Properties

Label 1849.4.a.j.1.33
Level $1849$
Weight $4$
Character 1849.1
Self dual yes
Analytic conductor $109.095$
Analytic rank $1$
Dimension $50$
CM no
Inner twists $1$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 1849 = 43^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1849.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(109.094531601\)
Analytic rank: \(1\)
Dimension: \(50\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.33
Character \(\chi\) \(=\) 1849.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.25115 q^{2} -4.02813 q^{3} -2.93234 q^{4} -4.98765 q^{5} -9.06790 q^{6} -5.25109 q^{7} -24.6103 q^{8} -10.7742 q^{9} +O(q^{10})\) \(q+2.25115 q^{2} -4.02813 q^{3} -2.93234 q^{4} -4.98765 q^{5} -9.06790 q^{6} -5.25109 q^{7} -24.6103 q^{8} -10.7742 q^{9} -11.2279 q^{10} +25.9553 q^{11} +11.8118 q^{12} +14.2068 q^{13} -11.8210 q^{14} +20.0909 q^{15} -31.9427 q^{16} +20.3859 q^{17} -24.2543 q^{18} +2.21919 q^{19} +14.6255 q^{20} +21.1520 q^{21} +58.4292 q^{22} +39.1220 q^{23} +99.1334 q^{24} -100.123 q^{25} +31.9817 q^{26} +152.159 q^{27} +15.3980 q^{28} +277.025 q^{29} +45.2275 q^{30} -47.2599 q^{31} +124.975 q^{32} -104.551 q^{33} +45.8917 q^{34} +26.1906 q^{35} +31.5936 q^{36} +43.9224 q^{37} +4.99572 q^{38} -57.2270 q^{39} +122.748 q^{40} +98.7920 q^{41} +47.6164 q^{42} -76.1098 q^{44} +53.7380 q^{45} +88.0694 q^{46} +488.535 q^{47} +128.669 q^{48} -315.426 q^{49} -225.392 q^{50} -82.1171 q^{51} -41.6593 q^{52} -230.167 q^{53} +342.533 q^{54} -129.456 q^{55} +129.231 q^{56} -8.93917 q^{57} +623.623 q^{58} -400.770 q^{59} -58.9133 q^{60} +13.3239 q^{61} -106.389 q^{62} +56.5763 q^{63} +536.878 q^{64} -70.8588 q^{65} -235.360 q^{66} -640.592 q^{67} -59.7785 q^{68} -157.588 q^{69} +58.9589 q^{70} +251.714 q^{71} +265.156 q^{72} -526.799 q^{73} +98.8758 q^{74} +403.309 q^{75} -6.50741 q^{76} -136.294 q^{77} -128.826 q^{78} +978.288 q^{79} +159.319 q^{80} -322.013 q^{81} +222.395 q^{82} -37.2953 q^{83} -62.0250 q^{84} -101.678 q^{85} -1115.89 q^{87} -638.768 q^{88} +437.612 q^{89} +120.972 q^{90} -74.6014 q^{91} -114.719 q^{92} +190.369 q^{93} +1099.76 q^{94} -11.0685 q^{95} -503.414 q^{96} -1121.71 q^{97} -710.070 q^{98} -279.648 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50q + 10q^{2} + 2q^{3} + 186q^{4} - 8q^{5} - 51q^{6} + 6q^{7} + 138q^{8} + 360q^{9} + O(q^{10}) \) \( 50q + 10q^{2} + 2q^{3} + 186q^{4} - 8q^{5} - 51q^{6} + 6q^{7} + 138q^{8} + 360q^{9} - 137q^{10} - 252q^{11} + 48q^{12} - 192q^{13} - 272q^{14} - 314q^{15} + 542q^{16} - 236q^{17} + 386q^{18} - 12q^{19} - 108q^{20} - 408q^{21} - 1235q^{22} - 630q^{23} - 613q^{24} + 1098q^{25} - 1493q^{26} - 10q^{27} + 242q^{28} - 208q^{29} + 48q^{30} - 932q^{31} + 1124q^{32} - 254q^{33} - 765q^{34} - 1452q^{35} + 747q^{36} + 90q^{37} - 1213q^{38} + 1610q^{39} - 1693q^{40} - 1354q^{41} + 16q^{42} - 2704q^{44} - 4508q^{45} - 233q^{46} - 3484q^{47} + 376q^{48} + 1324q^{49} + 408q^{50} - 4054q^{51} - 2176q^{52} - 726q^{53} - 6497q^{54} + 3288q^{55} - 7097q^{56} - 870q^{57} + 275q^{58} - 4370q^{59} - 3891q^{60} - 1172q^{61} + 1546q^{62} + 3686q^{63} + 606q^{64} - 2610q^{65} - 4697q^{66} - 344q^{67} - 3221q^{68} - 136q^{69} + 1310q^{70} - 162q^{71} + 5814q^{72} - 746q^{73} - 4332q^{74} - 236q^{75} - 1338q^{76} - 2024q^{77} - 2782q^{78} - 2656q^{79} + 5713q^{80} - 86q^{81} + 4168q^{82} - 3514q^{83} - 4269q^{84} + 7558q^{85} - 10278q^{87} - 11692q^{88} - 2640q^{89} - 8286q^{90} + 5946q^{91} - 4271q^{92} + 2q^{93} - 9062q^{94} - 12140q^{95} - 700q^{96} - 3864q^{97} + 2826q^{98} - 8174q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.25115 0.795900 0.397950 0.917407i \(-0.369722\pi\)
0.397950 + 0.917407i \(0.369722\pi\)
\(3\) −4.02813 −0.775213 −0.387607 0.921825i \(-0.626698\pi\)
−0.387607 + 0.921825i \(0.626698\pi\)
\(4\) −2.93234 −0.366543
\(5\) −4.98765 −0.446109 −0.223054 0.974806i \(-0.571603\pi\)
−0.223054 + 0.974806i \(0.571603\pi\)
\(6\) −9.06790 −0.616992
\(7\) −5.25109 −0.283532 −0.141766 0.989900i \(-0.545278\pi\)
−0.141766 + 0.989900i \(0.545278\pi\)
\(8\) −24.6103 −1.08763
\(9\) −10.7742 −0.399045
\(10\) −11.2279 −0.355058
\(11\) 25.9553 0.711438 0.355719 0.934593i \(-0.384236\pi\)
0.355719 + 0.934593i \(0.384236\pi\)
\(12\) 11.8118 0.284149
\(13\) 14.2068 0.303098 0.151549 0.988450i \(-0.451574\pi\)
0.151549 + 0.988450i \(0.451574\pi\)
\(14\) −11.8210 −0.225663
\(15\) 20.0909 0.345830
\(16\) −31.9427 −0.499104
\(17\) 20.3859 0.290842 0.145421 0.989370i \(-0.453546\pi\)
0.145421 + 0.989370i \(0.453546\pi\)
\(18\) −24.2543 −0.317600
\(19\) 2.21919 0.0267956 0.0133978 0.999910i \(-0.495735\pi\)
0.0133978 + 0.999910i \(0.495735\pi\)
\(20\) 14.6255 0.163518
\(21\) 21.1520 0.219798
\(22\) 58.4292 0.566234
\(23\) 39.1220 0.354674 0.177337 0.984150i \(-0.443252\pi\)
0.177337 + 0.984150i \(0.443252\pi\)
\(24\) 99.1334 0.843146
\(25\) −100.123 −0.800987
\(26\) 31.9817 0.241236
\(27\) 152.159 1.08456
\(28\) 15.3980 0.103927
\(29\) 277.025 1.77387 0.886934 0.461896i \(-0.152831\pi\)
0.886934 + 0.461896i \(0.152831\pi\)
\(30\) 45.2275 0.275246
\(31\) −47.2599 −0.273810 −0.136905 0.990584i \(-0.543716\pi\)
−0.136905 + 0.990584i \(0.543716\pi\)
\(32\) 124.975 0.690395
\(33\) −104.551 −0.551516
\(34\) 45.8917 0.231481
\(35\) 26.1906 0.126486
