Properties

Label 6010.2.a.c.1.7
Level 6010
Weight 2
Character 6010.1
Self dual Yes
Analytic conductor 47.990
Analytic rank 1
Dimension 16
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6010 = 2 \cdot 5 \cdot 601 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6010.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9900916148\)
Analytic rank: \(1\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Root \(-0.136067\)
Character \(\chi\) = 6010.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.13607 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.13607 q^{6} -1.31630 q^{7} +1.00000 q^{8} -1.70935 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -1.13607 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.13607 q^{6} -1.31630 q^{7} +1.00000 q^{8} -1.70935 q^{9} +1.00000 q^{10} -0.369645 q^{11} -1.13607 q^{12} -5.82020 q^{13} -1.31630 q^{14} -1.13607 q^{15} +1.00000 q^{16} +6.05036 q^{17} -1.70935 q^{18} +0.866620 q^{19} +1.00000 q^{20} +1.49540 q^{21} -0.369645 q^{22} -1.64764 q^{23} -1.13607 q^{24} +1.00000 q^{25} -5.82020 q^{26} +5.35014 q^{27} -1.31630 q^{28} +7.34705 q^{29} -1.13607 q^{30} -1.21756 q^{31} +1.00000 q^{32} +0.419942 q^{33} +6.05036 q^{34} -1.31630 q^{35} -1.70935 q^{36} -2.26909 q^{37} +0.866620 q^{38} +6.61214 q^{39} +1.00000 q^{40} +0.302941 q^{41} +1.49540 q^{42} +9.60599 q^{43} -0.369645 q^{44} -1.70935 q^{45} -1.64764 q^{46} -0.473050 q^{47} -1.13607 q^{48} -5.26737 q^{49} +1.00000 q^{50} -6.87361 q^{51} -5.82020 q^{52} -5.12183 q^{53} +5.35014 q^{54} -0.369645 q^{55} -1.31630 q^{56} -0.984538 q^{57} +7.34705 q^{58} +13.2821 q^{59} -1.13607 q^{60} -14.7830 q^{61} -1.21756 q^{62} +2.25001 q^{63} +1.00000 q^{64} -5.82020 q^{65} +0.419942 q^{66} -15.8988 q^{67} +6.05036 q^{68} +1.87183 q^{69} -1.31630 q^{70} -16.2197 q^{71} -1.70935 q^{72} +14.9111 q^{73} -2.26909 q^{74} -1.13607 q^{75} +0.866620 q^{76} +0.486562 q^{77} +6.61214 q^{78} -10.1102 q^{79} +1.00000 q^{80} -0.950058 q^{81} +0.302941 q^{82} -14.7761 q^{83} +1.49540 q^{84} +6.05036 q^{85} +9.60599 q^{86} -8.34674 q^{87} -0.369645 q^{88} -11.0303 q^{89} -1.70935 q^{90} +7.66110 q^{91} -1.64764 q^{92} +1.38323 q^{93} -0.473050 q^{94} +0.866620 q^{95} -1.13607 q^{96} -13.0791 q^{97} -5.26737 q^{98} +0.631854 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 16q^{2} - 8q^{3} + 16q^{4} + 16q^{5} - 8q^{6} - 10q^{7} + 16q^{8} - 2q^{9} + O(q^{10}) \) \( 16q + 16q^{2} - 8q^{3} + 16q^{4} + 16q^{5} - 8q^{6} - 10q^{7} + 16q^{8} - 2q^{9} + 16q^{10} - 14q^{11} - 8q^{12} - 20q^{13} - 10q^{14} - 8q^{15} + 16q^{16} - 27q^{17} - 2q^{18} - 17q^{19} + 16q^{20} - 12q^{21} - 14q^{22} - 9q^{23} - 8q^{24} + 16q^{25} - 20q^{26} - 11q^{27} - 10q^{28} - 23q^{29} - 8q^{30} - 21q^{31} + 16q^{32} - 9q^{33} - 27q^{34} - 10q^{35} - 2q^{36} - 16q^{37} - 17q^{38} - 6q^{39} + 16q^{40} - 35q^{41} - 12q^{42} + 3q^{43} - 14q^{44} - 2q^{45} - 9q^{46} - 25q^{47} - 8q^{48} - 24q^{49} + 16q^{50} - q^{51} - 20q^{52} - 39q^{53} - 11q^{54} - 14q^{55} - 10q^{56} - 6q^{57} - 23q^{58} - 32q^{59} - 8q^{60} - 38q^{61} - 21q^{62} + q^{63} + 16q^{64} - 20q^{65} - 9q^{66} + 5q^{67} - 27q^{68} - 25q^{69} - 10q^{70} - 16q^{71} - 2q^{72} - 17q^{73} - 16q^{74} - 8q^{75} - 17q^{76} - 34q^{77} - 6q^{78} - 40q^{79} + 16q^{80} - 28q^{81} - 35q^{82} - 22q^{83} - 12q^{84} - 27q^{85} + 3q^{86} + 10q^{87} - 14q^{88} - 46q^{89} - 2q^{90} - q^{91} - 9q^{92} + 14q^{93} - 25q^{94} - 17q^{95} - 8q^{96} - 21q^{97} - 24q^{98} + 15q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −1.13607 −0.655908 −0.327954 0.944694i \(-0.606359\pi\)
−0.327954 + 0.944694i \(0.606359\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.00000 0.447214
\(6\) −1.13607 −0.463797
\(7\) −1.31630 −0.497513 −0.248756 0.968566i \(-0.580022\pi\)
−0.248756 + 0.968566i \(0.580022\pi\)
\(8\) 1.00000 0.353553
\(9\) −1.70935 −0.569784
\(10\) 1.00000 0.316228
\(11\) −0.369645 −0.111452 −0.0557261 0.998446i \(-0.517747\pi\)
−0.0557261 + 0.998446i \(0.517747\pi\)
\(12\) −1.13607 −0.327954
\(13\) −5.82020 −1.61423 −0.807117 0.590392i \(-0.798973\pi\)
−0.807117 + 0.590392i \(0.798973\pi\)
\(14\) −1.31630 −0.351795
\(15\) −1.13607 −0.293331
\(16\) 1.00000 0.250000
\(17\) 6.05036 1.46743 0.733714 0.679459i \(-0.237785\pi\)
0.733714 + 0.679459i \(0.237785\pi\)
\(18\) −1.70935 −0.402898
\(19\) 0.866620 0.198816 0.0994082 0.995047i \(-0.468305\pi\)
0.0994082 + 0.995047i \(0.468305\pi\)
\(20\) 1.00000 0.223607
\(21\) 1.49540 0.326323
\(22\) −0.369645 −0.0788086
\(23\) −1.64764 −0.343557 −0.171778 0.985136i \(-0.554951\pi\)
−0.171778 + 0.985136i \(0.554951\pi\)
\(24\) −1.13607 −0.231899
\(25\) 1.00000 0.200000
\(26\) −5.82020 −1.14144
\(27\) 5.35014 1.02963
\(28\) −1.31630 −0.248756
\(29\) 7.34705 1.36431 0.682156 0.731206i \(-0.261042\pi\)
0.682156 + 0.731206i \(0.261042\pi\)
\(30\) −1.13607 −0.207416
\(31\) −1.21756 −0.218680 −0.109340 0.994004i \(-0.534874\pi\)
−0.109340 + 0.994004i \(0.534874\pi\)
\(32\) 1.00000 0.176777
\(33\) 0.419942 0.0731025
\(34\) 6.05036 1.03763
\(35\) −1.31630 −0.222495
\(36\) −1.70935 −0.284892
\(37\) −2.26909 −0.373036 −0.186518 0.982452i \(-0.559720\pi\)
−0.186518 + 0.982452i \(0.559720\pi\)
\(38\) 0.866620 0.140584
\(39\) 6.61214 1.05879
\(40\) 1.00000 0.158114
\(41\) 0.302941 0.0473115 0.0236558 0.999720i \(-0.492469\pi\)
