Properties

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

Related objects

Downloads

Learn more about

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 \(-0.628958\pi\)
−0.394142 + 0.919050i \(0.628958\pi\)
\(6\) −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 \(-0.645815\pi\)
−0.442237 + 0.896898i \(0.645815\pi\)
\(14\) 0 0
\(15\) −1.76265 −0.455115
\(16\) −2.95627 −0.739068
\(17\) 6.61037 1.60325 0.801625 0.597827i \(-0.203969\pi\)
0.801625 + 0.597827i \(0.203969\pi\)
\(18\) −1.25316 −0.295373
\(19\) −8.31403 −1.90737 −0.953685 0.300808i \(-0.902744\pi\)
−0.953685 + 0.300808i \(0.902744\pi\)
\(20\) 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 \(-0.529803\pi\)
−0.0934932 + 0.995620i \(0.529803\pi\)
\(32\) −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 \(-0.477608\pi\)
0.0702876 + 0.997527i \(0.477608\pi\)
\(48\) −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 \(-0.706472\pi\)
−0.604111 + 0.796900i \(0.706472\pi\)
\(60\) 0.757219 0.0977565
\(61\) 11.2178 1.43629 0.718145 0.695893i \(-0.244991\pi\)
0.718145 + 0.695893i \(0.244991\pi\)
\(62\) 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 \(-0.570578\pi\)
−0.219916 + 0.975519i \(0.570578\pi\)
\(74\) −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 \(-0.353149\pi\)
0.445155 + 0.895454i \(0.353149\pi\)
\(84\) 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 \(-0.687676\pi\)
−0.556029 + 0.831163i \(0.687676\pi\)
\(90\) 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 \(-0.694471\pi\)
−0.573644 + 0.819104i \(0.694471\pi\)
\(98\) 0 0
\(99\) −4.84306 −0.486746
\(100\) 0.813234 0.0813234
\(101\) 16.1294 1.60494 0.802469 0.596694i \(-0.203519\pi\)
0.802469 + 0.596694i \(0.203519\pi\)
\(102\) −8.28385 −0.820224
\(103\) −14.9966 −1.47766 −0.738828 0.673894i \(-0.764620\pi\)
−0.738828 + 0.673894i \(0.764620\pi\)
\(104\) −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 \(-0.424935\pi\)
0.233645 + 0.972322i \(0.424935\pi\)
\(132\) 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 \(-0.462731\pi\)
0.116818 + 0.993153i \(0.462731\pi\)
\(140\) 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 \(-0.643405\pi\)
−0.435434 + 0.900221i \(0.643405\pi\)
\(158\) 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 \(-0.638320\pi\)
−0.420999 + 0.907061i \(0.638320\pi\)
\(168\) 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 \(-0.686047\pi\)
−0.551769 + 0.833997i \(0.686047\pi\)
\(174\) 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 \(-0.632939\pi\)
−0.405604 + 0.914049i \(0.632939\pi\)
\(182\) 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 \(-0.540432\pi\)
−0.126680 + 0.991944i \(0.540432\pi\)
\(200\) −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 \(-0.513736\pi\)
−0.0431382 + 0.999069i \(0.513736\pi\)
\(224\) 0 0
\(225\) −1.89305 −0.126203
\(226\) 1.69274 0.112600
\(227\) 24.1040 1.59984 0.799919 0.600108i \(-0.204876\pi\)
0.799919 + 0.600108i \(0.204876\pi\)
\(228\) 3.57162 0.236537
\(229\) 0.361413 0.0238828 0.0119414 0.999929i \(-0.496199\pi\)
0.0119414 + 0.999929i \(0.496199\pi\)
\(230\) −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 \(-0.515372\pi\)
−0.0482739 + 0.998834i \(0.515372\pi\)
\(242\) −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 \(-0.433031\pi\)
0.208842 + 0.977949i \(0.433031\pi\)
\(252\) 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 \(-0.424890\pi\)
0.233781 + 0.972289i \(0.424890\pi\)
\(258\) −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 \(-0.383316\pi\)
