Properties

Label 2151.4.a.h.1.2
Level $2151$
Weight $4$
Character 2151.1
Self dual yes
Analytic conductor $126.913$
Analytic rank $0$
Dimension $59$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 2151 = 3^{2} \cdot 239 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2151.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(126.913108422\)
Analytic rank: \(0\)
Dimension: \(59\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Character \(\chi\) \(=\) 2151.1

$q$-expansion

\(f(q)\) \(=\) \(q-5.24697 q^{2} +19.5307 q^{4} +10.0958 q^{5} +0.804440 q^{7} -60.5014 q^{8} +O(q^{10})\) \(q-5.24697 q^{2} +19.5307 q^{4} +10.0958 q^{5} +0.804440 q^{7} -60.5014 q^{8} -52.9726 q^{10} +0.829353 q^{11} -86.7323 q^{13} -4.22087 q^{14} +161.203 q^{16} +50.2442 q^{17} +121.120 q^{19} +197.179 q^{20} -4.35159 q^{22} -76.0475 q^{23} -23.0740 q^{25} +455.082 q^{26} +15.7113 q^{28} +40.2936 q^{29} -81.0073 q^{31} -361.819 q^{32} -263.630 q^{34} +8.12150 q^{35} -321.670 q^{37} -635.511 q^{38} -610.813 q^{40} -147.774 q^{41} +32.4253 q^{43} +16.1979 q^{44} +399.019 q^{46} +271.172 q^{47} -342.353 q^{49} +121.068 q^{50} -1693.95 q^{52} -110.872 q^{53} +8.37302 q^{55} -48.6697 q^{56} -211.419 q^{58} +817.455 q^{59} -492.812 q^{61} +425.043 q^{62} +608.826 q^{64} -875.636 q^{65} +862.135 q^{67} +981.306 q^{68} -42.6133 q^{70} +395.164 q^{71} -1025.61 q^{73} +1687.79 q^{74} +2365.55 q^{76} +0.667165 q^{77} +210.661 q^{79} +1627.48 q^{80} +775.365 q^{82} +879.930 q^{83} +507.258 q^{85} -170.135 q^{86} -50.1770 q^{88} -461.975 q^{89} -69.7709 q^{91} -1485.26 q^{92} -1422.83 q^{94} +1222.80 q^{95} -372.791 q^{97} +1796.32 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 59q + 8q^{2} + 238q^{4} + 80q^{5} - 10q^{7} + 96q^{8} + O(q^{10}) \) \( 59q + 8q^{2} + 238q^{4} + 80q^{5} - 10q^{7} + 96q^{8} - 36q^{10} + 132q^{11} + 104q^{13} + 280q^{14} + 822q^{16} + 408q^{17} + 20q^{19} + 800q^{20} - 2q^{22} + 276q^{23} + 1477q^{25} + 780q^{26} + 224q^{28} + 696q^{29} - 380q^{31} + 896q^{32} - 72q^{34} + 700q^{35} + 224q^{37} + 988q^{38} - 258q^{40} + 2706q^{41} - 156q^{43} + 1584q^{44} + 428q^{46} + 1316q^{47} + 2135q^{49} + 1400q^{50} + 1092q^{52} + 1484q^{53} - 992q^{55} + 3360q^{56} - 120q^{58} + 3186q^{59} - 254q^{61} + 1240q^{62} + 3054q^{64} + 5120q^{65} + 288q^{67} + 9420q^{68} + 1108q^{70} + 4468q^{71} - 1770q^{73} + 6214q^{74} + 720q^{76} + 6352q^{77} - 746q^{79} + 7040q^{80} + 276q^{82} + 5484q^{83} + 588q^{85} + 10152q^{86} + 1186q^{88} + 11570q^{89} + 1768q^{91} + 15366q^{92} - 2142q^{94} + 5736q^{95} + 2390q^{97} + 6912q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −5.24697 −1.85509 −0.927543 0.373718i \(-0.878083\pi\)
−0.927543 + 0.373718i \(0.878083\pi\)
\(3\) 0 0
\(4\) 19.5307 2.44134
\(5\) 10.0958 0.903000 0.451500 0.892271i \(-0.350889\pi\)
0.451500 + 0.892271i \(0.350889\pi\)
\(6\) 0 0
\(7\) 0.804440 0.0434357 0.0217178 0.999764i \(-0.493086\pi\)
0.0217178 + 0.999764i \(0.493086\pi\)
\(8\) −60.5014 −2.67381
\(9\) 0 0
\(10\) −52.9726 −1.67514
\(11\) 0.829353 0.0227327 0.0113663 0.999935i \(-0.496382\pi\)
0.0113663 + 0.999935i \(0.496382\pi\)
\(12\) 0 0
\(13\) −86.7323 −1.85040 −0.925201 0.379478i \(-0.876104\pi\)
−0.925201 + 0.379478i \(0.876104\pi\)
\(14\) −4.22087 −0.0805768
\(15\) 0 0
\(16\) 161.203 2.51880
\(17\) 50.2442 0.716824 0.358412 0.933563i \(-0.383318\pi\)
0.358412 + 0.933563i \(0.383318\pi\)
\(18\) 0 0
\(19\) 121.120 1.46246 0.731230 0.682131i \(-0.238947\pi\)
0.731230 + 0.682131i \(0.238947\pi\)
\(20\) 197.179 2.20453
\(21\) 0 0
\(22\) −4.35159 −0.0421711
\(23\) −76.0475 −0.689435 −0.344717 0.938707i \(-0.612025\pi\)
−0.344717 + 0.938707i \(0.612025\pi\)
\(24\) 0 0
\(25\) −23.0740 −0.184592
\(26\) 455.082 3.43265
\(27\) 0 0
\(28\) 15.7113 0.106041
\(29\) 40.2936 0.258011 0.129006 0.991644i \(-0.458821\pi\)
0.129006 + 0.991644i \(0.458821\pi\)
\(30\) 0 0
\(31\) −81.0073 −0.469334 −0.234667 0.972076i \(-0.575400\pi\)
−0.234667 + 0.972076i \(0.575400\pi\)
\(32\) −361.819 −1.99879
\(33\) 0 0
\(34\) −263.630 −1.32977
\(35\) 8.12150 0.0392224
\(36\) 0 0
\(37\) −321.670 −1.42925 −0.714624 0.699509i \(-0.753402\pi\)
−0.714624 + 0.699509i \(0.753402\pi\)
\(38\) −635.511 −2.71299
\(39\) 0 0
\(40\) −610.813 −2.41445
\(41\) −147.774 −0.562887 −0.281444 0.959578i \(-0.590813\pi\)
−0.281444 + 0.959578i \(0.590813\pi\)
\(42\) 0 0
\(43\) 32.4253 0.114996 0.0574978 0.998346i \(-0.481688\pi\)
0.0574978 + 0.998346i \(0.481688\pi\)
\(44\) 16.1979 0.0554982
\(45\) 0 0
\(46\) 399.019 1.27896
\(47\) 271.172 0.841585 0.420792 0.907157i \(-0.361752\pi\)