0.0236558 + 0.999720i \(0.492469\pi\)
\(42\) 1.49540 0.230745
\(43\) 9.60599 1.46490 0.732450 0.680821i \(-0.238377\pi\)
0.732450 + 0.680821i \(0.238377\pi\)
\(44\) −0.369645 −0.0557261
\(45\) −1.70935 −0.254815
\(46\) −1.64764 −0.242931
\(47\) −0.473050 −0.0690014 −0.0345007 0.999405i \(-0.510984\pi\)
−0.0345007 + 0.999405i \(0.510984\pi\)
\(48\) −1.13607 −0.163977
\(49\) −5.26737 −0.752481
\(50\) 1.00000 0.141421
\(51\) −6.87361 −0.962498
\(52\) −5.82020 −0.807117
\(53\) −5.12183 −0.703537 −0.351769 0.936087i \(-0.614420\pi\)
−0.351769 + 0.936087i \(0.614420\pi\)
\(54\) 5.35014 0.728062
\(55\) −0.369645 −0.0498430
\(56\) −1.31630 −0.175897
\(57\) −0.984538 −0.130405
\(58\) 7.34705 0.964715
\(59\) 13.2821 1.72918 0.864592 0.502475i \(-0.167577\pi\)
0.864592 + 0.502475i \(0.167577\pi\)
\(60\) −1.13607 −0.146666
\(61\) −14.7830 −1.89277 −0.946384 0.323043i \(-0.895294\pi\)
−0.946384 + 0.323043i \(0.895294\pi\)
\(62\) −1.21756 −0.154630
\(63\) 2.25001 0.283475
\(64\) 1.00000 0.125000
\(65\) −5.82020 −0.721907
\(66\) 0.419942 0.0516912
\(67\) −15.8988 −1.94235 −0.971174 0.238373i \(-0.923386\pi\)
−0.971174 + 0.238373i \(0.923386\pi\)
\(68\) 6.05036 0.733714
\(69\) 1.87183 0.225342
\(70\) −1.31630 −0.157327
\(71\) −16.2197 −1.92493 −0.962463 0.271411i \(-0.912510\pi\)
−0.962463 + 0.271411i \(0.912510\pi\)
\(72\) −1.70935 −0.201449
\(73\) 14.9111 1.74521 0.872604 0.488429i \(-0.162430\pi\)
0.872604 + 0.488429i \(0.162430\pi\)
\(74\) −2.26909 −0.263776
\(75\) −1.13607 −0.131182
\(76\) 0.866620 0.0994082
\(77\) 0.486562 0.0554489
\(78\) 6.61214 0.748677
\(79\) −10.1102 −1.13749 −0.568745 0.822514i \(-0.692571\pi\)
−0.568745 + 0.822514i \(0.692571\pi\)
\(80\) 1.00000 0.111803
\(81\) −0.950058 −0.105562
\(82\) 0.302941 0.0334543
\(83\) −14.7761 −1.62189 −0.810946 0.585122i \(-0.801047\pi\)
−0.810946 + 0.585122i \(0.801047\pi\)
\(84\) 1.49540 0.163161
\(85\) 6.05036 0.656253
\(86\) 9.60599 1.03584
\(87\) −8.34674 −0.894864
\(88\) −0.369645 −0.0394043
\(89\) −11.0303 −1.16921 −0.584606 0.811317i \(-0.698751\pi\)
−0.584606 + 0.811317i \(0.698751\pi\)
\(90\) −1.70935 −0.180182
\(91\) 7.66110 0.803102
\(92\) −1.64764 −0.171778
\(93\) 1.38323 0.143434
\(94\) −0.473050 −0.0487914
\(95\) 0.866620 0.0889134
\(96\) −1.13607 −0.115949
\(97\) −13.0791 −1.32798 −0.663990 0.747742i \(-0.731138\pi\)
−0.663990 + 0.747742i \(0.731138\pi\)
\(98\) −5.26737 −0.532084
\(99\) 0.631854 0.0635037
\(100\) 1.00000 0.100000
\(101\) −14.2016 −1.41311 −0.706557 0.707656i \(-0.749753\pi\)
−0.706557 + 0.707656i \(0.749753\pi\)
\(102\) −6.87361 −0.680589
\(103\) 0.292816 0.0288520 0.0144260 0.999896i \(-0.495408\pi\)
0.0144260 + 0.999896i \(0.495408\pi\)
\(104\) −5.82020 −0.570718
\(105\) 1.49540 0.145936
\(106\) −5.12183 −0.497476
\(107\) 3.50855 0.339184 0.169592 0.985514i \(-0.445755\pi\)
0.169592 + 0.985514i \(0.445755\pi\)
\(108\) 5.35014 0.514817
\(109\) −17.1180 −1.63961 −0.819804 0.572645i \(-0.805918\pi\)
−0.819804 + 0.572645i \(0.805918\pi\)
\(110\) −0.369645 −0.0352443
\(111\) 2.57783 0.244677
\(112\) −1.31630 −0.124378
\(113\) 5.65902 0.532356 0.266178 0.963924i \(-0.414239\pi\)
0.266178 + 0.963924i \(0.414239\pi\)
\(114\) −0.984538 −0.0922105
\(115\) −1.64764 −0.153643
\(116\) 7.34705 0.682156
\(117\) 9.94877 0.919764
\(118\) 13.2821 1.22272
\(119\) −7.96406 −0.730064
\(120\) −1.13607 −0.103708
\(121\) −10.8634 −0.987578
\(122\) −14.7830 −1.33839
\(123\) −0.344162 −0.0310320
\(124\) −1.21756 −0.109340
\(125\) 1.00000 0.0894427
\(126\) 2.25001 0.200447
\(127\) −12.4503 −1.10479 −0.552393 0.833584i \(-0.686285\pi\)
−0.552393 + 0.833584i \(0.686285\pi\)
\(128\) 1.00000 0.0883883
\(129\) −10.9130 −0.960840
\(130\) −5.82020 −0.510465
\(131\) 17.1914 1.50202 0.751010 0.660291i \(-0.229567\pi\)
0.751010 + 0.660291i \(0.229567\pi\)
\(132\) 0.419942 0.0365512
\(133\) −1.14073 −0.0989137
\(134\) −15.8988 −1.37345
\(135\) 5.35014 0.460467
\(136\) 6.05036 0.518814
\(137\) 5.83901 0.498860 0.249430 0.968393i \(-0.419757\pi\)
0.249430 + 0.968393i \(0.419757\pi\)
\(138\) 1.87183 0.159341
\(139\) −9.86489 −0.836729 −0.418364 0.908279i \(-0.637396\pi\)
−0.418364 + 0.908279i \(0.637396\pi\)
\(140\) −1.31630 −0.111247
\(141\) 0.537416 0.0452586
\(142\) −16.2197 −1.36113
\(143\) 2.15141 0.179910
\(144\) −1.70935 −0.142446
\(145\) 7.34705 0.610139
\(146\) 14.9111 1.23405
\(147\) 5.98408 0.493559
\(148\) −2.26909 −0.186518
\(149\) 5.03587 0.412555 0.206277 0.978494i \(-0.433865\pi\)
0.206277 + 0.978494i \(0.433865\pi\)
\(150\) −1.13607 −0.0927595
\(151\) −3.59542 −0.292591 −0.146296 0.989241i \(-0.546735\pi\)
−0.146296 + 0.989241i \(0.546735\pi\)
\(152\) 0.866620 0.0702922
\(153\) −10.3422 −0.836117
\(154\) 0.486562 0.0392083
\(155\) −1.21756 −0.0977967
\(156\) 6.61214 0.529395
\(157\) −21.1133 −1.68502 −0.842512 0.538678i \(-0.818924\pi\)
−0.842512 + 0.538678i \(0.818924\pi\)
\(158\) −10.1102 −0.804327
\(159\) 5.81874 0.461456
\(160\) 1.00000 0.0790569
\(161\) 2.16878 0.170924
\(162\) −0.950058 −0.0746436
\(163\) 6.35927 0.498096 0.249048 0.968491i \(-0.419882\pi\)
0.249048 + 0.968491i \(0.419882\pi\)
\(164\) 0.302941 0.0236558
\(165\) 0.419942 0.0326924
\(166\) −14.7761 −1.14685
\(167\) 1.10367 0.0854044 0.0427022 0.999088i \(-0.486403\pi\)
0.0427022 + 0.999088i \(0.486403\pi\)
