Properties

Label 8001.2.a.v.1.12
Level 8001
Weight 2
Character 8001.1
Self dual Yes
Analytic conductor 63.888
Analytic rank 0
Dimension 19
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8001 = 3^{2} \cdot 7 \cdot 127 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8001.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.8883066572\)
Analytic rank: \(0\)
Dimension: \(19\)
Coefficient field: \(\mathbb{Q}[x]/(x^{19} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{2} \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Root \(-0.407951\)
Character \(\chi\) = 8001.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.407951 q^{2} -1.83358 q^{4} +1.08992 q^{5} +1.00000 q^{7} -1.56391 q^{8} +O(q^{10})\) \(q+0.407951 q^{2} -1.83358 q^{4} +1.08992 q^{5} +1.00000 q^{7} -1.56391 q^{8} +0.444635 q^{10} -2.30086 q^{11} -1.28207 q^{13} +0.407951 q^{14} +3.02915 q^{16} -3.85945 q^{17} -5.48075 q^{19} -1.99845 q^{20} -0.938637 q^{22} -5.15478 q^{23} -3.81207 q^{25} -0.523023 q^{26} -1.83358 q^{28} +3.35002 q^{29} -0.261843 q^{31} +4.36357 q^{32} -1.57447 q^{34} +1.08992 q^{35} +4.76674 q^{37} -2.23588 q^{38} -1.70454 q^{40} -4.53932 q^{41} +3.17008 q^{43} +4.21880 q^{44} -2.10290 q^{46} -0.491884 q^{47} +1.00000 q^{49} -1.55514 q^{50} +2.35078 q^{52} +11.3199 q^{53} -2.50775 q^{55} -1.56391 q^{56} +1.36664 q^{58} -1.96040 q^{59} +0.0291708 q^{61} -0.106819 q^{62} -4.27818 q^{64} -1.39736 q^{65} +13.7705 q^{67} +7.07659 q^{68} +0.444635 q^{70} -1.95435 q^{71} +10.9732 q^{73} +1.94460 q^{74} +10.0494 q^{76} -2.30086 q^{77} +1.31077 q^{79} +3.30154 q^{80} -1.85182 q^{82} +9.68361 q^{83} -4.20649 q^{85} +1.29324 q^{86} +3.59834 q^{88} -13.3023 q^{89} -1.28207 q^{91} +9.45169 q^{92} -0.200664 q^{94} -5.97359 q^{95} -2.44284 q^{97} +0.407951 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 19q - 4q^{2} + 22q^{4} - 5q^{5} + 19q^{7} - 9q^{8} + O(q^{10}) \) \( 19q - 4q^{2} + 22q^{4} - 5q^{5} + 19q^{7} - 9q^{8} + 9q^{11} + 24q^{13} - 4q^{14} + 20q^{16} - 17q^{17} + 23q^{19} - 5q^{20} - 3q^{22} + 17q^{23} + 38q^{25} - 28q^{26} + 22q^{28} - 2q^{29} + 16q^{31} - 17q^{32} + 29q^{34} - 5q^{35} + 56q^{37} - 2q^{38} - 13q^{40} + 7q^{41} + 19q^{43} + 29q^{44} + 10q^{46} - 25q^{47} + 19q^{49} + 9q^{50} + 16q^{52} - 18q^{53} + 10q^{55} - 9q^{56} + 31q^{58} - 11q^{59} + 26q^{61} - 26q^{62} + 45q^{64} - 27q^{65} + 24q^{67} - 14q^{68} + 32q^{71} + 51q^{73} + 12q^{76} + 9q^{77} + 30q^{79} + 30q^{80} - 52q^{82} - q^{83} + 44q^{85} + 24q^{86} - 30q^{88} - 5q^{89} + 24q^{91} + 88q^{92} + 7q^{94} + 24q^{95} + 5q^{97} - 4q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.407951 0.288465 0.144232 0.989544i \(-0.453929\pi\)
0.144232 + 0.989544i \(0.453929\pi\)
\(3\) 0 0
\(4\) −1.83358 −0.916788
\(5\) 1.08992 0.487428 0.243714 0.969847i \(-0.421634\pi\)
0.243714 + 0.969847i \(0.421634\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) −1.56391 −0.552926
\(9\) 0 0
\(10\) 0.444635 0.140606
\(11\) −2.30086 −0.693734 −0.346867 0.937914i \(-0.612755\pi\)
−0.346867 + 0.937914i \(0.612755\pi\)
\(12\) 0 0
\(13\) −1.28207 −0.355583 −0.177791 0.984068i \(-0.556895\pi\)
−0.177791 + 0.984068i \(0.556895\pi\)
\(14\) 0.407951 0.109030
\(15\) 0 0
\(16\) 3.02915 0.757288
\(17\) −3.85945 −0.936053 −0.468027 0.883714i \(-0.655035\pi\)
−0.468027 + 0.883714i \(0.655035\pi\)
\(18\) 0 0
\(19\) −5.48075 −1.25737 −0.628685 0.777660i \(-0.716406\pi\)
−0.628685 + 0.777660i \(0.716406\pi\)
\(20\) −1.99845 −0.446868
\(21\) 0 0
\(22\) −0.938637 −0.200118
\(23\) −5.15478 −1.07485 −0.537423 0.843313i \(-0.680602\pi\)
−0.537423 + 0.843313i \(0.680602\pi\)
\(24\) 0 0
\(25\) −3.81207 −0.762414
\(26\) −0.523023 −0.102573
\(27\) 0 0
\(28\) −1.83358 −0.346513
\(29\) 3.35002 0.622082 0.311041 0.950396i \(-0.399322\pi\)
0.311041 + 0.950396i \(0.399322\pi\)
\(30\) 0 0
\(31\) −0.261843 −0.0470284 −0.0235142 0.999724i \(-0.507485\pi\)
−0.0235142 + 0.999724i \(0.507485\pi\)
\(32\) 4.36357 0.771377
\(33\) 0 0
\(34\) −1.57447 −0.270019
\(35\) 1.08992 0.184230
\(36\) 0 0
\(37\) 4.76674 0.783648 0.391824 0.920040i \(-0.371844\pi\)
0.391824 + 0.920040i \(0.371844\pi\)
\(38\) −2.23588 −0.362707
\(39\) 0 0
\(40\) −1.70454 −0.269512
\(41\) −4.53932 −0.708923 −0.354461 0.935071i \(-0.615336\pi\)
−0.354461 + 0.935071i \(0.615336\pi\)
\(42\) 0 0
\(43\) 3.17008 0.483433 0.241716 0.970347i \(-0.422290\pi\)
0.241716 + 0.970347i \(0.422290\pi\)
\(44\) 4.21880 0.636007
\(45\) 0 0
\(46\) −2.10290 −0.310056
\(47\) −0.491884 −0.0717486 −0.0358743 0.999356i \(-0.511422\pi\)
