82556
\(273\) 0 0
\(274\) −10.7520 −0.649555
\(275\) −19.3815 −1.16875
\(276\) 6.45584 0.388596
\(277\) −19.3182 −1.16072 −0.580360 0.814360i \(-0.697088\pi\)
−0.580360 + 0.814360i \(0.697088\pi\)
\(278\) −14.7718 −0.885957
\(279\) 4.50254 0.269560
\(280\) 0 0
\(281\) −17.2205 −1.02729 −0.513645 0.858003i \(-0.671705\pi\)
−0.513645 + 0.858003i \(0.671705\pi\)
\(282\) 19.7557 1.17644
\(283\) 21.7400 1.29231 0.646156 0.763206i \(-0.276376\pi\)
0.646156 + 0.763206i \(0.276376\pi\)
\(284\) −4.16639 −0.247230
\(285\) −10.3067 −0.610513
\(286\) 31.7934 1.87998
\(287\) 0 0
\(288\) −3.81265 −0.224662
\(289\) 20.5699 1.20999
\(290\) −5.32110 −0.312466
\(291\) −11.7824 −0.690696
\(292\) 6.79817 0.397833
\(293\) 3.46874 0.202646 0.101323 0.994854i \(-0.467692\pi\)
0.101323 + 0.994854i \(0.467692\pi\)
\(294\) 0 0
\(295\) 36.8396 2.14488
\(296\) −25.1471 −1.46165
\(297\) 3.35789 0.194845
\(298\) 0.448788 0.0259976
\(299\) 52.8521 3.05652
\(300\) −4.06001 −0.234405
\(301\) 0 0
\(302\) −10.8980 −0.627107
\(303\) −4.37589 −0.251388
\(304\) 15.4252 0.884698
\(305\) 5.91653 0.338779
\(306\) −10.0780 −0.576123
\(307\) 26.8694 1.53352 0.766758 0.641937i \(-0.221869\pi\)
0.766758 + 0.641937i \(0.221869\pi\)
\(308\) 0 0
\(309\) 7.57841 0.431121
\(310\) −24.2974 −1.38000
\(311\) −28.0423 −1.59013 −0.795066 0.606523i \(-0.792564\pi\)
−0.795066 + 0.606523i \(0.792564\pi\)
\(312\) −12.2765 −0.695021
\(313\) −14.1597 −0.800356 −0.400178 0.916438i \(-0.631052\pi\)
−0.400178 + 0.916438i \(0.631052\pi\)
\(314\) −38.3314 −2.16317
\(315\) 0 0
\(316\) −5.94338 −0.334341
\(317\) 31.4411 1.76591 0.882955 0.469458i \(-0.155551\pi\)
0.882955 + 0.469458i \(0.155551\pi\)
\(318\) 4.29659 0.240941
\(319\) −3.31105 −0.185383
\(320\) −11.6687 −0.652301
\(321\) −20.3029 −1.13320
\(322\) 0 0
\(323\) 19.2482 1.07100
\(324\) 0.703405 0.0390780
\(325\) −33.2381 −1.84372
\(326\) −34.5791 −1.91516
\(327\) 6.23589 0.344845
\(328\) −2.13187 −0.117713
\(329\) 0 0
\(330\) −18.1204 −0.997498
\(331\) −13.1862 −0.724778 −0.362389 0.932027i \(-0.618039\pi\)
−0.362389 + 0.932027i \(0.618039\pi\)
\(332\) −4.17073 −0.228898
\(333\) 11.7958 0.646408
\(334\) 5.60195 0.306525
\(335\) 43.1756 2.35894
\(336\) 0 0
\(337\) 1.19410 0.0650470 0.0325235 0.999471i \(-0.489646\pi\)
0.0325235 + 0.999471i \(0.489646\pi\)
\(338\) 33.1491 1.80307
\(339\) 3.17038 0.172192
\(340\) 14.1505 0.767419
\(341\) −15.1190 −0.818742
\(342\) −5.16329 −0.279199
\(343\) 0 0
\(344\) −16.3721 −0.882723
\(345\) −30.1227 −1.62175
\(346\) −7.37395 −0.396426
\(347\) −1.39245 −0.0747507 −0.0373753 0.999301i \(-0.511900\pi\)
−0.0373753 + 0.999301i \(0.511900\pi\)
\(348\) −0.693592 −0.0371804
\(349\) −1.98813 −0.106422 −0.0532112 0.998583i \(-0.516946\pi\)
−0.0532112 + 0.998583i \(0.516946\pi\)
\(350\) 0 0
\(351\) 5.75857 0.307370
\(352\) 12.8024 0.682373
\(353\) −19.9677 −1.06277 −0.531387 0.847129i \(-0.678329\pi\)
−0.531387 + 0.847129i \(0.678329\pi\)
\(354\) 18.4554 0.980894
\(355\) 19.4402 1.03178
\(356\) −8.01337 −0.424708
\(357\) 0 0
\(358\) 22.9467 1.21277
\(359\) 18.9529 1.00029 0.500147 0.865940i \(-0.333279\pi\)
0.500147 + 0.865940i \(0.333279\pi\)
\(360\) 6.99692 0.368770
\(361\) −9.13853 −0.480975
\(362\) 15.1464 0.796076
