Properties

Label 1386.4.a.c.1.1
Level $1386$
Weight $4$
Character 1386.1
Self dual yes
Analytic conductor $81.777$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1386.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(81.7766472680\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 462)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1386.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.00000 q^{2} +4.00000 q^{4} -3.00000 q^{5} +7.00000 q^{7} -8.00000 q^{8} +O(q^{10})\) \(q-2.00000 q^{2} +4.00000 q^{4} -3.00000 q^{5} +7.00000 q^{7} -8.00000 q^{8} +6.00000 q^{10} +11.0000 q^{11} +41.0000 q^{13} -14.0000 q^{14} +16.0000 q^{16} -6.00000 q^{17} -43.0000 q^{19} -12.0000 q^{20} -22.0000 q^{22} -120.000 q^{23} -116.000 q^{25} -82.0000 q^{26} +28.0000 q^{28} -111.000 q^{29} +266.000 q^{31} -32.0000 q^{32} +12.0000 q^{34} -21.0000 q^{35} -79.0000 q^{37} +86.0000 q^{38} +24.0000 q^{40} -216.000 q^{41} +284.000 q^{43} +44.0000 q^{44} +240.000 q^{46} -213.000 q^{47} +49.0000 q^{49} +232.000 q^{50} +164.000 q^{52} +216.000 q^{53} -33.0000 q^{55} -56.0000 q^{56} +222.000 q^{58} -393.000 q^{59} +350.000 q^{61} -532.000 q^{62} +64.0000 q^{64} -123.000 q^{65} +821.000 q^{67} -24.0000 q^{68} +42.0000 q^{70} +264.000 q^{71} -865.000 q^{73} +158.000 q^{74} -172.000 q^{76} +77.0000 q^{77} -484.000 q^{79} -48.0000 q^{80} +432.000 q^{82} -1158.00 q^{83} +18.0000 q^{85} -568.000 q^{86} -88.0000 q^{88} -330.000 q^{89} +287.000 q^{91} -480.000 q^{92} +426.000 q^{94} +129.000 q^{95} +980.000 q^{97} -98.0000 q^{98} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.00000 −0.707107
\(3\) 0 0
\(4\) 4.00000 0.500000
\(5\) −3.00000 −0.268328 −0.134164 0.990959i \(-0.542835\pi\)
−0.134164 + 0.990959i \(0.542835\pi\)
\(6\) 0 0
\(7\) 7.00000 0.377964
\(8\) −8.00000 −0.353553
\(9\) 0 0
\(10\) 6.00000 0.189737
\(11\) 11.0000 0.301511
\(12\) 0 0
\(13\) 41.0000 0.874720 0.437360 0.899287i \(-0.355914\pi\)
0.437360 + 0.899287i \(0.355914\pi\)
\(14\) −14.0000 −0.267261
\(15\) 0 0
\(16\) 16.0000 0.250000
\(17\) −6.00000 −0.0856008 −0.0428004 0.999084i \(-0.513628\pi\)
−0.0428004 + 0.999084i \(0.513628\pi\)
\(18\) 0 0
\(19\) −43.0000 −0.519204 −0.259602 0.965716i \(-0.583591\pi\)
−0.259602 + 0.965716i \(0.583591\pi\)
\(20\) −12.0000 −0.134164
\(21\) 0 0
\(22\) −22.0000 −0.213201
\(23\) −120.000 −1.08790 −0.543951 0.839117i \(-0.683072\pi\)
−0.543951 + 0.839117i \(0.683072\pi\)
\(24\) 0 0
\(25\) −116.000 −0.928000
\(26\) −82.0000 −0.618520
\(27\) 0 0
\(28\) 28.0000 0.188982
\(29\) −111.000 −0.710765 −0.355382 0.934721i \(-0.615649\pi\)
−0.355382 + 0.934721i \(0.615649\pi\)
\(30\) 0 0
\(31\) 266.000 1.54113 0.770565 0.637362i \(-0.219974\pi\)
0.770565 + 0.637362i \(0.219974\pi\)
\(32\) −32.0000 −0.176777
\(33\) 0 0
\(34\) 12.0000 0.0605289
\(35\) −21.0000 −0.101419
\(36\) 0 0
\(37\) −79.0000 −0.351014 −0.175507 0.984478i \(-0.556156\pi\)
−0.175507 + 0.984478i \(0.556156\pi\)
\(38\) 86.0000 0.367133
\(39\) 0 0
\(40\) 24.0000 0.0948683
\(41\) −216.000 −0.822769 −0.411385 0.911462i \(-0.634955\pi\)
−0.411385 + 0.911462i \(0.634955\pi\)
\(42\) 0 0
\(43\) 284.000 1.00720 0.503600 0.863937i \(-0.332009\pi\)
0.503600 + 0.863937i \(0.332009\pi\)
\(44\) 44.0000 0.150756
\(45\) 0 0
\(46\) 240.000 0.769262
\(47\) −213.000 −0.661048 −0.330524 0.943798i \(-0.607225\pi\)
−0.330524 + 0.943798i \(0.607225\pi\)
\(48\) 0 0
\(49\) 49.0000 0.142857
\(50\) 232.000 0.656195
\(51\) 0 0
\(52\) 164.000 0.437360
\(53\) 216.000 0.559809 0.279905 0.960028i \(-0.409697\pi\)
0.279905 + 0.960028i \(0.409697\pi\)
\(54\) 0 0
\(55\) −33.0000 −0.0809040
\(56\) −56.0000 −0.133631
\(57\) 0 0
\(58\) 222.000 0.502587
\(59\) −393.000 −0.867191 −0.433595 0.901108i \(-0.642755\pi\)
−0.433595 + 0.901108i \(0.642755\pi\)
\(60\) 0 0
\(61\) 350.000 0.734638 0.367319 0.930095i \(-0.380276\pi\)
0.367319 + 0.930095i \(0.380276\pi\)
\(62\) −532.000 −1.08974
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) −123.000 −0.234712
\(66\) 0 0
\(67\) 821.000 1.49703 0.748516 0.663117i \(-0.230767\pi\)
0.748516 + 0.663117i \(0.230767\pi\)
\(68\) −24.0000 −0.0428004
\(69\) 0 0
\(70\) 42.0000 0.0717137
\(71\) 264.000 0.441282 0.220641 0.975355i \(-0.429185\pi\)
0.220641 + 0.975355i \(0.429185\pi\)
\(72\) 0 0
\(73\) −865.000 −1.38686 −0.693429 0.720525i \(-0.743901\pi\)
−0.693429 + 0.720525i \(0.743901\pi\)
\(74\) 158.000 0.248204
\(75\) 0 0
\(76\) −172.000 −0.259602
\(77\) 77.0000 0.113961
\(78\) 0 0
