Properties

Label 2151.4.a.h.1.5
Level $2151$
Weight $4$
Character 2151.1
Self dual yes
Analytic conductor $126.913$
Analytic rank $0$
Dimension $59$
CM no
Inner twists $1$

Related objects

Downloads

Learn more about

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 1.5
Character \(\chi\) \(=\) 2151.1

$q$-expansion

\(f(q)\) \(=\) \(q-5.09369 q^{2} +17.9457 q^{4} -15.2658 q^{5} -21.0984 q^{7} -50.6602 q^{8} +O(q^{10})\) \(q-5.09369 q^{2} +17.9457 q^{4} -15.2658 q^{5} -21.0984 q^{7} -50.6602 q^{8} +77.7594 q^{10} +65.8349 q^{11} -72.1125 q^{13} +107.469 q^{14} +114.482 q^{16} +51.9062 q^{17} +10.1429 q^{19} -273.955 q^{20} -335.343 q^{22} -9.17600 q^{23} +108.045 q^{25} +367.319 q^{26} -378.625 q^{28} +32.6852 q^{29} +212.392 q^{31} -177.853 q^{32} -264.394 q^{34} +322.084 q^{35} -53.7021 q^{37} -51.6646 q^{38} +773.369 q^{40} +49.4038 q^{41} -259.609 q^{43} +1181.45 q^{44} +46.7397 q^{46} +276.825 q^{47} +102.141 q^{49} -550.349 q^{50} -1294.11 q^{52} +226.029 q^{53} -1005.02 q^{55} +1068.85 q^{56} -166.488 q^{58} -894.934 q^{59} -118.405 q^{61} -1081.86 q^{62} -9.92451 q^{64} +1100.86 q^{65} -270.762 q^{67} +931.492 q^{68} -1640.60 q^{70} +314.378 q^{71} +338.874 q^{73} +273.542 q^{74} +182.021 q^{76} -1389.01 q^{77} -716.571 q^{79} -1747.66 q^{80} -251.648 q^{82} -632.265 q^{83} -792.391 q^{85} +1322.37 q^{86} -3335.21 q^{88} +187.187 q^{89} +1521.46 q^{91} -164.670 q^{92} -1410.06 q^{94} -154.839 q^{95} -483.286 q^{97} -520.277 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 59q + 8q^{2} + 238q^{4} + 80q^{5} - 10q^{7} + 96q^{8} + O(q^{10}) \) \( 59q + 8q^{2} + 238q^{4} + 80q^{5} - 10q^{7} + 96q^{8} - 36q^{10} + 132q^{11} + 104q^{13} + 280q^{14} + 822q^{16} + 408q^{17} + 20q^{19} + 800q^{20} - 2q^{22} + 276q^{23} + 1477q^{25} + 780q^{26} + 224q^{28} + 696q^{29} - 380q^{31} + 896q^{32} - 72q^{34} + 700q^{35} + 224q^{37} + 988q^{38} - 258q^{40} + 2706q^{41} - 156q^{43} + 1584q^{44} + 428q^{46} + 1316q^{47} + 2135q^{49} + 1400q^{50} + 1092q^{52} + 1484q^{53} - 992q^{55} + 3360q^{56} - 120q^{58} + 3186q^{59} - 254q^{61} + 1240q^{62} + 3054q^{64} + 5120q^{65} + 288q^{67} + 9420q^{68} + 1108q^{70} + 4468q^{71} - 1770q^{73} + 6214q^{74} + 720q^{76} + 6352q^{77} - 746q^{79} + 7040q^{80} + 276q^{82} + 5484q^{83} + 588q^{85} + 10152q^{86} + 1186q^{88} + 11570q^{89} + 1768q^{91} + 15366q^{92} - 2142q^{94} + 5736q^{95} + 2390q^{97} + 6912q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −5.09369 −1.80089 −0.900446 0.434969i \(-0.856759\pi\)
−0.900446 + 0.434969i \(0.856759\pi\)
\(3\) 0 0
\(4\) 17.9457 2.24321
\(5\) −15.2658 −1.36542 −0.682708 0.730691i \(-0.739198\pi\)
−0.682708 + 0.730691i \(0.739198\pi\)
\(6\) 0 0
\(7\) −21.0984 −1.13921 −0.569603 0.821920i \(-0.692903\pi\)
−0.569603 + 0.821920i \(0.692903\pi\)
\(8\) −50.6602 −2.23888
\(9\) 0 0
\(10\) 77.7594 2.45897
\(11\) 65.8349 1.80454 0.902272 0.431167i \(-0.141898\pi\)
0.902272 + 0.431167i \(0.141898\pi\)
\(12\) 0 0
\(13\) −72.1125 −1.53849 −0.769247 0.638952i \(-0.779368\pi\)
−0.769247 + 0.638952i \(0.779368\pi\)
\(14\) 107.469 2.05158
\(15\) 0 0
\(16\) 114.482 1.78878
\(17\) 51.9062 0.740536 0.370268 0.928925i \(-0.379266\pi\)
0.370268 + 0.928925i \(0.379266\pi\)
\(18\) 0 0
\(19\) 10.1429 0.122470 0.0612351 0.998123i \(-0.480496\pi\)
0.0612351 + 0.998123i \(0.480496\pi\)
\(20\) −273.955 −3.06292
\(21\) 0 0
\(22\) −335.343 −3.24979
\(23\) −9.17600 −0.0831882 −0.0415941 0.999135i \(-0.513244\pi\)
−0.0415941 + 0.999135i \(0.513244\pi\)
\(24\) 0 0
\(25\) 108.045 0.864363
\(26\) 367.319 2.77066
\(27\) 0 0
\(28\) −378.625 −2.55548
\(29\) 32.6852 0.209292 0.104646 0.994510i \(-0.466629\pi\)
0.104646 + 0.994510i \(0.466629\pi\)
\(30\) 0 0
\(31\) 212.392 1.23054 0.615270 0.788317i \(-0.289047\pi\)
0.615270 + 0.788317i \(0.289047\pi\)
\(32\) −177.853 −0.982510
\(33\) 0 0
\(34\) −264.394 −1.33362
\(35\) 322.084 1.55549
\(36\) 0 0
\(37\) −53.7021 −0.238610 −0.119305 0.992858i \(-0.538067\pi\)
−0.119305 + 0.992858i \(0.538067\pi\)
\(38\) −51.6646 −0.220556
\(39\) 0 0
\(40\) 773.369 3.05701
\(41\) 49.4038 0.188185 0.0940925 0.995563i \(-0.470005\pi\)
0.0940925 + 0.995563i \(0.470005\pi\)
\(42\) 0 0
\(43\) −259.609 −0.920697 −0.460348 0.887738i \(-0.652276\pi\)
−0.460348 + 0.887738i \(0.652276\pi\)
\(44\) 1181.45 4.04797
\(45\) 0 0
\(46\) 46.7397 0.149813
\(47\) 276.825 0.859131 0.429565 0.903036i \(-0.358667\pi\)
0.429565 + 0.903036i \(0.358667\pi\)
\(48\) 0 0
\(49\) 102.141 0.297788
\(50\) −550.349 −1.55662
\(51\) 0 0
\(52\) −1294.11 −3.45116