\(363\) −0.275433 −0.0144565
\(364\) 0 0
\(365\) −31.7200 −1.66030
\(366\) 2.96398 0.154930
\(367\) 3.57715 0.186726 0.0933630 0.995632i \(-0.470238\pi\)
0.0933630 + 0.995632i \(0.470238\pi\)
\(368\) 45.0826 2.35009
\(369\) 1.00000 0.0520579
\(370\) −63.6548 −3.30925
\(371\) 0 0
\(372\) −3.16711 −0.164207
\(373\) 22.8399 1.18261 0.591303 0.806450i \(-0.298614\pi\)
0.591303 + 0.806450i \(0.298614\pi\)
\(374\) 33.8409 1.74987
\(375\) 2.53353 0.130831
\(376\) 25.6152 1.32100
\(377\) −5.67824 −0.292444
\(378\) 0 0
\(379\) −24.3056 −1.24849 −0.624247 0.781227i \(-0.714594\pi\)
−0.624247 + 0.781227i \(0.714594\pi\)
\(380\) 7.24975 0.371904
\(381\) −8.07325 −0.413605
\(382\) −31.1515 −1.59385
\(383\) 14.8477 0.758682 0.379341 0.925257i \(-0.376151\pi\)
0.379341 + 0.925257i \(0.376151\pi\)
\(384\) −13.4709 −0.687435
\(385\) 0 0
\(386\) −25.5127 −1.29856
\(387\) 7.67969 0.390380
\(388\) 8.28779 0.420749
\(389\) −30.2374 −1.53310 −0.766548 0.642188i \(-0.778027\pi\)
−0.766548 + 0.642188i \(0.778027\pi\)
\(390\) −31.0754 −1.57357
\(391\) 56.2558 2.84498
\(392\) 0 0
\(393\) −9.14130 −0.461118
\(394\) 5.06298 0.255069
\(395\) 27.7316 1.39533
\(396\) −2.36196 −0.118693
\(397\) 16.8983 0.848101 0.424051 0.905639i \(-0.360608\pi\)
0.424051 + 0.905639i \(0.360608\pi\)
\(398\) −9.57313 −0.479858
\(399\) 0 0
\(400\) −28.3519 −1.41760
\(401\) −27.9165 −1.39408 −0.697042 0.717030i \(-0.745501\pi\)
−0.697042 + 0.717030i \(0.745501\pi\)
\(402\) 21.6295 1.07878
\(403\) −25.9282 −1.29158
\(404\) 3.07802 0.153137
\(405\) −3.28206 −0.163087
\(406\) 0 0
\(407\) −39.6091 −1.96335
\(408\) −13.0671 −0.646919
\(409\) −29.3409 −1.45081 −0.725407 0.688320i \(-0.758349\pi\)
−0.725407 + 0.688320i \(0.758349\pi\)
\(410\) −5.39638 −0.266508
\(411\) 6.53936 0.322563
\(412\) −5.33069 −0.262624
\(413\) 0 0
\(414\) −15.0905 −0.741656
\(415\) 19.4605 0.955277
\(416\) 21.9554 1.07645
\(417\) 8.98420 0.439958
\(418\) 17.3378 0.848018
\(419\) 9.50190 0.464198 0.232099 0.972692i \(-0.425441\pi\)
0.232099 + 0.972692i \(0.425441\pi\)
\(420\) 0 0
\(421\) −6.34695 −0.309331 −0.154666 0.987967i \(-0.549430\pi\)
−0.154666 + 0.987967i \(0.549430\pi\)
\(422\) −31.4100 −1.52902
\(423\) −12.0154 −0.584207
\(424\) 5.57093 0.270548
\(425\) −35.3787 −1.71612
\(426\) 9.73890 0.471851
\(427\) 0 0
\(428\) 14.2812 0.690307
\(429\) −19.3367 −0.933583
\(430\) −41.4425 −1.99853
\(431\) 5.67814 0.273507 0.136753 0.990605i \(-0.456333\pi\)
0.136753 + 0.990605i \(0.456333\pi\)
\(432\) 4.91203 0.236330
\(433\) 22.8926 1.10015 0.550075 0.835116i \(-0.314599\pi\)
0.550075 + 0.835116i \(0.314599\pi\)
\(434\) 0 0
\(435\) 3.23628 0.155168
\(436\) −4.38635 −0.210068
\(437\) 28.8216 1.37872
\(438\) −15.8907 −0.759285
\(439\) −13.8291 −0.660027 −0.330014 0.943976i \(-0.607053\pi\)
−0.330014 + 0.943976i \(0.607053\pi\)
\(440\) −23.4949 −1.12007
\(441\) 0 0
\(442\) 58.0351 2.76045
\(443\) −20.1776 −0.958669 −0.479334 0.877632i \(-0.659122\pi\)
−0.479334 + 0.877632i \(0.659122\pi\)
\(444\) −8.29724 −0.393770
\(445\) 37.3901 1.77246
\(446\) 44.9352 2.12775
\(447\) −0.272952 −0.0129102
\(448\) 0 0
\(449\) 2.97663 0.140476 0.0702379 0.997530i \(-0.477624\pi\)
0.0702379 + 0.997530i \(0.477624\pi\)
\(450\) 9.49023 0.447374
