Properties

Label 2151.4.a.h.1.19
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 1.19
Character \(\chi\) \(=\) 2151.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.12161 q^{2} -3.49876 q^{4} +4.52878 q^{5} +14.7886 q^{7} +24.3959 q^{8} +O(q^{10})\) \(q-2.12161 q^{2} -3.49876 q^{4} +4.52878 q^{5} +14.7886 q^{7} +24.3959 q^{8} -9.60831 q^{10} -61.2887 q^{11} -8.40363 q^{13} -31.3757 q^{14} -23.7686 q^{16} +127.628 q^{17} -43.6873 q^{19} -15.8451 q^{20} +130.031 q^{22} -165.626 q^{23} -104.490 q^{25} +17.8292 q^{26} -51.7418 q^{28} +212.984 q^{29} +213.376 q^{31} -144.740 q^{32} -270.778 q^{34} +66.9744 q^{35} +56.0146 q^{37} +92.6875 q^{38} +110.484 q^{40} -328.931 q^{41} +33.0560 q^{43} +214.435 q^{44} +351.394 q^{46} -259.011 q^{47} -124.297 q^{49} +221.688 q^{50} +29.4023 q^{52} +150.446 q^{53} -277.563 q^{55} +360.782 q^{56} -451.870 q^{58} +807.354 q^{59} -437.380 q^{61} -452.702 q^{62} +497.230 q^{64} -38.0582 q^{65} +641.805 q^{67} -446.541 q^{68} -142.094 q^{70} +417.719 q^{71} +236.933 q^{73} -118.841 q^{74} +152.851 q^{76} -906.375 q^{77} -67.8200 q^{79} -107.643 q^{80} +697.864 q^{82} +13.7102 q^{83} +578.000 q^{85} -70.1320 q^{86} -1495.19 q^{88} +1497.63 q^{89} -124.278 q^{91} +579.486 q^{92} +549.521 q^{94} -197.850 q^{95} +471.860 q^{97} +263.710 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 59q + 8q^{2} + 238q^{4} + 80q^{5} - 10q^{7} + 96q^{8} + O(q^{10}) \) \( 59q + 8q^{2} + 238q^{4} + 80q^{5} - 10q^{7} + 96q^{8} - 36q^{10} + 132q^{11} + 104q^{13} + 280q^{14} + 822q^{16} + 408q^{17} + 20q^{19} + 800q^{20} - 2q^{22} + 276q^{23} + 1477q^{25} + 780q^{26} + 224q^{28} + 696q^{29} - 380q^{31} + 896q^{32} - 72q^{34} + 700q^{35} + 224q^{37} + 988q^{38} - 258q^{40} + 2706q^{41} - 156q^{43} + 1584q^{44} + 428q^{46} + 1316q^{47} + 2135q^{49} + 1400q^{50} + 1092q^{52} + 1484q^{53} - 992q^{55} + 3360q^{56} - 120q^{58} + 3186q^{59} - 254q^{61} + 1240q^{62} + 3054q^{64} + 5120q^{65} + 288q^{67} + 9420q^{68} + 1108q^{70} + 4468q^{71} - 1770q^{73} + 6214q^{74} + 720q^{76} + 6352q^{77} - 746q^{79} + 7040q^{80} + 276q^{82} + 5484q^{83} + 588q^{85} + 10152q^{86} + 1186q^{88} + 11570q^{89} + 1768q^{91} + 15366q^{92} - 2142q^{94} + 5736q^{95} + 2390q^{97} + 6912q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.12161 −0.750103 −0.375052 0.927004i \(-0.622375\pi\)
−0.375052 + 0.927004i \(0.622375\pi\)
\(3\) 0 0
\(4\) −3.49876 −0.437345
\(5\) 4.52878 0.405066 0.202533 0.979275i \(-0.435083\pi\)
0.202533 + 0.979275i \(0.435083\pi\)
\(6\) 0 0
\(7\) 14.7886 0.798510 0.399255 0.916840i \(-0.369269\pi\)
0.399255 + 0.916840i \(0.369269\pi\)
\(8\) 24.3959 1.07816
\(9\) 0 0
\(10\) −9.60831 −0.303842
\(11\) −61.2887 −1.67993 −0.839965 0.542640i \(-0.817425\pi\)
−0.839965 + 0.542640i \(0.817425\pi\)
\(12\) 0 0
\(13\) −8.40363 −0.179288 −0.0896441 0.995974i \(-0.528573\pi\)
−0.0896441 + 0.995974i \(0.528573\pi\)
\(14\) −31.3757 −0.598965
\(15\) 0 0
\(16\) −23.7686 −0.371384
\(17\) 127.628 1.82085 0.910423 0.413678i \(-0.135756\pi\)
0.910423 + 0.413678i \(0.135756\pi\)
\(18\) 0 0
\(19\) −43.6873 −0.527503 −0.263751 0.964591i \(-0.584960\pi\)
−0.263751 + 0.964591i \(0.584960\pi\)
\(20\) −15.8451 −0.177154
\(21\) 0 0
\(22\) 130.031 1.26012
\(23\) −165.626 −1.50154 −0.750770 0.660564i \(-0.770317\pi\)
−0.750770 + 0.660564i \(0.770317\pi\)
\(24\) 0 0
\(25\) −104.490 −0.835921
\(26\) 17.8292 0.134485
\(27\) 0 0
\(28\) −51.7418 −0.349225
\(29\) 212.984 1.36380 0.681899 0.731446i \(-0.261154\pi\)
0.681899 + 0.731446i \(0.261154\pi\)
\(30\) 0 0
\(31\) 213.376 1.23624 0.618122 0.786082i \(-0.287894\pi\)
0.618122 + 0.786082i \(0.287894\pi\)
\(32\) −144.740 −0.799581
\(33\) 0 0
\(34\) −270.778 −1.36582
\(35\) 66.9744 0.323450
\(36\) 0 0
\(37\) 56.0146 0.248885 0.124443 0.992227i \(-0.460286\pi\)
0.124443 + 0.992227i \(0.460286\pi\)
\(38\) 92.6875 0.395682
\(39\) 0 0
\(40\) 110.484 0.436725
\(41\) −328.931 −1.25294 −0.626468 0.779447i \(-0.715500\pi\)
−0.626468 + 0.779447i \(0.715500\pi\)
\(42\) 0 0
\(43\) 33.0560 0.117232 0.0586161 0.998281i \(-0.481331\pi\)
0.0586161 + 0.998281i \(0.481331\pi\)
\(44\) 214.435 0.734710
\(45\) 0 0
\(46\) 351.394 1.12631
\(47\) −259.011 −0.803843 −0.401922 0.915674i \(-0.631658\pi\)
−0.401922 + 0.915674i \(0.631658\pi\)
\(48\) 0 0
\(49\) −124.297 −0.362381
\(50\) 221.688 0.627027
\(51\) 0 0
\(52\) 29.4023 0.0784108
\(53\) 150.446 0.389913 0.194957 0.980812i \(-0.437543\pi\)
0.194957 + 0.980812i \(0.437543\pi\)
\(54\) 0 0
\(55\) −277.563 −0.680483
\(56\) 360.782 0.860920
\(57\) 0 0