\(53\) 226.029 0.585800 0.292900 0.956143i \(-0.405380\pi\)
0.292900 + 0.956143i \(0.405380\pi\)
\(54\) 0 0
\(55\) −1005.02 −2.46395
\(56\) 1068.85 2.55055
\(57\) 0 0
\(58\) −166.488 −0.376913
\(59\) −894.934 −1.97475 −0.987377 0.158389i \(-0.949370\pi\)
−0.987377 + 0.158389i \(0.949370\pi\)
\(60\) 0 0
\(61\) −118.405 −0.248528 −0.124264 0.992249i \(-0.539657\pi\)
−0.124264 + 0.992249i \(0.539657\pi\)
\(62\) −1081.86 −2.21607
\(63\) 0 0
\(64\) −9.92451 −0.0193838
\(65\) 1100.86 2.10068
\(66\) 0 0
\(67\) −270.762 −0.493715 −0.246857 0.969052i \(-0.579398\pi\)
−0.246857 + 0.969052i \(0.579398\pi\)
\(68\) 931.492 1.66118
\(69\) 0 0
\(70\) −1640.60 −2.80127
\(71\) 314.378 0.525490 0.262745 0.964865i \(-0.415372\pi\)
0.262745 + 0.964865i \(0.415372\pi\)
\(72\) 0 0
\(73\) 338.874 0.543319 0.271659 0.962393i \(-0.412428\pi\)
0.271659 + 0.962393i \(0.412428\pi\)
\(74\) 273.542 0.429710
\(75\) 0 0
\(76\) 182.021 0.274726
\(77\) −1389.01 −2.05575
\(78\) 0 0
\(79\) −716.571 −1.02051 −0.510257 0.860022i \(-0.670450\pi\)
−0.510257 + 0.860022i \(0.670450\pi\)
\(80\) −1747.66 −2.44243
\(81\) 0 0
\(82\) −251.648 −0.338901
\(83\) −632.265 −0.836146 −0.418073 0.908413i \(-0.637294\pi\)
−0.418073 + 0.908413i \(0.637294\pi\)
\(84\) 0 0
\(85\) −792.391 −1.01114
\(86\) 1322.37 1.65807
\(87\) 0 0
\(88\) −3335.21 −4.04017
\(89\) 187.187 0.222941 0.111471 0.993768i \(-0.464444\pi\)
0.111471 + 0.993768i \(0.464444\pi\)
\(90\) 0 0
\(91\) 1521.46 1.75266
\(92\) −164.670 −0.186609
\(93\) 0 0
\(94\) −1410.06 −1.54720
\(95\) −154.839 −0.167223
\(96\) 0 0
\(97\) −483.286 −0.505879 −0.252939 0.967482i \(-0.581397\pi\)
−0.252939 + 0.967482i \(0.581397\pi\)
\(98\) −520.277 −0.536284
\(99\) 0 0
\(100\) 1938.95 1.93895
\(101\) −883.661 −0.870570 −0.435285 0.900293i \(-0.643352\pi\)
−0.435285 + 0.900293i \(0.643352\pi\)
\(102\) 0 0
\(103\) −303.031 −0.289889 −0.144945 0.989440i \(-0.546300\pi\)
−0.144945 + 0.989440i \(0.546300\pi\)
\(104\) 3653.23 3.44451
\(105\) 0 0
\(106\) −1151.32 −1.05496
\(107\) 287.390 0.259655 0.129827 0.991537i \(-0.458558\pi\)
0.129827 + 0.991537i \(0.458558\pi\)
\(108\) 0 0
\(109\) −1904.73 −1.67376 −0.836880 0.547386i \(-0.815623\pi\)
−0.836880 + 0.547386i \(0.815623\pi\)
\(110\) 5119.28 4.43731
\(111\) 0 0
\(112\) −2415.38 −2.03779
\(113\) 874.738 0.728217 0.364108 0.931357i \(-0.381374\pi\)
0.364108 + 0.931357i \(0.381374\pi\)
\(114\) 0 0
\(115\) 140.079 0.113587
\(116\) 586.557 0.469487
\(117\) 0 0
\(118\) 4558.52 3.55632
\(119\) −1095.14 −0.843622
\(120\) 0 0
\(121\) 3003.24 2.25638
\(122\) 603.119 0.447572
\(123\) 0 0
\(124\) 3811.52 2.76036
\(125\) 258.827 0.185202
\(126\) 0 0
\(127\) 1384.96 0.967677 0.483839 0.875157i \(-0.339242\pi\)
0.483839 + 0.875157i \(0.339242\pi\)
\(128\) 1473.38 1.01742
\(129\) 0 0
\(130\) −5607.42 −3.78311
\(131\) 717.700 0.478670 0.239335 0.970937i \(-0.423071\pi\)
0.239335 + 0.970937i \(0.423071\pi\)
\(132\) 0 0
\(133\) −213.998 −0.139519
\(134\) 1379.18 0.889127
\(135\) 0 0
\(136\) −2629.58 −1.65797
\(137\) −1873.04 −1.16806 −0.584032 0.811731i \(-0.698526\pi\)
−0.584032 + 0.811731i \(0.698526\pi\)
\(138\) 0 0
\(139\) 1957.96 1.19476 0.597381 0.801958i \(-0.296208\pi\)
0.597381 + 0.801958i \(0.296208\pi\)
\(140\) 5780.01 3.48929
\(141\) 0 0
\(142\) −1601.34 −0.946351
\(143\) −4747.52 −2.77628
\(144\) 0 0
\(145\) −498.966 −0.285771
\(146\) −1726.12 −0.978458
\(147\) 0 0
\(148\) −963.720 −0.535252
\(149\) 238.440 0.131099 0.0655497 0.997849i \(-0.479120\pi\)
0.0655497 + 0.997849i \(0.479120\pi\)
\(150\) 0 0
\(151\) 2937.31 1.58301 0.791507 0.611161i \(-0.209297\pi\)
0.791507 + 0.611161i \(0.209297\pi\)
\(152\) −513.840 −0.274197
\(153\) 0 0
\(154\) 7075.19 3.70217
\(155\) −3242.34 −1.68020
\(156\) 0 0
\(157\) −3524.14 −1.79145 −0.895723 0.444613i \(-0.853341\pi\)
−0.895723 + 0.444613i \(0.853341\pi\)
\(158\) 3649.99 1.83783
\(159\) 0 0
\(160\) 2715.08 1.34154
\(161\) 193.599 0.0947684
\(162\) 0 0
\(163\) −1629.25 −0.782901 −0.391451 0.920199i \(-0.628027\pi\)
−0.391451 + 0.920199i \(0.628027\pi\)
\(164\) 886.585 0.422138
\(165\) 0 0
\(166\) 3220.56 1.50581
\(167\) −3327.84 −1.54201 −0.771005 0.636829i \(-0.780246\pi\)
−0.771005 + 0.636829i \(0.780246\pi\)
\(168\) 0 0
\(169\) 3003.22 1.36696
\(170\) 4036.19 1.82095
\(171\) 0 0
\(172\) −4658.85 −2.06532
\(173\) −4303.92 −1.89145 −0.945725 0.324969i \(-0.894646\pi\)
−0.945725 + 0.324969i \(0.894646\pi\)
\(174\) 0 0
\(175\) −2279.58 −0.984686
\(176\) 7536.90 3.22793
\(177\) 0 0
\(178\) −953.473 −0.401493