\(79\) −484.000 −0.689294 −0.344647 0.938732i \(-0.612001\pi\)
−0.344647 + 0.938732i \(0.612001\pi\)
\(80\) −48.0000 −0.0670820
\(81\) 0 0
\(82\) 432.000 0.581786
\(83\) −1158.00 −1.53141 −0.765705 0.643192i \(-0.777610\pi\)
−0.765705 + 0.643192i \(0.777610\pi\)
\(84\) 0 0
\(85\) 18.0000 0.0229691
\(86\) −568.000 −0.712198
\(87\) 0 0
\(88\) −88.0000 −0.106600
\(89\) −330.000 −0.393033 −0.196516 0.980501i \(-0.562963\pi\)
−0.196516 + 0.980501i \(0.562963\pi\)
\(90\) 0 0
\(91\) 287.000 0.330613
\(92\) −480.000 −0.543951
\(93\) 0 0
\(94\) 426.000 0.467431
\(95\) 129.000 0.139317
\(96\) 0 0
\(97\) 980.000 1.02581 0.512907 0.858444i \(-0.328569\pi\)
0.512907 + 0.858444i \(0.328569\pi\)
\(98\) −98.0000 −0.101015
\(99\) 0 0
\(100\) −464.000 −0.464000
\(101\) −210.000 −0.206889 −0.103444 0.994635i \(-0.532986\pi\)
−0.103444 + 0.994635i \(0.532986\pi\)
\(102\) 0 0
\(103\) −1330.00 −1.27232 −0.636159 0.771558i \(-0.719478\pi\)
−0.636159 + 0.771558i \(0.719478\pi\)
\(104\) −328.000 −0.309260
\(105\) 0 0
\(106\) −432.000 −0.395845
\(107\) 1329.00 1.20074 0.600370 0.799722i \(-0.295020\pi\)
0.600370 + 0.799722i \(0.295020\pi\)
\(108\) 0 0
\(109\) −94.0000 −0.0826015 −0.0413008 0.999147i \(-0.513150\pi\)
−0.0413008 + 0.999147i \(0.513150\pi\)
\(110\) 66.0000 0.0572078
\(111\) 0 0
\(112\) 112.000 0.0944911
\(113\) −198.000 −0.164834 −0.0824171 0.996598i \(-0.526264\pi\)
−0.0824171 + 0.996598i \(0.526264\pi\)
\(114\) 0 0
\(115\) 360.000 0.291915
\(116\) −444.000 −0.355382
\(117\) 0 0
\(118\) 786.000 0.613196
\(119\) −42.0000 −0.0323541
\(120\) 0 0
\(121\) 121.000 0.0909091
\(122\) −700.000 −0.519467
\(123\) 0 0
\(124\) 1064.00 0.770565
\(125\) 723.000 0.517337
\(126\) 0 0
\(127\) −1066.00 −0.744821 −0.372410 0.928068i \(-0.621469\pi\)
−0.372410 + 0.928068i \(0.621469\pi\)
\(128\) −128.000 −0.0883883
\(129\) 0 0
\(130\) 246.000 0.165966
\(131\) 120.000 0.0800340 0.0400170 0.999199i \(-0.487259\pi\)
0.0400170 + 0.999199i \(0.487259\pi\)
\(132\) 0 0
\(133\) −301.000 −0.196241
\(134\) −1642.00 −1.05856
\(135\) 0 0
\(136\) 48.0000 0.0302645
\(137\) 1938.00 1.20857 0.604287 0.796767i \(-0.293458\pi\)
0.604287 + 0.796767i \(0.293458\pi\)
\(138\) 0 0
\(139\) 1712.00 1.04468 0.522338 0.852739i \(-0.325060\pi\)
0.522338 + 0.852739i \(0.325060\pi\)
\(140\) −84.0000 −0.0507093
\(141\) 0 0
\(142\) −528.000 −0.312034
\(143\) 451.000 0.263738
\(144\) 0 0
\(145\) 333.000 0.190718
\(146\) 1730.00 0.980656
\(147\) 0 0
\(148\) −316.000 −0.175507
\(149\) 1917.00 1.05401 0.527003 0.849864i \(-0.323316\pi\)
0.527003 + 0.849864i \(0.323316\pi\)
\(150\) 0 0
\(151\) −3022.00 −1.62865 −0.814327 0.580406i \(-0.802894\pi\)
−0.814327 + 0.580406i \(0.802894\pi\)
\(152\) 344.000 0.183566
\(153\) 0 0
\(154\) −154.000 −0.0805823
\(155\) −798.000 −0.413528
\(156\) 0 0
\(157\) −2200.00 −1.11834 −0.559169 0.829054i \(-0.688880\pi\)
−0.559169 + 0.829054i \(0.688880\pi\)
\(158\) 968.000 0.487405
\(159\) 0 0
\(160\) 96.0000 0.0474342
\(161\) −840.000 −0.411188
\(162\) 0 0
\(163\) −3715.00 −1.78516 −0.892581 0.450888i \(-0.851107\pi\)
−0.892581 + 0.450888i \(0.851107\pi\)
\(164\) −864.000 −0.411385
\(165\) 0 0
\(166\) 2316.00 1.08287
\(167\) −84.0000 −0.0389228 −0.0194614 0.999811i \(-0.506195\pi\)
−0.0194614 + 0.999811i \(0.506195\pi\)
\(168\) 0 0
\(169\) −516.000 −0.234866
\(170\) −36.0000 −0.0162416
\(171\) 0 0
\(172\) 1136.00 0.503600
\(173\) −1812.00 −0.796323 −0.398161 0.917315i \(-0.630352\pi\)
−0.398161 + 0.917315i \(0.630352\pi\)
\(174\) 0 0
\(175\) −812.000 −0.350751
\(176\) 176.000 0.0753778
\(177\) 0 0
\(178\) 660.000 0.277916
\(179\) −192.000 −0.0801718 −0.0400859 0.999196i \(-0.512763\pi\)
−0.0400859 + 0.999196i \(0.512763\pi\)
\(180\) 0 0
\(181\) −3148.00 −1.29276 −0.646378 0.763017i \(-0.723717\pi\)
−0.646378 + 0.763017i \(0.723717\pi\)
\(182\) −574.000 −0.233779
\(183\) 0 0
\(184\) 960.000 0.384631
\(185\) 237.000 0.0941870
\(186\) 0 0
\(187\) −66.0000 −0.0258096
\(188\) −852.000 −0.330524
\(189\) 0 0
\(190\) −258.000 −0.0985120
\(191\) −4554.00 −1.72521 −0.862607 0.505875i \(-0.831170\pi\)
−0.862607 + 0.505875i \(0.831170\pi\)
\(192\) 0 0
\(193\) −940.000 −0.350584 −0.175292 0.984517i \(-0.556087\pi\)
−0.175292 + 0.984517i \(0.556087\pi\)
\(194\) −1960.00 −0.725360
\(195\) 0 0
\(196\) 196.000 0.0714286
\(197\) 1122.00 0.405783 0.202891 0.979201i \(-0.434966\pi\)
0.202891 + 0.979201i \(0.434966\pi\)
\(198\) 0 0
\(199\) 3956.00 1.40921 0.704607 0.709598i \(-0.251124\pi\)
