Properties

Label 6027.2.a.bn.1.7
Level 6027
Weight 2
Character 6027.1
Self dual Yes
Analytic conductor 48.126
Analytic rank 0
Dimension 24
CM No

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Newspace parameters

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

Newform invariants

Self dual: Yes
Analytic conductor: \(48.1258372982\)
Analytic rank: \(0\)
Dimension: \(24\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.25316 q^{2} -1.00000 q^{3} -0.429590 q^{4} +1.76265 q^{5} +1.25316 q^{6} +3.04466 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.25316 q^{2} -1.00000 q^{3} -0.429590 q^{4} +1.76265 q^{5} +1.25316 q^{6} +3.04466 q^{8} +1.00000 q^{9} -2.20889 q^{10} -4.84306 q^{11} +0.429590 q^{12} +3.18902 q^{13} -1.76265 q^{15} -2.95627 q^{16} -6.61037 q^{17} -1.25316 q^{18} +8.31403 q^{19} -0.757219 q^{20} +6.06913 q^{22} -8.32423 q^{23} -3.04466 q^{24} -1.89305 q^{25} -3.99635 q^{26} -1.00000 q^{27} -7.79558 q^{29} +2.20889 q^{30} +1.04110 q^{31} -2.38465 q^{32} +4.84306 q^{33} +8.28385 q^{34} -0.429590 q^{36} +3.58658 q^{37} -10.4188 q^{38} -3.18902 q^{39} +5.36669 q^{40} +1.00000 q^{41} +4.05595 q^{43} +2.08053 q^{44} +1.76265 q^{45} +10.4316 q^{46} -0.963735 q^{47} +2.95627 q^{48} +2.37229 q^{50} +6.61037 q^{51} -1.36997 q^{52} +5.52023 q^{53} +1.25316 q^{54} -8.53664 q^{55} -8.31403 q^{57} +9.76911 q^{58} +9.28053 q^{59} +0.757219 q^{60} -11.2178 q^{61} -1.30466 q^{62} +8.90089 q^{64} +5.62114 q^{65} -6.06913 q^{66} +6.04854 q^{67} +2.83975 q^{68} +8.32423 q^{69} +9.94007 q^{71} +3.04466 q^{72} +3.75792 q^{73} -4.49456 q^{74} +1.89305 q^{75} -3.57162 q^{76} +3.99635 q^{78} -13.7937 q^{79} -5.21089 q^{80} +1.00000 q^{81} -1.25316 q^{82} -8.11111 q^{83} -11.6518 q^{85} -5.08276 q^{86} +7.79558 q^{87} -14.7455 q^{88} +10.4911 q^{89} -2.20889 q^{90} +3.57601 q^{92} -1.04110 q^{93} +1.20771 q^{94} +14.6548 q^{95} +2.38465 q^{96} +11.2995 q^{97} -4.84306 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 8q^{2} - 24q^{3} + 32q^{4} - 4q^{5} - 8q^{6} + 24q^{8} + 24q^{9} + O(q^{10}) \) \( 24q + 8q^{2} - 24q^{3} + 32q^{4} - 4q^{5} - 8q^{6} + 24q^{8} + 24q^{9} + 4q^{10} + 12q^{11} - 32q^{12} + 4q^{15} + 44q^{16} - 8q^{17} + 8q^{18} + 4q^{19} - 28q^{20} + 16q^{22} + 20q^{23} - 24q^{24} + 48q^{25} - 32q^{26} - 24q^{27} + 24q^{29} - 4q^{30} + 4q^{31} + 36q^{32} - 12q^{33} - 16q^{34} + 32q^{36} + 64q^{37} - 20q^{38} + 48q^{40} + 24q^{41} + 20q^{43} + 48q^{44} - 4q^{45} + 28q^{46} - 32q^{47} - 44q^{48} - 20q^{50} + 8q^{51} + 76q^{53} - 8q^{54} + 24q^{55} - 4q^{57} + 28q^{58} - 28q^{59} + 28q^{60} + 28q^{61} + 4q^{62} + 48q^{64} + 28q^{65} - 16q^{66} + 44q^{67} + 32q^{68} - 20q^{69} + 20q^{71} + 24q^{72} + 16q^{73} + 44q^{74} - 48q^{75} + 16q^{76} + 32q^{78} + 4q^{79} - 44q^{80} + 24q^{81} + 8q^{82} - 8q^{83} + 28q^{85} + 56q^{86} - 24q^{87} + 60q^{88} - 60q^{89} + 4q^{90} + 60q^{92} - 4q^{93} - 24q^{94} + 28q^{95} - 36q^{96} + 48q^{97} + 12q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.25316 −0.886118 −0.443059 0.896492i \(-0.646107\pi\)
−0.443059 + 0.896492i \(0.646107\pi\)
\(3\) −1.00000 −0.577350
\(4\) −0.429590 −0.214795
\(5\) 1.76265 0.788283 0.394142 0.919050i \(-0.371042\pi\)
0.394142 + 0.919050i \(0.371042\pi\)
\(6\) 1.25316 0.511600
\(7\) 0 0
\(8\) 3.04466 1.07645
\(9\) 1.00000 0.333333
\(10\) −2.20889 −0.698512
\(11\) −4.84306 −1.46024 −0.730119 0.683320i \(-0.760535\pi\)
−0.730119 + 0.683320i \(0.760535\pi\)
\(12\) 0.429590 0.124012
\(13\) 3.18902 0.884475 0.442237 0.896898i \(-0.354185\pi\)
0.442237 + 0.896898i \(0.354185\pi\)
\(14\) 0 0
\(15\) −1.76265 −0.455115
\(16\) −2.95627 −0.739068
\(17\) −6.61037 −1.60325 −0.801625 0.597827i \(-0.796031\pi\)
−0.801625 + 0.597827i \(0.796031\pi\)
\(18\) −1.25316 −0.295373
\(19\) 8.31403 1.90737 0.953685 0.300808i \(-0.0972564\pi\)
0.953685 + 0.300808i \(0.0972564\pi\)
\(20\) −0.757219 −0.169319
\(21\) 0 0
\(22\) 6.06913 1.29394
\(23\) −8.32423 −1.73572 −0.867861 0.496807i \(-0.834506\pi\)
−0.867861 + 0.496807i \(0.834506\pi\)
\(24\) −3.04466 −0.621490
\(25\) −1.89305 −0.378610
\(26\) −3.99635 −0.783749
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −7.79558 −1.44760 −0.723802 0.690008i \(-0.757607\pi\)
−0.723802 + 0.690008i \(0.757607\pi\)
\(30\) 2.20889 0.403286
\(31\) 1.04110 0.186986 0.0934932 0.995620i \(-0.470197\pi\)
0.0934932 + 0.995620i \(0.470197\pi\)
\(32\) −2.38465 −0.421550
\(33\) 4.84306 0.843068
\(34\) 8.28385 1.42067
\(35\) 0 0
\(36\) −0.429590 −0.0715983
\(37\) 3.58658 0.589630 0.294815 0.955554i \(-0.404742\pi\)
0.294815 + 0.955554i \(0.404742\pi\)
\(38\) −10.4188 −1.69015
\(39\) −3.18902 −0.510652
\(40\) 5.36669 0.848549
\(41\) 1.00000 0.156174
\(42\) 0 0
\(43\) 4.05595 0.618527 0.309263 0.950976i \(-0.399918\pi\)
0.309263 + 0.950976i \(0.399918\pi\)
\(44\) 2.08053 0.313652
\(45\) 1.76265 0.262761
\(46\) 10.4316 1.53805
\(47\) −0.963735 −0.140575 −0.0702876 0.997527i \(-0.522392\pi\)
