Properties

Label 6008.2.a.e.1.37
Level 6008
Weight 2
Character 6008.1
Self dual Yes
Analytic conductor 47.974
Analytic rank 0
Dimension 50
CM No

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Newspace parameters

Level: \( N \) = \( 6008 = 2^{3} \cdot 751 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6008.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9741215344\)
Analytic rank: \(0\)
Dimension: \(50\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.37
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.91672 q^{3} +3.07306 q^{5} -0.591659 q^{7} +0.673807 q^{9} +O(q^{10})\) \(q+1.91672 q^{3} +3.07306 q^{5} -0.591659 q^{7} +0.673807 q^{9} +1.99043 q^{11} +3.60968 q^{13} +5.89019 q^{15} +2.69279 q^{17} -1.18936 q^{19} -1.13404 q^{21} -8.54373 q^{23} +4.44370 q^{25} -4.45866 q^{27} +6.20864 q^{29} -7.60191 q^{31} +3.81510 q^{33} -1.81820 q^{35} +10.3205 q^{37} +6.91875 q^{39} +8.86075 q^{41} +6.29558 q^{43} +2.07065 q^{45} +1.22888 q^{47} -6.64994 q^{49} +5.16132 q^{51} +8.63575 q^{53} +6.11672 q^{55} -2.27968 q^{57} +3.53960 q^{59} -7.16899 q^{61} -0.398664 q^{63} +11.0928 q^{65} -0.813857 q^{67} -16.3759 q^{69} +12.1257 q^{71} +10.8866 q^{73} +8.51731 q^{75} -1.17766 q^{77} +13.0985 q^{79} -10.5674 q^{81} +0.290882 q^{83} +8.27510 q^{85} +11.9002 q^{87} -9.51040 q^{89} -2.13570 q^{91} -14.5707 q^{93} -3.65499 q^{95} +8.90446 q^{97} +1.34117 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} + O(q^{10}) \) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} - 5q^{11} + 36q^{13} + 5q^{15} + 14q^{17} + 9q^{19} + 30q^{21} + 3q^{23} + 71q^{25} + 24q^{27} + 61q^{29} + 27q^{31} + 24q^{33} - 7q^{35} + 56q^{37} - 2q^{39} + 10q^{41} + 19q^{43} + 76q^{45} + 3q^{47} + 82q^{49} - q^{51} + 56q^{53} + 7q^{55} + 35q^{57} - q^{59} + 67q^{61} + 25q^{63} + 27q^{65} + 46q^{67} + 68q^{69} + 4q^{71} + 62q^{73} + 27q^{75} + 71q^{77} + 7q^{79} + 74q^{81} - q^{83} + 72q^{85} + 25q^{87} + 19q^{89} + 45q^{91} + 72q^{93} - 24q^{95} + 81q^{97} + 16q^{99} + O(q^{100}) \)

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 0
\(3\) 1.91672 1.10662 0.553309 0.832976i \(-0.313365\pi\)
0.553309 + 0.832976i \(0.313365\pi\)
\(4\) 0 0
\(5\) 3.07306 1.37431 0.687157 0.726509i \(-0.258858\pi\)
0.687157 + 0.726509i \(0.258858\pi\)
\(6\) 0 0
\(7\) −0.591659 −0.223626 −0.111813 0.993729i \(-0.535666\pi\)
−0.111813 + 0.993729i \(0.535666\pi\)
\(8\) 0 0
\(9\) 0.673807 0.224602
\(10\) 0 0
\(11\) 1.99043 0.600138 0.300069 0.953918i \(-0.402990\pi\)
0.300069 + 0.953918i \(0.402990\pi\)
\(12\) 0 0
\(13\) 3.60968 1.00115 0.500573 0.865694i \(-0.333123\pi\)
0.500573 + 0.865694i \(0.333123\pi\)
\(14\) 0 0
\(15\) 5.89019 1.52084
\(16\) 0 0
\(17\) 2.69279 0.653097 0.326549 0.945180i \(-0.394114\pi\)
0.326549 + 0.945180i \(0.394114\pi\)
\(18\) 0 0
\(19\) −1.18936 −0.272859 −0.136430 0.990650i \(-0.543563\pi\)
−0.136430 + 0.990650i \(0.543563\pi\)
\(20\) 0 0
\(21\) −1.13404 −0.247469
\(22\) 0 0
\(23\) −8.54373 −1.78149 −0.890745 0.454503i \(-0.849817\pi\)
−0.890745 + 0.454503i \(0.849817\pi\)
\(24\) 0 0
\(25\) 4.44370 0.888739
\(26\) 0 0
\(27\) −4.45866 −0.858069
\(28\) 0 0
\(29\) 6.20864 1.15292 0.576458 0.817127i \(-0.304435\pi\)
0.576458 + 0.817127i \(0.304435\pi\)
\(30\) 0 0
\(31\) −7.60191 −1.36534 −0.682671 0.730725i \(-0.739182\pi\)
−0.682671 + 0.730725i \(0.739182\pi\)
\(32\) 0 0
\(33\) 3.81510 0.664123
\(34\) 0 0
\(35\) −1.81820 −0.307332
\(36\) 0 0
\(37\) 10.3205 1.69667 0.848337 0.529456i \(-0.177604\pi\)
0.848337 + 0.529456i \(0.177604\pi\)
\(38\) 0 0
\(39\) 6.91875 1.10789
\(40\) 0 0
\(41\) 8.86075 1.38382 0.691908 0.721986i \(-0.256770\pi\)
0.691908 + 0.721986i \(0.256770\pi\)
\(42\) 0 0
\(43\) 6.29558 0.960067 0.480033 0.877250i \(-0.340625\pi\)
0.480033 + 0.877250i \(0.340625\pi\)
\(44\) 0 0
\(45\) 2.07065 0.308674
\(46\) 0 0
\(47\) 1.22888 0.179251 0.0896254 0.995976i \(-0.471433\pi\)
0.0896254 + 0.995976i \(0.471433\pi\)
\(48\) 0 0
\(49\) −6.64994 −0.949991
\(50\) 0 0
\(51\) 5.16132 0.722729
\(52\) 0 0
\(53\) 8.63575 1.18621 0.593106 0.805124i \(-0.297901\pi\)
0.593106 + 0.805124i \(0.297901\pi\)
\(54\) 0 0
\(55\) 6.11672 0.824778
\(56\) 0 0
\(57\) −2.27968 −0.301951
\(58\) 0 0