−0.0358743 + 0.999356i \(0.511422\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) −1.55514 −0.219930
\(51\) 0 0
\(52\) 2.35078 0.325994
\(53\) 11.3199 1.55490 0.777452 0.628943i \(-0.216512\pi\)
0.777452 + 0.628943i \(0.216512\pi\)
\(54\) 0 0
\(55\) −2.50775 −0.338145
\(56\) −1.56391 −0.208986
\(57\) 0 0
\(58\) 1.36664 0.179449
\(59\) −1.96040 −0.255222 −0.127611 0.991824i \(-0.540731\pi\)
−0.127611 + 0.991824i \(0.540731\pi\)
\(60\) 0 0
\(61\) 0.0291708 0.00373494 0.00186747 0.999998i \(-0.499406\pi\)
0.00186747 + 0.999998i \(0.499406\pi\)
\(62\) −0.106819 −0.0135660
\(63\) 0 0
\(64\) −4.27818 −0.534773
\(65\) −1.39736 −0.173321
\(66\) 0 0
\(67\) 13.7705 1.68234 0.841169 0.540772i \(-0.181868\pi\)
0.841169 + 0.540772i \(0.181868\pi\)
\(68\) 7.07659 0.858162
\(69\) 0 0
\(70\) 0.444635 0.0531440
\(71\) −1.95435 −0.231938 −0.115969 0.993253i \(-0.536997\pi\)
−0.115969 + 0.993253i \(0.536997\pi\)
\(72\) 0 0
\(73\) 10.9732 1.28431 0.642155 0.766575i \(-0.278040\pi\)
0.642155 + 0.766575i \(0.278040\pi\)
\(74\) 1.94460 0.226055
\(75\) 0 0
\(76\) 10.0494 1.15274
\(77\) −2.30086 −0.262207
\(78\) 0 0
\(79\) 1.31077 0.147473 0.0737364 0.997278i \(-0.476508\pi\)
0.0737364 + 0.997278i \(0.476508\pi\)
\(80\) 3.30154 0.369123
\(81\) 0 0
\(82\) −1.85182 −0.204499
\(83\) 9.68361 1.06291 0.531457 0.847085i \(-0.321645\pi\)
0.531457 + 0.847085i \(0.321645\pi\)
\(84\) 0 0
\(85\) −4.20649 −0.456258
\(86\) 1.29324 0.139453
\(87\) 0 0
\(88\) 3.59834 0.383584
\(89\) −13.3023 −1.41004 −0.705022 0.709186i \(-0.749063\pi\)
−0.705022 + 0.709186i \(0.749063\pi\)
\(90\) 0 0
\(91\) −1.28207 −0.134398
\(92\) 9.45169 0.985406
\(93\) 0 0
\(94\) −0.200664 −0.0206970
\(95\) −5.97359 −0.612877
\(96\) 0 0
\(97\) −2.44284 −0.248033 −0.124016 0.992280i \(-0.539578\pi\)
−0.124016 + 0.992280i \(0.539578\pi\)
\(98\) 0.407951 0.0412093
\(99\) 0 0
\(100\) 6.98972 0.698972
\(101\) −16.2404 −1.61598 −0.807991 0.589195i \(-0.799445\pi\)
−0.807991 + 0.589195i \(0.799445\pi\)
\(102\) 0 0
\(103\) 16.7605 1.65146 0.825730 0.564066i \(-0.190764\pi\)
0.825730 + 0.564066i \(0.190764\pi\)
\(104\) 2.00505 0.196611
\(105\) 0 0
\(106\) 4.61795 0.448535
\(107\) 7.03427 0.680028 0.340014 0.940420i \(-0.389568\pi\)
0.340014 + 0.940420i \(0.389568\pi\)
\(108\) 0 0
\(109\) 8.64818 0.828345 0.414173 0.910198i \(-0.364071\pi\)
0.414173 + 0.910198i \(0.364071\pi\)
\(110\) −1.02304 −0.0975431
\(111\) 0 0
\(112\) 3.02915 0.286228
\(113\) 9.06671 0.852924 0.426462 0.904505i \(-0.359760\pi\)
0.426462 + 0.904505i \(0.359760\pi\)
\(114\) 0 0
\(115\) −5.61831 −0.523910
\(116\) −6.14251 −0.570318
\(117\) 0 0
\(118\) −0.799745 −0.0736225
\(119\) −3.85945 −0.353795
\(120\) 0 0
\(121\) −5.70606 −0.518733
\(122\) 0.0119003 0.00107740
\(123\) 0 0
\(124\) 0.480109 0.0431150
\(125\) −9.60447 −0.859050
\(126\) 0 0
\(127\) 1.00000 0.0887357
\(128\) −10.4724 −0.925640
\(129\) 0 0
\(130\) −0.570054 −0.0499970
\(131\) −13.6779 −1.19504 −0.597521 0.801853i \(-0.703847\pi\)
−0.597521 + 0.801853i \(0.703847\pi\)
\(132\) 0 0
\(133\) −5.48075 −0.475241
\(134\) 5.61770 0.485296
\(135\) 0 0
\(136\) 6.03583 0.517568
\(137\) 21.0777 1.80079 0.900394 0.435076i \(-0.143278\pi\)
0.900394 + 0.435076i \(0.143278\pi\)
\(138\) 0 0
\(139\) 10.4381 0.885348 0.442674 0.896683i \(-0.354030\pi\)
0.442674 + 0.896683i \(0.354030\pi\)
\(140\) −1.99845 −0.168900
\(141\) 0 0
\(142\) −0.797278 −0.0669061
\(143\) 2.94986 0.246680
\(144\) 0 0
\(145\) 3.65125 0.303220
\(146\) 4.47651 0.370479
\(147\) 0 0
\(148\) −8.74019 −0.718439
\(149\) −0.369201 −0.0302461 −0.0151231 0.999886i \(-0.504814\pi\)
−0.0151231 + 0.999886i \(0.504814\pi\)
\(150\) 0 0
\(151\) 10.3324 0.840841 0.420420 0.907329i \(-0.361883\pi\)
0.420420 + 0.907329i \(0.361883\pi\)
\(152\) 8.57140 0.695233
\(153\) 0 0
\(154\) −0.938637 −0.0756375
\(155\) −0.285388 −0.0229229
\(156\) 0 0
\(157\) 19.4698 1.55386 0.776929 0.629589i \(-0.216777\pi\)
0.776929 + 0.629589i \(0.216777\pi\)
\(158\) 0.534729 0.0425407
\(159\) 0 0
\(160\) 4.75595 0.375991
\(161\) −5.15478 −0.406254
\(162\) 0 0
\(163\) 13.8845 1.08752 0.543760 0.839241i \(-0.317000\pi\)
0.543760 + 0.839241i \(0.317000\pi\)
\(164\) 8.32319 0.649932
\(165\) 0 0
\(166\) 3.95044 0.306614
\(167\) 8.27086 0.640018 0.320009 0.947414i \(-0.396314\pi\)
0.320009 + 0.947414i \(0.396314\pi\)
\(168\) 0 0
\(169\) −11.3563 −0.873561
\(170\) −1.71604 −0.131615
\(171\) 0 0
\(172\) −5.81258 −0.443205
\(173\) −17.6707 −1.34348 −0.671738 0.740789i \(-0.734452\pi\)
−0.671738 + 0.740789i \(0.734452\pi\)
\(174\) 0 0
\(175\) −3.81207 −0.288165
\(176\) −6.96965 −0.525357
\(177\) 0 0
\(178\) −5.42670 −0.406748