\(58\) −451.870 −1.02299
\(59\) 807.354 1.78150 0.890750 0.454494i \(-0.150180\pi\)
0.890750 + 0.454494i \(0.150180\pi\)
\(60\) 0 0
\(61\) −437.380 −0.918044 −0.459022 0.888425i \(-0.651800\pi\)
−0.459022 + 0.888425i \(0.651800\pi\)
\(62\) −452.702 −0.927310
\(63\) 0 0
\(64\) 497.230 0.971152
\(65\) −38.0582 −0.0726236
\(66\) 0 0
\(67\) 641.805 1.17028 0.585141 0.810931i \(-0.301039\pi\)
0.585141 + 0.810931i \(0.301039\pi\)
\(68\) −446.541 −0.796338
\(69\) 0 0
\(70\) −142.094 −0.242621
\(71\) 417.719 0.698226 0.349113 0.937081i \(-0.386483\pi\)
0.349113 + 0.937081i \(0.386483\pi\)
\(72\) 0 0
\(73\) 236.933 0.379875 0.189937 0.981796i \(-0.439171\pi\)
0.189937 + 0.981796i \(0.439171\pi\)
\(74\) −118.841 −0.186690
\(75\) 0 0
\(76\) 152.851 0.230701
\(77\) −906.375 −1.34144
\(78\) 0 0
\(79\) −67.8200 −0.0965867 −0.0482934 0.998833i \(-0.515378\pi\)
−0.0482934 + 0.998833i \(0.515378\pi\)
\(80\) −107.643 −0.150435
\(81\) 0 0
\(82\) 697.864 0.939832
\(83\) 13.7102 0.0181312 0.00906559 0.999959i \(-0.497114\pi\)
0.00906559 + 0.999959i \(0.497114\pi\)
\(84\) 0 0
\(85\) 578.000 0.737563
\(86\) −70.1320 −0.0879363
\(87\) 0 0
\(88\) −1495.19 −1.81123
\(89\) 1497.63 1.78369 0.891847 0.452337i \(-0.149410\pi\)
0.891847 + 0.452337i \(0.149410\pi\)
\(90\) 0 0
\(91\) −124.278 −0.143163
\(92\) 579.486 0.656691
\(93\) 0 0
\(94\) 549.521 0.602966
\(95\) −197.850 −0.213674
\(96\) 0 0
\(97\) 471.860 0.493919 0.246959 0.969026i \(-0.420569\pi\)
0.246959 + 0.969026i \(0.420569\pi\)
\(98\) 263.710 0.271823
\(99\) 0 0
\(100\) 365.586 0.365586
\(101\) −1253.92 −1.23534 −0.617670 0.786437i \(-0.711923\pi\)
−0.617670 + 0.786437i \(0.711923\pi\)
\(102\) 0 0
\(103\) −664.452 −0.635635 −0.317817 0.948152i \(-0.602950\pi\)
−0.317817 + 0.948152i \(0.602950\pi\)
\(104\) −205.014 −0.193301
\(105\) 0 0
\(106\) −319.189 −0.292475
\(107\) 753.874 0.681119 0.340560 0.940223i \(-0.389384\pi\)
0.340560 + 0.940223i \(0.389384\pi\)
\(108\) 0 0
\(109\) −873.770 −0.767816 −0.383908 0.923371i \(-0.625422\pi\)
−0.383908 + 0.923371i \(0.625422\pi\)
\(110\) 588.881 0.510433
\(111\) 0 0
\(112\) −351.505 −0.296554
\(113\) −473.333 −0.394048 −0.197024 0.980399i \(-0.563128\pi\)
−0.197024 + 0.980399i \(0.563128\pi\)
\(114\) 0 0
\(115\) −750.084 −0.608223
\(116\) −745.180 −0.596450
\(117\) 0 0
\(118\) −1712.89 −1.33631
\(119\) 1887.44 1.45396
\(120\) 0 0
\(121\) 2425.31 1.82217
\(122\) 927.950 0.688628
\(123\) 0 0
\(124\) −746.553 −0.540665
\(125\) −1039.31 −0.743670
\(126\) 0 0
\(127\) −2576.49 −1.80021 −0.900104 0.435675i \(-0.856510\pi\)
−0.900104 + 0.435675i \(0.856510\pi\)
\(128\) 102.987 0.0711163
\(129\) 0 0
\(130\) 80.7447 0.0544752
\(131\) −2100.65 −1.40103 −0.700514 0.713639i \(-0.747046\pi\)
−0.700514 + 0.713639i \(0.747046\pi\)
\(132\) 0 0
\(133\) −646.075 −0.421216
\(134\) −1361.66 −0.877833
\(135\) 0 0
\(136\) 3113.61 1.96316
\(137\) 1943.15 1.21179 0.605893 0.795546i \(-0.292816\pi\)
0.605893 + 0.795546i \(0.292816\pi\)
\(138\) 0 0
\(139\) −412.166 −0.251507 −0.125754 0.992062i \(-0.540135\pi\)
−0.125754 + 0.992062i \(0.540135\pi\)
\(140\) −234.327 −0.141459
\(141\) 0 0
\(142\) −886.237 −0.523742
\(143\) 515.047 0.301192
\(144\) 0 0
\(145\) 964.558 0.552429
\(146\) −502.679 −0.284945
\(147\) 0 0
\(148\) −195.982 −0.108849
\(149\) −1864.74 −1.02527 −0.512635 0.858607i \(-0.671331\pi\)
−0.512635 + 0.858607i \(0.671331\pi\)
\(150\) 0 0
\(151\) −2491.43 −1.34271 −0.671356 0.741135i \(-0.734288\pi\)
−0.671356 + 0.741135i \(0.734288\pi\)
\(152\) −1065.79 −0.568731
\(153\) 0 0
\(154\) 1922.98 1.00622
\(155\) 966.335 0.500761
\(156\) 0 0
\(157\) −1467.06 −0.745761 −0.372880 0.927879i \(-0.621630\pi\)
−0.372880 + 0.927879i \(0.621630\pi\)
\(158\) 143.888 0.0724500
\(159\) 0 0
\(160\) −655.494 −0.323883
\(161\) −2449.38 −1.19899
\(162\) 0 0
\(163\) −1756.39 −0.843997 −0.421998 0.906597i \(-0.638671\pi\)
−0.421998 + 0.906597i \(0.638671\pi\)
\(164\) 1150.85 0.547966
\(165\) 0 0
\(166\) −29.0877 −0.0136003
\(167\) 2433.18 1.12746 0.563728 0.825961i \(-0.309367\pi\)
0.563728 + 0.825961i \(0.309367\pi\)
\(168\) 0 0
\(169\) −2126.38 −0.967856
\(170\) −1226.29 −0.553249
\(171\) 0 0
\(172\) −115.655 −0.0512710
\(173\) 2724.13 1.19718 0.598589 0.801056i \(-0.295728\pi\)
0.598589 + 0.801056i \(0.295728\pi\)
\(174\) 0 0
\(175\) −1545.26 −0.667492
\(176\) 1456.75 0.623900
\(177\) 0 0
\(178\) −3177.40 −1.33795
\(179\) 3760.40 1.57020 0.785099 0.619370i \(-0.212612\pi\)
0.785099 + 0.619370i \(0.212612\pi\)
\(180\) 0 0
\(181\) 967.404 0.397274 0.198637 0.980073i \(-0.436349\pi\)