\(59\) 3.53960 0.460816 0.230408 0.973094i \(-0.425994\pi\)
0.230408 + 0.973094i \(0.425994\pi\)
\(60\) 0 0
\(61\) −7.16899 −0.917895 −0.458947 0.888463i \(-0.651773\pi\)
−0.458947 + 0.888463i \(0.651773\pi\)
\(62\) 0 0
\(63\) −0.398664 −0.0502269
\(64\) 0 0
\(65\) 11.0928 1.37589
\(66\) 0 0
\(67\) −0.813857 −0.0994285 −0.0497142 0.998763i \(-0.515831\pi\)
−0.0497142 + 0.998763i \(0.515831\pi\)
\(68\) 0 0
\(69\) −16.3759 −1.97143
\(70\) 0 0
\(71\) 12.1257 1.43905 0.719526 0.694466i \(-0.244359\pi\)
0.719526 + 0.694466i \(0.244359\pi\)
\(72\) 0 0
\(73\) 10.8866 1.27418 0.637089 0.770790i \(-0.280138\pi\)
0.637089 + 0.770790i \(0.280138\pi\)
\(74\) 0 0
\(75\) 8.51731 0.983494
\(76\) 0 0
\(77\) −1.17766 −0.134206
\(78\) 0 0
\(79\) 13.0985 1.47370 0.736849 0.676057i \(-0.236313\pi\)
0.736849 + 0.676057i \(0.236313\pi\)
\(80\) 0 0
\(81\) −10.5674 −1.17416
\(82\) 0 0
\(83\) 0.290882 0.0319284 0.0159642 0.999873i \(-0.494918\pi\)
0.0159642 + 0.999873i \(0.494918\pi\)
\(84\) 0 0
\(85\) 8.27510 0.897561
\(86\) 0 0
\(87\) 11.9002 1.27584
\(88\) 0 0
\(89\) −9.51040 −1.00810 −0.504050 0.863674i \(-0.668157\pi\)
−0.504050 + 0.863674i \(0.668157\pi\)
\(90\) 0 0
\(91\) −2.13570 −0.223882
\(92\) 0 0
\(93\) −14.5707 −1.51091
\(94\) 0 0
\(95\) −3.65499 −0.374994
\(96\) 0 0
\(97\) 8.90446 0.904111 0.452055 0.891990i \(-0.350691\pi\)
0.452055 + 0.891990i \(0.350691\pi\)
\(98\) 0 0
\(99\) 1.34117 0.134792
\(100\) 0 0
\(101\) −4.81662 −0.479272 −0.239636 0.970863i \(-0.577028\pi\)
−0.239636 + 0.970863i \(0.577028\pi\)
\(102\) 0 0
\(103\) −6.11547 −0.602575 −0.301287 0.953533i \(-0.597416\pi\)
−0.301287 + 0.953533i \(0.597416\pi\)
\(104\) 0 0
\(105\) −3.48498 −0.340099
\(106\) 0 0
\(107\) −3.45962 −0.334454 −0.167227 0.985918i \(-0.553481\pi\)
−0.167227 + 0.985918i \(0.553481\pi\)
\(108\) 0 0
\(109\) 3.12839 0.299646 0.149823 0.988713i \(-0.452130\pi\)
0.149823 + 0.988713i \(0.452130\pi\)
\(110\) 0 0
\(111\) 19.7814 1.87757
\(112\) 0 0
\(113\) 1.01074 0.0950820 0.0475410 0.998869i \(-0.484862\pi\)
0.0475410 + 0.998869i \(0.484862\pi\)
\(114\) 0 0
\(115\) −26.2554 −2.44833
\(116\) 0 0
\(117\) 2.43223 0.224860
\(118\) 0 0
\(119\) −1.59321 −0.146050
\(120\) 0 0
\(121\) −7.03818 −0.639835
\(122\) 0 0
\(123\) 16.9835 1.53135
\(124\) 0 0
\(125\) −1.70955 −0.152907
\(126\) 0 0
\(127\) −7.58149 −0.672748 −0.336374 0.941728i \(-0.609201\pi\)
−0.336374 + 0.941728i \(0.609201\pi\)
\(128\) 0 0
\(129\) 12.0668 1.06243
\(130\) 0 0
\(131\) 7.81531 0.682827 0.341414 0.939913i \(-0.389094\pi\)
0.341414 + 0.939913i \(0.389094\pi\)
\(132\) 0 0
\(133\) 0.703698 0.0610184
\(134\) 0 0
\(135\) −13.7017 −1.17926
\(136\) 0 0
\(137\) −15.3633 −1.31258 −0.656289 0.754510i \(-0.727875\pi\)
−0.656289 + 0.754510i \(0.727875\pi\)
\(138\) 0 0
\(139\) −2.53672 −0.215162 −0.107581 0.994196i \(-0.534310\pi\)
−0.107581 + 0.994196i \(0.534310\pi\)
\(140\) 0 0
\(141\) 2.35542 0.198362
\(142\) 0 0
\(143\) 7.18483 0.600826
\(144\) 0 0
\(145\) 19.0795 1.58447
\(146\) 0 0
\(147\) −12.7461 −1.05128
\(148\) 0 0
\(149\) 11.7737 0.964538 0.482269 0.876023i \(-0.339813\pi\)
0.482269 + 0.876023i \(0.339813\pi\)
\(150\) 0 0
\(151\) −1.16607 −0.0948934 −0.0474467 0.998874i \(-0.515108\pi\)
−0.0474467 + 0.998874i \(0.515108\pi\)
\(152\) 0 0
\(153\) 1.81442 0.146687
\(154\) 0 0
\(155\) −23.3611 −1.87641
\(156\) 0 0
\(157\) −7.40450 −0.590943 −0.295472 0.955352i \(-0.595477\pi\)
−0.295472 + 0.955352i \(0.595477\pi\)
\(158\) 0 0
\(159\) 16.5523 1.31268
\(160\) 0 0
\(161\) 5.05497 0.398388
\(162\) 0 0
\(163\) −12.6435 −0.990313 −0.495157 0.868804i \(-0.664889\pi\)
−0.495157 + 0.868804i \(0.664889\pi\)
\(164\) 0 0
\(165\) 11.7240 0.912714
\(166\) 0 0
\(167\) −2.98639 −0.231094 −0.115547 0.993302i \(-0.536862\pi\)
−0.115547 + 0.993302i \(0.536862\pi\)
\(168\) 0 0
\(169\) 0.0298206 0.00229389
\(170\) 0 0
\(171\) −0.801403 −0.0612848
\(172\) 0 0
\(173\) −10.3330 −0.785600 −0.392800 0.919624i \(-0.628494\pi\)
−0.392800 + 0.919624i \(0.628494\pi\)
\(174\) 0 0
\(175\) −2.62915 −0.198745
\(176\) 0 0
\(177\) 6.78441 0.509948
\(178\) 0 0
\(179\) 4.34200 0.324536 0.162268 0.986747i \(-0.448119\pi\)
0.162268 + 0.986747i \(0.448119\pi\)
\(180\) 0 0
