Properties

Label 1386.4.a.a.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 154)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

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

$q$-expansion

\(f(q)\) \(=\) \(q-2.00000 q^{2} +4.00000 q^{4} -18.0000 q^{5} +7.00000 q^{7} -8.00000 q^{8} +O(q^{10})\) \(q-2.00000 q^{2} +4.00000 q^{4} -18.0000 q^{5} +7.00000 q^{7} -8.00000 q^{8} +36.0000 q^{10} +11.0000 q^{11} +56.0000 q^{13} -14.0000 q^{14} +16.0000 q^{16} -36.0000 q^{17} -28.0000 q^{19} -72.0000 q^{20} -22.0000 q^{22} -180.000 q^{23} +199.000 q^{25} -112.000 q^{26} +28.0000 q^{28} +54.0000 q^{29} -334.000 q^{31} -32.0000 q^{32} +72.0000 q^{34} -126.000 q^{35} +386.000 q^{37} +56.0000 q^{38} +144.000 q^{40} +444.000 q^{41} -316.000 q^{43} +44.0000 q^{44} +360.000 q^{46} +402.000 q^{47} +49.0000 q^{49} -398.000 q^{50} +224.000 q^{52} +486.000 q^{53} -198.000 q^{55} -56.0000 q^{56} -108.000 q^{58} +282.000 q^{59} +380.000 q^{61} +668.000 q^{62} +64.0000 q^{64} -1008.00 q^{65} +176.000 q^{67} -144.000 q^{68} +252.000 q^{70} +324.000 q^{71} +800.000 q^{73} -772.000 q^{74} -112.000 q^{76} +77.0000 q^{77} -1144.00 q^{79} -288.000 q^{80} -888.000 q^{82} -468.000 q^{83} +648.000 q^{85} +632.000 q^{86} -88.0000 q^{88} +870.000 q^{89} +392.000 q^{91} -720.000 q^{92} -804.000 q^{94} +504.000 q^{95} -1330.00 q^{97} -98.0000 q^{98} +O(q^{100})\)

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
\(5\) −18.0000 −1.60997 −0.804984 0.593296i \(-0.797826\pi\)
−0.804984 + 0.593296i \(0.797826\pi\)
\(6\) 0 0
\(7\) 7.00000 0.377964
\(8\) −8.00000 −0.353553
\(9\) 0 0
\(10\) 36.0000 1.13842
\(11\) 11.0000 0.301511
\(12\) 0 0
\(13\) 56.0000 1.19474 0.597369 0.801966i \(-0.296213\pi\)
0.597369 + 0.801966i \(0.296213\pi\)
\(14\) −14.0000 −0.267261
\(15\) 0 0
\(16\) 16.0000 0.250000
\(17\) −36.0000 −0.513605 −0.256802 0.966464i \(-0.582669\pi\)
−0.256802 + 0.966464i \(0.582669\pi\)
\(18\) 0 0
\(19\) −28.0000 −0.338086 −0.169043 0.985609i \(-0.554068\pi\)
−0.169043 + 0.985609i \(0.554068\pi\)
\(20\) −72.0000 −0.804984
\(21\) 0 0
\(22\) −22.0000 −0.213201
\(23\) −180.000 −1.63185 −0.815926 0.578156i \(-0.803772\pi\)
−0.815926 + 0.578156i \(0.803772\pi\)
\(24\) 0 0
\(25\) 199.000 1.59200
\(26\) −112.000 −0.844808
\(27\) 0 0
\(28\) 28.0000 0.188982
\(29\) 54.0000 0.345778 0.172889 0.984941i \(-0.444690\pi\)
0.172889 + 0.984941i \(0.444690\pi\)
\(30\) 0 0
\(31\) −334.000 −1.93510 −0.967551 0.252675i \(-0.918690\pi\)
−0.967551 + 0.252675i \(0.918690\pi\)
\(32\) −32.0000 −0.176777
\(33\) 0 0
\(34\) 72.0000 0.363173
\(35\) −126.000 −0.608511
\(36\) 0 0
\(37\) 386.000 1.71508 0.857541 0.514416i \(-0.171991\pi\)
0.857541 + 0.514416i \(0.171991\pi\)
\(38\) 56.0000 0.239063
\(39\) 0 0
\(40\) 144.000 0.569210
\(41\) 444.000 1.69125 0.845624 0.533779i \(-0.179229\pi\)
0.845624 + 0.533779i \(0.179229\pi\)
\(42\) 0 0
\(43\) −316.000 −1.12069 −0.560344 0.828260i \(-0.689331\pi\)
−0.560344 + 0.828260i \(0.689331\pi\)
\(44\) 44.0000 0.150756
\(45\) 0 0
\(46\) 360.000 1.15389
\(47\) 402.000 1.24761 0.623806 0.781580i \(-0.285586\pi\)
0.623806 + 0.781580i \(0.285586\pi\)
\(48\) 0 0
\(49\) 49.0000 0.142857
\(50\) −398.000 −1.12571
\(51\) 0 0
\(52\) 224.000 0.597369
\(53\) 486.000 1.25957 0.629785 0.776769i \(-0.283143\pi\)
0.629785 + 0.776769i \(0.283143\pi\)
\(54\) 0 0
\(55\) −198.000 −0.485424
\(56\) −56.0000 −0.133631
\(57\) 0 0
\(58\) −108.000 −0.244502
\(59\) 282.000 0.622259 0.311129 0.950368i \(-0.399293\pi\)
0.311129 + 0.950368i \(0.399293\pi\)
\(60\) 0 0
\(61\) 380.000 0.797607 0.398803 0.917036i \(-0.369426\pi\)
0.398803 + 0.917036i \(0.369426\pi\)
\(62\) 668.000 1.36832
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) −1008.00 −1.92349
\(66\) 0 0
\(67\) 176.000 0.320923 0.160461 0.987042i \(-0.448702\pi\)
0.160461 + 0.987042i \(0.448702\pi\)
\(68\) −144.000 −0.256802
\(69\) 0 0
\(70\) 252.000 0.430282
\(71\) 324.000 0.541574 0.270787 0.962639i \(-0.412716\pi\)
0.270787 + 0.962639i \(0.412716\pi\)
\(72\) 0 0
\(73\) 800.000 1.28264 0.641321 0.767272i \(-0.278387\pi\)
0.641321 + 0.767272i \(0.278387\pi\)
\(74\) −772.000 −1.21275
\(75\) 0 0
\(76\) −112.000 −0.169043
\(77\) 77.0000 0.113961
\(78\) 0 0
\(79\) −1144.00 −1.62924 −0.814621 0.579994i \(-0.803055\pi\)
−0.814621 + 0.579994i \(0.803055\pi\)
\(80\) −288.000 −0.402492
\(81\) 0 0
\(82\) −888.000 −1.19589
\(83\) −468.000 −0.618912 −0.309456 0.950914i \(-0.600147\pi\)