0.704607 + 0.709598i \(0.251124\pi\)
\(200\) 928.000 0.328098
\(201\) 0 0
\(202\) 420.000 0.146293
\(203\) −777.000 −0.268644
\(204\) 0 0
\(205\) 648.000 0.220772
\(206\) 2660.00 0.899665
\(207\) 0 0
\(208\) 656.000 0.218680
\(209\) −473.000 −0.156546
\(210\) 0 0
\(211\) 122.000 0.0398049 0.0199024 0.999802i \(-0.493664\pi\)
0.0199024 + 0.999802i \(0.493664\pi\)
\(212\) 864.000 0.279905
\(213\) 0 0
\(214\) −2658.00 −0.849052
\(215\) −852.000 −0.270260
\(216\) 0 0
\(217\) 1862.00 0.582492
\(218\) 188.000 0.0584081
\(219\) 0 0
\(220\) −132.000 −0.0404520
\(221\) −246.000 −0.0748767
\(222\) 0 0
\(223\) 602.000 0.180775 0.0903877 0.995907i \(-0.471189\pi\)
0.0903877 + 0.995907i \(0.471189\pi\)
\(224\) −224.000 −0.0668153
\(225\) 0 0
\(226\) 396.000 0.116555
\(227\) 426.000 0.124558 0.0622789 0.998059i \(-0.480163\pi\)
0.0622789 + 0.998059i \(0.480163\pi\)
\(228\) 0 0
\(229\) −4396.00 −1.26854 −0.634270 0.773111i \(-0.718699\pi\)
−0.634270 + 0.773111i \(0.718699\pi\)
\(230\) −720.000 −0.206415
\(231\) 0 0
\(232\) 888.000 0.251293
\(233\) −3198.00 −0.899176 −0.449588 0.893236i \(-0.648429\pi\)
−0.449588 + 0.893236i \(0.648429\pi\)
\(234\) 0 0
\(235\) 639.000 0.177378
\(236\) −1572.00 −0.433595
\(237\) 0 0
\(238\) 84.0000 0.0228778
\(239\) −2997.00 −0.811129 −0.405564 0.914066i \(-0.632925\pi\)
−0.405564 + 0.914066i \(0.632925\pi\)
\(240\) 0 0
\(241\) −6235.00 −1.66652 −0.833261 0.552880i \(-0.813529\pi\)
−0.833261 + 0.552880i \(0.813529\pi\)
\(242\) −242.000 −0.0642824
\(243\) 0 0
\(244\) 1400.00 0.367319
\(245\) −147.000 −0.0383326
\(246\) 0 0
\(247\) −1763.00 −0.454158
\(248\) −2128.00 −0.544872
\(249\) 0 0
\(250\) −1446.00 −0.365812
\(251\) −3735.00 −0.939247 −0.469624 0.882867i \(-0.655610\pi\)
−0.469624 + 0.882867i \(0.655610\pi\)
\(252\) 0 0
\(253\) −1320.00 −0.328015
\(254\) 2132.00 0.526668
\(255\) 0 0
\(256\) 256.000 0.0625000
\(257\) −1515.00 −0.367716 −0.183858 0.982953i \(-0.558859\pi\)
−0.183858 + 0.982953i \(0.558859\pi\)
\(258\) 0 0
\(259\) −553.000 −0.132671
\(260\) −492.000 −0.117356
\(261\) 0 0
\(262\) −240.000 −0.0565926
\(263\) 4317.00 1.01216 0.506079 0.862487i \(-0.331094\pi\)
0.506079 + 0.862487i \(0.331094\pi\)
\(264\) 0 0
\(265\) −648.000 −0.150213
\(266\) 602.000 0.138763
\(267\) 0 0
\(268\) 3284.00 0.748516
\(269\) 1434.00 0.325028 0.162514 0.986706i \(-0.448040\pi\)
0.162514 + 0.986706i \(0.448040\pi\)
\(270\) 0 0
\(271\) −943.000 −0.211377 −0.105689 0.994399i \(-0.533705\pi\)
−0.105689 + 0.994399i \(0.533705\pi\)
\(272\) −96.0000 −0.0214002
\(273\) 0 0
\(274\) −3876.00 −0.854590
\(275\) −1276.00 −0.279803
\(276\) 0 0
\(277\) −5776.00 −1.25287 −0.626437 0.779472i \(-0.715488\pi\)
−0.626437 + 0.779472i \(0.715488\pi\)
\(278\) −3424.00 −0.738697
\(279\) 0 0
\(280\) 168.000 0.0358569
\(281\) 1653.00 0.350924 0.175462 0.984486i \(-0.443858\pi\)
0.175462 + 0.984486i \(0.443858\pi\)
\(282\) 0 0
\(283\) 677.000 0.142203 0.0711015 0.997469i \(-0.477349\pi\)
0.0711015 + 0.997469i \(0.477349\pi\)
\(284\) 1056.00 0.220641
\(285\) 0 0
\(286\) −902.000 −0.186491
\(287\) −1512.00 −0.310977
\(288\) 0 0
\(289\) −4877.00 −0.992673
\(290\) −666.000 −0.134858
\(291\) 0 0
\(292\) −3460.00 −0.693429
\(293\) −4752.00 −0.947491 −0.473745 0.880662i \(-0.657098\pi\)
−0.473745 + 0.880662i \(0.657098\pi\)
\(294\) 0 0
\(295\) 1179.00 0.232692
\(296\) 632.000 0.124102
\(297\) 0 0
\(298\) −3834.00 −0.745294
\(299\) −4920.00 −0.951609
\(300\) 0 0
\(301\) 1988.00 0.380686
\(302\) 6044.00 1.15163
\(303\) 0 0
\(304\) −688.000 −0.129801
\(305\) −1050.00 −0.197124
\(306\) 0 0
\(307\) 1676.00 0.311578 0.155789 0.987790i \(-0.450208\pi\)
0.155789 + 0.987790i \(0.450208\pi\)
\(308\) 308.000 0.0569803
\(309\) 0 0
\(310\) 1596.00 0.292409
\(311\) 6288.00 1.14649 0.573247 0.819382i \(-0.305683\pi\)
0.573247 + 0.819382i \(0.305683\pi\)
\(312\) 0 0
\(313\) −430.000 −0.0776519 −0.0388259 0.999246i \(-0.512362\pi\)
−0.0388259 + 0.999246i \(0.512362\pi\)
\(314\) 4400.00 0.790785
\(315\) 0 0
\(316\) −1936.00 −0.344647
\(317\) −7176.00 −1.27143 −0.635717 0.771923i \(-0.719295\pi\)
−0.635717 + 0.771923i \(0.719295\pi\)
\(318\) 0 0
\(319\) −1221.00 −0.214304
\(320\) −192.000 −0.0335410
\(321\) 0 0
\(322\) 1680.00 0.290754
\(323\) 258.000 0.0444443
\(324\) 0 0
\(325\) −4756.00 −0.811740
\(326\) 7430.00 1.26230
\(327\) 0 0
\(328\) 1728.00 0.290893
\(329\) −1491.00 −0.249853
\(330\) 0 0
\(331\) 5360.00 0.890067 0.445034 0.895514i \(-0.353192\pi\)
