Properties

Label 6027.2.a.bm.1.1
Level 6027
Weight 2
Character 6027.1
Self dual Yes
Analytic conductor 48.126
Analytic rank 1
Dimension 16
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6027.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.1258372982\)
Analytic rank: \(1\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(2.72726\)
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.72726 q^{2} +1.00000 q^{3} +5.43794 q^{4} -0.416230 q^{5} -2.72726 q^{6} -9.37616 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.72726 q^{2} +1.00000 q^{3} +5.43794 q^{4} -0.416230 q^{5} -2.72726 q^{6} -9.37616 q^{8} +1.00000 q^{9} +1.13517 q^{10} -0.0467863 q^{11} +5.43794 q^{12} +3.00540 q^{13} -0.416230 q^{15} +14.6953 q^{16} -5.85587 q^{17} -2.72726 q^{18} +6.05832 q^{19} -2.26343 q^{20} +0.127598 q^{22} +0.952936 q^{23} -9.37616 q^{24} -4.82675 q^{25} -8.19650 q^{26} +1.00000 q^{27} +2.00826 q^{29} +1.13517 q^{30} -1.80066 q^{31} -21.3257 q^{32} -0.0467863 q^{33} +15.9705 q^{34} +5.43794 q^{36} +3.23743 q^{37} -16.5226 q^{38} +3.00540 q^{39} +3.90264 q^{40} +1.00000 q^{41} -9.90222 q^{43} -0.254421 q^{44} -0.416230 q^{45} -2.59890 q^{46} -9.28958 q^{47} +14.6953 q^{48} +13.1638 q^{50} -5.85587 q^{51} +16.3432 q^{52} -2.46073 q^{53} -2.72726 q^{54} +0.0194739 q^{55} +6.05832 q^{57} -5.47703 q^{58} -6.18781 q^{59} -2.26343 q^{60} -10.1483 q^{61} +4.91086 q^{62} +28.7700 q^{64} -1.25094 q^{65} +0.127598 q^{66} -9.49723 q^{67} -31.8439 q^{68} +0.952936 q^{69} +4.70904 q^{71} -9.37616 q^{72} -5.34672 q^{73} -8.82930 q^{74} -4.82675 q^{75} +32.9448 q^{76} -8.19650 q^{78} +14.0370 q^{79} -6.11664 q^{80} +1.00000 q^{81} -2.72726 q^{82} -3.23850 q^{83} +2.43739 q^{85} +27.0059 q^{86} +2.00826 q^{87} +0.438676 q^{88} +4.51179 q^{89} +1.13517 q^{90} +5.18201 q^{92} -1.80066 q^{93} +25.3351 q^{94} -2.52165 q^{95} -21.3257 q^{96} +12.3847 q^{97} -0.0467863 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 4q^{2} + 16q^{3} + 12q^{4} - 12q^{5} - 4q^{6} - 12q^{8} + 16q^{9} + O(q^{10}) \) \( 16q - 4q^{2} + 16q^{3} + 12q^{4} - 12q^{5} - 4q^{6} - 12q^{8} + 16q^{9} - 4q^{10} - 4q^{11} + 12q^{12} - 12q^{15} - 8q^{17} - 4q^{18} + 4q^{19} - 20q^{20} - 16q^{22} - 12q^{23} - 12q^{24} - 8q^{25} - 8q^{26} + 16q^{27} - 16q^{29} - 4q^{30} - 4q^{31} - 48q^{32} - 4q^{33} + 16q^{34} + 12q^{36} - 48q^{37} - 4q^{38} + 56q^{40} + 16q^{41} - 16q^{43} - 12q^{45} - 4q^{46} - 36q^{47} - 8q^{50} - 8q^{51} - 60q^{53} - 4q^{54} + 8q^{55} + 4q^{57} - 36q^{58} - 36q^{59} - 20q^{60} - 4q^{61} - 12q^{62} + 52q^{64} - 36q^{65} - 16q^{66} - 52q^{67} - 8q^{68} - 12q^{69} - 12q^{71} - 12q^{72} - 16q^{73} + 4q^{74} - 8q^{75} + 16q^{76} - 8q^{78} - 36q^{79} - 68q^{80} + 16q^{81} - 4q^{82} - 32q^{83} - 28q^{85} - 8q^{86} - 16q^{87} - 36q^{88} - 12q^{89} - 4q^{90} - 36q^{92} - 4q^{93} + 24q^{94} - 20q^{95} - 48q^{96} + 48q^{97} - 4q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.72726 −1.92846 −0.964232 0.265061i \(-0.914608\pi\)
−0.964232 + 0.265061i \(0.914608\pi\)
\(3\) 1.00000 0.577350
\(4\) 5.43794 2.71897
\(5\) −0.416230 −0.186144 −0.0930718 0.995659i \(-0.529669\pi\)
−0.0930718 + 0.995659i \(0.529669\pi\)
\(6\) −2.72726 −1.11340
\(7\) 0 0
\(8\) −9.37616 −3.31497
\(9\) 1.00000 0.333333
\(10\) 1.13517 0.358971
\(11\) −0.0467863 −0.0141066 −0.00705330 0.999975i \(-0.502245\pi\)
−0.00705330 + 0.999975i \(0.502245\pi\)
\(12\) 5.43794 1.56980
\(13\) 3.00540 0.833548 0.416774 0.909010i \(-0.363161\pi\)
0.416774 + 0.909010i \(0.363161\pi\)
\(14\) 0 0
\(15\) −0.416230 −0.107470
\(16\) 14.6953 3.67383
\(17\) −5.85587 −1.42026 −0.710129 0.704071i \(-0.751363\pi\)
−0.710129 + 0.704071i \(0.751363\pi\)
\(18\) −2.72726 −0.642821
\(19\) 6.05832 1.38987 0.694937 0.719071i \(-0.255432\pi\)
0.694937 + 0.719071i \(0.255432\pi\)
\(20\) −2.26343 −0.506119
\(21\) 0 0
\(22\) 0.127598 0.0272041
\(23\) 0.952936 0.198701 0.0993504 0.995053i \(-0.468324\pi\)
0.0993504 + 0.995053i \(0.468324\pi\)
\(24\) −9.37616 −1.91390
\(25\) −4.82675 −0.965351
\(26\) −8.19650 −1.60747
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 2.00826 0.372924 0.186462 0.982462i \(-0.440298\pi\)
0.186462 + 0.982462i \(0.440298\pi\)
\(30\) 1.13517 0.207252
\(31\) −1.80066 −0.323407 −0.161704 0.986839i \(-0.551699\pi\)
−0.161704 + 0.986839i \(0.551699\pi\)
\(32\) −21.3257 −3.76988
\(33\) −0.0467863 −0.00814445
\(34\) 15.9705 2.73892
\(35\) 0 0
\(36\) 5.43794 0.906324
\(37\) 3.23743 0.532230 0.266115 0.963941i \(-0.414260\pi\)
0.266115 + 0.963941i \(0.414260\pi\)
\(38\) −16.5226 −2.68032
\(39\) 3.00540 0.481249
\(40\) 3.90264 0.617061
\(41\) 1.00000 0.156174
\(42\) 0 0
\(43\) −9.90222 −1.51007 −0.755037 0.655682i \(-0.772381\pi\)
−0.755037 + 0.655682i \(0.772381\pi\)
\(44\) −0.254421 −0.0383555
\(45\) −0.416230 −0.0620479
\(46\) −2.59890 −0.383187
\(47\) −9.28958 −1.35503 −0.677513 0.735511i \(-0.736942\pi\)
−0.677513 + 0.735511i \(0.736942\pi\)
\(48\) 14.6953 2.12109