0.420792 + 0.907157i \(0.361752\pi\)
\(48\) 0 0
\(49\) −342.353 −0.998113
\(50\) 121.068 0.342433
\(51\) 0 0
\(52\) −1693.95 −4.51746
\(53\) −110.872 −0.287347 −0.143674 0.989625i \(-0.545892\pi\)
−0.143674 + 0.989625i \(0.545892\pi\)
\(54\) 0 0
\(55\) 8.37302 0.0205276
\(56\) −48.6697 −0.116139
\(57\) 0 0
\(58\) −211.419 −0.478633
\(59\) 817.455 1.80379 0.901894 0.431957i \(-0.142177\pi\)
0.901894 + 0.431957i \(0.142177\pi\)
\(60\) 0 0
\(61\) −492.812 −1.03440 −0.517198 0.855866i \(-0.673025\pi\)
−0.517198 + 0.855866i \(0.673025\pi\)
\(62\) 425.043 0.870654
\(63\) 0 0
\(64\) 608.826 1.18911
\(65\) −875.636 −1.67091
\(66\) 0 0
\(67\) 862.135 1.57204 0.786019 0.618202i \(-0.212139\pi\)
0.786019 + 0.618202i \(0.212139\pi\)
\(68\) 981.306 1.75001
\(69\) 0 0
\(70\) −42.6133 −0.0727609
\(71\) 395.164 0.660526 0.330263 0.943889i \(-0.392863\pi\)
0.330263 + 0.943889i \(0.392863\pi\)
\(72\) 0 0
\(73\) −1025.61 −1.64436 −0.822181 0.569227i \(-0.807243\pi\)
−0.822181 + 0.569227i \(0.807243\pi\)
\(74\) 1687.79 2.65138
\(75\) 0 0
\(76\) 2365.55 3.57036
\(77\) 0.667165 0.000987409 0
\(78\) 0 0
\(79\) 210.661 0.300015 0.150007 0.988685i \(-0.452070\pi\)
0.150007 + 0.988685i \(0.452070\pi\)
\(80\) 1627.48 2.27448
\(81\) 0 0
\(82\) 775.365 1.04420
\(83\) 879.930 1.16367 0.581836 0.813306i \(-0.302334\pi\)
0.581836 + 0.813306i \(0.302334\pi\)
\(84\) 0 0
\(85\) 507.258 0.647292
\(86\) −170.135 −0.213327
\(87\) 0 0
\(88\) −50.1770 −0.0607828
\(89\) −461.975 −0.550216 −0.275108 0.961413i \(-0.588714\pi\)
−0.275108 + 0.961413i \(0.588714\pi\)
\(90\) 0 0
\(91\) −69.7709 −0.0803734
\(92\) −1485.26 −1.68314
\(93\) 0 0
\(94\) −1422.83 −1.56121
\(95\) 1222.80 1.32060
\(96\) 0 0
\(97\) −372.791 −0.390218 −0.195109 0.980782i \(-0.562506\pi\)
−0.195109 + 0.980782i \(0.562506\pi\)
\(98\) 1796.32 1.85159
\(99\) 0 0
\(100\) −450.651 −0.450651
\(101\) 982.265 0.967713 0.483856 0.875147i \(-0.339236\pi\)
0.483856 + 0.875147i \(0.339236\pi\)
\(102\) 0 0
\(103\) 1237.81 1.18413 0.592065 0.805890i \(-0.298313\pi\)
0.592065 + 0.805890i \(0.298313\pi\)
\(104\) 5247.43 4.94762
\(105\) 0 0
\(106\) 581.741 0.533054
\(107\) 1287.57 1.16331 0.581657 0.813434i \(-0.302405\pi\)
0.581657 + 0.813434i \(0.302405\pi\)
\(108\) 0 0
\(109\) 2123.88 1.86634 0.933169 0.359438i \(-0.117032\pi\)
0.933169 + 0.359438i \(0.117032\pi\)
\(110\) −43.9330 −0.0380804
\(111\) 0 0
\(112\) 129.678 0.109406
\(113\) −633.826 −0.527658 −0.263829 0.964569i \(-0.584985\pi\)
−0.263829 + 0.964569i \(0.584985\pi\)
\(114\) 0 0
\(115\) −767.763 −0.622559
\(116\) 786.962 0.629893
\(117\) 0 0
\(118\) −4289.16 −3.34618
\(119\) 40.4184 0.0311357
\(120\) 0 0
\(121\) −1330.31 −0.999483
\(122\) 2585.77 1.91889
\(123\) 0 0
\(124\) −1582.13 −1.14580
\(125\) −1494.93 −1.06969
\(126\) 0 0
\(127\) −567.851 −0.396761 −0.198380 0.980125i \(-0.563568\pi\)
−0.198380 + 0.980125i \(0.563568\pi\)
\(128\) −299.943 −0.207121
\(129\) 0 0
\(130\) 4594.44 3.09968
\(131\) 1255.97 0.837671 0.418836 0.908062i \(-0.362438\pi\)
0.418836 + 0.908062i \(0.362438\pi\)
\(132\) 0 0
\(133\) 97.4334 0.0635229
\(134\) −4523.60 −2.91627
\(135\) 0 0
\(136\) −3039.85 −1.91665
\(137\) −1960.41 −1.22255 −0.611273 0.791420i \(-0.709342\pi\)
−0.611273 + 0.791420i \(0.709342\pi\)
\(138\) 0 0
\(139\) 36.7466 0.0224231 0.0112115 0.999937i \(-0.496431\pi\)
0.0112115 + 0.999937i \(0.496431\pi\)
\(140\) 158.619 0.0957552
\(141\) 0 0
\(142\) −2073.41 −1.22533
\(143\) −71.9318 −0.0420646
\(144\) 0 0
\(145\) 406.797 0.232984
\(146\) 5381.34 3.05043
\(147\) 0 0
\(148\) −6282.44 −3.48928
\(149\) 1648.67 0.906470 0.453235 0.891391i \(-0.350270\pi\)
0.453235 + 0.891391i \(0.350270\pi\)
\(150\) 0 0
\(151\) 418.856 0.225735 0.112868 0.993610i \(-0.463996\pi\)
0.112868 + 0.993610i \(0.463996\pi\)
\(152\) −7327.91 −3.91034
\(153\) 0 0
\(154\) −3.50060 −0.00183173
\(155\) −817.837 −0.423808
\(156\) 0 0
\(157\) 1258.72 0.639854 0.319927 0.947442i \(-0.396342\pi\)
0.319927 + 0.947442i \(0.396342\pi\)
\(158\) −1105.33 −0.556553
\(159\) 0 0
\(160\) −3652.86 −1.80490
\(161\) −61.1756 −0.0299460
\(162\) 0 0
\(163\) 1096.41 0.526855 0.263427 0.964679i \(-0.415147\pi\)
0.263427 + 0.964679i \(0.415147\pi\)
\(164\) −2886.13 −1.37420
\(165\) 0 0
\(166\) −4616.97 −2.15871
\(167\) −2947.26 −1.36567 −0.682833 0.730575i \(-0.739252\pi\)
−0.682833 + 0.730575i \(0.739252\pi\)
\(168\) 0 0
\(169\) 5325.50 2.42399
\(170\) −2661.57 −1.20078
\(171\) 0 0
\(172\) 633.290 0.280744
\(173\) 3254.19 1.43012 0.715062 0.699061i \(-0.246398\pi\)
0.715062 + 0.699061i \(0.246398\pi\)
\(174\) 0 0
\(175\) −18.5616 −0.00801786