−0.0702876 + 0.997527i \(0.522392\pi\)
\(48\) 2.95627 0.426701
\(49\) 0 0
\(50\) 2.37229 0.335493
\(51\) 6.61037 0.925637
\(52\) −1.36997 −0.189981
\(53\) 5.52023 0.758262 0.379131 0.925343i \(-0.376223\pi\)
0.379131 + 0.925343i \(0.376223\pi\)
\(54\) 1.25316 0.170533
\(55\) −8.53664 −1.15108
\(56\) 0 0
\(57\) −8.31403 −1.10122
\(58\) 9.76911 1.28275
\(59\) 9.28053 1.20822 0.604111 0.796900i \(-0.293528\pi\)
0.604111 + 0.796900i \(0.293528\pi\)
\(60\) 0.757219 0.0977565
\(61\) −11.2178 −1.43629 −0.718145 0.695893i \(-0.755009\pi\)
−0.718145 + 0.695893i \(0.755009\pi\)
\(62\) −1.30466 −0.165692
\(63\) 0 0
\(64\) 8.90089 1.11261
\(65\) 5.62114 0.697217
\(66\) −6.06913 −0.747058
\(67\) 6.04854 0.738946 0.369473 0.929241i \(-0.379538\pi\)
0.369473 + 0.929241i \(0.379538\pi\)
\(68\) 2.83975 0.344370
\(69\) 8.32423 1.00212
\(70\) 0 0
\(71\) 9.94007 1.17967 0.589834 0.807524i \(-0.299193\pi\)
0.589834 + 0.807524i \(0.299193\pi\)
\(72\) 3.04466 0.358817
\(73\) 3.75792 0.439832 0.219916 0.975519i \(-0.429422\pi\)
0.219916 + 0.975519i \(0.429422\pi\)
\(74\) −4.49456 −0.522482
\(75\) 1.89305 0.218590
\(76\) −3.57162 −0.409693
\(77\) 0 0
\(78\) 3.99635 0.452498
\(79\) −13.7937 −1.55192 −0.775958 0.630784i \(-0.782733\pi\)
−0.775958 + 0.630784i \(0.782733\pi\)
\(80\) −5.21089 −0.582595
\(81\) 1.00000 0.111111
\(82\) −1.25316 −0.138388
\(83\) −8.11111 −0.890309 −0.445155 0.895454i \(-0.646851\pi\)
−0.445155 + 0.895454i \(0.646851\pi\)
\(84\) 0 0
\(85\) −11.6518 −1.26382
\(86\) −5.08276 −0.548088
\(87\) 7.79558 0.835774
\(88\) −14.7455 −1.57187
\(89\) 10.4911 1.11206 0.556029 0.831163i \(-0.312324\pi\)
0.556029 + 0.831163i \(0.312324\pi\)
\(90\) −2.20889 −0.232837
\(91\) 0 0
\(92\) 3.57601 0.372824
\(93\) −1.04110 −0.107957
\(94\) 1.20771 0.124566
\(95\) 14.6548 1.50355
\(96\) 2.38465 0.243382
\(97\) 11.2995 1.14729 0.573644 0.819104i \(-0.305529\pi\)
0.573644 + 0.819104i \(0.305529\pi\)
\(98\) 0 0
\(99\) −4.84306 −0.486746
\(100\) 0.813234 0.0813234
\(101\) −16.1294 −1.60494 −0.802469 0.596694i \(-0.796481\pi\)
−0.802469 + 0.596694i \(0.796481\pi\)
\(102\) −8.28385 −0.820224
\(103\) 14.9966 1.47766 0.738828 0.673894i \(-0.235380\pi\)
0.738828 + 0.673894i \(0.235380\pi\)
\(104\) 9.70950 0.952094
\(105\) 0 0
\(106\) −6.91773 −0.671909
\(107\) −14.7499 −1.42593 −0.712963 0.701202i \(-0.752647\pi\)
−0.712963 + 0.701202i \(0.752647\pi\)
\(108\) 0.429590 0.0413373
\(109\) 6.63410 0.635432 0.317716 0.948186i \(-0.397084\pi\)
0.317716 + 0.948186i \(0.397084\pi\)
\(110\) 10.6978 1.01999
\(111\) −3.58658 −0.340423
\(112\) 0 0
\(113\) −1.35078 −0.127071 −0.0635354 0.997980i \(-0.520238\pi\)
−0.0635354 + 0.997980i \(0.520238\pi\)
\(114\) 10.4188 0.975811
\(115\) −14.6727 −1.36824
\(116\) 3.34890 0.310938
\(117\) 3.18902 0.294825
\(118\) −11.6300 −1.07063
\(119\) 0 0
\(120\) −5.36669 −0.489910
\(121\) 12.4552 1.13229
\(122\) 14.0577 1.27272
\(123\) −1.00000 −0.0901670
\(124\) −0.447244 −0.0401637
\(125\) −12.1501 −1.08673
\(126\) 0 0
\(127\) −9.16265 −0.813054 −0.406527 0.913639i \(-0.633260\pi\)
−0.406527 + 0.913639i \(0.633260\pi\)
\(128\) −6.38495 −0.564355
\(129\) −4.05595 −0.357107
\(130\) −7.04419 −0.617816
\(131\) −5.34838 −0.467291 −0.233645 0.972322i \(-0.575065\pi\)
−0.233645 + 0.972322i \(0.575065\pi\)
\(132\) −2.08053 −0.181087
\(133\) 0 0
\(134\) −7.57979 −0.654794
\(135\) −1.76265 −0.151705
\(136\) −20.1264 −1.72582
\(137\) 20.2802 1.73266 0.866329 0.499474i \(-0.166473\pi\)
0.866329 + 0.499474i \(0.166473\pi\)
\(138\) −10.4316 −0.887996
\(139\) −2.75452 −0.233635 −0.116818 0.993153i \(-0.537269\pi\)
−0.116818 + 0.993153i \(0.537269\pi\)
\(140\) 0 0
\(141\) 0.963735 0.0811611
\(142\) −12.4565 −1.04533
\(143\) −15.4446 −1.29154
\(144\) −2.95627 −0.246356
\(145\) −13.7409 −1.14112
\(146\) −4.70928 −0.389743
\(147\) 0 0
\(148\) −1.54076 −0.126650
\(149\) 9.53225 0.780912 0.390456 0.920622i \(-0.372317\pi\)
0.390456 + 0.920622i \(0.372317\pi\)
\(150\) −2.37229 −0.193697
\(151\) −5.68919 −0.462979 −0.231490 0.972837i \(-0.574360\pi\)
−0.231490 + 0.972837i \(0.574360\pi\)
\(152\) 25.3134 2.05319
\(153\) −6.61037 −0.534417
\(154\) 0 0
\(155\) 1.83509 0.147398
\(156\) 1.36997 0.109685
\(157\) 10.9120 0.870869 0.435434 0.900221i \(-0.356595\pi\)
0.435434 + 0.900221i \(0.356595\pi\)
\(158\) 17.2858 1.37518
\(159\) −5.52023 −0.437783
\(160\) −4.20331 −0.332301
\(161\) 0 0
\(162\) −1.25316 −0.0984576
\(163\) −2.69969 −0.211456 −0.105728 0.994395i \(-0.533717\pi\)
−0.105728 + 0.994395i \(0.533717\pi\)
\(164\) −0.429590 −0.0335453
\(165\) 8.53664 0.664577
\(166\) 10.1645 0.788919
\(167\) 10.8810 0.841998 0.420999 0.907061i \(-0.361680\pi\)
0.420999 + 0.907061i \(0.361680\pi\)
\(168\) 0 0
\(169\) −2.83016 −0.217704
\(170\) 14.6016 1.11989
\(171\) 8.31403 0.635790
\(172\) −1.74240 −0.132856
\(173\) 14.5148 1.10354 0.551769 0.833997i \(-0.313953\pi\)
0.551769 + 0.833997i \(0.313953\pi\)
\(174\) −9.76911 −0.740594
\(175\) 0 0