\(36\) 31.5936 0.146267
\(37\) 43.9224 0.195157 0.0975784 0.995228i \(-0.468890\pi\)
0.0975784 + 0.995228i \(0.468890\pi\)
\(38\) 4.99572 0.0213266
\(39\) −57.2270 −0.234965
\(40\) 122.748 0.485202
\(41\) 98.7920 0.376310 0.188155 0.982139i \(-0.439749\pi\)
0.188155 + 0.982139i \(0.439749\pi\)
\(42\) 47.6164 0.174937
\(43\) 0 0
\(44\) −76.1098 −0.260772
\(45\) 53.7380 0.178017
\(46\) 88.0694 0.282285
\(47\) 488.535 1.51617 0.758086 0.652154i \(-0.226134\pi\)
0.758086 + 0.652154i \(0.226134\pi\)
\(48\) 128.669 0.386912
\(49\) −315.426 −0.919609
\(50\) −225.392 −0.637506
\(51\) −82.1171 −0.225465
\(52\) −41.6593 −0.111098
\(53\) −230.167 −0.596525 −0.298263 0.954484i \(-0.596407\pi\)
−0.298263 + 0.954484i \(0.596407\pi\)
\(54\) 342.533 0.863200
\(55\) −129.456 −0.317379
\(56\) 129.231 0.308379
\(57\) −8.93917 −0.0207723
\(58\) 623.623 1.41182
\(59\) −400.770 −0.884335 −0.442167 0.896933i \(-0.645790\pi\)
−0.442167 + 0.896933i \(0.645790\pi\)
\(60\) −58.9133 −0.126761
\(61\) 13.3239 0.0279665 0.0139832 0.999902i \(-0.495549\pi\)
0.0139832 + 0.999902i \(0.495549\pi\)
\(62\) −106.389 −0.217926
\(63\) 56.5763 0.113142
\(64\) 536.878 1.04859
\(65\) −70.8588 −0.135215
\(66\) −235.360 −0.438952
\(67\) −640.592 −1.16807 −0.584036 0.811728i \(-0.698527\pi\)
−0.584036 + 0.811728i \(0.698527\pi\)
\(68\) −59.7785 −0.106606
\(69\) −157.588 −0.274948
\(70\) 58.9589 0.100670
\(71\) 251.714 0.420746 0.210373 0.977621i \(-0.432532\pi\)
0.210373 + 0.977621i \(0.432532\pi\)
\(72\) 265.156 0.434014
\(73\) −526.799 −0.844618 −0.422309 0.906452i \(-0.638780\pi\)
−0.422309 + 0.906452i \(0.638780\pi\)
\(74\) 98.8758 0.155325
\(75\) 403.309 0.620935
\(76\) −6.50741 −0.00982173
\(77\) −136.294 −0.201716
\(78\) −128.826 −0.187009
\(79\) 978.288 1.39324 0.696620 0.717440i \(-0.254686\pi\)
0.696620 + 0.717440i \(0.254686\pi\)
\(80\) 159.319 0.222655
\(81\) −322.013 −0.441719
\(82\) 222.395 0.299505
\(83\) −37.2953 −0.0493215 −0.0246608 0.999696i \(-0.507851\pi\)
−0.0246608 + 0.999696i \(0.507851\pi\)
\(84\) −62.0250 −0.0805653
\(85\) −101.678 −0.129747
\(86\) 0 0
\(87\) −1115.89 −1.37513
\(88\) −638.768 −0.773783
\(89\) 437.612 0.521200 0.260600 0.965447i \(-0.416080\pi\)
0.260600 + 0.965447i \(0.416080\pi\)
\(90\) 120.972 0.141684
\(91\) −74.6014 −0.0859380
\(92\) −114.719 −0.130003
\(93\) 190.369 0.212261
\(94\) 1099.76 1.20672
\(95\) −11.0685 −0.0119538
\(96\) −503.414 −0.535203
\(97\) −1121.71 −1.17415 −0.587075 0.809533i \(-0.699721\pi\)
−0.587075 + 0.809533i \(0.699721\pi\)
\(98\) −710.070 −0.731918
\(99\) −279.648 −0.283896
\(100\) 293.596 0.293596
\(101\) 1581.80 1.55837 0.779183 0.626796i \(-0.215634\pi\)
0.779183 + 0.626796i \(0.215634\pi\)
\(102\) −184.858 −0.179447
\(103\) −972.456 −0.930281 −0.465141 0.885237i \(-0.653996\pi\)
−0.465141 + 0.885237i \(0.653996\pi\)
\(104\) −349.635 −0.329659
\(105\) −105.499 −0.0980538
\(106\) −518.139 −0.474775
\(107\) 1961.57 1.77226 0.886132 0.463433i \(-0.153383\pi\)
0.886132 + 0.463433i \(0.153383\pi\)
\(108\) −446.183 −0.397537
\(109\) −2028.69 −1.78269 −0.891347 0.453322i \(-0.850239\pi\)
−0.891347 + 0.453322i \(0.850239\pi\)
\(110\) −291.424 −0.252602
\(111\) −176.925 −0.151288
\(112\) 167.734 0.141512
\(113\) 1359.59 1.13185 0.565925 0.824457i \(-0.308519\pi\)
0.565925 + 0.824457i \(0.308519\pi\)
\(114\) −20.1234 −0.0165327
\(115\) −195.127 −0.158223
\(116\) −812.330 −0.650198
\(117\) −153.067 −0.120950
\(118\) −902.191 −0.703842
\(119\) −107.048 −0.0824631
\(120\) −494.443 −0.376135
\(121\) −657.322 −0.493856
\(122\) 29.9941 0.0222585
\(123\) −397.946 −0.291720
\(124\) 138.582 0.100363
\(125\) 1122.84 0.803436
\(126\) 127.362 0.0900498
\(127\) 641.350 0.448115 0.224057 0.974576i \(-0.428070\pi\)
0.224057 + 0.974576i \(0.428070\pi\)
\(128\) 208.792 0.144178
\(129\) 0 0
\(130\) −159.513 −0.107617
\(131\) −1243.19 −0.829146 −0.414573 0.910016i \(-0.636069\pi\)
−0.414573 + 0.910016i \(0.636069\pi\)
\(132\) 306.580 0.202154
\(133\) −11.6532 −0.00759742
\(134\) −1442.07 −0.929669
\(135\) −758.917 −0.483831
\(136\) −501.704 −0.316329
\(137\) −2114.51 −1.31865 −0.659323 0.751860i \(-0.729157\pi\)
−0.659323 + 0.751860i \(0.729157\pi\)
\(138\) −354.755 −0.218831
\(139\) −3137.34 −1.91443 −0.957216 0.289374i \(-0.906553\pi\)
−0.957216 + 0.289374i \(0.906553\pi\)
\(140\) −76.7997 −0.0463626
\(141\) −1967.88 −1.17536
\(142\) 566.645 0.334872
\(143\) 368.743 0.215635
\(144\) 344.157 0.199165
\(145\) −1381.70 −0.791338
\(146\) −1185.90 −0.672232
\(147\) 1270.58 0.712893
\(148\) −128.795 −0.0715332
\(149\) −1460.78 −0.803167 −0.401584 0.915822i \(-0.631540\pi\)
−0.401584 + 0.915822i \(0.631540\pi\)
\(150\) 907.908 0.494203
\(151\) −3084.79 −1.66249 −0.831246 0.555905i \(-0.812372\pi\)
−0.831246 + 0.555905i \(0.812372\pi\)
\(152\) −54.6149 −0.0291438
\(153\) −219.642 −0.116059
\(154\) −306.817 −0.160546
\(155\) 235.716 0.122149
\(156\) 167.809 0.0861248
\(157\) 2713.54 1.37939 0.689695 0.724100i \(-0.257745\pi\)
0.689695 + 0.724100i \(0.257745\pi\)
\(158\) 2202.27 1.10888
\(159\) 927.141 0.462434
\(160\) −623.331 −0.307991
\(161\) −205.433 −0.100562
\(162\) −724.898 −0.351564
\(163\) −1564.36 −0.751721 −0.375860 0.926676i \(-0.622653\pi\)
−0.375860 + 0.926676i \(0.622653\pi\)
\(164\) −289.692 −0.137934
\(165\) 521.465 0.246036