\(49\) 0 0
\(50\) 13.1638 1.86164
\(51\) −5.85587 −0.819987
\(52\) 16.3432 2.26639
\(53\) −2.46073 −0.338007 −0.169004 0.985615i \(-0.554055\pi\)
−0.169004 + 0.985615i \(0.554055\pi\)
\(54\) −2.72726 −0.371133
\(55\) 0.0194739 0.00262586
\(56\) 0 0
\(57\) 6.05832 0.802444
\(58\) −5.47703 −0.719170
\(59\) −6.18781 −0.805584 −0.402792 0.915292i \(-0.631960\pi\)
−0.402792 + 0.915292i \(0.631960\pi\)
\(60\) −2.26343 −0.292208
\(61\) −10.1483 −1.29935 −0.649676 0.760212i \(-0.725095\pi\)
−0.649676 + 0.760212i \(0.725095\pi\)
\(62\) 4.91086 0.623679
\(63\) 0 0
\(64\) 28.7700 3.59625
\(65\) −1.25094 −0.155160
\(66\) 0.127598 0.0157063
\(67\) −9.49723 −1.16027 −0.580136 0.814520i \(-0.697001\pi\)
−0.580136 + 0.814520i \(0.697001\pi\)
\(68\) −31.8439 −3.86164
\(69\) 0.952936 0.114720
\(70\) 0 0
\(71\) 4.70904 0.558860 0.279430 0.960166i \(-0.409854\pi\)
0.279430 + 0.960166i \(0.409854\pi\)
\(72\) −9.37616 −1.10499
\(73\) −5.34672 −0.625786 −0.312893 0.949788i \(-0.601298\pi\)
−0.312893 + 0.949788i \(0.601298\pi\)
\(74\) −8.82930 −1.02639
\(75\) −4.82675 −0.557345
\(76\) 32.9448 3.77903
\(77\) 0 0
\(78\) −8.19650 −0.928071
\(79\) 14.0370 1.57928 0.789641 0.613570i \(-0.210267\pi\)
0.789641 + 0.613570i \(0.210267\pi\)
\(80\) −6.11664 −0.683861
\(81\) 1.00000 0.111111
\(82\) −2.72726 −0.301175
\(83\) −3.23850 −0.355472 −0.177736 0.984078i \(-0.556877\pi\)
−0.177736 + 0.984078i \(0.556877\pi\)
\(84\) 0 0
\(85\) 2.43739 0.264372
\(86\) 27.0059 2.91212
\(87\) 2.00826 0.215308
\(88\) 0.438676 0.0467630
\(89\) 4.51179 0.478249 0.239125 0.970989i \(-0.423140\pi\)
0.239125 + 0.970989i \(0.423140\pi\)
\(90\) 1.13517 0.119657
\(91\) 0 0
\(92\) 5.18201 0.540262
\(93\) −1.80066 −0.186719
\(94\) 25.3351 2.61312
\(95\) −2.52165 −0.258716
\(96\) −21.3257 −2.17654
\(97\) 12.3847 1.25748 0.628739 0.777617i \(-0.283572\pi\)
0.628739 + 0.777617i \(0.283572\pi\)
\(98\) 0 0
\(99\) −0.0467863 −0.00470220
\(100\) −26.2476 −2.62476
\(101\) 5.93765 0.590819 0.295409 0.955371i \(-0.404544\pi\)
0.295409 + 0.955371i \(0.404544\pi\)
\(102\) 15.9705 1.58131
\(103\) 11.4718 1.13035 0.565177 0.824970i \(-0.308808\pi\)
0.565177 + 0.824970i \(0.308808\pi\)
\(104\) −28.1791 −2.76319
\(105\) 0 0
\(106\) 6.71105 0.651834
\(107\) 12.0824 1.16805 0.584027 0.811734i \(-0.301476\pi\)
0.584027 + 0.811734i \(0.301476\pi\)
\(108\) 5.43794 0.523266
\(109\) −9.98086 −0.955993 −0.477996 0.878362i \(-0.658637\pi\)
−0.477996 + 0.878362i \(0.658637\pi\)
\(110\) −0.0531103 −0.00506387
\(111\) 3.23743 0.307283
\(112\) 0 0
\(113\) −14.0482 −1.32154 −0.660770 0.750589i \(-0.729770\pi\)
−0.660770 + 0.750589i \(0.729770\pi\)
\(114\) −16.5226 −1.54748
\(115\) −0.396640 −0.0369869
\(116\) 10.9208 1.01397
\(117\) 3.00540 0.277849
\(118\) 16.8758 1.55354
\(119\) 0 0
\(120\) 3.90264 0.356261
\(121\) −10.9978 −0.999801
\(122\) 27.6769 2.50575
\(123\) 1.00000 0.0901670
\(124\) −9.79187 −0.879336
\(125\) 4.09019 0.365837
\(126\) 0 0
\(127\) −2.80952 −0.249304 −0.124652 0.992201i \(-0.539782\pi\)
−0.124652 + 0.992201i \(0.539782\pi\)
\(128\) −35.8118 −3.16535
\(129\) −9.90222 −0.871842
\(130\) 3.41163 0.299220
\(131\) −8.38214 −0.732351 −0.366176 0.930546i \(-0.619333\pi\)
−0.366176 + 0.930546i \(0.619333\pi\)
\(132\) −0.254421 −0.0221445
\(133\) 0 0
\(134\) 25.9014 2.23754
\(135\) −0.416230 −0.0358234
\(136\) 54.9056 4.70812
\(137\) −22.1052 −1.88857 −0.944285 0.329128i \(-0.893245\pi\)
−0.944285 + 0.329128i \(0.893245\pi\)
\(138\) −2.59890 −0.221233
\(139\) −13.0683 −1.10844 −0.554219 0.832371i \(-0.686983\pi\)
−0.554219 + 0.832371i \(0.686983\pi\)
\(140\) 0 0
\(141\) −9.28958 −0.782324
\(142\) −12.8428 −1.07774
\(143\) −0.140612 −0.0117585
\(144\) 14.6953 1.22461
\(145\) −0.835896 −0.0694174
\(146\) 14.5819 1.20681
\(147\) 0 0
\(148\) 17.6049 1.44712
\(149\) 18.2459 1.49476 0.747382 0.664395i \(-0.231311\pi\)
0.747382 + 0.664395i \(0.231311\pi\)
\(150\) 13.1638 1.07482
\(151\) 3.74369 0.304657 0.152329 0.988330i \(-0.451323\pi\)
0.152329 + 0.988330i \(0.451323\pi\)
\(152\) −56.8038 −4.60740
\(153\) −5.85587 −0.473419
\(154\) 0 0
\(155\) 0.749487 0.0602002
\(156\) 16.3432 1.30850
\(157\) 2.17613 0.173674 0.0868370 0.996223i \(-0.472324\pi\)
0.0868370 + 0.996223i \(0.472324\pi\)
\(158\) −38.2824 −3.04559
\(159\) −2.46073 −0.195149
\(160\) 8.87638 0.701740
\(161\) 0 0
\(162\) −2.72726 −0.214274
\(163\) −3.84343 −0.301041 −0.150520 0.988607i \(-0.548095\pi\)
−0.150520 + 0.988607i \(0.548095\pi\)
\(164\) 5.43794 0.424632
\(165\) 0.0194739 0.00151604
\(166\) 8.83223 0.685514
\(167\) −10.5022 −0.812688 −0.406344 0.913720i \(-0.633197\pi\)
−0.406344 + 0.913720i \(0.633197\pi\)
\(168\) 0 0
\(169\) −3.96758 −0.305199
\(170\) −6.64739 −0.509832
\(171\) 6.05832 0.463291
\(172\) −53.8477 −4.10585
\(173\) 12.1600 0.924504 0.462252 0.886749i \(-0.347042\pi\)
0.462252 + 0.886749i \(0.347042\pi\)
\(174\) −5.47703 −0.415213
\(175\) 0 0
\(176\) −0.687541 −0.0518253
\(177\) −6.18781 −0.465104