−0.309456 + 0.950914i \(0.600147\pi\)
\(84\) 0 0
\(85\) 648.000 0.826888
\(86\) 632.000 0.792445
\(87\) 0 0
\(88\) −88.0000 −0.106600
\(89\) 870.000 1.03618 0.518089 0.855327i \(-0.326644\pi\)
0.518089 + 0.855327i \(0.326644\pi\)
\(90\) 0 0
\(91\) 392.000 0.451569
\(92\) −720.000 −0.815926
\(93\) 0 0
\(94\) −804.000 −0.882194
\(95\) 504.000 0.544309
\(96\) 0 0
\(97\) −1330.00 −1.39218 −0.696088 0.717957i \(-0.745078\pi\)
−0.696088 + 0.717957i \(0.745078\pi\)
\(98\) −98.0000 −0.101015
\(99\) 0 0
\(100\) 796.000 0.796000
\(101\) 120.000 0.118222 0.0591111 0.998251i \(-0.481173\pi\)
0.0591111 + 0.998251i \(0.481173\pi\)
\(102\) 0 0
\(103\) −1210.00 −1.15752 −0.578761 0.815497i \(-0.696464\pi\)
−0.578761 + 0.815497i \(0.696464\pi\)
\(104\) −448.000 −0.422404
\(105\) 0 0
\(106\) −972.000 −0.890651
\(107\) −1236.00 −1.11672 −0.558358 0.829600i \(-0.688568\pi\)
−0.558358 + 0.829600i \(0.688568\pi\)
\(108\) 0 0
\(109\) −694.000 −0.609845 −0.304923 0.952377i \(-0.598631\pi\)
−0.304923 + 0.952377i \(0.598631\pi\)
\(110\) 396.000 0.343247
\(111\) 0 0
\(112\) 112.000 0.0944911
\(113\) −978.000 −0.814181 −0.407091 0.913388i \(-0.633457\pi\)
−0.407091 + 0.913388i \(0.633457\pi\)
\(114\) 0 0
\(115\) 3240.00 2.62723
\(116\) 216.000 0.172889
\(117\) 0 0
\(118\) −564.000 −0.440003
\(119\) −252.000 −0.194124
\(120\) 0 0
\(121\) 121.000 0.0909091
\(122\) −760.000 −0.563993
\(123\) 0 0
\(124\) −1336.00 −0.967551
\(125\) −1332.00 −0.953102
\(126\) 0 0
\(127\) −1216.00 −0.849626 −0.424813 0.905281i \(-0.639660\pi\)
−0.424813 + 0.905281i \(0.639660\pi\)
\(128\) −128.000 −0.0883883
\(129\) 0 0
\(130\) 2016.00 1.36011
\(131\) −1680.00 −1.12048 −0.560238 0.828332i \(-0.689290\pi\)
−0.560238 + 0.828332i \(0.689290\pi\)
\(132\) 0 0
\(133\) −196.000 −0.127785
\(134\) −352.000 −0.226927
\(135\) 0 0
\(136\) 288.000 0.181587
\(137\) −1062.00 −0.662283 −0.331142 0.943581i \(-0.607434\pi\)
−0.331142 + 0.943581i \(0.607434\pi\)
\(138\) 0 0
\(139\) −508.000 −0.309986 −0.154993 0.987916i \(-0.549535\pi\)
−0.154993 + 0.987916i \(0.549535\pi\)
\(140\) −504.000 −0.304256
\(141\) 0 0
\(142\) −648.000 −0.382950
\(143\) 616.000 0.360227
\(144\) 0 0
\(145\) −972.000 −0.556691
\(146\) −1600.00 −0.906965
\(147\) 0 0
\(148\) 1544.00 0.857541
\(149\) −2598.00 −1.42843 −0.714216 0.699925i \(-0.753217\pi\)
−0.714216 + 0.699925i \(0.753217\pi\)
\(150\) 0 0
\(151\) 2648.00 1.42709 0.713547 0.700607i \(-0.247088\pi\)
0.713547 + 0.700607i \(0.247088\pi\)
\(152\) 224.000 0.119532
\(153\) 0 0
\(154\) −154.000 −0.0805823
\(155\) 6012.00 3.11545
\(156\) 0 0
\(157\) −790.000 −0.401585 −0.200793 0.979634i \(-0.564352\pi\)
−0.200793 + 0.979634i \(0.564352\pi\)
\(158\) 2288.00 1.15205
\(159\) 0 0
\(160\) 576.000 0.284605
\(161\) −1260.00 −0.616782
\(162\) 0 0
\(163\) −160.000 −0.0768845 −0.0384422 0.999261i \(-0.512240\pi\)
−0.0384422 + 0.999261i \(0.512240\pi\)
\(164\) 1776.00 0.845624
\(165\) 0 0
\(166\) 936.000 0.437637
\(167\) −264.000 −0.122329 −0.0611645 0.998128i \(-0.519481\pi\)
−0.0611645 + 0.998128i \(0.519481\pi\)
\(168\) 0 0
\(169\) 939.000 0.427401
\(170\) −1296.00 −0.584698
\(171\) 0 0
\(172\) −1264.00 −0.560344
\(173\) −1632.00 −0.717218 −0.358609 0.933488i \(-0.616749\pi\)
−0.358609 + 0.933488i \(0.616749\pi\)
\(174\) 0 0
\(175\) 1393.00 0.601719
\(176\) 176.000 0.0753778
\(177\) 0 0
\(178\) −1740.00 −0.732688
\(179\) 708.000 0.295634 0.147817 0.989015i \(-0.452775\pi\)
0.147817 + 0.989015i \(0.452775\pi\)
\(180\) 0 0
\(181\) 902.000 0.370415 0.185208 0.982699i \(-0.440704\pi\)
0.185208 + 0.982699i \(0.440704\pi\)
\(182\) −784.000 −0.319307
\(183\) 0 0
\(184\) 1440.00 0.576947
\(185\) −6948.00 −2.76123
\(186\) 0 0
\(187\) −396.000 −0.154858
\(188\) 1608.00 0.623806
\(189\) 0 0
\(190\) −1008.00 −0.384884
\(191\) −1824.00 −0.690995 −0.345497 0.938420i \(-0.612290\pi\)
−0.345497 + 0.938420i \(0.612290\pi\)
\(192\) 0 0
\(193\) 2090.00 0.779490 0.389745 0.920923i \(-0.372563\pi\)
0.389745 + 0.920923i \(0.372563\pi\)
\(194\) 2660.00 0.984417
\(195\) 0 0
\(196\) 196.000 0.0714286
\(197\) 1602.00 0.579380 0.289690 0.957121i \(-0.406448\pi\)
0.289690 + 0.957121i \(0.406448\pi\)
\(198\) 0 0
\(199\) −3274.00 −1.16627 −0.583135 0.812375i \(-0.698174\pi\)
−0.583135 + 0.812375i \(0.698174\pi\)
\(200\) −1592.00 −0.562857
\(201\) 0 0
\(202\) −240.000 −0.0835957
\(203\) 378.000 0.130692
\(204\) 0 0
\(205\) −7992.00 −2.72286
\(206\) 2420.00 0.818492
\(207\) 0 0