\(176\) 14.3174 1.07921
\(177\) −9.28053 −0.697567
\(178\) −13.1471 −0.985415
\(179\) 14.3925 1.07575 0.537873 0.843026i \(-0.319228\pi\)
0.537873 + 0.843026i \(0.319228\pi\)
\(180\) −0.757219 −0.0564397
\(181\) 10.9137 0.811208 0.405604 0.914049i \(-0.367061\pi\)
0.405604 + 0.914049i \(0.367061\pi\)
\(182\) 0 0
\(183\) 11.2178 0.829243
\(184\) −25.3445 −1.86842
\(185\) 6.32190 0.464795
\(186\) 1.30466 0.0956623
\(187\) 32.0144 2.34113
\(188\) 0.414011 0.0301948
\(189\) 0 0
\(190\) −18.3648 −1.33232
\(191\) 2.59146 0.187512 0.0937558 0.995595i \(-0.470113\pi\)
0.0937558 + 0.995595i \(0.470113\pi\)
\(192\) −8.90089 −0.642366
\(193\) −15.2810 −1.09995 −0.549977 0.835180i \(-0.685363\pi\)
−0.549977 + 0.835180i \(0.685363\pi\)
\(194\) −14.1601 −1.01663
\(195\) −5.62114 −0.402538
\(196\) 0 0
\(197\) 14.9063 1.06203 0.531013 0.847363i \(-0.321811\pi\)
0.531013 + 0.847363i \(0.321811\pi\)
\(198\) 6.06913 0.431314
\(199\) 3.57408 0.253360 0.126680 0.991944i \(-0.459568\pi\)
0.126680 + 0.991944i \(0.459568\pi\)
\(200\) −5.76370 −0.407555
\(201\) −6.04854 −0.426631
\(202\) 20.2128 1.42216
\(203\) 0 0
\(204\) −2.83975 −0.198822
\(205\) 1.76265 0.123109
\(206\) −18.7931 −1.30938
\(207\) −8.32423 −0.578574
\(208\) −9.42761 −0.653687
\(209\) −40.2653 −2.78521
\(210\) 0 0
\(211\) 1.16912 0.0804857 0.0402428 0.999190i \(-0.487187\pi\)
0.0402428 + 0.999190i \(0.487187\pi\)
\(212\) −2.37143 −0.162871
\(213\) −9.94007 −0.681082
\(214\) 18.4840 1.26354
\(215\) 7.14924 0.487574
\(216\) −3.04466 −0.207163
\(217\) 0 0
\(218\) −8.31359 −0.563067
\(219\) −3.75792 −0.253937
\(220\) 3.66725 0.247246
\(221\) −21.0806 −1.41803
\(222\) 4.49456 0.301655
\(223\) 1.28838 0.0862763 0.0431382 0.999069i \(-0.486264\pi\)
0.0431382 + 0.999069i \(0.486264\pi\)
\(224\) 0 0
\(225\) −1.89305 −0.126203
\(226\) 1.69274 0.112600
\(227\) −24.1040 −1.59984 −0.799919 0.600108i \(-0.795124\pi\)
−0.799919 + 0.600108i \(0.795124\pi\)
\(228\) 3.57162 0.236537
\(229\) −0.361413 −0.0238828 −0.0119414 0.999929i \(-0.503801\pi\)
−0.0119414 + 0.999929i \(0.503801\pi\)
\(230\) 18.3873 1.21242
\(231\) 0 0
\(232\) −23.7349 −1.55827
\(233\) 0.141975 0.00930108 0.00465054 0.999989i \(-0.498520\pi\)
0.00465054 + 0.999989i \(0.498520\pi\)
\(234\) −3.99635 −0.261250
\(235\) −1.69873 −0.110813
\(236\) −3.98682 −0.259520
\(237\) 13.7937 0.896000
\(238\) 0 0
\(239\) 11.9975 0.776055 0.388027 0.921648i \(-0.373157\pi\)
0.388027 + 0.921648i \(0.373157\pi\)
\(240\) 5.21089 0.336361
\(241\) 1.49883 0.0965478 0.0482739 0.998834i \(-0.484628\pi\)
0.0482739 + 0.998834i \(0.484628\pi\)
\(242\) −15.6084 −1.00335
\(243\) −1.00000 −0.0641500
\(244\) 4.81905 0.308508
\(245\) 0 0
\(246\) 1.25316 0.0798986
\(247\) 26.5136 1.68702
\(248\) 3.16979 0.201282
\(249\) 8.11111 0.514020
\(250\) 15.2260 0.962975
\(251\) −6.61735 −0.417683 −0.208842 0.977949i \(-0.566969\pi\)
−0.208842 + 0.977949i \(0.566969\pi\)
\(252\) 0 0
\(253\) 40.3147 2.53457
\(254\) 11.4823 0.720462
\(255\) 11.6518 0.729664
\(256\) −9.80042 −0.612526
\(257\) −7.49560 −0.467563 −0.233781 0.972289i \(-0.575110\pi\)
−0.233781 + 0.972289i \(0.575110\pi\)
\(258\) 5.08276 0.316439
\(259\) 0 0
\(260\) −2.41479 −0.149759
\(261\) −7.79558 −0.482534
\(262\) 6.70238 0.414075
\(263\) −18.6115 −1.14764 −0.573818 0.818983i \(-0.694538\pi\)
−0.573818 + 0.818983i \(0.694538\pi\)
\(264\) 14.7455 0.907522
\(265\) 9.73025 0.597725
\(266\) 0 0
\(267\) −10.4911 −0.642047
\(268\) −2.59839 −0.158722
\(269\) −11.7570 −0.716839 −0.358419 0.933561i \(-0.616684\pi\)
−0.358419 + 0.933561i \(0.616684\pi\)
\(270\) 2.20889 0.134429
\(271\) −23.0447 −1.39987 −0.699933 0.714208i \(-0.746787\pi\)
−0.699933 + 0.714208i \(0.746787\pi\)
\(272\) 19.5421 1.18491
\(273\) 0 0
\(274\) −25.4144 −1.53534
\(275\) 9.16814 0.552860
\(276\) −3.57601 −0.215250
\(277\) 29.0686 1.74656 0.873282 0.487216i \(-0.161987\pi\)
0.873282 + 0.487216i \(0.161987\pi\)
\(278\) 3.45185 0.207028
\(279\) 1.04110 0.0623288
\(280\) 0 0
\(281\) 14.9373 0.891087 0.445543 0.895260i \(-0.353010\pi\)
0.445543 + 0.895260i \(0.353010\pi\)
\(282\) −1.20771 −0.0719183
\(283\) 10.5976 0.629960 0.314980 0.949098i \(-0.398002\pi\)
0.314980 + 0.949098i \(0.398002\pi\)
\(284\) −4.27015 −0.253387
\(285\) −14.6548 −0.868073
\(286\) 19.3546 1.14446
\(287\) 0 0
\(288\) −2.38465 −0.140517
\(289\) 26.6970 1.57041
\(290\) 17.2196 1.01117
\(291\) −11.2995 −0.662388
\(292\) −1.61437 −0.0944736
\(293\) −32.6469 −1.90725 −0.953625 0.300998i \(-0.902680\pi\)
−0.953625 + 0.300998i \(0.902680\pi\)
\(294\) 0 0
\(295\) 16.3584 0.952421
\(296\) 10.9199 0.634708
\(297\) 4.84306 0.281023
\(298\) −11.9454 −0.691980
\(299\) −26.5461 −1.53520
\(300\) −0.813234 −0.0469521
\(301\) 0 0
\(302\) 7.12946 0.410254
\(303\) 16.1294 0.926611
\(304\) −24.5785 −1.40968
\(305\) −19.7731 −1.13220
\(306\) 8.28385 0.473556
\(307\) −14.5205 −0.828728 −0.414364 0.910111i \(-0.635996\pi\)
−0.414364 + 0.910111i \(0.635996\pi\)