0.198637 + 0.980073i \(0.436349\pi\)
\(182\) 263.670 0.107387
\(183\) 0 0
\(184\) −4040.60 −1.61890
\(185\) 253.678 0.100815
\(186\) 0 0
\(187\) −7822.17 −3.05890
\(188\) 906.218 0.351557
\(189\) 0 0
\(190\) 419.761 0.160277
\(191\) 835.684 0.316586 0.158293 0.987392i \(-0.449401\pi\)
0.158293 + 0.987392i \(0.449401\pi\)
\(192\) 0 0
\(193\) −1302.81 −0.485897 −0.242948 0.970039i \(-0.578115\pi\)
−0.242948 + 0.970039i \(0.578115\pi\)
\(194\) −1001.10 −0.370490
\(195\) 0 0
\(196\) 434.885 0.158486
\(197\) 3977.01 1.43833 0.719164 0.694841i \(-0.244525\pi\)
0.719164 + 0.694841i \(0.244525\pi\)
\(198\) 0 0
\(199\) 2651.64 0.944571 0.472285 0.881446i \(-0.343429\pi\)
0.472285 + 0.881446i \(0.343429\pi\)
\(200\) −2549.13 −0.901255
\(201\) 0 0
\(202\) 2660.33 0.926633
\(203\) 3149.74 1.08901
\(204\) 0 0
\(205\) −1489.66 −0.507522
\(206\) 1409.71 0.476792
\(207\) 0 0
\(208\) 199.742 0.0665848
\(209\) 2677.54 0.886168
\(210\) 0 0
\(211\) −1128.60 −0.368228 −0.184114 0.982905i \(-0.558942\pi\)
−0.184114 + 0.982905i \(0.558942\pi\)
\(212\) −526.376 −0.170527
\(213\) 0 0
\(214\) −1599.43 −0.510910
\(215\) 149.703 0.0474869
\(216\) 0 0
\(217\) 3155.54 0.987153
\(218\) 1853.80 0.575942
\(219\) 0 0
\(220\) 971.127 0.297606
\(221\) −1072.54 −0.326456
\(222\) 0 0
\(223\) −2515.64 −0.755426 −0.377713 0.925923i \(-0.623289\pi\)
−0.377713 + 0.925923i \(0.623289\pi\)
\(224\) −2140.50 −0.638473
\(225\) 0 0
\(226\) 1004.23 0.295577
\(227\) 346.735 0.101382 0.0506908 0.998714i \(-0.483858\pi\)
0.0506908 + 0.998714i \(0.483858\pi\)
\(228\) 0 0
\(229\) 1416.59 0.408782 0.204391 0.978889i \(-0.434479\pi\)
0.204391 + 0.978889i \(0.434479\pi\)
\(230\) 1591.39 0.456230
\(231\) 0 0
\(232\) 5195.94 1.47039
\(233\) 2713.73 0.763014 0.381507 0.924366i \(-0.375405\pi\)
0.381507 + 0.924366i \(0.375405\pi\)
\(234\) 0 0
\(235\) −1173.00 −0.325610
\(236\) −2824.74 −0.779130
\(237\) 0 0
\(238\) −4004.43 −1.09062
\(239\) −239.000 −0.0646846
\(240\) 0 0
\(241\) 5659.55 1.51271 0.756355 0.654161i \(-0.226978\pi\)
0.756355 + 0.654161i \(0.226978\pi\)
\(242\) −5145.56 −1.36681
\(243\) 0 0
\(244\) 1530.29 0.401502
\(245\) −562.913 −0.146789
\(246\) 0 0
\(247\) 367.132 0.0945750
\(248\) 5205.51 1.33286
\(249\) 0 0
\(250\) 2205.01 0.557829
\(251\) 3002.94 0.755154 0.377577 0.925978i \(-0.376757\pi\)
0.377577 + 0.925978i \(0.376757\pi\)
\(252\) 0 0
\(253\) 10151.0 2.52248
\(254\) 5466.31 1.35034
\(255\) 0 0
\(256\) −4196.34 −1.02450
\(257\) 6875.65 1.66884 0.834418 0.551132i \(-0.185804\pi\)
0.834418 + 0.551132i \(0.185804\pi\)
\(258\) 0 0
\(259\) 828.379 0.198737
\(260\) 133.156 0.0317616
\(261\) 0 0
\(262\) 4456.76 1.05092
\(263\) −1797.45 −0.421429 −0.210714 0.977548i \(-0.567579\pi\)
−0.210714 + 0.977548i \(0.567579\pi\)
\(264\) 0 0
\(265\) 681.339 0.157941
\(266\) 1370.72 0.315956
\(267\) 0 0
\(268\) −2245.52 −0.511817
\(269\) 8271.17 1.87473 0.937365 0.348349i \(-0.113258\pi\)
0.937365 + 0.348349i \(0.113258\pi\)
\(270\) 0 0
\(271\) −4182.05 −0.937422 −0.468711 0.883352i \(-0.655281\pi\)
−0.468711 + 0.883352i \(0.655281\pi\)
\(272\) −3033.54 −0.676233
\(273\) 0 0
\(274\) −4122.62 −0.908965
\(275\) 6404.07 1.40429
\(276\) 0 0
\(277\) 4445.28 0.964228 0.482114 0.876108i \(-0.339869\pi\)
0.482114 + 0.876108i \(0.339869\pi\)
\(278\) 874.458 0.188656
\(279\) 0 0
\(280\) 1633.90 0.348730
\(281\) −542.974 −0.115271 −0.0576355 0.998338i \(-0.518356\pi\)
−0.0576355 + 0.998338i \(0.518356\pi\)
\(282\) 0 0
\(283\) 7379.58 1.55007 0.775036 0.631917i \(-0.217731\pi\)
0.775036 + 0.631917i \(0.217731\pi\)
\(284\) −1461.50 −0.305366
\(285\) 0 0
\(286\) −1092.73 −0.225925
\(287\) −4864.43 −1.00048
\(288\) 0 0
\(289\) 11376.0 2.31548
\(290\) −2046.42 −0.414379
\(291\) 0 0
\(292\) −828.971 −0.166136
\(293\) 5272.35 1.05124 0.525621 0.850719i \(-0.323833\pi\)
0.525621 + 0.850719i \(0.323833\pi\)
\(294\) 0 0
\(295\) 3656.33 0.721626
\(296\) 1366.53 0.268337
\(297\) 0 0
\(298\) 3956.25 0.769059
\(299\) 1391.86 0.269208
\(300\) 0 0
\(301\) 488.852 0.0936112
\(302\) 5285.85 1.00717
\(303\) 0 0
\(304\) 1038.39 0.195906
\(305\) −1980.80 −0.371869
\(306\) 0 0
\(307\) −5750.06 −1.06897 −0.534484 0.845179i \(-0.679494\pi\)
−0.534484 + 0.845179i \(0.679494\pi\)
\(308\) 3171.19 0.586673
\(309\) 0 0
\(310\) −2050.19 −0.375622
\(311\) 7963.67 1.45202 0.726010 0.687684i \(-0.241372\pi\)
0.726010 + 0.687684i \(0.241372\pi\)
\(312\) 0 0
\(313\) 6104.69 1.10242 0.551210 0.834367i \(-0.314166\pi\)
0.551210 + 0.834367i \(0.314166\pi\)
\(314\) 3112.54 0.559398