\(179\) 812.139 0.339118 0.169559 0.985520i \(-0.445766\pi\)
0.169559 + 0.985520i \(0.445766\pi\)
\(180\) 0 0
\(181\) 2852.30 1.17132 0.585662 0.810555i \(-0.300834\pi\)
0.585662 + 0.810555i \(0.300834\pi\)
\(182\) −7749.83 −3.15635
\(183\) 0 0
\(184\) 464.858 0.186249
\(185\) 819.806 0.325802
\(186\) 0 0
\(187\) 3417.24 1.33633
\(188\) 4967.82 1.92721
\(189\) 0 0
\(190\) 788.703 0.301150
\(191\) −470.301 −0.178166 −0.0890831 0.996024i \(-0.528394\pi\)
−0.0890831 + 0.996024i \(0.528394\pi\)
\(192\) 0 0
\(193\) 597.809 0.222960 0.111480 0.993767i \(-0.464441\pi\)
0.111480 + 0.993767i \(0.464441\pi\)
\(194\) 2461.71 0.911033
\(195\) 0 0
\(196\) 1833.00 0.668001
\(197\) −3383.20 −1.22357 −0.611784 0.791025i \(-0.709548\pi\)
−0.611784 + 0.791025i \(0.709548\pi\)
\(198\) 0 0
\(199\) −2613.38 −0.930944 −0.465472 0.885063i \(-0.654115\pi\)
−0.465472 + 0.885063i \(0.654115\pi\)
\(200\) −5473.59 −1.93521
\(201\) 0 0
\(202\) 4501.09 1.56780
\(203\) −689.604 −0.238427
\(204\) 0 0
\(205\) −754.190 −0.256951
\(206\) 1543.55 0.522059
\(207\) 0 0
\(208\) −8255.57 −2.75202
\(209\) 667.755 0.221003
\(210\) 0 0
\(211\) −5044.71 −1.64593 −0.822967 0.568089i \(-0.807683\pi\)
−0.822967 + 0.568089i \(0.807683\pi\)
\(212\) 4056.24 1.31407
\(213\) 0 0
\(214\) −1463.88 −0.467610
\(215\) 3963.14 1.25713
\(216\) 0 0
\(217\) −4481.12 −1.40184
\(218\) 9702.09 3.01426
\(219\) 0 0
\(220\) −18035.8 −5.52716
\(221\) −3743.09 −1.13931
\(222\) 0 0
\(223\) 1710.18 0.513553 0.256777 0.966471i \(-0.417340\pi\)
0.256777 + 0.966471i \(0.417340\pi\)
\(224\) 3752.42 1.11928
\(225\) 0 0
\(226\) −4455.65 −1.31144
\(227\) 4856.18 1.41989 0.709947 0.704255i \(-0.248719\pi\)
0.709947 + 0.704255i \(0.248719\pi\)
\(228\) 0 0
\(229\) −6598.10 −1.90399 −0.951997 0.306108i \(-0.900973\pi\)
−0.951997 + 0.306108i \(0.900973\pi\)
\(230\) −713.520 −0.204557
\(231\) 0 0
\(232\) −1655.84 −0.468582
\(233\) −3530.52 −0.992670 −0.496335 0.868131i \(-0.665321\pi\)
−0.496335 + 0.868131i \(0.665321\pi\)
\(234\) 0 0
\(235\) −4225.97 −1.17307
\(236\) −16060.2 −4.42979
\(237\) 0 0
\(238\) 5578.29 1.51927
\(239\) −239.000 −0.0646846
\(240\) 0 0
\(241\) −894.168 −0.238998 −0.119499 0.992834i \(-0.538129\pi\)
−0.119499 + 0.992834i \(0.538129\pi\)
\(242\) −15297.6 −4.06349
\(243\) 0 0
\(244\) −2124.86 −0.557501
\(245\) −1559.27 −0.406605
\(246\) 0 0
\(247\) −731.428 −0.188420
\(248\) −10759.8 −2.75503
\(249\) 0 0
\(250\) −1318.38 −0.333528
\(251\) 6830.85 1.71777 0.858884 0.512171i \(-0.171158\pi\)
0.858884 + 0.512171i \(0.171158\pi\)
\(252\) 0 0
\(253\) −604.102 −0.150117
\(254\) −7054.54 −1.74268
\(255\) 0 0
\(256\) −7425.54 −1.81288
\(257\) 5522.18 1.34033 0.670164 0.742213i \(-0.266224\pi\)
0.670164 + 0.742213i \(0.266224\pi\)
\(258\) 0 0
\(259\) 1133.03 0.271826
\(260\) 19755.6 4.71228
\(261\) 0 0
\(262\) −3655.74 −0.862032
\(263\) −1758.65 −0.412330 −0.206165 0.978517i \(-0.566098\pi\)
−0.206165 + 0.978517i \(0.566098\pi\)
\(264\) 0 0
\(265\) −3450.51 −0.799862
\(266\) 1090.04 0.251258
\(267\) 0 0
\(268\) −4859.01 −1.10751
\(269\) −4098.64 −0.928990 −0.464495 0.885576i \(-0.653764\pi\)
−0.464495 + 0.885576i \(0.653764\pi\)
\(270\) 0 0
\(271\) 708.798 0.158880 0.0794398 0.996840i \(-0.474687\pi\)
0.0794398 + 0.996840i \(0.474687\pi\)
\(272\) 5942.32 1.32465
\(273\) 0 0
\(274\) 9540.69 2.10356
\(275\) 7113.16 1.55978
\(276\) 0 0
\(277\) −1802.14 −0.390904 −0.195452 0.980713i \(-0.562617\pi\)
−0.195452 + 0.980713i \(0.562617\pi\)
\(278\) −9973.23 −2.15164
\(279\) 0 0
\(280\) −16316.8 −3.48256
\(281\) 5937.56 1.26052 0.630258 0.776386i \(-0.282949\pi\)
0.630258 + 0.776386i \(0.282949\pi\)
\(282\) 0 0
\(283\) 2616.37 0.549566 0.274783 0.961506i \(-0.411394\pi\)
0.274783 + 0.961506i \(0.411394\pi\)
\(284\) 5641.73 1.17878
\(285\) 0 0
\(286\) 24182.4 4.99978
\(287\) −1042.34 −0.214381
\(288\) 0 0
\(289\) −2218.74 −0.451607
\(290\) 2541.58 0.514643
\(291\) 0 0
\(292\) 6081.33 1.21878
\(293\) −3627.53 −0.723285 −0.361642 0.932317i \(-0.617784\pi\)
−0.361642 + 0.932317i \(0.617784\pi\)
\(294\) 0 0
\(295\) 13661.9 2.69636
\(296\) 2720.56 0.534220
\(297\) 0 0
\(298\) −1214.54 −0.236096
\(299\) 661.705 0.127985
\(300\) 0 0
\(301\) 5477.32 1.04886
\(302\) −14961.8 −2.85083
\(303\) 0 0
\(304\) 1161.17 0.219072
\(305\) 1807.55 0.339345
\(306\) 0 0
\(307\) −351.968 −0.0654328 −0.0327164 0.999465i \(-0.510416\pi\)
−0.0327164 + 0.999465i \(0.510416\pi\)
\(308\) −24926.7 −4.61147
\(309\) 0 0
\(310\) 16515.5 3.02585
\(311\) 9713.56 1.77108 0.885540 0.464564i \(-0.153789\pi\)
0.885540 + 0.464564i \(0.153789\pi\)