\(208\) 896.000 0.298685
\(209\) −308.000 −0.101937
\(210\) 0 0
\(211\) −4948.00 −1.61438 −0.807190 0.590291i \(-0.799013\pi\)
−0.807190 + 0.590291i \(0.799013\pi\)
\(212\) 1944.00 0.629785
\(213\) 0 0
\(214\) 2472.00 0.789638
\(215\) 5688.00 1.80427
\(216\) 0 0
\(217\) −2338.00 −0.731400
\(218\) 1388.00 0.431226
\(219\) 0 0
\(220\) −792.000 −0.242712
\(221\) −2016.00 −0.613624
\(222\) 0 0
\(223\) 2342.00 0.703282 0.351641 0.936135i \(-0.385624\pi\)
0.351641 + 0.936135i \(0.385624\pi\)
\(224\) −224.000 −0.0668153
\(225\) 0 0
\(226\) 1956.00 0.575713
\(227\) −2064.00 −0.603491 −0.301746 0.953388i \(-0.597569\pi\)
−0.301746 + 0.953388i \(0.597569\pi\)
\(228\) 0 0
\(229\) −1666.00 −0.480753 −0.240376 0.970680i \(-0.577271\pi\)
−0.240376 + 0.970680i \(0.577271\pi\)
\(230\) −6480.00 −1.85773
\(231\) 0 0
\(232\) −432.000 −0.122251
\(233\) −4158.00 −1.16910 −0.584549 0.811359i \(-0.698728\pi\)
−0.584549 + 0.811359i \(0.698728\pi\)
\(234\) 0 0
\(235\) −7236.00 −2.00862
\(236\) 1128.00 0.311129
\(237\) 0 0
\(238\) 504.000 0.137267
\(239\) −72.0000 −0.0194866 −0.00974329 0.999953i \(-0.503101\pi\)
−0.00974329 + 0.999953i \(0.503101\pi\)
\(240\) 0 0
\(241\) 6860.00 1.83357 0.916787 0.399376i \(-0.130773\pi\)
0.916787 + 0.399376i \(0.130773\pi\)
\(242\) −242.000 −0.0642824
\(243\) 0 0
\(244\) 1520.00 0.398803
\(245\) −882.000 −0.229996
\(246\) 0 0
\(247\) −1568.00 −0.403925
\(248\) 2672.00 0.684162
\(249\) 0 0
\(250\) 2664.00 0.673945
\(251\) 150.000 0.0377208 0.0188604 0.999822i \(-0.493996\pi\)
0.0188604 + 0.999822i \(0.493996\pi\)
\(252\) 0 0
\(253\) −1980.00 −0.492022
\(254\) 2432.00 0.600777
\(255\) 0 0
\(256\) 256.000 0.0625000
\(257\) 2430.00 0.589802 0.294901 0.955528i \(-0.404713\pi\)
0.294901 + 0.955528i \(0.404713\pi\)
\(258\) 0 0
\(259\) 2702.00 0.648240
\(260\) −4032.00 −0.961746
\(261\) 0 0
\(262\) 3360.00 0.792296
\(263\) −3048.00 −0.714630 −0.357315 0.933984i \(-0.616308\pi\)
−0.357315 + 0.933984i \(0.616308\pi\)
\(264\) 0 0
\(265\) −8748.00 −2.02787
\(266\) 392.000 0.0903574
\(267\) 0 0
\(268\) 704.000 0.160461
\(269\) 3834.00 0.869008 0.434504 0.900670i \(-0.356924\pi\)
0.434504 + 0.900670i \(0.356924\pi\)
\(270\) 0 0
\(271\) −3508.00 −0.786331 −0.393166 0.919468i \(-0.628620\pi\)
−0.393166 + 0.919468i \(0.628620\pi\)
\(272\) −576.000 −0.128401
\(273\) 0 0
\(274\) 2124.00 0.468305
\(275\) 2189.00 0.480006
\(276\) 0 0
\(277\) 8294.00 1.79905 0.899527 0.436864i \(-0.143911\pi\)
0.899527 + 0.436864i \(0.143911\pi\)
\(278\) 1016.00 0.219193
\(279\) 0 0
\(280\) 1008.00 0.215141
\(281\) −8022.00 −1.70303 −0.851517 0.524327i \(-0.824317\pi\)
−0.851517 + 0.524327i \(0.824317\pi\)
\(282\) 0 0
\(283\) 392.000 0.0823392 0.0411696 0.999152i \(-0.486892\pi\)
0.0411696 + 0.999152i \(0.486892\pi\)
\(284\) 1296.00 0.270787
\(285\) 0 0
\(286\) −1232.00 −0.254719
\(287\) 3108.00 0.639231
\(288\) 0 0
\(289\) −3617.00 −0.736210
\(290\) 1944.00 0.393640
\(291\) 0 0
\(292\) 3200.00 0.641321
\(293\) 2748.00 0.547918 0.273959 0.961741i \(-0.411667\pi\)
0.273959 + 0.961741i \(0.411667\pi\)
\(294\) 0 0
\(295\) −5076.00 −1.00182
\(296\) −3088.00 −0.606373
\(297\) 0 0
\(298\) 5196.00 1.01005
\(299\) −10080.0 −1.94964
\(300\) 0 0
\(301\) −2212.00 −0.423580
\(302\) −5296.00 −1.00911
\(303\) 0 0
\(304\) −448.000 −0.0845216
\(305\) −6840.00 −1.28412
\(306\) 0 0
\(307\) −3064.00 −0.569615 −0.284807 0.958585i \(-0.591930\pi\)
−0.284807 + 0.958585i \(0.591930\pi\)
\(308\) 308.000 0.0569803
\(309\) 0 0
\(310\) −12024.0 −2.20296
\(311\) −4062.00 −0.740627 −0.370313 0.928907i \(-0.620750\pi\)
−0.370313 + 0.928907i \(0.620750\pi\)
\(312\) 0 0
\(313\) −4870.00 −0.879453 −0.439726 0.898132i \(-0.644925\pi\)
−0.439726 + 0.898132i \(0.644925\pi\)
\(314\) 1580.00 0.283964
\(315\) 0 0
\(316\) −4576.00 −0.814621
\(317\) −4806.00 −0.851520 −0.425760 0.904836i \(-0.639993\pi\)
−0.425760 + 0.904836i \(0.639993\pi\)
\(318\) 0 0
\(319\) 594.000 0.104256
\(320\) −1152.00 −0.201246
\(321\) 0 0
\(322\) 2520.00 0.436131
\(323\) 1008.00 0.173643
\(324\) 0 0
\(325\) 11144.0 1.90202
\(326\) 320.000 0.0543655
\(327\) 0 0
\(328\) −3552.00 −0.597946
\(329\) 2814.00 0.471553
\(330\) 0 0
\(331\) 6620.00 1.09930 0.549650 0.835395i \(-0.314761\pi\)
0.549650 + 0.835395i \(0.314761\pi\)
\(332\) −1872.00 −0.309456
\(333\) 0 0
\(334\) 528.000 0.0864996
\(335\) −3168.00 −0.516676
\(336\) 0 0
\(337\) 1094.00 0.176837 0.0884184 0.996083i \(-0.471819\pi\)