0.445034 + 0.895514i \(0.353192\pi\)
\(332\) −4632.00 −0.765705
\(333\) 0 0
\(334\) 168.000 0.0275226
\(335\) −2463.00 −0.401696
\(336\) 0 0
\(337\) −9376.00 −1.51556 −0.757779 0.652511i \(-0.773716\pi\)
−0.757779 + 0.652511i \(0.773716\pi\)
\(338\) 1032.00 0.166075
\(339\) 0 0
\(340\) 72.0000 0.0114846
\(341\) 2926.00 0.464668
\(342\) 0 0
\(343\) 343.000 0.0539949
\(344\) −2272.00 −0.356099
\(345\) 0 0
\(346\) 3624.00 0.563085
\(347\) −1608.00 −0.248766 −0.124383 0.992234i \(-0.539695\pi\)
−0.124383 + 0.992234i \(0.539695\pi\)
\(348\) 0 0
\(349\) 2477.00 0.379916 0.189958 0.981792i \(-0.439165\pi\)
0.189958 + 0.981792i \(0.439165\pi\)
\(350\) 1624.00 0.248018
\(351\) 0 0
\(352\) −352.000 −0.0533002
\(353\) 975.000 0.147009 0.0735043 0.997295i \(-0.476582\pi\)
0.0735043 + 0.997295i \(0.476582\pi\)
\(354\) 0 0
\(355\) −792.000 −0.118408
\(356\) −1320.00 −0.196516
\(357\) 0 0
\(358\) 384.000 0.0566900
\(359\) −4116.00 −0.605109 −0.302555 0.953132i \(-0.597839\pi\)
−0.302555 + 0.953132i \(0.597839\pi\)
\(360\) 0 0
\(361\) −5010.00 −0.730427
\(362\) 6296.00 0.914117
\(363\) 0 0
\(364\) 1148.00 0.165306
\(365\) 2595.00 0.372133
\(366\) 0 0
\(367\) 2066.00 0.293854 0.146927 0.989147i \(-0.453062\pi\)
0.146927 + 0.989147i \(0.453062\pi\)
\(368\) −1920.00 −0.271975
\(369\) 0 0
\(370\) −474.000 −0.0666002
\(371\) 1512.00 0.211588
\(372\) 0 0
\(373\) 1778.00 0.246813 0.123407 0.992356i \(-0.460618\pi\)
0.123407 + 0.992356i \(0.460618\pi\)
\(374\) 132.000 0.0182502
\(375\) 0 0
\(376\) 1704.00 0.233716
\(377\) −4551.00 −0.621720
\(378\) 0 0
\(379\) −10717.0 −1.45249 −0.726247 0.687434i \(-0.758737\pi\)
−0.726247 + 0.687434i \(0.758737\pi\)
\(380\) 516.000 0.0696585
\(381\) 0 0
\(382\) 9108.00 1.21991
\(383\) −9360.00 −1.24876 −0.624378 0.781122i \(-0.714648\pi\)
−0.624378 + 0.781122i \(0.714648\pi\)
\(384\) 0 0
\(385\) −231.000 −0.0305788
\(386\) 1880.00 0.247900
\(387\) 0 0
\(388\) 3920.00 0.512907
\(389\) −8364.00 −1.09016 −0.545079 0.838385i \(-0.683500\pi\)
−0.545079 + 0.838385i \(0.683500\pi\)
\(390\) 0 0
\(391\) 720.000 0.0931252
\(392\) −392.000 −0.0505076
\(393\) 0 0
\(394\) −2244.00 −0.286932
\(395\) 1452.00 0.184957
\(396\) 0 0
\(397\) −646.000 −0.0816670 −0.0408335 0.999166i \(-0.513001\pi\)
−0.0408335 + 0.999166i \(0.513001\pi\)
\(398\) −7912.00 −0.996464
\(399\) 0 0
\(400\) −1856.00 −0.232000
\(401\) −2808.00 −0.349688 −0.174844 0.984596i \(-0.555942\pi\)
−0.174844 + 0.984596i \(0.555942\pi\)
\(402\) 0 0
\(403\) 10906.0 1.34806
\(404\) −840.000 −0.103444
\(405\) 0 0
\(406\) 1554.00 0.189960
\(407\) −869.000 −0.105835
\(408\) 0 0
\(409\) 8750.00 1.05785 0.528924 0.848669i \(-0.322596\pi\)
0.528924 + 0.848669i \(0.322596\pi\)
\(410\) −1296.00 −0.156109
\(411\) 0 0
\(412\) −5320.00 −0.636159
\(413\) −2751.00 −0.327767
\(414\) 0 0
\(415\) 3474.00 0.410920
\(416\) −1312.00 −0.154630
\(417\) 0 0
\(418\) 946.000 0.110695
\(419\) −13263.0 −1.54640 −0.773198 0.634165i \(-0.781344\pi\)
−0.773198 + 0.634165i \(0.781344\pi\)
\(420\) 0 0
\(421\) −5785.00 −0.669700 −0.334850 0.942271i \(-0.608686\pi\)
−0.334850 + 0.942271i \(0.608686\pi\)
\(422\) −244.000 −0.0281463
\(423\) 0 0
\(424\) −1728.00 −0.197922
\(425\) 696.000 0.0794376
\(426\) 0 0
\(427\) 2450.00 0.277667
\(428\) 5316.00 0.600370
\(429\) 0 0
\(430\) 1704.00 0.191103
\(431\) −5019.00 −0.560920 −0.280460 0.959866i \(-0.590487\pi\)
−0.280460 + 0.959866i \(0.590487\pi\)
\(432\) 0 0
\(433\) 14768.0 1.63904 0.819521 0.573050i \(-0.194240\pi\)
0.819521 + 0.573050i \(0.194240\pi\)
\(434\) −3724.00 −0.411884
\(435\) 0 0
\(436\) −376.000 −0.0413008
\(437\) 5160.00 0.564843
\(438\) 0 0
\(439\) −2311.00 −0.251248 −0.125624 0.992078i \(-0.540093\pi\)
−0.125624 + 0.992078i \(0.540093\pi\)
\(440\) 264.000 0.0286039
\(441\) 0 0
\(442\) 492.000 0.0529458
\(443\) 252.000 0.0270268 0.0135134 0.999909i \(-0.495698\pi\)
0.0135134 + 0.999909i \(0.495698\pi\)
\(444\) 0 0
\(445\) 990.000 0.105462
\(446\) −1204.00 −0.127827
\(447\) 0 0
\(448\) 448.000 0.0472456
\(449\) −1980.00 −0.208111 −0.104056 0.994571i \(-0.533182\pi\)
−0.104056 + 0.994571i \(0.533182\pi\)
\(450\) 0 0
\(451\) −2376.00 −0.248074
\(452\) −792.000 −0.0824171
\(453\) 0 0
\(454\) −852.000 −0.0880756
\(455\) −861.000 −0.0887128
\(456\) 0 0
\(457\) 12164.0 1.24509 0.622547 0.782582i \(-0.286098\pi\)
0.622547 + 0.782582i \(0.286098\pi\)
\(458\) 8792.00 0.896994
\(459\) 0 0
\(460\) 1440.00 0.145957
\(461\) 18732.0 1.89249 0.946243 0.323456i \(-0.104845\pi\)