\(181\) 0.818680 0.0608520 0.0304260 0.999537i \(-0.490314\pi\)
0.0304260 + 0.999537i \(0.490314\pi\)
\(182\) 0 0
\(183\) −13.7409 −1.01576
\(184\) 0 0
\(185\) 31.7154 2.33176
\(186\) 0 0
\(187\) 5.35981 0.391948
\(188\) 0 0
\(189\) 2.63800 0.191886
\(190\) 0 0
\(191\) 0.682998 0.0494200 0.0247100 0.999695i \(-0.492134\pi\)
0.0247100 + 0.999695i \(0.492134\pi\)
\(192\) 0 0
\(193\) −5.59909 −0.403031 −0.201516 0.979485i \(-0.564587\pi\)
−0.201516 + 0.979485i \(0.564587\pi\)
\(194\) 0 0
\(195\) 21.2617 1.52258
\(196\) 0 0
\(197\) −13.9385 −0.993076 −0.496538 0.868015i \(-0.665396\pi\)
−0.496538 + 0.868015i \(0.665396\pi\)
\(198\) 0 0
\(199\) 3.68243 0.261041 0.130520 0.991446i \(-0.458335\pi\)
0.130520 + 0.991446i \(0.458335\pi\)
\(200\) 0 0
\(201\) −1.55993 −0.110029
\(202\) 0 0
\(203\) −3.67340 −0.257822
\(204\) 0 0
\(205\) 27.2296 1.90180
\(206\) 0 0
\(207\) −5.75683 −0.400127
\(208\) 0 0
\(209\) −2.36735 −0.163753
\(210\) 0 0
\(211\) 10.5819 0.728489 0.364244 0.931303i \(-0.381327\pi\)
0.364244 + 0.931303i \(0.381327\pi\)
\(212\) 0 0
\(213\) 23.2415 1.59248
\(214\) 0 0
\(215\) 19.3467 1.31943
\(216\) 0 0
\(217\) 4.49774 0.305326
\(218\) 0 0
\(219\) 20.8665 1.41003
\(220\) 0 0
\(221\) 9.72012 0.653846
\(222\) 0 0
\(223\) −26.1852 −1.75349 −0.876744 0.480957i \(-0.840289\pi\)
−0.876744 + 0.480957i \(0.840289\pi\)
\(224\) 0 0
\(225\) 2.99419 0.199613
\(226\) 0 0
\(227\) 6.72989 0.446678 0.223339 0.974741i \(-0.428304\pi\)
0.223339 + 0.974741i \(0.428304\pi\)
\(228\) 0 0
\(229\) 11.2832 0.745616 0.372808 0.927909i \(-0.378395\pi\)
0.372808 + 0.927909i \(0.378395\pi\)
\(230\) 0 0
\(231\) −2.25724 −0.148515
\(232\) 0 0
\(233\) 26.1165 1.71095 0.855476 0.517843i \(-0.173265\pi\)
0.855476 + 0.517843i \(0.173265\pi\)
\(234\) 0 0
\(235\) 3.77643 0.246347
\(236\) 0 0
\(237\) 25.1062 1.63082
\(238\) 0 0
\(239\) −8.96766 −0.580070 −0.290035 0.957016i \(-0.593667\pi\)
−0.290035 + 0.957016i \(0.593667\pi\)
\(240\) 0 0
\(241\) 8.31270 0.535468 0.267734 0.963493i \(-0.413725\pi\)
0.267734 + 0.963493i \(0.413725\pi\)
\(242\) 0 0
\(243\) −6.87877 −0.441273
\(244\) 0 0
\(245\) −20.4357 −1.30559
\(246\) 0 0
\(247\) −4.29323 −0.273172
\(248\) 0 0
\(249\) 0.557538 0.0353325
\(250\) 0 0
\(251\) −0.809235 −0.0510784 −0.0255392 0.999674i \(-0.508130\pi\)
−0.0255392 + 0.999674i \(0.508130\pi\)
\(252\) 0 0
\(253\) −17.0057 −1.06914
\(254\) 0 0
\(255\) 15.8610 0.993256
\(256\) 0 0
\(257\) 5.50371 0.343312 0.171656 0.985157i \(-0.445088\pi\)
0.171656 + 0.985157i \(0.445088\pi\)
\(258\) 0 0
\(259\) −6.10620 −0.379421
\(260\) 0 0
\(261\) 4.18343 0.258948
\(262\) 0 0
\(263\) 3.58265 0.220916 0.110458 0.993881i \(-0.464768\pi\)
0.110458 + 0.993881i \(0.464768\pi\)
\(264\) 0 0
\(265\) 26.5382 1.63023
\(266\) 0 0
\(267\) −18.2288 −1.11558
\(268\) 0 0
\(269\) −4.50112 −0.274438 −0.137219 0.990541i \(-0.543816\pi\)
−0.137219 + 0.990541i \(0.543816\pi\)
\(270\) 0 0
\(271\) 12.8762 0.782173 0.391087 0.920354i \(-0.372099\pi\)
0.391087 + 0.920354i \(0.372099\pi\)
\(272\) 0 0
\(273\) −4.09354 −0.247752
\(274\) 0 0
\(275\) 8.84487 0.533366
\(276\) 0 0
\(277\) −3.60991 −0.216899 −0.108449 0.994102i \(-0.534589\pi\)
−0.108449 + 0.994102i \(0.534589\pi\)
\(278\) 0 0
\(279\) −5.12222 −0.306659
\(280\) 0 0
\(281\) −8.92812 −0.532607 −0.266304 0.963889i \(-0.585802\pi\)
−0.266304 + 0.963889i \(0.585802\pi\)
\(282\) 0 0
\(283\) 6.55386 0.389587 0.194793 0.980844i \(-0.437596\pi\)
0.194793 + 0.980844i \(0.437596\pi\)
\(284\) 0 0
\(285\) −7.00558 −0.414975
\(286\) 0 0
\(287\) −5.24254 −0.309457
\(288\) 0 0
\(289\) −9.74889 −0.573464
\(290\) 0 0
\(291\) 17.0673 1.00050
\(292\) 0 0
\(293\) −6.70738 −0.391849 −0.195925 0.980619i \(-0.562771\pi\)
−0.195925 + 0.980619i \(0.562771\pi\)
\(294\) 0 0
\(295\) 10.8774 0.633307
\(296\) 0 0
\(297\) −8.87465 −0.514959
\(298\) 0 0
\(299\) −30.8402 −1.78353
\(300\) 0 0
\(301\) −3.72483 −0.214696
\(302\) 0 0
\(303\) −9.23211 −0.530371
\(304\) 0 0
\(305\) −22.0307 −1.26148
\(306\) 0 0
\(307\) −20.3998 −1.16428 −0.582140 0.813089i \(-0.697784\pi\)
−0.582140 + 0.813089i \(0.697784\pi\)
\(308\) 0 0
\(309\) −11.7216 −0.666820
\(310\) 0 0
\(311\) −4.96079 −0.281301 −0.140650 0.990059i \(-0.544919\pi\)
−0.140650 + 0.990059i \(0.544919\pi\)