\(312\) 0 0
\(313\) 1189.54 0.214814 0.107407 0.994215i \(-0.465745\pi\)
0.107407 + 0.994215i \(0.465745\pi\)
\(314\) 17950.9 3.22620
\(315\) 0 0
\(316\) −12859.3 −2.28922
\(317\) −7847.06 −1.39033 −0.695165 0.718850i \(-0.744669\pi\)
−0.695165 + 0.718850i \(0.744669\pi\)
\(318\) 0 0
\(319\) 2151.83 0.377677
\(320\) 151.506 0.0264670
\(321\) 0 0
\(322\) −986.132 −0.170668
\(323\) 526.478 0.0906936
\(324\) 0 0
\(325\) −7791.42 −1.32982
\(326\) 8298.90 1.40992
\(327\) 0 0
\(328\) −2502.81 −0.421324
\(329\) −5840.57 −0.978726
\(330\) 0 0
\(331\) 7868.75 1.30666 0.653332 0.757071i \(-0.273371\pi\)
0.653332 + 0.757071i \(0.273371\pi\)
\(332\) −11346.4 −1.87565
\(333\) 0 0
\(334\) 16951.0 2.77699
\(335\) 4133.41 0.674126
\(336\) 0 0
\(337\) −3434.71 −0.555194 −0.277597 0.960698i \(-0.589538\pi\)
−0.277597 + 0.960698i \(0.589538\pi\)
\(338\) −15297.5 −2.46175
\(339\) 0 0
\(340\) −14220.0 −2.26820
\(341\) 13982.8 2.22056
\(342\) 0 0
\(343\) 5081.73 0.799963
\(344\) 13151.8 2.06133
\(345\) 0 0
\(346\) 21922.8 3.40629
\(347\) −6802.75 −1.05242 −0.526211 0.850354i \(-0.676388\pi\)
−0.526211 + 0.850354i \(0.676388\pi\)
\(348\) 0 0
\(349\) 5753.22 0.882415 0.441208 0.897405i \(-0.354550\pi\)
0.441208 + 0.897405i \(0.354550\pi\)
\(350\) 11611.5 1.77331
\(351\) 0 0
\(352\) −11709.0 −1.77298
\(353\) 10610.4 1.59981 0.799907 0.600123i \(-0.204882\pi\)
0.799907 + 0.600123i \(0.204882\pi\)
\(354\) 0 0
\(355\) −4799.24 −0.717513
\(356\) 3359.20 0.500104
\(357\) 0 0
\(358\) −4136.79 −0.610715
\(359\) −931.791 −0.136986 −0.0684931 0.997652i \(-0.521819\pi\)
−0.0684931 + 0.997652i \(0.521819\pi\)
\(360\) 0 0
\(361\) −6756.12 −0.985001
\(362\) −14528.7 −2.10943
\(363\) 0 0
\(364\) 27303.6 3.93158
\(365\) −5173.20 −0.741856
\(366\) 0 0
\(367\) −82.0412 −0.0116690 −0.00583449 0.999983i \(-0.501857\pi\)
−0.00583449 + 0.999983i \(0.501857\pi\)
\(368\) −1050.49 −0.148805
\(369\) 0 0
\(370\) −4175.84 −0.586734
\(371\) −4768.84 −0.667347
\(372\) 0 0
\(373\) −14168.5 −1.96680 −0.983400 0.181448i \(-0.941922\pi\)
−0.983400 + 0.181448i \(0.941922\pi\)
\(374\) −17406.4 −2.40658
\(375\) 0 0
\(376\) −14024.0 −1.92349
\(377\) −2357.01 −0.321995
\(378\) 0 0
\(379\) 6954.02 0.942490 0.471245 0.882002i \(-0.343805\pi\)
0.471245 + 0.882002i \(0.343805\pi\)
\(380\) −2778.69 −0.375116
\(381\) 0 0
\(382\) 2395.57 0.320858
\(383\) −1197.77 −0.159799 −0.0798994 0.996803i \(-0.525460\pi\)
−0.0798994 + 0.996803i \(0.525460\pi\)
\(384\) 0 0
\(385\) 21204.4 2.80695
\(386\) −3045.05 −0.401526
\(387\) 0 0
\(388\) −8672.89 −1.13479
\(389\) 6557.56 0.854708 0.427354 0.904084i \(-0.359446\pi\)
0.427354 + 0.904084i \(0.359446\pi\)
\(390\) 0 0
\(391\) −476.292 −0.0616038
\(392\) −5174.50 −0.666714
\(393\) 0 0
\(394\) 17233.0 2.20351
\(395\) 10939.0 1.39343
\(396\) 0 0
\(397\) 10980.4 1.38814 0.694072 0.719906i \(-0.255815\pi\)
0.694072 + 0.719906i \(0.255815\pi\)
\(398\) 13311.8 1.67653
\(399\) 0 0
\(400\) 12369.2 1.54615
\(401\) −7274.21 −0.905877 −0.452939 0.891542i \(-0.649624\pi\)
−0.452939 + 0.891542i \(0.649624\pi\)
\(402\) 0 0
\(403\) −15316.1 −1.89318
\(404\) −15857.9 −1.95287
\(405\) 0 0
\(406\) 3512.63 0.429381
\(407\) −3535.47 −0.430582
\(408\) 0 0
\(409\) 3143.20 0.380003 0.190001 0.981784i \(-0.439151\pi\)
0.190001 + 0.981784i \(0.439151\pi\)
\(410\) 3841.61 0.462741
\(411\) 0 0
\(412\) −5438.10 −0.650282
\(413\) 18881.7 2.24965
\(414\) 0 0
\(415\) 9652.05 1.14169
\(416\) 12825.5 1.51159
\(417\) 0 0
\(418\) −3401.34 −0.398002
\(419\) 8638.09 1.00716 0.503578 0.863950i \(-0.332017\pi\)
0.503578 + 0.863950i \(0.332017\pi\)
\(420\) 0 0
\(421\) −15140.2 −1.75270 −0.876352 0.481671i \(-0.840030\pi\)
−0.876352 + 0.481671i \(0.840030\pi\)
\(422\) 25696.2 2.96415
\(423\) 0 0
\(424\) −11450.6 −1.31154
\(425\) 5608.22 0.640091
\(426\) 0 0
\(427\) 2498.15 0.283125
\(428\) 5157.42 0.582460
\(429\) 0 0
\(430\) −20187.0 −2.26396
\(431\) 17159.1 1.91770 0.958848 0.283921i \(-0.0916353\pi\)
0.958848 + 0.283921i \(0.0916353\pi\)
\(432\) 0 0
\(433\) −2686.61 −0.298176 −0.149088 0.988824i \(-0.547634\pi\)
−0.149088 + 0.988824i \(0.547634\pi\)
\(434\) 22825.5 2.52456
\(435\) 0 0
\(436\) −34181.6 −3.75459
\(437\) −93.0710 −0.0101881
\(438\) 0 0
\(439\) 6276.20 0.682339 0.341169 0.940002i \(-0.389177\pi\)
0.341169 + 0.940002i \(0.389177\pi\)
\(440\) 50914.7 5.51651
\(441\) 0 0
\(442\) 19066.1 2.05177
\(443\) 6764.78 0.725518 0.362759 0.931883i \(-0.381835\pi\)
0.362759 + 0.931883i \(0.381835\pi\)
\(444\) 0 0
\(445\) −2857.56 −0.304408
\(446\) −8711.15 −0.924854