0.0884184 + 0.996083i \(0.471819\pi\)
\(338\) −1878.00 −0.302218
\(339\) 0 0
\(340\) 2592.00 0.413444
\(341\) −3674.00 −0.583455
\(342\) 0 0
\(343\) 343.000 0.0539949
\(344\) 2528.00 0.396223
\(345\) 0 0
\(346\) 3264.00 0.507150
\(347\) −3468.00 −0.536519 −0.268259 0.963347i \(-0.586448\pi\)
−0.268259 + 0.963347i \(0.586448\pi\)
\(348\) 0 0
\(349\) −8188.00 −1.25586 −0.627928 0.778272i \(-0.716097\pi\)
−0.627928 + 0.778272i \(0.716097\pi\)
\(350\) −2786.00 −0.425480
\(351\) 0 0
\(352\) −352.000 −0.0533002
\(353\) 5070.00 0.764444 0.382222 0.924070i \(-0.375159\pi\)
0.382222 + 0.924070i \(0.375159\pi\)
\(354\) 0 0
\(355\) −5832.00 −0.871917
\(356\) 3480.00 0.518089
\(357\) 0 0
\(358\) −1416.00 −0.209044
\(359\) −1656.00 −0.243455 −0.121727 0.992564i \(-0.538843\pi\)
−0.121727 + 0.992564i \(0.538843\pi\)
\(360\) 0 0
\(361\) −6075.00 −0.885698
\(362\) −1804.00 −0.261923
\(363\) 0 0
\(364\) 1568.00 0.225784
\(365\) −14400.0 −2.06501
\(366\) 0 0
\(367\) 10166.0 1.44594 0.722971 0.690878i \(-0.242776\pi\)
0.722971 + 0.690878i \(0.242776\pi\)
\(368\) −2880.00 −0.407963
\(369\) 0 0
\(370\) 13896.0 1.95248
\(371\) 3402.00 0.476073
\(372\) 0 0
\(373\) −2722.00 −0.377855 −0.188927 0.981991i \(-0.560501\pi\)
−0.188927 + 0.981991i \(0.560501\pi\)
\(374\) 792.000 0.109501
\(375\) 0 0
\(376\) −3216.00 −0.441097
\(377\) 3024.00 0.413114
\(378\) 0 0
\(379\) −5872.00 −0.795843 −0.397921 0.917420i \(-0.630268\pi\)
−0.397921 + 0.917420i \(0.630268\pi\)
\(380\) 2016.00 0.272154
\(381\) 0 0
\(382\) 3648.00 0.488607
\(383\) −12330.0 −1.64500 −0.822498 0.568768i \(-0.807420\pi\)
−0.822498 + 0.568768i \(0.807420\pi\)
\(384\) 0 0
\(385\) −1386.00 −0.183473
\(386\) −4180.00 −0.551182
\(387\) 0 0
\(388\) −5320.00 −0.696088
\(389\) 14586.0 1.90113 0.950565 0.310526i \(-0.100505\pi\)
0.950565 + 0.310526i \(0.100505\pi\)
\(390\) 0 0
\(391\) 6480.00 0.838127
\(392\) −392.000 −0.0505076
\(393\) 0 0
\(394\) −3204.00 −0.409683
\(395\) 20592.0 2.62303
\(396\) 0 0
\(397\) 1874.00 0.236910 0.118455 0.992959i \(-0.462206\pi\)
0.118455 + 0.992959i \(0.462206\pi\)
\(398\) 6548.00 0.824677
\(399\) 0 0
\(400\) 3184.00 0.398000
\(401\) −13338.0 −1.66102 −0.830509 0.557006i \(-0.811950\pi\)
−0.830509 + 0.557006i \(0.811950\pi\)
\(402\) 0 0
\(403\) −18704.0 −2.31194
\(404\) 480.000 0.0591111
\(405\) 0 0
\(406\) −756.000 −0.0924129
\(407\) 4246.00 0.517116
\(408\) 0 0
\(409\) −8200.00 −0.991354 −0.495677 0.868507i \(-0.665080\pi\)
−0.495677 + 0.868507i \(0.665080\pi\)
\(410\) 15984.0 1.92535
\(411\) 0 0
\(412\) −4840.00 −0.578761
\(413\) 1974.00 0.235192
\(414\) 0 0
\(415\) 8424.00 0.996429
\(416\) −1792.00 −0.211202
\(417\) 0 0
\(418\) 616.000 0.0720803
\(419\) 7362.00 0.858370 0.429185 0.903216i \(-0.358801\pi\)
0.429185 + 0.903216i \(0.358801\pi\)
\(420\) 0 0
\(421\) −11710.0 −1.35561 −0.677803 0.735243i \(-0.737068\pi\)
−0.677803 + 0.735243i \(0.737068\pi\)
\(422\) 9896.00 1.14154
\(423\) 0 0
\(424\) −3888.00 −0.445325
\(425\) −7164.00 −0.817659
\(426\) 0 0
\(427\) 2660.00 0.301467
\(428\) −4944.00 −0.558358
\(429\) 0 0
\(430\) −11376.0 −1.27581
\(431\) 936.000 0.104607 0.0523034 0.998631i \(-0.483344\pi\)
0.0523034 + 0.998631i \(0.483344\pi\)
\(432\) 0 0
\(433\) 9038.00 1.00309 0.501546 0.865131i \(-0.332765\pi\)
0.501546 + 0.865131i \(0.332765\pi\)
\(434\) 4676.00 0.517178
\(435\) 0 0
\(436\) −2776.00 −0.304923
\(437\) 5040.00 0.551707
\(438\) 0 0
\(439\) 1964.00 0.213523 0.106762 0.994285i \(-0.465952\pi\)
0.106762 + 0.994285i \(0.465952\pi\)
\(440\) 1584.00 0.171623
\(441\) 0 0
\(442\) 4032.00 0.433897
\(443\) −10068.0 −1.07979 −0.539893 0.841734i \(-0.681535\pi\)
−0.539893 + 0.841734i \(0.681535\pi\)
\(444\) 0 0
\(445\) −15660.0 −1.66821
\(446\) −4684.00 −0.497296
\(447\) 0 0
\(448\) 448.000 0.0472456
\(449\) −3270.00 −0.343699 −0.171849 0.985123i \(-0.554974\pi\)
−0.171849 + 0.985123i \(0.554974\pi\)
\(450\) 0 0
\(451\) 4884.00 0.509930
\(452\) −3912.00 −0.407091
\(453\) 0 0
\(454\) 4128.00 0.426733
\(455\) −7056.00 −0.727012
\(456\) 0 0
\(457\) −15526.0 −1.58922 −0.794612 0.607117i \(-0.792326\pi\)
−0.794612 + 0.607117i \(0.792326\pi\)
\(458\) 3332.00 0.339944
\(459\) 0 0
\(460\) 12960.0 1.31362
\(461\) −10548.0 −1.06566 −0.532830 0.846222i \(-0.678872\pi\)
−0.532830 + 0.846222i \(0.678872\pi\)
\(462\) 0 0
\(463\) −3796.00 −0.381026 −0.190513 0.981685i \(-0.561015\pi\)
−0.190513 + 0.981685i \(0.561015\pi\)
\(464\) 864.000 0.0864444
\(465\) 0 0