\(451\) −3.35789 −0.158117
\(452\) −2.23006 −0.104893
\(453\) 6.62811 0.311416
\(454\) −10.3108 −0.483912
\(455\) 0 0
\(456\) −6.69470 −0.313508
\(457\) 1.48861 0.0696341 0.0348171 0.999394i \(-0.488915\pi\)
0.0348171 + 0.999394i \(0.488915\pi\)
\(458\) 12.4551 0.581988
\(459\) 6.12943 0.286097
\(460\) 21.1885 0.987917
\(461\) −26.5341 −1.23581 −0.617907 0.786251i \(-0.712019\pi\)
−0.617907 + 0.786251i \(0.712019\pi\)
\(462\) 0 0
\(463\) 14.3359 0.666245 0.333123 0.942883i \(-0.391898\pi\)
0.333123 + 0.942883i \(0.391898\pi\)
\(464\) −4.84351 −0.224854
\(465\) 14.7776 0.685296
\(466\) −1.81846 −0.0842385
\(467\) 26.7495 1.23782 0.618909 0.785462i \(-0.287575\pi\)
0.618909 + 0.785462i \(0.287575\pi\)
\(468\) −4.05061 −0.187239
\(469\) 0 0
\(470\) 64.8395 2.99082
\(471\) 23.3131 1.07421
\(472\) 23.9292 1.10143
\(473\) −25.7876 −1.18571
\(474\) 13.8926 0.638108
\(475\) −18.1256 −0.831659
\(476\) 0 0
\(477\) −2.61317 −0.119649
\(478\) 29.9097 1.36804
\(479\) 16.7956 0.767410 0.383705 0.923456i \(-0.374648\pi\)
0.383705 + 0.923456i \(0.374648\pi\)
\(480\) −12.5133 −0.571153
\(481\) −67.9272 −3.09721
\(482\) −34.0207 −1.54960
\(483\) 0 0
\(484\) 0.193741 0.00880639
\(485\) −38.6705 −1.75594
\(486\) −1.64420 −0.0745826
\(487\) −11.1089 −0.503392 −0.251696 0.967806i \(-0.580988\pi\)
−0.251696 + 0.967806i \(0.580988\pi\)
\(488\) 3.84309 0.173968
\(489\) 21.0309 0.951050
\(490\) 0 0
\(491\) −34.5338 −1.55849 −0.779244 0.626720i \(-0.784397\pi\)
−0.779244 + 0.626720i \(0.784397\pi\)
\(492\) −0.703405 −0.0317119
\(493\) −6.04392 −0.272205
\(494\) 29.7332 1.33776
\(495\) 11.0208 0.495348
\(496\) −22.1166 −0.993066
\(497\) 0 0
\(498\) 9.74905 0.436865
\(499\) −1.84774 −0.0827161 −0.0413580 0.999144i \(-0.513168\pi\)
−0.0413580 + 0.999144i \(0.513168\pi\)
\(500\) −1.78210 −0.0796979
\(501\) −3.40709 −0.152218
\(502\) 4.11037 0.183455
\(503\) 7.20636 0.321316 0.160658 0.987010i \(-0.448638\pi\)
0.160658 + 0.987010i \(0.448638\pi\)
\(504\) 0 0
\(505\) −14.3619 −0.639098
\(506\) 50.6722 2.25265
\(507\) −20.1612 −0.895389
\(508\) 5.67876 0.251954
\(509\) −9.61401 −0.426134 −0.213067 0.977038i \(-0.568345\pi\)
−0.213067 + 0.977038i \(0.568345\pi\)
\(510\) −33.0767 −1.46466
\(511\) 0 0
\(512\) −2.21575 −0.0979233
\(513\) 3.14030 0.138648
\(514\) −20.7350 −0.914581
\(515\) 24.8728 1.09603
\(516\) −5.40193 −0.237807
\(517\) 40.3463 1.77443
\(518\) 0 0
\(519\) 4.48482 0.196862
\(520\) −40.2923 −1.76693
\(521\) 16.5470 0.724936 0.362468 0.931996i \(-0.381934\pi\)
0.362468 + 0.931996i \(0.381934\pi\)
\(522\) 1.62127 0.0709609
\(523\) −26.9120 −1.17678 −0.588390 0.808577i \(-0.700238\pi\)
−0.588390 + 0.808577i \(0.700238\pi\)
\(524\) 6.43003 0.280897
\(525\) 0 0
\(526\) −34.9972 −1.52595
\(527\) −27.5980 −1.20219
\(528\) −16.4941 −0.717812
\(529\) 61.2354 2.66241
\(530\) 14.1017 0.612537
\(531\) −11.2245 −0.487103
\(532\) 0 0
\(533\) −5.75857 −0.249432
\(534\) 18.7312 0.810578
\(535\) −66.6355 −2.88090
\(536\) 28.0448 1.21135
\(537\) −13.9561 −0.602252
\(538\) 43.6703 1.88276
\(539\) 0 0
\(540\) 2.30862 0.0993471
\(541\) −22.1189 −0.950965 −0.475483 0.879725i \(-0.657727\pi\)
−0.475483 + 0.879725i \(0.657727\pi\)
\(542\) −19.4658 −0.836126
\(543\) −9.21198 −0.395324