\(447\) 0 0
\(448\) 209.391 0.0220821
\(449\) 11701.9 1.22995 0.614975 0.788546i \(-0.289166\pi\)
0.614975 + 0.788546i \(0.289166\pi\)
\(450\) 0 0
\(451\) 3252.50 0.339588
\(452\) 15697.8 1.63354
\(453\) 0 0
\(454\) −24735.9 −2.55707
\(455\) −23226.3 −2.39311
\(456\) 0 0
\(457\) 18533.1 1.89703 0.948515 0.316731i \(-0.102585\pi\)
0.948515 + 0.316731i \(0.102585\pi\)
\(458\) 33608.7 3.42889
\(459\) 0 0
\(460\) 2513.82 0.254798
\(461\) 4084.28 0.412634 0.206317 0.978485i \(-0.433852\pi\)
0.206317 + 0.978485i \(0.433852\pi\)
\(462\) 0 0
\(463\) 1285.93 0.129076 0.0645378 0.997915i \(-0.479443\pi\)
0.0645378 + 0.997915i \(0.479443\pi\)
\(464\) 3741.86 0.374378
\(465\) 0 0
\(466\) 17983.4 1.78769
\(467\) −2968.54 −0.294149 −0.147075 0.989125i \(-0.546986\pi\)
−0.147075 + 0.989125i \(0.546986\pi\)
\(468\) 0 0
\(469\) 5712.65 0.562442
\(470\) 21525.8 2.11257
\(471\) 0 0
\(472\) 45337.5 4.42125
\(473\) −17091.3 −1.66144
\(474\) 0 0
\(475\) 1095.89 0.105859
\(476\) −19653.0 −1.89242
\(477\) 0 0
\(478\) 1217.39 0.116490
\(479\) 7000.52 0.667771 0.333885 0.942614i \(-0.391640\pi\)
0.333885 + 0.942614i \(0.391640\pi\)
\(480\) 0 0
\(481\) 3872.59 0.367100
\(482\) 4554.61 0.430409
\(483\) 0 0
\(484\) 53895.2 5.06153
\(485\) 7377.76 0.690736
\(486\) 0 0
\(487\) −5513.98 −0.513064 −0.256532 0.966536i \(-0.582580\pi\)
−0.256532 + 0.966536i \(0.582580\pi\)
\(488\) 5998.42 0.556426
\(489\) 0 0
\(490\) 7942.45 0.732252
\(491\) −18652.2 −1.71439 −0.857193 0.514995i \(-0.827794\pi\)
−0.857193 + 0.514995i \(0.827794\pi\)
\(492\) 0 0
\(493\) 1696.56 0.154989
\(494\) 3725.67 0.339323
\(495\) 0 0
\(496\) 24315.0 2.20116
\(497\) −6632.87 −0.598641
\(498\) 0 0
\(499\) 6533.66 0.586146 0.293073 0.956090i \(-0.405322\pi\)
0.293073 + 0.956090i \(0.405322\pi\)
\(500\) 4644.83 0.415446
\(501\) 0 0
\(502\) −34794.2 −3.09351
\(503\) 8908.49 0.789681 0.394841 0.918750i \(-0.370800\pi\)
0.394841 + 0.918750i \(0.370800\pi\)
\(504\) 0 0
\(505\) 13489.8 1.18869
\(506\) 3077.11 0.270344
\(507\) 0 0
\(508\) 24854.0 2.17070
\(509\) 13951.4 1.21490 0.607451 0.794357i \(-0.292192\pi\)
0.607451 + 0.794357i \(0.292192\pi\)
\(510\) 0 0
\(511\) −7149.70 −0.618951
\(512\) 26036.4 2.24737
\(513\) 0 0
\(514\) −28128.3 −2.41378
\(515\) 4626.02 0.395819
\(516\) 0 0
\(517\) 18224.8 1.55034
\(518\) −5771.28 −0.489528
\(519\) 0 0
\(520\) −55769.6 −4.70319
\(521\) 11335.0 0.953155 0.476577 0.879132i \(-0.341877\pi\)
0.476577 + 0.879132i \(0.341877\pi\)
\(522\) 0 0
\(523\) 17354.8 1.45100 0.725499 0.688223i \(-0.241609\pi\)
0.725499 + 0.688223i \(0.241609\pi\)
\(524\) 12879.6 1.07376
\(525\) 0 0
\(526\) 8957.99 0.742561
\(527\) 11024.5 0.911258
\(528\) 0 0
\(529\) −12082.8 −0.993080
\(530\) 17575.8 1.44046
\(531\) 0 0
\(532\) −3840.34 −0.312970
\(533\) −3562.64 −0.289521
\(534\) 0 0
\(535\) −4387.25 −0.354537
\(536\) 13716.9 1.10537
\(537\) 0 0
\(538\) 20877.2 1.67301
\(539\) 6724.47 0.537372
\(540\) 0 0
\(541\) −5050.61 −0.401373 −0.200686 0.979656i \(-0.564317\pi\)
−0.200686 + 0.979656i \(0.564317\pi\)
\(542\) −3610.39 −0.286125
\(543\) 0 0
\(544\) −9231.70 −0.727584
\(545\) 29077.2 2.28538
\(546\) 0 0
\(547\) 13897.3 1.08630 0.543149 0.839636i \(-0.317232\pi\)
0.543149 + 0.839636i \(0.317232\pi\)
\(548\) −33613.0 −2.62021
\(549\) 0 0
\(550\) −36232.2 −2.80899
\(551\) 331.521 0.0256321
\(552\) 0 0
\(553\) 15118.5 1.16257
\(554\) 9179.56 0.703975
\(555\) 0 0
\(556\) 35136.9 2.68010
\(557\) −105.819 −0.00804975 −0.00402487 0.999992i \(-0.501281\pi\)
−0.00402487 + 0.999992i \(0.501281\pi\)
\(558\) 0 0
\(559\) 18721.0 1.41649
\(560\) 36872.8 2.78243
\(561\) 0 0
\(562\) −30244.1 −2.27005
\(563\) −19919.9 −1.49116 −0.745580 0.666416i \(-0.767827\pi\)
−0.745580 + 0.666416i \(0.767827\pi\)
\(564\) 0 0
\(565\) −13353.6 −0.994319
\(566\) −13327.0 −0.989708
\(567\) 0 0
\(568\) −15926.4 −1.17651
\(569\) 2973.81 0.219101 0.109551 0.993981i \(-0.465059\pi\)
0.109551 + 0.993981i \(0.465059\pi\)
\(570\) 0 0
\(571\) −22422.7 −1.64336 −0.821680 0.569948i \(-0.806963\pi\)
−0.821680 + 0.569948i \(0.806963\pi\)
\(572\) −85197.5 −6.22778
\(573\) 0 0
\(574\) 5309.36 0.386077
\(575\) −991.424 −0.0719048
\(576\) 0 0
\(577\) 4267.84 0.307925 0.153962 0.988077i \(-0.450797\pi\)
0.153962 + 0.988077i \(0.450797\pi\)
\(578\) 11301.6 0.813295
\(579\) 0 0
\(580\) −8954.28 −0.641045
\(581\) 13339.8 0.952542
\(582\) 0 0
\(583\) 14880.6 1.05710
\(584\) −17167.4 −1.21643
\(585\) 0 0
\(586\) 18477.5 1.30256
\(587\) 8210.74 0.577331 0.288666 0.957430i \(-0.406788\pi\)