\(178\) −12.3048 −0.922286
\(179\) 7.77291 0.580974 0.290487 0.956879i \(-0.406183\pi\)
0.290487 + 0.956879i \(0.406183\pi\)
\(180\) −2.26343 −0.168706
\(181\) 11.0255 0.819515 0.409758 0.912194i \(-0.365613\pi\)
0.409758 + 0.912194i \(0.365613\pi\)
\(182\) 0 0
\(183\) −10.1483 −0.750181
\(184\) −8.93488 −0.658688
\(185\) −1.34751 −0.0990712
\(186\) 4.91086 0.360081
\(187\) 0.273975 0.0200350
\(188\) −50.5162 −3.68427
\(189\) 0 0
\(190\) 6.87720 0.498925
\(191\) −7.32365 −0.529921 −0.264960 0.964259i \(-0.585359\pi\)
−0.264960 + 0.964259i \(0.585359\pi\)
\(192\) 28.7700 2.07629
\(193\) 1.51930 0.109362 0.0546809 0.998504i \(-0.482586\pi\)
0.0546809 + 0.998504i \(0.482586\pi\)
\(194\) −33.7763 −2.42500
\(195\) −1.25094 −0.0895814
\(196\) 0 0
\(197\) −15.3181 −1.09137 −0.545685 0.837990i \(-0.683730\pi\)
−0.545685 + 0.837990i \(0.683730\pi\)
\(198\) 0.127598 0.00906803
\(199\) −20.2178 −1.43320 −0.716599 0.697485i \(-0.754302\pi\)
−0.716599 + 0.697485i \(0.754302\pi\)
\(200\) 45.2564 3.20011
\(201\) −9.49723 −0.669883
\(202\) −16.1935 −1.13937
\(203\) 0 0
\(204\) −31.8439 −2.22952
\(205\) −0.416230 −0.0290708
\(206\) −31.2867 −2.17985
\(207\) 0.952936 0.0662336
\(208\) 44.1653 3.06232
\(209\) −0.283447 −0.0196064
\(210\) 0 0
\(211\) −19.1529 −1.31854 −0.659271 0.751906i \(-0.729135\pi\)
−0.659271 + 0.751906i \(0.729135\pi\)
\(212\) −13.3813 −0.919032
\(213\) 4.70904 0.322658
\(214\) −32.9520 −2.25255
\(215\) 4.12160 0.281091
\(216\) −9.37616 −0.637967
\(217\) 0 0
\(218\) 27.2204 1.84360
\(219\) −5.34672 −0.361298
\(220\) 0.105898 0.00713963
\(221\) −17.5992 −1.18385
\(222\) −8.82930 −0.592584
\(223\) −10.8935 −0.729481 −0.364740 0.931109i \(-0.618842\pi\)
−0.364740 + 0.931109i \(0.618842\pi\)
\(224\) 0 0
\(225\) −4.82675 −0.321784
\(226\) 38.3130 2.54854
\(227\) 1.93678 0.128549 0.0642744 0.997932i \(-0.479527\pi\)
0.0642744 + 0.997932i \(0.479527\pi\)
\(228\) 32.9448 2.18182
\(229\) −23.9066 −1.57980 −0.789898 0.613238i \(-0.789866\pi\)
−0.789898 + 0.613238i \(0.789866\pi\)
\(230\) 1.08174 0.0713279
\(231\) 0 0
\(232\) −18.8297 −1.23623
\(233\) −13.0814 −0.856989 −0.428495 0.903544i \(-0.640956\pi\)
−0.428495 + 0.903544i \(0.640956\pi\)
\(234\) −8.19650 −0.535822
\(235\) 3.86660 0.252229
\(236\) −33.6490 −2.19036
\(237\) 14.0370 0.911798
\(238\) 0 0
\(239\) −17.5892 −1.13775 −0.568876 0.822423i \(-0.692622\pi\)
−0.568876 + 0.822423i \(0.692622\pi\)
\(240\) −6.11664 −0.394827
\(241\) 24.9349 1.60620 0.803099 0.595846i \(-0.203183\pi\)
0.803099 + 0.595846i \(0.203183\pi\)
\(242\) 29.9939 1.92808
\(243\) 1.00000 0.0641500
\(244\) −55.1856 −3.53290
\(245\) 0 0
\(246\) −2.72726 −0.173884
\(247\) 18.2077 1.15853
\(248\) 16.8832 1.07209
\(249\) −3.23850 −0.205232
\(250\) −11.1550 −0.705504
\(251\) 16.0506 1.01310 0.506552 0.862209i \(-0.330920\pi\)
0.506552 + 0.862209i \(0.330920\pi\)
\(252\) 0 0
\(253\) −0.0445844 −0.00280300
\(254\) 7.66228 0.480774
\(255\) 2.43739 0.152635
\(256\) 40.1282 2.50801
\(257\) 3.53643 0.220596 0.110298 0.993899i \(-0.464819\pi\)
0.110298 + 0.993899i \(0.464819\pi\)
\(258\) 27.0059 1.68131
\(259\) 0 0
\(260\) −6.80252 −0.421874
\(261\) 2.00826 0.124308
\(262\) 22.8603 1.41231
\(263\) 21.2018 1.30736 0.653681 0.756770i \(-0.273224\pi\)
0.653681 + 0.756770i \(0.273224\pi\)
\(264\) 0.438676 0.0269987
\(265\) 1.02423 0.0629179
\(266\) 0 0
\(267\) 4.51179 0.276117
\(268\) −51.6454 −3.15475
\(269\) 6.80296 0.414784 0.207392 0.978258i \(-0.433503\pi\)
0.207392 + 0.978258i \(0.433503\pi\)
\(270\) 1.13517 0.0690840
\(271\) −0.369791 −0.0224632 −0.0112316 0.999937i \(-0.503575\pi\)
−0.0112316 + 0.999937i \(0.503575\pi\)
\(272\) −86.0541 −5.21779
\(273\) 0 0
\(274\) 60.2865 3.64204
\(275\) 0.225826 0.0136178
\(276\) 5.18201 0.311920
\(277\) 20.8105 1.25038 0.625191 0.780472i \(-0.285021\pi\)
0.625191 + 0.780472i \(0.285021\pi\)
\(278\) 35.6406 2.13758
\(279\) −1.80066 −0.107802
\(280\) 0 0
\(281\) 28.3373 1.69046 0.845232 0.534400i \(-0.179462\pi\)
0.845232 + 0.534400i \(0.179462\pi\)
\(282\) 25.3351 1.50868
\(283\) −20.3351 −1.20879 −0.604397 0.796683i \(-0.706586\pi\)
−0.604397 + 0.796683i \(0.706586\pi\)
\(284\) 25.6075 1.51952
\(285\) −2.52165 −0.149370
\(286\) 0.383484 0.0226759
\(287\) 0 0
\(288\) −21.3257 −1.25663
\(289\) 17.2913 1.01713
\(290\) 2.27970 0.133869
\(291\) 12.3847 0.726005
\(292\) −29.0751 −1.70149
\(293\) 6.54345 0.382272 0.191136 0.981564i \(-0.438783\pi\)
0.191136 + 0.981564i \(0.438783\pi\)
\(294\) 0 0
\(295\) 2.57555 0.149954
\(296\) −30.3546 −1.76433
\(297\) −0.0467863 −0.00271482
\(298\) −49.7613 −2.88260
\(299\) 2.86395 0.165627
\(300\) −26.2476 −1.51541
\(301\) 0 0
\(302\) −10.2100 −0.587520
\(303\) 5.93765 0.341109
\(304\) 89.0291 5.10617
\(305\) 4.22401 0.241866
\(306\) 15.9705 0.912972
\(307\) 27.3197 1.55922 0.779608 0.626268i \(-0.215419\pi\)
0.779608 + 0.626268i \(0.215419\pi\)
\(308\) 0 0
\(309\) 11.4718 0.652610
\(310\) −2.04404 −0.116094
