Properties

Label 6003.2.a.t.1.11
Level 6003
Weight 2
Character 6003.1
Self dual Yes
Analytic conductor 47.934
Analytic rank 1
Dimension 22
CM No

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Newspace parameters

Level: \( N \) = \( 6003 = 3^{2} \cdot 23 \cdot 29 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6003.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9341963334\)
Analytic rank: \(1\)
Dimension: \(22\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Character \(\chi\) = 6003.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.230149 q^{2} -1.94703 q^{4} +2.59479 q^{5} -4.77655 q^{7} +0.908406 q^{8} +O(q^{10})\) \(q-0.230149 q^{2} -1.94703 q^{4} +2.59479 q^{5} -4.77655 q^{7} +0.908406 q^{8} -0.597188 q^{10} -3.70131 q^{11} -3.06512 q^{13} +1.09932 q^{14} +3.68499 q^{16} +3.40309 q^{17} +5.00538 q^{19} -5.05213 q^{20} +0.851854 q^{22} +1.00000 q^{23} +1.73291 q^{25} +0.705435 q^{26} +9.30009 q^{28} +1.00000 q^{29} +6.71761 q^{31} -2.66491 q^{32} -0.783218 q^{34} -12.3941 q^{35} +1.21966 q^{37} -1.15198 q^{38} +2.35712 q^{40} -8.51699 q^{41} +8.34577 q^{43} +7.20657 q^{44} -0.230149 q^{46} +3.13922 q^{47} +15.8154 q^{49} -0.398828 q^{50} +5.96789 q^{52} +6.13173 q^{53} -9.60411 q^{55} -4.33904 q^{56} -0.230149 q^{58} -3.83602 q^{59} +3.39205 q^{61} -1.54605 q^{62} -6.75666 q^{64} -7.95333 q^{65} +1.42070 q^{67} -6.62592 q^{68} +2.85250 q^{70} -1.21273 q^{71} -8.66204 q^{73} -0.280704 q^{74} -9.74564 q^{76} +17.6795 q^{77} -12.2141 q^{79} +9.56177 q^{80} +1.96018 q^{82} +14.6713 q^{83} +8.83029 q^{85} -1.92077 q^{86} -3.36229 q^{88} -10.8906 q^{89} +14.6407 q^{91} -1.94703 q^{92} -0.722489 q^{94} +12.9879 q^{95} -1.64503 q^{97} -3.63990 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q - 3q^{2} + 17q^{4} - 6q^{7} - 6q^{8} + O(q^{10}) \) \( 22q - 3q^{2} + 17q^{4} - 6q^{7} - 6q^{8} - 12q^{10} - 28q^{13} - q^{14} + 3q^{16} - 10q^{17} - 8q^{19} - 11q^{22} + 22q^{23} + 11q^{26} - 21q^{28} + 22q^{29} - 18q^{31} + 5q^{32} - 33q^{34} + 2q^{35} - 28q^{37} + 14q^{38} - 30q^{40} - 10q^{41} - 14q^{43} + 37q^{44} - 3q^{46} - 18q^{47} + 2q^{49} + 7q^{50} - 57q^{52} + 20q^{53} - 42q^{55} - 2q^{56} - 3q^{58} - 20q^{59} - 38q^{61} + 4q^{62} - 24q^{64} + 12q^{65} - 50q^{67} + 11q^{68} - 48q^{70} + 12q^{71} - 46q^{73} - 6q^{74} - 16q^{76} - 14q^{77} - 20q^{79} - 58q^{80} - 42q^{82} + 22q^{83} - 66q^{85} + 22q^{86} - 68q^{88} - 14q^{89} - 16q^{91} + 17q^{92} - 27q^{94} - 20q^{95} - 48q^{97} - 28q^{98} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.230149 −0.162740 −0.0813700 0.996684i \(-0.525930\pi\)
−0.0813700 + 0.996684i \(0.525930\pi\)
\(3\) 0 0
\(4\) −1.94703 −0.973516
\(5\) 2.59479 1.16042 0.580212 0.814466i \(-0.302970\pi\)
0.580212 + 0.814466i \(0.302970\pi\)
\(6\) 0 0
\(7\) −4.77655 −1.80537 −0.902683 0.430307i \(-0.858405\pi\)
−0.902683 + 0.430307i \(0.858405\pi\)
\(8\) 0.908406 0.321170
\(9\) 0 0
\(10\) −0.597188 −0.188847
\(11\) −3.70131 −1.11599 −0.557994 0.829845i \(-0.688429\pi\)
−0.557994 + 0.829845i \(0.688429\pi\)
\(12\) 0 0
\(13\) −3.06512 −0.850112 −0.425056 0.905167i \(-0.639746\pi\)
−0.425056 + 0.905167i \(0.639746\pi\)
\(14\) 1.09932 0.293805
\(15\) 0 0
\(16\) 3.68499 0.921248
\(17\) 3.40309 0.825370 0.412685 0.910874i \(-0.364591\pi\)
0.412685 + 0.910874i \(0.364591\pi\)
\(18\) 0 0
\(19\) 5.00538 1.14831 0.574157 0.818745i \(-0.305330\pi\)
0.574157 + 0.818745i \(0.305330\pi\)
\(20\) −5.05213 −1.12969
\(21\) 0 0
\(22\) 0.851854 0.181616
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) 1.73291 0.346582
\(26\) 0.705435 0.138347
\(27\) 0 0
\(28\) 9.30009 1.75755
\(29\) 1.00000 0.185695
\(30\) 0 0
\(31\) 6.71761 1.20652 0.603259 0.797545i \(-0.293869\pi\)
0.603259 + 0.797545i \(0.293869\pi\)
\(32\) −2.66491 −0.471094
\(33\) 0 0
\(34\) −0.783218 −0.134321
\(35\) −12.3941 −2.09499
\(36\) 0 0
\(37\) 1.21966 0.200511 0.100256 0.994962i \(-0.468034\pi\)
0.100256 + 0.994962i \(0.468034\pi\)
\(38\) −1.15198 −0.186877
\(39\) 0 0
\(40\) 2.35712 0.372693
\(41\) −8.51699 −1.33013 −0.665065 0.746785i \(-0.731596\pi\)
−0.665065 + 0.746785i \(0.731596\pi\)
\(42\) 0 0
\(43\) 8.34577 1.27272 0.636359 0.771393i \(-0.280440\pi\)
0.636359 + 0.771393i \(0.280440\pi\)
\(44\) 7.20657 1.08643
\(45\) 0 0
\(46\) −0.230149 −0.0339336
\(47\) 3.13922 0.457903 0.228951 0.973438i \(-0.426470\pi\)
0.228951 + 0.973438i \(0.426470\pi\)
\(48\) 0 0
\(49\) 15.8154 2.25934
\(50\) −0.398828 −0.0564028
\(51\) 0 0
\(52\) 5.96789 0.827597
\(53\) 6.13173 0.842258 0.421129 0.907001i \(-0.361634\pi\)