\(166\) −83.9571 −0.0392550
\(167\) 508.284 0.235522 0.117761 0.993042i \(-0.462428\pi\)
0.117761 + 0.993042i \(0.462428\pi\)
\(168\) −520.558 −0.239059
\(169\) −1995.17 −0.908132
\(170\) −228.892 −0.103266
\(171\) −23.9100 −0.0106926
\(172\) 0 0
\(173\) −2615.65 −1.14950 −0.574751 0.818328i \(-0.694901\pi\)
−0.574751 + 0.818328i \(0.694901\pi\)
\(174\) −2512.03 −1.09446
\(175\) 525.757 0.227106
\(176\) −829.082 −0.355082
\(177\) 1614.35 0.685548
\(178\) 985.129 0.414823
\(179\) 1299.11 0.542458 0.271229 0.962515i \(-0.412570\pi\)
0.271229 + 0.962515i \(0.412570\pi\)
\(180\) −157.578 −0.0652509
\(181\) −1263.14 −0.518721 −0.259360 0.965781i \(-0.583512\pi\)
−0.259360 + 0.965781i \(0.583512\pi\)
\(182\) −167.939 −0.0683981
\(183\) −53.6705 −0.0216800
\(184\) −962.805 −0.385755
\(185\) −219.070 −0.0870612
\(186\) 428.548 0.168939
\(187\) 529.123 0.206916
\(188\) −1432.55 −0.555742
\(189\) −799.002 −0.307507
\(190\) −24.9169 −0.00951400
\(191\) 1507.21 0.570985 0.285493 0.958381i \(-0.407843\pi\)
0.285493 + 0.958381i \(0.407843\pi\)
\(192\) −2162.61 −0.812880
\(193\) 643.966 0.240175 0.120087 0.992763i \(-0.461683\pi\)
0.120087 + 0.992763i \(0.461683\pi\)
\(194\) −2525.14 −0.934506
\(195\) 285.428 0.104820
\(196\) 924.937 0.337076
\(197\) −3128.98 −1.13163 −0.565813 0.824534i \(-0.691438\pi\)
−0.565813 + 0.824534i \(0.691438\pi\)
\(198\) −629.528 −0.225953
\(199\) 4879.50 1.73818 0.869092 0.494650i \(-0.164704\pi\)
0.869092 + 0.494650i \(0.164704\pi\)
\(200\) 2464.07 0.871179
\(201\) 2580.39 0.905505
\(202\) 3560.86 1.24030
\(203\) −1454.68 −0.502949
\(204\) 240.795 0.0826424
\(205\) −492.740 −0.167875
\(206\) −2189.14 −0.740411
\(207\) −421.509 −0.141531
\(208\) −453.804 −0.151277
\(209\) 57.5997 0.0190634
\(210\) −237.494 −0.0780411
\(211\) 79.4254 0.0259141 0.0129570 0.999916i \(-0.495876\pi\)
0.0129570 + 0.999916i \(0.495876\pi\)
\(212\) 674.927 0.218652
\(213\) −1013.94 −0.326168
\(214\) 4415.78 1.41055
\(215\) 0 0
\(216\) −3744.68 −1.17960
\(217\) 248.166 0.0776341
\(218\) −4566.89 −1.41885
\(219\) 2122.01 0.654759
\(220\) 379.609 0.116333
\(221\) 289.620 0.0881536
\(222\) −398.284 −0.120410
\(223\) −2831.34 −0.850226 −0.425113 0.905140i \(-0.639766\pi\)
−0.425113 + 0.905140i \(0.639766\pi\)
\(224\) −656.254 −0.195749
\(225\) 1078.75 0.319629
\(226\) 3060.63 0.900840
\(227\) −3030.54 −0.886097 −0.443049 0.896498i \(-0.646103\pi\)
−0.443049 + 0.896498i \(0.646103\pi\)
\(228\) 26.2127 0.00761393
\(229\) 6084.93 1.75591 0.877956 0.478742i \(-0.158907\pi\)
0.877956 + 0.478742i \(0.158907\pi\)
\(230\) −439.260 −0.125930
\(231\) 549.008 0.156373
\(232\) −6817.66 −1.92932
\(233\) 5872.34 1.65111 0.825557 0.564319i \(-0.190861\pi\)
0.825557 + 0.564319i \(0.190861\pi\)
\(234\) −344.577 −0.0962638
\(235\) −2436.64 −0.676378
\(236\) 1175.19 0.324146
\(237\) −3940.66 −1.08006
\(238\) −240.982 −0.0656324
\(239\) −1168.26 −0.316187 −0.158093 0.987424i \(-0.550535\pi\)
−0.158093 + 0.987424i \(0.550535\pi\)
\(240\) −641.756 −0.172605
\(241\) −2150.85 −0.574890 −0.287445 0.957797i \(-0.592806\pi\)
−0.287445 + 0.957797i \(0.592806\pi\)
\(242\) −1479.73 −0.393060
\(243\) −2811.19 −0.742132
\(244\) −39.0703 −0.0102509
\(245\) 1573.23 0.410246
\(246\) −895.836 −0.232180
\(247\) 31.5277 0.00812169
\(248\) 1163.08 0.297805
\(249\) 150.230 0.0382347
\(250\) 2527.67 0.639455
\(251\) −982.679 −0.247116 −0.123558 0.992337i \(-0.539431\pi\)
−0.123558 + 0.992337i \(0.539431\pi\)
\(252\) −165.901 −0.0414714
\(253\) 1015.42 0.252329
\(254\) 1443.77 0.356655
\(255\) 409.572 0.100582
\(256\) −3825.00 −0.933838
\(257\) −585.060 −0.142004 −0.0710020 0.997476i \(-0.522620\pi\)
−0.0710020 + 0.997476i \(0.522620\pi\)
\(258\) 0 0
\(259\) −230.640 −0.0553332
\(260\) 207.782 0.0495619
\(261\) −2984.72 −0.707852
\(262\) −2798.60 −0.659917
\(263\) 104.375 0.0244715 0.0122358 0.999925i \(-0.496105\pi\)
0.0122358 + 0.999925i \(0.496105\pi\)
\(264\) 2573.04 0.599847
\(265\) 1147.99 0.266115
\(266\) −26.2329 −0.00604679
\(267\) −1762.76 −0.404041
\(268\) 1878.44 0.428148
\(269\) 5940.70 1.34651 0.673254 0.739411i \(-0.264896\pi\)
0.673254 + 0.739411i \(0.264896\pi\)
\(270\) −1708.43 −0.385081
\(271\) 3256.54 0.729965 0.364982 0.931014i \(-0.381075\pi\)
0.364982 + 0.931014i \(0.381075\pi\)
\(272\) −651.181 −0.145160
\(273\) 300.504 0.0666202
\(274\) −4760.06 −1.04951
\(275\) −2598.73 −0.569853
\(276\) 462.103 0.100780
\(277\) 5348.68 1.16018 0.580092 0.814551i \(-0.303017\pi\)
0.580092 + 0.814551i \(0.303017\pi\)
\(278\) −7062.62 −1.52370
\(279\) 509.187 0.109263
\(280\) −644.558 −0.137570
\(281\) −3582.54 −0.760557 −0.380279 0.924872i \(-0.624172\pi\)
−0.380279 + 0.924872i \(0.624172\pi\)
\(282\) −4429.98 −0.935467
\(283\) −7997.08 −1.67978 −0.839889 0.542759i \(-0.817380\pi\)
−0.839889 + 0.542759i \(0.817380\pi\)
\(284\) −738.111 −0.154221
\(285\) 44.5854 0.00926671
\(286\) 830.095 0.171624
\(287\) −518.765 −0.106696
\(288\) −1346.50 −0.275498
\(289\) −4497.41 −0.915411
\(290\) −3110.41 −0.629827
\(291\) 4518.39 0.910216
\(292\) 1544.75 0.309589
\(293\) −8020.77 −1.59924 −0.799621 0.600504i \(-0.794966\pi\)
−0.799621 + 0.600504i \(0.794966\pi\)
\(294\) 2860.25 0.567392
\(295\) 1998.90 0.394510
\(296\) −1080.94 −0.212259
\(297\) 3949.34 0.771596
\(298\) −3288.43 −0.639241