\(179\) −17.8016 −1.33056 −0.665279 0.746595i \(-0.731687\pi\)
−0.665279 + 0.746595i \(0.731687\pi\)
\(180\) 0 0
\(181\) 24.5660 1.82598 0.912989 0.407984i \(-0.133768\pi\)
0.912989 + 0.407984i \(0.133768\pi\)
\(182\) −0.523023 −0.0387690
\(183\) 0 0
\(184\) 8.06162 0.594311
\(185\) 5.19538 0.381972
\(186\) 0 0
\(187\) 8.88003 0.649372
\(188\) 0.901906 0.0657783
\(189\) 0 0
\(190\) −2.43693 −0.176794
\(191\) −23.1438 −1.67463 −0.837314 0.546723i \(-0.815875\pi\)
−0.837314 + 0.546723i \(0.815875\pi\)
\(192\) 0 0
\(193\) 4.89303 0.352208 0.176104 0.984372i \(-0.443651\pi\)
0.176104 + 0.984372i \(0.443651\pi\)
\(194\) −0.996560 −0.0715488
\(195\) 0 0
\(196\) −1.83358 −0.130970
\(197\) −23.9211 −1.70431 −0.852155 0.523289i \(-0.824705\pi\)
−0.852155 + 0.523289i \(0.824705\pi\)
\(198\) 0 0
\(199\) −12.8048 −0.907707 −0.453853 0.891076i \(-0.649951\pi\)
−0.453853 + 0.891076i \(0.649951\pi\)
\(200\) 5.96174 0.421559
\(201\) 0 0
\(202\) −6.62530 −0.466154
\(203\) 3.35002 0.235125
\(204\) 0 0
\(205\) −4.94751 −0.345549
\(206\) 6.83746 0.476388
\(207\) 0 0
\(208\) −3.88359 −0.269279
\(209\) 12.6104 0.872281
\(210\) 0 0
\(211\) −3.97912 −0.273934 −0.136967 0.990576i \(-0.543735\pi\)
−0.136967 + 0.990576i \(0.543735\pi\)
\(212\) −20.7558 −1.42552
\(213\) 0 0
\(214\) 2.86964 0.196164
\(215\) 3.45514 0.235639
\(216\) 0 0
\(217\) −0.261843 −0.0177751
\(218\) 3.52803 0.238949
\(219\) 0 0
\(220\) 4.59816 0.310008
\(221\) 4.94809 0.332844
\(222\) 0 0
\(223\) 1.15283 0.0771992 0.0385996 0.999255i \(-0.487710\pi\)
0.0385996 + 0.999255i \(0.487710\pi\)
\(224\) 4.36357 0.291553
\(225\) 0 0
\(226\) 3.69877 0.246039
\(227\) 16.2210 1.07663 0.538314 0.842744i \(-0.319061\pi\)
0.538314 + 0.842744i \(0.319061\pi\)
\(228\) 0 0
\(229\) −16.9029 −1.11698 −0.558488 0.829512i \(-0.688618\pi\)
−0.558488 + 0.829512i \(0.688618\pi\)
\(230\) −2.29200 −0.151130
\(231\) 0 0
\(232\) −5.23913 −0.343966
\(233\) 6.97836 0.457168 0.228584 0.973524i \(-0.426591\pi\)
0.228584 + 0.973524i \(0.426591\pi\)
\(234\) 0 0
\(235\) −0.536115 −0.0349723
\(236\) 3.59453 0.233984
\(237\) 0 0
\(238\) −1.57447 −0.102057
\(239\) 27.3643 1.77005 0.885025 0.465544i \(-0.154141\pi\)
0.885025 + 0.465544i \(0.154141\pi\)
\(240\) 0 0
\(241\) −25.1019 −1.61695 −0.808477 0.588528i \(-0.799708\pi\)
−0.808477 + 0.588528i \(0.799708\pi\)
\(242\) −2.32779 −0.149636
\(243\) 0 0
\(244\) −0.0534869 −0.00342415
\(245\) 1.08992 0.0696325
\(246\) 0 0
\(247\) 7.02671 0.447099
\(248\) 0.409499 0.0260032
\(249\) 0 0
\(250\) −3.91815 −0.247806
\(251\) −7.05092 −0.445050 −0.222525 0.974927i \(-0.571430\pi\)
−0.222525 + 0.974927i \(0.571430\pi\)
\(252\) 0 0
\(253\) 11.8604 0.745658
\(254\) 0.407951 0.0255971
\(255\) 0 0
\(256\) 4.28413 0.267758
\(257\) −0.0574366 −0.00358280 −0.00179140 0.999998i \(-0.500570\pi\)
−0.00179140 + 0.999998i \(0.500570\pi\)
\(258\) 0 0
\(259\) 4.76674 0.296191
\(260\) 2.56216 0.158899
\(261\) 0 0
\(262\) −5.57990 −0.344728
\(263\) 14.6910 0.905885 0.452943 0.891540i \(-0.350374\pi\)
0.452943 + 0.891540i \(0.350374\pi\)
\(264\) 0 0
\(265\) 12.3378 0.757903
\(266\) −2.23588 −0.137090
\(267\) 0 0
\(268\) −25.2493 −1.54235
\(269\) 9.26332 0.564795 0.282397 0.959298i \(-0.408870\pi\)
0.282397 + 0.959298i \(0.408870\pi\)
\(270\) 0 0
\(271\) 13.1700 0.800024 0.400012 0.916510i \(-0.369006\pi\)
0.400012 + 0.916510i \(0.369006\pi\)
\(272\) −11.6909 −0.708862
\(273\) 0 0
\(274\) 8.59866 0.519464
\(275\) 8.77103 0.528913
\(276\) 0 0
\(277\) 16.3591 0.982922 0.491461 0.870900i \(-0.336463\pi\)
0.491461 + 0.870900i \(0.336463\pi\)
\(278\) 4.25823 0.255392
\(279\) 0 0
\(280\) −1.70454 −0.101866
\(281\) 7.16275 0.427294 0.213647 0.976911i \(-0.431466\pi\)
0.213647 + 0.976911i \(0.431466\pi\)
\(282\) 0 0
\(283\) −2.99945 −0.178299 −0.0891494 0.996018i \(-0.528415\pi\)
−0.0891494 + 0.996018i \(0.528415\pi\)
\(284\) 3.58345 0.212638
\(285\) 0 0
\(286\) 1.20340 0.0711585
\(287\) −4.53932 −0.267948
\(288\) 0 0
\(289\) −2.10467 −0.123804
\(290\) 1.48953 0.0874684
\(291\) 0 0
\(292\) −20.1201 −1.17744
\(293\) 7.96629 0.465396 0.232698 0.972549i \(-0.425245\pi\)
0.232698 + 0.972549i \(0.425245\pi\)
\(294\) 0 0
\(295\) −2.13668 −0.124402
\(296\) −7.45476 −0.433299
\(297\) 0 0
\(298\) −0.150616 −0.00872495
\(299\) 6.60880 0.382197
\(300\) 0 0
\(301\) 3.17008 0.182720
\(302\) 4.21512 0.242553
\(303\) 0 0
\(304\) −16.6020 −0.952191
\(305\) 0.0317939 0.00182051
\(306\) 0 0
\(307\) 9.84980 0.562158 0.281079 0.959685i \(-0.409308\pi\)
0.281079 + 0.959685i \(0.409308\pi\)
\(308\) 4.21880 0.240388
\(309\) 0 0
\(310\) −0.116424 −0.00661246