\(176\) 133.695 0.0572591
\(177\) 0 0
\(178\) 2423.97 1.02070
\(179\) 690.970 0.288523 0.144261 0.989540i \(-0.453919\pi\)
0.144261 + 0.989540i \(0.453919\pi\)
\(180\) 0 0
\(181\) 4480.00 1.83975 0.919877 0.392207i \(-0.128288\pi\)
0.919877 + 0.392207i \(0.128288\pi\)
\(182\) 366.086 0.149100
\(183\) 0 0
\(184\) 4600.98 1.84342
\(185\) −3247.53 −1.29061
\(186\) 0 0
\(187\) 41.6702 0.0162953
\(188\) 5296.18 2.05459
\(189\) 0 0
\(190\) −6416.02 −2.44983
\(191\) 3071.51 1.16359 0.581797 0.813334i \(-0.302350\pi\)
0.581797 + 0.813334i \(0.302350\pi\)
\(192\) 0 0
\(193\) −1090.71 −0.406793 −0.203397 0.979096i \(-0.565198\pi\)
−0.203397 + 0.979096i \(0.565198\pi\)
\(194\) 1956.02 0.723888
\(195\) 0 0
\(196\) −6686.40 −2.43673
\(197\) −4977.93 −1.80032 −0.900160 0.435560i \(-0.856550\pi\)
−0.900160 + 0.435560i \(0.856550\pi\)
\(198\) 0 0
\(199\) −1050.73 −0.374294 −0.187147 0.982332i \(-0.559924\pi\)
−0.187147 + 0.982332i \(0.559924\pi\)
\(200\) 1396.01 0.493563
\(201\) 0 0
\(202\) −5153.92 −1.79519
\(203\) 32.4137 0.0112069
\(204\) 0 0
\(205\) −1491.90 −0.508287
\(206\) −6494.77 −2.19666
\(207\) 0 0
\(208\) −13981.5 −4.66080
\(209\) 100.451 0.0332456
\(210\) 0 0
\(211\) −467.437 −0.152510 −0.0762551 0.997088i \(-0.524296\pi\)
−0.0762551 + 0.997088i \(0.524296\pi\)
\(212\) −2165.41 −0.701513
\(213\) 0 0
\(214\) −6755.87 −2.15804
\(215\) 327.361 0.103841
\(216\) 0 0
\(217\) −65.1655 −0.0203858
\(218\) −11143.9 −3.46222
\(219\) 0 0
\(220\) 163.531 0.0501149
\(221\) −4357.80 −1.32641
\(222\) 0 0
\(223\) −1929.50 −0.579411 −0.289706 0.957116i \(-0.593557\pi\)
−0.289706 + 0.957116i \(0.593557\pi\)
\(224\) −291.061 −0.0868185
\(225\) 0 0
\(226\) 3325.67 0.978851
\(227\) −3767.18 −1.10148 −0.550741 0.834676i \(-0.685655\pi\)
−0.550741 + 0.834676i \(0.685655\pi\)
\(228\) 0 0
\(229\) 3912.29 1.12896 0.564480 0.825447i \(-0.309077\pi\)
0.564480 + 0.825447i \(0.309077\pi\)
\(230\) 4028.43 1.15490
\(231\) 0 0
\(232\) −2437.82 −0.689873
\(233\) 2768.47 0.778406 0.389203 0.921152i \(-0.372750\pi\)
0.389203 + 0.921152i \(0.372750\pi\)
\(234\) 0 0
\(235\) 2737.71 0.759950
\(236\) 15965.5 4.40366
\(237\) 0 0
\(238\) −212.074 −0.0577594
\(239\) −239.000 −0.0646846
\(240\) 0 0
\(241\) 649.271 0.173540 0.0867701 0.996228i \(-0.472345\pi\)
0.0867701 + 0.996228i \(0.472345\pi\)
\(242\) 6980.11 1.85413
\(243\) 0 0
\(244\) −9624.98 −2.52531
\(245\) −3456.34 −0.901296
\(246\) 0 0
\(247\) −10505.0 −2.70614
\(248\) 4901.05 1.25491
\(249\) 0 0
\(250\) 7843.86 1.98436
\(251\) −2455.96 −0.617604 −0.308802 0.951126i \(-0.599928\pi\)
−0.308802 + 0.951126i \(0.599928\pi\)
\(252\) 0 0
\(253\) −63.0702 −0.0156727
\(254\) 2979.50 0.736025
\(255\) 0 0
\(256\) −3296.82 −0.804887
\(257\) −382.561 −0.0928541 −0.0464271 0.998922i \(-0.514784\pi\)
−0.0464271 + 0.998922i \(0.514784\pi\)
\(258\) 0 0
\(259\) −258.764 −0.0620803
\(260\) −17101.8 −4.07927
\(261\) 0 0
\(262\) −6590.06 −1.55395
\(263\) 2500.94 0.586367 0.293183 0.956056i \(-0.405285\pi\)
0.293183 + 0.956056i \(0.405285\pi\)
\(264\) 0 0
\(265\) −1119.34 −0.259474
\(266\) −511.231 −0.117840
\(267\) 0 0
\(268\) 16838.1 3.83788
\(269\) 7654.24 1.73490 0.867448 0.497527i \(-0.165759\pi\)
0.867448 + 0.497527i \(0.165759\pi\)
\(270\) 0 0
\(271\) −7244.71 −1.62393 −0.811964 0.583707i \(-0.801602\pi\)
−0.811964 + 0.583707i \(0.801602\pi\)
\(272\) 8099.54 1.80554
\(273\) 0 0
\(274\) 10286.2 2.26793
\(275\) −19.1365 −0.00419626
\(276\) 0 0
\(277\) 3761.47 0.815901 0.407951 0.913004i \(-0.366244\pi\)
0.407951 + 0.913004i \(0.366244\pi\)
\(278\) −192.809 −0.0415967
\(279\) 0 0
\(280\) −491.362 −0.104873
\(281\) 1308.50 0.277789 0.138894 0.990307i \(-0.455645\pi\)
0.138894 + 0.990307i \(0.455645\pi\)
\(282\) 0 0
\(283\) −6594.73 −1.38521 −0.692607 0.721315i \(-0.743538\pi\)
−0.692607 + 0.721315i \(0.743538\pi\)
\(284\) 7717.84 1.61257
\(285\) 0 0
\(286\) 377.424 0.0780334
\(287\) −118.875 −0.0244494
\(288\) 0 0
\(289\) −2388.52 −0.486163
\(290\) −2134.45 −0.432205
\(291\) 0 0
\(292\) −20030.9 −4.01445
\(293\) 54.5617 0.0108789 0.00543947 0.999985i \(-0.498269\pi\)
0.00543947 + 0.999985i \(0.498269\pi\)
\(294\) 0 0
\(295\) 8252.89 1.62882
\(296\) 19461.5 3.82154
\(297\) 0 0
\(298\) −8650.51 −1.68158
\(299\) 6595.78 1.27573
\(300\) 0 0
\(301\) 26.0842 0.00499491
\(302\) −2197.73 −0.418758
\(303\) 0 0
\(304\) 19524.9 3.68365
\(305\) −4975.36 −0.934059
\(306\) 0 0
\(307\) 401.434 0.0746288 0.0373144 0.999304i \(-0.488120\pi\)
0.0373144 + 0.999304i \(0.488120\pi\)
\(308\) 13.0302 0.00241060
\(309\) 0 0
\(310\) 4291.17 0.786200