\(299\) 555.801 0.107501
\(300\) −1182.64 −0.227599
\(301\) 0 0
\(302\) −6944.30 −1.32318
\(303\) −6371.69 −1.20807
\(304\) −70.8867 −0.0133738
\(305\) −66.4552 −0.0124761
\(306\) −494.447 −0.0923714
\(307\) 4940.98 0.918556 0.459278 0.888292i \(-0.348108\pi\)
0.459278 + 0.888292i \(0.348108\pi\)
\(308\) 399.659 0.0739374
\(309\) 3917.18 0.721166
\(310\) 530.630 0.0972186
\(311\) 3934.00 0.717288 0.358644 0.933474i \(-0.383239\pi\)
0.358644 + 0.933474i \(0.383239\pi\)
\(312\) 1408.37 0.255556
\(313\) −2101.15 −0.379437 −0.189719 0.981839i \(-0.560758\pi\)
−0.189719 + 0.981839i \(0.560758\pi\)
\(314\) 6108.58 1.09786
\(315\) −282.183 −0.0504737
\(316\) −2868.67 −0.510682
\(317\) 5062.65 0.896993 0.448497 0.893785i \(-0.351960\pi\)
0.448497 + 0.893785i \(0.351960\pi\)
\(318\) 2087.13 0.368051
\(319\) 7190.26 1.26200
\(320\) −2677.76 −0.467785
\(321\) −7901.45 −1.37388
\(322\) −462.460 −0.0800370
\(323\) 45.2402 0.00779329
\(324\) 944.252 0.161909
\(325\) −1422.44 −0.242777
\(326\) −3521.61 −0.598295
\(327\) 8171.83 1.38197
\(328\) −2431.30 −0.409287
\(329\) −2565.34 −0.429884
\(330\) 1173.89 0.195820
\(331\) 7137.29 1.18520 0.592599 0.805497i \(-0.298102\pi\)
0.592599 + 0.805497i \(0.298102\pi\)
\(332\) 109.362 0.0180784
\(333\) −473.229 −0.0778762
\(334\) 1144.22 0.187452
\(335\) 3195.05 0.521087
\(336\) −675.653 −0.109702
\(337\) −6668.67 −1.07794 −0.538970 0.842325i \(-0.681186\pi\)
−0.538970 + 0.842325i \(0.681186\pi\)
\(338\) −4491.41 −0.722782
\(339\) −5476.58 −0.877425
\(340\) 298.154 0.0475579
\(341\) −1226.64 −0.194799
\(342\) −53.8249 −0.00851028
\(343\) 3457.45 0.544271
\(344\) 0 0
\(345\) 785.996 0.122657
\(346\) −5888.20 −0.914889
\(347\) −7743.07 −1.19790 −0.598948 0.800788i \(-0.704414\pi\)
−0.598948 + 0.800788i \(0.704414\pi\)
\(348\) 3272.17 0.504042
\(349\) −928.356 −0.142389 −0.0711945 0.997462i \(-0.522681\pi\)
−0.0711945 + 0.997462i \(0.522681\pi\)
\(350\) 1183.56 0.180753
\(351\) 2161.70 0.328727
\(352\) 3243.76 0.491173
\(353\) −4940.92 −0.744982 −0.372491 0.928036i \(-0.621496\pi\)
−0.372491 + 0.928036i \(0.621496\pi\)
\(354\) 3634.14 0.545628
\(355\) −1255.46 −0.187699
\(356\) −1283.23 −0.191042
\(357\) 431.204 0.0639265
\(358\) 2924.49 0.431743
\(359\) −308.245 −0.0453163 −0.0226581 0.999743i \(-0.507213\pi\)
−0.0226581 + 0.999743i \(0.507213\pi\)
\(360\) −1322.51 −0.193617
\(361\) −6854.08 −0.999282
\(362\) −2843.51 −0.412850
\(363\) 2647.78 0.382843
\(364\) 218.757 0.0314999
\(365\) 2627.49 0.376792
\(366\) −120.820 −0.0172551
\(367\) −8207.98 −1.16745 −0.583724 0.811952i \(-0.698405\pi\)
−0.583724 + 0.811952i \(0.698405\pi\)
\(368\) −1249.66 −0.177019
\(369\) −1064.40 −0.150164
\(370\) −493.158 −0.0692920
\(371\) 1208.63 0.169134
\(372\) −558.226 −0.0778028
\(373\) −6480.94 −0.899653 −0.449826 0.893116i \(-0.648514\pi\)
−0.449826 + 0.893116i \(0.648514\pi\)
\(374\) 1191.13 0.164685
\(375\) −4522.93 −0.622834
\(376\) −12023.0 −1.64904
\(377\) 3935.65 0.537655
\(378\) −1798.67 −0.244745
\(379\) −7927.62 −1.07444 −0.537222 0.843441i \(-0.680526\pi\)
−0.537222 + 0.843441i \(0.680526\pi\)
\(380\) 32.4567 0.00438156
\(381\) −2583.44 −0.347384
\(382\) 3392.96 0.454447
\(383\) 13330.3 1.77845 0.889227 0.457467i \(-0.151243\pi\)
0.889227 + 0.457467i \(0.151243\pi\)
\(384\) −841.041 −0.111769
\(385\) 679.785 0.0899872
\(386\) 1449.66 0.191155
\(387\) 0 0
\(388\) 3289.24 0.430376
\(389\) 83.9976 0.0109482 0.00547410 0.999985i \(-0.498258\pi\)
0.00547410 + 0.999985i \(0.498258\pi\)
\(390\) 642.540 0.0834264
\(391\) 797.540 0.103154
\(392\) 7762.73 1.00020
\(393\) 5007.73 0.642765
\(394\) −7043.78 −0.900661
\(395\) −4879.36 −0.621537
\(396\) 820.023 0.104060
\(397\) −3720.21 −0.470307 −0.235154 0.971958i \(-0.575559\pi\)
−0.235154 + 0.971958i \(0.575559\pi\)
\(398\) 10984.5 1.38342
\(399\) 46.9404 0.00588962
\(400\) 3198.21 0.399776
\(401\) −10601.0 −1.32018 −0.660088 0.751188i \(-0.729481\pi\)
−0.660088 + 0.751188i \(0.729481\pi\)
\(402\) 5808.83 0.720692
\(403\) −671.414 −0.0829913
\(404\) −4638.38 −0.571208
\(405\) 1606.09 0.197055
\(406\) −3274.70 −0.400297
\(407\) 1140.02 0.138842
\(408\) 2020.93 0.245223
\(409\) 3919.36 0.473839 0.236919 0.971529i \(-0.423862\pi\)
0.236919 + 0.971529i \(0.423862\pi\)
\(410\) −1109.23 −0.133612
\(411\) 8517.50 1.02223
\(412\) 2851.57 0.340988
\(413\) 2104.48 0.250737
\(414\) −948.878 −0.112644
\(415\) 186.016 0.0220028
\(416\) 1775.50 0.209257
\(417\) 12637.6 1.48409
\(418\) 129.665 0.0151726
\(419\) −4415.24 −0.514793 −0.257397 0.966306i \(-0.582865\pi\)
−0.257397 + 0.966306i \(0.582865\pi\)
\(420\) 309.359 0.0359409
\(421\) 7715.34 0.893165 0.446583 0.894742i \(-0.352641\pi\)
0.446583 + 0.894742i \(0.352641\pi\)
\(422\) 178.798 0.0206250
\(423\) −5263.57 −0.605021
\(424\) 5664.47 0.648800
\(425\) −2041.11 −0.232961
\(426\) −2282.52 −0.259597
\(427\) −69.9652 −0.00792940
\(428\) −5751.99 −0.649610
\(429\) −1485.34 −0.167163
\(430\) 0 0
\(431\) 10963.5 1.22527 0.612636 0.790365i \(-0.290109\pi\)
0.612636 + 0.790365i \(0.290109\pi\)
\(432\) −4860.37 −0.541307
\(433\) 3896.75 0.432485 0.216242 0.976340i \(-0.430620\pi\)
0.216242 + 0.976340i \(0.430620\pi\)
\(434\) 558.657 0.0617890
\(435\) 5565.67 0.613456
\(436\) 5948.82 0.653433
\(437\) 86.8191 0.00950371
\(438\) 4776.96 0.521123