\(311\) 31.7455 1.80012 0.900062 0.435762i \(-0.143521\pi\)
0.900062 + 0.435762i \(0.143521\pi\)
\(312\) 0 0
\(313\) −12.9459 −0.731748 −0.365874 0.930664i \(-0.619230\pi\)
−0.365874 + 0.930664i \(0.619230\pi\)
\(314\) 7.94272 0.448233
\(315\) 0 0
\(316\) −2.40339 −0.135201
\(317\) 4.65835 0.261639 0.130819 0.991406i \(-0.458239\pi\)
0.130819 + 0.991406i \(0.458239\pi\)
\(318\) 0 0
\(319\) −7.70791 −0.431560
\(320\) −4.66288 −0.260663
\(321\) 0 0
\(322\) −2.10290 −0.117190
\(323\) 21.1527 1.17697
\(324\) 0 0
\(325\) 4.88735 0.271101
\(326\) 5.66421 0.313712
\(327\) 0 0
\(328\) 7.09910 0.391982
\(329\) −0.491884 −0.0271184
\(330\) 0 0
\(331\) 14.0354 0.771458 0.385729 0.922612i \(-0.373950\pi\)
0.385729 + 0.922612i \(0.373950\pi\)
\(332\) −17.7556 −0.974467
\(333\) 0 0
\(334\) 3.37410 0.184623
\(335\) 15.0088 0.820018
\(336\) 0 0
\(337\) −19.7961 −1.07836 −0.539182 0.842190i \(-0.681266\pi\)
−0.539182 + 0.842190i \(0.681266\pi\)
\(338\) −4.63281 −0.251992
\(339\) 0 0
\(340\) 7.71293 0.418292
\(341\) 0.602463 0.0326252
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) −4.95772 −0.267303
\(345\) 0 0
\(346\) −7.20877 −0.387546
\(347\) 21.2045 1.13832 0.569158 0.822228i \(-0.307269\pi\)
0.569158 + 0.822228i \(0.307269\pi\)
\(348\) 0 0
\(349\) −3.55610 −0.190354 −0.0951769 0.995460i \(-0.530342\pi\)
−0.0951769 + 0.995460i \(0.530342\pi\)
\(350\) −1.55514 −0.0831256
\(351\) 0 0
\(352\) −10.0399 −0.535131
\(353\) 15.4845 0.824156 0.412078 0.911149i \(-0.364803\pi\)
0.412078 + 0.911149i \(0.364803\pi\)
\(354\) 0 0
\(355\) −2.13009 −0.113053
\(356\) 24.3908 1.29271
\(357\) 0 0
\(358\) −7.26220 −0.383819
\(359\) −14.4272 −0.761436 −0.380718 0.924691i \(-0.624323\pi\)
−0.380718 + 0.924691i \(0.624323\pi\)
\(360\) 0 0
\(361\) 11.0386 0.580979
\(362\) 10.0217 0.526731
\(363\) 0 0
\(364\) 2.35078 0.123214
\(365\) 11.9599 0.626009
\(366\) 0 0
\(367\) 37.0573 1.93438 0.967188 0.254063i \(-0.0817671\pi\)
0.967188 + 0.254063i \(0.0817671\pi\)
\(368\) −15.6146 −0.813969
\(369\) 0 0
\(370\) 2.11946 0.110185
\(371\) 11.3199 0.587698
\(372\) 0 0
\(373\) 29.5070 1.52782 0.763908 0.645325i \(-0.223278\pi\)
0.763908 + 0.645325i \(0.223278\pi\)
\(374\) 3.62262 0.187321
\(375\) 0 0
\(376\) 0.769262 0.0396717
\(377\) −4.29496 −0.221202
\(378\) 0 0
\(379\) 20.2256 1.03892 0.519460 0.854495i \(-0.326133\pi\)
0.519460 + 0.854495i \(0.326133\pi\)
\(380\) 10.9530 0.561878
\(381\) 0 0
\(382\) −9.44154 −0.483071
\(383\) 1.33594 0.0682635 0.0341317 0.999417i \(-0.489133\pi\)
0.0341317 + 0.999417i \(0.489133\pi\)
\(384\) 0 0
\(385\) −2.50775 −0.127807
\(386\) 1.99612 0.101600
\(387\) 0 0
\(388\) 4.47914 0.227394
\(389\) 31.0104 1.57229 0.786144 0.618044i \(-0.212075\pi\)
0.786144 + 0.618044i \(0.212075\pi\)
\(390\) 0 0
\(391\) 19.8946 1.00611
\(392\) −1.56391 −0.0789894
\(393\) 0 0
\(394\) −9.75865 −0.491634
\(395\) 1.42863 0.0718823
\(396\) 0 0
\(397\) −1.70559 −0.0856012 −0.0428006 0.999084i \(-0.513628\pi\)
−0.0428006 + 0.999084i \(0.513628\pi\)
\(398\) −5.22372 −0.261842
\(399\) 0 0
\(400\) −11.5473 −0.577367
\(401\) −31.1528 −1.55570 −0.777849 0.628451i \(-0.783689\pi\)
−0.777849 + 0.628451i \(0.783689\pi\)
\(402\) 0 0
\(403\) 0.335701 0.0167225
\(404\) 29.7780 1.48151
\(405\) 0 0
\(406\) 1.36664 0.0678253
\(407\) −10.9676 −0.543643
\(408\) 0 0
\(409\) 28.7531 1.42175 0.710875 0.703318i \(-0.248299\pi\)
0.710875 + 0.703318i \(0.248299\pi\)
\(410\) −2.01834 −0.0996787
\(411\) 0 0
\(412\) −30.7316 −1.51404
\(413\) −1.96040 −0.0964647
\(414\) 0 0
\(415\) 10.5544 0.518094
\(416\) −5.59441 −0.274288
\(417\) 0 0
\(418\) 5.14443 0.251622
\(419\) 10.0450 0.490730 0.245365 0.969431i \(-0.421092\pi\)
0.245365 + 0.969431i \(0.421092\pi\)
\(420\) 0 0
\(421\) −24.2888 −1.18376 −0.591882 0.806025i \(-0.701615\pi\)
−0.591882 + 0.806025i \(0.701615\pi\)
\(422\) −1.62329 −0.0790203
\(423\) 0 0
\(424\) −17.7033 −0.859747
\(425\) 14.7125 0.713660
\(426\) 0 0
\(427\) 0.0291708 0.00141167
\(428\) −12.8979 −0.623442
\(429\) 0 0
\(430\) 1.40953 0.0679735
\(431\) −8.94786 −0.431003 −0.215502 0.976503i \(-0.569139\pi\)
−0.215502 + 0.976503i \(0.569139\pi\)
\(432\) 0 0
\(433\) −12.7200 −0.611282 −0.305641 0.952147i \(-0.598871\pi\)
−0.305641 + 0.952147i \(0.598871\pi\)
\(434\) −0.106819 −0.00512748
\(435\) 0 0
\(436\) −15.8571 −0.759417
\(437\) 28.2521 1.35148
\(438\) 0 0
\(439\) 20.2200 0.965048 0.482524 0.875883i \(-0.339720\pi\)
0.482524 + 0.875883i \(0.339720\pi\)
\(440\) 3.92190 0.186969
\(441\) 0 0
\(442\) 2.01858 0.0960140
\(443\) 8.70900 0.413777 0.206889 0.978364i \(-0.433666\pi\)