0.421129 + 0.907001i \(0.361634\pi\)
\(54\) 0 0
\(55\) −9.60411 −1.29502
\(56\) −4.33904 −0.579829
\(57\) 0 0
\(58\) −0.230149 −0.0302201
\(59\) −3.83602 −0.499408 −0.249704 0.968322i \(-0.580333\pi\)
−0.249704 + 0.968322i \(0.580333\pi\)
\(60\) 0 0
\(61\) 3.39205 0.434307 0.217154 0.976137i \(-0.430323\pi\)
0.217154 + 0.976137i \(0.430323\pi\)
\(62\) −1.54605 −0.196349
\(63\) 0 0
\(64\) −6.75666 −0.844583
\(65\) −7.95333 −0.986490
\(66\) 0 0
\(67\) 1.42070 0.173566 0.0867830 0.996227i \(-0.472341\pi\)
0.0867830 + 0.996227i \(0.472341\pi\)
\(68\) −6.62592 −0.803511
\(69\) 0 0
\(70\) 2.85250 0.340938
\(71\) −1.21273 −0.143925 −0.0719626 0.997407i \(-0.522926\pi\)
−0.0719626 + 0.997407i \(0.522926\pi\)
\(72\) 0 0
\(73\) −8.66204 −1.01382 −0.506908 0.862000i \(-0.669212\pi\)
−0.506908 + 0.862000i \(0.669212\pi\)
\(74\) −0.280704 −0.0326312
\(75\) 0 0
\(76\) −9.74564 −1.11790
\(77\) 17.6795 2.01477
\(78\) 0 0
\(79\) −12.2141 −1.37419 −0.687095 0.726567i \(-0.741115\pi\)
−0.687095 + 0.726567i \(0.741115\pi\)
\(80\) 9.56177 1.06904
\(81\) 0 0
\(82\) 1.96018 0.216465
\(83\) 14.6713 1.61038 0.805192 0.593014i \(-0.202062\pi\)
0.805192 + 0.593014i \(0.202062\pi\)
\(84\) 0 0
\(85\) 8.83029 0.957779
\(86\) −1.92077 −0.207122
\(87\) 0 0
\(88\) −3.36229 −0.358422
\(89\) −10.8906 −1.15440 −0.577198 0.816604i \(-0.695854\pi\)
−0.577198 + 0.816604i \(0.695854\pi\)
\(90\) 0 0
\(91\) 14.6407 1.53476
\(92\) −1.94703 −0.202992
\(93\) 0 0
\(94\) −0.722489 −0.0745191
\(95\) 12.9879 1.33253
\(96\) 0 0
\(97\) −1.64503 −0.167027 −0.0835137 0.996507i \(-0.526614\pi\)
−0.0835137 + 0.996507i \(0.526614\pi\)
\(98\) −3.63990 −0.367686
\(99\) 0 0
\(100\) −3.37403 −0.337403
\(101\) −18.2082 −1.81178 −0.905890 0.423512i \(-0.860797\pi\)
−0.905890 + 0.423512i \(0.860797\pi\)
\(102\) 0 0
\(103\) −7.91947 −0.780329 −0.390164 0.920745i \(-0.627582\pi\)
−0.390164 + 0.920745i \(0.627582\pi\)
\(104\) −2.78437 −0.273030
\(105\) 0 0
\(106\) −1.41121 −0.137069
\(107\) 10.1399 0.980259 0.490130 0.871650i \(-0.336949\pi\)
0.490130 + 0.871650i \(0.336949\pi\)
\(108\) 0 0
\(109\) −18.2734 −1.75027 −0.875137 0.483874i \(-0.839229\pi\)
−0.875137 + 0.483874i \(0.839229\pi\)
\(110\) 2.21038 0.210751
\(111\) 0 0
\(112\) −17.6015 −1.66319
\(113\) −8.88638 −0.835961 −0.417980 0.908456i \(-0.637262\pi\)
−0.417980 + 0.908456i \(0.637262\pi\)
\(114\) 0 0
\(115\) 2.59479 0.241965
\(116\) −1.94703 −0.180777
\(117\) 0 0
\(118\) 0.882858 0.0812737
\(119\) −16.2550 −1.49009
\(120\) 0 0
\(121\) 2.69971 0.245428
\(122\) −0.780677 −0.0706791
\(123\) 0 0
\(124\) −13.0794 −1.17456
\(125\) −8.47739 −0.758241
\(126\) 0 0
\(127\) 9.25291 0.821063 0.410532 0.911846i \(-0.365343\pi\)
0.410532 + 0.911846i \(0.365343\pi\)
\(128\) 6.88486 0.608541
\(129\) 0 0
\(130\) 1.83045 0.160541
\(131\) 3.01107 0.263078 0.131539 0.991311i \(-0.458008\pi\)
0.131539 + 0.991311i \(0.458008\pi\)
\(132\) 0 0
\(133\) −23.9085 −2.07313
\(134\) −0.326972 −0.0282461
\(135\) 0 0
\(136\) 3.09139 0.265084
\(137\) −14.1358 −1.20770 −0.603850 0.797098i \(-0.706367\pi\)
−0.603850 + 0.797098i \(0.706367\pi\)
\(138\) 0 0
\(139\) 7.05151 0.598101 0.299051 0.954237i \(-0.403330\pi\)
0.299051 + 0.954237i \(0.403330\pi\)
\(140\) 24.1317 2.03950
\(141\) 0 0
\(142\) 0.279110 0.0234224
\(143\) 11.3450 0.948714
\(144\) 0 0
\(145\) 2.59479 0.215485
\(146\) 1.99356 0.164988
\(147\) 0 0
\(148\) −2.37472 −0.195201
\(149\) −8.33724 −0.683013 −0.341507 0.939879i \(-0.610937\pi\)
−0.341507 + 0.939879i \(0.610937\pi\)
\(150\) 0 0
\(151\) −10.0416 −0.817170 −0.408585 0.912720i \(-0.633978\pi\)
−0.408585 + 0.912720i \(0.633978\pi\)
\(152\) 4.54692 0.368804
\(153\) 0 0
\(154\) −4.06892 −0.327883
\(155\) 17.4308 1.40007
\(156\) 0 0
\(157\) −3.30825 −0.264027 −0.132014 0.991248i \(-0.542144\pi\)
−0.132014 + 0.991248i \(0.542144\pi\)
\(158\) 2.81106 0.223636
\(159\) 0 0
\(160\) −6.91487 −0.546668
\(161\) −4.77655 −0.376445
\(162\) 0 0
\(163\) −1.69369 −0.132660 −0.0663301 0.997798i \(-0.521129\pi\)
−0.0663301 + 0.997798i \(0.521129\pi\)
\(164\) 16.5828 1.29490
\(165\) 0 0
\(166\) −3.37659 −0.262074
\(167\) −4.53024 −0.350561 −0.175280 0.984519i \(-0.556083\pi\)
−0.175280 + 0.984519i \(0.556083\pi\)
\(168\) 0 0
\(169\) −3.60503 −0.277310
\(170\) −2.03228 −0.155869
\(171\) 0 0
\(172\) −16.2495 −1.23901
\(173\) −21.7611 −1.65447 −0.827234 0.561858i \(-0.810087\pi\)
−0.827234 + 0.561858i \(0.810087\pi\)
\(174\) 0 0
\(175\) −8.27734 −0.625708
\(176\) −13.6393 −1.02810
\(177\) 0 0
\(178\) 2.50645 0.187866
\(179\) 20.8274 1.55671 0.778357 0.627822i \(-0.216053\pi\)