\(315\) 0 0
\(316\) 237.286 0.0422417
\(317\) −4949.91 −0.877018 −0.438509 0.898727i \(-0.644493\pi\)
−0.438509 + 0.898727i \(0.644493\pi\)
\(318\) 0 0
\(319\) −13053.5 −2.29109
\(320\) 2251.84 0.393381
\(321\) 0 0
\(322\) 5196.63 0.899370
\(323\) −5575.73 −0.960502
\(324\) 0 0
\(325\) 878.096 0.149871
\(326\) 3726.39 0.633085
\(327\) 0 0
\(328\) −8024.57 −1.35086
\(329\) −3830.42 −0.641877
\(330\) 0 0
\(331\) −2722.03 −0.452013 −0.226007 0.974126i \(-0.572567\pi\)
−0.226007 + 0.974126i \(0.572567\pi\)
\(332\) −47.9687 −0.00792958
\(333\) 0 0
\(334\) −5162.26 −0.845708
\(335\) 2906.59 0.474042
\(336\) 0 0
\(337\) 6453.19 1.04311 0.521554 0.853218i \(-0.325352\pi\)
0.521554 + 0.853218i \(0.325352\pi\)
\(338\) 4511.35 0.725992
\(339\) 0 0
\(340\) −2022.28 −0.322570
\(341\) −13077.6 −2.07680
\(342\) 0 0
\(343\) −6910.67 −1.08788
\(344\) 806.431 0.126395
\(345\) 0 0
\(346\) −5779.55 −0.898007
\(347\) 2579.75 0.399101 0.199551 0.979888i \(-0.436052\pi\)
0.199551 + 0.979888i \(0.436052\pi\)
\(348\) 0 0
\(349\) −3787.07 −0.580852 −0.290426 0.956897i \(-0.593797\pi\)
−0.290426 + 0.956897i \(0.593797\pi\)
\(350\) 3278.45 0.500688
\(351\) 0 0
\(352\) 8870.90 1.34324
\(353\) 10562.0 1.59252 0.796262 0.604952i \(-0.206808\pi\)
0.796262 + 0.604952i \(0.206808\pi\)
\(354\) 0 0
\(355\) 1891.76 0.282828
\(356\) −5239.86 −0.780090
\(357\) 0 0
\(358\) −7978.11 −1.17781
\(359\) −7215.46 −1.06077 −0.530386 0.847756i \(-0.677953\pi\)
−0.530386 + 0.847756i \(0.677953\pi\)
\(360\) 0 0
\(361\) −4950.42 −0.721741
\(362\) −2052.46 −0.297996
\(363\) 0 0
\(364\) 434.819 0.0626118
\(365\) 1073.02 0.153875
\(366\) 0 0
\(367\) 6325.12 0.899642 0.449821 0.893119i \(-0.351488\pi\)
0.449821 + 0.893119i \(0.351488\pi\)
\(368\) 3936.70 0.557648
\(369\) 0 0
\(370\) −538.206 −0.0756217
\(371\) 2224.90 0.311350
\(372\) 0 0
\(373\) −1950.11 −0.270704 −0.135352 0.990798i \(-0.543217\pi\)
−0.135352 + 0.990798i \(0.543217\pi\)
\(374\) 16595.6 2.29449
\(375\) 0 0
\(376\) −6318.81 −0.866670
\(377\) −1789.84 −0.244513
\(378\) 0 0
\(379\) 11140.9 1.50994 0.754972 0.655757i \(-0.227651\pi\)
0.754972 + 0.655757i \(0.227651\pi\)
\(380\) 692.230 0.0934491
\(381\) 0 0
\(382\) −1773.00 −0.237472
\(383\) 3581.16 0.477777 0.238888 0.971047i \(-0.423217\pi\)
0.238888 + 0.971047i \(0.423217\pi\)
\(384\) 0 0
\(385\) −4104.77 −0.543373
\(386\) 2764.05 0.364473
\(387\) 0 0
\(388\) −1650.93 −0.216013
\(389\) −2412.86 −0.314491 −0.157245 0.987560i \(-0.550261\pi\)
−0.157245 + 0.987560i \(0.550261\pi\)
\(390\) 0 0
\(391\) −21138.6 −2.73407
\(392\) −3032.33 −0.390704
\(393\) 0 0
\(394\) −8437.68 −1.07889
\(395\) −307.142 −0.0391240
\(396\) 0 0
\(397\) 13611.6 1.72078 0.860388 0.509640i \(-0.170221\pi\)
0.860388 + 0.509640i \(0.170221\pi\)
\(398\) −5625.75 −0.708525
\(399\) 0 0
\(400\) 2483.58 0.310448
\(401\) −947.640 −0.118012 −0.0590061 0.998258i \(-0.518793\pi\)
−0.0590061 + 0.998258i \(0.518793\pi\)
\(402\) 0 0
\(403\) −1793.14 −0.221644
\(404\) 4387.15 0.540270
\(405\) 0 0
\(406\) −6682.53 −0.816868
\(407\) −3433.07 −0.418110
\(408\) 0 0
\(409\) −2212.57 −0.267493 −0.133746 0.991016i \(-0.542701\pi\)
−0.133746 + 0.991016i \(0.542701\pi\)
\(410\) 3160.47 0.380694
\(411\) 0 0
\(412\) 2324.76 0.277992
\(413\) 11939.6 1.42255
\(414\) 0 0
\(415\) 62.0904 0.00734433
\(416\) 1216.34 0.143355
\(417\) 0 0
\(418\) −5680.70 −0.664718
\(419\) 7516.47 0.876380 0.438190 0.898882i \(-0.355620\pi\)
0.438190 + 0.898882i \(0.355620\pi\)
\(420\) 0 0
\(421\) −5276.93 −0.610883 −0.305441 0.952211i \(-0.598804\pi\)
−0.305441 + 0.952211i \(0.598804\pi\)
\(422\) 2394.45 0.276209
\(423\) 0 0
\(424\) 3670.28 0.420388
\(425\) −13335.9 −1.52208
\(426\) 0 0
\(427\) −6468.24 −0.733068
\(428\) −2637.62 −0.297884
\(429\) 0 0
\(430\) −317.612 −0.0356200
\(431\) 2177.53 0.243359 0.121680 0.992569i \(-0.461172\pi\)
0.121680 + 0.992569i \(0.461172\pi\)
\(432\) 0 0
\(433\) 1636.35 0.181611 0.0908057 0.995869i \(-0.471056\pi\)
0.0908057 + 0.995869i \(0.471056\pi\)
\(434\) −6694.84 −0.740467
\(435\) 0 0
\(436\) 3057.11 0.335801
\(437\) 7235.76 0.792067
\(438\) 0 0
\(439\) 7565.28 0.822486 0.411243 0.911526i \(-0.365095\pi\)
0.411243 + 0.911526i \(0.365095\pi\)
\(440\) −6771.40 −0.733668
\(441\) 0 0
\(442\) 2275.51 0.244876
\(443\) 1414.15 0.151667 0.0758334 0.997121i \(-0.475838\pi\)
0.0758334 + 0.997121i \(0.475838\pi\)
\(444\) 0 0
\(445\) 6782.45 0.722514
\(446\) 5337.22 0.566647
\(447\) 0 0
\(448\) 7353.34 0.775475
\(449\) −6478.28 −0.680911 −0.340455 0.940261i \(-0.610581\pi\)
−0.340455 + 0.940261i \(0.610581\pi\)