\(311\) −181.977 −0.0331800 −0.0165900 0.999862i \(-0.505281\pi\)
−0.0165900 + 0.999862i \(0.505281\pi\)
\(312\) 0 0
\(313\) 3794.05 0.685151 0.342575 0.939490i \(-0.388701\pi\)
0.342575 + 0.939490i \(0.388701\pi\)
\(314\) −6604.49 −1.18698
\(315\) 0 0
\(316\) 4114.35 0.732438
\(317\) 5855.74 1.03751 0.518756 0.854923i \(-0.326395\pi\)
0.518756 + 0.854923i \(0.326395\pi\)
\(318\) 0 0
\(319\) 33.4176 0.00586529
\(320\) 6146.61 1.07377
\(321\) 0 0
\(322\) 320.987 0.0555525
\(323\) 6085.56 1.04833
\(324\) 0 0
\(325\) 2001.26 0.341569
\(326\) −5752.82 −0.977360
\(327\) 0 0
\(328\) 8940.52 1.50505
\(329\) 218.141 0.0365548
\(330\) 0 0
\(331\) 5803.68 0.963744 0.481872 0.876242i \(-0.339957\pi\)
0.481872 + 0.876242i \(0.339957\pi\)
\(332\) 17185.7 2.84092
\(333\) 0 0
\(334\) 15464.2 2.53343
\(335\) 8703.98 1.41955
\(336\) 0 0
\(337\) −9871.07 −1.59558 −0.797792 0.602933i \(-0.793999\pi\)
−0.797792 + 0.602933i \(0.793999\pi\)
\(338\) −27942.8 −4.49670
\(339\) 0 0
\(340\) 9907.11 1.58026
\(341\) −67.1837 −0.0106692
\(342\) 0 0
\(343\) −551.325 −0.0867894
\(344\) −1961.78 −0.307477
\(345\) 0 0
\(346\) −17074.7 −2.65300
\(347\) −1360.44 −0.210468 −0.105234 0.994447i \(-0.533559\pi\)
−0.105234 + 0.994447i \(0.533559\pi\)
\(348\) 0 0
\(349\) 7884.72 1.20934 0.604670 0.796476i \(-0.293305\pi\)
0.604670 + 0.796476i \(0.293305\pi\)
\(350\) 97.3923 0.0148738
\(351\) 0 0
\(352\) −300.076 −0.0454377
\(353\) −3655.13 −0.551113 −0.275557 0.961285i \(-0.588862\pi\)
−0.275557 + 0.961285i \(0.588862\pi\)
\(354\) 0 0
\(355\) 3989.51 0.596454
\(356\) −9022.70 −1.34326
\(357\) 0 0
\(358\) −3625.50 −0.535234
\(359\) −10645.2 −1.56499 −0.782497 0.622654i \(-0.786054\pi\)
−0.782497 + 0.622654i \(0.786054\pi\)
\(360\) 0 0
\(361\) 7810.96 1.13879
\(362\) −23506.4 −3.41290
\(363\) 0 0
\(364\) −1362.68 −0.196219
\(365\) −10354.4 −1.48486
\(366\) 0 0
\(367\) 5002.35 0.711500 0.355750 0.934581i \(-0.384225\pi\)
0.355750 + 0.934581i \(0.384225\pi\)
\(368\) −12259.1 −1.73655
\(369\) 0 0
\(370\) 17039.7 2.39419
\(371\) −89.1896 −0.0124811
\(372\) 0 0
\(373\) 9773.39 1.35669 0.678347 0.734741i \(-0.262697\pi\)
0.678347 + 0.734741i \(0.262697\pi\)
\(374\) −218.642 −0.0302292
\(375\) 0 0
\(376\) −16406.3 −2.25024
\(377\) −3494.75 −0.477424
\(378\) 0 0
\(379\) 565.733 0.0766748 0.0383374 0.999265i \(-0.487794\pi\)
0.0383374 + 0.999265i \(0.487794\pi\)
\(380\) 23882.3 3.22404
\(381\) 0 0
\(382\) −16116.1 −2.15857
\(383\) 7907.81 1.05501 0.527507 0.849551i \(-0.323127\pi\)
0.527507 + 0.849551i \(0.323127\pi\)
\(384\) 0 0
\(385\) 6.73559 0.000891630 0
\(386\) 5722.93 0.754636
\(387\) 0 0
\(388\) −7280.88 −0.952656
\(389\) −2665.09 −0.347367 −0.173683 0.984802i \(-0.555567\pi\)
−0.173683 + 0.984802i \(0.555567\pi\)
\(390\) 0 0
\(391\) −3820.95 −0.494204
\(392\) 20712.8 2.66876
\(393\) 0 0
\(394\) 26119.1 3.33975
\(395\) 2126.80 0.270913
\(396\) 0 0
\(397\) 1845.78 0.233343 0.116671 0.993171i \(-0.462778\pi\)
0.116671 + 0.993171i \(0.462778\pi\)
\(398\) 5513.17 0.694347
\(399\) 0 0
\(400\) −3719.60 −0.464950
\(401\) −8399.16 −1.04597 −0.522985 0.852342i \(-0.675182\pi\)
−0.522985 + 0.852342i \(0.675182\pi\)
\(402\) 0 0
\(403\) 7025.95 0.868456
\(404\) 19184.3 2.36252
\(405\) 0 0
\(406\) −170.074 −0.0207897
\(407\) −266.778 −0.0324906
\(408\) 0 0
\(409\) 103.382 0.0124986 0.00624929 0.999980i \(-0.498011\pi\)
0.00624929 + 0.999980i \(0.498011\pi\)
\(410\) 7827.96 0.942916
\(411\) 0 0
\(412\) 24175.4 2.89086
\(413\) 657.593 0.0783487
\(414\) 0 0
\(415\) 8883.63 1.05080
\(416\) 31381.4 3.69856
\(417\) 0 0
\(418\) −527.063 −0.0616735
\(419\) 10313.4 1.20249 0.601247 0.799063i \(-0.294671\pi\)
0.601247 + 0.799063i \(0.294671\pi\)
\(420\) 0 0
\(421\) 4651.67 0.538500 0.269250 0.963070i \(-0.413224\pi\)
0.269250 + 0.963070i \(0.413224\pi\)
\(422\) 2452.63 0.282919
\(423\) 0 0
\(424\) 6707.90 0.768312
\(425\) −1159.33 −0.132320
\(426\) 0 0
\(427\) −396.438 −0.0449297
\(428\) 25147.3 2.84004
\(429\) 0 0
\(430\) −1717.65 −0.192634
\(431\) −17304.9 −1.93398 −0.966991 0.254811i \(-0.917987\pi\)
−0.966991 + 0.254811i \(0.917987\pi\)
\(432\) 0 0
\(433\) 4053.60 0.449893 0.224947 0.974371i \(-0.427779\pi\)
0.224947 + 0.974371i \(0.427779\pi\)
\(434\) 341.922 0.0378174
\(435\) 0 0
\(436\) 41480.9 4.55637
\(437\) −9210.84 −1.00827
\(438\) 0 0
\(439\) 11949.7 1.29916 0.649578 0.760295i \(-0.274946\pi\)
0.649578 + 0.760295i \(0.274946\pi\)
\(440\) −506.579 −0.0548869
\(441\) 0 0
\(442\) 22865.3 2.46061
\(443\) 9196.35 0.986302 0.493151 0.869944i \(-0.335845\pi\)
0.493151 + 0.869944i \(0.335845\pi\)
\(444\) 0 0
\(445\) −4664.02 −0.496845