\(466\) 8316.00 0.826677
\(467\) −7122.00 −0.705711 −0.352855 0.935678i \(-0.614789\pi\)
−0.352855 + 0.935678i \(0.614789\pi\)
\(468\) 0 0
\(469\) 1232.00 0.121297
\(470\) 14472.0 1.42031
\(471\) 0 0
\(472\) −2256.00 −0.220002
\(473\) −3476.00 −0.337900
\(474\) 0 0
\(475\) −5572.00 −0.538233
\(476\) −1008.00 −0.0970622
\(477\) 0 0
\(478\) 144.000 0.0137791
\(479\) −2292.00 −0.218631 −0.109315 0.994007i \(-0.534866\pi\)
−0.109315 + 0.994007i \(0.534866\pi\)
\(480\) 0 0
\(481\) 21616.0 2.04907
\(482\) −13720.0 −1.29653
\(483\) 0 0
\(484\) 484.000 0.0454545
\(485\) 23940.0 2.24136
\(486\) 0 0
\(487\) 5132.00 0.477522 0.238761 0.971078i \(-0.423259\pi\)
0.238761 + 0.971078i \(0.423259\pi\)
\(488\) −3040.00 −0.281997
\(489\) 0 0
\(490\) 1764.00 0.162631
\(491\) −4188.00 −0.384932 −0.192466 0.981304i \(-0.561649\pi\)
−0.192466 + 0.981304i \(0.561649\pi\)
\(492\) 0 0
\(493\) −1944.00 −0.177593
\(494\) 3136.00 0.285618
\(495\) 0 0
\(496\) −5344.00 −0.483776
\(497\) 2268.00 0.204696
\(498\) 0 0
\(499\) 3848.00 0.345211 0.172605 0.984991i \(-0.444781\pi\)
0.172605 + 0.984991i \(0.444781\pi\)
\(500\) −5328.00 −0.476551
\(501\) 0 0
\(502\) −300.000 −0.0266726
\(503\) 1068.00 0.0946715 0.0473358 0.998879i \(-0.484927\pi\)
0.0473358 + 0.998879i \(0.484927\pi\)
\(504\) 0 0
\(505\) −2160.00 −0.190334
\(506\) 3960.00 0.347912
\(507\) 0 0
\(508\) −4864.00 −0.424813
\(509\) 6162.00 0.536593 0.268297 0.963336i \(-0.413539\pi\)
0.268297 + 0.963336i \(0.413539\pi\)
\(510\) 0 0
\(511\) 5600.00 0.484793
\(512\) −512.000 −0.0441942
\(513\) 0 0
\(514\) −4860.00 −0.417053
\(515\) 21780.0 1.86358
\(516\) 0 0
\(517\) 4422.00 0.376169
\(518\) −5404.00 −0.458375
\(519\) 0 0
\(520\) 8064.00 0.680057
\(521\) 20946.0 1.76135 0.880673 0.473725i \(-0.157091\pi\)
0.880673 + 0.473725i \(0.157091\pi\)
\(522\) 0 0
\(523\) −4696.00 −0.392623 −0.196311 0.980542i \(-0.562896\pi\)
−0.196311 + 0.980542i \(0.562896\pi\)
\(524\) −6720.00 −0.560238
\(525\) 0 0
\(526\) 6096.00 0.505320
\(527\) 12024.0 0.993878
\(528\) 0 0
\(529\) 20233.0 1.66294
\(530\) 17496.0 1.43392
\(531\) 0 0
\(532\) −784.000 −0.0638923
\(533\) 24864.0 2.02060
\(534\) 0 0
\(535\) 22248.0 1.79788
\(536\) −1408.00 −0.113463
\(537\) 0 0
\(538\) −7668.00 −0.614481
\(539\) 539.000 0.0430730
\(540\) 0 0
\(541\) 19358.0 1.53838 0.769192 0.639018i \(-0.220659\pi\)
0.769192 + 0.639018i \(0.220659\pi\)
\(542\) 7016.00 0.556020
\(543\) 0 0
\(544\) 1152.00 0.0907934
\(545\) 12492.0 0.981832
\(546\) 0 0
\(547\) 18020.0 1.40855 0.704277 0.709925i \(-0.251271\pi\)
0.704277 + 0.709925i \(0.251271\pi\)
\(548\) −4248.00 −0.331142
\(549\) 0 0
\(550\) −4378.00 −0.339416
\(551\) −1512.00 −0.116903
\(552\) 0 0
\(553\) −8008.00 −0.615795
\(554\) −16588.0 −1.27212
\(555\) 0 0
\(556\) −2032.00 −0.154993
\(557\) −14622.0 −1.11231 −0.556153 0.831080i \(-0.687723\pi\)
−0.556153 + 0.831080i \(0.687723\pi\)
\(558\) 0 0
\(559\) −17696.0 −1.33893
\(560\) −2016.00 −0.152128
\(561\) 0 0
\(562\) 16044.0 1.20423
\(563\) 2244.00 0.167981 0.0839905 0.996467i \(-0.473233\pi\)
0.0839905 + 0.996467i \(0.473233\pi\)
\(564\) 0 0
\(565\) 17604.0 1.31081
\(566\) −784.000 −0.0582226
\(567\) 0 0
\(568\) −2592.00 −0.191475
\(569\) 3258.00 0.240039 0.120020 0.992772i \(-0.461704\pi\)
0.120020 + 0.992772i \(0.461704\pi\)
\(570\) 0 0
\(571\) −6604.00 −0.484008 −0.242004 0.970275i \(-0.577805\pi\)
−0.242004 + 0.970275i \(0.577805\pi\)
\(572\) 2464.00 0.180114
\(573\) 0 0
\(574\) −6216.00 −0.452005
\(575\) −35820.0 −2.59791
\(576\) 0 0
\(577\) −16594.0 −1.19726 −0.598628 0.801027i \(-0.704287\pi\)
−0.598628 + 0.801027i \(0.704287\pi\)
\(578\) 7234.00 0.520579
\(579\) 0 0
\(580\) −3888.00 −0.278346
\(581\) −3276.00 −0.233927
\(582\) 0 0
\(583\) 5346.00 0.379775
\(584\) −6400.00 −0.453483
\(585\) 0 0
\(586\) −5496.00 −0.387436
\(587\) 19062.0 1.34033 0.670164 0.742213i \(-0.266224\pi\)
0.670164 + 0.742213i \(0.266224\pi\)
\(588\) 0 0
\(589\) 9352.00 0.654232
\(590\) 10152.0 0.708392
\(591\) 0 0
\(592\) 6176.00 0.428770
\(593\) 4776.00 0.330737 0.165368 0.986232i \(-0.447119\pi\)
0.165368 + 0.986232i \(0.447119\pi\)
\(594\) 0 0
\(595\) 4536.00 0.312534
\(596\) −10392.0 −0.714216
\(597\) 0 0
\(598\) 20160.0 1.37860
\(599\) −7956.00 −0.542693 −0.271347 0.962482i \(-0.587469\pi\)
−0.271347 + 0.962482i \(0.587469\pi\)
\(600\) 0 0
\(601\) 14348.0 0.973822 0.486911 0.873452i \(-0.338124\pi\)
0.486911 + 0.873452i \(0.338124\pi\)