0.206889 + 0.978364i \(0.433666\pi\)
\(444\) 0 0
\(445\) −14.4985 −0.687295
\(446\) 0.470298 0.0222693
\(447\) 0 0
\(448\) −4.27818 −0.202125
\(449\) 2.31692 0.109342 0.0546711 0.998504i \(-0.482589\pi\)
0.0546711 + 0.998504i \(0.482589\pi\)
\(450\) 0 0
\(451\) 10.4443 0.491804
\(452\) −16.6245 −0.781951
\(453\) 0 0
\(454\) 6.61739 0.310570
\(455\) −1.39736 −0.0655092
\(456\) 0 0
\(457\) −2.94767 −0.137886 −0.0689430 0.997621i \(-0.521963\pi\)
−0.0689430 + 0.997621i \(0.521963\pi\)
\(458\) −6.89557 −0.322209
\(459\) 0 0
\(460\) 10.3016 0.480314
\(461\) −14.1185 −0.657564 −0.328782 0.944406i \(-0.606638\pi\)
−0.328782 + 0.944406i \(0.606638\pi\)
\(462\) 0 0
\(463\) −37.5227 −1.74383 −0.871913 0.489661i \(-0.837121\pi\)
−0.871913 + 0.489661i \(0.837121\pi\)
\(464\) 10.1477 0.471096
\(465\) 0 0
\(466\) 2.84683 0.131877
\(467\) −30.4306 −1.40816 −0.704081 0.710120i \(-0.748641\pi\)
−0.704081 + 0.710120i \(0.748641\pi\)
\(468\) 0 0
\(469\) 13.7705 0.635864
\(470\) −0.218709 −0.0100883
\(471\) 0 0
\(472\) 3.06588 0.141119
\(473\) −7.29390 −0.335374
\(474\) 0 0
\(475\) 20.8930 0.958637
\(476\) 7.07659 0.324355
\(477\) 0 0
\(478\) 11.1633 0.510597
\(479\) −25.2836 −1.15524 −0.577619 0.816306i \(-0.696018\pi\)
−0.577619 + 0.816306i \(0.696018\pi\)
\(480\) 0 0
\(481\) −6.11131 −0.278652
\(482\) −10.2403 −0.466434
\(483\) 0 0
\(484\) 10.4625 0.475568
\(485\) −2.66251 −0.120898
\(486\) 0 0
\(487\) −23.6931 −1.07364 −0.536819 0.843697i \(-0.680374\pi\)
−0.536819 + 0.843697i \(0.680374\pi\)
\(488\) −0.0456206 −0.00206515
\(489\) 0 0
\(490\) 0.444635 0.0200865
\(491\) −29.3480 −1.32445 −0.662227 0.749303i \(-0.730389\pi\)
−0.662227 + 0.749303i \(0.730389\pi\)
\(492\) 0 0
\(493\) −12.9292 −0.582302
\(494\) 2.86656 0.128972
\(495\) 0 0
\(496\) −0.793162 −0.0356140
\(497\) −1.95435 −0.0876645
\(498\) 0 0
\(499\) 23.3986 1.04746 0.523732 0.851883i \(-0.324539\pi\)
0.523732 + 0.851883i \(0.324539\pi\)
\(500\) 17.6105 0.787566
\(501\) 0 0
\(502\) −2.87643 −0.128381
\(503\) 15.4011 0.686701 0.343351 0.939207i \(-0.388438\pi\)
0.343351 + 0.939207i \(0.388438\pi\)
\(504\) 0 0
\(505\) −17.7008 −0.787675
\(506\) 4.83847 0.215096
\(507\) 0 0
\(508\) −1.83358 −0.0813518
\(509\) 9.83148 0.435773 0.217886 0.975974i \(-0.430084\pi\)
0.217886 + 0.975974i \(0.430084\pi\)
\(510\) 0 0
\(511\) 10.9732 0.485424
\(512\) 22.6926 1.00288
\(513\) 0 0
\(514\) −0.0234313 −0.00103351
\(515\) 18.2676 0.804967
\(516\) 0 0
\(517\) 1.13175 0.0497745
\(518\) 1.94460 0.0854407
\(519\) 0 0
\(520\) 2.18534 0.0958337
\(521\) 0.581283 0.0254665 0.0127332 0.999919i \(-0.495947\pi\)
0.0127332 + 0.999919i \(0.495947\pi\)
\(522\) 0 0
\(523\) 9.39466 0.410800 0.205400 0.978678i \(-0.434150\pi\)
0.205400 + 0.978678i \(0.434150\pi\)
\(524\) 25.0794 1.09560
\(525\) 0 0
\(526\) 5.99320 0.261316
\(527\) 1.01057 0.0440211
\(528\) 0 0
\(529\) 3.57179 0.155295
\(530\) 5.03321 0.218628
\(531\) 0 0
\(532\) 10.0494 0.435695
\(533\) 5.81974 0.252081
\(534\) 0 0
\(535\) 7.66680 0.331465
\(536\) −21.5359 −0.930209
\(537\) 0 0
\(538\) 3.77898 0.162923
\(539\) −2.30086 −0.0991049
\(540\) 0 0
\(541\) 16.0235 0.688905 0.344452 0.938804i \(-0.388065\pi\)
0.344452 + 0.938804i \(0.388065\pi\)
\(542\) 5.37274 0.230779
\(543\) 0 0
\(544\) −16.8410 −0.722050
\(545\) 9.42584 0.403758
\(546\) 0 0
\(547\) −21.8696 −0.935077 −0.467538 0.883973i \(-0.654859\pi\)
−0.467538 + 0.883973i \(0.654859\pi\)
\(548\) −38.6475 −1.65094
\(549\) 0 0
\(550\) 3.57815 0.152573
\(551\) −18.3606 −0.782188
\(552\) 0 0
\(553\) 1.31077 0.0557395
\(554\) 6.67370 0.283539
\(555\) 0 0
\(556\) −19.1390 −0.811676
\(557\) −9.18821 −0.389317 −0.194658 0.980871i \(-0.562360\pi\)
−0.194658 + 0.980871i \(0.562360\pi\)
\(558\) 0 0
\(559\) −4.06427 −0.171900
\(560\) 3.30154 0.139515
\(561\) 0 0
\(562\) 2.92205 0.123259
\(563\) 26.1377 1.10157 0.550786 0.834647i \(-0.314328\pi\)
0.550786 + 0.834647i \(0.314328\pi\)
\(564\) 0 0
\(565\) 9.88200 0.415739
\(566\) −1.22363 −0.0514330
\(567\) 0 0
\(568\) 3.05643 0.128245
\(569\) 17.4717 0.732451 0.366225 0.930526i \(-0.380650\pi\)
0.366225 + 0.930526i \(0.380650\pi\)
\(570\) 0 0
\(571\) 23.0247 0.963553 0.481776 0.876294i \(-0.339992\pi\)
0.481776 + 0.876294i \(0.339992\pi\)
\(572\) −5.40880 −0.226153
\(573\) 0 0
\(574\) −1.85182 −0.0772935
\(575\) 19.6504 0.819478
\(576\) 0 0
\(577\) 4.55690 0.189706 0.0948531 0.995491i \(-0.469762\pi\)
0.0948531 + 0.995491i \(0.469762\pi\)
\(578\) −0.858603 −0.0357132
\(579\) 0 0
\(580\) −6.69485 −0.277989
\(581\) 9.68361 0.401744
\(582\) 0 0
\(583\) −26.0454 −1.07869