\(446\) 10124.0 1.07486
\(447\) 0 0
\(448\) 489.764 0.0516499
\(449\) 14223.8 1.49501 0.747506 0.664255i \(-0.231251\pi\)
0.747506 + 0.664255i \(0.231251\pi\)
\(450\) 0 0
\(451\) −122.557 −0.0127959
\(452\) −12379.1 −1.28819
\(453\) 0 0
\(454\) 19766.3 2.04334
\(455\) −704.396 −0.0725772
\(456\) 0 0
\(457\) 8717.68 0.892333 0.446166 0.894950i \(-0.352789\pi\)
0.446166 + 0.894950i \(0.352789\pi\)
\(458\) −20527.7 −2.09432
\(459\) 0 0
\(460\) −14995.0 −1.51988
\(461\) 627.326 0.0633785 0.0316893 0.999498i \(-0.489911\pi\)
0.0316893 + 0.999498i \(0.489911\pi\)
\(462\) 0 0
\(463\) −2601.88 −0.261165 −0.130583 0.991437i \(-0.541685\pi\)
−0.130583 + 0.991437i \(0.541685\pi\)
\(464\) 6495.46 0.649880
\(465\) 0 0
\(466\) −14526.1 −1.44401
\(467\) 12141.3 1.20307 0.601533 0.798848i \(-0.294557\pi\)
0.601533 + 0.798848i \(0.294557\pi\)
\(468\) 0 0
\(469\) 693.536 0.0682825
\(470\) −14364.7 −1.40977
\(471\) 0 0
\(472\) −49457.1 −4.82299
\(473\) 26.8920 0.00261416
\(474\) 0 0
\(475\) −2794.71 −0.269958
\(476\) 789.402 0.0760129
\(477\) 0 0
\(478\) 1254.03 0.119995
\(479\) 7262.80 0.692789 0.346394 0.938089i \(-0.387406\pi\)
0.346394 + 0.938089i \(0.387406\pi\)
\(480\) 0 0
\(481\) 27899.2 2.64468
\(482\) −3406.71 −0.321932
\(483\) 0 0
\(484\) −25982.0 −2.44008
\(485\) −3763.64 −0.352367
\(486\) 0 0
\(487\) 6346.92 0.590568 0.295284 0.955410i \(-0.404586\pi\)
0.295284 + 0.955410i \(0.404586\pi\)
\(488\) 29815.8 2.76578
\(489\) 0 0
\(490\) 18135.3 1.67198
\(491\) 4676.73 0.429853 0.214926 0.976630i \(-0.431049\pi\)
0.214926 + 0.976630i \(0.431049\pi\)
\(492\) 0 0
\(493\) 2024.52 0.184949
\(494\) 55119.4 5.02012
\(495\) 0 0
\(496\) −13058.7 −1.18216
\(497\) 317.885 0.0286904
\(498\) 0 0
\(499\) −4655.75 −0.417676 −0.208838 0.977950i \(-0.566968\pi\)
−0.208838 + 0.977950i \(0.566968\pi\)
\(500\) −29197.1 −2.61147
\(501\) 0 0
\(502\) 12886.3 1.14571
\(503\) −2338.40 −0.207285 −0.103642 0.994615i \(-0.533050\pi\)
−0.103642 + 0.994615i \(0.533050\pi\)
\(504\) 0 0
\(505\) 9916.79 0.873844
\(506\) 330.928 0.0290742
\(507\) 0 0
\(508\) −11090.5 −0.968628
\(509\) −7899.22 −0.687872 −0.343936 0.938993i \(-0.611760\pi\)
−0.343936 + 0.938993i \(0.611760\pi\)
\(510\) 0 0
\(511\) −825.040 −0.0714239
\(512\) 19697.8 1.70025
\(513\) 0 0
\(514\) 2007.29 0.172252
\(515\) 12496.8 1.06927
\(516\) 0 0
\(517\) 224.897 0.0191315
\(518\) 1357.73 0.115164
\(519\) 0 0
\(520\) 52977.2 4.46770
\(521\) −7815.67 −0.657219 −0.328609 0.944466i \(-0.606580\pi\)
−0.328609 + 0.944466i \(0.606580\pi\)
\(522\) 0 0
\(523\) 19469.3 1.62779 0.813895 0.581012i \(-0.197343\pi\)
0.813895 + 0.581012i \(0.197343\pi\)
\(524\) 24530.1 2.04504
\(525\) 0 0
\(526\) −13122.4 −1.08776
\(527\) −4070.15 −0.336430
\(528\) 0 0
\(529\) −6383.78 −0.524680
\(530\) 5873.17 0.481347
\(531\) 0 0
\(532\) 1902.95 0.155081
\(533\) 12816.8 1.04157
\(534\) 0 0
\(535\) 12999.1 1.05047
\(536\) −52160.4 −4.20333
\(537\) 0 0
\(538\) −40161.6 −3.21838
\(539\) −283.932 −0.0226898
\(540\) 0 0
\(541\) −8167.14 −0.649044 −0.324522 0.945878i \(-0.605203\pi\)
−0.324522 + 0.945878i \(0.605203\pi\)
\(542\) 38012.8 3.01253
\(543\) 0 0
\(544\) −18179.3 −1.43278
\(545\) 21442.4 1.68530
\(546\) 0 0
\(547\) −300.206 −0.0234660 −0.0117330 0.999931i \(-0.503735\pi\)
−0.0117330 + 0.999931i \(0.503735\pi\)
\(548\) −38288.2 −2.98465
\(549\) 0 0
\(550\) 100.409 0.00778443
\(551\) 4880.34 0.377331
\(552\) 0 0
\(553\) 169.464 0.0130313
\(554\) −19736.3 −1.51357
\(555\) 0 0
\(556\) 717.688 0.0547424
\(557\) −21047.1 −1.60106 −0.800532 0.599289i \(-0.795450\pi\)
−0.800532 + 0.599289i \(0.795450\pi\)
\(558\) 0 0
\(559\) −2812.32 −0.212788
\(560\) 1309.21 0.0987935
\(561\) 0 0
\(562\) −6865.67 −0.515322
\(563\) 337.232 0.0252445 0.0126222 0.999920i \(-0.495982\pi\)
0.0126222 + 0.999920i \(0.495982\pi\)
\(564\) 0 0
\(565\) −6399.01 −0.476475
\(566\) 34602.3 2.56969
\(567\) 0 0
\(568\) −23908.0 −1.76612
\(569\) 16539.0 1.21854 0.609270 0.792963i \(-0.291462\pi\)
0.609270 + 0.792963i \(0.291462\pi\)
\(570\) 0 0
\(571\) −9813.91 −0.719263 −0.359632 0.933094i \(-0.617098\pi\)
−0.359632 + 0.933094i \(0.617098\pi\)
\(572\) −1404.88 −0.102694
\(573\) 0 0
\(574\) 623.734 0.0453557
\(575\) 1754.72 0.127264
\(576\) 0 0
\(577\) 9201.66 0.663900 0.331950 0.943297i \(-0.392293\pi\)
0.331950 + 0.943297i \(0.392293\pi\)
\(578\) 12532.5 0.901873
\(579\) 0 0
\(580\) 7945.05 0.568793
\(581\) 707.851 0.0505449
\(582\) 0 0
\(583\) −91.9519 −0.00653217
\(584\) 62050.7 4.39671
\(585\) 0 0
\(586\) −286.284 −0.0201813
\(587\) 22231.6 1.56320 0.781599 0.623782i \(-0.214405\pi\)