\(602\) 4424.00 0.299516
\(603\) 0 0
\(604\) 10592.0 0.713547
\(605\) −2178.00 −0.146361
\(606\) 0 0
\(607\) 24488.0 1.63746 0.818729 0.574180i \(-0.194679\pi\)
0.818729 + 0.574180i \(0.194679\pi\)
\(608\) 896.000 0.0597658
\(609\) 0 0
\(610\) 13680.0 0.908011
\(611\) 22512.0 1.49057
\(612\) 0 0
\(613\) −19654.0 −1.29497 −0.647486 0.762078i \(-0.724179\pi\)
−0.647486 + 0.762078i \(0.724179\pi\)
\(614\) 6128.00 0.402778
\(615\) 0 0
\(616\) −616.000 −0.0402911
\(617\) −2694.00 −0.175780 −0.0878901 0.996130i \(-0.528012\pi\)
−0.0878901 + 0.996130i \(0.528012\pi\)
\(618\) 0 0
\(619\) 10178.0 0.660886 0.330443 0.943826i \(-0.392802\pi\)
0.330443 + 0.943826i \(0.392802\pi\)
\(620\) 24048.0 1.55773
\(621\) 0 0
\(622\) 8124.00 0.523702
\(623\) 6090.00 0.391638
\(624\) 0 0
\(625\) −899.000 −0.0575360
\(626\) 9740.00 0.621867
\(627\) 0 0
\(628\) −3160.00 −0.200793
\(629\) −13896.0 −0.880874
\(630\) 0 0
\(631\) −7648.00 −0.482507 −0.241254 0.970462i \(-0.577559\pi\)
−0.241254 + 0.970462i \(0.577559\pi\)
\(632\) 9152.00 0.576024
\(633\) 0 0
\(634\) 9612.00 0.602116
\(635\) 21888.0 1.36787
\(636\) 0 0
\(637\) 2744.00 0.170677
\(638\) −1188.00 −0.0737200
\(639\) 0 0
\(640\) 2304.00 0.142302
\(641\) −270.000 −0.0166371 −0.00831853 0.999965i \(-0.502648\pi\)
−0.00831853 + 0.999965i \(0.502648\pi\)
\(642\) 0 0
\(643\) 16250.0 0.996637 0.498318 0.866994i \(-0.333951\pi\)
0.498318 + 0.866994i \(0.333951\pi\)
\(644\) −5040.00 −0.308391
\(645\) 0 0
\(646\) −2016.00 −0.122784
\(647\) −10242.0 −0.622341 −0.311170 0.950354i \(-0.600721\pi\)
−0.311170 + 0.950354i \(0.600721\pi\)
\(648\) 0 0
\(649\) 3102.00 0.187618
\(650\) −22288.0 −1.34493
\(651\) 0 0
\(652\) −640.000 −0.0384422
\(653\) 17322.0 1.03807 0.519037 0.854752i \(-0.326291\pi\)
0.519037 + 0.854752i \(0.326291\pi\)
\(654\) 0 0
\(655\) 30240.0 1.80393
\(656\) 7104.00 0.422812
\(657\) 0 0
\(658\) −5628.00 −0.333438
\(659\) −11676.0 −0.690186 −0.345093 0.938569i \(-0.612153\pi\)
−0.345093 + 0.938569i \(0.612153\pi\)
\(660\) 0 0
\(661\) −20710.0 −1.21865 −0.609323 0.792922i \(-0.708559\pi\)
−0.609323 + 0.792922i \(0.708559\pi\)
\(662\) −13240.0 −0.777322
\(663\) 0 0
\(664\) 3744.00 0.218818
\(665\) 3528.00 0.205729
\(666\) 0 0
\(667\) −9720.00 −0.564258
\(668\) −1056.00 −0.0611645
\(669\) 0 0
\(670\) 6336.00 0.365345
\(671\) 4180.00 0.240487
\(672\) 0 0
\(673\) −10354.0 −0.593042 −0.296521 0.955026i \(-0.595827\pi\)
−0.296521 + 0.955026i \(0.595827\pi\)
\(674\) −2188.00 −0.125042
\(675\) 0 0
\(676\) 3756.00 0.213701
\(677\) 10920.0 0.619926 0.309963 0.950749i \(-0.399683\pi\)
0.309963 + 0.950749i \(0.399683\pi\)
\(678\) 0 0
\(679\) −9310.00 −0.526193
\(680\) −5184.00 −0.292349
\(681\) 0 0
\(682\) 7348.00 0.412565
\(683\) −27804.0 −1.55767 −0.778836 0.627227i \(-0.784190\pi\)
−0.778836 + 0.627227i \(0.784190\pi\)
\(684\) 0 0
\(685\) 19116.0 1.06626
\(686\) −686.000 −0.0381802
\(687\) 0 0
\(688\) −5056.00 −0.280172
\(689\) 27216.0 1.50486
\(690\) 0 0
\(691\) −25834.0 −1.42225 −0.711123 0.703068i \(-0.751813\pi\)
−0.711123 + 0.703068i \(0.751813\pi\)
\(692\) −6528.00 −0.358609
\(693\) 0 0
\(694\) 6936.00 0.379376
\(695\) 9144.00 0.499067
\(696\) 0 0
\(697\) −15984.0 −0.868633
\(698\) 16376.0 0.888024
\(699\) 0 0
\(700\) 5572.00 0.300860
\(701\) 10590.0 0.570583 0.285292 0.958441i \(-0.407910\pi\)
0.285292 + 0.958441i \(0.407910\pi\)
\(702\) 0 0
\(703\) −10808.0 −0.579846
\(704\) 704.000 0.0376889
\(705\) 0 0
\(706\) −10140.0 −0.540544
\(707\) 840.000 0.0446838
\(708\) 0 0
\(709\) −6802.00 −0.360302 −0.180151 0.983639i \(-0.557659\pi\)
−0.180151 + 0.983639i \(0.557659\pi\)
\(710\) 11664.0 0.616538
\(711\) 0 0
\(712\) −6960.00 −0.366344
\(713\) 60120.0 3.15780
\(714\) 0 0
\(715\) −11088.0 −0.579955
\(716\) 2832.00 0.147817
\(717\) 0 0
\(718\) 3312.00 0.172149
\(719\) −23010.0 −1.19350 −0.596751 0.802426i \(-0.703542\pi\)
−0.596751 + 0.802426i \(0.703542\pi\)
\(720\) 0 0
\(721\) −8470.00 −0.437502
\(722\) 12150.0 0.626283
\(723\) 0 0
\(724\) 3608.00 0.185208
\(725\) 10746.0 0.550478
\(726\) 0 0
\(727\) 4682.00 0.238853 0.119426 0.992843i \(-0.461894\pi\)
0.119426 + 0.992843i \(0.461894\pi\)
\(728\) −3136.00 −0.159654
\(729\) 0 0
\(730\) 28800.0 1.46019
\(731\) 11376.0 0.575590
\(732\) 0 0
\(733\) −17860.0 −0.899965 −0.449982 0.893037i \(-0.648570\pi\)
−0.449982 + 0.893037i \(0.648570\pi\)
\(734\) −20332.0 −1.02244
\(735\) 0 0
\(736\) 5760.00 0.288473
\(737\) 1936.00 0.0967618