\(439\) −7414.58 −0.806102 −0.403051 0.915178i \(-0.632050\pi\)
−0.403051 + 0.915178i \(0.632050\pi\)
\(440\) 3185.95 0.345191
\(441\) 3398.46 0.366965
\(442\) 651.977 0.0701615
\(443\) −8192.89 −0.878681 −0.439341 0.898321i \(-0.644788\pi\)
−0.439341 + 0.898321i \(0.644788\pi\)
\(444\) 518.804 0.0554535
\(445\) −2182.66 −0.232512
\(446\) −6373.76 −0.676695
\(447\) 5884.21 0.622626
\(448\) −2819.19 −0.297309
\(449\) 8163.71 0.858061 0.429031 0.903290i \(-0.358855\pi\)
0.429031 + 0.903290i \(0.358855\pi\)
\(450\) 2428.42 0.254393
\(451\) 2564.18 0.267721
\(452\) −3986.77 −0.414871
\(453\) 12425.9 1.28879
\(454\) −6822.19 −0.705245
\(455\) 372.086 0.0383377
\(456\) 219.996 0.0225926
\(457\) 7695.45 0.787698 0.393849 0.919175i \(-0.371143\pi\)
0.393849 + 0.919175i \(0.371143\pi\)
\(458\) 13698.1 1.39753
\(459\) 3101.91 0.315435
\(460\) 572.179 0.0579956
\(461\) −2082.47 −0.210392 −0.105196 0.994452i \(-0.533547\pi\)
−0.105196 + 0.994452i \(0.533547\pi\)
\(462\) 1235.90 0.124457
\(463\) −2804.81 −0.281535 −0.140767 0.990043i \(-0.544957\pi\)
−0.140767 + 0.990043i \(0.544957\pi\)
\(464\) −8848.90 −0.885345
\(465\) −949.492 −0.0946917
\(466\) 13219.5 1.31412
\(467\) 17860.1 1.76974 0.884869 0.465839i \(-0.154248\pi\)
0.884869 + 0.465839i \(0.154248\pi\)
\(468\) 448.846 0.0443331
\(469\) 3363.81 0.331186
\(470\) −5485.23 −0.538330
\(471\) −10930.5 −1.06932
\(472\) 9863.06 0.961831
\(473\) 0 0
\(474\) −8871.01 −0.859618
\(475\) −222.192 −0.0214629
\(476\) 313.902 0.0302262
\(477\) 2479.86 0.238040
\(478\) −2629.93 −0.251653
\(479\) 920.735 0.0878277 0.0439138 0.999035i \(-0.486017\pi\)
0.0439138 + 0.999035i \(0.486017\pi\)
\(480\) 2510.85 0.238759
\(481\) 623.999 0.0591516
\(482\) −4841.88 −0.457555
\(483\) 827.511 0.0779567
\(484\) 1927.49 0.181019
\(485\) 5594.70 0.523799
\(486\) −6328.40 −0.590663
\(487\) 1931.99 0.179768 0.0898839 0.995952i \(-0.471350\pi\)
0.0898839 + 0.995952i \(0.471350\pi\)
\(488\) −327.906 −0.0304172
\(489\) 6301.46 0.582744
\(490\) 3541.58 0.326515
\(491\) −14234.0 −1.30830 −0.654148 0.756367i \(-0.726973\pi\)
−0.654148 + 0.756367i \(0.726973\pi\)
\(492\) 1166.91 0.106928
\(493\) 5647.41 0.515916
\(494\) 70.9734 0.00646405
\(495\) 1394.79 0.126648
\(496\) 1509.61 0.136660
\(497\) −1321.77 −0.119295
\(498\) 338.190 0.0304310
\(499\) 477.809 0.0428651 0.0214325 0.999770i \(-0.493177\pi\)
0.0214325 + 0.999770i \(0.493177\pi\)
\(500\) −3292.54 −0.294494
\(501\) −2047.43 −0.182580
\(502\) −2212.15 −0.196680
\(503\) 2881.02 0.255384 0.127692 0.991814i \(-0.459243\pi\)
0.127692 + 0.991814i \(0.459243\pi\)
\(504\) −1392.36 −0.123057
\(505\) −7889.47 −0.695201
\(506\) 2285.87 0.200829
\(507\) 8036.78 0.703996
\(508\) −1880.66 −0.164253
\(509\) −15177.9 −1.32171 −0.660854 0.750514i \(-0.729806\pi\)
−0.660854 + 0.750514i \(0.729806\pi\)
\(510\) 922.005 0.0800531
\(511\) 2766.27 0.239476
\(512\) −10281.0 −0.887420
\(513\) 337.670 0.0290614
\(514\) −1317.05 −0.113021
\(515\) 4850.27 0.415007
\(516\) 0 0
\(517\) 12680.1 1.07866
\(518\) −519.205 −0.0440397
\(519\) 10536.1 0.891109
\(520\) 1743.86 0.147064
\(521\) −5817.50 −0.489192 −0.244596 0.969625i \(-0.578655\pi\)
−0.244596 + 0.969625i \(0.578655\pi\)
\(522\) −6719.04 −0.563380
\(523\) −7595.81 −0.635070 −0.317535 0.948247i \(-0.602855\pi\)
−0.317535 + 0.948247i \(0.602855\pi\)
\(524\) 3645.46 0.303917
\(525\) −2117.81 −0.176055
\(526\) 234.962 0.0194769
\(527\) −963.437 −0.0796356
\(528\) 3339.64 0.275264
\(529\) −10636.5 −0.874206
\(530\) 2584.30 0.211801
\(531\) 4317.97 0.352889
\(532\) 34.1710 0.00278478
\(533\) 1403.52 0.114059
\(534\) −3968.22 −0.321576
\(535\) −9783.63 −0.790623
\(536\) 15765.2 1.27043
\(537\) −5232.98 −0.420521
\(538\) 13373.4 1.07169
\(539\) −8186.98 −0.654245
\(540\) 2225.40 0.177345
\(541\) 5132.13 0.407851 0.203925 0.978986i \(-0.434630\pi\)
0.203925 + 0.978986i \(0.434630\pi\)
\(542\) 7330.94 0.580979
\(543\) 5088.09 0.402119
\(544\) 2547.73 0.200796
\(545\) 10118.4 0.795276
\(546\) 676.478 0.0530231
\(547\) 6569.33 0.513500 0.256750 0.966478i \(-0.417348\pi\)
0.256750 + 0.966478i \(0.417348\pi\)
\(548\) 6200.45 0.483340
\(549\) −143.555 −0.0111599
\(550\) −5850.13 −0.453546
\(551\) 614.769 0.0475319
\(552\) 3878.30 0.299042
\(553\) −5137.08 −0.395028
\(554\) 12040.7 0.923390
\(555\) 882.440 0.0674910
\(556\) 9199.76 0.701721
\(557\) 7594.11 0.577689 0.288845 0.957376i \(-0.406729\pi\)
0.288845 + 0.957376i \(0.406729\pi\)
\(558\) 1146.26 0.0869621
\(559\) 0 0
\(560\) −836.597 −0.0631298
\(561\) −2131.38 −0.160404
\(562\) −8064.83 −0.605328
\(563\) 12214.0 0.914318 0.457159 0.889385i \(-0.348867\pi\)
0.457159 + 0.889385i \(0.348867\pi\)
\(564\) 5770.49 0.430818
\(565\) −6781.14 −0.504929
\(566\) −18002.6 −1.33694
\(567\) 1690.92 0.125241
\(568\) −6194.76 −0.457617
\(569\) −11696.6 −0.861772 −0.430886 0.902406i \(-0.641799\pi\)
−0.430886 + 0.902406i \(0.641799\pi\)
\(570\) 100.368 0.00737538
\(571\) −17353.9 −1.27187 −0.635936 0.771742i \(-0.719386\pi\)
−0.635936 + 0.771742i \(0.719386\pi\)
\(572\) −1081.28 −0.0790395
\(573\) −6071.25 −0.442635
\(574\) −1167.82 −0.0849194
\(575\) −3917.03 −0.284089
\(576\) −5784.43 −0.418434
\(577\) 14209.3 1.02520 0.512602 0.858626i \(-0.328682\pi\)
0.512602 + 0.858626i \(0.328682\pi\)
\(578\) −10124.3 −0.728576
