Properties

Label 1232.4.a.f.1.1
Level $1232$
Weight $4$
Character 1232.1
Self dual yes
Analytic conductor $72.690$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1232 = 2^{4} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1232.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(72.6903531271\)
Analytic rank: \(0\)
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 \(\chi\) \(=\) 1232.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.00000 q^{3} +18.0000 q^{5} -7.00000 q^{7} -23.0000 q^{9} +O(q^{10})\) \(q+2.00000 q^{3} +18.0000 q^{5} -7.00000 q^{7} -23.0000 q^{9} +11.0000 q^{11} +56.0000 q^{13} +36.0000 q^{15} +36.0000 q^{17} +28.0000 q^{19} -14.0000 q^{21} -180.000 q^{23} +199.000 q^{25} -100.000 q^{27} -54.0000 q^{29} +334.000 q^{31} +22.0000 q^{33} -126.000 q^{35} +386.000 q^{37} +112.000 q^{39} -444.000 q^{41} +316.000 q^{43} -414.000 q^{45} +402.000 q^{47} +49.0000 q^{49} +72.0000 q^{51} -486.000 q^{53} +198.000 q^{55} +56.0000 q^{57} +282.000 q^{59} +380.000 q^{61} +161.000 q^{63} +1008.00 q^{65} -176.000 q^{67} -360.000 q^{69} +324.000 q^{71} +800.000 q^{73} +398.000 q^{75} -77.0000 q^{77} +1144.00 q^{79} +421.000 q^{81} -468.000 q^{83} +648.000 q^{85} -108.000 q^{87} -870.000 q^{89} -392.000 q^{91} +668.000 q^{93} +504.000 q^{95} -1330.00 q^{97} -253.000 q^{99} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 2.00000 0.384900 0.192450 0.981307i \(-0.438357\pi\)
0.192450 + 0.981307i \(0.438357\pi\)
\(4\) 0 0
\(5\) 18.0000 1.60997 0.804984 0.593296i \(-0.202174\pi\)
0.804984 + 0.593296i \(0.202174\pi\)
\(6\) 0 0
\(7\) −7.00000 −0.377964
\(8\) 0 0
\(9\) −23.0000 −0.851852
\(10\) 0 0
\(11\) 11.0000 0.301511
\(12\) 0 0
\(13\) 56.0000 1.19474 0.597369 0.801966i \(-0.296213\pi\)
0.597369 + 0.801966i \(0.296213\pi\)
\(14\) 0 0
\(15\) 36.0000 0.619677
\(16\) 0 0
\(17\) 36.0000 0.513605 0.256802 0.966464i \(-0.417331\pi\)
0.256802 + 0.966464i \(0.417331\pi\)
\(18\) 0 0
\(19\) 28.0000 0.338086 0.169043 0.985609i \(-0.445932\pi\)
0.169043 + 0.985609i \(0.445932\pi\)
\(20\) 0 0
\(21\) −14.0000 −0.145479
\(22\) 0 0
\(23\) −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
\(26\) 0 0
\(27\) −100.000 −0.712778
\(28\) 0 0
\(29\) −54.0000 −0.345778 −0.172889 0.984941i \(-0.555310\pi\)
−0.172889 + 0.984941i \(0.555310\pi\)
\(30\) 0 0
\(31\) 334.000 1.93510 0.967551 0.252675i \(-0.0813104\pi\)
0.967551 + 0.252675i \(0.0813104\pi\)
\(32\) 0 0
\(33\) 22.0000 0.116052
\(34\) 0 0
\(35\) −126.000 −0.608511
\(36\) 0 0
\(37\) 386.000 1.71508 0.857541 0.514416i \(-0.171991\pi\)
0.857541 + 0.514416i \(0.171991\pi\)
\(38\) 0 0
\(39\) 112.000 0.459855
\(40\) 0 0
\(41\) −444.000 −1.69125 −0.845624 0.533779i \(-0.820771\pi\)
−0.845624 + 0.533779i \(0.820771\pi\)
\(42\) 0 0
\(43\) 316.000 1.12069 0.560344 0.828260i \(-0.310669\pi\)