\(308\) 0 0
\(309\) −14.9966 −0.853125
\(310\) −2.29967 −0.130612
\(311\) 3.08406 0.174881 0.0874404 0.996170i \(-0.472131\pi\)
0.0874404 + 0.996170i \(0.472131\pi\)
\(312\) −9.70950 −0.549692
\(313\) −8.36990 −0.473094 −0.236547 0.971620i \(-0.576016\pi\)
−0.236547 + 0.971620i \(0.576016\pi\)
\(314\) −13.6744 −0.771692
\(315\) 0 0
\(316\) 5.92565 0.333344
\(317\) 24.4448 1.37295 0.686477 0.727151i \(-0.259156\pi\)
0.686477 + 0.727151i \(0.259156\pi\)
\(318\) 6.91773 0.387927
\(319\) 37.7545 2.11384
\(320\) 15.6892 0.877053
\(321\) 14.7499 0.823259
\(322\) 0 0
\(323\) −54.9588 −3.05799
\(324\) −0.429590 −0.0238661
\(325\) −6.03697 −0.334871
\(326\) 3.38315 0.187375
\(327\) −6.63410 −0.366867
\(328\) 3.04466 0.168114
\(329\) 0 0
\(330\) −10.6978 −0.588893
\(331\) −17.2362 −0.947390 −0.473695 0.880689i \(-0.657080\pi\)
−0.473695 + 0.880689i \(0.657080\pi\)
\(332\) 3.48445 0.191234
\(333\) 3.58658 0.196543
\(334\) −13.6357 −0.746110
\(335\) 10.6615 0.582499
\(336\) 0 0
\(337\) −12.2679 −0.668274 −0.334137 0.942525i \(-0.608445\pi\)
−0.334137 + 0.942525i \(0.608445\pi\)
\(338\) 3.54664 0.192912
\(339\) 1.35078 0.0733643
\(340\) 5.00550 0.271461
\(341\) −5.04209 −0.273045
\(342\) −10.4188 −0.563385
\(343\) 0 0
\(344\) 12.3490 0.665814
\(345\) 14.6727 0.789954
\(346\) −18.1893 −0.977864
\(347\) −28.5063 −1.53030 −0.765149 0.643853i \(-0.777335\pi\)
−0.765149 + 0.643853i \(0.777335\pi\)
\(348\) −3.34890 −0.179520
\(349\) 25.5334 1.36677 0.683385 0.730058i \(-0.260507\pi\)
0.683385 + 0.730058i \(0.260507\pi\)
\(350\) 0 0
\(351\) −3.18902 −0.170217
\(352\) 11.5490 0.615563
\(353\) 13.8669 0.738058 0.369029 0.929418i \(-0.379690\pi\)
0.369029 + 0.929418i \(0.379690\pi\)
\(354\) 11.6300 0.618127
\(355\) 17.5209 0.929913
\(356\) −4.50689 −0.238865
\(357\) 0 0
\(358\) −18.0361 −0.953237
\(359\) 31.5191 1.66352 0.831758 0.555139i \(-0.187335\pi\)
0.831758 + 0.555139i \(0.187335\pi\)
\(360\) 5.36669 0.282850
\(361\) 50.1231 2.63806
\(362\) −13.6766 −0.718826
\(363\) −12.4552 −0.653730
\(364\) 0 0
\(365\) 6.62392 0.346712
\(366\) −14.0577 −0.734807
\(367\) −9.06523 −0.473201 −0.236601 0.971607i \(-0.576033\pi\)
−0.236601 + 0.971607i \(0.576033\pi\)
\(368\) 24.6087 1.28282
\(369\) 1.00000 0.0520579
\(370\) −7.92235 −0.411864
\(371\) 0 0
\(372\) 0.447244 0.0231885
\(373\) 8.28576 0.429021 0.214510 0.976722i \(-0.431184\pi\)
0.214510 + 0.976722i \(0.431184\pi\)
\(374\) −40.1192 −2.07451
\(375\) 12.1501 0.627427
\(376\) −2.93425 −0.151322
\(377\) −24.8603 −1.28037
\(378\) 0 0
\(379\) −20.9123 −1.07419 −0.537096 0.843521i \(-0.680479\pi\)
−0.537096 + 0.843521i \(0.680479\pi\)
\(380\) −6.29554 −0.322954
\(381\) 9.16265 0.469417
\(382\) −3.24752 −0.166157
\(383\) 4.72176 0.241270 0.120635 0.992697i \(-0.461507\pi\)
0.120635 + 0.992697i \(0.461507\pi\)
\(384\) 6.38495 0.325830
\(385\) 0 0
\(386\) 19.1496 0.974688
\(387\) 4.05595 0.206176
\(388\) −4.85414 −0.246432
\(389\) 27.0332 1.37064 0.685319 0.728243i \(-0.259663\pi\)
0.685319 + 0.728243i \(0.259663\pi\)
\(390\) 7.04419 0.356696
\(391\) 55.0263 2.78280
\(392\) 0 0
\(393\) 5.34838 0.269790
\(394\) −18.6799 −0.941081
\(395\) −24.3136 −1.22335
\(396\) 2.08053 0.104551
\(397\) 28.9049 1.45070 0.725348 0.688383i \(-0.241679\pi\)
0.725348 + 0.688383i \(0.241679\pi\)
\(398\) −4.47890 −0.224507
\(399\) 0 0
\(400\) 5.59637 0.279818
\(401\) 35.6608 1.78082 0.890408 0.455163i \(-0.150419\pi\)
0.890408 + 0.455163i \(0.150419\pi\)
\(402\) 7.57979 0.378045
\(403\) 3.32008 0.165385
\(404\) 6.92904 0.344733
\(405\) 1.76265 0.0875870
\(406\) 0 0
\(407\) −17.3700 −0.861000
\(408\) 20.1264 0.996404
\(409\) 1.70039 0.0840788 0.0420394 0.999116i \(-0.486614\pi\)
0.0420394 + 0.999116i \(0.486614\pi\)
\(410\) −2.20889 −0.109089
\(411\) −20.2802 −1.00035
\(412\) −6.44237 −0.317393
\(413\) 0 0
\(414\) 10.4316 0.512685
\(415\) −14.2971 −0.701816
\(416\) −7.60469 −0.372850
\(417\) 2.75452 0.134889
\(418\) 50.4589 2.46803
\(419\) 12.6493 0.617957 0.308978 0.951069i \(-0.400013\pi\)
0.308978 + 0.951069i \(0.400013\pi\)
\(420\) 0 0
\(421\) 32.5413 1.58597 0.792983 0.609244i \(-0.208527\pi\)
0.792983 + 0.609244i \(0.208527\pi\)
\(422\) −1.46510 −0.0713198
\(423\) −0.963735 −0.0468584
\(424\) 16.8072 0.816232
\(425\) 12.5138 0.607006
\(426\) 12.4565 0.603519
\(427\) 0 0
\(428\) 6.33640 0.306282
\(429\) 15.4446 0.745673
\(430\) −8.95914 −0.432048
\(431\) −24.0660 −1.15922 −0.579609 0.814895i \(-0.696795\pi\)
−0.579609 + 0.814895i \(0.696795\pi\)
\(432\) 2.95627 0.142234
\(433\) 2.53991 0.122061 0.0610303 0.998136i \(-0.480561\pi\)
0.0610303 + 0.998136i \(0.480561\pi\)
\(434\) 0 0
\(435\) 13.7409 0.658827
\(436\) −2.84994 −0.136488
\(437\) −69.2079 −3.31066
\(438\) 4.70928 0.225018
\(439\) 12.6793 0.605149 0.302575 0.953126i \(-0.402154\pi\)
0.302575 + 0.953126i \(0.402154\pi\)
\(440\) −25.9912 −1.23908
\(441\) 0 0
\(442\) 26.4174 1.25655
\(443\) 10.4222 0.495175 0.247587 0.968866i \(-0.420362\pi\)