0.778357 + 0.627822i \(0.216053\pi\)
\(180\) 0 0
\(181\) −6.54612 −0.486569 −0.243285 0.969955i \(-0.578225\pi\)
−0.243285 + 0.969955i \(0.578225\pi\)
\(182\) −3.36954 −0.249767
\(183\) 0 0
\(184\) 0.908406 0.0669686
\(185\) 3.16476 0.232678
\(186\) 0 0
\(187\) −12.5959 −0.921103
\(188\) −6.11216 −0.445775
\(189\) 0 0
\(190\) −2.98915 −0.216856
\(191\) −21.0972 −1.52654 −0.763271 0.646078i \(-0.776408\pi\)
−0.763271 + 0.646078i \(0.776408\pi\)
\(192\) 0 0
\(193\) 5.55042 0.399528 0.199764 0.979844i \(-0.435982\pi\)
0.199764 + 0.979844i \(0.435982\pi\)
\(194\) 0.378602 0.0271820
\(195\) 0 0
\(196\) −30.7931 −2.19951
\(197\) 20.1657 1.43674 0.718372 0.695659i \(-0.244888\pi\)
0.718372 + 0.695659i \(0.244888\pi\)
\(198\) 0 0
\(199\) −23.4093 −1.65944 −0.829719 0.558181i \(-0.811500\pi\)
−0.829719 + 0.558181i \(0.811500\pi\)
\(200\) 1.57419 0.111312
\(201\) 0 0
\(202\) 4.19060 0.294849
\(203\) −4.77655 −0.335248
\(204\) 0 0
\(205\) −22.0998 −1.54351
\(206\) 1.82266 0.126991
\(207\) 0 0
\(208\) −11.2950 −0.783164
\(209\) −18.5265 −1.28150
\(210\) 0 0
\(211\) 26.1869 1.80278 0.901391 0.433007i \(-0.142547\pi\)
0.901391 + 0.433007i \(0.142547\pi\)
\(212\) −11.9387 −0.819952
\(213\) 0 0
\(214\) −2.33369 −0.159527
\(215\) 21.6555 1.47689
\(216\) 0 0
\(217\) −32.0870 −2.17821
\(218\) 4.20561 0.284840
\(219\) 0 0
\(220\) 18.6995 1.26072
\(221\) −10.4309 −0.701657
\(222\) 0 0
\(223\) −14.4965 −0.970755 −0.485378 0.874305i \(-0.661318\pi\)
−0.485378 + 0.874305i \(0.661318\pi\)
\(224\) 12.7291 0.850497
\(225\) 0 0
\(226\) 2.04519 0.136044
\(227\) −13.7819 −0.914738 −0.457369 0.889277i \(-0.651208\pi\)
−0.457369 + 0.889277i \(0.651208\pi\)
\(228\) 0 0
\(229\) 27.3057 1.80441 0.902207 0.431303i \(-0.141946\pi\)
0.902207 + 0.431303i \(0.141946\pi\)
\(230\) −0.597188 −0.0393774
\(231\) 0 0
\(232\) 0.908406 0.0596398
\(233\) −8.33427 −0.545996 −0.272998 0.962015i \(-0.588015\pi\)
−0.272998 + 0.962015i \(0.588015\pi\)
\(234\) 0 0
\(235\) 8.14561 0.531361
\(236\) 7.46886 0.486181
\(237\) 0 0
\(238\) 3.74108 0.242498
\(239\) 21.1215 1.36624 0.683119 0.730307i \(-0.260623\pi\)
0.683119 + 0.730307i \(0.260623\pi\)
\(240\) 0 0
\(241\) −6.71214 −0.432367 −0.216184 0.976353i \(-0.569361\pi\)
−0.216184 + 0.976353i \(0.569361\pi\)
\(242\) −0.621336 −0.0399410
\(243\) 0 0
\(244\) −6.60442 −0.422805
\(245\) 41.0376 2.62180
\(246\) 0 0
\(247\) −15.3421 −0.976195
\(248\) 6.10231 0.387497
\(249\) 0 0
\(250\) 1.95106 0.123396
\(251\) 23.6023 1.48976 0.744882 0.667197i \(-0.232506\pi\)
0.744882 + 0.667197i \(0.232506\pi\)
\(252\) 0 0
\(253\) −3.70131 −0.232699
\(254\) −2.12955 −0.133620
\(255\) 0 0
\(256\) 11.9288 0.745549
\(257\) −11.8463 −0.738955 −0.369477 0.929240i \(-0.620463\pi\)
−0.369477 + 0.929240i \(0.620463\pi\)
\(258\) 0 0
\(259\) −5.82578 −0.361996
\(260\) 15.4854 0.960363
\(261\) 0 0
\(262\) −0.692995 −0.0428134
\(263\) 3.24225 0.199926 0.0999630 0.994991i \(-0.468128\pi\)
0.0999630 + 0.994991i \(0.468128\pi\)
\(264\) 0 0
\(265\) 15.9105 0.977376
\(266\) 5.50251 0.337381
\(267\) 0 0
\(268\) −2.76614 −0.168969
\(269\) 3.56842 0.217570 0.108785 0.994065i \(-0.465304\pi\)
0.108785 + 0.994065i \(0.465304\pi\)
\(270\) 0 0
\(271\) 6.17978 0.375395 0.187697 0.982227i \(-0.439898\pi\)
0.187697 + 0.982227i \(0.439898\pi\)
\(272\) 12.5404 0.760371
\(273\) 0 0
\(274\) 3.25333 0.196541
\(275\) −6.41405 −0.386782
\(276\) 0 0
\(277\) 20.3224 1.22106 0.610529 0.791994i \(-0.290957\pi\)
0.610529 + 0.791994i \(0.290957\pi\)
\(278\) −1.62290 −0.0973350
\(279\) 0 0
\(280\) −11.2589 −0.672847
\(281\) 2.07151 0.123576 0.0617880 0.998089i \(-0.480320\pi\)
0.0617880 + 0.998089i \(0.480320\pi\)
\(282\) 0 0
\(283\) −5.58757 −0.332147 −0.166073 0.986113i \(-0.553109\pi\)
−0.166073 + 0.986113i \(0.553109\pi\)
\(284\) 2.36123 0.140113
\(285\) 0 0
\(286\) −2.61104 −0.154394
\(287\) 40.6818 2.40137
\(288\) 0 0
\(289\) −5.41898 −0.318764
\(290\) −0.597188 −0.0350681
\(291\) 0 0
\(292\) 16.8653 0.986965
\(293\) 17.7965 1.03969 0.519843 0.854262i \(-0.325991\pi\)
0.519843 + 0.854262i \(0.325991\pi\)
\(294\) 0 0
\(295\) −9.95366 −0.579525
\(296\) 1.10795 0.0643982
\(297\) 0 0
\(298\) 1.91881 0.111154
\(299\) −3.06512 −0.177261
\(300\) 0 0
\(301\) −39.8640 −2.29772
\(302\) 2.31105 0.132986
\(303\) 0 0
\(304\) 18.4448 1.05788
\(305\) 8.80163 0.503980
\(306\) 0 0
\(307\) −13.7399 −0.784180 −0.392090 0.919927i \(-0.628248\pi\)
−0.392090 + 0.919927i \(0.628248\pi\)
\(308\) −34.4225 −1.96141
\(309\) 0 0
\(310\) −4.01167 −0.227848
\(311\) 5.10837 0.289669 0.144835 0.989456i \(-0.453735\pi\)