\(311\) −9.86057 −0.559142 −0.279571 0.960125i \(-0.590192\pi\)
−0.279571 + 0.960125i \(0.590192\pi\)
\(312\) −28.1791 −1.59533
\(313\) −10.1230 −0.572187 −0.286094 0.958202i \(-0.592357\pi\)
−0.286094 + 0.958202i \(0.592357\pi\)
\(314\) −5.93487 −0.334924
\(315\) 0 0
\(316\) 76.3322 4.29402
\(317\) −25.6530 −1.44082 −0.720409 0.693549i \(-0.756046\pi\)
−0.720409 + 0.693549i \(0.756046\pi\)
\(318\) 6.71105 0.376337
\(319\) −0.0939589 −0.00526069
\(320\) −11.9749 −0.669418
\(321\) 12.0824 0.674376
\(322\) 0 0
\(323\) −35.4768 −1.97398
\(324\) 5.43794 0.302108
\(325\) −14.5063 −0.804666
\(326\) 10.4820 0.580546
\(327\) −9.98086 −0.551943
\(328\) −9.37616 −0.517712
\(329\) 0 0
\(330\) −0.0531103 −0.00292362
\(331\) −1.38318 −0.0760264 −0.0380132 0.999277i \(-0.512103\pi\)
−0.0380132 + 0.999277i \(0.512103\pi\)
\(332\) −17.6108 −0.966517
\(333\) 3.23743 0.177410
\(334\) 28.6423 1.56724
\(335\) 3.95303 0.215977
\(336\) 0 0
\(337\) 15.4787 0.843177 0.421588 0.906787i \(-0.361473\pi\)
0.421588 + 0.906787i \(0.361473\pi\)
\(338\) 10.8206 0.588564
\(339\) −14.0482 −0.762991
\(340\) 13.2544 0.718820
\(341\) 0.0842461 0.00456218
\(342\) −16.5226 −0.893440
\(343\) 0 0
\(344\) 92.8448 5.00586
\(345\) −0.396640 −0.0213544
\(346\) −33.1633 −1.78287
\(347\) −10.2007 −0.547604 −0.273802 0.961786i \(-0.588281\pi\)
−0.273802 + 0.961786i \(0.588281\pi\)
\(348\) 10.9208 0.585415
\(349\) −19.2750 −1.03177 −0.515883 0.856659i \(-0.672536\pi\)
−0.515883 + 0.856659i \(0.672536\pi\)
\(350\) 0 0
\(351\) 3.00540 0.160416
\(352\) 0.997750 0.0531803
\(353\) −36.6606 −1.95125 −0.975624 0.219450i \(-0.929574\pi\)
−0.975624 + 0.219450i \(0.929574\pi\)
\(354\) 16.8758 0.896937
\(355\) −1.96004 −0.104028
\(356\) 24.5349 1.30035
\(357\) 0 0
\(358\) −21.1987 −1.12039
\(359\) 30.4236 1.60570 0.802849 0.596182i \(-0.203316\pi\)
0.802849 + 0.596182i \(0.203316\pi\)
\(360\) 3.90264 0.205687
\(361\) 17.7032 0.931750
\(362\) −30.0693 −1.58041
\(363\) −10.9978 −0.577235
\(364\) 0 0
\(365\) 2.22546 0.116486
\(366\) 27.6769 1.44670
\(367\) 10.5725 0.551882 0.275941 0.961175i \(-0.411011\pi\)
0.275941 + 0.961175i \(0.411011\pi\)
\(368\) 14.0037 0.729994
\(369\) 1.00000 0.0520579
\(370\) 3.67502 0.191055
\(371\) 0 0
\(372\) −9.79187 −0.507685
\(373\) 12.4721 0.645783 0.322892 0.946436i \(-0.395345\pi\)
0.322892 + 0.946436i \(0.395345\pi\)
\(374\) −0.747200 −0.0386368
\(375\) 4.09019 0.211216
\(376\) 87.1006 4.49187
\(377\) 6.03561 0.310850
\(378\) 0 0
\(379\) −5.18412 −0.266290 −0.133145 0.991097i \(-0.542508\pi\)
−0.133145 + 0.991097i \(0.542508\pi\)
\(380\) −13.7126 −0.703442
\(381\) −2.80952 −0.143936
\(382\) 19.9735 1.02193
\(383\) −25.0431 −1.27964 −0.639821 0.768524i \(-0.720992\pi\)
−0.639821 + 0.768524i \(0.720992\pi\)
\(384\) −35.8118 −1.82751
\(385\) 0 0
\(386\) −4.14353 −0.210900
\(387\) −9.90222 −0.503358
\(388\) 67.3474 3.41904
\(389\) 26.7641 1.35699 0.678496 0.734604i \(-0.262632\pi\)
0.678496 + 0.734604i \(0.262632\pi\)
\(390\) 3.41163 0.172754
\(391\) −5.58027 −0.282207
\(392\) 0 0
\(393\) −8.38214 −0.422823
\(394\) 41.7764 2.10467
\(395\) −5.84260 −0.293973
\(396\) −0.254421 −0.0127852
\(397\) 24.8660 1.24799 0.623993 0.781430i \(-0.285509\pi\)
0.623993 + 0.781430i \(0.285509\pi\)
\(398\) 55.1391 2.76387
\(399\) 0 0
\(400\) −70.9308 −3.54654
\(401\) −35.9364 −1.79458 −0.897288 0.441446i \(-0.854466\pi\)
−0.897288 + 0.441446i \(0.854466\pi\)
\(402\) 25.9014 1.29185
\(403\) −5.41169 −0.269575
\(404\) 32.2886 1.60642
\(405\) −0.416230 −0.0206826
\(406\) 0 0
\(407\) −0.151467 −0.00750796
\(408\) 54.9056 2.71823
\(409\) −17.2575 −0.853328 −0.426664 0.904410i \(-0.640311\pi\)
−0.426664 + 0.904410i \(0.640311\pi\)
\(410\) 1.13517 0.0560619
\(411\) −22.1052 −1.09037
\(412\) 62.3832 3.07340
\(413\) 0 0
\(414\) −2.59890 −0.127729
\(415\) 1.34796 0.0661688
\(416\) −64.0921 −3.14238
\(417\) −13.0683 −0.639957
\(418\) 0.773032 0.0378102
\(419\) −5.11135 −0.249706 −0.124853 0.992175i \(-0.539846\pi\)
−0.124853 + 0.992175i \(0.539846\pi\)
\(420\) 0 0
\(421\) −19.6763 −0.958965 −0.479482 0.877551i \(-0.659176\pi\)
−0.479482 + 0.877551i \(0.659176\pi\)
\(422\) 52.2350 2.54276
\(423\) −9.28958 −0.451675
\(424\) 23.0722 1.12048
\(425\) 28.2649 1.37105
\(426\) −12.8428 −0.622234
\(427\) 0 0
\(428\) 65.7036 3.17591
\(429\) −0.140612 −0.00678879
\(430\) −11.2407 −0.542073
\(431\) −41.3547 −1.99198 −0.995992 0.0894383i \(-0.971493\pi\)
−0.995992 + 0.0894383i \(0.971493\pi\)
\(432\) 14.6953 0.707030
\(433\) 27.9849 1.34487 0.672435 0.740156i \(-0.265249\pi\)
0.672435 + 0.740156i \(0.265249\pi\)
\(434\) 0 0
\(435\) −0.835896 −0.0400781
\(436\) −54.2753 −2.59932
\(437\) 5.77319 0.276169
\(438\) 14.5819 0.696749
\(439\) 15.6955 0.749104 0.374552 0.927206i \(-0.377797\pi\)
0.374552 + 0.927206i \(0.377797\pi\)
\(440\) −0.182590 −0.00870464
\(441\) 0 0
\(442\) 47.9977 2.28302
\(443\) −35.8815 −1.70478 −0.852390 0.522906i \(-0.824848\pi\)