0.358419 + 0.933561i \(0.383316\pi\)
\(270\) 2.20889 0.134429
\(271\) 23.0447 1.39987 0.699933 0.714208i \(-0.253213\pi\)
0.699933 + 0.714208i \(0.253213\pi\)
\(272\) −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 \(-0.601998\pi\)
−0.314980 + 0.949098i \(0.601998\pi\)
\(284\) −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 \(-0.0973198\pi\)
0.953625 + 0.300998i \(0.0973198\pi\)
\(294\) 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 \(-0.364004\pi\)
0.414364 + 0.910111i \(0.364004\pi\)
\(308\) 0 0
\(309\) −14.9966 −0.853125
\(310\) −2.29967 −0.130612
\(311\) −3.08406 −0.174881 −0.0874404 0.996170i \(-0.527869\pi\)
−0.0874404 + 0.996170i \(0.527869\pi\)
\(312\) −9.70950 −0.549692
\(313\) 8.36990 0.473094 0.236547 0.971620i \(-0.423984\pi\)
0.236547 + 0.971620i \(0.423984\pi\)
\(314\) 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 \(-0.739493\pi\)
−0.683385 + 0.730058i \(0.739493\pi\)
\(350\) 0 0
\(351\) −3.18902 −0.170217
\(352\) 11.5490 0.615563
\(353\) −13.8669 −0.738058 −0.369029 0.929418i \(-0.620310\pi\)
−0.369029 + 0.929418i \(0.620310\pi\)
\(354\) 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 \(-0.423967\pi\)
0.236601 + 0.971607i \(0.423967\pi\)
\(368\) 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 \(-0.538493\pi\)
−0.120635 + 0.992697i \(0.538493\pi\)
\(384\) −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 \(-0.758321\pi\)
−0.725348 + 0.688383i \(0.758321\pi\)
\(398\) 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 \(-0.513386\pi\)
−0.0420394 + 0.999116i \(0.513386\pi\)
\(410\) −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 \(-0.599987\pi\)
−0.308978 + 0.951069i \(0.599987\pi\)
\(420\) 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 \(-0.519439\pi\)
−0.0610303 + 0.998136i \(0.519439\pi\)
\(434\) 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 \(-0.597846\pi\)
−0.302575 + 0.953126i \(0.597846\pi\)
\(440\) 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 \(-0.867337\pi\)
−0.914400 + 0.404811i \(0.867337\pi\)
\(462\) 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 \(-0.898062\pi\)
−0.949157 + 0.314802i \(0.898062\pi\)
\(468\) 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 \(-0.489841\pi\)
0.0319096 + 0.999491i \(0.489841\pi\)
\(480\) 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 \(-0.723341\pi\)
−0.645476 + 0.763780i \(0.723341\pi\)
\(504\) 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 \(-0.384139\pi\)
0.356005 + 0.934484i \(0.384139\pi\)
\(510\) 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 \(-0.836546\pi\)
−0.871028 + 0.491234i \(0.836546\pi\)
\(522\) 9.76911 0.427582
\(523\) 22.5014 0.983918 0.491959 0.870618i \(-0.336281\pi\)
0.491959 + 0.870618i \(0.336281\pi\)
\(524\) −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 \(-0.738591\pi\)
−0.681313 + 0.731992i \(0.738591\pi\)
\(564\) −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 \(-0.630168\pi\)
−0.397633 + 0.917544i \(0.630168\pi\)
\(578\) −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 \(-0.185087\pi\)
0.835658 + 0.549251i \(0.185087\pi\)
\(588\) 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 \(-0.676989\pi\)
−0.527817 + 0.849358i \(0.676989\pi\)
\(594\) 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 \(-0.301973\pi\)
0.582760 + 0.812644i \(0.301973\pi\)
\(602\) 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 \(-0.468618\pi\)
0.0984293 + 0.995144i \(0.468618\pi\)
\(608\) 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 \(-0.417721\pi\)