\(450\) 0 0
\(451\) 20159.8 2.10485
\(452\) 1656.08 0.172335
\(453\) 0 0
\(454\) −735.637 −0.0760466
\(455\) −562.828 −0.0579907
\(456\) 0 0
\(457\) 7137.95 0.730633 0.365317 0.930883i \(-0.380961\pi\)
0.365317 + 0.930883i \(0.380961\pi\)
\(458\) −3005.46 −0.306628
\(459\) 0 0
\(460\) 2624.36 0.266003
\(461\) 1376.00 0.139016 0.0695082 0.997581i \(-0.477857\pi\)
0.0695082 + 0.997581i \(0.477857\pi\)
\(462\) 0 0
\(463\) 9939.58 0.997692 0.498846 0.866691i \(-0.333757\pi\)
0.498846 + 0.866691i \(0.333757\pi\)
\(464\) −5062.33 −0.506493
\(465\) 0 0
\(466\) −5757.48 −0.572340
\(467\) 4325.57 0.428616 0.214308 0.976766i \(-0.431250\pi\)
0.214308 + 0.976766i \(0.431250\pi\)
\(468\) 0 0
\(469\) 9491.41 0.934483
\(470\) 2488.66 0.244241
\(471\) 0 0
\(472\) 19696.1 1.92074
\(473\) −2025.96 −0.196942
\(474\) 0 0
\(475\) 4564.89 0.440951
\(476\) −6603.72 −0.635884
\(477\) 0 0
\(478\) 507.065 0.0485201
\(479\) 2362.70 0.225375 0.112687 0.993631i \(-0.464054\pi\)
0.112687 + 0.993631i \(0.464054\pi\)
\(480\) 0 0
\(481\) −470.726 −0.0446222
\(482\) −12007.4 −1.13469
\(483\) 0 0
\(484\) −8485.56 −0.796916
\(485\) 2136.95 0.200070
\(486\) 0 0
\(487\) −3588.96 −0.333945 −0.166972 0.985962i \(-0.553399\pi\)
−0.166972 + 0.985962i \(0.553399\pi\)
\(488\) −10670.3 −0.989796
\(489\) 0 0
\(490\) 1194.28 0.110107
\(491\) −20576.6 −1.89126 −0.945632 0.325238i \(-0.894555\pi\)
−0.945632 + 0.325238i \(0.894555\pi\)
\(492\) 0 0
\(493\) 27182.8 2.48327
\(494\) −778.911 −0.0709411
\(495\) 0 0
\(496\) −5071.66 −0.459121
\(497\) 6177.48 0.557541
\(498\) 0 0
\(499\) 14629.4 1.31243 0.656213 0.754576i \(-0.272157\pi\)
0.656213 + 0.754576i \(0.272157\pi\)
\(500\) 3636.30 0.325240
\(501\) 0 0
\(502\) −6371.06 −0.566443
\(503\) 5101.70 0.452233 0.226117 0.974100i \(-0.427397\pi\)
0.226117 + 0.974100i \(0.427397\pi\)
\(504\) 0 0
\(505\) −5678.71 −0.500395
\(506\) −21536.5 −1.89212
\(507\) 0 0
\(508\) 9014.52 0.787312
\(509\) −756.470 −0.0658741 −0.0329371 0.999457i \(-0.510486\pi\)
−0.0329371 + 0.999457i \(0.510486\pi\)
\(510\) 0 0
\(511\) 3503.91 0.303334
\(512\) 8079.11 0.697362
\(513\) 0 0
\(514\) −14587.5 −1.25180
\(515\) −3009.16 −0.257474
\(516\) 0 0
\(517\) 15874.5 1.35040
\(518\) −1757.50 −0.149074
\(519\) 0 0
\(520\) −928.464 −0.0782997
\(521\) −4918.37 −0.413585 −0.206792 0.978385i \(-0.566302\pi\)
−0.206792 + 0.978385i \(0.566302\pi\)
\(522\) 0 0
\(523\) −9376.44 −0.783945 −0.391972 0.919977i \(-0.628207\pi\)
−0.391972 + 0.919977i \(0.628207\pi\)
\(524\) 7349.67 0.612733
\(525\) 0 0
\(526\) 3813.50 0.316115
\(527\) 27232.9 2.25101
\(528\) 0 0
\(529\) 15265.0 1.25462
\(530\) −1445.54 −0.118472
\(531\) 0 0
\(532\) 2260.46 0.184217
\(533\) 2764.21 0.224637
\(534\) 0 0
\(535\) 3414.13 0.275898
\(536\) 15657.4 1.26175
\(537\) 0 0
\(538\) −17548.2 −1.40624
\(539\) 7617.99 0.608776
\(540\) 0 0
\(541\) −581.756 −0.0462322 −0.0231161 0.999733i \(-0.507359\pi\)
−0.0231161 + 0.999733i \(0.507359\pi\)
\(542\) 8872.69 0.703163
\(543\) 0 0
\(544\) −18472.9 −1.45591
\(545\) −3957.11 −0.311017
\(546\) 0 0
\(547\) 11639.1 0.909784 0.454892 0.890547i \(-0.349678\pi\)
0.454892 + 0.890547i \(0.349678\pi\)
\(548\) −6798.63 −0.529969
\(549\) 0 0
\(550\) −13586.9 −1.05336
\(551\) −9304.70 −0.719408
\(552\) 0 0
\(553\) −1002.96 −0.0771255
\(554\) −9431.17 −0.723271
\(555\) 0 0
\(556\) 1442.07 0.109995
\(557\) 12074.7 0.918533 0.459267 0.888298i \(-0.348112\pi\)
0.459267 + 0.888298i \(0.348112\pi\)
\(558\) 0 0
\(559\) −277.790 −0.0210184
\(560\) −1591.89 −0.120124
\(561\) 0 0
\(562\) 1151.98 0.0864651
\(563\) −22157.6 −1.65867 −0.829335 0.558751i \(-0.811281\pi\)
−0.829335 + 0.558751i \(0.811281\pi\)
\(564\) 0 0
\(565\) −2143.62 −0.159616
\(566\) −15656.6 −1.16271
\(567\) 0 0
\(568\) 10190.6 0.752798
\(569\) 20839.2 1.53537 0.767683 0.640830i \(-0.221410\pi\)
0.767683 + 0.640830i \(0.221410\pi\)
\(570\) 0 0
\(571\) 15783.4 1.15677 0.578384 0.815765i \(-0.303683\pi\)
0.578384 + 0.815765i \(0.303683\pi\)
\(572\) −1802.03 −0.131725
\(573\) 0 0
\(574\) 10320.4 0.750465
\(575\) 17306.3 1.25517
\(576\) 0 0
\(577\) 6568.74 0.473934 0.236967 0.971518i \(-0.423847\pi\)
0.236967 + 0.971518i \(0.423847\pi\)
\(578\) −24135.4 −1.73685
\(579\) 0 0
\(580\) −3374.76 −0.241602
\(581\) 202.755 0.0144779
\(582\) 0 0
\(583\) −9220.67 −0.655028
\(584\) 5780.19 0.409565
\(585\) 0 0
\(586\) −11185.9 −0.788540
\(587\) 21007.0 1.47709 0.738546 0.674204i \(-0.235513\pi\)
0.738546 + 0.674204i \(0.235513\pi\)
\(588\) 0 0
\(589\) −9321.84 −0.652122
\(590\) −7757.31 −0.541294