\(579\) −2593.98 −0.186186
\(580\) 4051.62 0.290059
\(581\) 195.841 0.0139842
\(582\) 10171.6 0.724441
\(583\) −5974.05 −0.424391
\(584\) 12964.7 0.918634
\(585\) 763.447 0.0539567
\(586\) −18055.9 −1.27284
\(587\) −12326.7 −0.866740 −0.433370 0.901216i \(-0.642676\pi\)
−0.433370 + 0.901216i \(0.642676\pi\)
\(588\) −3725.76 −0.261306
\(589\) −104.878 −0.00733691
\(590\) 4499.81 0.313990
\(591\) 12603.9 0.877251
\(592\) −1403.00 −0.0974035
\(593\) 18961.8 1.31310 0.656548 0.754284i \(-0.272016\pi\)
0.656548 + 0.754284i \(0.272016\pi\)
\(594\) 8890.54 0.614113
\(595\) 533.920 0.0367875
\(596\) 4283.51 0.294395
\(597\) −19655.3 −1.34746
\(598\) 1251.19 0.0855601
\(599\) 14749.8 1.00611 0.503054 0.864255i \(-0.332210\pi\)
0.503054 + 0.864255i \(0.332210\pi\)
\(600\) −9925.56 −0.675349
\(601\) −14740.4 −1.00045 −0.500227 0.865894i \(-0.666750\pi\)
−0.500227 + 0.865894i \(0.666750\pi\)
\(602\) 0 0
\(603\) 6901.87 0.466113
\(604\) 9045.64 0.609374
\(605\) 3278.49 0.220313
\(606\) −14343.6 −0.961501
\(607\) −28252.6 −1.88919 −0.944595 0.328239i \(-0.893545\pi\)
−0.944595 + 0.328239i \(0.893545\pi\)
\(608\) 277.342 0.0184995
\(609\) 5859.64 0.389892
\(610\) −149.600 −0.00992973
\(611\) 6940.54 0.459549
\(612\) 644.066 0.0425406
\(613\) −24635.3 −1.62318 −0.811591 0.584226i \(-0.801398\pi\)
−0.811591 + 0.584226i \(0.801398\pi\)
\(614\) 11122.9 0.731079
\(615\) 1984.82 0.130139
\(616\) 3354.23 0.219392
\(617\) −2636.49 −0.172028 −0.0860140 0.996294i \(-0.527413\pi\)
−0.0860140 + 0.996294i \(0.527413\pi\)
\(618\) 8818.14 0.573977
\(619\) 9682.05 0.628683 0.314341 0.949310i \(-0.398216\pi\)
0.314341 + 0.949310i \(0.398216\pi\)
\(620\) −691.198 −0.0447729
\(621\) 5952.78 0.384665
\(622\) 8856.01 0.570890
\(623\) −2297.94 −0.147777
\(624\) 1827.98 0.117272
\(625\) 6915.10 0.442567
\(626\) −4729.99 −0.301994
\(627\) −232.019 −0.0147782
\(628\) −7957.03 −0.505605
\(629\) 895.400 0.0567598
\(630\) −635.235 −0.0401720
\(631\) 6750.28 0.425871 0.212935 0.977066i \(-0.431698\pi\)
0.212935 + 0.977066i \(0.431698\pi\)
\(632\) −24075.9 −1.51533
\(633\) −319.936 −0.0200889
\(634\) 11396.8 0.713917
\(635\) −3198.83 −0.199908
\(636\) −2718.69 −0.169502
\(637\) −4481.21 −0.278732
\(638\) 16186.3 1.00442
\(639\) −2712.02 −0.167896
\(640\) −1041.38 −0.0643191
\(641\) 4005.28 0.246801 0.123400 0.992357i \(-0.460620\pi\)
0.123400 + 0.992357i \(0.460620\pi\)
\(642\) −17787.3 −1.09347
\(643\) 21183.8 1.29923 0.649617 0.760262i \(-0.274929\pi\)
0.649617 + 0.760262i \(0.274929\pi\)
\(644\) 602.401 0.0368601
\(645\) 0 0
\(646\) 101.842 0.00620268
\(647\) 8425.30 0.511952 0.255976 0.966683i \(-0.417603\pi\)
0.255976 + 0.966683i \(0.417603\pi\)
\(648\) 7924.84 0.480427
\(649\) −10402.1 −0.629150
\(650\) −3202.11 −0.193227
\(651\) −999.643 −0.0601829
\(652\) 4587.25 0.275538
\(653\) −15075.9 −0.903467 −0.451733 0.892153i \(-0.649194\pi\)
−0.451733 + 0.892153i \(0.649194\pi\)
\(654\) 18396.0 1.09991
\(655\) 6200.60 0.369889
\(656\) −3155.68 −0.187818
\(657\) 5675.84 0.337040
\(658\) −5774.96 −0.342145
\(659\) −15177.4 −0.897159 −0.448580 0.893743i \(-0.648070\pi\)
−0.448580 + 0.893743i \(0.648070\pi\)
\(660\) −1529.11 −0.0901828
\(661\) 8032.86 0.472681 0.236340 0.971670i \(-0.424052\pi\)
0.236340 + 0.971670i \(0.424052\pi\)
\(662\) 16067.1 0.943300
\(663\) −1166.63 −0.0683378
\(664\) 917.848 0.0536437
\(665\) 58.1218 0.00338928
\(666\) −1065.31 −0.0619817
\(667\) 10837.8 0.629145
\(668\) −1490.46 −0.0863288
\(669\) 11405.0 0.659107
\(670\) 7192.53 0.414734
\(671\) 345.827 0.0198964
\(672\) 2643.47 0.151747
\(673\) −2275.45 −0.130330 −0.0651651 0.997874i \(-0.520757\pi\)
−0.0651651 + 0.997874i \(0.520757\pi\)
\(674\) −15012.1 −0.857932
\(675\) −15234.7 −0.868716
\(676\) 5850.50 0.332869
\(677\) 10618.2 0.602793 0.301397 0.953499i \(-0.402547\pi\)
0.301397 + 0.953499i \(0.402547\pi\)
\(678\) −12328.6 −0.698343
\(679\) 5890.21 0.332909
\(680\) 2502.32 0.141117
\(681\) 12207.4 0.686914
\(682\) −2761.36 −0.155041
\(683\) −19742.9 −1.10606 −0.553031 0.833161i \(-0.686529\pi\)
−0.553031 + 0.833161i \(0.686529\pi\)
\(684\) 70.1122 0.00391931
\(685\) 10546.4 0.588260
\(686\) 7783.24 0.433186
\(687\) −24510.9 −1.36121
\(688\) 0 0
\(689\) −3269.94 −0.180805
\(690\) 1769.39 0.0976226
\(691\) 8138.94 0.448075 0.224037 0.974581i \(-0.428076\pi\)
0.224037 + 0.974581i \(0.428076\pi\)
\(692\) 7669.96 0.421341
\(693\) 1468.46 0.0804935
\(694\) −17430.8 −0.953406
\(695\) 15648.0 0.854045
\(696\) 27462.4 1.49563
\(697\) 2013.97 0.109447
\(698\) −2089.86 −0.113327
\(699\) −23654.5 −1.27997
\(700\) −1541.70 −0.0832438
\(701\) 30481.7 1.64234 0.821169 0.570685i \(-0.193322\pi\)
0.821169 + 0.570685i \(0.193322\pi\)
\(702\) 4866.31 0.261634
\(703\) 97.4720 0.00522934
\(704\) 13934.8 0.746007
\(705\) 9815.09 0.524337
\(706\) −11122.7 −0.592931
\(707\) −8306.18 −0.441847
\(708\) −4733.82 −0.251283
\(709\) −84.5679 −0.00447957 −0.00223978 0.999997i \(-0.500713\pi\)
−0.00223978 + 0.999997i \(0.500713\pi\)
\(710\) −2826.23 −0.149389
\(711\) −10540.3 −0.555965
\(712\) −10769.8 −0.566873
\(713\) −1848.90 −0.0971135
\(714\) 970.704 0.0508791
\(715\) −1839.16 −0.0961968
\(716\) −3809.43 −0.198834
\(717\) 4705.91 0.245112
\(718\) −693.905 −0.0360673
\(719\) 19339.8 1.00314 0.501568 0.865118i \(-0.332757\pi\)