0.247587 + 0.968866i \(0.420362\pi\)
\(444\) 1.54076 0.0731212
\(445\) 18.4923 0.876617
\(446\) −1.61455 −0.0764510
\(447\) −9.53225 −0.450860
\(448\) 0 0
\(449\) 36.1665 1.70680 0.853401 0.521255i \(-0.174536\pi\)
0.853401 + 0.521255i \(0.174536\pi\)
\(450\) 2.37229 0.111831
\(451\) −4.84306 −0.228051
\(452\) 0.580282 0.0272942
\(453\) 5.68919 0.267301
\(454\) 30.2061 1.41764
\(455\) 0 0
\(456\) −25.3134 −1.18541
\(457\) −3.44773 −0.161278 −0.0806390 0.996743i \(-0.525696\pi\)
−0.0806390 + 0.996743i \(0.525696\pi\)
\(458\) 0.452908 0.0211630
\(459\) 6.61037 0.308546
\(460\) 6.30326 0.293891
\(461\) 39.2660 1.82880 0.914400 0.404811i \(-0.132663\pi\)
0.914400 + 0.404811i \(0.132663\pi\)
\(462\) 0 0
\(463\) 17.1115 0.795240 0.397620 0.917550i \(-0.369836\pi\)
0.397620 + 0.917550i \(0.369836\pi\)
\(464\) 23.0459 1.06988
\(465\) −1.83509 −0.0851004
\(466\) −0.177917 −0.00824185
\(467\) 41.0229 1.89831 0.949157 0.314802i \(-0.101938\pi\)
0.949157 + 0.314802i \(0.101938\pi\)
\(468\) −1.36997 −0.0633269
\(469\) 0 0
\(470\) 2.12878 0.0981934
\(471\) −10.9120 −0.502796
\(472\) 28.2561 1.30059
\(473\) −19.6432 −0.903196
\(474\) −17.2858 −0.793961
\(475\) −15.7389 −0.722148
\(476\) 0 0
\(477\) 5.52023 0.252754
\(478\) −15.0348 −0.687676
\(479\) −1.39675 −0.0638191 −0.0319096 0.999491i \(-0.510159\pi\)
−0.0319096 + 0.999491i \(0.510159\pi\)
\(480\) 4.20331 0.191854
\(481\) 11.4377 0.521513
\(482\) −1.87827 −0.0855527
\(483\) 0 0
\(484\) −5.35064 −0.243211
\(485\) 19.9171 0.904388
\(486\) 1.25316 0.0568445
\(487\) 30.7325 1.39262 0.696312 0.717739i \(-0.254823\pi\)
0.696312 + 0.717739i \(0.254823\pi\)
\(488\) −34.1544 −1.54610
\(489\) 2.69969 0.122084
\(490\) 0 0
\(491\) 23.7792 1.07314 0.536570 0.843856i \(-0.319720\pi\)
0.536570 + 0.843856i \(0.319720\pi\)
\(492\) 0.429590 0.0193674
\(493\) 51.5317 2.32087
\(494\) −33.2258 −1.49490
\(495\) −8.53664 −0.383693
\(496\) −3.07776 −0.138196
\(497\) 0 0
\(498\) −10.1645 −0.455483
\(499\) −8.09580 −0.362418 −0.181209 0.983445i \(-0.558001\pi\)
−0.181209 + 0.983445i \(0.558001\pi\)
\(500\) 5.21954 0.233425
\(501\) −10.8810 −0.486128
\(502\) 8.29260 0.370117
\(503\) 28.9531 1.29095 0.645476 0.763780i \(-0.276659\pi\)
0.645476 + 0.763780i \(0.276659\pi\)
\(504\) 0 0
\(505\) −28.4306 −1.26515
\(506\) −50.5208 −2.24592
\(507\) 2.83016 0.125692
\(508\) 3.93618 0.174640
\(509\) −16.0637 −0.712009 −0.356005 0.934484i \(-0.615861\pi\)
−0.356005 + 0.934484i \(0.615861\pi\)
\(510\) −14.6016 −0.646569
\(511\) 0 0
\(512\) 25.0514 1.10713
\(513\) −8.31403 −0.367073
\(514\) 9.39319 0.414316
\(515\) 26.4338 1.16481
\(516\) 1.74240 0.0767047
\(517\) 4.66743 0.205273
\(518\) 0 0
\(519\) −14.5148 −0.637128
\(520\) 17.1145 0.750520
\(521\) 39.7632 1.74206 0.871028 0.491234i \(-0.163454\pi\)
0.871028 + 0.491234i \(0.163454\pi\)
\(522\) 9.76911 0.427582
\(523\) −22.5014 −0.983918 −0.491959 0.870618i \(-0.663719\pi\)
−0.491959 + 0.870618i \(0.663719\pi\)
\(524\) 2.29761 0.100372
\(525\) 0 0
\(526\) 23.3232 1.01694
\(527\) −6.88203 −0.299786
\(528\) −14.3174 −0.623085
\(529\) 46.2928 2.01273
\(530\) −12.1936 −0.529655
\(531\) 9.28053 0.402741
\(532\) 0 0
\(533\) 3.18902 0.138132
\(534\) 13.1471 0.568930
\(535\) −25.9990 −1.12403
\(536\) 18.4158 0.795440
\(537\) −14.3925 −0.621082
\(538\) 14.7334 0.635204
\(539\) 0 0
\(540\) 0.757219 0.0325855
\(541\) −15.6936 −0.674720 −0.337360 0.941376i \(-0.609534\pi\)
−0.337360 + 0.941376i \(0.609534\pi\)
\(542\) 28.8787 1.24045
\(543\) −10.9137 −0.468351
\(544\) 15.7634 0.675850
\(545\) 11.6936 0.500900
\(546\) 0 0
\(547\) 9.27073 0.396388 0.198194 0.980163i \(-0.436492\pi\)
0.198194 + 0.980163i \(0.436492\pi\)
\(548\) −8.71219 −0.372166
\(549\) −11.2178 −0.478764
\(550\) −11.4892 −0.489899
\(551\) −64.8127 −2.76111
\(552\) 25.3445 1.07873
\(553\) 0 0
\(554\) −36.4276 −1.54766
\(555\) −6.32190 −0.268350
\(556\) 1.18331 0.0501837
\(557\) −5.25651 −0.222725 −0.111363 0.993780i \(-0.535522\pi\)
−0.111363 + 0.993780i \(0.535522\pi\)
\(558\) −1.30466 −0.0552307
\(559\) 12.9345 0.547071
\(560\) 0 0
\(561\) −32.0144 −1.35165
\(562\) −18.7189 −0.789608
\(563\) 32.3319 1.36263 0.681313 0.731992i \(-0.261409\pi\)
0.681313 + 0.731992i \(0.261409\pi\)
\(564\) −0.414011 −0.0174330
\(565\) −2.38096 −0.100168
\(566\) −13.2804 −0.558219
\(567\) 0 0
\(568\) 30.2642 1.26986
\(569\) 26.4828 1.11022 0.555109 0.831777i \(-0.312676\pi\)
0.555109 + 0.831777i \(0.312676\pi\)
\(570\) 18.3648 0.769215
\(571\) −20.4141 −0.854304 −0.427152 0.904180i \(-0.640483\pi\)
−0.427152 + 0.904180i \(0.640483\pi\)
\(572\) 6.63485 0.277417
\(573\) −2.59146 −0.108260
\(574\) 0 0
\(575\) 15.7582 0.657161
\(576\) 8.90089 0.370870
\(577\) 19.1030 0.795267 0.397633 0.917544i \(-0.369832\pi\)
0.397633 + 0.917544i \(0.369832\pi\)
\(578\) −33.4556 −1.39157
\(579\) 15.2810 0.635058
\(580\) 5.90296 0.245107
\(581\) 0 0
\(582\) 14.1601 0.586953
\(583\) −26.7348 −1.10724
\(584\) 11.4416 0.473457