\(591\) 0 0
\(592\) −1331.39 −0.0924320
\(593\) −4418.62 −0.305988 −0.152994 0.988227i \(-0.548892\pi\)
−0.152994 + 0.988227i \(0.548892\pi\)
\(594\) 0 0
\(595\) 8547.82 0.588952
\(596\) 6524.27 0.448397
\(597\) 0 0
\(598\) −2952.99 −0.201934
\(599\) −6648.83 −0.453529 −0.226764 0.973950i \(-0.572815\pi\)
−0.226764 + 0.973950i \(0.572815\pi\)
\(600\) 0 0
\(601\) −14071.6 −0.955064 −0.477532 0.878614i \(-0.658468\pi\)
−0.477532 + 0.878614i \(0.658468\pi\)
\(602\) −1037.15 −0.0702181
\(603\) 0 0
\(604\) 8716.92 0.587229
\(605\) 10983.7 0.738099
\(606\) 0 0
\(607\) 7017.00 0.469212 0.234606 0.972091i \(-0.424620\pi\)
0.234606 + 0.972091i \(0.424620\pi\)
\(608\) 6323.28 0.421781
\(609\) 0 0
\(610\) 4202.48 0.278940
\(611\) 2176.63 0.144120
\(612\) 0 0
\(613\) 21273.7 1.40169 0.700845 0.713314i \(-0.252807\pi\)
0.700845 + 0.713314i \(0.252807\pi\)
\(614\) 12199.4 0.801836
\(615\) 0 0
\(616\) −22111.9 −1.44629
\(617\) 1330.68 0.0868254 0.0434127 0.999057i \(-0.486177\pi\)
0.0434127 + 0.999057i \(0.486177\pi\)
\(618\) 0 0
\(619\) 19837.9 1.28813 0.644066 0.764970i \(-0.277246\pi\)
0.644066 + 0.764970i \(0.277246\pi\)
\(620\) −3380.98 −0.219005
\(621\) 0 0
\(622\) −16895.8 −1.08917
\(623\) 22147.9 1.42430
\(624\) 0 0
\(625\) 8354.46 0.534686
\(626\) −12951.8 −0.826929
\(627\) 0 0
\(628\) 5132.91 0.326155
\(629\) 7149.05 0.453182
\(630\) 0 0
\(631\) −20162.9 −1.27206 −0.636032 0.771663i \(-0.719425\pi\)
−0.636032 + 0.771663i \(0.719425\pi\)
\(632\) −1654.53 −0.104136
\(633\) 0 0
\(634\) 10501.8 0.657854
\(635\) −11668.4 −0.729204
\(636\) 0 0
\(637\) 1044.54 0.0649707
\(638\) 27694.5 1.71855
\(639\) 0 0
\(640\) 466.407 0.0288068
\(641\) −4425.57 −0.272698 −0.136349 0.990661i \(-0.543537\pi\)
−0.136349 + 0.990661i \(0.543537\pi\)
\(642\) 0 0
\(643\) 1555.17 0.0953809 0.0476905 0.998862i \(-0.484814\pi\)
0.0476905 + 0.998862i \(0.484814\pi\)
\(644\) 8569.79 0.524375
\(645\) 0 0
\(646\) 11829.5 0.720475
\(647\) 14141.3 0.859277 0.429639 0.903001i \(-0.358641\pi\)
0.429639 + 0.903001i \(0.358641\pi\)
\(648\) 0 0
\(649\) −49481.7 −2.99280
\(650\) −1862.98 −0.112419
\(651\) 0 0
\(652\) 6145.21 0.369118
\(653\) 13309.6 0.797618 0.398809 0.917034i \(-0.369424\pi\)
0.398809 + 0.917034i \(0.369424\pi\)
\(654\) 0 0
\(655\) −9513.38 −0.567509
\(656\) 7818.22 0.465321
\(657\) 0 0
\(658\) 8126.66 0.481474
\(659\) −23689.3 −1.40031 −0.700155 0.713991i \(-0.746886\pi\)
−0.700155 + 0.713991i \(0.746886\pi\)
\(660\) 0 0
\(661\) 216.801 0.0127573 0.00637867 0.999980i \(-0.497970\pi\)
0.00637867 + 0.999980i \(0.497970\pi\)
\(662\) 5775.10 0.339057
\(663\) 0 0
\(664\) 334.472 0.0195483
\(665\) −2925.93 −0.170621
\(666\) 0 0
\(667\) −35275.7 −2.04780
\(668\) −8513.11 −0.493087
\(669\) 0 0
\(670\) −6166.66 −0.355581
\(671\) 26806.4 1.54225
\(672\) 0 0
\(673\) 3912.27 0.224082 0.112041 0.993704i \(-0.464261\pi\)
0.112041 + 0.993704i \(0.464261\pi\)
\(674\) −13691.2 −0.782439
\(675\) 0 0
\(676\) 7439.69 0.423287
\(677\) 25774.0 1.46318 0.731590 0.681744i \(-0.238778\pi\)
0.731590 + 0.681744i \(0.238778\pi\)
\(678\) 0 0
\(679\) 6978.16 0.394399
\(680\) 14100.8 0.795209
\(681\) 0 0
\(682\) 27745.5 1.55782
\(683\) −18936.2 −1.06087 −0.530435 0.847725i \(-0.677971\pi\)
−0.530435 + 0.847725i \(0.677971\pi\)
\(684\) 0 0
\(685\) 8800.11 0.490854
\(686\) 14661.8 0.816019
\(687\) 0 0
\(688\) −785.694 −0.0435382
\(689\) −1264.30 −0.0699069
\(690\) 0 0
\(691\) 17599.7 0.968922 0.484461 0.874813i \(-0.339016\pi\)
0.484461 + 0.874813i \(0.339016\pi\)
\(692\) −9531.08 −0.523580
\(693\) 0 0
\(694\) −5473.23 −0.299367
\(695\) −1866.61 −0.101877
\(696\) 0 0
\(697\) −41980.9 −2.28140
\(698\) 8034.70 0.435699
\(699\) 0 0
\(700\) 5406.51 0.291924
\(701\) −14300.1 −0.770482 −0.385241 0.922816i \(-0.625882\pi\)
−0.385241 + 0.922816i \(0.625882\pi\)
\(702\) 0 0
\(703\) −2447.13 −0.131288
\(704\) −30474.6 −1.63147
\(705\) 0 0
\(706\) −22408.6 −1.19456
\(707\) −18543.7 −0.986432
\(708\) 0 0
\(709\) 955.389 0.0506070 0.0253035 0.999680i \(-0.491945\pi\)
0.0253035 + 0.999680i \(0.491945\pi\)
\(710\) −4013.57 −0.212150
\(711\) 0 0
\(712\) 36536.1 1.92310
\(713\) −35340.7 −1.85627
\(714\) 0 0
\(715\) 2332.54 0.122003
\(716\) −13156.7 −0.686719
\(717\) 0 0
\(718\) 15308.4 0.795689
\(719\) −34178.1 −1.77278 −0.886390 0.462940i \(-0.846795\pi\)
−0.886390 + 0.462940i \(0.846795\pi\)
\(720\) 0 0
\(721\) −9826.32 −0.507561
\(722\) 10502.9 0.541380
\(723\) 0 0
\(724\) −3384.72 −0.173746
\(725\) −22254.7 −1.14003
\(726\) 0 0
\(727\) −12282.6 −0.626599 −0.313299 0.949654i \(-0.601434\pi\)