−0.852390 + 0.522906i \(0.824848\pi\)
\(444\) 17.6049 0.835494
\(445\) −1.87794 −0.0890230
\(446\) 29.7093 1.40678
\(447\) 18.2459 0.863002
\(448\) 0 0
\(449\) 12.8859 0.608123 0.304061 0.952652i \(-0.401657\pi\)
0.304061 + 0.952652i \(0.401657\pi\)
\(450\) 13.1638 0.620548
\(451\) −0.0467863 −0.00220308
\(452\) −76.3931 −3.59323
\(453\) 3.74369 0.175894
\(454\) −5.28211 −0.247902
\(455\) 0 0
\(456\) −56.8038 −2.66008
\(457\) −33.7488 −1.57870 −0.789351 0.613942i \(-0.789583\pi\)
−0.789351 + 0.613942i \(0.789583\pi\)
\(458\) 65.1996 3.04658
\(459\) −5.85587 −0.273329
\(460\) −2.15691 −0.100566
\(461\) 14.3109 0.666523 0.333262 0.942834i \(-0.391851\pi\)
0.333262 + 0.942834i \(0.391851\pi\)
\(462\) 0 0
\(463\) −26.1933 −1.21731 −0.608654 0.793436i \(-0.708290\pi\)
−0.608654 + 0.793436i \(0.708290\pi\)
\(464\) 29.5120 1.37006
\(465\) 0.749487 0.0347566
\(466\) 35.6763 1.65267
\(467\) 22.3888 1.03603 0.518014 0.855372i \(-0.326671\pi\)
0.518014 + 0.855372i \(0.326671\pi\)
\(468\) 16.3432 0.755464
\(469\) 0 0
\(470\) −10.5452 −0.486415
\(471\) 2.17613 0.100271
\(472\) 58.0179 2.67049
\(473\) 0.463288 0.0213020
\(474\) −38.2824 −1.75837
\(475\) −29.2420 −1.34172
\(476\) 0 0
\(477\) −2.46073 −0.112669
\(478\) 47.9703 2.19411
\(479\) −12.0786 −0.551887 −0.275943 0.961174i \(-0.588990\pi\)
−0.275943 + 0.961174i \(0.588990\pi\)
\(480\) 8.87638 0.405150
\(481\) 9.72976 0.443639
\(482\) −68.0039 −3.09749
\(483\) 0 0
\(484\) −59.8055 −2.71843
\(485\) −5.15489 −0.234071
\(486\) −2.72726 −0.123711
\(487\) 24.1912 1.09621 0.548104 0.836410i \(-0.315350\pi\)
0.548104 + 0.836410i \(0.315350\pi\)
\(488\) 95.1517 4.30731
\(489\) −3.84343 −0.173806
\(490\) 0 0
\(491\) 6.30741 0.284650 0.142325 0.989820i \(-0.454542\pi\)
0.142325 + 0.989820i \(0.454542\pi\)
\(492\) 5.43794 0.245161
\(493\) −11.7601 −0.529648
\(494\) −49.6570 −2.23418
\(495\) 0.0194739 0.000875285 0
\(496\) −26.4613 −1.18815
\(497\) 0 0
\(498\) 8.83223 0.395782
\(499\) −37.1859 −1.66467 −0.832335 0.554273i \(-0.812996\pi\)
−0.832335 + 0.554273i \(0.812996\pi\)
\(500\) 22.2422 0.994702
\(501\) −10.5022 −0.469206
\(502\) −43.7741 −1.95373
\(503\) 6.02057 0.268444 0.134222 0.990951i \(-0.457147\pi\)
0.134222 + 0.990951i \(0.457147\pi\)
\(504\) 0 0
\(505\) −2.47143 −0.109977
\(506\) 0.121593 0.00540547
\(507\) −3.96758 −0.176206
\(508\) −15.2780 −0.677851
\(509\) 19.2491 0.853200 0.426600 0.904440i \(-0.359711\pi\)
0.426600 + 0.904440i \(0.359711\pi\)
\(510\) −6.64739 −0.294352
\(511\) 0 0
\(512\) −37.8163 −1.67126
\(513\) 6.05832 0.267481
\(514\) −9.64476 −0.425412
\(515\) −4.77492 −0.210408
\(516\) −53.8477 −2.37051
\(517\) 0.434625 0.0191148
\(518\) 0 0
\(519\) 12.1600 0.533763
\(520\) 11.7290 0.514350
\(521\) −27.9157 −1.22301 −0.611505 0.791241i \(-0.709436\pi\)
−0.611505 + 0.791241i \(0.709436\pi\)
\(522\) −5.47703 −0.239723
\(523\) 14.1196 0.617408 0.308704 0.951158i \(-0.400105\pi\)
0.308704 + 0.951158i \(0.400105\pi\)
\(524\) −45.5816 −1.99124
\(525\) 0 0
\(526\) −57.8229 −2.52120
\(527\) 10.5444 0.459322
\(528\) −0.687541 −0.0299214
\(529\) −22.0919 −0.960518
\(530\) −2.79334 −0.121335
\(531\) −6.18781 −0.268528
\(532\) 0 0
\(533\) 3.00540 0.130178
\(534\) −12.3048 −0.532482
\(535\) −5.02907 −0.217426
\(536\) 89.0476 3.84627
\(537\) 7.77291 0.335426
\(538\) −18.5534 −0.799895
\(539\) 0 0
\(540\) −2.26343 −0.0974027
\(541\) 32.0222 1.37674 0.688370 0.725360i \(-0.258327\pi\)
0.688370 + 0.725360i \(0.258327\pi\)
\(542\) 1.00852 0.0433195
\(543\) 11.0255 0.473147
\(544\) 124.880 5.35421
\(545\) 4.15433 0.177952
\(546\) 0 0
\(547\) −16.2757 −0.695897 −0.347949 0.937514i \(-0.613122\pi\)
−0.347949 + 0.937514i \(0.613122\pi\)
\(548\) −120.207 −5.13497
\(549\) −10.1483 −0.433117
\(550\) −0.615886 −0.0262615
\(551\) 12.1667 0.518317
\(552\) −8.93488 −0.380294
\(553\) 0 0
\(554\) −56.7557 −2.41132
\(555\) −1.34751 −0.0571988
\(556\) −71.0646 −3.01381
\(557\) −13.4419 −0.569552 −0.284776 0.958594i \(-0.591919\pi\)
−0.284776 + 0.958594i \(0.591919\pi\)
\(558\) 4.91086 0.207893
\(559\) −29.7601 −1.25872
\(560\) 0 0
\(561\) 0.273975 0.0115672
\(562\) −77.2832 −3.26000
\(563\) −16.0633 −0.676988 −0.338494 0.940969i \(-0.609917\pi\)
−0.338494 + 0.940969i \(0.609917\pi\)
\(564\) −50.5162 −2.12712
\(565\) 5.84726 0.245996
\(566\) 55.4590 2.33112
\(567\) 0 0
\(568\) −44.1527 −1.85261
\(569\) 14.8609 0.623001 0.311501 0.950246i \(-0.399168\pi\)
0.311501 + 0.950246i \(0.399168\pi\)
\(570\) 6.87720 0.288054
\(571\) 10.1204 0.423526 0.211763 0.977321i \(-0.432079\pi\)
0.211763 + 0.977321i \(0.432079\pi\)
\(572\) −0.764638 −0.0319711
\(573\) −7.32365 −0.305950
\(574\) 0 0
\(575\) −4.59959 −0.191816
\(576\) 28.7700 1.19875
\(577\) 6.51473 0.271212 0.135606 0.990763i \(-0.456702\pi\)
0.135606 + 0.990763i \(0.456702\pi\)
\(578\) −47.1578 −1.96151
\(579\) 1.51930 0.0631401
\(580\) −4.54555 −0.188744
\(581\) 0 0
\(582\) −33.7763 −1.40007
\(583\) 0.115128 0.00476813