0.946243 + 0.323456i \(0.104845\pi\)
\(462\) 0 0
\(463\) −13051.0 −1.31000 −0.655002 0.755628i \(-0.727332\pi\)
−0.655002 + 0.755628i \(0.727332\pi\)
\(464\) −1776.00 −0.177691
\(465\) 0 0
\(466\) 6396.00 0.635813
\(467\) −6717.00 −0.665580 −0.332790 0.943001i \(-0.607990\pi\)
−0.332790 + 0.943001i \(0.607990\pi\)
\(468\) 0 0
\(469\) 5747.00 0.565825
\(470\) −1278.00 −0.125425
\(471\) 0 0
\(472\) 3144.00 0.306598
\(473\) 3124.00 0.303682
\(474\) 0 0
\(475\) 4988.00 0.481821
\(476\) −168.000 −0.0161770
\(477\) 0 0
\(478\) 5994.00 0.573555
\(479\) 18438.0 1.75878 0.879388 0.476106i \(-0.157952\pi\)
0.879388 + 0.476106i \(0.157952\pi\)
\(480\) 0 0
\(481\) −3239.00 −0.307039
\(482\) 12470.0 1.17841
\(483\) 0 0
\(484\) 484.000 0.0454545
\(485\) −2940.00 −0.275255
\(486\) 0 0
\(487\) −10648.0 −0.990774 −0.495387 0.868672i \(-0.664974\pi\)
−0.495387 + 0.868672i \(0.664974\pi\)
\(488\) −2800.00 −0.259734
\(489\) 0 0
\(490\) 294.000 0.0271052
\(491\) −16863.0 −1.54993 −0.774966 0.632003i \(-0.782233\pi\)
−0.774966 + 0.632003i \(0.782233\pi\)
\(492\) 0 0
\(493\) 666.000 0.0608421
\(494\) 3526.00 0.321138
\(495\) 0 0
\(496\) 4256.00 0.385282
\(497\) 1848.00 0.166789
\(498\) 0 0
\(499\) 12683.0 1.13781 0.568907 0.822402i \(-0.307366\pi\)
0.568907 + 0.822402i \(0.307366\pi\)
\(500\) 2892.00 0.258668
\(501\) 0 0
\(502\) 7470.00 0.664148
\(503\) −14472.0 −1.28285 −0.641426 0.767185i \(-0.721657\pi\)
−0.641426 + 0.767185i \(0.721657\pi\)
\(504\) 0 0
\(505\) 630.000 0.0555141
\(506\) 2640.00 0.231941
\(507\) 0 0
\(508\) −4264.00 −0.372410
\(509\) 10722.0 0.933682 0.466841 0.884341i \(-0.345392\pi\)
0.466841 + 0.884341i \(0.345392\pi\)
\(510\) 0 0
\(511\) −6055.00 −0.524183
\(512\) −512.000 −0.0441942
\(513\) 0 0
\(514\) 3030.00 0.260015
\(515\) 3990.00 0.341399
\(516\) 0 0
\(517\) −2343.00 −0.199313
\(518\) 1106.00 0.0938125
\(519\) 0 0
\(520\) 984.000 0.0829832
\(521\) 10341.0 0.869573 0.434786 0.900534i \(-0.356824\pi\)
0.434786 + 0.900534i \(0.356824\pi\)
\(522\) 0 0
\(523\) 5819.00 0.486515 0.243257 0.969962i \(-0.421784\pi\)
0.243257 + 0.969962i \(0.421784\pi\)
\(524\) 480.000 0.0400170
\(525\) 0 0
\(526\) −8634.00 −0.715704
\(527\) −1596.00 −0.131922
\(528\) 0 0
\(529\) 2233.00 0.183529
\(530\) 1296.00 0.106216
\(531\) 0 0
\(532\) −1204.00 −0.0981203
\(533\) −8856.00 −0.719692
\(534\) 0 0
\(535\) −3987.00 −0.322193
\(536\) −6568.00 −0.529281
\(537\) 0 0
\(538\) −2868.00 −0.229829
\(539\) 539.000 0.0430730
\(540\) 0 0
\(541\) 9668.00 0.768318 0.384159 0.923267i \(-0.374492\pi\)
0.384159 + 0.923267i \(0.374492\pi\)
\(542\) 1886.00 0.149466
\(543\) 0 0
\(544\) 192.000 0.0151322
\(545\) 282.000 0.0221643
\(546\) 0 0
\(547\) 13160.0 1.02867 0.514334 0.857590i \(-0.328039\pi\)
0.514334 + 0.857590i \(0.328039\pi\)
\(548\) 7752.00 0.604287
\(549\) 0 0
\(550\) 2552.00 0.197850
\(551\) 4773.00 0.369032
\(552\) 0 0
\(553\) −3388.00 −0.260529
\(554\) 11552.0 0.885916
\(555\) 0 0
\(556\) 6848.00 0.522338
\(557\) 2253.00 0.171387 0.0856936 0.996322i \(-0.472689\pi\)
0.0856936 + 0.996322i \(0.472689\pi\)
\(558\) 0 0
\(559\) 11644.0 0.881017
\(560\) −336.000 −0.0253546
\(561\) 0 0
\(562\) −3306.00 −0.248141
\(563\) 984.000 0.0736601 0.0368301 0.999322i \(-0.488274\pi\)
0.0368301 + 0.999322i \(0.488274\pi\)
\(564\) 0 0
\(565\) 594.000 0.0442297
\(566\) −1354.00 −0.100553
\(567\) 0 0
\(568\) −2112.00 −0.156017
\(569\) 16878.0 1.24352 0.621760 0.783208i \(-0.286418\pi\)
0.621760 + 0.783208i \(0.286418\pi\)
\(570\) 0 0
\(571\) 4736.00 0.347102 0.173551 0.984825i \(-0.444476\pi\)
0.173551 + 0.984825i \(0.444476\pi\)
\(572\) 1804.00 0.131869
\(573\) 0 0
\(574\) 3024.00 0.219894
\(575\) 13920.0 1.00957
\(576\) 0 0
\(577\) −3694.00 −0.266522 −0.133261 0.991081i \(-0.542545\pi\)
−0.133261 + 0.991081i \(0.542545\pi\)
\(578\) 9754.00 0.701925
\(579\) 0 0
\(580\) 1332.00 0.0953591
\(581\) −8106.00 −0.578818
\(582\) 0 0
\(583\) 2376.00 0.168789
\(584\) 6920.00 0.490328
\(585\) 0 0
\(586\) 9504.00 0.669977
\(587\) 21237.0 1.49326 0.746631 0.665238i \(-0.231670\pi\)
0.746631 + 0.665238i \(0.231670\pi\)
\(588\) 0 0
\(589\) −11438.0 −0.800161
\(590\) −2358.00 −0.164538
\(591\) 0 0
\(592\) −1264.00 −0.0877535
\(593\) 7416.00 0.513556 0.256778 0.966470i \(-0.417339\pi\)
0.256778 + 0.966470i \(0.417339\pi\)
\(594\) 0 0
\(595\) 126.000 0.00868151
\(596\) 7668.00 0.527003
\(597\) 0 0
\(598\) 9840.00 0.672889
\(599\) 5484.00 0.374074 0.187037 0.982353i \(-0.440112\pi\)