0.288666 + 0.957430i \(0.406788\pi\)
\(588\) 0 0
\(589\) 2154.26 0.150704
\(590\) −69589.5 −4.85585
\(591\) 0 0
\(592\) −6147.91 −0.426820
\(593\) 1843.22 0.127642 0.0638211 0.997961i \(-0.479671\pi\)
0.0638211 + 0.997961i \(0.479671\pi\)
\(594\) 0 0
\(595\) 16718.2 1.15190
\(596\) 4278.97 0.294083
\(597\) 0 0
\(598\) −3370.52 −0.230486
\(599\) −5234.62 −0.357063 −0.178532 0.983934i \(-0.557135\pi\)
−0.178532 + 0.983934i \(0.557135\pi\)
\(600\) 0 0
\(601\) 17417.4 1.18215 0.591073 0.806618i \(-0.298704\pi\)
0.591073 + 0.806618i \(0.298704\pi\)
\(602\) −27899.8 −1.88889
\(603\) 0 0
\(604\) 52712.0 3.55103
\(605\) −45846.9 −3.08090
\(606\) 0 0
\(607\) 10280.6 0.687444 0.343722 0.939071i \(-0.388312\pi\)
0.343722 + 0.939071i \(0.388312\pi\)
\(608\) −1803.94 −0.120328
\(609\) 0 0
\(610\) −9207.10 −0.611123
\(611\) −19962.6 −1.32177
\(612\) 0 0
\(613\) −1205.97 −0.0794596 −0.0397298 0.999210i \(-0.512650\pi\)
−0.0397298 + 0.999210i \(0.512650\pi\)
\(614\) 1792.82 0.117837
\(615\) 0 0
\(616\) 70367.5 4.60258
\(617\) 8577.63 0.559680 0.279840 0.960047i \(-0.409719\pi\)
0.279840 + 0.960047i \(0.409719\pi\)
\(618\) 0 0
\(619\) 17638.8 1.14533 0.572667 0.819788i \(-0.305909\pi\)
0.572667 + 0.819788i \(0.305909\pi\)
\(620\) −58185.9 −3.76904
\(621\) 0 0
\(622\) −49477.9 −3.18952
\(623\) −3949.34 −0.253976
\(624\) 0 0
\(625\) −17456.9 −1.11724
\(626\) −6059.16 −0.386858
\(627\) 0 0
\(628\) −63243.1 −4.01859
\(629\) −2787.47 −0.176699
\(630\) 0 0
\(631\) −28112.5 −1.77360 −0.886799 0.462156i \(-0.847076\pi\)
−0.886799 + 0.462156i \(0.847076\pi\)
\(632\) 36301.6 2.28481
\(633\) 0 0
\(634\) 39970.5 2.50383
\(635\) −21142.5 −1.32128
\(636\) 0 0
\(637\) −7365.67 −0.458145
\(638\) −10960.7 −0.680156
\(639\) 0 0
\(640\) −22492.3 −1.38920
\(641\) −2280.32 −0.140511 −0.0702554 0.997529i \(-0.522381\pi\)
−0.0702554 + 0.997529i \(0.522381\pi\)
\(642\) 0 0
\(643\) 15435.3 0.946672 0.473336 0.880882i \(-0.343050\pi\)
0.473336 + 0.880882i \(0.343050\pi\)
\(644\) 3474.26 0.212585
\(645\) 0 0
\(646\) −2681.72 −0.163329
\(647\) −26247.4 −1.59489 −0.797443 0.603394i \(-0.793815\pi\)
−0.797443 + 0.603394i \(0.793815\pi\)
\(648\) 0 0
\(649\) −58917.9 −3.56353
\(650\) 39687.1 2.39485
\(651\) 0 0
\(652\) −29238.0 −1.75621
\(653\) −5590.95 −0.335055 −0.167527 0.985867i \(-0.553578\pi\)
−0.167527 + 0.985867i \(0.553578\pi\)
\(654\) 0 0
\(655\) −10956.3 −0.653584
\(656\) 5655.84 0.336621
\(657\) 0 0
\(658\) 29750.0 1.76258
\(659\) −9664.49 −0.571282 −0.285641 0.958337i \(-0.592207\pi\)
−0.285641 + 0.958337i \(0.592207\pi\)
\(660\) 0 0
\(661\) −20072.6 −1.18114 −0.590570 0.806986i \(-0.701097\pi\)
−0.590570 + 0.806986i \(0.701097\pi\)
\(662\) −40081.0 −2.35316
\(663\) 0 0
\(664\) 32030.7 1.87203
\(665\) 3266.86 0.190501
\(666\) 0 0
\(667\) −299.919 −0.0174107
\(668\) −59720.3 −3.45905
\(669\) 0 0
\(670\) −21054.3 −1.21403
\(671\) −7795.19 −0.448480
\(672\) 0 0
\(673\) −17473.0 −1.00079 −0.500396 0.865796i \(-0.666812\pi\)
−0.500396 + 0.865796i \(0.666812\pi\)
\(674\) 17495.3 0.999844
\(675\) 0 0
\(676\) 53894.8 3.06638
\(677\) −9879.28 −0.560844 −0.280422 0.959877i \(-0.590474\pi\)
−0.280422 + 0.959877i \(0.590474\pi\)
\(678\) 0 0
\(679\) 10196.5 0.576300
\(680\) 40142.7 2.26383
\(681\) 0 0
\(682\) −71224.1 −3.99899
\(683\) 20749.8 1.16248 0.581238 0.813734i \(-0.302569\pi\)
0.581238 + 0.813734i \(0.302569\pi\)
\(684\) 0 0
\(685\) 28593.5 1.59489
\(686\) −25884.7 −1.44065
\(687\) 0 0
\(688\) −29720.5 −1.64692
\(689\) −16299.5 −0.901250
\(690\) 0 0
\(691\) −328.098 −0.0180628 −0.00903142 0.999959i \(-0.502875\pi\)
−0.00903142 + 0.999959i \(0.502875\pi\)
\(692\) −77236.7 −4.24292
\(693\) 0 0
\(694\) 34651.1 1.89530
\(695\) −29889.9 −1.63135
\(696\) 0 0
\(697\) 2564.37 0.139358
\(698\) −29305.1 −1.58913
\(699\) 0 0
\(700\) −40908.6 −2.20886
\(701\) 25860.5 1.39335 0.696675 0.717387i \(-0.254662\pi\)
0.696675 + 0.717387i \(0.254662\pi\)
\(702\) 0 0
\(703\) −544.693 −0.0292226
\(704\) −653.379 −0.0349789
\(705\) 0 0
\(706\) −54046.1 −2.88109
\(707\) 18643.8 0.991758
\(708\) 0 0
\(709\) 4489.98 0.237834 0.118917 0.992904i \(-0.462058\pi\)
0.118917 + 0.992904i \(0.462058\pi\)
\(710\) 24445.8 1.29216
\(711\) 0 0
\(712\) −9482.93 −0.499140
\(713\) −1948.91 −0.102366
\(714\) 0 0
\(715\) 72474.9 3.79078
\(716\) 14574.4 0.760713
\(717\) 0 0
\(718\) 4746.26 0.246697
\(719\) 12971.5 0.672817 0.336409 0.941716i \(-0.390788\pi\)
0.336409 + 0.941716i \(0.390788\pi\)
\(720\) 0 0
\(721\) 6393.47 0.330243
\(722\) 34413.6 1.77388
\(723\) 0 0
\(724\) 51186.4 2.62753