−0.313299 + 0.949654i \(0.601434\pi\)
\(728\) −3031.88 −0.154353
\(729\) 0 0
\(730\) −2276.52 −0.115422
\(731\) 4218.87 0.213462
\(732\) 0 0
\(733\) −4269.39 −0.215134 −0.107567 0.994198i \(-0.534306\pi\)
−0.107567 + 0.994198i \(0.534306\pi\)
\(734\) −13419.5 −0.674824
\(735\) 0 0
\(736\) 23972.6 1.20060
\(737\) −39335.4 −1.96599
\(738\) 0 0
\(739\) −5321.85 −0.264909 −0.132454 0.991189i \(-0.542286\pi\)
−0.132454 + 0.991189i \(0.542286\pi\)
\(740\) −887.559 −0.0440909
\(741\) 0 0
\(742\) −4720.37 −0.233545
\(743\) 27587.5 1.36216 0.681080 0.732209i \(-0.261510\pi\)
0.681080 + 0.732209i \(0.261510\pi\)
\(744\) 0 0
\(745\) −8444.99 −0.415303
\(746\) 4137.37 0.203056
\(747\) 0 0
\(748\) 27367.9 1.33779
\(749\) 11148.8 0.543881
\(750\) 0 0
\(751\) 32157.3 1.56250 0.781249 0.624220i \(-0.214583\pi\)
0.781249 + 0.624220i \(0.214583\pi\)
\(752\) 6156.33 0.298535
\(753\) 0 0
\(754\) 3797.34 0.183410
\(755\) −11283.1 −0.543888
\(756\) 0 0
\(757\) 6817.36 0.327320 0.163660 0.986517i \(-0.447670\pi\)
0.163660 + 0.986517i \(0.447670\pi\)
\(758\) −23636.6 −1.13261
\(759\) 0 0
\(760\) −4826.74 −0.230374
\(761\) 20761.9 0.988986 0.494493 0.869182i \(-0.335354\pi\)
0.494493 + 0.869182i \(0.335354\pi\)
\(762\) 0 0
\(763\) −12921.8 −0.613109
\(764\) −2923.86 −0.138457
\(765\) 0 0
\(766\) −7597.82 −0.358382
\(767\) −6784.70 −0.319402
\(768\) 0 0
\(769\) −18990.3 −0.890515 −0.445258 0.895403i \(-0.646888\pi\)
−0.445258 + 0.895403i \(0.646888\pi\)
\(770\) 8708.74 0.407586
\(771\) 0 0
\(772\) 4558.21 0.212505
\(773\) −9384.47 −0.436657 −0.218329 0.975875i \(-0.570060\pi\)
−0.218329 + 0.975875i \(0.570060\pi\)
\(774\) 0 0
\(775\) −22295.7 −1.03340
\(776\) 11511.5 0.532522
\(777\) 0 0
\(778\) 5119.16 0.235901
\(779\) 14370.1 0.660928
\(780\) 0 0
\(781\) −25601.4 −1.17297
\(782\) 44847.8 2.05084
\(783\) 0 0
\(784\) 2954.36 0.134583
\(785\) −6644.01 −0.302083
\(786\) 0 0
\(787\) −41767.3 −1.89180 −0.945898 0.324464i \(-0.894816\pi\)
−0.945898 + 0.324464i \(0.894816\pi\)
\(788\) −13914.6 −0.629045
\(789\) 0 0
\(790\) 651.636 0.0293471
\(791\) −6999.94 −0.314651
\(792\) 0 0
\(793\) 3675.57 0.164595
\(794\) −28878.6 −1.29076
\(795\) 0 0
\(796\) −9277.44 −0.413103
\(797\) −9656.69 −0.429181 −0.214591 0.976704i \(-0.568842\pi\)
−0.214591 + 0.976704i \(0.568842\pi\)
\(798\) 0 0
\(799\) −33057.1 −1.46368
\(800\) 15123.9 0.668387
\(801\) 0 0
\(802\) 2010.53 0.0885214
\(803\) −14521.3 −0.638164
\(804\) 0 0
\(805\) −11092.7 −0.485673
\(806\) 3804.34 0.166256
\(807\) 0 0
\(808\) −30590.4 −1.33189
\(809\) 28931.7 1.25734 0.628668 0.777674i \(-0.283600\pi\)
0.628668 + 0.777674i \(0.283600\pi\)
\(810\) 0 0
\(811\) −33280.0 −1.44096 −0.720480 0.693476i \(-0.756079\pi\)
−0.720480 + 0.693476i \(0.756079\pi\)
\(812\) −11020.2 −0.476272
\(813\) 0 0
\(814\) 7283.63 0.313626
\(815\) −7954.33 −0.341875
\(816\) 0 0
\(817\) −1444.13 −0.0618404
\(818\) 4694.22 0.200647
\(819\) 0 0
\(820\) 5211.95 0.221962
\(821\) −7615.15 −0.323716 −0.161858 0.986814i \(-0.551749\pi\)
−0.161858 + 0.986814i \(0.551749\pi\)
\(822\) 0 0
\(823\) 4847.61 0.205318 0.102659 0.994717i \(-0.467265\pi\)
0.102659 + 0.994717i \(0.467265\pi\)
\(824\) −16209.9 −0.685314
\(825\) 0 0
\(826\) −25331.3 −1.06706
\(827\) 36284.3 1.52567 0.762834 0.646595i \(-0.223807\pi\)
0.762834 + 0.646595i \(0.223807\pi\)
\(828\) 0 0
\(829\) −26834.3 −1.12424 −0.562118 0.827057i \(-0.690013\pi\)
−0.562118 + 0.827057i \(0.690013\pi\)
\(830\) −131.732 −0.00550901
\(831\) 0 0
\(832\) −4178.53 −0.174116
\(833\) −15863.8 −0.659841
\(834\) 0 0
\(835\) 11019.3 0.456694
\(836\) −9368.07 −0.387561
\(837\) 0 0
\(838\) −15947.0 −0.657376
\(839\) −22500.9 −0.925883 −0.462942 0.886389i \(-0.653206\pi\)
−0.462942 + 0.886389i \(0.653206\pi\)
\(840\) 0 0
\(841\) 20973.2 0.859945
\(842\) 11195.6 0.458225
\(843\) 0 0
\(844\) 3948.71 0.161043
\(845\) −9629.90 −0.392046
\(846\) 0 0
\(847\) 35866.9 1.45502
\(848\) −3575.90 −0.144808
\(849\) 0 0
\(850\) 28293.6 1.14172
\(851\) −9277.48 −0.373711
\(852\) 0 0
\(853\) −11019.1 −0.442308 −0.221154 0.975239i \(-0.570982\pi\)
−0.221154 + 0.975239i \(0.570982\pi\)
\(854\) 13723.1 0.549877
\(855\) 0 0
\(856\) 18391.4 0.734353
\(857\) 22920.3 0.913586 0.456793 0.889573i \(-0.348998\pi\)
0.456793 + 0.889573i \(0.348998\pi\)
\(858\) 0 0
\(859\) −29518.9 −1.17249 −0.586246 0.810133i \(-0.699395\pi\)
−0.586246 + 0.810133i \(0.699395\pi\)
\(860\) −523.776 −0.0207681
\(861\) 0 0
\(862\) −4619.87 −0.182544
\(863\) 22986.6 0.906688 0.453344 0.891336i \(-0.350231\pi\)