0.501568 + 0.865118i \(0.332757\pi\)
\(720\) −1716.53 −0.0888492
\(721\) 5106.46 0.263765
\(722\) −15429.5 −0.795329
\(723\) 8663.90 0.445662
\(724\) 3703.96 0.190133
\(725\) −27736.6 −1.42084
\(726\) 5960.53 0.304705
\(727\) −25267.6 −1.28903 −0.644514 0.764592i \(-0.722940\pi\)
−0.644514 + 0.764592i \(0.722940\pi\)
\(728\) 1835.96 0.0934688
\(729\) 20018.2 1.01703
\(730\) 5914.86 0.299889
\(731\) 0 0
\(732\) 157.380 0.00794664
\(733\) 22425.0 1.13000 0.564998 0.825092i \(-0.308877\pi\)
0.564998 + 0.825092i \(0.308877\pi\)
\(734\) −18477.4 −0.929172
\(735\) −6337.19 −0.318028
\(736\) 4889.27 0.244865
\(737\) −16626.8 −0.831011
\(738\) −2396.13 −0.119516
\(739\) −31297.4 −1.55791 −0.778953 0.627083i \(-0.784249\pi\)
−0.778953 + 0.627083i \(0.784249\pi\)
\(740\) 642.387 0.0319116
\(741\) −126.997 −0.00629604
\(742\) 2720.79 0.134614
\(743\) 26708.5 1.31876 0.659380 0.751810i \(-0.270819\pi\)
0.659380 + 0.751810i \(0.270819\pi\)
\(744\) −4685.03 −0.230862
\(745\) 7285.87 0.358300
\(746\) −14589.6 −0.716034
\(747\) 401.827 0.0196815
\(748\) −1551.57 −0.0758436
\(749\) −10300.4 −0.502494
\(750\) −10181.8 −0.495714
\(751\) 36421.1 1.76967 0.884837 0.465901i \(-0.154270\pi\)
0.884837 + 0.465901i \(0.154270\pi\)
\(752\) −15605.1 −0.756728
\(753\) 3958.35 0.191568
\(754\) 8859.71 0.427920
\(755\) 15385.8 0.741653
\(756\) 2342.95 0.112714
\(757\) −16912.5 −0.812016 −0.406008 0.913870i \(-0.633079\pi\)
−0.406008 + 0.913870i \(0.633079\pi\)
\(758\) −17846.2 −0.855151
\(759\) −4090.26 −0.195609
\(760\) 272.400 0.0130013
\(761\) −39596.2 −1.88615 −0.943075 0.332581i \(-0.892081\pi\)
−0.943075 + 0.332581i \(0.892081\pi\)
\(762\) −5815.69 −0.276483
\(763\) 10652.9 0.505451
\(764\) −4419.66 −0.209290
\(765\) 1095.50 0.0517750
\(766\) 30008.5 1.41547
\(767\) −5693.67 −0.268040
\(768\) 15407.6 0.723924
\(769\) 35365.1 1.65839 0.829193 0.558962i \(-0.188800\pi\)
0.829193 + 0.558962i \(0.188800\pi\)
\(770\) 1530.30 0.0716208
\(771\) 2356.69 0.110083
\(772\) −1888.33 −0.0880342
\(773\) −3602.72 −0.167634 −0.0838169 0.996481i \(-0.526711\pi\)
−0.0838169 + 0.996481i \(0.526711\pi\)
\(774\) 0 0
\(775\) 4731.82 0.219318
\(776\) 27605.6 1.27704
\(777\) 929.049 0.0428950
\(778\) 189.091 0.00871367
\(779\) 219.238 0.0100835
\(780\) −836.972 −0.0384210
\(781\) 6533.32 0.299335
\(782\) 1795.38 0.0821005
\(783\) 42151.8 1.92386
\(784\) 10075.5 0.458981
\(785\) −13534.2 −0.615358
\(786\) 11273.1 0.511577
\(787\) −18197.3 −0.824224 −0.412112 0.911133i \(-0.635209\pi\)
−0.412112 + 0.911133i \(0.635209\pi\)
\(788\) 9175.22 0.414789
\(789\) −420.434 −0.0189706
\(790\) −10984.1 −0.494681
\(791\) −7139.31 −0.320916
\(792\) 6882.22 0.308774
\(793\) 189.291 0.00847658
\(794\) −8374.74 −0.374318
\(795\) −4624.25 −0.206296
\(796\) −14308.4 −0.637119
\(797\) −5337.43 −0.237216 −0.118608 0.992941i \(-0.537843\pi\)
−0.118608 + 0.992941i \(0.537843\pi\)
\(798\) 105.670 0.00468755
\(799\) 9959.24 0.440967
\(800\) −12512.9 −0.552997
\(801\) −4714.92 −0.207982
\(802\) −23864.5 −1.05073
\(803\) −13673.2 −0.600894
\(804\) −7566.57 −0.331906
\(805\) 1024.63 0.0448614
\(806\) −1511.45 −0.0660528
\(807\) −23929.9 −1.04383
\(808\) −38928.6 −1.69493
\(809\) 29582.7 1.28563 0.642813 0.766023i \(-0.277767\pi\)
0.642813 + 0.766023i \(0.277767\pi\)
\(810\) 3615.54 0.156836
\(811\) −28394.0 −1.22941 −0.614703 0.788759i \(-0.710724\pi\)
−0.614703 + 0.788759i \(0.710724\pi\)
\(812\) 4265.62 0.184352
\(813\) −13117.7 −0.565878
\(814\) 2566.35 0.110504
\(815\) 7802.50 0.335349
\(816\) 2623.04 0.112530
\(817\) 0 0
\(818\) 8823.06 0.377129
\(819\) 803.771 0.0342931
\(820\) 1444.88 0.0615334
\(821\) −11641.0 −0.494852 −0.247426 0.968907i \(-0.579585\pi\)
−0.247426 + 0.968907i \(0.579585\pi\)
\(822\) 19174.1 0.813594
\(823\) −12556.6 −0.531827 −0.265914 0.963997i \(-0.585674\pi\)
−0.265914 + 0.963997i \(0.585674\pi\)
\(824\) 23932.4 1.01180
\(825\) 10468.0 0.441757
\(826\) 4737.49 0.199562
\(827\) −38940.8 −1.63737 −0.818684 0.574245i \(-0.805296\pi\)
−0.818684 + 0.574245i \(0.805296\pi\)
\(828\) 1236.01 0.0518771
\(829\) −23760.5 −0.995461 −0.497731 0.867332i \(-0.665833\pi\)
−0.497731 + 0.867332i \(0.665833\pi\)
\(830\) 418.749 0.0175120
\(831\) −21545.1 −0.899389
\(832\) 7627.34 0.317825
\(833\) −6430.26 −0.267461
\(834\) 28449.1 1.18119
\(835\) −2535.14 −0.105068
\(836\) −168.902 −0.00698755
\(837\) −7191.02 −0.296963
\(838\) −9939.34 −0.409724
\(839\) −1611.44 −0.0663087 −0.0331544 0.999450i \(-0.510555\pi\)
−0.0331544 + 0.999450i \(0.510555\pi\)
\(840\) 2596.36 0.106646
\(841\) 52353.6 2.14661
\(842\) 17368.4 0.710871
\(843\) 14430.9 0.589594
\(844\) −232.902 −0.00949862
\(845\) 9951.19 0.405126
\(846\) −11849.1 −0.481536
\(847\) 3451.66 0.140024
\(848\) 7352.14 0.297728
\(849\) 32213.2 1.30219
\(850\) −4594.83 −0.185414
\(851\) 1718.33 0.0692171
\(852\) 2973.21 0.119554
\(853\) −38499.2 −1.54536 −0.772678 0.634799i \(-0.781083\pi\)
−0.772678 + 0.634799i \(0.781083\pi\)
\(854\) −157.502 −0.00631101
\(855\) 119.255 0.00477008
\(856\) −48274.8 −1.92757
\(857\) −1365.17 −0.0544146 −0.0272073 0.999630i \(-0.508661\pi\)
−0.0272073 + 0.999630i \(0.508661\pi\)
\(858\) −3343.73 −0.133045
\(859\) −35044.7 −1.39198 −0.695989 0.718052i \(-0.745034\pi\)
−0.695989 + 0.718052i \(0.745034\pi\)