\(584\) −17.1610 −0.710129
\(585\) 0 0
\(586\) 3.24986 0.134250
\(587\) 3.20341 0.132219 0.0661094 0.997812i \(-0.478941\pi\)
0.0661094 + 0.997812i \(0.478941\pi\)
\(588\) 0 0
\(589\) 1.43509 0.0591321
\(590\) −0.871660 −0.0358857
\(591\) 0 0
\(592\) 14.4392 0.593447
\(593\) 36.9825 1.51869 0.759344 0.650689i \(-0.225520\pi\)
0.759344 + 0.650689i \(0.225520\pi\)
\(594\) 0 0
\(595\) −4.20649 −0.172449
\(596\) 0.676958 0.0277293
\(597\) 0 0
\(598\) 2.69607 0.110250
\(599\) 38.3476 1.56684 0.783421 0.621491i \(-0.213473\pi\)
0.783421 + 0.621491i \(0.213473\pi\)
\(600\) 0 0
\(601\) −33.1185 −1.35093 −0.675467 0.737391i \(-0.736058\pi\)
−0.675467 + 0.737391i \(0.736058\pi\)
\(602\) 1.29324 0.0527084
\(603\) 0 0
\(604\) −18.9453 −0.770873
\(605\) −6.21916 −0.252845
\(606\) 0 0
\(607\) −1.37747 −0.0559096 −0.0279548 0.999609i \(-0.508899\pi\)
−0.0279548 + 0.999609i \(0.508899\pi\)
\(608\) −23.9156 −0.969907
\(609\) 0 0
\(610\) 0.0129704 0.000525154 0
\(611\) 0.630630 0.0255126
\(612\) 0 0
\(613\) 6.71060 0.271039 0.135519 0.990775i \(-0.456730\pi\)
0.135519 + 0.990775i \(0.456730\pi\)
\(614\) 4.01824 0.162163
\(615\) 0 0
\(616\) 3.59834 0.144981
\(617\) 20.8740 0.840356 0.420178 0.907442i \(-0.361968\pi\)
0.420178 + 0.907442i \(0.361968\pi\)
\(618\) 0 0
\(619\) 10.0657 0.404576 0.202288 0.979326i \(-0.435162\pi\)
0.202288 + 0.979326i \(0.435162\pi\)
\(620\) 0.523281 0.0210155
\(621\) 0 0
\(622\) 12.9506 0.519273
\(623\) −13.3023 −0.532946
\(624\) 0 0
\(625\) 8.59224 0.343689
\(626\) −5.28131 −0.211084
\(627\) 0 0
\(628\) −35.6993 −1.42456
\(629\) −18.3970 −0.733536
\(630\) 0 0
\(631\) −45.6084 −1.81564 −0.907821 0.419359i \(-0.862255\pi\)
−0.907821 + 0.419359i \(0.862255\pi\)
\(632\) −2.04992 −0.0815416
\(633\) 0 0
\(634\) 1.90038 0.0754736
\(635\) 1.08992 0.0432522
\(636\) 0 0
\(637\) −1.28207 −0.0507975
\(638\) −3.14445 −0.124490
\(639\) 0 0
\(640\) −11.4141 −0.451183
\(641\) 36.7175 1.45025 0.725126 0.688616i \(-0.241781\pi\)
0.725126 + 0.688616i \(0.241781\pi\)
\(642\) 0 0
\(643\) −45.1998 −1.78250 −0.891252 0.453508i \(-0.850172\pi\)
−0.891252 + 0.453508i \(0.850172\pi\)
\(644\) 9.45169 0.372449
\(645\) 0 0
\(646\) 8.62925 0.339513
\(647\) −4.64930 −0.182783 −0.0913915 0.995815i \(-0.529131\pi\)
−0.0913915 + 0.995815i \(0.529131\pi\)
\(648\) 0 0
\(649\) 4.51059 0.177056
\(650\) 1.99380 0.0782032
\(651\) 0 0
\(652\) −25.4584 −0.997026
\(653\) −38.9603 −1.52463 −0.762317 0.647204i \(-0.775938\pi\)
−0.762317 + 0.647204i \(0.775938\pi\)
\(654\) 0 0
\(655\) −14.9078 −0.582496
\(656\) −13.7503 −0.536859
\(657\) 0 0
\(658\) −0.200664 −0.00782271
\(659\) 19.9316 0.776425 0.388212 0.921570i \(-0.373093\pi\)
0.388212 + 0.921570i \(0.373093\pi\)
\(660\) 0 0
\(661\) −36.2288 −1.40914 −0.704569 0.709635i \(-0.748860\pi\)
−0.704569 + 0.709635i \(0.748860\pi\)
\(662\) 5.72578 0.222539
\(663\) 0 0
\(664\) −15.1443 −0.587713
\(665\) −5.97359 −0.231646
\(666\) 0 0
\(667\) −17.2686 −0.668643
\(668\) −15.1652 −0.586761
\(669\) 0 0
\(670\) 6.12286 0.236547
\(671\) −0.0671179 −0.00259106
\(672\) 0 0
\(673\) 10.0220 0.386320 0.193160 0.981167i \(-0.438126\pi\)
0.193160 + 0.981167i \(0.438126\pi\)
\(674\) −8.07585 −0.311070
\(675\) 0 0
\(676\) 20.8226 0.800870
\(677\) −2.27813 −0.0875555 −0.0437778 0.999041i \(-0.513939\pi\)
−0.0437778 + 0.999041i \(0.513939\pi\)
\(678\) 0 0
\(679\) −2.44284 −0.0937477
\(680\) 6.57858 0.252277
\(681\) 0 0
\(682\) 0.245775 0.00941123
\(683\) 34.7013 1.32781 0.663904 0.747817i \(-0.268898\pi\)
0.663904 + 0.747817i \(0.268898\pi\)
\(684\) 0 0
\(685\) 22.9730 0.877754
\(686\) 0.407951 0.0155756
\(687\) 0 0
\(688\) 9.60266 0.366098
\(689\) −14.5129 −0.552897
\(690\) 0 0
\(691\) 25.5923 0.973576 0.486788 0.873520i \(-0.338168\pi\)
0.486788 + 0.873520i \(0.338168\pi\)
\(692\) 32.4005 1.23168
\(693\) 0 0
\(694\) 8.65038 0.328364
\(695\) 11.3767 0.431543
\(696\) 0 0
\(697\) 17.5193 0.663590
\(698\) −1.45072 −0.0549104
\(699\) 0 0
\(700\) 6.98972 0.264187
\(701\) 34.4738 1.30206 0.651028 0.759054i \(-0.274338\pi\)
0.651028 + 0.759054i \(0.274338\pi\)
\(702\) 0 0
\(703\) −26.1253 −0.985335
\(704\) 9.84349 0.370990
\(705\) 0 0
\(706\) 6.31691 0.237740
\(707\) −16.2404 −0.610784
\(708\) 0 0
\(709\) −5.12099 −0.192323 −0.0961614 0.995366i \(-0.530656\pi\)
−0.0961614 + 0.995366i \(0.530656\pi\)
\(710\) −0.868971 −0.0326119
\(711\) 0 0
\(712\) 20.8037 0.779650
\(713\) 1.34974 0.0505483
\(714\) 0 0
\(715\) 3.21512 0.120239
\(716\) 32.6407 1.21984
\(717\) 0 0
\(718\) −5.88557 −0.219648
\(719\) 9.38376 0.349955 0.174978 0.984572i \(-0.444015\pi\)
0.174978 + 0.984572i \(0.444015\pi\)