\(585\) 5.62114 0.232406
\(586\) 40.9117 1.69005
\(587\) −40.4928 −1.67132 −0.835658 0.549251i \(-0.814913\pi\)
−0.835658 + 0.549251i \(0.814913\pi\)
\(588\) 0 0
\(589\) 8.65571 0.356652
\(590\) −20.4997 −0.843957
\(591\) −14.9063 −0.613161
\(592\) −10.6029 −0.435777
\(593\) 25.7064 1.05563 0.527817 0.849358i \(-0.323011\pi\)
0.527817 + 0.849358i \(0.323011\pi\)
\(594\) −6.06913 −0.249019
\(595\) 0 0
\(596\) −4.09496 −0.167736
\(597\) −3.57408 −0.146277
\(598\) 33.2666 1.36037
\(599\) −33.6227 −1.37378 −0.686892 0.726759i \(-0.741026\pi\)
−0.686892 + 0.726759i \(0.741026\pi\)
\(600\) 5.76370 0.235302
\(601\) −28.5731 −1.16552 −0.582760 0.812644i \(-0.698027\pi\)
−0.582760 + 0.812644i \(0.698027\pi\)
\(602\) 0 0
\(603\) 6.04854 0.246315
\(604\) 2.44402 0.0994456
\(605\) 21.9543 0.892567
\(606\) −20.2128 −0.821087
\(607\) −4.85008 −0.196859 −0.0984293 0.995144i \(-0.531382\pi\)
−0.0984293 + 0.995144i \(0.531382\pi\)
\(608\) −19.8260 −0.804052
\(609\) 0 0
\(610\) 24.7788 1.00327
\(611\) −3.07337 −0.124335
\(612\) 2.83975 0.114790
\(613\) 38.6074 1.55934 0.779668 0.626193i \(-0.215388\pi\)
0.779668 + 0.626193i \(0.215388\pi\)
\(614\) 18.1965 0.734351
\(615\) −1.76265 −0.0710771
\(616\) 0 0
\(617\) 3.33494 0.134260 0.0671298 0.997744i \(-0.478616\pi\)
0.0671298 + 0.997744i \(0.478616\pi\)
\(618\) 18.7931 0.755969
\(619\) −12.7195 −0.511239 −0.255620 0.966777i \(-0.582279\pi\)
−0.255620 + 0.966777i \(0.582279\pi\)
\(620\) −0.788338 −0.0316604
\(621\) 8.32423 0.334040
\(622\) −3.86482 −0.154965
\(623\) 0 0
\(624\) 9.42761 0.377406
\(625\) −11.9511 −0.478045
\(626\) 10.4888 0.419217
\(627\) 40.2653 1.60804
\(628\) −4.68766 −0.187058
\(629\) −23.7086 −0.945325
\(630\) 0 0
\(631\) 11.7041 0.465934 0.232967 0.972485i \(-0.425157\pi\)
0.232967 + 0.972485i \(0.425157\pi\)
\(632\) −41.9973 −1.67056
\(633\) −1.16912 −0.0464684
\(634\) −30.6332 −1.21660
\(635\) −16.1506 −0.640917
\(636\) 2.37143 0.0940335
\(637\) 0 0
\(638\) −47.3124 −1.87312
\(639\) 9.94007 0.393223
\(640\) −11.2545 −0.444871
\(641\) −26.0873 −1.03039 −0.515193 0.857074i \(-0.672280\pi\)
−0.515193 + 0.857074i \(0.672280\pi\)
\(642\) −18.4840 −0.729504
\(643\) 29.1704 1.15037 0.575183 0.818025i \(-0.304931\pi\)
0.575183 + 0.818025i \(0.304931\pi\)
\(644\) 0 0
\(645\) −7.14924 −0.281501
\(646\) 68.8722 2.70974
\(647\) 23.9403 0.941190 0.470595 0.882349i \(-0.344039\pi\)
0.470595 + 0.882349i \(0.344039\pi\)
\(648\) 3.04466 0.119606
\(649\) −44.9461 −1.76429
\(650\) 7.56529 0.296735
\(651\) 0 0
\(652\) 1.15976 0.0454198
\(653\) −2.94297 −0.115167 −0.0575837 0.998341i \(-0.518340\pi\)
−0.0575837 + 0.998341i \(0.518340\pi\)
\(654\) 8.31359 0.325087
\(655\) −9.42736 −0.368357
\(656\) −2.95627 −0.115423
\(657\) 3.75792 0.146611
\(658\) 0 0
\(659\) 12.3049 0.479330 0.239665 0.970856i \(-0.422962\pi\)
0.239665 + 0.970856i \(0.422962\pi\)
\(660\) −3.66725 −0.142748
\(661\) 14.4635 0.562565 0.281283 0.959625i \(-0.409240\pi\)
0.281283 + 0.959625i \(0.409240\pi\)
\(662\) 21.5998 0.839499
\(663\) 21.0806 0.818703
\(664\) −24.6956 −0.958375
\(665\) 0 0
\(666\) −4.49456 −0.174161
\(667\) 64.8922 2.51264
\(668\) −4.67437 −0.180857
\(669\) −1.28838 −0.0498117
\(670\) −13.3605 −0.516163
\(671\) 54.3284 2.09733
\(672\) 0 0
\(673\) 15.1510 0.584028 0.292014 0.956414i \(-0.405675\pi\)
0.292014 + 0.956414i \(0.405675\pi\)
\(674\) 15.3736 0.592169
\(675\) 1.89305 0.0728635
\(676\) 1.21581 0.0467618
\(677\) −1.19895 −0.0460794 −0.0230397 0.999735i \(-0.507334\pi\)
−0.0230397 + 0.999735i \(0.507334\pi\)
\(678\) −1.69274 −0.0650095
\(679\) 0 0
\(680\) −35.4758 −1.36044
\(681\) 24.1040 0.923667
\(682\) 6.31855 0.241950
\(683\) 47.9227 1.83371 0.916855 0.399219i \(-0.130719\pi\)
0.916855 + 0.399219i \(0.130719\pi\)
\(684\) −3.57162 −0.136564
\(685\) 35.7471 1.36583
\(686\) 0 0
\(687\) 0.361413 0.0137888
\(688\) −11.9905 −0.457133
\(689\) 17.6041 0.670663
\(690\) −18.3873 −0.699993
\(691\) −20.1592 −0.766891 −0.383446 0.923563i \(-0.625263\pi\)
−0.383446 + 0.923563i \(0.625263\pi\)
\(692\) −6.23540 −0.237034
\(693\) 0 0
\(694\) 35.7229 1.35602
\(695\) −4.85527 −0.184171
\(696\) 23.7349 0.899670
\(697\) −6.61037 −0.250386
\(698\) −31.9974 −1.21112
\(699\) −0.141975 −0.00536998
\(700\) 0 0
\(701\) −23.4825 −0.886921 −0.443461 0.896294i \(-0.646249\pi\)
−0.443461 + 0.896294i \(0.646249\pi\)
\(702\) 3.99635 0.150833
\(703\) 29.8189 1.12464
\(704\) −43.1075 −1.62468
\(705\) 1.69873 0.0639780
\(706\) −17.3774 −0.654007
\(707\) 0 0
\(708\) 3.98682 0.149834
\(709\) −37.8630 −1.42197 −0.710987 0.703205i \(-0.751752\pi\)
−0.710987 + 0.703205i \(0.751752\pi\)
\(710\) −21.9565 −0.824013
\(711\) −13.7937 −0.517306
\(712\) 31.9420 1.19708
\(713\) −8.66633 −0.324556
\(714\) 0 0
\(715\) −27.2235 −1.01810
\(716\) −6.18287 −0.231065
\(717\) −11.9975 −0.448056
\(718\) −39.4985 −1.47407
\(719\) −11.3752 −0.424222 −0.212111 0.977246i \(-0.568034\pi\)
−0.212111 + 0.977246i \(0.568034\pi\)