\(168\) 1.49540 0.115373
\(169\) 20.8747 1.60575
\(170\) 6.05036 0.464041
\(171\) −1.48136 −0.113282
\(172\) 9.60599 0.732450
\(173\) 4.02327 0.305884 0.152942 0.988235i \(-0.451125\pi\)
0.152942 + 0.988235i \(0.451125\pi\)
\(174\) −8.34674 −0.632764
\(175\) −1.31630 −0.0995026
\(176\) −0.369645 −0.0278631
\(177\) −15.0894 −1.13419
\(178\) −11.0303 −0.826758
\(179\) −3.90503 −0.291875 −0.145938 0.989294i \(-0.546620\pi\)
−0.145938 + 0.989294i \(0.546620\pi\)
\(180\) −1.70935 −0.127408
\(181\) −19.2250 −1.42898 −0.714490 0.699646i \(-0.753341\pi\)
−0.714490 + 0.699646i \(0.753341\pi\)
\(182\) 7.66110 0.567879
\(183\) 16.7945 1.24148
\(184\) −1.64764 −0.121466
\(185\) −2.26909 −0.166827
\(186\) 1.38323 0.101423
\(187\) −2.23649 −0.163548
\(188\) −0.473050 −0.0345007
\(189\) −7.04236 −0.512257
\(190\) 0.866620 0.0628712
\(191\) 16.5153 1.19500 0.597501 0.801868i \(-0.296160\pi\)
0.597501 + 0.801868i \(0.296160\pi\)
\(192\) −1.13607 −0.0819886
\(193\) 10.4471 0.751998 0.375999 0.926620i \(-0.377300\pi\)
0.375999 + 0.926620i \(0.377300\pi\)
\(194\) −13.0791 −0.939024
\(195\) 6.61214 0.473505
\(196\) −5.26737 −0.376240
\(197\) 5.66850 0.403864 0.201932 0.979400i \(-0.435278\pi\)
0.201932 + 0.979400i \(0.435278\pi\)
\(198\) 0.631854 0.0449039
\(199\) 4.57095 0.324026 0.162013 0.986789i \(-0.448201\pi\)
0.162013 + 0.986789i \(0.448201\pi\)
\(200\) 1.00000 0.0707107
\(201\) 18.0621 1.27400
\(202\) −14.2016 −0.999222
\(203\) −9.67089 −0.678763
\(204\) −6.87361 −0.481249
\(205\) 0.302941 0.0211584
\(206\) 0.292816 0.0204015
\(207\) 2.81640 0.195753
\(208\) −5.82020 −0.403558
\(209\) −0.320342 −0.0221585
\(210\) 1.49540 0.103192
\(211\) −21.2038 −1.45973 −0.729865 0.683591i \(-0.760417\pi\)
−0.729865 + 0.683591i \(0.760417\pi\)
\(212\) −5.12183 −0.351769
\(213\) 18.4267 1.26258
\(214\) 3.50855 0.239839
\(215\) 9.60599 0.655123
\(216\) 5.35014 0.364031
\(217\) 1.60267 0.108796
\(218\) −17.1180 −1.15938
\(219\) −16.9400 −1.14470
\(220\) −0.369645 −0.0249215
\(221\) −35.2143 −2.36877
\(222\) 2.57783 0.173013
\(223\) −14.8044 −0.991374 −0.495687 0.868501i \(-0.665084\pi\)
−0.495687 + 0.868501i \(0.665084\pi\)
\(224\) −1.31630 −0.0879487
\(225\) −1.70935 −0.113957
\(226\) 5.65902 0.376433
\(227\) 17.0876 1.13414 0.567071 0.823669i \(-0.308076\pi\)
0.567071 + 0.823669i \(0.308076\pi\)
\(228\) −0.984538 −0.0652027
\(229\) 17.3259 1.14493 0.572465 0.819929i \(-0.305987\pi\)
0.572465 + 0.819929i \(0.305987\pi\)
\(230\) −1.64764 −0.108642
\(231\) −0.552767 −0.0363694
\(232\) 7.34705 0.482357
\(233\) −0.738526 −0.0483825 −0.0241912 0.999707i \(-0.507701\pi\)
−0.0241912 + 0.999707i \(0.507701\pi\)
\(234\) 9.94877 0.650372
\(235\) −0.473050 −0.0308584
\(236\) 13.2821 0.864592
\(237\) 11.4859 0.746090
\(238\) −7.96406 −0.516233
\(239\) −7.74912 −0.501249 −0.250625 0.968084i \(-0.580636\pi\)
−0.250625 + 0.968084i \(0.580636\pi\)
\(240\) −1.13607 −0.0733328
\(241\) −18.0098 −1.16012 −0.580058 0.814575i \(-0.696970\pi\)
−0.580058 + 0.814575i \(0.696970\pi\)
\(242\) −10.8634 −0.698323
\(243\) −14.9711 −0.960396
\(244\) −14.7830 −0.946384
\(245\) −5.26737 −0.336520
\(246\) −0.344162 −0.0219430
\(247\) −5.04390 −0.320936
\(248\) −1.21756 −0.0773151
\(249\) 16.7867 1.06381
\(250\) 1.00000 0.0632456
\(251\) 20.4697 1.29204 0.646019 0.763321i \(-0.276433\pi\)
0.646019 + 0.763321i \(0.276433\pi\)
\(252\) 2.25001 0.141737
\(253\) 0.609043 0.0382902
\(254\) −12.4503 −0.781202
\(255\) −6.87361 −0.430442
\(256\) 1.00000 0.0625000
\(257\) 10.0700 0.628151 0.314075 0.949398i \(-0.398306\pi\)
0.314075 + 0.949398i \(0.398306\pi\)
\(258\) −10.9130 −0.679416
\(259\) 2.98679 0.185590
\(260\) −5.82020 −0.360954
\(261\) −12.5587 −0.777363
\(262\) 17.1914 1.06209
\(263\) 17.5066 1.07950 0.539752 0.841824i \(-0.318518\pi\)
0.539752 + 0.841824i \(0.318518\pi\)
\(264\) 0.419942 0.0258456
\(265\) −5.12183 −0.314631
\(266\) −1.14073 −0.0699425
\(267\) 12.5312 0.766896
\(268\) −15.8988 −0.971174
\(269\) 2.08606 0.127190 0.0635948 0.997976i \(-0.479743\pi\)
0.0635948 + 0.997976i \(0.479743\pi\)
\(270\) 5.35014 0.325599
\(271\) 3.58645 0.217861 0.108931 0.994049i \(-0.465257\pi\)
0.108931 + 0.994049i \(0.465257\pi\)
\(272\) 6.05036 0.366857
\(273\) −8.70353 −0.526761
\(274\) 5.83901 0.352747
\(275\) −0.369645 −0.0222904
\(276\) 1.87183 0.112671
\(277\) −11.8816 −0.713898 −0.356949 0.934124i \(-0.616183\pi\)
−0.356949 + 0.934124i \(0.616183\pi\)
\(278\) −9.86489 −0.591657
\(279\) 2.08124 0.124600
\(280\) −1.31630 −0.0786637
\(281\) 3.65872 0.218261 0.109130 0.994027i \(-0.465193\pi\)
0.109130 + 0.994027i \(0.465193\pi\)
\(282\) 0.537416 0.0320027
\(283\) −10.6073 −0.630541 −0.315271 0.949002i \(-0.602095\pi\)
−0.315271 + 0.949002i \(0.602095\pi\)
\(284\) −16.2197 −0.962463
\(285\) −0.984538 −0.0583190
\(286\) 2.15141 0.127215
\(287\) −0.398761 −0.0235381
\(288\) −1.70935 −0.100725
\(289\) 19.6068 1.15334
\(290\) 7.34705 0.431433
\(291\) 14.8587 0.871033
\(292\) 14.9111 0.872604
\(293\) −18.5346 −1.08280 −0.541401 0.840765i \(-0.682106\pi\)
−0.541401 + 0.840765i \(0.682106\pi\)
\(294\) 5.98408 0.348999
\(295\) 13.2821 0.773314
\(296\) −2.26909 −0.131888
\(297\) −1.97765 −0.114755
\(298\) 5.03587 0.291720
\(299\) 9.58960 0.554581
\(300\) −1.13607 −0.0655908
\(301\) −12.6443 −0.728806