0.144835 + 0.989456i \(0.453735\pi\)
\(312\) 0 0
\(313\) −31.5536 −1.78351 −0.891756 0.452516i \(-0.850527\pi\)
−0.891756 + 0.452516i \(0.850527\pi\)
\(314\) 0.761391 0.0429678
\(315\) 0 0
\(316\) 23.7812 1.33780
\(317\) 6.59462 0.370391 0.185195 0.982702i \(-0.440708\pi\)
0.185195 + 0.982702i \(0.440708\pi\)
\(318\) 0 0
\(319\) −3.70131 −0.207234
\(320\) −17.5321 −0.980073
\(321\) 0 0
\(322\) 1.09932 0.0612626
\(323\) 17.0338 0.947784
\(324\) 0 0
\(325\) −5.31159 −0.294634
\(326\) 0.389802 0.0215891
\(327\) 0 0
\(328\) −7.73688 −0.427198
\(329\) −14.9946 −0.826681
\(330\) 0 0
\(331\) −16.9553 −0.931947 −0.465974 0.884799i \(-0.654296\pi\)
−0.465974 + 0.884799i \(0.654296\pi\)
\(332\) −28.5655 −1.56773
\(333\) 0 0
\(334\) 1.04263 0.0570502
\(335\) 3.68641 0.201410
\(336\) 0 0
\(337\) 27.3791 1.49143 0.745717 0.666263i \(-0.232107\pi\)
0.745717 + 0.666263i \(0.232107\pi\)
\(338\) 0.829694 0.0451294
\(339\) 0 0
\(340\) −17.1928 −0.932413
\(341\) −24.8640 −1.34646
\(342\) 0 0
\(343\) −42.1072 −2.27358
\(344\) 7.58135 0.408759
\(345\) 0 0
\(346\) 5.00830 0.269248
\(347\) −2.62438 −0.140884 −0.0704421 0.997516i \(-0.522441\pi\)
−0.0704421 + 0.997516i \(0.522441\pi\)
\(348\) 0 0
\(349\) 6.65979 0.356490 0.178245 0.983986i \(-0.442958\pi\)
0.178245 + 0.983986i \(0.442958\pi\)
\(350\) 1.90502 0.101828
\(351\) 0 0
\(352\) 9.86366 0.525735
\(353\) −3.89509 −0.207315 −0.103657 0.994613i \(-0.533055\pi\)
−0.103657 + 0.994613i \(0.533055\pi\)
\(354\) 0 0
\(355\) −3.14679 −0.167014
\(356\) 21.2042 1.12382
\(357\) 0 0
\(358\) −4.79341 −0.253340
\(359\) 13.3307 0.703565 0.351783 0.936082i \(-0.385576\pi\)
0.351783 + 0.936082i \(0.385576\pi\)
\(360\) 0 0
\(361\) 6.05387 0.318625
\(362\) 1.50658 0.0791843
\(363\) 0 0
\(364\) −28.5059 −1.49412
\(365\) −22.4761 −1.17646
\(366\) 0 0
\(367\) −1.83274 −0.0956684 −0.0478342 0.998855i \(-0.515232\pi\)
−0.0478342 + 0.998855i \(0.515232\pi\)
\(368\) 3.68499 0.192094
\(369\) 0 0
\(370\) −0.728368 −0.0378660
\(371\) −29.2885 −1.52058
\(372\) 0 0
\(373\) −37.0251 −1.91709 −0.958544 0.284945i \(-0.908025\pi\)
−0.958544 + 0.284945i \(0.908025\pi\)
\(374\) 2.89893 0.149900
\(375\) 0 0
\(376\) 2.85169 0.147065
\(377\) −3.06512 −0.157862
\(378\) 0 0
\(379\) 8.53785 0.438560 0.219280 0.975662i \(-0.429629\pi\)
0.219280 + 0.975662i \(0.429629\pi\)
\(380\) −25.2878 −1.29724
\(381\) 0 0
\(382\) 4.85551 0.248430
\(383\) −18.2560 −0.932841 −0.466420 0.884563i \(-0.654457\pi\)
−0.466420 + 0.884563i \(0.654457\pi\)
\(384\) 0 0
\(385\) 45.8745 2.33798
\(386\) −1.27743 −0.0650192
\(387\) 0 0
\(388\) 3.20292 0.162604
\(389\) −19.6829 −0.997965 −0.498983 0.866612i \(-0.666293\pi\)
−0.498983 + 0.866612i \(0.666293\pi\)
\(390\) 0 0
\(391\) 3.40309 0.172102
\(392\) 14.3668 0.725633
\(393\) 0 0
\(394\) −4.64111 −0.233816
\(395\) −31.6929 −1.59464
\(396\) 0 0
\(397\) −1.39049 −0.0697869 −0.0348934 0.999391i \(-0.511109\pi\)
−0.0348934 + 0.999391i \(0.511109\pi\)
\(398\) 5.38762 0.270057
\(399\) 0 0
\(400\) 6.38577 0.319289
\(401\) 5.28138 0.263739 0.131870 0.991267i \(-0.457902\pi\)
0.131870 + 0.991267i \(0.457902\pi\)
\(402\) 0 0
\(403\) −20.5903 −1.02568
\(404\) 35.4519 1.76380
\(405\) 0 0
\(406\) 1.09932 0.0545583
\(407\) −4.51435 −0.223768
\(408\) 0 0
\(409\) 3.95248 0.195438 0.0977188 0.995214i \(-0.468845\pi\)
0.0977188 + 0.995214i \(0.468845\pi\)
\(410\) 5.08624 0.251192
\(411\) 0 0
\(412\) 15.4195 0.759662
\(413\) 18.3230 0.901614
\(414\) 0 0
\(415\) 38.0689 1.86873
\(416\) 8.16827 0.400483
\(417\) 0 0
\(418\) 4.26386 0.208552
\(419\) −6.29691 −0.307624 −0.153812 0.988100i \(-0.549155\pi\)
−0.153812 + 0.988100i \(0.549155\pi\)
\(420\) 0 0
\(421\) 4.87154 0.237424 0.118712 0.992929i \(-0.462123\pi\)
0.118712 + 0.992929i \(0.462123\pi\)
\(422\) −6.02690 −0.293385
\(423\) 0 0
\(424\) 5.57010 0.270508
\(425\) 5.89725 0.286059
\(426\) 0 0
\(427\) −16.2023 −0.784083
\(428\) −19.7427 −0.954298
\(429\) 0 0
\(430\) −4.98399 −0.240349
\(431\) −24.0540 −1.15864 −0.579321 0.815100i \(-0.696682\pi\)
−0.579321 + 0.815100i \(0.696682\pi\)
\(432\) 0 0
\(433\) −20.1836 −0.969961 −0.484980 0.874525i \(-0.661173\pi\)
−0.484980 + 0.874525i \(0.661173\pi\)
\(434\) 7.38479 0.354481
\(435\) 0 0
\(436\) 35.5789 1.70392
\(437\) 5.00538 0.239440
\(438\) 0 0
\(439\) −26.4320 −1.26153 −0.630766 0.775973i \(-0.717259\pi\)
−0.630766 + 0.775973i \(0.717259\pi\)
\(440\) −8.72443 −0.415921
\(441\) 0 0
\(442\) 2.40066 0.114188
\(443\) −31.8533 −1.51339 −0.756697 0.653765i \(-0.773188\pi\)
−0.756697 + 0.653765i \(0.773188\pi\)