\(584\) 50.1317 2.07446
\(585\) −1.25094 −0.0517199
\(586\) −17.8457 −0.737198
\(587\) 43.9501 1.81402 0.907008 0.421113i \(-0.138360\pi\)
0.907008 + 0.421113i \(0.138360\pi\)
\(588\) 0 0
\(589\) −10.9090 −0.449496
\(590\) −7.02419 −0.289182
\(591\) −15.3181 −0.630103
\(592\) 47.5751 1.95532
\(593\) 18.3336 0.752873 0.376436 0.926443i \(-0.377149\pi\)
0.376436 + 0.926443i \(0.377149\pi\)
\(594\) 0.127598 0.00523543
\(595\) 0 0
\(596\) 99.2202 4.06422
\(597\) −20.2178 −0.827458
\(598\) −7.81074 −0.319405
\(599\) −33.2968 −1.36047 −0.680234 0.732995i \(-0.738122\pi\)
−0.680234 + 0.732995i \(0.738122\pi\)
\(600\) 45.2564 1.84759
\(601\) −10.6328 −0.433720 −0.216860 0.976203i \(-0.569582\pi\)
−0.216860 + 0.976203i \(0.569582\pi\)
\(602\) 0 0
\(603\) −9.49723 −0.386757
\(604\) 20.3580 0.828354
\(605\) 4.57762 0.186107
\(606\) −16.1935 −0.657817
\(607\) −40.0459 −1.62541 −0.812706 0.582674i \(-0.802007\pi\)
−0.812706 + 0.582674i \(0.802007\pi\)
\(608\) −129.198 −5.23966
\(609\) 0 0
\(610\) −11.5200 −0.466430
\(611\) −27.9189 −1.12948
\(612\) −31.8439 −1.28721
\(613\) −29.4237 −1.18841 −0.594207 0.804312i \(-0.702534\pi\)
−0.594207 + 0.804312i \(0.702534\pi\)
\(614\) −74.5078 −3.00689
\(615\) −0.416230 −0.0167840
\(616\) 0 0
\(617\) 17.7795 0.715775 0.357888 0.933765i \(-0.383497\pi\)
0.357888 + 0.933765i \(0.383497\pi\)
\(618\) −31.2867 −1.25853
\(619\) 42.7487 1.71822 0.859109 0.511793i \(-0.171019\pi\)
0.859109 + 0.511793i \(0.171019\pi\)
\(620\) 4.07567 0.163683
\(621\) 0.952936 0.0382400
\(622\) 26.8923 1.07828
\(623\) 0 0
\(624\) 44.1653 1.76803
\(625\) 22.4313 0.897252
\(626\) 27.6081 1.10344
\(627\) −0.283447 −0.0113198
\(628\) 11.8337 0.472215
\(629\) −18.9580 −0.755904
\(630\) 0 0
\(631\) −12.1892 −0.485245 −0.242622 0.970121i \(-0.578008\pi\)
−0.242622 + 0.970121i \(0.578008\pi\)
\(632\) −131.613 −5.23528
\(633\) −19.1529 −0.761260
\(634\) 69.9625 2.77857
\(635\) 1.16940 0.0464064
\(636\) −13.3813 −0.530603
\(637\) 0 0
\(638\) 0.256250 0.0101450
\(639\) 4.70904 0.186287
\(640\) 14.9059 0.589209
\(641\) −30.9625 −1.22295 −0.611473 0.791265i \(-0.709423\pi\)
−0.611473 + 0.791265i \(0.709423\pi\)
\(642\) −32.9520 −1.30051
\(643\) 31.7205 1.25094 0.625468 0.780250i \(-0.284908\pi\)
0.625468 + 0.780250i \(0.284908\pi\)
\(644\) 0 0
\(645\) 4.12160 0.162288
\(646\) 96.7543 3.80675
\(647\) −4.13242 −0.162462 −0.0812311 0.996695i \(-0.525885\pi\)
−0.0812311 + 0.996695i \(0.525885\pi\)
\(648\) −9.37616 −0.368330
\(649\) 0.289505 0.0113641
\(650\) 39.5625 1.55177
\(651\) 0 0
\(652\) −20.9004 −0.818521
\(653\) −21.6772 −0.848293 −0.424147 0.905593i \(-0.639426\pi\)
−0.424147 + 0.905593i \(0.639426\pi\)
\(654\) 27.2204 1.06440
\(655\) 3.48890 0.136323
\(656\) 14.6953 0.573757
\(657\) −5.34672 −0.208595
\(658\) 0 0
\(659\) 38.7978 1.51135 0.755673 0.654949i \(-0.227310\pi\)
0.755673 + 0.654949i \(0.227310\pi\)
\(660\) 0.105898 0.00412206
\(661\) −20.2968 −0.789455 −0.394728 0.918798i \(-0.629161\pi\)
−0.394728 + 0.918798i \(0.629161\pi\)
\(662\) 3.77229 0.146614
\(663\) −17.5992 −0.683498
\(664\) 30.3647 1.17838
\(665\) 0 0
\(666\) −8.82930 −0.342129
\(667\) 1.91374 0.0741003
\(668\) −57.1106 −2.20968
\(669\) −10.8935 −0.421166
\(670\) −10.7809 −0.416504
\(671\) 0.474800 0.0183294
\(672\) 0 0
\(673\) −38.4819 −1.48337 −0.741684 0.670750i \(-0.765972\pi\)
−0.741684 + 0.670750i \(0.765972\pi\)
\(674\) −42.2143 −1.62604
\(675\) −4.82675 −0.185782
\(676\) −21.5755 −0.829826
\(677\) 34.3408 1.31982 0.659911 0.751343i \(-0.270594\pi\)
0.659911 + 0.751343i \(0.270594\pi\)
\(678\) 38.3130 1.47140
\(679\) 0 0
\(680\) −22.8534 −0.876386
\(681\) 1.93678 0.0742176
\(682\) −0.229761 −0.00879800
\(683\) −46.7531 −1.78896 −0.894479 0.447109i \(-0.852454\pi\)
−0.894479 + 0.447109i \(0.852454\pi\)
\(684\) 32.9448 1.25968
\(685\) 9.20082 0.351545
\(686\) 0 0
\(687\) −23.9066 −0.912096
\(688\) −145.516 −5.54776
\(689\) −7.39547 −0.281745
\(690\) 1.08174 0.0411812
\(691\) 0.631161 0.0240105 0.0120052 0.999928i \(-0.496179\pi\)
0.0120052 + 0.999928i \(0.496179\pi\)
\(692\) 66.1251 2.51370
\(693\) 0 0
\(694\) 27.8200 1.05603
\(695\) 5.43941 0.206329
\(696\) −18.8297 −0.713739
\(697\) −5.85587 −0.221807
\(698\) 52.5678 1.98972
\(699\) −13.0814 −0.494783
\(700\) 0 0
\(701\) −18.3514 −0.693122 −0.346561 0.938027i \(-0.612651\pi\)
−0.346561 + 0.938027i \(0.612651\pi\)
\(702\) −8.19650 −0.309357
\(703\) 19.6134 0.739732
\(704\) −1.34604 −0.0507308
\(705\) 3.86660 0.145625
\(706\) 99.9830 3.76291
\(707\) 0 0
\(708\) −33.6490 −1.26461
\(709\) −50.9531 −1.91358 −0.956791 0.290776i \(-0.906086\pi\)
−0.956791 + 0.290776i \(0.906086\pi\)
\(710\) 5.34554 0.200615
\(711\) 14.0370 0.526427
\(712\) −42.3033 −1.58538
\(713\) −1.71591 −0.0642613
\(714\) 0 0
\(715\) 0.0585267 0.00218878
\(716\) 42.2686 1.57965
\(717\) −17.5892 −0.656881
\(718\) −82.9731 −3.09653
\(719\) −31.7735 −1.18495 −0.592475 0.805588i \(-0.701849\pi\)