\(302\) −3.59542 −0.206893
\(303\) 16.1340 0.926873
\(304\) 0.866620 0.0497041
\(305\) −14.7830 −0.846472
\(306\) −10.3422 −0.591224
\(307\) 31.5036 1.79801 0.899003 0.437941i \(-0.144292\pi\)
0.899003 + 0.437941i \(0.144292\pi\)
\(308\) 0.486562 0.0277245
\(309\) −0.332659 −0.0189243
\(310\) −1.21756 −0.0691527
\(311\) 4.14482 0.235031 0.117516 0.993071i \(-0.462507\pi\)
0.117516 + 0.993071i \(0.462507\pi\)
\(312\) 6.61214 0.374339
\(313\) 8.30083 0.469191 0.234595 0.972093i \(-0.424624\pi\)
0.234595 + 0.972093i \(0.424624\pi\)
\(314\) −21.1133 −1.19149
\(315\) 2.25001 0.126774
\(316\) −10.1102 −0.568745
\(317\) −32.1457 −1.80548 −0.902740 0.430187i \(-0.858448\pi\)
−0.902740 + 0.430187i \(0.858448\pi\)
\(318\) 5.81874 0.326299
\(319\) −2.71580 −0.152056
\(320\) 1.00000 0.0559017
\(321\) −3.98595 −0.222474
\(322\) 2.16878 0.120862
\(323\) 5.24336 0.291748
\(324\) −0.950058 −0.0527810
\(325\) −5.82020 −0.322847
\(326\) 6.35927 0.352207
\(327\) 19.4472 1.07543
\(328\) 0.302941 0.0167271
\(329\) 0.622673 0.0343291
\(330\) 0.419942 0.0231170
\(331\) 10.3413 0.568409 0.284204 0.958764i \(-0.408271\pi\)
0.284204 + 0.958764i \(0.408271\pi\)
\(332\) −14.7761 −0.810946
\(333\) 3.87867 0.212550
\(334\) 1.10367 0.0603900
\(335\) −15.8988 −0.868644
\(336\) 1.49540 0.0815807
\(337\) −0.770786 −0.0419874 −0.0209937 0.999780i \(-0.506683\pi\)
−0.0209937 + 0.999780i \(0.506683\pi\)
\(338\) 20.8747 1.13544
\(339\) −6.42903 −0.349177
\(340\) 6.05036 0.328127
\(341\) 0.450065 0.0243724
\(342\) −1.48136 −0.0801027
\(343\) 16.1475 0.871882
\(344\) 9.60599 0.517920
\(345\) 1.87183 0.100776
\(346\) 4.02327 0.216292
\(347\) 36.6959 1.96994 0.984970 0.172725i \(-0.0552572\pi\)
0.984970 + 0.172725i \(0.0552572\pi\)
\(348\) −8.34674 −0.447432
\(349\) −21.2787 −1.13902 −0.569511 0.821984i \(-0.692867\pi\)
−0.569511 + 0.821984i \(0.692867\pi\)
\(350\) −1.31630 −0.0703590
\(351\) −31.1389 −1.66207
\(352\) −0.369645 −0.0197022
\(353\) 19.6791 1.04741 0.523706 0.851899i \(-0.324549\pi\)
0.523706 + 0.851899i \(0.324549\pi\)
\(354\) −15.0894 −0.801991
\(355\) −16.2197 −0.860854
\(356\) −11.0303 −0.584606
\(357\) 9.04770 0.478855
\(358\) −3.90503 −0.206387
\(359\) 8.74875 0.461741 0.230871 0.972984i \(-0.425843\pi\)
0.230871 + 0.972984i \(0.425843\pi\)
\(360\) −1.70935 −0.0900908
\(361\) −18.2490 −0.960472
\(362\) −19.2250 −1.01044
\(363\) 12.3415 0.647761
\(364\) 7.66110 0.401551
\(365\) 14.9111 0.780480
\(366\) 16.7945 0.877861
\(367\) −21.8025 −1.13808 −0.569040 0.822310i \(-0.692685\pi\)
−0.569040 + 0.822310i \(0.692685\pi\)
\(368\) −1.64764 −0.0858892
\(369\) −0.517834 −0.0269573
\(370\) −2.26909 −0.117964
\(371\) 6.74184 0.350019
\(372\) 1.38323 0.0717171
\(373\) 17.6367 0.913193 0.456596 0.889674i \(-0.349068\pi\)
0.456596 + 0.889674i \(0.349068\pi\)
\(374\) −2.23649 −0.115646
\(375\) −1.13607 −0.0586662
\(376\) −0.473050 −0.0243957
\(377\) −42.7613 −2.20232
\(378\) −7.04236 −0.362220
\(379\) 3.12987 0.160771 0.0803853 0.996764i \(-0.474385\pi\)
0.0803853 + 0.996764i \(0.474385\pi\)
\(380\) 0.866620 0.0444567
\(381\) 14.1444 0.724639
\(382\) 16.5153 0.844995
\(383\) −4.78232 −0.244365 −0.122183 0.992508i \(-0.538989\pi\)
−0.122183 + 0.992508i \(0.538989\pi\)
\(384\) −1.13607 −0.0579747
\(385\) 0.486562 0.0247975
\(386\) 10.4471 0.531743
\(387\) −16.4200 −0.834676
\(388\) −13.0791 −0.663990
\(389\) 24.0116 1.21743 0.608717 0.793387i \(-0.291684\pi\)
0.608717 + 0.793387i \(0.291684\pi\)
\(390\) 6.61214 0.334819
\(391\) −9.96882 −0.504145
\(392\) −5.26737 −0.266042
\(393\) −19.5306 −0.985188
\(394\) 5.66850 0.285575
\(395\) −10.1102 −0.508701
\(396\) 0.631854 0.0317519
\(397\) 14.4230 0.723870 0.361935 0.932203i \(-0.382116\pi\)
0.361935 + 0.932203i \(0.382116\pi\)
\(398\) 4.57095 0.229121
\(399\) 1.29594 0.0648783
\(400\) 1.00000 0.0500000
\(401\) 14.6177 0.729971 0.364985 0.931013i \(-0.381074\pi\)
0.364985 + 0.931013i \(0.381074\pi\)
\(402\) 18.0621 0.900856
\(403\) 7.08644 0.353001
\(404\) −14.2016 −0.706557
\(405\) −0.950058 −0.0472088
\(406\) −9.67089 −0.479958
\(407\) 0.838757 0.0415756
\(408\) −6.87361 −0.340294
\(409\) −18.7903 −0.929122 −0.464561 0.885541i \(-0.653788\pi\)
−0.464561 + 0.885541i \(0.653788\pi\)
\(410\) 0.302941 0.0149612
\(411\) −6.63350 −0.327207
\(412\) 0.292816 0.0144260
\(413\) −17.4832 −0.860291
\(414\) 2.81640 0.138418
\(415\) −14.7761 −0.725332
\(416\) −5.82020 −0.285359
\(417\) 11.2072 0.548818
\(418\) −0.320342 −0.0156684
\(419\) 7.37928 0.360502 0.180251 0.983621i \(-0.442309\pi\)
0.180251 + 0.983621i \(0.442309\pi\)
\(420\) 1.49540 0.0729680
\(421\) 7.33963 0.357712 0.178856 0.983875i \(-0.442760\pi\)
0.178856 + 0.983875i \(0.442760\pi\)
\(422\) −21.2038 −1.03219
\(423\) 0.808609 0.0393159
\(424\) −5.12183 −0.248738
\(425\) 6.05036 0.293485
\(426\) 18.4267 0.892776
\(427\) 19.4588 0.941677
\(428\) 3.50855 0.169592
\(429\) −2.44414 −0.118004
\(430\) 9.60599 0.463242
\(431\) 16.6986 0.804345 0.402173 0.915564i \(-0.368255\pi\)
0.402173 + 0.915564i \(0.368255\pi\)
\(432\) 5.35014 0.257409
\(433\) −29.9018 −1.43699 −0.718495 0.695532i \(-0.755169\pi\)
−0.718495 + 0.695532i \(0.755169\pi\)
\(434\) 1.60267 0.0769305
\(435\) −8.34674 −0.400195
\(436\) −17.1180 −0.819804
\(437\) −1.42788 −0.0683047
\(438\) −16.9400 −0.809422