\(544\) 23.3693 1.00195
\(545\) 20.4666 0.876692
\(546\) 0 0
\(547\) 9.32996 0.398920 0.199460 0.979906i \(-0.436081\pi\)
0.199460 + 0.979906i \(0.436081\pi\)
\(548\) −4.59982 −0.196495
\(549\) −1.80269 −0.0769368
\(550\) −31.8672 −1.35882
\(551\) −3.09649 −0.131915
\(552\) −19.5662 −0.832795
\(553\) 0 0
\(554\) −31.7631 −1.34948
\(555\) 38.7147 1.64335
\(556\) −6.31953 −0.268008
\(557\) 35.5298 1.50545 0.752723 0.658338i \(-0.228740\pi\)
0.752723 + 0.658338i \(0.228740\pi\)
\(558\) 7.40309 0.313398
\(559\) −44.2241 −1.87048
\(560\) 0 0
\(561\) −20.5820 −0.868971
\(562\) −28.3141 −1.19436
\(563\) 11.6691 0.491795 0.245897 0.969296i \(-0.420917\pi\)
0.245897 + 0.969296i \(0.420917\pi\)
\(564\) 8.45167 0.355879
\(565\) 10.4054 0.437758
\(566\) 35.7450 1.50248
\(567\) 0 0
\(568\) 12.6274 0.529834
\(569\) 10.1162 0.424095 0.212047 0.977259i \(-0.431987\pi\)
0.212047 + 0.977259i \(0.431987\pi\)
\(570\) −16.9462 −0.709800
\(571\) −7.08972 −0.296696 −0.148348 0.988935i \(-0.547395\pi\)
−0.148348 + 0.988935i \(0.547395\pi\)
\(572\) 13.6015 0.568707
\(573\) 18.9462 0.791491
\(574\) 0 0
\(575\) −52.9747 −2.20920
\(576\) 3.55530 0.148137
\(577\) 16.7129 0.695767 0.347884 0.937538i \(-0.386900\pi\)
0.347884 + 0.937538i \(0.386900\pi\)
\(578\) 33.8211 1.40677
\(579\) 15.5168 0.644855
\(580\) −2.27641 −0.0945229
\(581\) 0 0
\(582\) −19.3726 −0.803022
\(583\) 8.77475 0.363413
\(584\) −20.6038 −0.852590
\(585\) 18.9000 0.781419
\(586\) 5.70332 0.235602
\(587\) −18.0499 −0.745000 −0.372500 0.928032i \(-0.621499\pi\)
−0.372500 + 0.928032i \(0.621499\pi\)
\(588\) 0 0
\(589\) −14.1393 −0.582601
\(590\) 60.5718 2.49370
\(591\) −3.07929 −0.126665
\(592\) −57.9415 −2.38138
\(593\) 2.63006 0.108004 0.0540018 0.998541i \(-0.482802\pi\)
0.0540018 + 0.998541i \(0.482802\pi\)
\(594\) 5.52106 0.226532
\(595\) 0 0
\(596\) 0.191996 0.00786444
\(597\) 5.82235 0.238293
\(598\) 86.8996 3.55359
\(599\) −41.3763 −1.69059 −0.845296 0.534299i \(-0.820576\pi\)
−0.845296 + 0.534299i \(0.820576\pi\)
\(600\) 12.3050 0.502349
\(601\) 7.93199 0.323552 0.161776 0.986827i \(-0.448278\pi\)
0.161776 + 0.986827i \(0.448278\pi\)
\(602\) 0 0
\(603\) −13.1550 −0.535714
\(604\) −4.66224 −0.189704
\(605\) −0.903987 −0.0367523
\(606\) −7.19485 −0.292271
\(607\) −25.0957 −1.01860 −0.509302 0.860588i \(-0.670096\pi\)
−0.509302 + 0.860588i \(0.670096\pi\)
\(608\) 11.9728 0.485563
\(609\) 0 0
\(610\) 9.72798 0.393874
\(611\) 69.1914 2.79918
\(612\) −4.31147 −0.174281
\(613\) 39.5202 1.59621 0.798103 0.602521i \(-0.205837\pi\)
0.798103 + 0.602521i \(0.205837\pi\)
\(614\) 44.1787 1.78291
\(615\) 3.28206 0.132346
\(616\) 0 0
\(617\) −16.0390 −0.645705 −0.322853 0.946449i \(-0.604642\pi\)
−0.322853 + 0.946449i \(0.604642\pi\)
\(618\) 12.4604 0.501233
\(619\) 4.05138 0.162839 0.0814194 0.996680i \(-0.474055\pi\)
0.0814194 + 0.996680i \(0.474055\pi\)
\(620\) −10.3946 −0.417459
\(621\) 9.17799 0.368300
\(622\) −46.1072 −1.84873
\(623\) 0 0
\(624\) −28.2863 −1.13236
\(625\) −20.5445 −0.821778
\(626\) −23.2815 −0.930515
\(627\) −10.5448 −0.421118
\(628\) −16.3985 −0.654372
\(629\) −72.3017 −2.88286
\(630\) 0 0
\(631\) −35.7081 −1.42152 −0.710759 0.703436i \(-0.751648\pi\)
−0.710759 + 0.703436i \(0.751648\pi\)