\(312\) 0 0
\(313\) −0.291763 −0.0164914 −0.00824572 0.999966i \(-0.502625\pi\)
−0.00824572 + 0.999966i \(0.502625\pi\)
\(314\) 0 0
\(315\) −1.22512 −0.0690276
\(316\) 0 0
\(317\) 25.4045 1.42686 0.713428 0.700728i \(-0.247142\pi\)
0.713428 + 0.700728i \(0.247142\pi\)
\(318\) 0 0
\(319\) 12.3579 0.691908
\(320\) 0 0
\(321\) −6.63111 −0.370112
\(322\) 0 0
\(323\) −3.20271 −0.178203
\(324\) 0 0
\(325\) 16.0403 0.889758
\(326\) 0 0
\(327\) 5.99624 0.331593
\(328\) 0 0
\(329\) −0.727079 −0.0400852
\(330\) 0 0
\(331\) −16.1956 −0.890192 −0.445096 0.895483i \(-0.646830\pi\)
−0.445096 + 0.895483i \(0.646830\pi\)
\(332\) 0 0
\(333\) 6.95401 0.381077
\(334\) 0 0
\(335\) −2.50103 −0.136646
\(336\) 0 0
\(337\) −29.3642 −1.59957 −0.799785 0.600287i \(-0.795053\pi\)
−0.799785 + 0.600287i \(0.795053\pi\)
\(338\) 0 0
\(339\) 1.93729 0.105219
\(340\) 0 0
\(341\) −15.1311 −0.819394
\(342\) 0 0
\(343\) 8.07611 0.436069
\(344\) 0 0
\(345\) −50.3242 −2.70936
\(346\) 0 0
\(347\) −11.3409 −0.608812 −0.304406 0.952542i \(-0.598458\pi\)
−0.304406 + 0.952542i \(0.598458\pi\)
\(348\) 0 0
\(349\) −20.0166 −1.07147 −0.535733 0.844387i \(-0.679965\pi\)
−0.535733 + 0.844387i \(0.679965\pi\)
\(350\) 0 0
\(351\) −16.0943 −0.859052
\(352\) 0 0
\(353\) 1.57600 0.0838819 0.0419409 0.999120i \(-0.486646\pi\)
0.0419409 + 0.999120i \(0.486646\pi\)
\(354\) 0 0
\(355\) 37.2629 1.97771
\(356\) 0 0
\(357\) −3.05374 −0.161621
\(358\) 0 0
\(359\) −17.9274 −0.946172 −0.473086 0.881016i \(-0.656860\pi\)
−0.473086 + 0.881016i \(0.656860\pi\)
\(360\) 0 0
\(361\) −17.5854 −0.925548
\(362\) 0 0
\(363\) −13.4902 −0.708052
\(364\) 0 0
\(365\) 33.4551 1.75112
\(366\) 0 0
\(367\) 29.6454 1.54748 0.773738 0.633506i \(-0.218385\pi\)
0.773738 + 0.633506i \(0.218385\pi\)
\(368\) 0 0
\(369\) 5.97043 0.310808
\(370\) 0 0
\(371\) −5.10942 −0.265268
\(372\) 0 0
\(373\) 10.6698 0.552459 0.276230 0.961092i \(-0.410915\pi\)
0.276230 + 0.961092i \(0.410915\pi\)
\(374\) 0 0
\(375\) −3.27673 −0.169210
\(376\) 0 0
\(377\) 22.4112 1.15424
\(378\) 0 0
\(379\) −20.7572 −1.06622 −0.533112 0.846045i \(-0.678978\pi\)
−0.533112 + 0.846045i \(0.678978\pi\)
\(380\) 0 0
\(381\) −14.5316 −0.744475
\(382\) 0 0
\(383\) 10.0399 0.513013 0.256506 0.966543i \(-0.417429\pi\)
0.256506 + 0.966543i \(0.417429\pi\)
\(384\) 0 0
\(385\) −3.61901 −0.184442
\(386\) 0 0
\(387\) 4.24201 0.215633
\(388\) 0 0
\(389\) −10.7264 −0.543852 −0.271926 0.962318i \(-0.587661\pi\)
−0.271926 + 0.962318i \(0.587661\pi\)
\(390\) 0 0
\(391\) −23.0065 −1.16349
\(392\) 0 0
\(393\) 14.9798 0.755628
\(394\) 0 0
\(395\) 40.2525 2.02532
\(396\) 0 0
\(397\) −28.9918 −1.45506 −0.727530 0.686076i \(-0.759332\pi\)
−0.727530 + 0.686076i \(0.759332\pi\)
\(398\) 0 0
\(399\) 1.34879 0.0675240
\(400\) 0 0
\(401\) 8.66132 0.432526 0.216263 0.976335i \(-0.430613\pi\)
0.216263 + 0.976335i \(0.430613\pi\)
\(402\) 0 0
\(403\) −27.4405 −1.36691
\(404\) 0 0
\(405\) −32.4743 −1.61366
\(406\) 0 0
\(407\) 20.5422 1.01824
\(408\) 0 0
\(409\) 16.4025 0.811050 0.405525 0.914084i \(-0.367089\pi\)
0.405525 + 0.914084i \(0.367089\pi\)
\(410\) 0 0
\(411\) −29.4472 −1.45252
\(412\) 0 0
\(413\) −2.09423 −0.103051
\(414\) 0 0
\(415\) 0.893897 0.0438797
\(416\) 0 0
\(417\) −4.86217 −0.238102
\(418\) 0 0
\(419\) 11.5441 0.563964 0.281982 0.959420i \(-0.409008\pi\)
0.281982 + 0.959420i \(0.409008\pi\)
\(420\) 0 0
\(421\) −29.0480 −1.41571 −0.707855 0.706357i \(-0.750337\pi\)
−0.707855 + 0.706357i \(0.750337\pi\)
\(422\) 0 0
\(423\) 0.828029 0.0402602
\(424\) 0 0
\(425\) 11.9659 0.580433
\(426\) 0 0
\(427\) 4.24160 0.205265
\(428\) 0 0
\(429\) 13.7713 0.664884
\(430\) 0 0
\(431\) −10.5338 −0.507394 −0.253697 0.967284i \(-0.581647\pi\)
−0.253697 + 0.967284i \(0.581647\pi\)
\(432\) 0 0
\(433\) 20.0401 0.963066 0.481533 0.876428i \(-0.340080\pi\)
0.481533 + 0.876428i \(0.340080\pi\)
\(434\) 0 0
\(435\) 36.5701 1.75340
\(436\) 0 0
\(437\) 10.1616 0.486096
\(438\) 0 0
\(439\) 5.26237 0.251159 0.125580 0.992084i \(-0.459921\pi\)
0.125580 + 0.992084i \(0.459921\pi\)
\(440\) 0 0
\(441\) −4.48078 −0.213370
\(442\) 0 0
\(443\) −14.7666 −0.701582 −0.350791 0.936454i \(-0.614087\pi\)
−0.350791 + 0.936454i \(0.614087\pi\)