\(439\) −33.8204 −1.61416 −0.807080 0.590442i \(-0.798953\pi\)
−0.807080 + 0.590442i \(0.798953\pi\)
\(440\) −0.369645 −0.0176221
\(441\) 9.00378 0.428752
\(442\) −35.2143 −1.67497
\(443\) 8.00923 0.380530 0.190265 0.981733i \(-0.439065\pi\)
0.190265 + 0.981733i \(0.439065\pi\)
\(444\) 2.57783 0.122339
\(445\) −11.0303 −0.522887
\(446\) −14.8044 −0.701007
\(447\) −5.72109 −0.270598
\(448\) −1.31630 −0.0621891
\(449\) −8.81951 −0.416219 −0.208109 0.978106i \(-0.566731\pi\)
−0.208109 + 0.978106i \(0.566731\pi\)
\(450\) −1.70935 −0.0805796
\(451\) −0.111981 −0.00527297
\(452\) 5.65902 0.266178
\(453\) 4.08464 0.191913
\(454\) 17.0876 0.801960
\(455\) 7.66110 0.359158
\(456\) −0.984538 −0.0461052
\(457\) −2.75550 −0.128897 −0.0644484 0.997921i \(-0.520529\pi\)
−0.0644484 + 0.997921i \(0.520529\pi\)
\(458\) 17.3259 0.809588
\(459\) 32.3703 1.51091
\(460\) −1.64764 −0.0768217
\(461\) −4.50213 −0.209685 −0.104843 0.994489i \(-0.533434\pi\)
−0.104843 + 0.994489i \(0.533434\pi\)
\(462\) −0.552767 −0.0257171
\(463\) −23.3048 −1.08306 −0.541532 0.840680i \(-0.682155\pi\)
−0.541532 + 0.840680i \(0.682155\pi\)
\(464\) 7.34705 0.341078
\(465\) 1.38323 0.0641457
\(466\) −0.738526 −0.0342116
\(467\) 5.67434 0.262577 0.131289 0.991344i \(-0.458089\pi\)
0.131289 + 0.991344i \(0.458089\pi\)
\(468\) 9.94877 0.459882
\(469\) 20.9275 0.966343
\(470\) −0.473050 −0.0218202
\(471\) 23.9861 1.10522
\(472\) 13.2821 0.611359
\(473\) −3.55081 −0.163266
\(474\) 11.4859 0.527565
\(475\) 0.866620 0.0397633
\(476\) −7.96406 −0.365032
\(477\) 8.75501 0.400864
\(478\) −7.74912 −0.354437
\(479\) −29.8542 −1.36407 −0.682037 0.731317i \(-0.738906\pi\)
−0.682037 + 0.731317i \(0.738906\pi\)
\(480\) −1.13607 −0.0518541
\(481\) 13.2065 0.602166
\(482\) −18.0098 −0.820326
\(483\) −2.46388 −0.112111
\(484\) −10.8634 −0.493789
\(485\) −13.0791 −0.593891
\(486\) −14.9711 −0.679102
\(487\) −37.7136 −1.70897 −0.854484 0.519478i \(-0.826126\pi\)
−0.854484 + 0.519478i \(0.826126\pi\)
\(488\) −14.7830 −0.669195
\(489\) −7.22455 −0.326706
\(490\) −5.26737 −0.237955
\(491\) −28.3165 −1.27791 −0.638954 0.769245i \(-0.720632\pi\)
−0.638954 + 0.769245i \(0.720632\pi\)
\(492\) −0.344162 −0.0155160
\(493\) 44.4523 2.00203
\(494\) −5.04390 −0.226936
\(495\) 0.631854 0.0283997
\(496\) −1.21756 −0.0546700
\(497\) 21.3500 0.957676
\(498\) 16.7867 0.752229
\(499\) −25.6119 −1.14655 −0.573273 0.819364i \(-0.694327\pi\)
−0.573273 + 0.819364i \(0.694327\pi\)
\(500\) 1.00000 0.0447214
\(501\) −1.25384 −0.0560175
\(502\) 20.4697 0.913609
\(503\) 8.17948 0.364705 0.182352 0.983233i \(-0.441629\pi\)
0.182352 + 0.983233i \(0.441629\pi\)
\(504\) 2.25001 0.100224
\(505\) −14.2016 −0.631964
\(506\) 0.609043 0.0270752
\(507\) −23.7151 −1.05322
\(508\) −12.4503 −0.552393
\(509\) −1.70424 −0.0755390 −0.0377695 0.999286i \(-0.512025\pi\)
−0.0377695 + 0.999286i \(0.512025\pi\)
\(510\) −6.87361 −0.304369
\(511\) −19.6274 −0.868263
\(512\) 1.00000 0.0441942
\(513\) 4.63654 0.204708
\(514\) 10.0700 0.444170
\(515\) 0.292816 0.0129030
\(516\) −10.9130 −0.480420
\(517\) 0.174861 0.00769036
\(518\) 2.98679 0.131232
\(519\) −4.57070 −0.200632
\(520\) −5.82020 −0.255233
\(521\) −25.1989 −1.10398 −0.551991 0.833850i \(-0.686132\pi\)
−0.551991 + 0.833850i \(0.686132\pi\)
\(522\) −12.5587 −0.549679
\(523\) 40.2666 1.76074 0.880368 0.474292i \(-0.157296\pi\)
0.880368 + 0.474292i \(0.157296\pi\)
\(524\) 17.1914 0.751010
\(525\) 1.49540 0.0652646
\(526\) 17.5066 0.763324
\(527\) −7.36667 −0.320897
\(528\) 0.419942 0.0182756
\(529\) −20.2853 −0.881969
\(530\) −5.12183 −0.222478
\(531\) −22.7038 −0.985261
\(532\) −1.14073 −0.0494568
\(533\) −1.76318 −0.0763718
\(534\) 12.5312 0.542277
\(535\) 3.50855 0.151688
\(536\) −15.8988 −0.686724
\(537\) 4.43637 0.191443
\(538\) 2.08606 0.0899366
\(539\) 1.94706 0.0838657
\(540\) 5.35014 0.230233
\(541\) 16.6343 0.715163 0.357581 0.933882i \(-0.383602\pi\)
0.357581 + 0.933882i \(0.383602\pi\)
\(542\) 3.58645 0.154051
\(543\) 21.8408 0.937280
\(544\) 6.05036 0.259407
\(545\) −17.1180 −0.733255
\(546\) −8.70353 −0.372477
\(547\) 12.2347 0.523118 0.261559 0.965187i \(-0.415763\pi\)
0.261559 + 0.965187i \(0.415763\pi\)
\(548\) 5.83901 0.249430
\(549\) 25.2693 1.07847
\(550\) −0.369645 −0.0157617
\(551\) 6.36710 0.271248
\(552\) 1.87183 0.0796704
\(553\) 13.3081 0.565916
\(554\) −11.8816 −0.504802
\(555\) 2.57783 0.109423
\(556\) −9.86489 −0.418364
\(557\) −29.6081 −1.25454 −0.627268 0.778804i \(-0.715827\pi\)
−0.627268 + 0.778804i \(0.715827\pi\)
\(558\) 2.08124 0.0881058
\(559\) −55.9088 −2.36469
\(560\) −1.31630 −0.0556236
\(561\) 2.54080 0.107273
\(562\) 3.65872 0.154334
\(563\) −6.36777 −0.268370 −0.134185 0.990956i \(-0.542842\pi\)
−0.134185 + 0.990956i \(0.542842\pi\)
\(564\) 0.537416 0.0226293
\(565\) 5.65902 0.238077
\(566\) −10.6073 −0.445860
\(567\) 1.25056 0.0525185
\(568\) −16.2197 −0.680564
\(569\) 5.58077 0.233958 0.116979 0.993134i \(-0.462679\pi\)
0.116979 + 0.993134i \(0.462679\pi\)
\(570\) −0.984538 −0.0412378
\(571\) −22.0264 −0.921778 −0.460889 0.887458i \(-0.652469\pi\)
−0.460889 + 0.887458i \(0.652469\pi\)
\(572\) 2.15141 0.0899549
\(573\) −18.7624 −0.783812
\(574\) −0.398761 −0.0166439
\(575\) −1.64764 −0.0687114
\(576\) −1.70935 −0.0712230
\(577\) −5.35466 −0.222918 −0.111459 0.993769i \(-0.535552\pi\)