−0.592475 + 0.805588i \(0.701849\pi\)
\(720\) −6.11664 −0.227954
\(721\) 0 0
\(722\) −48.2813 −1.79685
\(723\) 24.9349 0.927339
\(724\) 59.9558 2.22824
\(725\) −9.69335 −0.360002
\(726\) 29.9939 1.11318
\(727\) −14.2783 −0.529551 −0.264776 0.964310i \(-0.585298\pi\)
−0.264776 + 0.964310i \(0.585298\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −6.06942 −0.224639
\(731\) 57.9861 2.14469
\(732\) −55.1856 −2.03972
\(733\) −34.2139 −1.26372 −0.631861 0.775082i \(-0.717708\pi\)
−0.631861 + 0.775082i \(0.717708\pi\)
\(734\) −28.8340 −1.06428
\(735\) 0 0
\(736\) −20.3220 −0.749079
\(737\) 0.444341 0.0163675
\(738\) −2.72726 −0.100392
\(739\) −29.2298 −1.07524 −0.537619 0.843188i \(-0.680676\pi\)
−0.537619 + 0.843188i \(0.680676\pi\)
\(740\) −7.32770 −0.269372
\(741\) 18.2077 0.668875
\(742\) 0 0
\(743\) −28.0271 −1.02821 −0.514107 0.857726i \(-0.671876\pi\)
−0.514107 + 0.857726i \(0.671876\pi\)
\(744\) 16.8832 0.618970
\(745\) −7.59449 −0.278241
\(746\) −34.0148 −1.24537
\(747\) −3.23850 −0.118491
\(748\) 1.48986 0.0544747
\(749\) 0 0
\(750\) −11.1550 −0.407323
\(751\) 34.5204 1.25967 0.629834 0.776730i \(-0.283123\pi\)
0.629834 + 0.776730i \(0.283123\pi\)
\(752\) −136.514 −4.97814
\(753\) 16.0506 0.584916
\(754\) −16.4607 −0.599462
\(755\) −1.55824 −0.0567100
\(756\) 0 0
\(757\) −43.9296 −1.59665 −0.798325 0.602227i \(-0.794280\pi\)
−0.798325 + 0.602227i \(0.794280\pi\)
\(758\) 14.1384 0.513531
\(759\) −0.0445844 −0.00161831
\(760\) 23.6434 0.857637
\(761\) −31.2348 −1.13226 −0.566131 0.824315i \(-0.691560\pi\)
−0.566131 + 0.824315i \(0.691560\pi\)
\(762\) 7.66228 0.277575
\(763\) 0 0
\(764\) −39.8256 −1.44084
\(765\) 2.43739 0.0881240
\(766\) 68.2990 2.46774
\(767\) −18.5968 −0.671493
\(768\) 40.1282 1.44800
\(769\) 40.3776 1.45606 0.728028 0.685548i \(-0.240437\pi\)
0.728028 + 0.685548i \(0.240437\pi\)
\(770\) 0 0
\(771\) 3.53643 0.127361
\(772\) 8.26188 0.297352
\(773\) 28.0706 1.00963 0.504814 0.863228i \(-0.331561\pi\)
0.504814 + 0.863228i \(0.331561\pi\)
\(774\) 27.0059 0.970707
\(775\) 8.69132 0.312202
\(776\) −116.121 −4.16850
\(777\) 0 0
\(778\) −72.9926 −2.61691
\(779\) 6.05832 0.217062
\(780\) −6.80252 −0.243569
\(781\) −0.220319 −0.00788362
\(782\) 15.2189 0.544225
\(783\) 2.00826 0.0717692
\(784\) 0 0
\(785\) −0.905770 −0.0323283
\(786\) 22.8603 0.815399
\(787\) −40.3706 −1.43906 −0.719529 0.694462i \(-0.755642\pi\)
−0.719529 + 0.694462i \(0.755642\pi\)
\(788\) −83.2990 −2.96740
\(789\) 21.2018 0.754806
\(790\) 15.9343 0.566916
\(791\) 0 0
\(792\) 0.438676 0.0155877
\(793\) −30.4996 −1.08307
\(794\) −67.8159 −2.40670
\(795\) 1.02423 0.0363257
\(796\) −109.943 −3.89683
\(797\) −8.74108 −0.309625 −0.154812 0.987944i \(-0.549477\pi\)
−0.154812 + 0.987944i \(0.549477\pi\)
\(798\) 0 0
\(799\) 54.3986 1.92449
\(800\) 102.934 3.63926
\(801\) 4.51179 0.159416
\(802\) 98.0077 3.46077
\(803\) 0.250153 0.00882772
\(804\) −51.6454 −1.82139
\(805\) 0 0
\(806\) 14.7591 0.519866
\(807\) 6.80296 0.239475
\(808\) −55.6724 −1.95855
\(809\) 6.74812 0.237251 0.118626 0.992939i \(-0.462151\pi\)
0.118626 + 0.992939i \(0.462151\pi\)
\(810\) 1.13517 0.0398857
\(811\) 30.3742 1.06658 0.533291 0.845932i \(-0.320955\pi\)
0.533291 + 0.845932i \(0.320955\pi\)
\(812\) 0 0
\(813\) −0.369791 −0.0129691
\(814\) 0.413091 0.0144788
\(815\) 1.59975 0.0560368
\(816\) −86.0541 −3.01249
\(817\) −59.9908 −2.09881
\(818\) 47.0657 1.64561
\(819\) 0 0
\(820\) −2.26343 −0.0790425
\(821\) 28.1089 0.981008 0.490504 0.871439i \(-0.336813\pi\)
0.490504 + 0.871439i \(0.336813\pi\)
\(822\) 60.2865 2.10273
\(823\) 29.3386 1.02268 0.511339 0.859379i \(-0.329150\pi\)
0.511339 + 0.859379i \(0.329150\pi\)
\(824\) −107.562 −3.74709
\(825\) 0.225826 0.00786225
\(826\) 0 0
\(827\) −6.75490 −0.234891 −0.117445 0.993079i \(-0.537471\pi\)
−0.117445 + 0.993079i \(0.537471\pi\)
\(828\) 5.18201 0.180087
\(829\) 46.2748 1.60719 0.803595 0.595176i \(-0.202918\pi\)
0.803595 + 0.595176i \(0.202918\pi\)
\(830\) −3.67624 −0.127604
\(831\) 20.8105 0.721909
\(832\) 86.4652 2.99764
\(833\) 0 0
\(834\) 35.6406 1.23413
\(835\) 4.37135 0.151277
\(836\) −1.54137 −0.0533093
\(837\) −1.80066 −0.0622398
\(838\) 13.9400 0.481548
\(839\) −22.2264 −0.767340 −0.383670 0.923470i \(-0.625340\pi\)
−0.383670 + 0.923470i \(0.625340\pi\)
\(840\) 0 0
\(841\) −24.9669 −0.860928
\(842\) 53.6624 1.84933
\(843\) 28.3373 0.975989
\(844\) −104.152 −3.58508
\(845\) 1.65143 0.0568108
\(846\) 25.3351 0.871039
\(847\) 0 0
\(848\) −36.1613 −1.24178
\(849\) −20.3351 −0.697898
\(850\) −77.0856 −2.64401
\(851\) 3.08506 0.105755
\(852\) 25.6075 0.877298
\(853\) −32.4363 −1.11060 −0.555298 0.831651i \(-0.687396\pi\)
−0.555298 + 0.831651i \(0.687396\pi\)
\(854\) 0 0
\(855\) −2.52165 −0.0862387
\(856\) −113.287 −3.87207
\(857\) 18.7376 0.640063 0.320031 0.947407i \(-0.396307\pi\)
0.320031 + 0.947407i \(0.396307\pi\)
\(858\) 0.383484 0.0130919
\(859\) 6.87509 0.234575 0.117288 0.993098i \(-0.462580\pi\)