\(444\) 0 0
\(445\) −28.2586 −1.33959
\(446\) 3.33635 0.157981
\(447\) 0 0
\(448\) 32.2735 1.52478
\(449\) 29.9464 1.41326 0.706629 0.707584i \(-0.250215\pi\)
0.706629 + 0.707584i \(0.250215\pi\)
\(450\) 0 0
\(451\) 31.5240 1.48441
\(452\) 17.3021 0.813821
\(453\) 0 0
\(454\) 3.17190 0.148864
\(455\) 37.9895 1.78097
\(456\) 0 0
\(457\) −23.3812 −1.09373 −0.546864 0.837221i \(-0.684179\pi\)
−0.546864 + 0.837221i \(0.684179\pi\)
\(458\) −6.28439 −0.293650
\(459\) 0 0
\(460\) −5.05213 −0.235557
\(461\) 3.01774 0.140550 0.0702751 0.997528i \(-0.477612\pi\)
0.0702751 + 0.997528i \(0.477612\pi\)
\(462\) 0 0
\(463\) −2.43464 −0.113147 −0.0565736 0.998398i \(-0.518018\pi\)
−0.0565736 + 0.998398i \(0.518018\pi\)
\(464\) 3.68499 0.171072
\(465\) 0 0
\(466\) 1.91812 0.0888554
\(467\) 6.71105 0.310551 0.155275 0.987871i \(-0.450374\pi\)
0.155275 + 0.987871i \(0.450374\pi\)
\(468\) 0 0
\(469\) −6.78603 −0.313350
\(470\) −1.87470 −0.0864737
\(471\) 0 0
\(472\) −3.48467 −0.160395
\(473\) −30.8903 −1.42034
\(474\) 0 0
\(475\) 8.67389 0.397985
\(476\) 31.6490 1.45063
\(477\) 0 0
\(478\) −4.86110 −0.222342
\(479\) 33.6174 1.53602 0.768008 0.640440i \(-0.221248\pi\)
0.768008 + 0.640440i \(0.221248\pi\)
\(480\) 0 0
\(481\) −3.73842 −0.170457
\(482\) 1.54479 0.0703634
\(483\) 0 0
\(484\) −5.25642 −0.238928
\(485\) −4.26850 −0.193822
\(486\) 0 0
\(487\) −22.3802 −1.01414 −0.507072 0.861904i \(-0.669272\pi\)
−0.507072 + 0.861904i \(0.669272\pi\)
\(488\) 3.08135 0.139486
\(489\) 0 0
\(490\) −9.44477 −0.426671
\(491\) 13.3390 0.601983 0.300991 0.953627i \(-0.402682\pi\)
0.300991 + 0.953627i \(0.402682\pi\)
\(492\) 0 0
\(493\) 3.40309 0.153267
\(494\) 3.53097 0.158866
\(495\) 0 0
\(496\) 24.7543 1.11150
\(497\) 5.79269 0.259837
\(498\) 0 0
\(499\) −15.5475 −0.696001 −0.348000 0.937494i \(-0.613139\pi\)
−0.348000 + 0.937494i \(0.613139\pi\)
\(500\) 16.5057 0.738160
\(501\) 0 0
\(502\) −5.43205 −0.242444
\(503\) −25.5361 −1.13860 −0.569300 0.822130i \(-0.692786\pi\)
−0.569300 + 0.822130i \(0.692786\pi\)
\(504\) 0 0
\(505\) −47.2463 −2.10243
\(506\) 0.851854 0.0378695
\(507\) 0 0
\(508\) −18.0157 −0.799318
\(509\) 10.4831 0.464653 0.232327 0.972638i \(-0.425366\pi\)
0.232327 + 0.972638i \(0.425366\pi\)
\(510\) 0 0
\(511\) 41.3747 1.83031
\(512\) −16.5151 −0.729872
\(513\) 0 0
\(514\) 2.72643 0.120257
\(515\) −20.5493 −0.905512
\(516\) 0 0
\(517\) −11.6192 −0.511013
\(518\) 1.34080 0.0589113
\(519\) 0 0
\(520\) −7.22486 −0.316831
\(521\) −13.6878 −0.599673 −0.299836 0.953991i \(-0.596932\pi\)
−0.299836 + 0.953991i \(0.596932\pi\)
\(522\) 0 0
\(523\) 6.86730 0.300286 0.150143 0.988664i \(-0.452027\pi\)
0.150143 + 0.988664i \(0.452027\pi\)
\(524\) −5.86265 −0.256111
\(525\) 0 0
\(526\) −0.746202 −0.0325360
\(527\) 22.8606 0.995824
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) −3.66180 −0.159058
\(531\) 0 0
\(532\) 46.5505 2.01822
\(533\) 26.1056 1.13076
\(534\) 0 0
\(535\) 26.3108 1.13752
\(536\) 1.29057 0.0557442
\(537\) 0 0
\(538\) −0.821268 −0.0354074
\(539\) −58.5377 −2.52140
\(540\) 0 0
\(541\) 12.8009 0.550355 0.275178 0.961393i \(-0.411263\pi\)
0.275178 + 0.961393i \(0.411263\pi\)
\(542\) −1.42227 −0.0610917
\(543\) 0 0
\(544\) −9.06893 −0.388827
\(545\) −47.4156 −2.03106
\(546\) 0 0
\(547\) 37.3728 1.59794 0.798972 0.601368i \(-0.205377\pi\)
0.798972 + 0.601368i \(0.205377\pi\)
\(548\) 27.5228 1.17571
\(549\) 0 0
\(550\) 1.47619 0.0629449
\(551\) 5.00538 0.213237
\(552\) 0 0
\(553\) 58.3411 2.48092
\(554\) −4.67719 −0.198715
\(555\) 0 0
\(556\) −13.7295 −0.582261
\(557\) −35.1787 −1.49057 −0.745286 0.666745i \(-0.767687\pi\)
−0.745286 + 0.666745i \(0.767687\pi\)
\(558\) 0 0
\(559\) −25.5808 −1.08195
\(560\) −45.6722 −1.93000
\(561\) 0 0
\(562\) −0.476757 −0.0201108
\(563\) −26.0407 −1.09749 −0.548743 0.835991i \(-0.684894\pi\)
−0.548743 + 0.835991i \(0.684894\pi\)
\(564\) 0 0
\(565\) −23.0583 −0.970068
\(566\) 1.28597 0.0540535
\(567\) 0 0
\(568\) −1.10166 −0.0462244
\(569\) −17.4792 −0.732767 −0.366383 0.930464i \(-0.619404\pi\)
−0.366383 + 0.930464i \(0.619404\pi\)
\(570\) 0 0
\(571\) 8.05298 0.337007 0.168503 0.985701i \(-0.446107\pi\)
0.168503 + 0.985701i \(0.446107\pi\)
\(572\) −22.0890 −0.923588
\(573\) 0 0
\(574\) −9.36288 −0.390799
\(575\) 1.73291 0.0722674
\(576\) 0 0
\(577\) −38.1194 −1.58693 −0.793466 0.608614i \(-0.791726\pi\)
−0.793466 + 0.608614i \(0.791726\pi\)
\(578\) 1.24717 0.0518756
\(579\) 0 0
\(580\) −5.05213 −0.209778
\(581\) −70.0782 −2.90733
\(582\) 0 0
\(583\) −22.6955 −0.939950