−0.111459 + 0.993769i \(0.535552\pi\)
\(578\) 19.6068 0.815536
\(579\) −11.8686 −0.493242
\(580\) 7.34705 0.305070
\(581\) 19.4498 0.806912
\(582\) 14.8587 0.615914
\(583\) 1.89326 0.0784108
\(584\) 14.9111 0.617024
\(585\) 9.94877 0.411331
\(586\) −18.5346 −0.765657
\(587\) −0.510618 −0.0210755 −0.0105377 0.999944i \(-0.503354\pi\)
−0.0105377 + 0.999944i \(0.503354\pi\)
\(588\) 5.98408 0.246779
\(589\) −1.05516 −0.0434772
\(590\) 13.2821 0.546816
\(591\) −6.43979 −0.264898
\(592\) −2.26909 −0.0932589
\(593\) −1.84834 −0.0759023 −0.0379511 0.999280i \(-0.512083\pi\)
−0.0379511 + 0.999280i \(0.512083\pi\)
\(594\) −1.97765 −0.0811441
\(595\) −7.96406 −0.326495
\(596\) 5.03587 0.206277
\(597\) −5.19291 −0.212532
\(598\) 9.58960 0.392148
\(599\) 35.1951 1.43803 0.719016 0.694993i \(-0.244593\pi\)
0.719016 + 0.694993i \(0.244593\pi\)
\(600\) −1.13607 −0.0463797
\(601\) −1.00000 −0.0407909
\(602\) −12.6443 −0.515344
\(603\) 27.1766 1.10672
\(604\) −3.59542 −0.146296
\(605\) −10.8634 −0.441658
\(606\) 16.1340 0.655398
\(607\) 27.3914 1.11178 0.555891 0.831255i \(-0.312377\pi\)
0.555891 + 0.831255i \(0.312377\pi\)
\(608\) 0.866620 0.0351461
\(609\) 10.9868 0.445207
\(610\) −14.7830 −0.598546
\(611\) 2.75325 0.111384
\(612\) −10.3422 −0.418058
\(613\) 1.27636 0.0515518 0.0257759 0.999668i \(-0.491794\pi\)
0.0257759 + 0.999668i \(0.491794\pi\)
\(614\) 31.5036 1.27138
\(615\) −0.344162 −0.0138779
\(616\) 0.486562 0.0196042
\(617\) 22.5375 0.907326 0.453663 0.891173i \(-0.350117\pi\)
0.453663 + 0.891173i \(0.350117\pi\)
\(618\) −0.332659 −0.0133815
\(619\) 5.54288 0.222787 0.111394 0.993776i \(-0.464469\pi\)
0.111394 + 0.993776i \(0.464469\pi\)
\(620\) −1.21756 −0.0488984
\(621\) −8.81511 −0.353738
\(622\) 4.14482 0.166192
\(623\) 14.5192 0.581698
\(624\) 6.61214 0.264697
\(625\) 1.00000 0.0400000
\(626\) 8.30083 0.331768
\(627\) 0.363930 0.0145340
\(628\) −21.1133 −0.842512
\(629\) −13.7288 −0.547403
\(630\) 2.25001 0.0896427
\(631\) 26.5157 1.05557 0.527787 0.849377i \(-0.323022\pi\)
0.527787 + 0.849377i \(0.323022\pi\)
\(632\) −10.1102 −0.402164
\(633\) 24.0889 0.957450
\(634\) −32.1457 −1.27667
\(635\) −12.4503 −0.494076
\(636\) 5.81874 0.230728
\(637\) 30.6571 1.21468
\(638\) −2.71580 −0.107520
\(639\) 27.7252 1.09679
\(640\) 1.00000 0.0395285
\(641\) 26.0522 1.02900 0.514501 0.857490i \(-0.327977\pi\)
0.514501 + 0.857490i \(0.327977\pi\)
\(642\) −3.98595 −0.157313
\(643\) 36.0166 1.42036 0.710178 0.704022i \(-0.248615\pi\)
0.710178 + 0.704022i \(0.248615\pi\)
\(644\) 2.16878 0.0854620
\(645\) −10.9130 −0.429701
\(646\) 5.24336 0.206297
\(647\) 31.9782 1.25719 0.628597 0.777731i \(-0.283630\pi\)
0.628597 + 0.777731i \(0.283630\pi\)
\(648\) −0.950058 −0.0373218
\(649\) −4.90967 −0.192721
\(650\) −5.82020 −0.228287
\(651\) −1.82074 −0.0713604
\(652\) 6.35927 0.249048
\(653\) 13.6903 0.535741 0.267871 0.963455i \(-0.413680\pi\)
0.267871 + 0.963455i \(0.413680\pi\)
\(654\) 19.4472 0.760446
\(655\) 17.1914 0.671724
\(656\) 0.302941 0.0118279
\(657\) −25.4882 −0.994391
\(658\) 0.622673 0.0242743
\(659\) −30.0868 −1.17202 −0.586008 0.810305i \(-0.699301\pi\)
−0.586008 + 0.810305i \(0.699301\pi\)
\(660\) 0.419942 0.0163462
\(661\) −22.8812 −0.889976 −0.444988 0.895536i \(-0.646792\pi\)
−0.444988 + 0.895536i \(0.646792\pi\)
\(662\) 10.3413 0.401926
\(663\) 40.0058 1.55370
\(664\) −14.7761 −0.573425
\(665\) −1.14073 −0.0442356
\(666\) 3.87867 0.150295
\(667\) −12.1053 −0.468719
\(668\) 1.10367 0.0427022
\(669\) 16.8188 0.650251
\(670\) −15.8988 −0.614224
\(671\) 5.46446 0.210953
\(672\) 1.49540 0.0576863
\(673\) −22.5000 −0.867312 −0.433656 0.901079i \(-0.642777\pi\)
−0.433656 + 0.901079i \(0.642777\pi\)
\(674\) −0.770786 −0.0296896
\(675\) 5.35014 0.205927
\(676\) 20.8747 0.802874
\(677\) −23.6948 −0.910666 −0.455333 0.890321i \(-0.650480\pi\)
−0.455333 + 0.890321i \(0.650480\pi\)
\(678\) −6.42903 −0.246905
\(679\) 17.2159 0.660687
\(680\) 6.05036 0.232021
\(681\) −19.4126 −0.743893
\(682\) 0.450065 0.0172339
\(683\) −47.3804 −1.81296 −0.906481 0.422246i \(-0.861242\pi\)
−0.906481 + 0.422246i \(0.861242\pi\)
\(684\) −1.48136 −0.0566412
\(685\) 5.83901 0.223097
\(686\) 16.1475 0.616514
\(687\) −19.6834 −0.750970
\(688\) 9.60599 0.366225
\(689\) 29.8101 1.13567
\(690\) 1.87183 0.0712594
\(691\) 4.42633 0.168385 0.0841927 0.996449i \(-0.473169\pi\)
0.0841927 + 0.996449i \(0.473169\pi\)
\(692\) 4.02327 0.152942
\(693\) −0.831706 −0.0315939
\(694\) 36.6959 1.39296
\(695\) −9.86489 −0.374196
\(696\) −8.34674 −0.316382
\(697\) 1.83290 0.0694262
\(698\) −21.2787 −0.805410
\(699\) 0.839015 0.0317345
\(700\) −1.31630 −0.0497513
\(701\) −8.81618 −0.332982 −0.166491 0.986043i \(-0.553244\pi\)
−0.166491 + 0.986043i \(0.553244\pi\)
\(702\) −31.1389 −1.17526
\(703\) −1.96644 −0.0741656
\(704\) −0.369645 −0.0139315
\(705\) 0.537416 0.0202403
\(706\) 19.6791 0.740632
\(707\) 18.6935 0.703042
\(708\) −15.0894 −0.567093
\(709\) −24.7455 −0.929338 −0.464669 0.885484i \(-0.653827\pi\)
−0.464669 + 0.885484i \(0.653827\pi\)
\(710\) −16.2197 −0.608715
\(711\) 17.2820 0.648124
\(712\) −11.0303 −0.413379
\(713\) 2.00610 0.0751291
\(714\) 9.04770 0.338602
\(715\) 2.15141 0.0804581
\(716\) −3.90503 −0.145938
\(717\) 8.80352 0.328774
\(718\) 8.74875 0.326500