0.117288 + 0.993098i \(0.462580\pi\)
\(860\) 22.4130 0.764277
\(861\) 0 0
\(862\) 112.785 3.84147
\(863\) −23.0107 −0.783292 −0.391646 0.920116i \(-0.628094\pi\)
−0.391646 + 0.920116i \(0.628094\pi\)
\(864\) −21.3257 −0.725514
\(865\) −5.06133 −0.172091
\(866\) −76.3221 −2.59353
\(867\) 17.2913 0.587242
\(868\) 0 0
\(869\) −0.656738 −0.0222783
\(870\) 2.27970 0.0772892
\(871\) −28.5430 −0.967142
\(872\) 93.5821 3.16909
\(873\) 12.3847 0.419159
\(874\) −15.7450 −0.532582
\(875\) 0 0
\(876\) −29.0751 −0.982358
\(877\) −46.3732 −1.56591 −0.782955 0.622078i \(-0.786289\pi\)
−0.782955 + 0.622078i \(0.786289\pi\)
\(878\) −42.8056 −1.44462
\(879\) 6.54345 0.220705
\(880\) 0.286175 0.00964696
\(881\) 10.6982 0.360431 0.180216 0.983627i \(-0.442320\pi\)
0.180216 + 0.983627i \(0.442320\pi\)
\(882\) 0 0
\(883\) 21.2931 0.716569 0.358285 0.933612i \(-0.383362\pi\)
0.358285 + 0.933612i \(0.383362\pi\)
\(884\) −95.7036 −3.21886
\(885\) 2.57555 0.0865762
\(886\) 97.8581 3.28761
\(887\) −16.7878 −0.563678 −0.281839 0.959462i \(-0.590944\pi\)
−0.281839 + 0.959462i \(0.590944\pi\)
\(888\) −30.3546 −1.01864
\(889\) 0 0
\(890\) 5.12164 0.171678
\(891\) −0.0467863 −0.00156740
\(892\) −59.2381 −1.98344
\(893\) −56.2793 −1.88331
\(894\) −49.7613 −1.66427
\(895\) −3.23532 −0.108145
\(896\) 0 0
\(897\) 2.86395 0.0956246
\(898\) −35.1432 −1.17274
\(899\) −3.61618 −0.120606
\(900\) −26.2476 −0.874920
\(901\) 14.4097 0.480057
\(902\) 0.127598 0.00424856
\(903\) 0 0
\(904\) 131.718 4.38087
\(905\) −4.58912 −0.152548
\(906\) −10.2100 −0.339205
\(907\) 32.9902 1.09542 0.547711 0.836667i \(-0.315499\pi\)
0.547711 + 0.836667i \(0.315499\pi\)
\(908\) 10.5321 0.349520
\(909\) 5.93765 0.196940
\(910\) 0 0
\(911\) 39.6694 1.31431 0.657154 0.753757i \(-0.271760\pi\)
0.657154 + 0.753757i \(0.271760\pi\)
\(912\) 89.0291 2.94805
\(913\) 0.151518 0.00501450
\(914\) 92.0417 3.04447
\(915\) 4.22401 0.139641
\(916\) −130.003 −4.29542
\(917\) 0 0
\(918\) 15.9705 0.527105
\(919\) −36.6457 −1.20883 −0.604415 0.796669i \(-0.706593\pi\)
−0.604415 + 0.796669i \(0.706593\pi\)
\(920\) 3.71896 0.122611
\(921\) 27.3197 0.900213
\(922\) −39.0294 −1.28537
\(923\) 14.1525 0.465837
\(924\) 0 0
\(925\) −15.6263 −0.513788
\(926\) 71.4361 2.34753
\(927\) 11.4718 0.376785
\(928\) −42.8274 −1.40588
\(929\) −48.7399 −1.59911 −0.799553 0.600596i \(-0.794930\pi\)
−0.799553 + 0.600596i \(0.794930\pi\)
\(930\) −2.04404 −0.0670269
\(931\) 0 0
\(932\) −71.1358 −2.33013
\(933\) −9.86057 −0.322821
\(934\) −61.0600 −1.99794
\(935\) −0.114037 −0.00372939
\(936\) −28.1791 −0.921063
\(937\) 40.9631 1.33821 0.669103 0.743170i \(-0.266679\pi\)
0.669103 + 0.743170i \(0.266679\pi\)
\(938\) 0 0
\(939\) −10.1230 −0.330352
\(940\) 21.0264 0.685804
\(941\) 10.7987 0.352026 0.176013 0.984388i \(-0.443680\pi\)
0.176013 + 0.984388i \(0.443680\pi\)
\(942\) −5.93487 −0.193368
\(943\) 0.952936 0.0310319
\(944\) −90.9320 −2.95958
\(945\) 0 0
\(946\) −1.26351 −0.0410802
\(947\) 10.4430 0.339351 0.169676 0.985500i \(-0.445728\pi\)
0.169676 + 0.985500i \(0.445728\pi\)
\(948\) 76.3322 2.47915
\(949\) −16.0690 −0.521622
\(950\) 79.7506 2.58745
\(951\) −25.6530 −0.831857
\(952\) 0 0
\(953\) −9.99144 −0.323655 −0.161827 0.986819i \(-0.551739\pi\)
−0.161827 + 0.986819i \(0.551739\pi\)
\(954\) 6.71105 0.217278
\(955\) 3.04832 0.0986413
\(956\) −95.6491 −3.09351
\(957\) −0.0939589 −0.00303726
\(958\) 32.9415 1.06429
\(959\) 0 0
\(960\) −11.9749 −0.386489
\(961\) −27.7576 −0.895408
\(962\) −26.5356 −0.855541
\(963\) 12.0824 0.389351
\(964\) 135.595 4.36721
\(965\) −0.632379 −0.0203570
\(966\) 0 0
\(967\) −47.6624 −1.53272 −0.766360 0.642411i \(-0.777934\pi\)
−0.766360 + 0.642411i \(0.777934\pi\)
\(968\) 103.117 3.31431
\(969\) −35.4768 −1.13968
\(970\) 14.0587 0.451398
\(971\) 55.4444 1.77929 0.889647 0.456649i \(-0.150950\pi\)
0.889647 + 0.456649i \(0.150950\pi\)
\(972\) 5.43794 0.174422
\(973\) 0 0
\(974\) −65.9757 −2.11400
\(975\) −14.5063 −0.464574
\(976\) −149.132 −4.77360
\(977\) 2.47040 0.0790352 0.0395176 0.999219i \(-0.487418\pi\)
0.0395176 + 0.999219i \(0.487418\pi\)
\(978\) 10.4820 0.335178
\(979\) −0.211090 −0.00674647
\(980\) 0 0
\(981\) −9.98086 −0.318664
\(982\) −17.2019 −0.548936
\(983\) −7.12844 −0.227362 −0.113681 0.993517i \(-0.536264\pi\)
−0.113681 + 0.993517i \(0.536264\pi\)
\(984\) −9.37616 −0.298901
\(985\) 6.37585 0.203152
\(986\) 32.0728 1.02141
\(987\) 0 0
\(988\) 99.0123 3.15000
\(989\) −9.43618 −0.300053
\(990\) −0.0531103 −0.00168796
\(991\) −28.3333 −0.900037 −0.450019 0.893019i \(-0.648583\pi\)
−0.450019 + 0.893019i \(0.648583\pi\)
\(992\) 38.4002 1.21921
\(993\) −1.38318 −0.0438939
\(994\) 0 0
\(995\) 8.41523 0.266781
\(996\) −17.6108 −0.558019
\(997\) −42.5700 −1.34821 −0.674103 0.738637i \(-0.735470\pi\)
−0.674103 + 0.738637i \(0.735470\pi\)
\(998\) 101.416 3.21026
\(999\) 3.23743 0.102428
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 \(a_p\))