\(444\) 0 0
\(445\) −29.2260 −1.38545
\(446\) 0 0
\(447\) 22.5668 1.06737
\(448\) 0 0
\(449\) −40.7260 −1.92198 −0.960990 0.276583i \(-0.910798\pi\)
−0.960990 + 0.276583i \(0.910798\pi\)
\(450\) 0 0
\(451\) 17.6367 0.830480
\(452\) 0 0
\(453\) −2.23503 −0.105011
\(454\) 0 0
\(455\) −6.56314 −0.307685
\(456\) 0 0
\(457\) −11.1750 −0.522746 −0.261373 0.965238i \(-0.584175\pi\)
−0.261373 + 0.965238i \(0.584175\pi\)
\(458\) 0 0
\(459\) −12.0062 −0.560402
\(460\) 0 0
\(461\) −4.71844 −0.219760 −0.109880 0.993945i \(-0.535047\pi\)
−0.109880 + 0.993945i \(0.535047\pi\)
\(462\) 0 0
\(463\) 16.6542 0.773987 0.386993 0.922082i \(-0.373514\pi\)
0.386993 + 0.922082i \(0.373514\pi\)
\(464\) 0 0
\(465\) −44.7767 −2.07647
\(466\) 0 0
\(467\) −25.7421 −1.19120 −0.595600 0.803281i \(-0.703086\pi\)
−0.595600 + 0.803281i \(0.703086\pi\)
\(468\) 0 0
\(469\) 0.481526 0.0222348
\(470\) 0 0
\(471\) −14.1923 −0.653948
\(472\) 0 0
\(473\) 12.5309 0.576172
\(474\) 0 0
\(475\) −5.28518 −0.242501
\(476\) 0 0
\(477\) 5.81883 0.266426
\(478\) 0 0
\(479\) 4.74722 0.216906 0.108453 0.994102i \(-0.465410\pi\)
0.108453 + 0.994102i \(0.465410\pi\)
\(480\) 0 0
\(481\) 37.2536 1.69862
\(482\) 0 0
\(483\) 9.68896 0.440863
\(484\) 0 0
\(485\) 27.3639 1.24253
\(486\) 0 0
\(487\) −0.0262545 −0.00118970 −0.000594852 1.00000i \(-0.500189\pi\)
−0.000594852 1.00000i \(0.500189\pi\)
\(488\) 0 0
\(489\) −24.2340 −1.09590
\(490\) 0 0
\(491\) 39.3877 1.77754 0.888772 0.458350i \(-0.151559\pi\)
0.888772 + 0.458350i \(0.151559\pi\)
\(492\) 0 0
\(493\) 16.7186 0.752966
\(494\) 0 0
\(495\) 4.12149 0.185247
\(496\) 0 0
\(497\) −7.17426 −0.321809
\(498\) 0 0
\(499\) −9.81624 −0.439435 −0.219718 0.975563i \(-0.570514\pi\)
−0.219718 + 0.975563i \(0.570514\pi\)
\(500\) 0 0
\(501\) −5.72406 −0.255732
\(502\) 0 0
\(503\) 34.9463 1.55818 0.779088 0.626914i \(-0.215682\pi\)
0.779088 + 0.626914i \(0.215682\pi\)
\(504\) 0 0
\(505\) −14.8018 −0.658670
\(506\) 0 0
\(507\) 0.0571577 0.00253846
\(508\) 0 0
\(509\) −13.0838 −0.579929 −0.289965 0.957037i \(-0.593644\pi\)
−0.289965 + 0.957037i \(0.593644\pi\)
\(510\) 0 0
\(511\) −6.44114 −0.284939
\(512\) 0 0
\(513\) 5.30297 0.234132
\(514\) 0 0
\(515\) −18.7932 −0.828127
\(516\) 0 0
\(517\) 2.44601 0.107575
\(518\) 0 0
\(519\) −19.8054 −0.869359
\(520\) 0 0
\(521\) 42.4840 1.86126 0.930630 0.365963i \(-0.119260\pi\)
0.930630 + 0.365963i \(0.119260\pi\)
\(522\) 0 0
\(523\) −29.4564 −1.28804 −0.644018 0.765010i \(-0.722734\pi\)
−0.644018 + 0.765010i \(0.722734\pi\)
\(524\) 0 0
\(525\) −5.03934 −0.219935
\(526\) 0 0
\(527\) −20.4703 −0.891702
\(528\) 0 0
\(529\) 49.9953 2.17371
\(530\) 0 0
\(531\) 2.38501 0.103500
\(532\) 0 0
\(533\) 31.9845 1.38540
\(534\) 0 0
\(535\) −10.6316 −0.459644
\(536\) 0 0
\(537\) 8.32239 0.359138
\(538\) 0 0
\(539\) −13.2363 −0.570126
\(540\) 0 0
\(541\) −16.2781 −0.699849 −0.349925 0.936778i \(-0.613793\pi\)
−0.349925 + 0.936778i \(0.613793\pi\)
\(542\) 0 0
\(543\) 1.56918 0.0673399
\(544\) 0 0
\(545\) 9.61373 0.411807
\(546\) 0 0
\(547\) −44.1323 −1.88696 −0.943480 0.331428i \(-0.892470\pi\)
−0.943480 + 0.331428i \(0.892470\pi\)
\(548\) 0 0
\(549\) −4.83052 −0.206161
\(550\) 0 0
\(551\) −7.38434 −0.314583
\(552\) 0 0
\(553\) −7.74986 −0.329557
\(554\) 0 0
\(555\) 60.7895 2.58037
\(556\) 0 0
\(557\) 32.5372 1.37864 0.689322 0.724455i \(-0.257909\pi\)
0.689322 + 0.724455i \(0.257909\pi\)
\(558\) 0 0
\(559\) 22.7250 0.961167
\(560\) 0 0
\(561\) 10.2732 0.433737
\(562\) 0 0
\(563\) −4.45639 −0.187814 −0.0939072 0.995581i \(-0.529936\pi\)
−0.0939072 + 0.995581i \(0.529936\pi\)
\(564\) 0 0
\(565\) 3.10605 0.130672
\(566\) 0 0
\(567\) 6.25230 0.262572
\(568\) 0 0
\(569\) 17.8170 0.746928 0.373464 0.927645i \(-0.378170\pi\)
0.373464 + 0.927645i \(0.378170\pi\)
\(570\) 0 0
\(571\) 28.5784 1.19597 0.597984 0.801508i \(-0.295968\pi\)
0.597984 + 0.801508i \(0.295968\pi\)
\(572\) 0 0
\(573\) 1.30911 0.0546891
\(574\) 0 0
\(575\) −37.9657 −1.58328
\(576\) 0 0
\(577\) −10.9615 −0.456331 −0.228166 0.973622i \(-0.573273\pi\)
−0.228166 + 0.973622i \(0.573273\pi\)
\(578\) 0 0
\(579\) −10.7319 −0.446002
\(580\) 0 0
\(581\) −0.172103 −0.00714002
\(582\) 0 0
\(583\) 17.1889 0.711891
\(584\) 0 0