\(725\) 3531.48 0.180905
\(726\) 0 0
\(727\) 36346.8 1.85424 0.927118 0.374770i \(-0.122278\pi\)
0.927118 + 0.374770i \(0.122278\pi\)
\(728\) −77077.3 −3.92400
\(729\) 0 0
\(730\) 26350.7 1.33600
\(731\) −13475.3 −0.681809
\(732\) 0 0
\(733\) 5914.92 0.298053 0.149026 0.988833i \(-0.452386\pi\)
0.149026 + 0.988833i \(0.452386\pi\)
\(734\) 417.892 0.0210146
\(735\) 0 0
\(736\) 1631.98 0.0817333
\(737\) −17825.6 −0.890930
\(738\) 0 0
\(739\) −17782.1 −0.885148 −0.442574 0.896732i \(-0.645935\pi\)
−0.442574 + 0.896732i \(0.645935\pi\)
\(740\) 14712.0 0.730842
\(741\) 0 0
\(742\) 24291.0 1.20182
\(743\) 30917.1 1.52657 0.763283 0.646064i \(-0.223586\pi\)
0.763283 + 0.646064i \(0.223586\pi\)
\(744\) 0 0
\(745\) −3639.99 −0.179005
\(746\) 72169.9 3.54199
\(747\) 0 0
\(748\) 61324.7 2.99767
\(749\) −6063.47 −0.295800
\(750\) 0 0
\(751\) 20251.5 0.984006 0.492003 0.870594i \(-0.336265\pi\)
0.492003 + 0.870594i \(0.336265\pi\)
\(752\) 31691.5 1.53679
\(753\) 0 0
\(754\) 12005.9 0.579878
\(755\) −44840.5 −2.16147
\(756\) 0 0
\(757\) 21481.8 1.03140 0.515701 0.856769i \(-0.327532\pi\)
0.515701 + 0.856769i \(0.327532\pi\)
\(758\) −35421.6 −1.69732
\(759\) 0 0
\(760\) 7844.18 0.374393
\(761\) 16871.2 0.803654 0.401827 0.915716i \(-0.368375\pi\)
0.401827 + 0.915716i \(0.368375\pi\)
\(762\) 0 0
\(763\) 40186.7 1.90676
\(764\) −8439.86 −0.399664
\(765\) 0 0
\(766\) 6101.05 0.287780
\(767\) 64536.0 3.03815
\(768\) 0 0
\(769\) −29154.0 −1.36713 −0.683563 0.729891i \(-0.739571\pi\)
−0.683563 + 0.729891i \(0.739571\pi\)
\(770\) −108009. −5.05501
\(771\) 0 0
\(772\) 10728.1 0.500146
\(773\) 39247.5 1.82618 0.913089 0.407760i \(-0.133690\pi\)
0.913089 + 0.407760i \(0.133690\pi\)
\(774\) 0 0
\(775\) 22948.0 1.06363
\(776\) 24483.4 1.13260
\(777\) 0 0
\(778\) −33402.2 −1.53924
\(779\) 501.097 0.0230471
\(780\) 0 0
\(781\) 20697.1 0.948270
\(782\) 2426.08 0.110942
\(783\) 0 0
\(784\) 11693.3 0.532677
\(785\) 53798.9 2.44607
\(786\) 0 0
\(787\) 2925.52 0.132508 0.0662539 0.997803i \(-0.478895\pi\)
0.0662539 + 0.997803i \(0.478895\pi\)
\(788\) −60713.8 −2.74472
\(789\) 0 0
\(790\) −55720.1 −2.50941
\(791\) −18455.6 −0.829588
\(792\) 0 0
\(793\) 8538.49 0.382359
\(794\) −55931.0 −2.49990
\(795\) 0 0
\(796\) −46898.9 −2.08830
\(797\) −36424.5 −1.61885 −0.809423 0.587226i \(-0.800220\pi\)
−0.809423 + 0.587226i \(0.800220\pi\)
\(798\) 0 0
\(799\) 14369.0 0.636217
\(800\) −19216.2 −0.849245
\(801\) 0 0
\(802\) 37052.6 1.63139
\(803\) 22309.8 0.980442
\(804\) 0 0
\(805\) −2955.44 −0.129398
\(806\) 78015.6 3.40941
\(807\) 0 0
\(808\) 44766.4 1.94911
\(809\) 9574.01 0.416074 0.208037 0.978121i \(-0.433293\pi\)
0.208037 + 0.978121i \(0.433293\pi\)
\(810\) 0 0
\(811\) 28563.4 1.23674 0.618371 0.785886i \(-0.287793\pi\)
0.618371 + 0.785886i \(0.287793\pi\)
\(812\) −12375.4 −0.534842
\(813\) 0 0
\(814\) 18008.6 0.775431
\(815\) 24871.9 1.06899
\(816\) 0 0
\(817\) −2633.18 −0.112758
\(818\) −16010.5 −0.684344
\(819\) 0 0
\(820\) −13534.5 −0.576395
\(821\) 17217.3 0.731899 0.365949 0.930635i \(-0.380744\pi\)
0.365949 + 0.930635i \(0.380744\pi\)
\(822\) 0 0
\(823\) −32703.7 −1.38515 −0.692575 0.721346i \(-0.743524\pi\)
−0.692575 + 0.721346i \(0.743524\pi\)
\(824\) 15351.6 0.649028
\(825\) 0 0
\(826\) −96177.3 −4.05137
\(827\) −26106.9 −1.09773 −0.548867 0.835909i \(-0.684941\pi\)
−0.548867 + 0.835909i \(0.684941\pi\)
\(828\) 0 0
\(829\) −6260.31 −0.262279 −0.131140 0.991364i \(-0.541864\pi\)
−0.131140 + 0.991364i \(0.541864\pi\)
\(830\) −49164.5 −2.05606
\(831\) 0 0
\(832\) 715.681 0.0298219
\(833\) 5301.77 0.220523
\(834\) 0 0
\(835\) 50802.2 2.10549
\(836\) 11983.3 0.495756
\(837\) 0 0
\(838\) −43999.8 −1.81378
\(839\) 28092.5 1.15597 0.577987 0.816046i \(-0.303838\pi\)
0.577987 + 0.816046i \(0.303838\pi\)
\(840\) 0 0
\(841\) −23320.7 −0.956197
\(842\) 77119.5 3.15643
\(843\) 0 0
\(844\) −90530.7 −3.69217
\(845\) −45846.6 −1.86647
\(846\) 0 0
\(847\) −63363.5 −2.57048
\(848\) 25876.2 1.04787
\(849\) 0 0
\(850\) −28566.6 −1.15273
\(851\) 492.770 0.0198495
\(852\) 0 0
\(853\) 15997.1 0.642123 0.321061 0.947058i \(-0.395960\pi\)
0.321061 + 0.947058i \(0.395960\pi\)
\(854\) −12724.8 −0.509877
\(855\) 0 0
\(856\) −14559.3 −0.581338
\(857\) 29799.1 1.18777 0.593885 0.804550i \(-0.297593\pi\)
0.593885 + 0.804550i \(0.297593\pi\)
\(858\) 0 0
\(859\) 12684.4 0.503824 0.251912 0.967750i \(-0.418941\pi\)
0.251912 + 0.967750i \(0.418941\pi\)
\(860\) 71121.2 2.82002
\(861\) 0 0
\(862\) −87403.3 −3.45356
\(863\) −17526.2 −0.691308 −0.345654 0.938362i \(-0.612343\pi\)