0.187037 + 0.982353i \(0.440112\pi\)
\(600\) 0 0
\(601\) −11077.0 −0.751814 −0.375907 0.926657i \(-0.622669\pi\)
−0.375907 + 0.926657i \(0.622669\pi\)
\(602\) −3976.00 −0.269185
\(603\) 0 0
\(604\) −12088.0 −0.814327
\(605\) −363.000 −0.0243935
\(606\) 0 0
\(607\) −5047.00 −0.337482 −0.168741 0.985660i \(-0.553970\pi\)
−0.168741 + 0.985660i \(0.553970\pi\)
\(608\) 1376.00 0.0917832
\(609\) 0 0
\(610\) 2100.00 0.139388
\(611\) −8733.00 −0.578231
\(612\) 0 0
\(613\) 20066.0 1.32212 0.661059 0.750334i \(-0.270107\pi\)
0.661059 + 0.750334i \(0.270107\pi\)
\(614\) −3352.00 −0.220319
\(615\) 0 0
\(616\) −616.000 −0.0402911
\(617\) 16626.0 1.08483 0.542413 0.840112i \(-0.317511\pi\)
0.542413 + 0.840112i \(0.317511\pi\)
\(618\) 0 0
\(619\) −10162.0 −0.659847 −0.329923 0.944008i \(-0.607023\pi\)
−0.329923 + 0.944008i \(0.607023\pi\)
\(620\) −3192.00 −0.206764
\(621\) 0 0
\(622\) −12576.0 −0.810694
\(623\) −2310.00 −0.148552
\(624\) 0 0
\(625\) 12331.0 0.789184
\(626\) 860.000 0.0549082
\(627\) 0 0
\(628\) −8800.00 −0.559169
\(629\) 474.000 0.0300471
\(630\) 0 0
\(631\) −16108.0 −1.01624 −0.508122 0.861285i \(-0.669660\pi\)
−0.508122 + 0.861285i \(0.669660\pi\)
\(632\) 3872.00 0.243702
\(633\) 0 0
\(634\) 14352.0 0.899039
\(635\) 3198.00 0.199856
\(636\) 0 0
\(637\) 2009.00 0.124960
\(638\) 2442.00 0.151536
\(639\) 0 0
\(640\) 384.000 0.0237171
\(641\) 19950.0 1.22929 0.614647 0.788802i \(-0.289298\pi\)
0.614647 + 0.788802i \(0.289298\pi\)
\(642\) 0 0
\(643\) −8260.00 −0.506598 −0.253299 0.967388i \(-0.581516\pi\)
−0.253299 + 0.967388i \(0.581516\pi\)
\(644\) −3360.00 −0.205594
\(645\) 0 0
\(646\) −516.000 −0.0314269
\(647\) 28833.0 1.75200 0.875999 0.482314i \(-0.160203\pi\)
0.875999 + 0.482314i \(0.160203\pi\)
\(648\) 0 0
\(649\) −4323.00 −0.261468
\(650\) 9512.00 0.573987
\(651\) 0 0
\(652\) −14860.0 −0.892581
\(653\) 13152.0 0.788174 0.394087 0.919073i \(-0.371061\pi\)
0.394087 + 0.919073i \(0.371061\pi\)
\(654\) 0 0
\(655\) −360.000 −0.0214754
\(656\) −3456.00 −0.205692
\(657\) 0 0
\(658\) 2982.00 0.176672
\(659\) 32229.0 1.90510 0.952552 0.304376i \(-0.0984478\pi\)
0.952552 + 0.304376i \(0.0984478\pi\)
\(660\) 0 0
\(661\) −460.000 −0.0270680 −0.0135340 0.999908i \(-0.504308\pi\)
−0.0135340 + 0.999908i \(0.504308\pi\)
\(662\) −10720.0 −0.629373
\(663\) 0 0
\(664\) 9264.00 0.541435
\(665\) 903.000 0.0526569
\(666\) 0 0
\(667\) 13320.0 0.773242
\(668\) −336.000 −0.0194614
\(669\) 0 0
\(670\) 4926.00 0.284042
\(671\) 3850.00 0.221502
\(672\) 0 0
\(673\) −12784.0 −0.732224 −0.366112 0.930571i \(-0.619311\pi\)
−0.366112 + 0.930571i \(0.619311\pi\)
\(674\) 18752.0 1.07166
\(675\) 0 0
\(676\) −2064.00 −0.117433
\(677\) −2190.00 −0.124326 −0.0621629 0.998066i \(-0.519800\pi\)
−0.0621629 + 0.998066i \(0.519800\pi\)
\(678\) 0 0
\(679\) 6860.00 0.387721
\(680\) −144.000 −0.00812081
\(681\) 0 0
\(682\) −5852.00 −0.328570
\(683\) −11514.0 −0.645053 −0.322526 0.946560i \(-0.604532\pi\)
−0.322526 + 0.946560i \(0.604532\pi\)
\(684\) 0 0
\(685\) −5814.00 −0.324294
\(686\) −686.000 −0.0381802
\(687\) 0 0
\(688\) 4544.00 0.251800
\(689\) 8856.00 0.489676
\(690\) 0 0
\(691\) −11554.0 −0.636085 −0.318043 0.948076i \(-0.603026\pi\)
−0.318043 + 0.948076i \(0.603026\pi\)
\(692\) −7248.00 −0.398161
\(693\) 0 0
\(694\) 3216.00 0.175904
\(695\) −5136.00 −0.280316
\(696\) 0 0
\(697\) 1296.00 0.0704297
\(698\) −4954.00 −0.268641
\(699\) 0 0
\(700\) −3248.00 −0.175376
\(701\) 18450.0 0.994075 0.497038 0.867729i \(-0.334421\pi\)
0.497038 + 0.867729i \(0.334421\pi\)
\(702\) 0 0
\(703\) 3397.00 0.182248
\(704\) 704.000 0.0376889
\(705\) 0 0
\(706\) −1950.00 −0.103951
\(707\) −1470.00 −0.0781967
\(708\) 0 0
\(709\) 15203.0 0.805304 0.402652 0.915353i \(-0.368088\pi\)
0.402652 + 0.915353i \(0.368088\pi\)
\(710\) 1584.00 0.0837274
\(711\) 0 0
\(712\) 2640.00 0.138958
\(713\) −31920.0 −1.67660
\(714\) 0 0
\(715\) −1353.00 −0.0707683
\(716\) −768.000 −0.0400859
\(717\) 0 0
\(718\) 8232.00 0.427877
\(719\) −28515.0 −1.47904 −0.739520 0.673134i \(-0.764948\pi\)
−0.739520 + 0.673134i \(0.764948\pi\)
\(720\) 0 0
\(721\) −9310.00 −0.480891
\(722\) 10020.0 0.516490
\(723\) 0 0
\(724\) −12592.0 −0.646378
\(725\) 12876.0 0.659590
\(726\) 0 0
\(727\) 15932.0 0.812772 0.406386 0.913702i \(-0.366789\pi\)
0.406386 + 0.913702i \(0.366789\pi\)
\(728\) −2296.00 −0.116889
\(729\) 0 0
\(730\) −5190.00 −0.263138
\(731\) −1704.00 −0.0862171
\(732\) 0 0