0.453344 + 0.891336i \(0.350231\pi\)
\(864\) 0 0
\(865\) 12337.0 0.484936
\(866\) −3471.69 −0.136227
\(867\) 0 0
\(868\) −11040.5 −0.431727
\(869\) 4156.60 0.162259
\(870\) 0 0
\(871\) −5393.49 −0.209818
\(872\) −21316.4 −0.827827
\(873\) 0 0
\(874\) −15351.5 −0.594132
\(875\) −15370.0 −0.593828
\(876\) 0 0
\(877\) 1336.66 0.0514660 0.0257330 0.999669i \(-0.491808\pi\)
0.0257330 + 0.999669i \(0.491808\pi\)
\(878\) −16050.6 −0.616949
\(879\) 0 0
\(880\) 6597.28 0.252721
\(881\) −18598.2 −0.711227 −0.355613 0.934633i \(-0.615728\pi\)
−0.355613 + 0.934633i \(0.615728\pi\)
\(882\) 0 0
\(883\) 43727.7 1.66654 0.833269 0.552867i \(-0.186466\pi\)
0.833269 + 0.552867i \(0.186466\pi\)
\(884\) 3752.56 0.142774
\(885\) 0 0
\(886\) −3000.28 −0.113766
\(887\) 18665.8 0.706579 0.353289 0.935514i \(-0.385063\pi\)
0.353289 + 0.935514i \(0.385063\pi\)
\(888\) 0 0
\(889\) −38102.7 −1.43748
\(890\) −14389.7 −0.541960
\(891\) 0 0
\(892\) 8801.64 0.330382
\(893\) 11315.5 0.424030
\(894\) 0 0
\(895\) 17030.0 0.636035
\(896\) 1523.04 0.0567871
\(897\) 0 0
\(898\) 13744.4 0.510753
\(899\) 45445.8 1.68599
\(900\) 0 0
\(901\) 19201.2 0.709972
\(902\) −42771.2 −1.57885
\(903\) 0 0
\(904\) −11547.4 −0.424846
\(905\) 4381.16 0.160922
\(906\) 0 0
\(907\) −21624.4 −0.791649 −0.395825 0.918326i \(-0.629541\pi\)
−0.395825 + 0.918326i \(0.629541\pi\)
\(908\) −1213.14 −0.0443387
\(909\) 0 0
\(910\) 1194.10 0.0434990
\(911\) 15510.6 0.564093 0.282046 0.959401i \(-0.408987\pi\)
0.282046 + 0.959401i \(0.408987\pi\)
\(912\) 0 0
\(913\) −840.279 −0.0304591
\(914\) −15144.0 −0.548050
\(915\) 0 0
\(916\) −4956.31 −0.178779
\(917\) −31065.7 −1.11874
\(918\) 0 0
\(919\) 348.853 0.0125219 0.00626093 0.999980i \(-0.498007\pi\)
0.00626093 + 0.999980i \(0.498007\pi\)
\(920\) −18299.0 −0.655760
\(921\) 0 0
\(922\) −2919.33 −0.104277
\(923\) −3510.35 −0.125184
\(924\) 0 0
\(925\) −5852.98 −0.208048
\(926\) −21087.9 −0.748372
\(927\) 0 0
\(928\) −30827.2 −1.09047
\(929\) 25420.2 0.897749 0.448875 0.893595i \(-0.351825\pi\)
0.448875 + 0.893595i \(0.351825\pi\)
\(930\) 0 0
\(931\) 5430.19 0.191157
\(932\) −9494.69 −0.333701
\(933\) 0 0
\(934\) −9177.19 −0.321506
\(935\) −35424.9 −1.23906
\(936\) 0 0
\(937\) 37546.0 1.30904 0.654521 0.756044i \(-0.272870\pi\)
0.654521 + 0.756044i \(0.272870\pi\)
\(938\) −20137.1 −0.700959
\(939\) 0 0
\(940\) 4104.06 0.142404
\(941\) −35076.2 −1.21514 −0.607572 0.794265i \(-0.707856\pi\)
−0.607572 + 0.794265i \(0.707856\pi\)
\(942\) 0 0
\(943\) 54479.5 1.88133
\(944\) −19189.7 −0.661621
\(945\) 0 0
\(946\) 4298.30 0.147727
\(947\) −42212.3 −1.44849 −0.724243 0.689545i \(-0.757811\pi\)
−0.724243 + 0.689545i \(0.757811\pi\)
\(948\) 0 0
\(949\) −1991.09 −0.0681071
\(950\) −9684.93 −0.330759
\(951\) 0 0
\(952\) 46045.9 1.56760
\(953\) 25142.4 0.854610 0.427305 0.904108i \(-0.359463\pi\)
0.427305 + 0.904108i \(0.359463\pi\)
\(954\) 0 0
\(955\) 3784.63 0.128238
\(956\) 836.204 0.0282895
\(957\) 0 0
\(958\) −5012.73 −0.169054
\(959\) 28736.5 0.967624
\(960\) 0 0
\(961\) 15738.5 0.528298
\(962\) 998.698 0.0334712
\(963\) 0 0
\(964\) −19801.4 −0.661577
\(965\) −5900.12 −0.196820
\(966\) 0 0
\(967\) 36960.6 1.22913 0.614566 0.788865i \(-0.289331\pi\)
0.614566 + 0.788865i \(0.289331\pi\)
\(968\) 59167.5 1.96458
\(969\) 0 0
\(970\) −4533.78 −0.150073
\(971\) 14076.6 0.465231 0.232615 0.972569i \(-0.425272\pi\)
0.232615 + 0.972569i \(0.425272\pi\)
\(972\) 0 0
\(973\) −6095.37 −0.200831
\(974\) 7614.37 0.250493
\(975\) 0 0
\(976\) 10395.9 0.340947
\(977\) −40542.1 −1.32759 −0.663795 0.747915i \(-0.731055\pi\)
−0.663795 + 0.747915i \(0.731055\pi\)
\(978\) 0 0
\(979\) −91788.0 −2.99648
\(980\) 1969.50 0.0641972
\(981\) 0 0
\(982\) 43655.7 1.41864
\(983\) −20946.5 −0.679644 −0.339822 0.940490i \(-0.610367\pi\)
−0.339822 + 0.940490i \(0.610367\pi\)
\(984\) 0 0
\(985\) 18011.0 0.582618
\(986\) −57671.3 −1.86271
\(987\) 0 0
\(988\) −1284.51 −0.0413619
\(989\) −5474.93 −0.176029
\(990\) 0 0
\(991\) −14016.6 −0.449295 −0.224648 0.974440i \(-0.572123\pi\)
−0.224648 + 0.974440i \(0.572123\pi\)
\(992\) −30884.0 −0.988477
\(993\) 0 0
\(994\) −13106.2 −0.418213
\(995\) 12008.7 0.382614
\(996\) 0 0
\(997\) −31149.2 −0.989474 −0.494737 0.869043i \(-0.664736\pi\)
−0.494737 + 0.869043i \(0.664736\pi\)
\(998\) −31037.8 −0.984454
\(999\) 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.1.19 yes 59
3.2 odd 2 2151.4.a.g.1.41 59
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2151.4.a.g.1.41 59 3.2 odd 2
2151.4.a.h.1.19 yes 59 1.1 even 1 trivial