\(584\) −7.86865 −0.325607
\(585\) 0 0
\(586\) −4.09586 −0.169198
\(587\) −31.8205 −1.31337 −0.656687 0.754163i \(-0.728043\pi\)
−0.656687 + 0.754163i \(0.728043\pi\)
\(588\) 0 0
\(589\) 33.6242 1.38546
\(590\) 2.29083 0.0943118
\(591\) 0 0
\(592\) 4.49445 0.184721
\(593\) 33.9571 1.39445 0.697226 0.716852i \(-0.254418\pi\)
0.697226 + 0.716852i \(0.254418\pi\)
\(594\) 0 0
\(595\) −42.1783 −1.72914
\(596\) 16.2329 0.664924
\(597\) 0 0
\(598\) 0.705435 0.0288474
\(599\) 4.88042 0.199408 0.0997042 0.995017i \(-0.468210\pi\)
0.0997042 + 0.995017i \(0.468210\pi\)
\(600\) 0 0
\(601\) 3.53581 0.144229 0.0721143 0.997396i \(-0.477025\pi\)
0.0721143 + 0.997396i \(0.477025\pi\)
\(602\) 9.17466 0.373931
\(603\) 0 0
\(604\) 19.5512 0.795528
\(605\) 7.00517 0.284800
\(606\) 0 0
\(607\) −23.9417 −0.971764 −0.485882 0.874024i \(-0.661502\pi\)
−0.485882 + 0.874024i \(0.661502\pi\)
\(608\) −13.3389 −0.540964
\(609\) 0 0
\(610\) −2.02569 −0.0820177
\(611\) −9.62210 −0.389268
\(612\) 0 0
\(613\) 24.8422 1.00337 0.501684 0.865051i \(-0.332714\pi\)
0.501684 + 0.865051i \(0.332714\pi\)
\(614\) 3.16223 0.127617
\(615\) 0 0
\(616\) 16.0602 0.647082
\(617\) −14.1565 −0.569919 −0.284960 0.958539i \(-0.591980\pi\)
−0.284960 + 0.958539i \(0.591980\pi\)
\(618\) 0 0
\(619\) 15.7115 0.631500 0.315750 0.948842i \(-0.397744\pi\)
0.315750 + 0.948842i \(0.397744\pi\)
\(620\) −33.9382 −1.36299
\(621\) 0 0
\(622\) −1.17569 −0.0471408
\(623\) 52.0192 2.08411
\(624\) 0 0
\(625\) −30.6616 −1.22646
\(626\) 7.26203 0.290249
\(627\) 0 0
\(628\) 6.44127 0.257035
\(629\) 4.15062 0.165496
\(630\) 0 0
\(631\) 26.8165 1.06755 0.533774 0.845627i \(-0.320773\pi\)
0.533774 + 0.845627i \(0.320773\pi\)
\(632\) −11.0953 −0.441349
\(633\) 0 0
\(634\) −1.51775 −0.0602774
\(635\) 24.0093 0.952781
\(636\) 0 0
\(637\) −48.4761 −1.92069
\(638\) 0.851854 0.0337252
\(639\) 0 0
\(640\) 17.8647 0.706166
\(641\) −9.40758 −0.371577 −0.185789 0.982590i \(-0.559484\pi\)
−0.185789 + 0.982590i \(0.559484\pi\)
\(642\) 0 0
\(643\) −16.8530 −0.664616 −0.332308 0.943171i \(-0.607827\pi\)
−0.332308 + 0.943171i \(0.607827\pi\)
\(644\) 9.30009 0.366475
\(645\) 0 0
\(646\) −3.92031 −0.154242
\(647\) 7.52867 0.295983 0.147991 0.988989i \(-0.452719\pi\)
0.147991 + 0.988989i \(0.452719\pi\)
\(648\) 0 0
\(649\) 14.1983 0.557333
\(650\) 1.22246 0.0479487
\(651\) 0 0
\(652\) 3.29767 0.129147
\(653\) −8.35597 −0.326995 −0.163497 0.986544i \(-0.552277\pi\)
−0.163497 + 0.986544i \(0.552277\pi\)
\(654\) 0 0
\(655\) 7.81308 0.305282
\(656\) −31.3851 −1.22538
\(657\) 0 0
\(658\) 3.45100 0.134534
\(659\) −47.0599 −1.83319 −0.916596 0.399815i \(-0.869074\pi\)
−0.916596 + 0.399815i \(0.869074\pi\)
\(660\) 0 0
\(661\) −19.4971 −0.758350 −0.379175 0.925325i \(-0.623792\pi\)
−0.379175 + 0.925325i \(0.623792\pi\)
\(662\) 3.90225 0.151665
\(663\) 0 0
\(664\) 13.3275 0.517207
\(665\) −62.0373 −2.40570
\(666\) 0 0
\(667\) 1.00000 0.0387202
\(668\) 8.82052 0.341276
\(669\) 0 0
\(670\) −0.848423 −0.0327775
\(671\) −12.5550 −0.484681
\(672\) 0 0
\(673\) −25.3526 −0.977271 −0.488636 0.872488i \(-0.662505\pi\)
−0.488636 + 0.872488i \(0.662505\pi\)
\(674\) −6.30127 −0.242716
\(675\) 0 0
\(676\) 7.01910 0.269965
\(677\) 10.0166 0.384969 0.192485 0.981300i \(-0.438345\pi\)
0.192485 + 0.981300i \(0.438345\pi\)
\(678\) 0 0
\(679\) 7.85756 0.301545
\(680\) 8.02148 0.307610
\(681\) 0 0
\(682\) 5.72242 0.219123
\(683\) −22.0140 −0.842342 −0.421171 0.906981i \(-0.638381\pi\)
−0.421171 + 0.906981i \(0.638381\pi\)
\(684\) 0 0
\(685\) −36.6793 −1.40144
\(686\) 9.69094 0.370002
\(687\) 0 0
\(688\) 30.7541 1.17249
\(689\) −18.7945 −0.716014
\(690\) 0 0
\(691\) −23.6597 −0.900059 −0.450029 0.893014i \(-0.648586\pi\)
−0.450029 + 0.893014i \(0.648586\pi\)
\(692\) 42.3696 1.61065
\(693\) 0 0
\(694\) 0.603999 0.0229275
\(695\) 18.2972 0.694051
\(696\) 0 0
\(697\) −28.9841 −1.09785
\(698\) −1.53275 −0.0580153
\(699\) 0 0
\(700\) 16.1162 0.609136
\(701\) 44.6815 1.68760 0.843799 0.536659i \(-0.180314\pi\)
0.843799 + 0.536659i \(0.180314\pi\)
\(702\) 0 0
\(703\) 6.10488 0.230250
\(704\) 25.0085 0.942544
\(705\) 0 0
\(706\) 0.896452 0.0337384
\(707\) 86.9722 3.27093
\(708\) 0 0
\(709\) −15.8352 −0.594705 −0.297353 0.954768i \(-0.596104\pi\)
−0.297353 + 0.954768i \(0.596104\pi\)
\(710\) 0.724230 0.0271799
\(711\) 0 0
\(712\) −9.89304 −0.370757
\(713\) 6.71761 0.251576
\(714\) 0 0
\(715\) 29.4378 1.10091
\(716\) −40.5516 −1.51549
\(717\) 0 0
\(718\) −3.06804 −0.114498
\(719\) −52.1881 −1.94629 −0.973144 0.230196i \(-0.926063\pi\)