\(733\) 26630.0 1.34188 0.670942 0.741510i \(-0.265890\pi\)
0.670942 + 0.741510i \(0.265890\pi\)
\(734\) −4132.00 −0.207786
\(735\) 0 0
\(736\) 3840.00 0.192316
\(737\) 9031.00 0.451372
\(738\) 0 0
\(739\) −3940.00 −0.196123 −0.0980617 0.995180i \(-0.531264\pi\)
−0.0980617 + 0.995180i \(0.531264\pi\)
\(740\) 948.000 0.0470935
\(741\) 0 0
\(742\) −3024.00 −0.149615
\(743\) −25203.0 −1.24443 −0.622213 0.782848i \(-0.713766\pi\)
−0.622213 + 0.782848i \(0.713766\pi\)
\(744\) 0 0
\(745\) −5751.00 −0.282819
\(746\) −3556.00 −0.174523
\(747\) 0 0
\(748\) −264.000 −0.0129048
\(749\) 9303.00 0.453837
\(750\) 0 0
\(751\) −17611.0 −0.855705 −0.427853 0.903849i \(-0.640730\pi\)
−0.427853 + 0.903849i \(0.640730\pi\)
\(752\) −3408.00 −0.165262
\(753\) 0 0
\(754\) 9102.00 0.439622
\(755\) 9066.00 0.437014
\(756\) 0 0
\(757\) −28543.0 −1.37043 −0.685213 0.728342i \(-0.740291\pi\)
−0.685213 + 0.728342i \(0.740291\pi\)
\(758\) 21434.0 1.02707
\(759\) 0 0
\(760\) −1032.00 −0.0492560
\(761\) 16884.0 0.804263 0.402132 0.915582i \(-0.368269\pi\)
0.402132 + 0.915582i \(0.368269\pi\)
\(762\) 0 0
\(763\) −658.000 −0.0312204
\(764\) −18216.0 −0.862607
\(765\) 0 0
\(766\) 18720.0 0.883004
\(767\) −16113.0 −0.758549
\(768\) 0 0
\(769\) −22963.0 −1.07681 −0.538405 0.842686i \(-0.680973\pi\)
−0.538405 + 0.842686i \(0.680973\pi\)
\(770\) 462.000 0.0216225
\(771\) 0 0
\(772\) −3760.00 −0.175292
\(773\) 32601.0 1.51692 0.758458 0.651722i \(-0.225953\pi\)
0.758458 + 0.651722i \(0.225953\pi\)
\(774\) 0 0
\(775\) −30856.0 −1.43017
\(776\) −7840.00 −0.362680
\(777\) 0 0
\(778\) 16728.0 0.770858
\(779\) 9288.00 0.427185
\(780\) 0 0
\(781\) 2904.00 0.133052
\(782\) −1440.00 −0.0658495
\(783\) 0 0
\(784\) 784.000 0.0357143
\(785\) 6600.00 0.300082
\(786\) 0 0
\(787\) 17867.0 0.809263 0.404631 0.914480i \(-0.367400\pi\)
0.404631 + 0.914480i \(0.367400\pi\)
\(788\) 4488.00 0.202891
\(789\) 0 0
\(790\) −2904.00 −0.130784
\(791\) −1386.00 −0.0623015
\(792\) 0 0
\(793\) 14350.0 0.642602
\(794\) 1292.00 0.0577473
\(795\) 0 0
\(796\) 15824.0 0.704607
\(797\) −17505.0 −0.777991 −0.388996 0.921240i \(-0.627178\pi\)
−0.388996 + 0.921240i \(0.627178\pi\)
\(798\) 0 0
\(799\) 1278.00 0.0565862
\(800\) 3712.00 0.164049
\(801\) 0 0
\(802\) 5616.00 0.247267
\(803\) −9515.00 −0.418153
\(804\) 0 0
\(805\) 2520.00 0.110333
\(806\) −21812.0 −0.953220
\(807\) 0 0
\(808\) 1680.00 0.0731463
\(809\) −11079.0 −0.481479 −0.240740 0.970590i \(-0.577390\pi\)
−0.240740 + 0.970590i \(0.577390\pi\)
\(810\) 0 0
\(811\) −28021.0 −1.21326 −0.606628 0.794986i \(-0.707478\pi\)
−0.606628 + 0.794986i \(0.707478\pi\)
\(812\) −3108.00 −0.134322
\(813\) 0 0
\(814\) 1738.00 0.0748364
\(815\) 11145.0 0.479009
\(816\) 0 0
\(817\) −12212.0 −0.522942
\(818\) −17500.0 −0.748011
\(819\) 0 0
\(820\) 2592.00 0.110386
\(821\) −12309.0 −0.523249 −0.261624 0.965170i \(-0.584258\pi\)
−0.261624 + 0.965170i \(0.584258\pi\)
\(822\) 0 0
\(823\) 3893.00 0.164886 0.0824432 0.996596i \(-0.473728\pi\)
0.0824432 + 0.996596i \(0.473728\pi\)
\(824\) 10640.0 0.449832
\(825\) 0 0
\(826\) 5502.00 0.231766
\(827\) −45063.0 −1.89479 −0.947397 0.320062i \(-0.896296\pi\)
−0.947397 + 0.320062i \(0.896296\pi\)
\(828\) 0 0
\(829\) −15136.0 −0.634131 −0.317066 0.948404i \(-0.602698\pi\)
−0.317066 + 0.948404i \(0.602698\pi\)
\(830\) −6948.00 −0.290565
\(831\) 0 0
\(832\) 2624.00 0.109340
\(833\) −294.000 −0.0122287
\(834\) 0 0
\(835\) 252.000 0.0104441
\(836\) −1892.00 −0.0782730
\(837\) 0 0
\(838\) 26526.0 1.09347
\(839\) 20739.0 0.853385 0.426692 0.904397i \(-0.359679\pi\)
0.426692 + 0.904397i \(0.359679\pi\)
\(840\) 0 0
\(841\) −12068.0 −0.494813
\(842\) 11570.0 0.473549
\(843\) 0 0
\(844\) 488.000 0.0199024
\(845\) 1548.00 0.0630211
\(846\) 0 0
\(847\) 847.000 0.0343604
\(848\) 3456.00 0.139952
\(849\) 0 0
\(850\) −1392.00 −0.0561708
\(851\) 9480.00 0.381869
\(852\) 0 0
\(853\) 37610.0 1.50966 0.754831 0.655919i \(-0.227719\pi\)
0.754831 + 0.655919i \(0.227719\pi\)
\(854\) −4900.00 −0.196340
\(855\) 0 0
\(856\) −10632.0 −0.424526
\(857\) 37470.0 1.49352 0.746762 0.665091i \(-0.231607\pi\)
0.746762 + 0.665091i \(0.231607\pi\)
\(858\) 0 0
\(859\) −15604.0 −0.619792 −0.309896 0.950770i \(-0.600294\pi\)
−0.309896 + 0.950770i \(0.600294\pi\)
\(860\) −3408.00 −0.135130
\(861\) 0 0
\(862\) 10038.0 0.396631
\(863\) −20004.0 −0.789043 −0.394521 0.918887i \(-0.629090\pi\)
−0.394521 + 0.918887i \(0.629090\pi\)
\(864\) 0 0
\(865\) 5436.00 0.213676