\(720\) 0 0
\(721\) 16.7605 0.624193
\(722\) 4.50321 0.167592
\(723\) 0 0
\(724\) −45.0437 −1.67404
\(725\) −12.7705 −0.474284
\(726\) 0 0
\(727\) −17.8615 −0.662445 −0.331222 0.943553i \(-0.607461\pi\)
−0.331222 + 0.943553i \(0.607461\pi\)
\(728\) 2.00505 0.0743120
\(729\) 0 0
\(730\) 4.87904 0.180582
\(731\) −12.2348 −0.452519
\(732\) 0 0
\(733\) 20.4202 0.754238 0.377119 0.926165i \(-0.376915\pi\)
0.377119 + 0.926165i \(0.376915\pi\)
\(734\) 15.1176 0.557999
\(735\) 0 0
\(736\) −22.4932 −0.829112
\(737\) −31.6840 −1.16710
\(738\) 0 0
\(739\) 51.1576 1.88186 0.940931 0.338597i \(-0.109952\pi\)
0.940931 + 0.338597i \(0.109952\pi\)
\(740\) −9.52612 −0.350187
\(741\) 0 0
\(742\) 4.61795 0.169530
\(743\) −32.3657 −1.18738 −0.593691 0.804693i \(-0.702330\pi\)
−0.593691 + 0.804693i \(0.702330\pi\)
\(744\) 0 0
\(745\) −0.402400 −0.0147428
\(746\) 12.0374 0.440722
\(747\) 0 0
\(748\) −16.2822 −0.595337
\(749\) 7.03427 0.257027
\(750\) 0 0
\(751\) −50.9969 −1.86090 −0.930452 0.366414i \(-0.880585\pi\)
−0.930452 + 0.366414i \(0.880585\pi\)
\(752\) −1.48999 −0.0543344
\(753\) 0 0
\(754\) −1.75213 −0.0638090
\(755\) 11.2615 0.409849
\(756\) 0 0
\(757\) 37.7384 1.37162 0.685812 0.727779i \(-0.259447\pi\)
0.685812 + 0.727779i \(0.259447\pi\)
\(758\) 8.25106 0.299692
\(759\) 0 0
\(760\) 9.34216 0.338876
\(761\) −43.9468 −1.59307 −0.796535 0.604593i \(-0.793336\pi\)
−0.796535 + 0.604593i \(0.793336\pi\)
\(762\) 0 0
\(763\) 8.64818 0.313085
\(764\) 42.4359 1.53528
\(765\) 0 0
\(766\) 0.544999 0.0196916
\(767\) 2.51337 0.0907525
\(768\) 0 0
\(769\) 42.1961 1.52163 0.760816 0.648968i \(-0.224799\pi\)
0.760816 + 0.648968i \(0.224799\pi\)
\(770\) −1.02304 −0.0368678
\(771\) 0 0
\(772\) −8.97174 −0.322900
\(773\) 40.4493 1.45486 0.727430 0.686182i \(-0.240715\pi\)
0.727430 + 0.686182i \(0.240715\pi\)
\(774\) 0 0
\(775\) 0.998164 0.0358551
\(776\) 3.82039 0.137144
\(777\) 0 0
\(778\) 12.6507 0.453550
\(779\) 24.8789 0.891378
\(780\) 0 0
\(781\) 4.49667 0.160904
\(782\) 8.11603 0.290229
\(783\) 0 0
\(784\) 3.02915 0.108184
\(785\) 21.2205 0.757393
\(786\) 0 0
\(787\) 17.1152 0.610090 0.305045 0.952338i \(-0.401329\pi\)
0.305045 + 0.952338i \(0.401329\pi\)
\(788\) 43.8612 1.56249
\(789\) 0 0
\(790\) 0.582812 0.0207355
\(791\) 9.06671 0.322375
\(792\) 0 0
\(793\) −0.0373991 −0.00132808
\(794\) −0.695798 −0.0246929
\(795\) 0 0
\(796\) 23.4785 0.832175
\(797\) −6.60740 −0.234046 −0.117023 0.993129i \(-0.537335\pi\)
−0.117023 + 0.993129i \(0.537335\pi\)
\(798\) 0 0
\(799\) 1.89840 0.0671605
\(800\) −16.6342 −0.588109
\(801\) 0 0
\(802\) −12.7088 −0.448764
\(803\) −25.2477 −0.890970
\(804\) 0 0
\(805\) −5.61831 −0.198019
\(806\) 0.136950 0.00482385
\(807\) 0 0
\(808\) 25.3986 0.893519
\(809\) 8.40122 0.295371 0.147686 0.989034i \(-0.452818\pi\)
0.147686 + 0.989034i \(0.452818\pi\)
\(810\) 0 0
\(811\) 40.8644 1.43494 0.717472 0.696588i \(-0.245299\pi\)
0.717472 + 0.696588i \(0.245299\pi\)
\(812\) −6.14251 −0.215560
\(813\) 0 0
\(814\) −4.47424 −0.156822
\(815\) 15.1331 0.530088
\(816\) 0 0
\(817\) −17.3744 −0.607854
\(818\) 11.7299 0.410125
\(819\) 0 0
\(820\) 9.07163 0.316795
\(821\) −5.24790 −0.183153 −0.0915764 0.995798i \(-0.529191\pi\)
−0.0915764 + 0.995798i \(0.529191\pi\)
\(822\) 0 0
\(823\) −13.5425 −0.472060 −0.236030 0.971746i \(-0.575846\pi\)
−0.236030 + 0.971746i \(0.575846\pi\)
\(824\) −26.2119 −0.913135
\(825\) 0 0
\(826\) −0.799745 −0.0278267
\(827\) 21.6919 0.754301 0.377150 0.926152i \(-0.376904\pi\)
0.377150 + 0.926152i \(0.376904\pi\)
\(828\) 0 0
\(829\) 51.7300 1.79666 0.898328 0.439325i \(-0.144782\pi\)
0.898328 + 0.439325i \(0.144782\pi\)
\(830\) 4.30567 0.149452
\(831\) 0 0
\(832\) 5.48494 0.190156
\(833\) −3.85945 −0.133722
\(834\) 0 0
\(835\) 9.01459 0.311963
\(836\) −23.1222 −0.799697
\(837\) 0 0
\(838\) 4.09787 0.141558
\(839\) 21.3671 0.737673 0.368836 0.929494i \(-0.379756\pi\)
0.368836 + 0.929494i \(0.379756\pi\)
\(840\) 0 0
\(841\) −17.7774 −0.613014
\(842\) −9.90865 −0.341474
\(843\) 0 0
\(844\) 7.29601 0.251139
\(845\) −12.3775 −0.425798
\(846\) 0 0
\(847\) −5.70606 −0.196062
\(848\) 34.2896 1.17751
\(849\) 0 0
\(850\) 6.00197 0.205866
\(851\) −24.5715 −0.842301
\(852\) 0 0
\(853\) −33.7067 −1.15410 −0.577048 0.816710i \(-0.695796\pi\)
−0.577048 + 0.816710i \(0.695796\pi\)
\(854\) 0.0119003 0.000407219 0
\(855\) 0 0
\(856\) −11.0010 −0.376005
\(857\) −18.6766 −0.637982 −0.318991 0.947758i \(-0.603344\pi\)
−0.318991 + 0.947758i \(0.603344\pi\)
\(858\) 0 0
\(859\) −37.7733 −1.28881 −0.644405 0.764684i \(-0.722895\pi\)