\(585\) 7.47439 0.309028
\(586\) 0 0
\(587\) −20.8966 −0.862494 −0.431247 0.902234i \(-0.641926\pi\)
−0.431247 + 0.902234i \(0.641926\pi\)
\(588\) 0 0
\(589\) 9.04144 0.372546
\(590\) 0 0
\(591\) −26.7161 −1.09896
\(592\) 0 0
\(593\) 5.40031 0.221764 0.110882 0.993834i \(-0.464632\pi\)
0.110882 + 0.993834i \(0.464632\pi\)
\(594\) 0 0
\(595\) −4.89604 −0.200718
\(596\) 0 0
\(597\) 7.05819 0.288872
\(598\) 0 0
\(599\) 12.3782 0.505758 0.252879 0.967498i \(-0.418623\pi\)
0.252879 + 0.967498i \(0.418623\pi\)
\(600\) 0 0
\(601\) 11.2084 0.457202 0.228601 0.973520i \(-0.426585\pi\)
0.228601 + 0.973520i \(0.426585\pi\)
\(602\) 0 0
\(603\) −0.548383 −0.0223319
\(604\) 0 0
\(605\) −21.6288 −0.879334
\(606\) 0 0
\(607\) 0.746563 0.0303020 0.0151510 0.999885i \(-0.495177\pi\)
0.0151510 + 0.999885i \(0.495177\pi\)
\(608\) 0 0
\(609\) −7.04086 −0.285310
\(610\) 0 0
\(611\) 4.43588 0.179456
\(612\) 0 0
\(613\) 4.93806 0.199447 0.0997233 0.995015i \(-0.468204\pi\)
0.0997233 + 0.995015i \(0.468204\pi\)
\(614\) 0 0
\(615\) 52.1915 2.10456
\(616\) 0 0
\(617\) 45.7806 1.84306 0.921530 0.388308i \(-0.126940\pi\)
0.921530 + 0.388308i \(0.126940\pi\)
\(618\) 0 0
\(619\) −12.0362 −0.483776 −0.241888 0.970304i \(-0.577767\pi\)
−0.241888 + 0.970304i \(0.577767\pi\)
\(620\) 0 0
\(621\) 38.0935 1.52864
\(622\) 0 0
\(623\) 5.62691 0.225437
\(624\) 0 0
\(625\) −27.4720 −1.09888
\(626\) 0 0
\(627\) −4.53754 −0.181212
\(628\) 0 0
\(629\) 27.7908 1.10809
\(630\) 0 0
\(631\) 1.36801 0.0544596 0.0272298 0.999629i \(-0.491331\pi\)
0.0272298 + 0.999629i \(0.491331\pi\)
\(632\) 0 0
\(633\) 20.2825 0.806159
\(634\) 0 0
\(635\) −23.2984 −0.924568
\(636\) 0 0
\(637\) −24.0042 −0.951080
\(638\) 0 0
\(639\) 8.17036 0.323215
\(640\) 0 0
\(641\) −23.1653 −0.914975 −0.457487 0.889216i \(-0.651250\pi\)
−0.457487 + 0.889216i \(0.651250\pi\)
\(642\) 0 0
\(643\) −14.6533 −0.577869 −0.288935 0.957349i \(-0.593301\pi\)
−0.288935 + 0.957349i \(0.593301\pi\)
\(644\) 0 0
\(645\) 37.0821 1.46011
\(646\) 0 0
\(647\) 39.4759 1.55196 0.775979 0.630758i \(-0.217256\pi\)
0.775979 + 0.630758i \(0.217256\pi\)
\(648\) 0 0
\(649\) 7.04533 0.276553
\(650\) 0 0
\(651\) 8.62089 0.337879
\(652\) 0 0
\(653\) 2.67703 0.104760 0.0523800 0.998627i \(-0.483319\pi\)
0.0523800 + 0.998627i \(0.483319\pi\)
\(654\) 0 0
\(655\) 24.0169 0.938419
\(656\) 0 0
\(657\) 7.33545 0.286183
\(658\) 0 0
\(659\) −46.2181 −1.80040 −0.900202 0.435473i \(-0.856581\pi\)
−0.900202 + 0.435473i \(0.856581\pi\)
\(660\) 0 0
\(661\) 1.20188 0.0467477 0.0233739 0.999727i \(-0.492559\pi\)
0.0233739 + 0.999727i \(0.492559\pi\)
\(662\) 0 0
\(663\) 18.6307 0.723557
\(664\) 0 0
\(665\) 2.16251 0.0838584
\(666\) 0 0
\(667\) −53.0449 −2.05391
\(668\) 0 0
\(669\) −50.1896 −1.94044
\(670\) 0 0
\(671\) −14.2694 −0.550863
\(672\) 0 0
\(673\) −31.5411 −1.21582 −0.607909 0.794007i \(-0.707992\pi\)
−0.607909 + 0.794007i \(0.707992\pi\)
\(674\) 0 0
\(675\) −19.8129 −0.762599
\(676\) 0 0
\(677\) 1.50118 0.0576950 0.0288475 0.999584i \(-0.490816\pi\)
0.0288475 + 0.999584i \(0.490816\pi\)
\(678\) 0 0
\(679\) −5.26840 −0.202183
\(680\) 0 0
\(681\) 12.8993 0.494302
\(682\) 0 0
\(683\) −38.2646 −1.46415 −0.732077 0.681221i \(-0.761449\pi\)
−0.732077 + 0.681221i \(0.761449\pi\)
\(684\) 0 0
\(685\) −47.2124 −1.80389
\(686\) 0 0
\(687\) 21.6267 0.825112
\(688\) 0 0
\(689\) 31.1723 1.18757
\(690\) 0 0
\(691\) −32.6983 −1.24390 −0.621952 0.783056i \(-0.713660\pi\)
−0.621952 + 0.783056i \(0.713660\pi\)
\(692\) 0 0
\(693\) −0.793514 −0.0301431
\(694\) 0 0
\(695\) −7.79548 −0.295700
\(696\) 0 0
\(697\) 23.8601 0.903766
\(698\) 0 0
\(699\) 50.0580 1.89337
\(700\) 0 0
\(701\) −17.5244 −0.661886 −0.330943 0.943651i \(-0.607367\pi\)
−0.330943 + 0.943651i \(0.607367\pi\)
\(702\) 0 0
\(703\) −12.2748 −0.462953
\(704\) 0 0
\(705\) 7.23834 0.272612
\(706\) 0 0
\(707\) 2.84980 0.107178
\(708\) 0 0
\(709\) 34.0779 1.27982 0.639912 0.768448i \(-0.278971\pi\)
0.639912 + 0.768448i \(0.278971\pi\)
\(710\) 0 0
\(711\) 8.82588 0.330996
\(712\) 0 0
\(713\) 64.9486 2.43235
\(714\) 0 0
\(715\) 22.0794 0.825723
\(716\) 0 0
\(717\) −17.1885 −0.641916
\(718\) 0 0
\(719\) 29.1090 1.08558 0.542791 0.839868i \(-0.317368\pi\)