0.781599 + 0.623782i \(0.214405\pi\)
\(588\) 0 0
\(589\) −9811.57 −0.686382
\(590\) −43302.7 −3.02160
\(591\) 0 0
\(592\) −51854.3 −3.60000
\(593\) −11178.1 −0.774081 −0.387040 0.922063i \(-0.626503\pi\)
−0.387040 + 0.922063i \(0.626503\pi\)
\(594\) 0 0
\(595\) 408.058 0.0281156
\(596\) 32199.6 2.21300
\(597\) 0 0
\(598\) −34607.9 −2.36659
\(599\) −3692.27 −0.251856 −0.125928 0.992039i \(-0.540191\pi\)
−0.125928 + 0.992039i \(0.540191\pi\)
\(600\) 0 0
\(601\) −14403.8 −0.977608 −0.488804 0.872394i \(-0.662567\pi\)
−0.488804 + 0.872394i \(0.662567\pi\)
\(602\) −136.863 −0.00926599
\(603\) 0 0
\(604\) 8180.57 0.551097
\(605\) −13430.6 −0.902533
\(606\) 0 0
\(607\) 17874.2 1.19521 0.597604 0.801792i \(-0.296120\pi\)
0.597604 + 0.801792i \(0.296120\pi\)
\(608\) −43823.3 −2.92314
\(609\) 0 0
\(610\) 26105.6 1.73276
\(611\) −23519.4 −1.55727
\(612\) 0 0
\(613\) 315.861 0.0208116 0.0104058 0.999946i \(-0.496688\pi\)
0.0104058 + 0.999946i \(0.496688\pi\)
\(614\) −2106.31 −0.138443
\(615\) 0 0
\(616\) −40.3644 −0.00264014
\(617\) 7184.59 0.468786 0.234393 0.972142i \(-0.424690\pi\)
0.234393 + 0.972142i \(0.424690\pi\)
\(618\) 0 0
\(619\) −2840.58 −0.184447 −0.0922235 0.995738i \(-0.529397\pi\)
−0.0922235 + 0.995738i \(0.529397\pi\)
\(620\) −15972.9 −1.03466
\(621\) 0 0
\(622\) 954.829 0.0615517
\(623\) −371.631 −0.0238990
\(624\) 0 0
\(625\) −12208.3 −0.781334
\(626\) −19907.3 −1.27101
\(627\) 0 0
\(628\) 24583.8 1.56210
\(629\) −16162.0 −1.02452
\(630\) 0 0
\(631\) 836.274 0.0527599 0.0263800 0.999652i \(-0.491602\pi\)
0.0263800 + 0.999652i \(0.491602\pi\)
\(632\) −12745.3 −0.802183
\(633\) 0 0
\(634\) −30724.9 −1.92467
\(635\) −5732.93 −0.358275
\(636\) 0 0
\(637\) 29693.1 1.84691
\(638\) −175.341 −0.0108806
\(639\) 0 0
\(640\) −3028.17 −0.187030
\(641\) 31860.5 1.96320 0.981601 0.190944i \(-0.0611548\pi\)
0.981601 + 0.190944i \(0.0611548\pi\)
\(642\) 0 0
\(643\) 26267.6 1.61103 0.805517 0.592573i \(-0.201888\pi\)
0.805517 + 0.592573i \(0.201888\pi\)
\(644\) −1194.80 −0.0731085
\(645\) 0 0
\(646\) −31930.8 −1.94474
\(647\) −20151.8 −1.22450 −0.612248 0.790666i \(-0.709735\pi\)
−0.612248 + 0.790666i \(0.709735\pi\)
\(648\) 0 0
\(649\) 677.959 0.0410049
\(650\) −10500.6 −0.633639
\(651\) 0 0
\(652\) 21413.6 1.28623
\(653\) −26410.1 −1.58270 −0.791352 0.611361i \(-0.790622\pi\)
−0.791352 + 0.611361i \(0.790622\pi\)
\(654\) 0 0
\(655\) 12680.1 0.756417
\(656\) −23821.6 −1.41780
\(657\) 0 0
\(658\) −1144.58 −0.0678122
\(659\) −720.199 −0.0425721 −0.0212860 0.999773i \(-0.506776\pi\)
−0.0212860 + 0.999773i \(0.506776\pi\)
\(660\) 0 0
\(661\) −20377.6 −1.19909 −0.599544 0.800342i \(-0.704651\pi\)
−0.599544 + 0.800342i \(0.704651\pi\)
\(662\) −30451.8 −1.78783
\(663\) 0 0
\(664\) −53237.0 −3.11144
\(665\) 983.672 0.0573612
\(666\) 0 0
\(667\) −3064.22 −0.177882
\(668\) −57562.2 −3.33406
\(669\) 0 0
\(670\) −45669.6 −2.63339
\(671\) −408.716 −0.0235146
\(672\) 0 0
\(673\) −7590.31 −0.434747 −0.217374 0.976088i \(-0.569749\pi\)
−0.217374 + 0.976088i \(0.569749\pi\)
\(674\) 51793.3 2.95994
\(675\) 0 0
\(676\) 104011. 5.91778
\(677\) −27177.2 −1.54284 −0.771421 0.636325i \(-0.780454\pi\)
−0.771421 + 0.636325i \(0.780454\pi\)
\(678\) 0 0
\(679\) −299.888 −0.0169494
\(680\) −30689.8 −1.73074
\(681\) 0 0
\(682\) 352.511 0.0197923
\(683\) 23544.6 1.31905 0.659524 0.751684i \(-0.270758\pi\)
0.659524 + 0.751684i \(0.270758\pi\)
\(684\) 0 0
\(685\) −19792.0 −1.10396
\(686\) 2892.79 0.161002
\(687\) 0 0
\(688\) 5227.07 0.289652
\(689\) 9616.17 0.531708
\(690\) 0 0
\(691\) −5593.57 −0.307944 −0.153972 0.988075i \(-0.549207\pi\)
−0.153972 + 0.988075i \(0.549207\pi\)
\(692\) 63556.7 3.49142
\(693\) 0 0
\(694\) 7138.22 0.390437
\(695\) 370.988 0.0202480
\(696\) 0 0
\(697\) −7424.78 −0.403491
\(698\) −41370.9 −2.24343
\(699\) 0 0
\(700\) −362.522 −0.0195743
\(701\) 29596.7 1.59465 0.797327 0.603548i \(-0.206247\pi\)
0.797327 + 0.603548i \(0.206247\pi\)
\(702\) 0 0
\(703\) −38960.5 −2.09022
\(704\) 504.932 0.0270317
\(705\) 0 0
\(706\) 19178.4 1.02236
\(707\) 790.173 0.0420333
\(708\) 0 0
\(709\) 11431.8 0.605542 0.302771 0.953063i \(-0.402088\pi\)
0.302771 + 0.953063i \(0.402088\pi\)
\(710\) −20932.9 −1.10647
\(711\) 0 0
\(712\) 27950.1 1.47117
\(713\) 6160.40 0.323575
\(714\) 0 0
\(715\) −726.212 −0.0379843
\(716\) 13495.1 0.704382
\(717\) 0 0
\(718\) 55855.2 2.90320
\(719\) −14447.3 −0.749364 −0.374682 0.927153i \(-0.622248\pi\)
−0.374682 + 0.927153i \(0.622248\pi\)
\(720\) 0 0
\(721\) 995.746 0.0514335
\(722\) −40983.9 −2.11255
\(723\) 0 0
\(724\) 87497.6 4.49147