\(860\) 0 0
\(861\) 2089.65 0.0827121
\(862\) 24680.4 0.975195
\(863\) 41315.3 1.62965 0.814826 0.579706i \(-0.196833\pi\)
0.814826 + 0.579706i \(0.196833\pi\)
\(864\) 19016.1 0.748773
\(865\) 13045.9 0.512803
\(866\) 8772.16 0.344215
\(867\) 18116.1 0.709638
\(868\) −727.707 −0.0284562
\(869\) 25391.8 0.991204
\(870\) 12529.1 0.488250
\(871\) −9100.80 −0.354040
\(872\) 49926.8 1.93891
\(873\) 12085.5 0.468538
\(874\) 195.443 0.00756401
\(875\) −5896.11 −0.227800
\(876\) −6222.46 −0.239997
\(877\) 27801.4 1.07045 0.535227 0.844708i \(-0.320226\pi\)
0.535227 + 0.844708i \(0.320226\pi\)
\(878\) −16691.3 −0.641577
\(879\) 32308.7 1.23975
\(880\) 4135.17 0.158405
\(881\) −34464.0 −1.31796 −0.658980 0.752161i \(-0.729012\pi\)
−0.658980 + 0.752161i \(0.729012\pi\)
\(882\) 7650.44 0.292068
\(883\) 37024.3 1.41106 0.705531 0.708679i \(-0.250709\pi\)
0.705531 + 0.708679i \(0.250709\pi\)
\(884\) −849.264 −0.0323120
\(885\) −8051.81 −0.305829
\(886\) −18443.4 −0.699343
\(887\) 13945.5 0.527898 0.263949 0.964537i \(-0.414975\pi\)
0.263949 + 0.964537i \(0.414975\pi\)
\(888\) 4354.18 0.164546
\(889\) −3367.78 −0.127055
\(890\) −4913.48 −0.185056
\(891\) −8357.95 −0.314256
\(892\) 8302.45 0.311644
\(893\) 1084.15 0.0406268
\(894\) 13246.2 0.495548
\(895\) −6479.50 −0.241995
\(896\) −1096.39 −0.0408791
\(897\) −2238.84 −0.0833362
\(898\) 18377.7 0.682931
\(899\) −13092.1 −0.485703
\(900\) −3163.26 −0.117158
\(901\) −4692.17 −0.173495
\(902\) 5772.34 0.213080
\(903\) 0 0
\(904\) −33459.8 −1.23104
\(905\) 6300.10 0.231406
\(906\) 27972.5 1.02574
\(907\) −24719.4 −0.904955 −0.452478 0.891776i \(-0.649460\pi\)
−0.452478 + 0.891776i \(0.649460\pi\)
\(908\) 8886.58 0.324792
\(909\) −17042.6 −0.621858
\(910\) 837.619 0.0305130
\(911\) −29271.0 −1.06454 −0.532268 0.846576i \(-0.678660\pi\)
−0.532268 + 0.846576i \(0.678660\pi\)
\(912\) 285.541 0.0103675
\(913\) −968.011 −0.0350892
\(914\) 17323.6 0.626929
\(915\) 267.690 0.00967164
\(916\) −17843.1 −0.643616
\(917\) 6528.11 0.235090
\(918\) 6982.85 0.251055
\(919\) 8933.98 0.320680 0.160340 0.987062i \(-0.448741\pi\)
0.160340 + 0.987062i \(0.448741\pi\)
\(920\) 4802.13 0.172089
\(921\) −19902.9 −0.712077
\(922\) −4687.95 −0.167451
\(923\) 3576.06 0.127527
\(924\) −1609.88 −0.0573172
\(925\) −4397.66 −0.156318
\(926\) −6314.04 −0.224074
\(927\) 10477.4 0.371224
\(928\) 34621.1 1.22467
\(929\) −34274.1 −1.21044 −0.605218 0.796060i \(-0.706914\pi\)
−0.605218 + 0.796060i \(0.706914\pi\)
\(930\) −2137.45 −0.0753652
\(931\) −699.989 −0.0246415
\(932\) −17219.7 −0.605204
\(933\) −15846.6 −0.556051
\(934\) 40205.7 1.40854
\(935\) −2639.08 −0.0923072
\(936\) 3767.04 0.131549
\(937\) −15930.4 −0.555414 −0.277707 0.960666i \(-0.589575\pi\)
−0.277707 + 0.960666i \(0.589575\pi\)
\(938\) 7572.42 0.263591
\(939\) 8463.68 0.294145
\(940\) 7145.06 0.247921
\(941\) −10078.6 −0.349154 −0.174577 0.984644i \(-0.555856\pi\)
−0.174577 + 0.984644i \(0.555856\pi\)
\(942\) −24606.1 −0.851073
\(943\) 3864.94 0.133468
\(944\) 12801.6 0.441375
\(945\) 3985.14 0.137182
\(946\) 0 0
\(947\) 17097.1 0.586675 0.293338 0.956009i \(-0.405234\pi\)
0.293338 + 0.956009i \(0.405234\pi\)
\(948\) 11555.4 0.395887
\(949\) −7484.15 −0.256002
\(950\) −500.188 −0.0170824
\(951\) −20393.0 −0.695361
\(952\) 2634.49 0.0896895
\(953\) −3511.84 −0.119370 −0.0596850 0.998217i \(-0.519010\pi\)
−0.0596850 + 0.998217i \(0.519010\pi\)
\(954\) 5582.54 0.189456
\(955\) −7517.46 −0.254722
\(956\) 3425.74 0.115896
\(957\) −28963.3 −0.978317
\(958\) 2072.71 0.0699021
\(959\) 11103.5 0.373878
\(960\) 10786.3 0.362633
\(961\) −27557.5 −0.925028
\(962\) 1404.71 0.0470787
\(963\) −21134.4 −0.707212
\(964\) 6307.03 0.210722
\(965\) −3211.88 −0.107144
\(966\) 1862.85 0.0620457
\(967\) −24101.7 −0.801509 −0.400755 0.916185i \(-0.631252\pi\)
−0.400755 + 0.916185i \(0.631252\pi\)
\(968\) 16176.9 0.537133
\(969\) −182.233 −0.00604146
\(970\) 12594.5 0.416892
\(971\) −43736.1 −1.44548 −0.722739 0.691121i \(-0.757117\pi\)
−0.722739 + 0.691121i \(0.757117\pi\)
\(972\) 8243.37 0.272023
\(973\) 16474.5 0.542803
\(974\) 4349.20 0.143077
\(975\) 5729.75 0.188204
\(976\) −425.602 −0.0139582
\(977\) 10718.7 0.350995 0.175497 0.984480i \(-0.443847\pi\)
0.175497 + 0.984480i \(0.443847\pi\)
\(978\) 14185.5 0.463806
\(979\) 11358.4 0.370801
\(980\) −4613.26 −0.150373
\(981\) 21857.6 0.711374
\(982\) −32042.9 −1.04127
\(983\) −47327.5 −1.53562 −0.767809 0.640679i \(-0.778653\pi\)
−0.767809 + 0.640679i \(0.778653\pi\)
\(984\) 9793.58 0.317284
\(985\) 15606.2 0.504828
\(986\) 12713.1 0.410617
\(987\) 10333.5 0.333252
\(988\) −92.4498 −0.00297694
\(989\) 0 0
\(990\) 3139.87 0.100799
\(991\) −20633.6 −0.661402 −0.330701 0.943736i \(-0.607285\pi\)
−0.330701 + 0.943736i \(0.607285\pi\)
\(992\) −5906.29 −0.189037
\(993\) −28749.9 −0.918781
\(994\) −2975.50 −0.0949470
\(995\) −24337.3 −0.775420
\(996\) −440.526 −0.0140146
\(997\) −18221.2 −0.578806 −0.289403 0.957207i \(-0.593457\pi\)
−0.289403 + 0.957207i \(0.593457\pi\)
\(998\) 1075.62 0.0341163
\(999\) 6683.20 0.211659
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1849.4.a.j.1.33 yes 50
43.42 odd 2 1849.4.a.i.1.18 50
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1849.4.a.i.1.18 50 43.42 odd 2
1849.4.a.j.1.33 yes 50 1.1 even 1 trivial