−0.973144 + 0.230196i \(0.926063\pi\)
\(720\) 0 0
\(721\) 37.8277 1.40878
\(722\) −1.39329 −0.0518530
\(723\) 0 0
\(724\) 12.7455 0.473683
\(725\) 1.73291 0.0643587
\(726\) 0 0
\(727\) −14.0872 −0.522467 −0.261233 0.965276i \(-0.584129\pi\)
−0.261233 + 0.965276i \(0.584129\pi\)
\(728\) 13.2997 0.492920
\(729\) 0 0
\(730\) 5.17287 0.191456
\(731\) 28.4014 1.05046
\(732\) 0 0
\(733\) −32.7271 −1.20880 −0.604401 0.796680i \(-0.706588\pi\)
−0.604401 + 0.796680i \(0.706588\pi\)
\(734\) 0.421804 0.0155691
\(735\) 0 0
\(736\) −2.66491 −0.0982299
\(737\) −5.25845 −0.193697
\(738\) 0 0
\(739\) 27.7120 1.01940 0.509701 0.860351i \(-0.329756\pi\)
0.509701 + 0.860351i \(0.329756\pi\)
\(740\) −6.16189 −0.226516
\(741\) 0 0
\(742\) 6.74073 0.247460
\(743\) 21.1573 0.776186 0.388093 0.921620i \(-0.373134\pi\)
0.388093 + 0.921620i \(0.373134\pi\)
\(744\) 0 0
\(745\) −21.6334 −0.792585
\(746\) 8.52130 0.311987
\(747\) 0 0
\(748\) 24.5246 0.896708
\(749\) −48.4336 −1.76973
\(750\) 0 0
\(751\) 29.3387 1.07058 0.535291 0.844668i \(-0.320202\pi\)
0.535291 + 0.844668i \(0.320202\pi\)
\(752\) 11.5680 0.421842
\(753\) 0 0
\(754\) 0.705435 0.0256904
\(755\) −26.0557 −0.948263
\(756\) 0 0
\(757\) −38.3555 −1.39405 −0.697027 0.717045i \(-0.745494\pi\)
−0.697027 + 0.717045i \(0.745494\pi\)
\(758\) −1.96498 −0.0713712
\(759\) 0 0
\(760\) 11.7983 0.427969
\(761\) 5.41281 0.196214 0.0981071 0.995176i \(-0.468721\pi\)
0.0981071 + 0.995176i \(0.468721\pi\)
\(762\) 0 0
\(763\) 87.2838 3.15989
\(764\) 41.0770 1.48611
\(765\) 0 0
\(766\) 4.20161 0.151810
\(767\) 11.7579 0.424553
\(768\) 0 0
\(769\) −15.7821 −0.569119 −0.284559 0.958658i \(-0.591847\pi\)
−0.284559 + 0.958658i \(0.591847\pi\)
\(770\) −10.5580 −0.380483
\(771\) 0 0
\(772\) −10.8068 −0.388947
\(773\) 35.5162 1.27743 0.638715 0.769443i \(-0.279466\pi\)
0.638715 + 0.769443i \(0.279466\pi\)
\(774\) 0 0
\(775\) 11.6410 0.418158
\(776\) −1.49435 −0.0536442
\(777\) 0 0
\(778\) 4.53001 0.162409
\(779\) −42.6308 −1.52741
\(780\) 0 0
\(781\) 4.48871 0.160619
\(782\) −0.783218 −0.0280078
\(783\) 0 0
\(784\) 58.2797 2.08142
\(785\) −8.58420 −0.306383
\(786\) 0 0
\(787\) 45.4908 1.62157 0.810785 0.585344i \(-0.199040\pi\)
0.810785 + 0.585344i \(0.199040\pi\)
\(788\) −39.2632 −1.39869
\(789\) 0 0
\(790\) 7.29409 0.259512
\(791\) 42.4462 1.50921
\(792\) 0 0
\(793\) −10.3970 −0.369210
\(794\) 0.320021 0.0113571
\(795\) 0 0
\(796\) 45.5786 1.61549
\(797\) −30.5490 −1.08210 −0.541051 0.840990i \(-0.681973\pi\)
−0.541051 + 0.840990i \(0.681973\pi\)
\(798\) 0 0
\(799\) 10.6831 0.377939
\(800\) −4.61806 −0.163273
\(801\) 0 0
\(802\) −1.21550 −0.0429210
\(803\) 32.0609 1.13141
\(804\) 0 0
\(805\) −12.3941 −0.436835
\(806\) 4.73884 0.166918
\(807\) 0 0
\(808\) −16.5404 −0.581890
\(809\) −25.5128 −0.896981 −0.448491 0.893788i \(-0.648038\pi\)
−0.448491 + 0.893788i \(0.648038\pi\)
\(810\) 0 0
\(811\) 50.4381 1.77112 0.885560 0.464524i \(-0.153775\pi\)
0.885560 + 0.464524i \(0.153775\pi\)
\(812\) 9.30009 0.326369
\(813\) 0 0
\(814\) 1.03897 0.0364160
\(815\) −4.39477 −0.153942
\(816\) 0 0
\(817\) 41.7738 1.46148
\(818\) −0.909660 −0.0318055
\(819\) 0 0
\(820\) 43.0289 1.50264
\(821\) −2.96844 −0.103599 −0.0517996 0.998657i \(-0.516496\pi\)
−0.0517996 + 0.998657i \(0.516496\pi\)
\(822\) 0 0
\(823\) 18.1118 0.631336 0.315668 0.948870i \(-0.397771\pi\)
0.315668 + 0.948870i \(0.397771\pi\)
\(824\) −7.19410 −0.250618
\(825\) 0 0
\(826\) −4.21701 −0.146729
\(827\) 40.2128 1.39834 0.699168 0.714957i \(-0.253554\pi\)
0.699168 + 0.714957i \(0.253554\pi\)
\(828\) 0 0
\(829\) −40.4489 −1.40485 −0.702424 0.711759i \(-0.747899\pi\)
−0.702424 + 0.711759i \(0.747899\pi\)
\(830\) −8.76152 −0.304117
\(831\) 0 0
\(832\) 20.7100 0.717990
\(833\) 53.8212 1.86480
\(834\) 0 0
\(835\) −11.7550 −0.406799
\(836\) 36.0717 1.24756
\(837\) 0 0
\(838\) 1.44923 0.0500627
\(839\) 33.9645 1.17259 0.586293 0.810099i \(-0.300587\pi\)
0.586293 + 0.810099i \(0.300587\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) −1.12118 −0.0386384
\(843\) 0 0
\(844\) −50.9867 −1.75504
\(845\) −9.35427 −0.321797
\(846\) 0 0
\(847\) −12.8953 −0.443087
\(848\) 22.5954 0.775929
\(849\) 0 0
\(850\) −1.35725 −0.0465532
\(851\) 1.21966 0.0418095
\(852\) 0 0
\(853\) 21.1443 0.723967 0.361983 0.932185i \(-0.382100\pi\)
0.361983 + 0.932185i \(0.382100\pi\)
\(854\) 3.72894 0.127602
\(855\) 0 0
\(856\) 9.21113 0.314830
\(857\) 20.8537 0.712350 0.356175 0.934419i \(-0.384081\pi\)
0.356175 + 0.934419i \(0.384081\pi\)
\(858\) 0 0
\(859\) −39.2514 −1.33924 −0.669621 0.742703i \(-0.733543\pi\)