\(725\) −929.732 −0.0476267
\(726\) 0 0
\(727\) −30498.2 −1.55587 −0.777935 0.628345i \(-0.783733\pi\)
−0.777935 + 0.628345i \(0.783733\pi\)
\(728\) 4221.24 0.214903
\(729\) 0 0
\(730\) 54329.2 2.75454
\(731\) 1629.18 0.0824317
\(732\) 0 0
\(733\) −3580.60 −0.180426 −0.0902132 0.995922i \(-0.528755\pi\)
−0.0902132 + 0.995922i \(0.528755\pi\)
\(734\) −26247.2 −1.31989
\(735\) 0 0
\(736\) 27515.4 1.37803
\(737\) 715.015 0.0357366
\(738\) 0 0
\(739\) 25098.0 1.24932 0.624658 0.780899i \(-0.285238\pi\)
0.624658 + 0.780899i \(0.285238\pi\)
\(740\) −63426.6 −3.15082
\(741\) 0 0
\(742\) 467.976 0.0231535
\(743\) 15887.1 0.784443 0.392221 0.919871i \(-0.371707\pi\)
0.392221 + 0.919871i \(0.371707\pi\)
\(744\) 0 0
\(745\) 16644.7 0.818542
\(746\) −51280.7 −2.51678
\(747\) 0 0
\(748\) 813.850 0.0397825
\(749\) 1035.78 0.0505293
\(750\) 0 0
\(751\) −5066.16 −0.246161 −0.123080 0.992397i \(-0.539277\pi\)
−0.123080 + 0.992397i \(0.539277\pi\)
\(752\) 43713.8 2.11979
\(753\) 0 0
\(754\) 18336.9 0.885663
\(755\) 4228.71 0.203839
\(756\) 0 0
\(757\) 29118.9 1.39808 0.699039 0.715084i \(-0.253612\pi\)
0.699039 + 0.715084i \(0.253612\pi\)
\(758\) −2968.39 −0.142238
\(759\) 0 0
\(760\) −73981.4 −3.53104
\(761\) 39582.7 1.88551 0.942755 0.333487i \(-0.108225\pi\)
0.942755 + 0.333487i \(0.108225\pi\)
\(762\) 0 0
\(763\) 1708.53 0.0810656
\(764\) 59988.7 2.84073
\(765\) 0 0
\(766\) −41492.1 −1.95714
\(767\) −70899.8 −3.33773
\(768\) 0 0
\(769\) 3581.25 0.167936 0.0839682 0.996468i \(-0.473241\pi\)
0.0839682 + 0.996468i \(0.473241\pi\)
\(770\) −35.3415 −0.00165405
\(771\) 0 0
\(772\) −21302.4 −0.993121
\(773\) 1820.20 0.0846935 0.0423468 0.999103i \(-0.486517\pi\)
0.0423468 + 0.999103i \(0.486517\pi\)
\(774\) 0 0
\(775\) 1869.16 0.0866351
\(776\) 22554.4 1.04337
\(777\) 0 0
\(778\) 13983.7 0.644395
\(779\) −17898.3 −0.823200
\(780\) 0 0
\(781\) 327.730 0.0150155
\(782\) 20048.4 0.916790
\(783\) 0 0
\(784\) −55188.5 −2.51405
\(785\) 12707.9 0.577788
\(786\) 0 0
\(787\) −38042.7 −1.72310 −0.861548 0.507676i \(-0.830505\pi\)
−0.861548 + 0.507676i \(0.830505\pi\)
\(788\) −97222.6 −4.39519
\(789\) 0 0
\(790\) −11159.2 −0.502567
\(791\) −509.875 −0.0229192
\(792\) 0 0
\(793\) 42742.8 1.91405
\(794\) −9684.76 −0.432871
\(795\) 0 0
\(796\) −20521.6 −0.913779
\(797\) 34264.4 1.52285 0.761423 0.648255i \(-0.224501\pi\)
0.761423 + 0.648255i \(0.224501\pi\)
\(798\) 0 0
\(799\) 13624.8 0.603268
\(800\) 8348.59 0.368959
\(801\) 0 0
\(802\) 44070.1 1.94036
\(803\) −850.592 −0.0373807
\(804\) 0 0
\(805\) −617.619 −0.0270413
\(806\) −36865.0 −1.61106
\(807\) 0 0
\(808\) −59428.4 −2.58748
\(809\) 8842.40 0.384280 0.192140 0.981368i \(-0.438457\pi\)
0.192140 + 0.981368i \(0.438457\pi\)
\(810\) 0 0
\(811\) 16775.4 0.726341 0.363170 0.931723i \(-0.381694\pi\)
0.363170 + 0.931723i \(0.381694\pi\)
\(812\) 633.064 0.0273598
\(813\) 0 0
\(814\) 1399.78 0.0602729
\(815\) 11069.2 0.475749
\(816\) 0 0
\(817\) 3927.34 0.168177
\(818\) −542.444 −0.0231859
\(819\) 0 0
\(820\) −29137.9 −1.24090
\(821\) −16529.4 −0.702657 −0.351328 0.936252i \(-0.614270\pi\)
−0.351328 + 0.936252i \(0.614270\pi\)
\(822\) 0 0
\(823\) 17811.2 0.754386 0.377193 0.926135i \(-0.376889\pi\)
0.377193 + 0.926135i \(0.376889\pi\)
\(824\) −74889.4 −3.16614
\(825\) 0 0
\(826\) −3450.37 −0.145344
\(827\) −18973.0 −0.797772 −0.398886 0.917001i \(-0.630603\pi\)
−0.398886 + 0.917001i \(0.630603\pi\)
\(828\) 0 0
\(829\) −29108.6 −1.21952 −0.609762 0.792585i \(-0.708735\pi\)
−0.609762 + 0.792585i \(0.708735\pi\)
\(830\) −46612.2 −1.94932
\(831\) 0 0
\(832\) −52804.9 −2.20034
\(833\) −17201.3 −0.715472
\(834\) 0 0
\(835\) −29755.1 −1.23320
\(836\) 1961.88 0.0811639
\(837\) 0 0
\(838\) −54114.4 −2.23073
\(839\) 32777.9 1.34877 0.674386 0.738379i \(-0.264408\pi\)
0.674386 + 0.738379i \(0.264408\pi\)
\(840\) 0 0
\(841\) −22765.4 −0.933430
\(842\) −24407.2 −0.998964
\(843\) 0 0
\(844\) −9129.37 −0.372329
\(845\) 53765.4 2.18886
\(846\) 0 0
\(847\) −1070.16 −0.0434132
\(848\) −17872.9 −0.723771
\(849\) 0 0
\(850\) 6082.99 0.245465
\(851\) 24462.2 0.985373
\(852\) 0 0
\(853\) 11519.2 0.462380 0.231190 0.972909i \(-0.425738\pi\)
0.231190 + 0.972909i \(0.425738\pi\)
\(854\) 2080.10 0.0833484
\(855\) 0 0
\(856\) −77900.0 −3.11048
\(857\) 21343.7 0.850743 0.425372 0.905019i \(-0.360143\pi\)
0.425372 + 0.905019i \(0.360143\pi\)
\(858\) 0 0
\(859\) 21764.2 0.864475 0.432238 0.901760i \(-0.357724\pi\)
0.432238 + 0.901760i \(0.357724\pi\)
\(860\) 6393.60 0.253511
\(861\) 0 0
\(862\) 90798.2 3.58770
\(863\) 22120.1 0.872510 0.436255 0.899823i \(-0.356305\pi\)