\(719\) −0.234057 −0.00872886 −0.00436443 0.999990i \(-0.501389\pi\)
−0.00436443 + 0.999990i \(0.501389\pi\)
\(720\) −1.70935 −0.0637038
\(721\) −0.385433 −0.0143543
\(722\) −18.2490 −0.679156
\(723\) 20.4604 0.760930
\(724\) −19.2250 −0.714490
\(725\) 7.34705 0.272862
\(726\) 12.3415 0.458036
\(727\) −36.6345 −1.35870 −0.679350 0.733814i \(-0.737738\pi\)
−0.679350 + 0.733814i \(0.737738\pi\)
\(728\) 7.66110 0.283939
\(729\) 19.8583 0.735494
\(730\) 14.9111 0.551883
\(731\) 58.1197 2.14963
\(732\) 16.7945 0.620742
\(733\) 26.7468 0.987917 0.493959 0.869485i \(-0.335549\pi\)
0.493959 + 0.869485i \(0.335549\pi\)
\(734\) −21.8025 −0.804744
\(735\) 5.98408 0.220726
\(736\) −1.64764 −0.0607329
\(737\) 5.87691 0.216479
\(738\) −0.517834 −0.0190617
\(739\) 8.19880 0.301598 0.150799 0.988564i \(-0.451815\pi\)
0.150799 + 0.988564i \(0.451815\pi\)
\(740\) −2.26909 −0.0834133
\(741\) 5.73021 0.210505
\(742\) 6.74184 0.247501
\(743\) −11.2264 −0.411855 −0.205928 0.978567i \(-0.566021\pi\)
−0.205928 + 0.978567i \(0.566021\pi\)
\(744\) 1.38323 0.0507116
\(745\) 5.03587 0.184500
\(746\) 17.6367 0.645725
\(747\) 25.2576 0.924128
\(748\) −2.23649 −0.0817740
\(749\) −4.61829 −0.168749
\(750\) −1.13607 −0.0414833
\(751\) −33.2136 −1.21198 −0.605991 0.795471i \(-0.707223\pi\)
−0.605991 + 0.795471i \(0.707223\pi\)
\(752\) −0.473050 −0.0172504
\(753\) −23.2550 −0.847459
\(754\) −42.7613 −1.55727
\(755\) −3.59542 −0.130851
\(756\) −7.04236 −0.256128
\(757\) −1.70262 −0.0618827 −0.0309414 0.999521i \(-0.509851\pi\)
−0.0309414 + 0.999521i \(0.509851\pi\)
\(758\) 3.12987 0.113682
\(759\) −0.691913 −0.0251149
\(760\) 0.866620 0.0314356
\(761\) −28.0640 −1.01732 −0.508659 0.860968i \(-0.669859\pi\)
−0.508659 + 0.860968i \(0.669859\pi\)
\(762\) 14.1444 0.512397
\(763\) 22.5324 0.815726
\(764\) 16.5153 0.597501
\(765\) −10.3422 −0.373923
\(766\) −4.78232 −0.172792
\(767\) −77.3045 −2.79130
\(768\) −1.13607 −0.0409943
\(769\) 37.2306 1.34257 0.671285 0.741199i \(-0.265743\pi\)
0.671285 + 0.741199i \(0.265743\pi\)
\(770\) 0.486562 0.0175345
\(771\) −11.4402 −0.412009
\(772\) 10.4471 0.375999
\(773\) −28.4453 −1.02311 −0.511554 0.859251i \(-0.670930\pi\)
−0.511554 + 0.859251i \(0.670930\pi\)
\(774\) −16.4200 −0.590205
\(775\) −1.21756 −0.0437360
\(776\) −13.0791 −0.469512
\(777\) −3.39319 −0.121730
\(778\) 24.0116 0.860856
\(779\) 0.262535 0.00940630
\(780\) 6.61214 0.236752
\(781\) 5.99554 0.214537
\(782\) −9.96882 −0.356484
\(783\) 39.3077 1.40474
\(784\) −5.26737 −0.188120
\(785\) −21.1133 −0.753565
\(786\) −19.5306 −0.696633
\(787\) 30.5131 1.08767 0.543837 0.839191i \(-0.316971\pi\)
0.543837 + 0.839191i \(0.316971\pi\)
\(788\) 5.66850 0.201932
\(789\) −19.8887 −0.708056
\(790\) −10.1102 −0.359706
\(791\) −7.44895 −0.264854
\(792\) 0.631854 0.0224519
\(793\) 86.0400 3.05537
\(794\) 14.4230 0.511853
\(795\) 5.81874 0.206369
\(796\) 4.57095 0.162013
\(797\) −27.2930 −0.966766 −0.483383 0.875409i \(-0.660592\pi\)
−0.483383 + 0.875409i \(0.660592\pi\)
\(798\) 1.29594 0.0458759
\(799\) −2.86212 −0.101255
\(800\) 1.00000 0.0353553
\(801\) 18.8547 0.666198
\(802\) 14.6177 0.516167
\(803\) −5.51180 −0.194507
\(804\) 18.0621 0.637001
\(805\) 2.16878 0.0764395
\(806\) 7.08644 0.249609
\(807\) −2.36991 −0.0834247
\(808\) −14.2016 −0.499611
\(809\) 30.4224 1.06959 0.534797 0.844980i \(-0.320388\pi\)
0.534797 + 0.844980i \(0.320388\pi\)
\(810\) −0.950058 −0.0333816
\(811\) −7.08206 −0.248685 −0.124342 0.992239i \(-0.539682\pi\)
−0.124342 + 0.992239i \(0.539682\pi\)
\(812\) −9.67089 −0.339382
\(813\) −4.07444 −0.142897
\(814\) 0.838757 0.0293984
\(815\) 6.35927 0.222755
\(816\) −6.87361 −0.240624
\(817\) 8.32474 0.291246
\(818\) −18.7903 −0.656989
\(819\) −13.0955 −0.457595
\(820\) 0.302941 0.0105792
\(821\) 36.2527 1.26523 0.632614 0.774468i \(-0.281982\pi\)
0.632614 + 0.774468i \(0.281982\pi\)
\(822\) −6.63350 −0.231370
\(823\) 16.8269 0.586548 0.293274 0.956028i \(-0.405255\pi\)
0.293274 + 0.956028i \(0.405255\pi\)
\(824\) 0.292816 0.0102007
\(825\) 0.419942 0.0146205
\(826\) −17.4832 −0.608318
\(827\) 47.8389 1.66352 0.831761 0.555135i \(-0.187333\pi\)
0.831761 + 0.555135i \(0.187333\pi\)
\(828\) 2.81640 0.0978766
\(829\) −19.4286 −0.674782 −0.337391 0.941365i \(-0.609545\pi\)
−0.337391 + 0.941365i \(0.609545\pi\)
\(830\) −14.7761 −0.512887
\(831\) 13.4983 0.468251
\(832\) −5.82020 −0.201779
\(833\) −31.8694 −1.10421
\(834\) 11.2072 0.388073
\(835\) 1.10367 0.0381940
\(836\) −0.320342 −0.0110793
\(837\) −6.51411 −0.225161
\(838\) 7.37928 0.254913
\(839\) 25.6879 0.886845 0.443422 0.896313i \(-0.353764\pi\)
0.443422 + 0.896313i \(0.353764\pi\)
\(840\) 1.49540 0.0515962
\(841\) 24.9791 0.861348
\(842\) 7.33963 0.252940
\(843\) −4.15655 −0.143159
\(844\) −21.2038 −0.729865
\(845\) 20.8747 0.718113
\(846\) 0.808609 0.0278005
\(847\) 14.2994 0.491333
\(848\) −5.12183 −0.175884
\(849\) 12.0507 0.413577
\(850\) 6.05036 0.207526
\(851\) 3.73864 0.128159
\(852\) 18.4267 0.631288
\(853\) 5.13181 0.175710 0.0878549 0.996133i \(-0.471999\pi\)
0.0878549 + 0.996133i \(0.471999\pi\)
\(854\) 19.4588 0.665866
\(855\) −1.48136 −0.0506614
\(856\) 3.50855 0.119920
\(857\) −57.5631 −1.96632 −0.983159 0.182754i \(-0.941499\pi\)
−0.983159 + 0.182754i \(0.941499\pi\)
\(858\) −2.44414 −0.0834417