\(632\) 18.0131 0.716522
\(633\) 19.1035 0.759295
\(634\) 51.6956 2.05310
\(635\) −26.4969 −1.05150
\(636\) 1.83812 0.0728861
\(637\) 0 0
\(638\) −5.44404 −0.215531
\(639\) −5.92317 −0.234317
\(640\) −44.2124 −1.74765
\(641\) 16.1373 0.637383 0.318692 0.947858i \(-0.396757\pi\)
0.318692 + 0.947858i \(0.396757\pi\)
\(642\) −33.3822 −1.31749
\(643\) 17.6523 0.696137 0.348068 0.937469i \(-0.386838\pi\)
0.348068 + 0.937469i \(0.386838\pi\)
\(644\) 0 0
\(645\) 25.2052 0.992454
\(646\) 31.6480 1.24517
\(647\) 0.0105799 0.000415939 0 0.000207970 1.00000i \(-0.499934\pi\)
0.000207970 1.00000i \(0.499934\pi\)
\(648\) −2.13187 −0.0837476
\(649\) 37.6907 1.47949
\(650\) −54.6502 −2.14356
\(651\) 0 0
\(652\) −14.7932 −0.579348
\(653\) −35.3931 −1.38504 −0.692519 0.721399i \(-0.743499\pi\)
−0.692519 + 0.721399i \(0.743499\pi\)
\(654\) 10.2531 0.400927
\(655\) −30.0023 −1.17229
\(656\) −4.91203 −0.191783
\(657\) 9.66466 0.377054
\(658\) 0 0
\(659\) 2.98465 0.116266 0.0581328 0.998309i \(-0.481485\pi\)
0.0581328 + 0.998309i \(0.481485\pi\)
\(660\) −7.75209 −0.301750
\(661\) −46.2120 −1.79744 −0.898718 0.438526i \(-0.855501\pi\)
−0.898718 + 0.438526i \(0.855501\pi\)
\(662\) −21.6807 −0.842646
\(663\) −35.2968 −1.37081
\(664\) 12.6406 0.490549
\(665\) 0 0
\(666\) 19.3947 0.751531
\(667\) −9.04995 −0.350416
\(668\) 2.39656 0.0927258
\(669\) −27.3295 −1.05662
\(670\) 70.9895 2.74256
\(671\) 6.05322 0.233682
\(672\) 0 0
\(673\) −14.0235 −0.540565 −0.270282 0.962781i \(-0.587117\pi\)
−0.270282 + 0.962781i \(0.587117\pi\)
\(674\) 1.96335 0.0756254
\(675\) −5.77193 −0.222162
\(676\) 14.1815 0.545441
\(677\) 2.26496 0.0870497 0.0435248 0.999052i \(-0.486141\pi\)
0.0435248 + 0.999052i \(0.486141\pi\)
\(678\) 5.21275 0.200195
\(679\) 0 0
\(680\) −42.8871 −1.64465
\(681\) 6.27102 0.240306
\(682\) −24.8588 −0.951892
\(683\) −3.25047 −0.124376 −0.0621879 0.998064i \(-0.519808\pi\)
−0.0621879 + 0.998064i \(0.519808\pi\)
\(684\) −2.20890 −0.0844594
\(685\) 21.4626 0.820044
\(686\) 0 0
\(687\) −7.57515 −0.289010
\(688\) −37.7229 −1.43817
\(689\) 15.0481 0.573289
\(690\) −49.5279 −1.88549
\(691\) 5.13808 0.195462 0.0977309 0.995213i \(-0.468842\pi\)
0.0977309 + 0.995213i \(0.468842\pi\)
\(692\) −3.15464 −0.119921
\(693\) 0 0
\(694\) −2.28947 −0.0869072
\(695\) 29.4867 1.11849
\(696\) 2.10213 0.0796809
\(697\) −6.12943 −0.232169
\(698\) −3.26890 −0.123730
\(699\) 1.10598 0.0418321
\(700\) 0 0
\(701\) 33.0426 1.24800 0.624001 0.781424i \(-0.285506\pi\)
0.624001 + 0.781424i \(0.285506\pi\)
\(702\) 9.46827 0.357357
\(703\) −37.0424 −1.39708
\(704\) −11.9383 −0.449942
\(705\) −39.4352 −1.48522
\(706\) −32.8310 −1.23561
\(707\) 0 0
\(708\) 7.89538 0.296727
\(709\) −40.5637 −1.52340 −0.761701 0.647928i \(-0.775636\pi\)
−0.761701 + 0.647928i \(0.775636\pi\)
\(710\) 31.9637 1.19957
\(711\) −8.44944 −0.316879
\(712\) 24.2868 0.910185
\(713\) −41.3243 −1.54761
\(714\) 0 0
\(715\) −63.4641 −2.37342
\(716\) 9.81682 0.366872
\(717\) −18.1910 −0.679355
\(718\) 31.1624 1.16297
\(719\) −18.0190 −0.671994 −0.335997 0.941863i \(-0.609073\pi\)
−0.335997 + 0.941863i \(0.609073\pi\)
\(720\) 16.1216 0.600816
\(721\) 0 0
\(722\) −15.0256 −0.559195
\(723\) 20.6913 0.769517
\(724\) 6.47975 0.240818