\(738\) 0 0
\(739\) 6860.00 0.341474 0.170737 0.985317i \(-0.445385\pi\)
0.170737 + 0.985317i \(0.445385\pi\)
\(740\) −27792.0 −1.38061
\(741\) 0 0
\(742\) −6804.00 −0.336634
\(743\) 22752.0 1.12341 0.561703 0.827339i \(-0.310147\pi\)
0.561703 + 0.827339i \(0.310147\pi\)
\(744\) 0 0
\(745\) 46764.0 2.29973
\(746\) 5444.00 0.267184
\(747\) 0 0
\(748\) −1584.00 −0.0774288
\(749\) −8652.00 −0.422079
\(750\) 0 0
\(751\) 7364.00 0.357811 0.178906 0.983866i \(-0.442744\pi\)
0.178906 + 0.983866i \(0.442744\pi\)
\(752\) 6432.00 0.311903
\(753\) 0 0
\(754\) −6048.00 −0.292116
\(755\) −47664.0 −2.29758
\(756\) 0 0
\(757\) −34378.0 −1.65058 −0.825290 0.564709i \(-0.808989\pi\)
−0.825290 + 0.564709i \(0.808989\pi\)
\(758\) 11744.0 0.562746
\(759\) 0 0
\(760\) −4032.00 −0.192442
\(761\) −27456.0 −1.30786 −0.653929 0.756556i \(-0.726880\pi\)
−0.653929 + 0.756556i \(0.726880\pi\)
\(762\) 0 0
\(763\) −4858.00 −0.230500
\(764\) −7296.00 −0.345497
\(765\) 0 0
\(766\) 24660.0 1.16319
\(767\) 15792.0 0.743437
\(768\) 0 0
\(769\) 7952.00 0.372895 0.186448 0.982465i \(-0.440303\pi\)
0.186448 + 0.982465i \(0.440303\pi\)
\(770\) 2772.00 0.129735
\(771\) 0 0
\(772\) 8360.00 0.389745
\(773\) 4986.00 0.231997 0.115999 0.993249i \(-0.462993\pi\)
0.115999 + 0.993249i \(0.462993\pi\)
\(774\) 0 0
\(775\) −66466.0 −3.08068
\(776\) 10640.0 0.492208
\(777\) 0 0
\(778\) −29172.0 −1.34430
\(779\) −12432.0 −0.571788
\(780\) 0 0
\(781\) 3564.00 0.163291
\(782\) −12960.0 −0.592645
\(783\) 0 0
\(784\) 784.000 0.0357143
\(785\) 14220.0 0.646540
\(786\) 0 0
\(787\) −42748.0 −1.93622 −0.968108 0.250534i \(-0.919394\pi\)
−0.968108 + 0.250534i \(0.919394\pi\)
\(788\) 6408.00 0.289690
\(789\) 0 0
\(790\) −41184.0 −1.85476
\(791\) −6846.00 −0.307732
\(792\) 0 0
\(793\) 21280.0 0.952932
\(794\) −3748.00 −0.167521
\(795\) 0 0
\(796\) −13096.0 −0.583135
\(797\) −35610.0 −1.58265 −0.791324 0.611397i \(-0.790608\pi\)
−0.791324 + 0.611397i \(0.790608\pi\)
\(798\) 0 0
\(799\) −14472.0 −0.640779
\(800\) −6368.00 −0.281428
\(801\) 0 0
\(802\) 26676.0 1.17452
\(803\) 8800.00 0.386731
\(804\) 0 0
\(805\) 22680.0 0.993000
\(806\) 37408.0 1.63479
\(807\) 0 0
\(808\) −960.000 −0.0417979
\(809\) 17046.0 0.740798 0.370399 0.928873i \(-0.379221\pi\)
0.370399 + 0.928873i \(0.379221\pi\)
\(810\) 0 0
\(811\) −2176.00 −0.0942166 −0.0471083 0.998890i \(-0.515001\pi\)
−0.0471083 + 0.998890i \(0.515001\pi\)
\(812\) 1512.00 0.0653458
\(813\) 0 0
\(814\) −8492.00 −0.365657
\(815\) 2880.00 0.123782
\(816\) 0 0
\(817\) 8848.00 0.378889
\(818\) 16400.0 0.700993
\(819\) 0 0
\(820\) −31968.0 −1.36143
\(821\) −2094.00 −0.0890147 −0.0445074 0.999009i \(-0.514172\pi\)
−0.0445074 + 0.999009i \(0.514172\pi\)
\(822\) 0 0
\(823\) 7328.00 0.310374 0.155187 0.987885i \(-0.450402\pi\)
0.155187 + 0.987885i \(0.450402\pi\)
\(824\) 9680.00 0.409246
\(825\) 0 0
\(826\) −3948.00 −0.166306
\(827\) 12492.0 0.525259 0.262630 0.964897i \(-0.415410\pi\)
0.262630 + 0.964897i \(0.415410\pi\)
\(828\) 0 0
\(829\) −37486.0 −1.57050 −0.785249 0.619180i \(-0.787465\pi\)
−0.785249 + 0.619180i \(0.787465\pi\)
\(830\) −16848.0 −0.704581
\(831\) 0 0
\(832\) 3584.00 0.149342
\(833\) −1764.00 −0.0733721
\(834\) 0 0
\(835\) 4752.00 0.196946
\(836\) −1232.00 −0.0509684
\(837\) 0 0
\(838\) −14724.0 −0.606960
\(839\) 17574.0 0.723149 0.361574 0.932343i \(-0.382239\pi\)
0.361574 + 0.932343i \(0.382239\pi\)
\(840\) 0 0
\(841\) −21473.0 −0.880438
\(842\) 23420.0 0.958559
\(843\) 0 0
\(844\) −19792.0 −0.807190
\(845\) −16902.0 −0.688102
\(846\) 0 0
\(847\) 847.000 0.0343604
\(848\) 7776.00 0.314893
\(849\) 0 0
\(850\) 14328.0 0.578172
\(851\) −69480.0 −2.79876
\(852\) 0 0
\(853\) 9440.00 0.378921 0.189460 0.981888i \(-0.439326\pi\)
0.189460 + 0.981888i \(0.439326\pi\)
\(854\) −5320.00 −0.213169
\(855\) 0 0
\(856\) 9888.00 0.394819
\(857\) 28440.0 1.13360 0.566798 0.823857i \(-0.308182\pi\)
0.566798 + 0.823857i \(0.308182\pi\)
\(858\) 0 0
\(859\) −24334.0 −0.966549 −0.483274 0.875469i \(-0.660553\pi\)
−0.483274 + 0.875469i \(0.660553\pi\)
\(860\) 22752.0 0.902136
\(861\) 0 0
\(862\) −1872.00 −0.0739682
\(863\) −39264.0 −1.54874 −0.774370 0.632733i \(-0.781933\pi\)
−0.774370 + 0.632733i \(0.781933\pi\)
\(864\) 0 0
\(865\) 29376.0 1.15470
\(866\) −18076.0 −0.709293
\(867\) 0 0
\(868\) −9352.00 −0.365700
\(869\) −12584.0 −0.491235
\(870\) 0 0
\(871\) 9856.00 0.383419
\(872\) 5552.00 0.215613
\(873\) 0 0
\(874\) −10080.0 −0.390116