0.436255 + 0.899823i \(0.356305\pi\)
\(864\) 0 0
\(865\) 32853.8 1.29140
\(866\) −21269.1 −0.834590
\(867\) 0 0
\(868\) −1272.73 −0.0497687
\(869\) 174.712 0.00682014
\(870\) 0 0
\(871\) −74775.0 −2.90890
\(872\) −128498. −4.99023
\(873\) 0 0
\(874\) 48329.0 1.87043
\(875\) −1202.58 −0.0464625
\(876\) 0 0
\(877\) 45552.7 1.75394 0.876970 0.480545i \(-0.159561\pi\)
0.876970 + 0.480545i \(0.159561\pi\)
\(878\) −62699.9 −2.41004
\(879\) 0 0
\(880\) 1349.76 0.0517050
\(881\) −16750.7 −0.640576 −0.320288 0.947320i \(-0.603780\pi\)
−0.320288 + 0.947320i \(0.603780\pi\)
\(882\) 0 0
\(883\) −7820.30 −0.298045 −0.149023 0.988834i \(-0.547613\pi\)
−0.149023 + 0.988834i \(0.547613\pi\)
\(884\) −85111.0 −3.23823
\(885\) 0 0
\(886\) −48253.0 −1.82967
\(887\) −3307.54 −0.125205 −0.0626023 0.998039i \(-0.519940\pi\)
−0.0626023 + 0.998039i \(0.519940\pi\)
\(888\) 0 0
\(889\) −456.802 −0.0172336
\(890\) 24472.0 0.921690
\(891\) 0 0
\(892\) −37684.5 −1.41454
\(893\) 32844.2 1.23078
\(894\) 0 0
\(895\) 6975.93 0.260536
\(896\) −241.286 −0.00899642
\(897\) 0 0
\(898\) −74631.7 −2.77337
\(899\) −3264.07 −0.121093
\(900\) 0 0
\(901\) −5570.66 −0.205978
\(902\) 643.052 0.0237376
\(903\) 0 0
\(904\) 38347.4 1.41086
\(905\) 45229.3 1.66130
\(906\) 0 0
\(907\) 22776.0 0.833807 0.416904 0.908951i \(-0.363115\pi\)
0.416904 + 0.908951i \(0.363115\pi\)
\(908\) −73575.7 −2.68909
\(909\) 0 0
\(910\) 3695.95 0.134637
\(911\) 19433.9 0.706777 0.353388 0.935477i \(-0.385029\pi\)
0.353388 + 0.935477i \(0.385029\pi\)
\(912\) 0 0
\(913\) 729.773 0.0264534
\(914\) −45741.5 −1.65535
\(915\) 0 0
\(916\) 76409.9 2.75617
\(917\) 1010.36 0.0363848
\(918\) 0 0
\(919\) 3518.51 0.126295 0.0631473 0.998004i \(-0.479886\pi\)
0.0631473 + 0.998004i \(0.479886\pi\)
\(920\) 46450.8 1.66460
\(921\) 0 0
\(922\) −3291.56 −0.117573
\(923\) −34273.5 −1.22224
\(924\) 0 0
\(925\) 7422.20 0.263827
\(926\) 13652.0 0.484484
\(927\) 0 0
\(928\) −14579.0 −0.515709
\(929\) 29305.0 1.03495 0.517474 0.855699i \(-0.326872\pi\)
0.517474 + 0.855699i \(0.326872\pi\)
\(930\) 0 0
\(931\) −41465.6 −1.45970
\(932\) 54070.3 1.90035
\(933\) 0 0
\(934\) −63705.0 −2.23179
\(935\) 420.696 0.0147147
\(936\) 0 0
\(937\) 3989.30 0.139087 0.0695436 0.997579i \(-0.477846\pi\)
0.0695436 + 0.997579i \(0.477846\pi\)
\(938\) −3638.96 −0.126670
\(939\) 0 0
\(940\) 53469.4 1.85530
\(941\) −5735.38 −0.198691 −0.0993453 0.995053i \(-0.531675\pi\)
−0.0993453 + 0.995053i \(0.531675\pi\)
\(942\) 0 0
\(943\) 11237.8 0.388074
\(944\) 131776. 4.54339
\(945\) 0 0
\(946\) −141.102 −0.00484949
\(947\) 9209.74 0.316026 0.158013 0.987437i \(-0.449491\pi\)
0.158013 + 0.987437i \(0.449491\pi\)
\(948\) 0 0
\(949\) 88953.4 3.04273
\(950\) 14663.8 0.500795
\(951\) 0 0
\(952\) −2445.37 −0.0832510
\(953\) −37747.8 −1.28307 −0.641537 0.767092i \(-0.721703\pi\)
−0.641537 + 0.767092i \(0.721703\pi\)
\(954\) 0 0
\(955\) 31009.4 1.05072
\(956\) −4667.84 −0.157917
\(957\) 0 0
\(958\) −38107.7 −1.28518
\(959\) −1577.03 −0.0531021
\(960\) 0 0
\(961\) −23228.8 −0.779726
\(962\) −146386. −4.90611
\(963\) 0 0
\(964\) 12680.7 0.423671
\(965\) −11011.6 −0.367334
\(966\) 0 0
\(967\) 57837.6 1.92340 0.961702 0.274099i \(-0.0883795\pi\)
0.961702 + 0.274099i \(0.0883795\pi\)
\(968\) 80485.8 2.67243
\(969\) 0 0
\(970\) 19747.7 0.653671
\(971\) 47828.7 1.58074 0.790369 0.612631i \(-0.209889\pi\)
0.790369 + 0.612631i \(0.209889\pi\)
\(972\) 0 0
\(973\) 29.5604 0.000973961 0
\(974\) −33302.1 −1.09555
\(975\) 0 0
\(976\) −79443.0 −2.60544
\(977\) 39670.3 1.29904 0.649522 0.760343i \(-0.274969\pi\)
0.649522 + 0.760343i \(0.274969\pi\)
\(978\) 0 0
\(979\) −383.140 −0.0125079
\(980\) −67504.8 −2.20037
\(981\) 0 0
\(982\) −24538.7 −0.797413
\(983\) 51418.1 1.66834 0.834172 0.551505i \(-0.185946\pi\)
0.834172 + 0.551505i \(0.185946\pi\)
\(984\) 0 0
\(985\) −50256.4 −1.62569
\(986\) −10622.6 −0.343096
\(987\) 0 0
\(988\) −205170. −6.60661
\(989\) −2465.86 −0.0792820
\(990\) 0 0
\(991\) 28309.2 0.907438 0.453719 0.891145i \(-0.350097\pi\)
0.453719 + 0.891145i \(0.350097\pi\)
\(992\) 29310.0 0.938097
\(993\) 0 0
\(994\) −1667.94 −0.0532231
\(995\) −10608.0 −0.337987
\(996\) 0 0
\(997\) −25372.2 −0.805962 −0.402981 0.915208i \(-0.632026\pi\)
−0.402981 + 0.915208i \(0.632026\pi\)
\(998\) 24428.6 0.774824
\(999\) 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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 2151.4.a.h.1.2 yes 59
3.2 odd 2 2151.4.a.g.1.58 59
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2151.4.a.g.1.58 59 3.2 odd 2
2151.4.a.h.1.2 yes 59 1.1 even 1 trivial