\(725\) 5.69141 0.211374
\(726\) −0.452867 −0.0168075
\(727\) −10.1884 −0.377868 −0.188934 0.981990i \(-0.560503\pi\)
−0.188934 + 0.981990i \(0.560503\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −52.1542 −1.93031
\(731\) −47.0721 −1.74102
\(732\) 1.26802 0.0468673
\(733\) 42.6537 1.57545 0.787726 0.616026i \(-0.211258\pi\)
0.787726 + 0.616026i \(0.211258\pi\)
\(734\) 5.88157 0.217093
\(735\) 0 0
\(736\) 34.9924 1.28984
\(737\) 44.1731 1.62714
\(738\) 1.64420 0.0605240
\(739\) 16.1174 0.592887 0.296444 0.955050i \(-0.404199\pi\)
0.296444 + 0.955050i \(0.404199\pi\)
\(740\) −27.2321 −1.00107
\(741\) −18.0836 −0.664319
\(742\) 0 0
\(743\) −27.9584 −1.02569 −0.512846 0.858480i \(-0.671409\pi\)
−0.512846 + 0.858480i \(0.671409\pi\)
\(744\) 9.59882 0.351910
\(745\) −0.895844 −0.0328212
\(746\) 37.5534 1.37493
\(747\) −5.92934 −0.216943
\(748\) 14.4774 0.529348
\(749\) 0 0
\(750\) 4.16564 0.152108
\(751\) 17.5578 0.640695 0.320347 0.947300i \(-0.396200\pi\)
0.320347 + 0.947300i \(0.396200\pi\)
\(752\) 59.0199 2.15223
\(753\) −2.49992 −0.0911020
\(754\) −9.33618 −0.340004
\(755\) 21.7539 0.791704
\(756\) 0 0
\(757\) −5.87592 −0.213564 −0.106782 0.994282i \(-0.534055\pi\)
−0.106782 + 0.994282i \(0.534055\pi\)
\(758\) −39.9633 −1.45153
\(759\) −30.8187 −1.11865
\(760\) −21.9724 −0.797023
\(761\) −26.4642 −0.959326 −0.479663 0.877453i \(-0.659241\pi\)
−0.479663 + 0.877453i \(0.659241\pi\)
\(762\) −13.2741 −0.480869
\(763\) 0 0
\(764\) −13.3269 −0.482150
\(765\) 20.1172 0.727338
\(766\) 24.4126 0.882065
\(767\) 64.6373 2.33392
\(768\) −15.0383 −0.542649
\(769\) −30.5496 −1.10165 −0.550823 0.834622i \(-0.685686\pi\)
−0.550823 + 0.834622i \(0.685686\pi\)
\(770\) 0 0
\(771\) 12.6110 0.454173
\(772\) −10.9146 −0.392824
\(773\) 33.4890 1.20452 0.602258 0.798302i \(-0.294268\pi\)
0.602258 + 0.798302i \(0.294268\pi\)
\(774\) 12.6270 0.453867
\(775\) 25.9884 0.933530
\(776\) −25.1185 −0.901701
\(777\) 0 0
\(778\) −49.7164 −1.78242
\(779\) −3.14030 −0.112513
\(780\) −13.2943 −0.476014
\(781\) 19.8894 0.711697
\(782\) 92.4960 3.30765
\(783\) −0.986050 −0.0352386
\(784\) 0 0
\(785\) 76.5149 2.73093
\(786\) −15.0302 −0.536108
\(787\) −6.84173 −0.243881 −0.121941 0.992537i \(-0.538912\pi\)
−0.121941 + 0.992537i \(0.538912\pi\)
\(788\) 2.16599 0.0771601
\(789\) 21.2852 0.757772
\(790\) 45.5964 1.62225
\(791\) 0 0
\(792\) 7.15857 0.254369
\(793\) 10.3809 0.368637
\(794\) 27.7842 0.986026
\(795\) −8.57659 −0.304180
\(796\) −4.09547 −0.145160
\(797\) 9.72791 0.344580 0.172290 0.985046i \(-0.444883\pi\)
0.172290 + 0.985046i \(0.444883\pi\)
\(798\) 0 0
\(799\) 73.6474 2.60546
\(800\) −22.0063 −0.778041
\(801\) −11.3923 −0.402526
\(802\) −45.9004 −1.62080
\(803\) −32.4529 −1.14524
\(804\) 9.25331 0.326339
\(805\) 0 0
\(806\) −42.6313 −1.50162
\(807\) −26.5602 −0.934963
\(808\) −9.32880 −0.328186
\(809\) 23.9599 0.842386 0.421193 0.906971i \(-0.361611\pi\)
0.421193 + 0.906971i \(0.361611\pi\)
\(810\) −5.39638 −0.189609
\(811\) −30.6208 −1.07524 −0.537622 0.843186i \(-0.680677\pi\)
−0.537622 + 0.843186i \(0.680677\pi\)
\(812\) 0 0
\(813\) 11.8390 0.415213
\(814\) −65.1254 −2.28265
\(815\) 69.0247 2.41783
\(816\) −30.1080 −1.05399
\(817\) −24.1165 −0.843730
\(818\) −48.2424 −1.68676