\(720\) −5.21089 −0.194198
\(721\) 0 0
\(722\) −62.8123 −2.33763
\(723\) −1.49883 −0.0557419
\(724\) −4.68841 −0.174243
\(725\) 14.7574 0.548077
\(726\) 15.6084 0.579282
\(727\) −16.0406 −0.594913 −0.297456 0.954735i \(-0.596138\pi\)
−0.297456 + 0.954735i \(0.596138\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −8.30083 −0.307228
\(731\) −26.8113 −0.991654
\(732\) −4.81905 −0.178117
\(733\) −51.7349 −1.91087 −0.955436 0.295197i \(-0.904615\pi\)
−0.955436 + 0.295197i \(0.904615\pi\)
\(734\) 11.3602 0.419312
\(735\) 0 0
\(736\) 19.8504 0.731694
\(737\) −29.2934 −1.07904
\(738\) −1.25316 −0.0461295
\(739\) −6.31420 −0.232272 −0.116136 0.993233i \(-0.537051\pi\)
−0.116136 + 0.993233i \(0.537051\pi\)
\(740\) −2.71582 −0.0998357
\(741\) −26.5136 −0.974002
\(742\) 0 0
\(743\) 21.6582 0.794562 0.397281 0.917697i \(-0.369954\pi\)
0.397281 + 0.917697i \(0.369954\pi\)
\(744\) −3.16979 −0.116210
\(745\) 16.8021 0.615580
\(746\) −10.3834 −0.380163
\(747\) −8.11111 −0.296770
\(748\) −13.7531 −0.502862
\(749\) 0 0
\(750\) −15.2260 −0.555974
\(751\) −44.2185 −1.61355 −0.806777 0.590856i \(-0.798790\pi\)
−0.806777 + 0.590856i \(0.798790\pi\)
\(752\) 2.84906 0.103895
\(753\) 6.61735 0.241150
\(754\) 31.1539 1.13456
\(755\) −10.0281 −0.364959
\(756\) 0 0
\(757\) 7.39895 0.268919 0.134460 0.990919i \(-0.457070\pi\)
0.134460 + 0.990919i \(0.457070\pi\)
\(758\) 26.2064 0.951861
\(759\) −40.3147 −1.46333
\(760\) 44.6189 1.61850
\(761\) −19.8652 −0.720112 −0.360056 0.932931i \(-0.617242\pi\)
−0.360056 + 0.932931i \(0.617242\pi\)
\(762\) −11.4823 −0.415959
\(763\) 0 0
\(764\) −1.11327 −0.0402765
\(765\) −11.6518 −0.421272
\(766\) −5.91712 −0.213794
\(767\) 29.5958 1.06864
\(768\) 9.80042 0.353642
\(769\) 39.2767 1.41635 0.708177 0.706034i \(-0.249518\pi\)
0.708177 + 0.706034i \(0.249518\pi\)
\(770\) 0 0
\(771\) 7.49560 0.269947
\(772\) 6.56458 0.236264
\(773\) −47.1966 −1.69754 −0.848771 0.528760i \(-0.822657\pi\)
−0.848771 + 0.528760i \(0.822657\pi\)
\(774\) −5.08276 −0.182696
\(775\) −1.97085 −0.0707949
\(776\) 34.4031 1.23500
\(777\) 0 0
\(778\) −33.8769 −1.21455
\(779\) 8.31403 0.297881
\(780\) 2.41479 0.0864632
\(781\) −48.1403 −1.72260
\(782\) −68.9567 −2.46589
\(783\) 7.79558 0.278591
\(784\) 0 0
\(785\) 19.2340 0.686491
\(786\) −6.70238 −0.239066
\(787\) 13.5666 0.483598 0.241799 0.970326i \(-0.422262\pi\)
0.241799 + 0.970326i \(0.422262\pi\)
\(788\) −6.40358 −0.228118
\(789\) 18.6115 0.662588
\(790\) 30.4688 1.08403
\(791\) 0 0
\(792\) −14.7455 −0.523958
\(793\) −35.7738 −1.27036
\(794\) −36.2225 −1.28549
\(795\) −9.73025 −0.345097
\(796\) −1.53539 −0.0544204
\(797\) −11.8546 −0.419911 −0.209955 0.977711i \(-0.567332\pi\)
−0.209955 + 0.977711i \(0.567332\pi\)
\(798\) 0 0
\(799\) 6.37065 0.225377
\(800\) 4.51425 0.159603
\(801\) 10.4911 0.370686
\(802\) −44.6887 −1.57801
\(803\) −18.1998 −0.642258
\(804\) 2.59839 0.0916382
\(805\) 0 0
\(806\) −4.16059 −0.146550
\(807\) 11.7570 0.413867
\(808\) −49.1087 −1.72764
\(809\) 15.5888 0.548072 0.274036 0.961719i \(-0.411641\pi\)
0.274036 + 0.961719i \(0.411641\pi\)
\(810\) −2.20889 −0.0776124
\(811\) −18.1848 −0.638556 −0.319278 0.947661i \(-0.603440\pi\)
−0.319278 + 0.947661i \(0.603440\pi\)
\(812\) 0 0
\(813\) 23.0447 0.808213
\(814\) 21.7674 0.762947
\(815\) −4.75863 −0.166687
\(816\) −19.5421 −0.684109
\(817\) 33.7213 1.17976
\(818\) −2.13086 −0.0745038
\(819\) 0 0
\(820\) −0.757219 −0.0264432
\(821\) 2.30128 0.0803152 0.0401576 0.999193i \(-0.487214\pi\)
0.0401576 + 0.999193i \(0.487214\pi\)
\(822\) 25.4144 0.886429
\(823\) −12.7773 −0.445389 −0.222694 0.974888i \(-0.571485\pi\)
−0.222694 + 0.974888i \(0.571485\pi\)
\(824\) 45.6595 1.59062
\(825\) −9.16814 −0.319194
\(826\) 0 0
\(827\) −11.2044 −0.389615 −0.194808 0.980841i \(-0.562408\pi\)
−0.194808 + 0.980841i \(0.562408\pi\)
\(828\) 3.57601 0.124275
\(829\) 39.4628 1.37060 0.685300 0.728261i \(-0.259671\pi\)
0.685300 + 0.728261i \(0.259671\pi\)
\(830\) 17.9165 0.621892
\(831\) −29.0686 −1.00838
\(832\) 28.3851 0.984077
\(833\) 0 0
\(834\) −3.45185 −0.119528
\(835\) 19.1795 0.663733
\(836\) 17.2976 0.598249
\(837\) −1.04110 −0.0359856
\(838\) −15.8515 −0.547582
\(839\) −36.6572 −1.26555 −0.632773 0.774338i \(-0.718083\pi\)
−0.632773 + 0.774338i \(0.718083\pi\)
\(840\) 0 0
\(841\) 31.7711 1.09555
\(842\) −40.7794 −1.40535
\(843\) −14.9373 −0.514469
\(844\) −0.502243 −0.0172879
\(845\) −4.98859 −0.171613
\(846\) 1.20771 0.0415221
\(847\) 0 0
\(848\) −16.3193 −0.560407
\(849\) −10.5976 −0.363707
\(850\) −15.6817 −0.537879
\(851\) −29.8555 −1.02343
\(852\) 4.27015 0.146293
\(853\) 31.0819 1.06422 0.532112 0.846674i \(-0.321399\pi\)
0.532112 + 0.846674i \(0.321399\pi\)
\(854\) 0 0
\(855\) 14.6548 0.501182
\(856\) −44.9085 −1.53494
\(857\) 53.1841 1.81674 0.908368 0.418173i \(-0.137329\pi\)
0.908368 + 0.418173i \(0.137329\pi\)
\(858\) −19.3546 −0.660754
\(859\) −12.7611 −0.435404 −0.217702 0.976015i \(-0.569856\pi\)