\(866\) −29536.0 −1.15898
\(867\) 0 0
\(868\) 7448.00 0.291246
\(869\) −5324.00 −0.207830
\(870\) 0 0
\(871\) 33661.0 1.30948
\(872\) 752.000 0.0292041
\(873\) 0 0
\(874\) −10320.0 −0.399404
\(875\) 5061.00 0.195535
\(876\) 0 0
\(877\) 1064.00 0.0409678 0.0204839 0.999790i \(-0.493479\pi\)
0.0204839 + 0.999790i \(0.493479\pi\)
\(878\) 4622.00 0.177659
\(879\) 0 0
\(880\) −528.000 −0.0202260
\(881\) −4179.00 −0.159812 −0.0799058 0.996802i \(-0.525462\pi\)
−0.0799058 + 0.996802i \(0.525462\pi\)
\(882\) 0 0
\(883\) −44509.0 −1.69632 −0.848158 0.529743i \(-0.822288\pi\)
−0.848158 + 0.529743i \(0.822288\pi\)
\(884\) −984.000 −0.0374384
\(885\) 0 0
\(886\) −504.000 −0.0191108
\(887\) −12642.0 −0.478553 −0.239277 0.970951i \(-0.576910\pi\)
−0.239277 + 0.970951i \(0.576910\pi\)
\(888\) 0 0
\(889\) −7462.00 −0.281516
\(890\) −1980.00 −0.0745728
\(891\) 0 0
\(892\) 2408.00 0.0903877
\(893\) 9159.00 0.343219
\(894\) 0 0
\(895\) 576.000 0.0215124
\(896\) −896.000 −0.0334077
\(897\) 0 0
\(898\) 3960.00 0.147157
\(899\) −29526.0 −1.09538
\(900\) 0 0
\(901\) −1296.00 −0.0479201
\(902\) 4752.00 0.175415
\(903\) 0 0
\(904\) 1584.00 0.0582777
\(905\) 9444.00 0.346883
\(906\) 0 0
\(907\) −28.0000 −0.00102505 −0.000512527 1.00000i \(-0.500163\pi\)
−0.000512527 1.00000i \(0.500163\pi\)
\(908\) 1704.00 0.0622789
\(909\) 0 0
\(910\) 1722.00 0.0627294
\(911\) 9774.00 0.355463 0.177732 0.984079i \(-0.443124\pi\)
0.177732 + 0.984079i \(0.443124\pi\)
\(912\) 0 0
\(913\) −12738.0 −0.461737
\(914\) −24328.0 −0.880414
\(915\) 0 0
\(916\) −17584.0 −0.634270
\(917\) 840.000 0.0302500
\(918\) 0 0
\(919\) 23204.0 0.832894 0.416447 0.909160i \(-0.363275\pi\)
0.416447 + 0.909160i \(0.363275\pi\)
\(920\) −2880.00 −0.103207
\(921\) 0 0
\(922\) −37464.0 −1.33819
\(923\) 10824.0 0.385998
\(924\) 0 0
\(925\) 9164.00 0.325741
\(926\) 26102.0 0.926312
\(927\) 0 0
\(928\) 3552.00 0.125647
\(929\) −3633.00 −0.128304 −0.0641522 0.997940i \(-0.520434\pi\)
−0.0641522 + 0.997940i \(0.520434\pi\)
\(930\) 0 0
\(931\) −2107.00 −0.0741720
\(932\) −12792.0 −0.449588
\(933\) 0 0
\(934\) 13434.0 0.470636
\(935\) 198.000 0.00692545
\(936\) 0 0
\(937\) 18938.0 0.660275 0.330137 0.943933i \(-0.392905\pi\)
0.330137 + 0.943933i \(0.392905\pi\)
\(938\) −11494.0 −0.400099
\(939\) 0 0
\(940\) 2556.00 0.0886889
\(941\) −14784.0 −0.512162 −0.256081 0.966655i \(-0.582431\pi\)
−0.256081 + 0.966655i \(0.582431\pi\)
\(942\) 0 0
\(943\) 25920.0 0.895092
\(944\) −6288.00 −0.216798
\(945\) 0 0
\(946\) −6248.00 −0.214736
\(947\) 31266.0 1.07287 0.536435 0.843941i \(-0.319771\pi\)
0.536435 + 0.843941i \(0.319771\pi\)
\(948\) 0 0
\(949\) −35465.0 −1.21311
\(950\) −9976.00 −0.340699
\(951\) 0 0
\(952\) 336.000 0.0114389
\(953\) −33951.0 −1.15402 −0.577010 0.816737i \(-0.695781\pi\)
−0.577010 + 0.816737i \(0.695781\pi\)
\(954\) 0 0
\(955\) 13662.0 0.462923
\(956\) −11988.0 −0.405564
\(957\) 0 0
\(958\) −36876.0 −1.24364
\(959\) 13566.0 0.456798
\(960\) 0 0
\(961\) 40965.0 1.37508
\(962\) 6478.00 0.217109
\(963\) 0 0
\(964\) −24940.0 −0.833261
\(965\) 2820.00 0.0940715
\(966\) 0 0
\(967\) 16322.0 0.542792 0.271396 0.962468i \(-0.412515\pi\)
0.271396 + 0.962468i \(0.412515\pi\)
\(968\) −968.000 −0.0321412
\(969\) 0 0
\(970\) 5880.00 0.194634
\(971\) −40779.0 −1.34774 −0.673872 0.738848i \(-0.735370\pi\)
−0.673872 + 0.738848i \(0.735370\pi\)
\(972\) 0 0
\(973\) 11984.0 0.394850
\(974\) 21296.0 0.700583
\(975\) 0 0
\(976\) 5600.00 0.183659
\(977\) −21804.0 −0.713994 −0.356997 0.934106i \(-0.616199\pi\)
−0.356997 + 0.934106i \(0.616199\pi\)
\(978\) 0 0
\(979\) −3630.00 −0.118504
\(980\) −588.000 −0.0191663
\(981\) 0 0
\(982\) 33726.0 1.09597
\(983\) 35424.0 1.14939 0.574695 0.818368i \(-0.305121\pi\)
0.574695 + 0.818368i \(0.305121\pi\)
\(984\) 0 0
\(985\) −3366.00 −0.108883
\(986\) −1332.00 −0.0430218
\(987\) 0 0
\(988\) −7052.00 −0.227079
\(989\) −34080.0 −1.09573
\(990\) 0 0
\(991\) −37315.0 −1.19612 −0.598058 0.801453i \(-0.704061\pi\)
−0.598058 + 0.801453i \(0.704061\pi\)
\(992\) −8512.00 −0.272436
\(993\) 0 0
\(994\) −3696.00 −0.117938
\(995\) −11868.0 −0.378132
\(996\) 0 0
\(997\) 30674.0 0.974378 0.487189 0.873296i \(-0.338022\pi\)
0.487189 + 0.873296i \(0.338022\pi\)
\(998\) −25366.0 −0.804556
\(999\) 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 1386.4.a.c.1.1 1
3.2 odd 2 462.4.a.g.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
462.4.a.g.1.1 1 3.2 odd 2
1386.4.a.c.1.1 1 1.1 even 1 trivial