0.542791 + 0.839868i \(0.317368\pi\)
\(720\) 0 0
\(721\) 3.61827 0.134751
\(722\) 0 0
\(723\) 15.9331 0.592558
\(724\) 0 0
\(725\) 27.5893 1.02464
\(726\) 0 0
\(727\) 26.9888 1.00096 0.500480 0.865748i \(-0.333157\pi\)
0.500480 + 0.865748i \(0.333157\pi\)
\(728\) 0 0
\(729\) 18.5176 0.685835
\(730\) 0 0
\(731\) 16.9527 0.627017
\(732\) 0 0
\(733\) 6.76159 0.249745 0.124873 0.992173i \(-0.460148\pi\)
0.124873 + 0.992173i \(0.460148\pi\)
\(734\) 0 0
\(735\) −39.1694 −1.44479
\(736\) 0 0
\(737\) −1.61993 −0.0596708
\(738\) 0 0
\(739\) 14.4347 0.530989 0.265494 0.964112i \(-0.414465\pi\)
0.265494 + 0.964112i \(0.414465\pi\)
\(740\) 0 0
\(741\) −8.22891 −0.302297
\(742\) 0 0
\(743\) −0.739099 −0.0271149 −0.0135575 0.999908i \(-0.504316\pi\)
−0.0135575 + 0.999908i \(0.504316\pi\)
\(744\) 0 0
\(745\) 36.1813 1.32558
\(746\) 0 0
\(747\) 0.195998 0.00717120
\(748\) 0 0
\(749\) 2.04691 0.0747925
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) −1.55107 −0.0565243
\(754\) 0 0
\(755\) −3.58340 −0.130413
\(756\) 0 0
\(757\) 3.11668 0.113278 0.0566388 0.998395i \(-0.481962\pi\)
0.0566388 + 0.998395i \(0.481962\pi\)
\(758\) 0 0
\(759\) −32.5951 −1.18313
\(760\) 0 0
\(761\) −24.4341 −0.885736 −0.442868 0.896587i \(-0.646039\pi\)
−0.442868 + 0.896587i \(0.646039\pi\)
\(762\) 0 0
\(763\) −1.85094 −0.0670086
\(764\) 0 0
\(765\) 5.57582 0.201594
\(766\) 0 0
\(767\) 12.7768 0.461345
\(768\) 0 0
\(769\) 0.429693 0.0154951 0.00774757 0.999970i \(-0.497534\pi\)
0.00774757 + 0.999970i \(0.497534\pi\)
\(770\) 0 0
\(771\) 10.5491 0.379915
\(772\) 0 0
\(773\) −38.5249 −1.38564 −0.692821 0.721109i \(-0.743633\pi\)
−0.692821 + 0.721109i \(0.743633\pi\)
\(774\) 0 0
\(775\) −33.7806 −1.21343
\(776\) 0 0
\(777\) −11.7039 −0.419874
\(778\) 0 0
\(779\) −10.5387 −0.377587
\(780\) 0 0
\(781\) 24.1353 0.863629
\(782\) 0 0
\(783\) −27.6822 −0.989280
\(784\) 0 0
\(785\) −22.7545 −0.812142
\(786\) 0 0
\(787\) 7.54525 0.268959 0.134480 0.990916i \(-0.457064\pi\)
0.134480 + 0.990916i \(0.457064\pi\)
\(788\) 0 0
\(789\) 6.86693 0.244469
\(790\) 0 0
\(791\) −0.598011 −0.0212628
\(792\) 0 0
\(793\) −25.8778 −0.918947
\(794\) 0 0
\(795\) 50.8662 1.80404
\(796\) 0 0
\(797\) −34.8787 −1.23547 −0.617733 0.786388i \(-0.711949\pi\)
−0.617733 + 0.786388i \(0.711949\pi\)
\(798\) 0 0
\(799\) 3.30912 0.117068
\(800\) 0 0
\(801\) −6.40818 −0.226422
\(802\) 0 0
\(803\) 21.6690 0.764682
\(804\) 0 0
\(805\) 15.5342 0.547510
\(806\) 0 0
\(807\) −8.62738 −0.303698
\(808\) 0 0
\(809\) 18.3170 0.643990 0.321995 0.946741i \(-0.395647\pi\)
0.321995 + 0.946741i \(0.395647\pi\)
\(810\) 0 0
\(811\) −17.2941 −0.607279 −0.303639 0.952787i \(-0.598202\pi\)
−0.303639 + 0.952787i \(0.598202\pi\)
\(812\) 0 0
\(813\) 24.6800 0.865566
\(814\) 0 0
\(815\) −38.8541 −1.36100
\(816\) 0 0
\(817\) −7.48774 −0.261963
\(818\) 0 0
\(819\) −1.43905 −0.0502845
\(820\) 0 0
\(821\) 9.34588 0.326173 0.163087 0.986612i \(-0.447855\pi\)
0.163087 + 0.986612i \(0.447855\pi\)
\(822\) 0 0
\(823\) 17.5716 0.612508 0.306254 0.951950i \(-0.400924\pi\)
0.306254 + 0.951950i \(0.400924\pi\)
\(824\) 0 0
\(825\) 16.9531 0.590232
\(826\) 0 0
\(827\) 3.37473 0.117351 0.0586755 0.998277i \(-0.481312\pi\)
0.0586755 + 0.998277i \(0.481312\pi\)
\(828\) 0 0
\(829\) 47.9279 1.66460 0.832302 0.554323i \(-0.187023\pi\)
0.832302 + 0.554323i \(0.187023\pi\)
\(830\) 0 0
\(831\) −6.91919 −0.240024
\(832\) 0 0
\(833\) −17.9069 −0.620437
\(834\) 0 0
\(835\) −9.17735 −0.317595
\(836\) 0 0
\(837\) 33.8943 1.17156
\(838\) 0 0
\(839\) 40.5911 1.40136 0.700680 0.713476i \(-0.252880\pi\)
0.700680 + 0.713476i \(0.252880\pi\)
\(840\) 0 0
\(841\) 9.54719 0.329213
\(842\) 0 0
\(843\) −17.1127 −0.589392
\(844\) 0 0
\(845\) 0.0916405 0.00315253
\(846\) 0 0
\(847\) 4.16420 0.143084
\(848\) 0 0
\(849\) 12.5619 0.431124
\(850\) 0 0
\(851\) −88.1753 −3.02261
\(852\) 0 0
\(853\) −14.3673 −0.491928 −0.245964 0.969279i \(-0.579104\pi\)
−0.245964 + 0.969279i \(0.579104\pi\)
\(854\) 0 0
\(855\) −2.46276 −0.0842246
\(856\) 0 0
\(857\) −10.3293 −0.352843 −0.176422 0.984315i \(-0.556452\pi\)
−0.176422 + 0.984315i \(0.556452\pi\)
\(858\) 0 0
\(859\) 22.5762 0.770289 0.385144 0.922856i \(-0.374152\pi\)