−0.217702 + 0.976015i \(0.569856\pi\)
\(860\) −3.07124 −0.104728
\(861\) 0 0
\(862\) 30.1585 1.02720
\(863\) −9.99019 −0.340070 −0.170035 0.985438i \(-0.554388\pi\)
−0.170035 + 0.985438i \(0.554388\pi\)
\(864\) 2.38465 0.0811273
\(865\) 25.5845 0.869900
\(866\) −3.18292 −0.108160
\(867\) −26.6970 −0.906678
\(868\) 0 0
\(869\) 66.8039 2.26617
\(870\) −17.2196 −0.583798
\(871\) 19.2889 0.653580
\(872\) 20.1986 0.684011
\(873\) 11.2995 0.382430
\(874\) 86.7286 2.93364
\(875\) 0 0
\(876\) 1.61437 0.0545444
\(877\) 33.4455 1.12938 0.564688 0.825305i \(-0.308997\pi\)
0.564688 + 0.825305i \(0.308997\pi\)
\(878\) −15.8892 −0.536234
\(879\) 32.6469 1.10115
\(880\) 25.2366 0.850727
\(881\) 42.8300 1.44298 0.721489 0.692425i \(-0.243458\pi\)
0.721489 + 0.692425i \(0.243458\pi\)
\(882\) 0 0
\(883\) −35.3926 −1.19106 −0.595529 0.803334i \(-0.703057\pi\)
−0.595529 + 0.803334i \(0.703057\pi\)
\(884\) 9.05602 0.304587
\(885\) −16.3584 −0.549881
\(886\) −13.0607 −0.438783
\(887\) −3.59794 −0.120807 −0.0604035 0.998174i \(-0.519239\pi\)
−0.0604035 + 0.998174i \(0.519239\pi\)
\(888\) −10.9199 −0.366449
\(889\) 0 0
\(890\) −23.1738 −0.776786
\(891\) −4.84306 −0.162249
\(892\) −0.553475 −0.0185317
\(893\) −8.01252 −0.268129
\(894\) 11.9454 0.399515
\(895\) 25.3690 0.847992
\(896\) 0 0
\(897\) 26.5461 0.886350
\(898\) −45.3224 −1.51243
\(899\) −8.11595 −0.270682
\(900\) 0.813234 0.0271078
\(901\) −36.4908 −1.21568
\(902\) 6.06913 0.202080
\(903\) 0 0
\(904\) −4.11268 −0.136786
\(905\) 19.2371 0.639462
\(906\) −7.12946 −0.236860
\(907\) −17.9810 −0.597050 −0.298525 0.954402i \(-0.596495\pi\)
−0.298525 + 0.954402i \(0.596495\pi\)
\(908\) 10.3548 0.343637
\(909\) −16.1294 −0.534979
\(910\) 0 0
\(911\) 45.4282 1.50510 0.752552 0.658533i \(-0.228823\pi\)
0.752552 + 0.658533i \(0.228823\pi\)
\(912\) 24.5785 0.813877
\(913\) 39.2826 1.30006
\(914\) 4.32056 0.142911
\(915\) 19.7731 0.653678
\(916\) 0.155259 0.00512991
\(917\) 0 0
\(918\) −8.28385 −0.273408
\(919\) 17.0040 0.560910 0.280455 0.959867i \(-0.409515\pi\)
0.280455 + 0.959867i \(0.409515\pi\)
\(920\) −44.6736 −1.47284
\(921\) 14.5205 0.478467
\(922\) −49.2066 −1.62053
\(923\) 31.6991 1.04339
\(924\) 0 0
\(925\) −6.78957 −0.223240
\(926\) −21.4435 −0.704676
\(927\) 14.9966 0.492552
\(928\) 18.5897 0.610237
\(929\) −6.37929 −0.209298 −0.104649 0.994509i \(-0.533372\pi\)
−0.104649 + 0.994509i \(0.533372\pi\)
\(930\) 2.29967 0.0754090
\(931\) 0 0
\(932\) −0.0609909 −0.00199782
\(933\) −3.08406 −0.100967
\(934\) −51.4083 −1.68213
\(935\) 56.4304 1.84547
\(936\) 9.70950 0.317365
\(937\) 25.1791 0.822565 0.411282 0.911508i \(-0.365081\pi\)
0.411282 + 0.911508i \(0.365081\pi\)
\(938\) 0 0
\(939\) 8.36990 0.273141
\(940\) 0.729758 0.0238021
\(941\) −23.3195 −0.760195 −0.380097 0.924946i \(-0.624110\pi\)
−0.380097 + 0.924946i \(0.624110\pi\)
\(942\) 13.6744 0.445537
\(943\) −8.32423 −0.271074
\(944\) −27.4358 −0.892958
\(945\) 0 0
\(946\) 24.6161 0.800338
\(947\) 31.0089 1.00765 0.503827 0.863805i \(-0.331925\pi\)
0.503827 + 0.863805i \(0.331925\pi\)
\(948\) −5.92565 −0.192456
\(949\) 11.9841 0.389020
\(950\) 19.7233 0.639909
\(951\) −24.4448 −0.792676
\(952\) 0 0
\(953\) 32.2352 1.04420 0.522101 0.852884i \(-0.325149\pi\)
0.522101 + 0.852884i \(0.325149\pi\)
\(954\) −6.91773 −0.223970
\(955\) 4.56785 0.147812
\(956\) −5.15401 −0.166693
\(957\) −37.7545 −1.22043
\(958\) 1.75035 0.0565513
\(959\) 0 0
\(960\) −15.6892 −0.506367
\(961\) −29.9161 −0.965036
\(962\) −14.3332 −0.462122
\(963\) −14.7499 −0.475309
\(964\) −0.643880 −0.0207380
\(965\) −26.9352 −0.867075
\(966\) 0 0
\(967\) 40.3185 1.29656 0.648279 0.761403i \(-0.275489\pi\)
0.648279 + 0.761403i \(0.275489\pi\)
\(968\) 37.9220 1.21886
\(969\) 54.9588 1.76553
\(970\) −24.9593 −0.801395
\(971\) −32.0847 −1.02965 −0.514824 0.857296i \(-0.672143\pi\)
−0.514824 + 0.857296i \(0.672143\pi\)
\(972\) 0.429590 0.0137791
\(973\) 0 0
\(974\) −38.5128 −1.23403
\(975\) 6.03697 0.193338
\(976\) 33.1628 1.06152
\(977\) −57.6281 −1.84369 −0.921844 0.387562i \(-0.873317\pi\)
−0.921844 + 0.387562i \(0.873317\pi\)
\(978\) −3.38315 −0.108181
\(979\) −50.8092 −1.62387
\(980\) 0 0
\(981\) 6.63410 0.211811
\(982\) −29.7991 −0.950929
\(983\) 3.19824 0.102008 0.0510040 0.998698i \(-0.483758\pi\)
0.0510040 + 0.998698i \(0.483758\pi\)
\(984\) −3.04466 −0.0970604
\(985\) 26.2746 0.837178
\(986\) −64.5775 −2.05657
\(987\) 0 0
\(988\) −11.3900 −0.362363
\(989\) −33.7627 −1.07359
\(990\) 10.6978 0.339998
\(991\) 59.2649 1.88261 0.941306 0.337553i \(-0.109599\pi\)
0.941306 + 0.337553i \(0.109599\pi\)
\(992\) −2.48265 −0.0788241
\(993\) 17.2362 0.546976
\(994\) 0 0
\(995\) 6.29987 0.199719
\(996\) −3.48445 −0.110409
\(997\) 37.9055 1.20048 0.600239 0.799820i \(-0.295072\pi\)
0.600239 + 0.799820i \(0.295072\pi\)
\(998\) 10.1453 0.321145
\(999\) −3.58658 −0.113474
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 \(a_p\))