\(875\) −9324.00 −0.360239
\(876\) 0 0
\(877\) 32114.0 1.23650 0.618251 0.785981i \(-0.287841\pi\)
0.618251 + 0.785981i \(0.287841\pi\)
\(878\) −3928.00 −0.150984
\(879\) 0 0
\(880\) −3168.00 −0.121356
\(881\) −41454.0 −1.58527 −0.792634 0.609698i \(-0.791291\pi\)
−0.792634 + 0.609698i \(0.791291\pi\)
\(882\) 0 0
\(883\) 2876.00 0.109609 0.0548047 0.998497i \(-0.482546\pi\)
0.0548047 + 0.998497i \(0.482546\pi\)
\(884\) −8064.00 −0.306812
\(885\) 0 0
\(886\) 20136.0 0.763524
\(887\) −13932.0 −0.527385 −0.263693 0.964607i \(-0.584940\pi\)
−0.263693 + 0.964607i \(0.584940\pi\)
\(888\) 0 0
\(889\) −8512.00 −0.321129
\(890\) 31320.0 1.17961
\(891\) 0 0
\(892\) 9368.00 0.351641
\(893\) −11256.0 −0.421800
\(894\) 0 0
\(895\) −12744.0 −0.475961
\(896\) −896.000 −0.0334077
\(897\) 0 0
\(898\) 6540.00 0.243032
\(899\) −18036.0 −0.669115
\(900\) 0 0
\(901\) −17496.0 −0.646921
\(902\) −9768.00 −0.360575
\(903\) 0 0
\(904\) 7824.00 0.287857
\(905\) −16236.0 −0.596357
\(906\) 0 0
\(907\) −19768.0 −0.723689 −0.361844 0.932239i \(-0.617853\pi\)
−0.361844 + 0.932239i \(0.617853\pi\)
\(908\) −8256.00 −0.301746
\(909\) 0 0
\(910\) 14112.0 0.514075
\(911\) −43836.0 −1.59424 −0.797119 0.603822i \(-0.793644\pi\)
−0.797119 + 0.603822i \(0.793644\pi\)
\(912\) 0 0
\(913\) −5148.00 −0.186609
\(914\) 31052.0 1.12375
\(915\) 0 0
\(916\) −6664.00 −0.240376
\(917\) −11760.0 −0.423500
\(918\) 0 0
\(919\) 31544.0 1.13225 0.566127 0.824318i \(-0.308441\pi\)
0.566127 + 0.824318i \(0.308441\pi\)
\(920\) −25920.0 −0.928866
\(921\) 0 0
\(922\) 21096.0 0.753536
\(923\) 18144.0 0.647039
\(924\) 0 0
\(925\) 76814.0 2.73041
\(926\) 7592.00 0.269426
\(927\) 0 0
\(928\) −1728.00 −0.0611254
\(929\) −11118.0 −0.392648 −0.196324 0.980539i \(-0.562900\pi\)
−0.196324 + 0.980539i \(0.562900\pi\)
\(930\) 0 0
\(931\) −1372.00 −0.0482980
\(932\) −16632.0 −0.584549
\(933\) 0 0
\(934\) 14244.0 0.499013
\(935\) 7128.00 0.249316
\(936\) 0 0
\(937\) 10568.0 0.368454 0.184227 0.982884i \(-0.441022\pi\)
0.184227 + 0.982884i \(0.441022\pi\)
\(938\) −2464.00 −0.0857702
\(939\) 0 0
\(940\) −28944.0 −1.00431
\(941\) −14964.0 −0.518398 −0.259199 0.965824i \(-0.583459\pi\)
−0.259199 + 0.965824i \(0.583459\pi\)
\(942\) 0 0
\(943\) −79920.0 −2.75987
\(944\) 4512.00 0.155565
\(945\) 0 0
\(946\) 6952.00 0.238931
\(947\) −3324.00 −0.114061 −0.0570304 0.998372i \(-0.518163\pi\)
−0.0570304 + 0.998372i \(0.518163\pi\)
\(948\) 0 0
\(949\) 44800.0 1.53242
\(950\) 11144.0 0.380589
\(951\) 0 0
\(952\) 2016.00 0.0686333
\(953\) −3906.00 −0.132768 −0.0663839 0.997794i \(-0.521146\pi\)
−0.0663839 + 0.997794i \(0.521146\pi\)
\(954\) 0 0
\(955\) 32832.0 1.11248
\(956\) −288.000 −0.00974329
\(957\) 0 0
\(958\) 4584.00 0.154595
\(959\) −7434.00 −0.250319
\(960\) 0 0
\(961\) 81765.0 2.74462
\(962\) −43232.0 −1.44891
\(963\) 0 0
\(964\) 27440.0 0.916787
\(965\) −37620.0 −1.25495
\(966\) 0 0
\(967\) −36448.0 −1.21209 −0.606044 0.795431i \(-0.707244\pi\)
−0.606044 + 0.795431i \(0.707244\pi\)
\(968\) −968.000 −0.0321412
\(969\) 0 0
\(970\) −47880.0 −1.58488
\(971\) 20526.0 0.678384 0.339192 0.940717i \(-0.389846\pi\)
0.339192 + 0.940717i \(0.389846\pi\)
\(972\) 0 0
\(973\) −3556.00 −0.117164
\(974\) −10264.0 −0.337659
\(975\) 0 0
\(976\) 6080.00 0.199402
\(977\) −37434.0 −1.22581 −0.612907 0.790155i \(-0.710000\pi\)
−0.612907 + 0.790155i \(0.710000\pi\)
\(978\) 0 0
\(979\) 9570.00 0.312419
\(980\) −3528.00 −0.114998
\(981\) 0 0
\(982\) 8376.00 0.272188
\(983\) 52194.0 1.69352 0.846760 0.531975i \(-0.178550\pi\)
0.846760 + 0.531975i \(0.178550\pi\)
\(984\) 0 0
\(985\) −28836.0 −0.932783
\(986\) 3888.00 0.125577
\(987\) 0 0
\(988\) −6272.00 −0.201962
\(989\) 56880.0 1.82880
\(990\) 0 0
\(991\) −15220.0 −0.487870 −0.243935 0.969792i \(-0.578438\pi\)
−0.243935 + 0.969792i \(0.578438\pi\)
\(992\) 10688.0 0.342081
\(993\) 0 0
\(994\) −4536.00 −0.144742
\(995\) 58932.0 1.87766
\(996\) 0 0
\(997\) 37664.0 1.19642 0.598210 0.801339i \(-0.295879\pi\)
0.598210 + 0.801339i \(0.295879\pi\)
\(998\) −7696.00 −0.244101
\(999\) 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.a.1.1 1
3.2 odd 2 154.4.a.d.1.1 1
12.11 even 2 1232.4.a.f.1.1 1
21.20 even 2 1078.4.a.g.1.1 1
33.32 even 2 1694.4.a.c.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
154.4.a.d.1.1 1 3.2 odd 2
1078.4.a.g.1.1 1 21.20 even 2
1232.4.a.f.1.1 1 12.11 even 2
1386.4.a.a.1.1 1 1.1 even 1 trivial
1694.4.a.c.1.1 1 33.32 even 2