\(819\) 0 0
\(820\) −2.30862 −0.0806204
\(821\) 19.7037 0.687662 0.343831 0.939031i \(-0.388275\pi\)
0.343831 + 0.939031i \(0.388275\pi\)
\(822\) 10.7520 0.375021
\(823\) −26.6490 −0.928926 −0.464463 0.885593i \(-0.653753\pi\)
−0.464463 + 0.885593i \(0.653753\pi\)
\(824\) 16.1562 0.562826
\(825\) 19.3815 0.674778
\(826\) 0 0
\(827\) 2.60475 0.0905761 0.0452881 0.998974i \(-0.485579\pi\)
0.0452881 + 0.998974i \(0.485579\pi\)
\(828\) −6.45584 −0.224356
\(829\) −7.20154 −0.250120 −0.125060 0.992149i \(-0.539912\pi\)
−0.125060 + 0.992149i \(0.539912\pi\)
\(830\) 31.9970 1.11063
\(831\) 19.3182 0.670142
\(832\) −20.4734 −0.709789
\(833\) 0 0
\(834\) 14.7718 0.511507
\(835\) −11.1823 −0.386979
\(836\) 7.41725 0.256531
\(837\) −4.50254 −0.155631
\(838\) 15.6231 0.539689
\(839\) 3.36252 0.116087 0.0580436 0.998314i \(-0.481514\pi\)
0.0580436 + 0.998314i \(0.481514\pi\)
\(840\) 0 0
\(841\) −28.0277 −0.966473
\(842\) −10.4357 −0.359637
\(843\) 17.2205 0.593107
\(844\) −13.4375 −0.462537
\(845\) −66.1702 −2.27633
\(846\) −19.7557 −0.679215
\(847\) 0 0
\(848\) 12.8360 0.440789
\(849\) −21.7400 −0.746116
\(850\) −58.1697 −1.99520
\(851\) −108.262 −3.71117
\(852\) 4.16639 0.142738
\(853\) −4.03938 −0.138306 −0.0691529 0.997606i \(-0.522030\pi\)
−0.0691529 + 0.997606i \(0.522030\pi\)
\(854\) 0 0
\(855\) 10.3067 0.352480
\(856\) −43.2832 −1.47939
\(857\) −21.4868 −0.733975 −0.366987 0.930226i \(-0.619611\pi\)
−0.366987 + 0.930226i \(0.619611\pi\)
\(858\) −31.7934 −1.08541
\(859\) 24.7283 0.843717 0.421859 0.906662i \(-0.361378\pi\)
0.421859 + 0.906662i \(0.361378\pi\)
\(860\) −17.7295 −0.604570
\(861\) 0 0
\(862\) 9.33602 0.317986
\(863\) −0.835485 −0.0284402 −0.0142201 0.999899i \(-0.504527\pi\)
−0.0142201 + 0.999899i \(0.504527\pi\)
\(864\) 3.81265 0.129709
\(865\) 14.7194 0.500476
\(866\) 37.6401 1.27906
\(867\) −20.5699 −0.698591
\(868\) 0 0
\(869\) 28.3723 0.962465
\(870\) 5.32110 0.180402
\(871\) 75.7542 2.56683
\(872\) 13.2941 0.450194
\(873\) 11.7824 0.398774
\(874\) 47.3886 1.60294
\(875\) 0 0
\(876\) −6.79817 −0.229689
\(877\) −43.9609 −1.48445 −0.742227 0.670148i \(-0.766230\pi\)
−0.742227 + 0.670148i \(0.766230\pi\)
\(878\) −22.7379 −0.767366
\(879\) −3.46874 −0.116998
\(880\) −54.1346 −1.82488
\(881\) −49.2250 −1.65843 −0.829217 0.558927i \(-0.811213\pi\)
−0.829217 + 0.558927i \(0.811213\pi\)
\(882\) 0 0
\(883\) −28.1493 −0.947300 −0.473650 0.880713i \(-0.657064\pi\)
−0.473650 + 0.880713i \(0.657064\pi\)
\(884\) 24.8279 0.835053
\(885\) −36.8396 −1.23835
\(886\) −33.1761 −1.11457
\(887\) −39.1184 −1.31347 −0.656733 0.754123i \(-0.728062\pi\)
−0.656733 + 0.754123i \(0.728062\pi\)
\(888\) 25.1471 0.843883
\(889\) 0 0
\(890\) 61.4769 2.06071
\(891\) −3.35789 −0.112494
\(892\) 19.2237 0.643657
\(893\) 37.7318 1.26265
\(894\) −0.448788 −0.0150097
\(895\) −45.8049 −1.53109
\(896\) 0 0
\(897\) −52.8521 −1.76468
\(898\) 4.89418 0.163321
\(899\) 4.43973 0.148073
\(900\) 4.06001 0.135334
\(901\) 16.0173 0.533612
\(902\) −5.52106 −0.183831
\(903\) 0 0
\(904\) 6.75883 0.224795
\(905\) −30.2343 −1.00502
\(906\) 10.8980 0.362061
\(907\) −35.8670 −1.19094 −0.595472 0.803376i \(-0.703035\pi\)
−0.595472 + 0.803376i \(0.703035\pi\)
\(908\) −4.41107 −0.146386