−0.644405 + 0.764684i \(0.722895\pi\)
\(860\) −6.33526 −0.216031
\(861\) 0 0
\(862\) −3.65029 −0.124329
\(863\) 19.9811 0.680166 0.340083 0.940395i \(-0.389545\pi\)
0.340083 + 0.940395i \(0.389545\pi\)
\(864\) 0 0
\(865\) −19.2597 −0.654848
\(866\) −5.18912 −0.176334
\(867\) 0 0
\(868\) 0.480109 0.0162960
\(869\) −3.01589 −0.102307
\(870\) 0 0
\(871\) −17.6548 −0.598211
\(872\) −13.5250 −0.458014
\(873\) 0 0
\(874\) 11.5255 0.389855
\(875\) −9.60447 −0.324690
\(876\) 0 0
\(877\) −20.6716 −0.698030 −0.349015 0.937117i \(-0.613484\pi\)
−0.349015 + 0.937117i \(0.613484\pi\)
\(878\) 8.24877 0.278382
\(879\) 0 0
\(880\) −7.59637 −0.256074
\(881\) 5.74429 0.193530 0.0967651 0.995307i \(-0.469150\pi\)
0.0967651 + 0.995307i \(0.469150\pi\)
\(882\) 0 0
\(883\) 0.269530 0.00907042 0.00453521 0.999990i \(-0.498556\pi\)
0.00453521 + 0.999990i \(0.498556\pi\)
\(884\) −9.07270 −0.305148
\(885\) 0 0
\(886\) 3.55285 0.119360
\(887\) −7.13439 −0.239550 −0.119775 0.992801i \(-0.538217\pi\)
−0.119775 + 0.992801i \(0.538217\pi\)
\(888\) 0 0
\(889\) 1.00000 0.0335389
\(890\) −5.91468 −0.198260
\(891\) 0 0
\(892\) −2.11380 −0.0707753
\(893\) 2.69589 0.0902145
\(894\) 0 0
\(895\) −19.4024 −0.648551
\(896\) −10.4724 −0.349859
\(897\) 0 0
\(898\) 0.945190 0.0315414
\(899\) −0.877178 −0.0292555
\(900\) 0 0
\(901\) −43.6884 −1.45547
\(902\) 4.26077 0.141868
\(903\) 0 0
\(904\) −14.1795 −0.471604
\(905\) 26.7750 0.890033
\(906\) 0 0
\(907\) 18.4478 0.612549 0.306275 0.951943i \(-0.400917\pi\)
0.306275 + 0.951943i \(0.400917\pi\)
\(908\) −29.7425 −0.987040
\(909\) 0 0
\(910\) −0.570054 −0.0188971
\(911\) −48.1253 −1.59446 −0.797231 0.603675i \(-0.793703\pi\)
−0.797231 + 0.603675i \(0.793703\pi\)
\(912\) 0 0
\(913\) −22.2806 −0.737380
\(914\) −1.20250 −0.0397753
\(915\) 0 0
\(916\) 30.9928 1.02403
\(917\) −13.6779 −0.451683
\(918\) 0 0
\(919\) −44.9642 −1.48323 −0.741615 0.670825i \(-0.765940\pi\)
−0.741615 + 0.670825i \(0.765940\pi\)
\(920\) 8.78654 0.289684
\(921\) 0 0
\(922\) −5.75966 −0.189684
\(923\) 2.50561 0.0824733
\(924\) 0 0
\(925\) −18.1712 −0.597464
\(926\) −15.3074 −0.503033
\(927\) 0 0
\(928\) 14.6180 0.479860
\(929\) −12.6354 −0.414553 −0.207276 0.978282i \(-0.566460\pi\)
−0.207276 + 0.978282i \(0.566460\pi\)
\(930\) 0 0
\(931\) −5.48075 −0.179624
\(932\) −12.7954 −0.419126
\(933\) 0 0
\(934\) −12.4142 −0.406205
\(935\) 9.67854 0.316522
\(936\) 0 0
\(937\) 46.3648 1.51467 0.757335 0.653026i \(-0.226501\pi\)
0.757335 + 0.653026i \(0.226501\pi\)
\(938\) 5.61770 0.183424
\(939\) 0 0
\(940\) 0.983007 0.0320622
\(941\) −2.85670 −0.0931259 −0.0465629 0.998915i \(-0.514827\pi\)
−0.0465629 + 0.998915i \(0.514827\pi\)
\(942\) 0 0
\(943\) 23.3992 0.761983
\(944\) −5.93834 −0.193276
\(945\) 0 0
\(946\) −2.97555 −0.0967436
\(947\) −10.6467 −0.345971 −0.172985 0.984924i \(-0.555341\pi\)
−0.172985 + 0.984924i \(0.555341\pi\)
\(948\) 0 0
\(949\) −14.0684 −0.456679
\(950\) 8.52332 0.276533
\(951\) 0 0
\(952\) 6.03583 0.195622
\(953\) 26.1036 0.845577 0.422789 0.906228i \(-0.361051\pi\)
0.422789 + 0.906228i \(0.361051\pi\)
\(954\) 0 0
\(955\) −25.2249 −0.816260
\(956\) −50.1745 −1.62276
\(957\) 0 0
\(958\) −10.3145 −0.333246
\(959\) 21.0777 0.680634
\(960\) 0 0
\(961\) −30.9314 −0.997788
\(962\) −2.49311 −0.0803812
\(963\) 0 0
\(964\) 46.0262 1.48240
\(965\) 5.33302 0.171676
\(966\) 0 0
\(967\) −13.5836 −0.436818 −0.218409 0.975857i \(-0.570087\pi\)
−0.218409 + 0.975857i \(0.570087\pi\)
\(968\) 8.92377 0.286821
\(969\) 0 0
\(970\) −1.08617 −0.0348749
\(971\) 39.0472 1.25308 0.626542 0.779388i \(-0.284470\pi\)
0.626542 + 0.779388i \(0.284470\pi\)
\(972\) 0 0
\(973\) 10.4381 0.334630
\(974\) −9.66564 −0.309707
\(975\) 0 0
\(976\) 0.0883629 0.00282843
\(977\) −13.9595 −0.446604 −0.223302 0.974749i \(-0.571684\pi\)
−0.223302 + 0.974749i \(0.571684\pi\)
\(978\) 0 0
\(979\) 30.6067 0.978196
\(980\) −1.99845 −0.0638383
\(981\) 0 0
\(982\) −11.9725 −0.382059
\(983\) −11.1853 −0.356755 −0.178378 0.983962i \(-0.557085\pi\)
−0.178378 + 0.983962i \(0.557085\pi\)
\(984\) 0 0
\(985\) −26.0722 −0.830728
\(986\) −5.27448 −0.167974
\(987\) 0 0
\(988\) −12.8840 −0.409895
\(989\) −16.3411 −0.519616
\(990\) 0 0
\(991\) 36.4779 1.15876 0.579379 0.815059i \(-0.303295\pi\)
0.579379 + 0.815059i \(0.303295\pi\)
\(992\) −1.14257 −0.0362766
\(993\) 0 0
\(994\) −0.797278 −0.0252881
\(995\) −13.9562 −0.442442
\(996\) 0 0
\(997\) −34.7863 −1.10169 −0.550846 0.834607i \(-0.685695\pi\)
−0.550846 + 0.834607i \(0.685695\pi\)
\(998\) 9.54548 0.302157
\(999\) 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 \(a_p\))