\(859\) −11.8463 −0.404192 −0.202096 0.979366i \(-0.564775\pi\)
−0.202096 + 0.979366i \(0.564775\pi\)
\(860\) 9.60599 0.327561
\(861\) 0.453019 0.0154388
\(862\) 16.6986 0.568758
\(863\) 29.7253 1.01186 0.505930 0.862574i \(-0.331149\pi\)
0.505930 + 0.862574i \(0.331149\pi\)
\(864\) 5.35014 0.182015
\(865\) 4.02327 0.136795
\(866\) −29.9018 −1.01610
\(867\) −22.2747 −0.756487
\(868\) 1.60267 0.0543981
\(869\) 3.73720 0.126776
\(870\) −8.34674 −0.282981
\(871\) 92.5342 3.13540
\(872\) −17.1180 −0.579689
\(873\) 22.3568 0.756662
\(874\) −1.42788 −0.0482987
\(875\) −1.31630 −0.0444989
\(876\) −16.9400 −0.572348
\(877\) 18.9424 0.639640 0.319820 0.947478i \(-0.396378\pi\)
0.319820 + 0.947478i \(0.396378\pi\)
\(878\) −33.8204 −1.14138
\(879\) 21.0565 0.710219
\(880\) −0.369645 −0.0124607
\(881\) −27.7289 −0.934212 −0.467106 0.884201i \(-0.654703\pi\)
−0.467106 + 0.884201i \(0.654703\pi\)
\(882\) 9.00378 0.303173
\(883\) 18.5282 0.623525 0.311762 0.950160i \(-0.399081\pi\)
0.311762 + 0.950160i \(0.399081\pi\)
\(884\) −35.2143 −1.18438
\(885\) −15.0894 −0.507223
\(886\) 8.00923 0.269076
\(887\) −8.28570 −0.278207 −0.139103 0.990278i \(-0.544422\pi\)
−0.139103 + 0.990278i \(0.544422\pi\)
\(888\) 2.57783 0.0865064
\(889\) 16.3883 0.549646
\(890\) −11.0303 −0.369737
\(891\) 0.351185 0.0117651
\(892\) −14.8044 −0.495687
\(893\) −0.409955 −0.0137186
\(894\) −5.72109 −0.191342
\(895\) −3.90503 −0.130531
\(896\) −1.31630 −0.0439744
\(897\) −10.8944 −0.363754
\(898\) −8.81951 −0.294311
\(899\) −8.94547 −0.298348
\(900\) −1.70935 −0.0569784
\(901\) −30.9889 −1.03239
\(902\) −0.111981 −0.00372856
\(903\) 14.3648 0.478030
\(904\) 5.65902 0.188216
\(905\) −19.2250 −0.639059
\(906\) 4.08464 0.135703
\(907\) 35.5442 1.18023 0.590113 0.807321i \(-0.299083\pi\)
0.590113 + 0.807321i \(0.299083\pi\)
\(908\) 17.0876 0.567071
\(909\) 24.2756 0.805170
\(910\) 7.66110 0.253963
\(911\) 16.1787 0.536026 0.268013 0.963415i \(-0.413633\pi\)
0.268013 + 0.963415i \(0.413633\pi\)
\(912\) −0.984538 −0.0326013
\(913\) 5.46193 0.180763
\(914\) −2.75550 −0.0911438
\(915\) 16.7945 0.555208
\(916\) 17.3259 0.572465
\(917\) −22.6290 −0.747275
\(918\) 32.3703 1.06838
\(919\) 37.2319 1.22817 0.614083 0.789242i \(-0.289526\pi\)
0.614083 + 0.789242i \(0.289526\pi\)
\(920\) −1.64764 −0.0543211
\(921\) −35.7902 −1.17933
\(922\) −4.50213 −0.148270
\(923\) 94.4020 3.10728
\(924\) −0.552767 −0.0181847
\(925\) −2.26909 −0.0746071
\(926\) −23.3048 −0.765842
\(927\) −0.500526 −0.0164394
\(928\) 7.34705 0.241179
\(929\) −51.7214 −1.69692 −0.848462 0.529256i \(-0.822471\pi\)
−0.848462 + 0.529256i \(0.822471\pi\)
\(930\) 1.38323 0.0453579
\(931\) −4.56481 −0.149605
\(932\) −0.738526 −0.0241912
\(933\) −4.70879 −0.154159
\(934\) 5.67434 0.185670
\(935\) −2.23649 −0.0731409
\(936\) 9.94877 0.325186
\(937\) −18.8974 −0.617350 −0.308675 0.951168i \(-0.599886\pi\)
−0.308675 + 0.951168i \(0.599886\pi\)
\(938\) 20.9275 0.683308
\(939\) −9.43030 −0.307746
\(940\) −0.473050 −0.0154292
\(941\) −50.5652 −1.64838 −0.824189 0.566315i \(-0.808368\pi\)
−0.824189 + 0.566315i \(0.808368\pi\)
\(942\) 23.9861 0.781509
\(943\) −0.499139 −0.0162542
\(944\) 13.2821 0.432296
\(945\) −7.04236 −0.229088
\(946\) −3.55081 −0.115447
\(947\) −26.8304 −0.871871 −0.435935 0.899978i \(-0.643582\pi\)
−0.435935 + 0.899978i \(0.643582\pi\)
\(948\) 11.4859 0.373045
\(949\) −86.7853 −2.81717
\(950\) 0.866620 0.0281169
\(951\) 36.5196 1.18423
\(952\) −7.96406 −0.258117
\(953\) 53.1760 1.72254 0.861270 0.508147i \(-0.169669\pi\)
0.861270 + 0.508147i \(0.169669\pi\)
\(954\) 8.75501 0.283454
\(955\) 16.5153 0.534421
\(956\) −7.74912 −0.250625
\(957\) 3.08533 0.0997346
\(958\) −29.8542 −0.964547
\(959\) −7.68586 −0.248189
\(960\) −1.13607 −0.0366664
\(961\) −29.5175 −0.952179
\(962\) 13.2065 0.425796
\(963\) −5.99735 −0.193262
\(964\) −18.0098 −0.580058
\(965\) 10.4471 0.336304
\(966\) −2.46388 −0.0792741
\(967\) −18.6025 −0.598217 −0.299109 0.954219i \(-0.596689\pi\)
−0.299109 + 0.954219i \(0.596689\pi\)
\(968\) −10.8634 −0.349162
\(969\) −5.95681 −0.191360
\(970\) −13.0791 −0.419944
\(971\) 0.967502 0.0310486 0.0155243 0.999879i \(-0.495058\pi\)
0.0155243 + 0.999879i \(0.495058\pi\)
\(972\) −14.9711 −0.480198
\(973\) 12.9851 0.416283
\(974\) −37.7136 −1.20842
\(975\) 6.61214 0.211758
\(976\) −14.7830 −0.473192
\(977\) −27.6148 −0.883475 −0.441737 0.897144i \(-0.645638\pi\)
−0.441737 + 0.897144i \(0.645638\pi\)
\(978\) −7.22455 −0.231016
\(979\) 4.07731 0.130311
\(980\) −5.26737 −0.168260
\(981\) 29.2607 0.934222
\(982\) −28.3165 −0.903617
\(983\) 11.6694 0.372197 0.186098 0.982531i \(-0.440416\pi\)
0.186098 + 0.982531i \(0.440416\pi\)
\(984\) −0.344162 −0.0109715
\(985\) 5.66850 0.180613
\(986\) 44.4523 1.41565
\(987\) −0.707399 −0.0225167
\(988\) −5.04390 −0.160468
\(989\) −15.8272 −0.503276
\(990\) 0.631854 0.0200816
\(991\) −44.3184 −1.40782 −0.703911 0.710288i \(-0.748565\pi\)
−0.703911 + 0.710288i \(0.748565\pi\)
\(992\) −1.21756 −0.0386576
\(993\) −11.7484 −0.372824
\(994\) 21.3500 0.677179
\(995\) 4.57095 0.144909
\(996\) 16.7867 0.531906
\(997\) −4.38308 −0.138813 −0.0694067 0.997588i \(-0.522111\pi\)
−0.0694067 + 0.997588i \(0.522111\pi\)
\(998\) −25.6119 −0.810731
\(999\) −12.1399 −0.384090
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 \(a_p\))