\(909\) 4.37589 0.145139
\(910\) 0 0
\(911\) −17.2869 −0.572741 −0.286371 0.958119i \(-0.592449\pi\)
−0.286371 + 0.958119i \(0.592449\pi\)
\(912\) −15.4252 −0.510781
\(913\) 19.9101 0.658928
\(914\) 2.44757 0.0809585
\(915\) −5.91653 −0.195594
\(916\) 5.32840 0.176055
\(917\) 0 0
\(918\) 10.0780 0.332625
\(919\) −22.0788 −0.728312 −0.364156 0.931338i \(-0.618643\pi\)
−0.364156 + 0.931338i \(0.618643\pi\)
\(920\) −64.2176 −2.11719
\(921\) −26.8694 −0.885376
\(922\) −43.6274 −1.43679
\(923\) 34.1090 1.12271
\(924\) 0 0
\(925\) 68.0847 2.23861
\(926\) 23.5711 0.774595
\(927\) −7.57841 −0.248908
\(928\) −3.75946 −0.123410
\(929\) −33.4705 −1.09813 −0.549066 0.835779i \(-0.685016\pi\)
−0.549066 + 0.835779i \(0.685016\pi\)
\(930\) 24.2974 0.796744
\(931\) 0 0
\(932\) −0.777953 −0.0254827
\(933\) 28.0423 0.918063
\(934\) 43.9816 1.43912
\(935\) −67.5513 −2.20916
\(936\) 12.2765 0.401270
\(937\) 34.1088 1.11429 0.557143 0.830416i \(-0.311897\pi\)
0.557143 + 0.830416i \(0.311897\pi\)
\(938\) 0 0
\(939\) 14.1597 0.462086
\(940\) 27.7389 0.904743
\(941\) 2.69587 0.0878829 0.0439415 0.999034i \(-0.486008\pi\)
0.0439415 + 0.999034i \(0.486008\pi\)
\(942\) 38.3314 1.24890
\(943\) −9.17799 −0.298876
\(944\) 55.1352 1.79450
\(945\) 0 0
\(946\) −42.4000 −1.37854
\(947\) 24.9949 0.812226 0.406113 0.913823i \(-0.366884\pi\)
0.406113 + 0.913823i \(0.366884\pi\)
\(948\) 5.94338 0.193032
\(949\) −55.6547 −1.80663
\(950\) −29.8022 −0.966910
\(951\) −31.4411 −1.01955
\(952\) 0 0
\(953\) −29.7561 −0.963895 −0.481948 0.876200i \(-0.660070\pi\)
−0.481948 + 0.876200i \(0.660070\pi\)
\(954\) −4.29659 −0.139107
\(955\) 62.1828 2.01219
\(956\) 12.7956 0.413840
\(957\) 3.31105 0.107031
\(958\) 27.6154 0.892212
\(959\) 0 0
\(960\) 11.6687 0.376606
\(961\) −10.7271 −0.346036
\(962\) −111.686 −3.60090
\(963\) 20.3029 0.654253
\(964\) −14.5544 −0.468764
\(965\) 50.9270 1.63940
\(966\) 0 0
\(967\) 40.3371 1.29715 0.648577 0.761149i \(-0.275364\pi\)
0.648577 + 0.761149i \(0.275364\pi\)
\(968\) −0.587185 −0.0188729
\(969\) −19.2482 −0.618342
\(970\) −63.5822 −2.04150
\(971\) −57.5004 −1.84527 −0.922637 0.385669i \(-0.873971\pi\)
−0.922637 + 0.385669i \(0.873971\pi\)
\(972\) −0.703405 −0.0225617
\(973\) 0 0
\(974\) −18.2653 −0.585258
\(975\) 33.2381 1.06447
\(976\) 8.85485 0.283437
\(977\) 40.1369 1.28409 0.642047 0.766665i \(-0.278085\pi\)
0.642047 + 0.766665i \(0.278085\pi\)
\(978\) 34.5791 1.10572
\(979\) 38.2540 1.22260
\(980\) 0 0
\(981\) −6.23589 −0.199097
\(982\) −56.7806 −1.81194
\(983\) 7.02052 0.223920 0.111960 0.993713i \(-0.464287\pi\)
0.111960 + 0.993713i \(0.464287\pi\)
\(984\) 2.13187 0.0679614
\(985\) −10.1064 −0.322017
\(986\) −9.93744 −0.316473
\(987\) 0 0
\(988\) 12.7201 0.404681
\(989\) −70.4841 −2.24126
\(990\) 18.1204 0.575906
\(991\) −1.28810 −0.0409177 −0.0204589 0.999791i \(-0.506513\pi\)
−0.0204589 + 0.999791i \(0.506513\pi\)
\(992\) −17.1666 −0.545040
\(993\) 13.1862 0.418450
\(994\) 0 0
\(995\) 19.1093 0.605806
\(996\) 4.17073 0.132155
\(997\) 24.1834 0.765895 0.382948 0.923770i \(-0.374909\pi\)
0.382948 + 0.923770i \(0.374909\pi\)
\(998\) −3.03805 −0.0961679
\(999\) −11.7958 −0.373204
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 \(a_p\))