0.255620 + 0.966777i \(0.417721\pi\)
\(620\) −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 \(-0.695069\pi\)
−0.575183 + 0.818025i \(0.695069\pi\)
\(644\) 0 0
\(645\) −7.14924 −0.281501
\(646\) 68.8722 2.70974
\(647\) −23.9403 −0.941190 −0.470595 0.882349i \(-0.655961\pi\)
−0.470595 + 0.882349i \(0.655961\pi\)
\(648\) 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 \(-0.590760\pi\)
−0.281283 + 0.959625i \(0.590760\pi\)
\(662\) 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 \(-0.492666\pi\)
0.0230397 + 0.999735i \(0.492666\pi\)
\(678\) 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 \(-0.374737\pi\)
0.383446 + 0.923563i \(0.374737\pi\)
\(692\) 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 \(-0.431966\pi\)
0.212111 + 0.977246i \(0.431966\pi\)
\(720\) 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 \(-0.403862\pi\)
0.297456 + 0.954735i \(0.403862\pi\)
\(728\) 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 \(-0.0953853\pi\)
0.955436 + 0.295197i \(0.0953853\pi\)
\(734\) −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 \(-0.382758\pi\)
0.360056 + 0.932931i \(0.382758\pi\)
\(762\) 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 \(-0.750482\pi\)
−0.708177 + 0.706034i \(0.750482\pi\)
\(770\) 0 0
\(771\) 7.49560 0.269947
\(772\) 6.56458 0.236264
\(773\) 47.1966 1.69754 0.848771 0.528760i \(-0.177343\pi\)
0.848771 + 0.528760i \(0.177343\pi\)
\(774\) −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 \(-0.577738\pi\)
−0.241799 + 0.970326i \(0.577738\pi\)
\(788\) −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 \(-0.432668\pi\)
0.209955 + 0.977711i \(0.432668\pi\)
\(798\) 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 \(-0.396560\pi\)
0.319278 + 0.947661i \(0.396560\pi\)
\(812\) 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 \(-0.740329\pi\)
−0.685300 + 0.728261i \(0.740329\pi\)
\(830\) 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 \(-0.281917\pi\)
0.632773 + 0.774338i \(0.281917\pi\)
\(840\) 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 \(-0.678601\pi\)
−0.532112 + 0.846674i \(0.678601\pi\)
\(854\) 0 0
\(855\) 14.6548 0.501182
\(856\) −44.9085 −1.53494
\(857\) −53.1841 −1.81674 −0.908368 0.418173i \(-0.862671\pi\)
−0.908368 + 0.418173i \(0.862671\pi\)
\(858\) −19.3546 −0.660754
\(859\) 12.7611 0.435404 0.217702 0.976015i \(-0.430144\pi\)
0.217702 + 0.976015i \(0.430144\pi\)
\(860\) 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 \(-0.756542\pi\)
−0.721489 + 0.692425i \(0.756542\pi\)
\(882\) 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 \(-0.480761\pi\)
0.0604035 + 0.998174i \(0.480761\pi\)
\(888\) 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 \(-0.466628\pi\)
0.104649 + 0.994509i \(0.466628\pi\)
\(930\) −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 \(-0.634919\pi\)
−0.411282 + 0.911508i \(0.634919\pi\)
\(938\) 0 0
\(939\) 8.36990 0.273141
\(940\) 0.729758 0.0238021
\(941\) 23.3195 0.760195 0.380097 0.924946i \(-0.375890\pi\)
0.380097 + 0.924946i \(0.375890\pi\)
\(942\) 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 \(-0.327857\pi\)
0.514824 + 0.857296i \(0.327857\pi\)
\(972\) −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 \(-0.516242\pi\)
−0.0510040 + 0.998698i \(0.516242\pi\)
\(984\) −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 \(-0.704928\pi\)
−0.600239 + 0.799820i \(0.704928\pi\)
\(998\) 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 \(a_p\))