0.385144 + 0.922856i \(0.374152\pi\)
\(860\) 0 0
\(861\) −10.0485 −0.342451
\(862\) 0 0
\(863\) 22.6420 0.770742 0.385371 0.922762i \(-0.374073\pi\)
0.385371 + 0.922762i \(0.374073\pi\)
\(864\) 0 0
\(865\) −31.7538 −1.07966
\(866\) 0 0
\(867\) −18.6859 −0.634605
\(868\) 0 0
\(869\) 26.0717 0.884422
\(870\) 0 0
\(871\) −2.93777 −0.0995424
\(872\) 0 0
\(873\) 5.99989 0.203065
\(874\) 0 0
\(875\) 1.01147 0.0341940
\(876\) 0 0
\(877\) 56.2365 1.89897 0.949485 0.313812i \(-0.101606\pi\)
0.949485 + 0.313812i \(0.101606\pi\)
\(878\) 0 0
\(879\) −12.8562 −0.433627
\(880\) 0 0
\(881\) −53.9520 −1.81769 −0.908844 0.417136i \(-0.863034\pi\)
−0.908844 + 0.417136i \(0.863034\pi\)
\(882\) 0 0
\(883\) −9.13695 −0.307483 −0.153741 0.988111i \(-0.549132\pi\)
−0.153741 + 0.988111i \(0.549132\pi\)
\(884\) 0 0
\(885\) 20.8489 0.700828
\(886\) 0 0
\(887\) −42.2248 −1.41777 −0.708884 0.705325i \(-0.750801\pi\)
−0.708884 + 0.705325i \(0.750801\pi\)
\(888\) 0 0
\(889\) 4.48566 0.150444
\(890\) 0 0
\(891\) −21.0337 −0.704655
\(892\) 0 0
\(893\) −1.46159 −0.0489102
\(894\) 0 0
\(895\) 13.3432 0.446015
\(896\) 0 0
\(897\) −59.1119 −1.97369
\(898\) 0 0
\(899\) −47.1975 −1.57412
\(900\) 0 0
\(901\) 23.2543 0.774712
\(902\) 0 0
\(903\) −7.13946 −0.237586
\(904\) 0 0
\(905\) 2.51585 0.0836298
\(906\) 0 0
\(907\) −26.6789 −0.885857 −0.442929 0.896557i \(-0.646061\pi\)
−0.442929 + 0.896557i \(0.646061\pi\)
\(908\) 0 0
\(909\) −3.24548 −0.107646
\(910\) 0 0
\(911\) −48.4608 −1.60558 −0.802789 0.596263i \(-0.796652\pi\)
−0.802789 + 0.596263i \(0.796652\pi\)
\(912\) 0 0
\(913\) 0.578980 0.0191614
\(914\) 0 0
\(915\) −42.2267 −1.39597
\(916\) 0 0
\(917\) −4.62400 −0.152698
\(918\) 0 0
\(919\) 8.67151 0.286047 0.143023 0.989719i \(-0.454318\pi\)
0.143023 + 0.989719i \(0.454318\pi\)
\(920\) 0 0
\(921\) −39.1007 −1.28841
\(922\) 0 0
\(923\) 43.7698 1.44070
\(924\) 0 0
\(925\) 45.8610 1.50790
\(926\) 0 0
\(927\) −4.12065 −0.135340
\(928\) 0 0
\(929\) −52.4420 −1.72057 −0.860283 0.509817i \(-0.829713\pi\)
−0.860283 + 0.509817i \(0.829713\pi\)
\(930\) 0 0
\(931\) 7.90921 0.259214
\(932\) 0 0
\(933\) −9.50844 −0.311292
\(934\) 0 0
\(935\) 16.4710 0.538660
\(936\) 0 0
\(937\) −6.01007 −0.196340 −0.0981702 0.995170i \(-0.531299\pi\)
−0.0981702 + 0.995170i \(0.531299\pi\)
\(938\) 0 0
\(939\) −0.559228 −0.0182497
\(940\) 0 0
\(941\) −19.8695 −0.647728 −0.323864 0.946104i \(-0.604982\pi\)
−0.323864 + 0.946104i \(0.604982\pi\)
\(942\) 0 0
\(943\) −75.7038 −2.46526
\(944\) 0 0
\(945\) 8.10674 0.263712
\(946\) 0 0
\(947\) 10.6701 0.346731 0.173365 0.984858i \(-0.444536\pi\)
0.173365 + 0.984858i \(0.444536\pi\)
\(948\) 0 0
\(949\) 39.2971 1.27564
\(950\) 0 0
\(951\) 48.6932 1.57898
\(952\) 0 0
\(953\) −52.7635 −1.70918 −0.854589 0.519305i \(-0.826191\pi\)
−0.854589 + 0.519305i \(0.826191\pi\)
\(954\) 0 0
\(955\) 2.09889 0.0679186
\(956\) 0 0
\(957\) 23.6866 0.765677
\(958\) 0 0
\(959\) 9.08985 0.293527
\(960\) 0 0
\(961\) 26.7890 0.864161
\(962\) 0 0
\(963\) −2.33111 −0.0751191
\(964\) 0 0
\(965\) −17.2063 −0.553892
\(966\) 0 0
\(967\) −22.6426 −0.728138 −0.364069 0.931372i \(-0.618613\pi\)
−0.364069 + 0.931372i \(0.618613\pi\)
\(968\) 0 0
\(969\) −6.13869 −0.197203
\(970\) 0 0
\(971\) 28.7801 0.923599 0.461799 0.886984i \(-0.347204\pi\)
0.461799 + 0.886984i \(0.347204\pi\)
\(972\) 0 0
\(973\) 1.50087 0.0481157
\(974\) 0 0
\(975\) 30.7448 0.984622
\(976\) 0 0
\(977\) 13.3853 0.428235 0.214118 0.976808i \(-0.431312\pi\)
0.214118 + 0.976808i \(0.431312\pi\)
\(978\) 0 0
\(979\) −18.9298 −0.604999
\(980\) 0 0
\(981\) 2.10793 0.0673011
\(982\) 0 0
\(983\) −46.5305 −1.48409 −0.742047 0.670348i \(-0.766145\pi\)
−0.742047 + 0.670348i \(0.766145\pi\)
\(984\) 0 0
\(985\) −42.8338 −1.36480
\(986\) 0 0
\(987\) −1.39360 −0.0443589
\(988\) 0 0
\(989\) −53.7877 −1.71035
\(990\) 0 0
\(991\) −22.6594 −0.719798 −0.359899 0.932991i \(-0.617189\pi\)
−0.359899 + 0.932991i \(0.617189\pi\)
\(992\) 0 0
\(993\) −31.0424 −0.985102
\(994\) 0 0
\(995\) 11.3163 0.358752
\(996\) 0 0
\(997\) 43.4733 1.37681 0.688406 0.725325i \(-0.258311\pi\)
0.688406 + 0.725325i \(0.258311\pi\)
\(998\) 0 0
\(999\) −46.0154 −1.45586
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 \(a_p\))