−0.669621 + 0.742703i \(0.733543\pi\)
\(860\) −42.1639 −1.43778
\(861\) 0 0
\(862\) 5.53601 0.188557
\(863\) −57.0716 −1.94274 −0.971371 0.237569i \(-0.923649\pi\)
−0.971371 + 0.237569i \(0.923649\pi\)
\(864\) 0 0
\(865\) −56.4654 −1.91988
\(866\) 4.64523 0.157851
\(867\) 0 0
\(868\) 62.4743 2.12052
\(869\) 45.2081 1.53358
\(870\) 0 0
\(871\) −4.35461 −0.147550
\(872\) −16.5997 −0.562136
\(873\) 0 0
\(874\) −1.15198 −0.0389665
\(875\) 40.4927 1.36890
\(876\) 0 0
\(877\) 1.49604 0.0505176 0.0252588 0.999681i \(-0.491959\pi\)
0.0252588 + 0.999681i \(0.491959\pi\)
\(878\) 6.08331 0.205302
\(879\) 0 0
\(880\) −35.3911 −1.19303
\(881\) 34.7534 1.17087 0.585435 0.810719i \(-0.300924\pi\)
0.585435 + 0.810719i \(0.300924\pi\)
\(882\) 0 0
\(883\) −21.5140 −0.724002 −0.362001 0.932178i \(-0.617906\pi\)
−0.362001 + 0.932178i \(0.617906\pi\)
\(884\) 20.3093 0.683074
\(885\) 0 0
\(886\) 7.33100 0.246290
\(887\) 10.3028 0.345934 0.172967 0.984928i \(-0.444665\pi\)
0.172967 + 0.984928i \(0.444665\pi\)
\(888\) 0 0
\(889\) −44.1970 −1.48232
\(890\) 6.50370 0.218005
\(891\) 0 0
\(892\) 28.2251 0.945045
\(893\) 15.7130 0.525816
\(894\) 0 0
\(895\) 54.0427 1.80645
\(896\) −32.8859 −1.09864
\(897\) 0 0
\(898\) −6.89214 −0.229994
\(899\) 6.71761 0.224045
\(900\) 0 0
\(901\) 20.8668 0.695175
\(902\) −7.25523 −0.241573
\(903\) 0 0
\(904\) −8.07244 −0.268485
\(905\) −16.9858 −0.564626
\(906\) 0 0
\(907\) −17.4319 −0.578818 −0.289409 0.957206i \(-0.593459\pi\)
−0.289409 + 0.957206i \(0.593459\pi\)
\(908\) 26.8338 0.890511
\(909\) 0 0
\(910\) −8.74325 −0.289836
\(911\) 33.5503 1.11157 0.555785 0.831326i \(-0.312418\pi\)
0.555785 + 0.831326i \(0.312418\pi\)
\(912\) 0 0
\(913\) −54.3030 −1.79717
\(914\) 5.38117 0.177993
\(915\) 0 0
\(916\) −53.1651 −1.75663
\(917\) −14.3825 −0.474953
\(918\) 0 0
\(919\) −24.8480 −0.819661 −0.409831 0.912162i \(-0.634412\pi\)
−0.409831 + 0.912162i \(0.634412\pi\)
\(920\) 2.35712 0.0777119
\(921\) 0 0
\(922\) −0.694531 −0.0228732
\(923\) 3.71718 0.122352
\(924\) 0 0
\(925\) 2.11357 0.0694937
\(926\) 0.560330 0.0184136
\(927\) 0 0
\(928\) −2.66491 −0.0874800
\(929\) 30.1456 0.989044 0.494522 0.869165i \(-0.335343\pi\)
0.494522 + 0.869165i \(0.335343\pi\)
\(930\) 0 0
\(931\) 79.1622 2.59444
\(932\) 16.2271 0.531536
\(933\) 0 0
\(934\) −1.54454 −0.0505390
\(935\) −32.6836 −1.06887
\(936\) 0 0
\(937\) −50.8757 −1.66204 −0.831019 0.556244i \(-0.812242\pi\)
−0.831019 + 0.556244i \(0.812242\pi\)
\(938\) 1.56180 0.0509946
\(939\) 0 0
\(940\) −15.8598 −0.517288
\(941\) 55.5956 1.81236 0.906182 0.422888i \(-0.138984\pi\)
0.906182 + 0.422888i \(0.138984\pi\)
\(942\) 0 0
\(943\) −8.51699 −0.277351
\(944\) −14.1357 −0.460079
\(945\) 0 0
\(946\) 7.10938 0.231146
\(947\) −54.0049 −1.75492 −0.877462 0.479647i \(-0.840765\pi\)
−0.877462 + 0.479647i \(0.840765\pi\)
\(948\) 0 0
\(949\) 26.5502 0.861857
\(950\) −1.99629 −0.0647682
\(951\) 0 0
\(952\) −14.7662 −0.478574
\(953\) 51.8326 1.67902 0.839511 0.543342i \(-0.182841\pi\)
0.839511 + 0.543342i \(0.182841\pi\)
\(954\) 0 0
\(955\) −54.7428 −1.77144
\(956\) −41.1243 −1.33005
\(957\) 0 0
\(958\) −7.73701 −0.249971
\(959\) 67.5202 2.18034
\(960\) 0 0
\(961\) 14.1263 0.455686
\(962\) 0.860393 0.0277402
\(963\) 0 0
\(964\) 13.0688 0.420916
\(965\) 14.4022 0.463622
\(966\) 0 0
\(967\) −37.8809 −1.21817 −0.609083 0.793106i \(-0.708462\pi\)
−0.609083 + 0.793106i \(0.708462\pi\)
\(968\) 2.45243 0.0788241
\(969\) 0 0
\(970\) 0.982391 0.0315427
\(971\) −2.62752 −0.0843210 −0.0421605 0.999111i \(-0.513424\pi\)
−0.0421605 + 0.999111i \(0.513424\pi\)
\(972\) 0 0
\(973\) −33.6819 −1.07979
\(974\) 5.15078 0.165042
\(975\) 0 0
\(976\) 12.4997 0.400105
\(977\) −29.4200 −0.941229 −0.470615 0.882339i \(-0.655968\pi\)
−0.470615 + 0.882339i \(0.655968\pi\)
\(978\) 0 0
\(979\) 40.3093 1.28829
\(980\) −79.9015 −2.55236
\(981\) 0 0
\(982\) −3.06997 −0.0979667
\(983\) 23.9487 0.763845 0.381923 0.924194i \(-0.375262\pi\)
0.381923 + 0.924194i \(0.375262\pi\)
\(984\) 0 0
\(985\) 52.3256 1.66723
\(986\) −0.783218 −0.0249427
\(987\) 0 0
\(988\) 29.8716 0.950341
\(989\) 8.34577 0.265380
\(990\) 0 0
\(991\) 0.962968 0.0305897 0.0152948 0.999883i \(-0.495131\pi\)
0.0152948 + 0.999883i \(0.495131\pi\)
\(992\) −17.9018 −0.568383
\(993\) 0 0
\(994\) −1.33318 −0.0422860
\(995\) −60.7420 −1.92565
\(996\) 0 0
\(997\) −50.5602 −1.60126 −0.800629 0.599161i \(-0.795501\pi\)
−0.800629 + 0.599161i \(0.795501\pi\)
\(998\) 3.57824 0.113267
\(999\) 0 0
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 \(a_p\))