−0.345654 + 0.938362i \(0.612343\pi\)
\(864\) 0 0
\(865\) 65702.8 2.58262
\(866\) 13684.7 0.536982
\(867\) 0 0
\(868\) −80416.8 −3.14461
\(869\) −47175.4 −1.84156
\(870\) 0 0
\(871\) 19525.4 0.759577
\(872\) 96493.8 3.74736
\(873\) 0 0
\(874\) 474.075 0.0183476
\(875\) −5460.83 −0.210983
\(876\) 0 0
\(877\) −20669.9 −0.795863 −0.397932 0.917415i \(-0.630272\pi\)
−0.397932 + 0.917415i \(0.630272\pi\)
\(878\) −31969.0 −1.22882
\(879\) 0 0
\(880\) −115057. −4.40747
\(881\) 12261.9 0.468914 0.234457 0.972126i \(-0.424669\pi\)
0.234457 + 0.972126i \(0.424669\pi\)
\(882\) 0 0
\(883\) 36489.9 1.39069 0.695347 0.718674i \(-0.255251\pi\)
0.695347 + 0.718674i \(0.255251\pi\)
\(884\) −67172.3 −2.55571
\(885\) 0 0
\(886\) −34457.7 −1.30658
\(887\) −4328.08 −0.163836 −0.0819182 0.996639i \(-0.526105\pi\)
−0.0819182 + 0.996639i \(0.526105\pi\)
\(888\) 0 0
\(889\) −29220.3 −1.10238
\(890\) 14555.5 0.548206
\(891\) 0 0
\(892\) 30690.4 1.15201
\(893\) 2807.80 0.105218
\(894\) 0 0
\(895\) −12398.0 −0.463038
\(896\) −31085.9 −1.15905
\(897\) 0 0
\(898\) −59605.9 −2.21501
\(899\) 6942.06 0.257543
\(900\) 0 0
\(901\) 11732.3 0.433806
\(902\) −16567.2 −0.611561
\(903\) 0 0
\(904\) −44314.4 −1.63039
\(905\) −43542.7 −1.59935
\(906\) 0 0
\(907\) 47757.6 1.74836 0.874182 0.485599i \(-0.161398\pi\)
0.874182 + 0.485599i \(0.161398\pi\)
\(908\) 87147.4 3.18512
\(909\) 0 0
\(910\) 118308. 4.30973
\(911\) 33658.7 1.22411 0.612054 0.790816i \(-0.290344\pi\)
0.612054 + 0.790816i \(0.290344\pi\)
\(912\) 0 0
\(913\) −41625.1 −1.50886
\(914\) −94402.0 −3.41635
\(915\) 0 0
\(916\) −118407. −4.27106
\(917\) −15142.3 −0.545303
\(918\) 0 0
\(919\) 21314.5 0.765072 0.382536 0.923941i \(-0.375051\pi\)
0.382536 + 0.923941i \(0.375051\pi\)
\(920\) −7096.44 −0.254307
\(921\) 0 0
\(922\) −20804.1 −0.743108
\(923\) −22670.6 −0.808464
\(924\) 0 0
\(925\) −5802.26 −0.206245
\(926\) −6550.10 −0.232451
\(927\) 0 0
\(928\) −5813.17 −0.205632
\(929\) −37123.4 −1.31106 −0.655532 0.755167i \(-0.727556\pi\)
−0.655532 + 0.755167i \(0.727556\pi\)
\(930\) 0 0
\(931\) 1036.01 0.0364702
\(932\) −63357.6 −2.22677
\(933\) 0 0
\(934\) 15120.8 0.529731
\(935\) −52167.0 −1.82465
\(936\) 0 0
\(937\) −9025.33 −0.314669 −0.157334 0.987545i \(-0.550290\pi\)
−0.157334 + 0.987545i \(0.550290\pi\)
\(938\) −29098.4 −1.01290
\(939\) 0 0
\(940\) −75837.8 −2.63144
\(941\) 2003.99 0.0694241 0.0347121 0.999397i \(-0.488949\pi\)
0.0347121 + 0.999397i \(0.488949\pi\)
\(942\) 0 0
\(943\) −453.330 −0.0156548
\(944\) −102454. −3.53240
\(945\) 0 0
\(946\) 87057.9 2.99207
\(947\) 27399.7 0.940200 0.470100 0.882613i \(-0.344218\pi\)
0.470100 + 0.882613i \(0.344218\pi\)
\(948\) 0 0
\(949\) −24437.1 −0.835892
\(950\) −5582.12 −0.190640
\(951\) 0 0
\(952\) 55479.8 1.88877
\(953\) 33468.6 1.13762 0.568811 0.822468i \(-0.307404\pi\)
0.568811 + 0.822468i \(0.307404\pi\)
\(954\) 0 0
\(955\) 7179.53 0.243271
\(956\) −4289.02 −0.145101
\(957\) 0 0
\(958\) −35658.5 −1.20258
\(959\) 39518.1 1.33066
\(960\) 0 0
\(961\) 15319.3 0.514227
\(962\) −19725.8 −0.661107
\(963\) 0 0
\(964\) −16046.4 −0.536122
\(965\) −9126.05 −0.304433
\(966\) 0 0
\(967\) −610.226 −0.0202932 −0.0101466 0.999949i \(-0.503230\pi\)
−0.0101466 + 0.999949i \(0.503230\pi\)
\(968\) −152145. −5.05177
\(969\) 0 0
\(970\) −37580.0 −1.24394
\(971\) 43937.4 1.45213 0.726066 0.687625i \(-0.241347\pi\)
0.726066 + 0.687625i \(0.241347\pi\)
\(972\) 0 0
\(973\) −41309.8 −1.36108
\(974\) 28086.5 0.923972
\(975\) 0 0
\(976\) −13555.2 −0.444562
\(977\) −7713.22 −0.252577 −0.126289 0.991994i \(-0.540307\pi\)
−0.126289 + 0.991994i \(0.540307\pi\)
\(978\) 0 0
\(979\) 12323.5 0.402308
\(980\) −27982.2 −0.912100
\(981\) 0 0
\(982\) 95008.7 3.08742
\(983\) −44381.4 −1.44003 −0.720013 0.693961i \(-0.755864\pi\)
−0.720013 + 0.693961i \(0.755864\pi\)
\(984\) 0 0
\(985\) 51647.3 1.67068
\(986\) −8641.77 −0.279118
\(987\) 0 0
\(988\) −13126.0 −0.422665
\(989\) 2382.17 0.0765911
\(990\) 0 0
\(991\) 30319.3 0.971871 0.485936 0.873995i \(-0.338479\pi\)
0.485936 + 0.873995i \(0.338479\pi\)
\(992\) −37774.6 −1.20902
\(993\) 0 0
\(994\) 33785.8 1.07809
\(995\) 39895.4 1.27113
\(996\) 0 0
\(997\) −37153.6 −1.18021 −0.590103 0.807328i \(-0.700913\pi\)
−0.590103 + 0.807328i \(0.700913\pi\)
\(998\) −33280.4 −1.05559
\(999\) 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.1.5 yes 59
3.2 odd 2 2151.4.a.g.1.55 59
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2151.4.a.g.1.55 59 3.2 odd 2
2151.4.a.h.1.5 yes 59 1.1 even 1 trivial