0.560344 + 0.828260i \(0.310669\pi\)
\(44\) 0 0
\(45\) −414.000 −1.37146
\(46\) 0 0
\(47\) 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
\(50\) 0 0
\(51\) 72.0000 0.197687
\(52\) 0 0
\(53\) −486.000 −1.25957 −0.629785 0.776769i \(-0.716857\pi\)
−0.629785 + 0.776769i \(0.716857\pi\)
\(54\) 0 0
\(55\) 198.000 0.485424
\(56\) 0 0
\(57\) 56.0000 0.130129
\(58\) 0 0
\(59\) 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 \(0.369426\pi\)
\(62\) 0 0
\(63\) 161.000 0.321970
\(64\) 0 0
\(65\) 1008.00 1.92349
\(66\) 0 0
\(67\) −176.000 −0.320923 −0.160461 0.987042i \(-0.551298\pi\)
−0.160461 + 0.987042i \(0.551298\pi\)
\(68\) 0 0
\(69\) −360.000 −0.628100
\(70\) 0 0
\(71\) 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 \(0.278387\pi\)
\(74\) 0 0
\(75\) 398.000 0.612761
\(76\) 0 0
\(77\) −77.0000 −0.113961
\(78\) 0 0
\(79\) 1144.00 1.62924 0.814621 0.579994i \(-0.196945\pi\)
0.814621 + 0.579994i \(0.196945\pi\)
\(80\) 0 0
\(81\) 421.000 0.577503
\(82\) 0 0
\(83\) −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
\(86\) 0 0
\(87\) −108.000 −0.133090
\(88\) 0 0
\(89\) −870.000 −1.03618 −0.518089 0.855327i \(-0.673356\pi\)
−0.518089 + 0.855327i \(0.673356\pi\)
\(90\) 0 0
\(91\) −392.000 −0.451569
\(92\) 0 0
\(93\) 668.000 0.744821
\(94\) 0 0
\(95\) 504.000 0.544309
\(96\) 0 0
\(97\) −1330.00 −1.39218 −0.696088 0.717957i \(-0.745078\pi\)
−0.696088 + 0.717957i \(0.745078\pi\)
\(98\) 0 0
\(99\) −253.000 −0.256843
\(100\) 0 0
\(101\) −120.000 −0.118222 −0.0591111 0.998251i \(-0.518827\pi\)
−0.0591111 + 0.998251i \(0.518827\pi\)
\(102\) 0 0
\(103\) 1210.00 1.15752 0.578761 0.815497i \(-0.303536\pi\)
0.578761 + 0.815497i \(0.303536\pi\)
\(104\) 0 0
\(105\) −252.000 −0.234216
\(106\) 0 0
\(107\) −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 \(0.598631\pi\)
\(110\) 0 0
\(111\) 772.000 0.660135
\(112\) 0 0
\(113\) 978.000 0.814181 0.407091 0.913388i \(-0.366543\pi\)
0.407091 + 0.913388i \(0.366543\pi\)
\(114\) 0 0
\(115\) −3240.00 −2.62723
\(116\) 0 0
\(117\) −1288.00 −1.01774
\(118\) 0 0
\(119\) −252.000 −0.194124
\(120\) 0 0
\(121\) 121.000 0.0909091
\(122\) 0 0
\(123\) −888.000 −0.650961
\(124\) 0 0
\(125\) 1332.00 0.953102
\(126\) 0 0
\(127\) 1216.00 0.849626 0.424813 0.905281i \(-0.360340\pi\)
0.424813 + 0.905281i \(0.360340\pi\)
\(128\) 0 0
\(129\) 632.000 0.431353
\(130\) 0 0
\(131\) −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
\(134\) 0 0
\(135\) −1800.00 −1.14755
\(136\) 0 0
\(137\) 1062.00 0.662283 0.331142 0.943581i \(-0.392566\pi\)
0.331142 + 0.943581i \(0.392566\pi\)
\(138\) 0 0
\(139\) 508.000 0.309986 0.154993 0.987916i \(-0.450465\pi\)
0.154993 + 0.987916i \(0.450465\pi\)
\(140\) 0 0
\(141\) 804.000 0.480206
\(142\) 0 0
\(143\) 616.000 0.360227
\(144\) 0 0
\(145\) −972.000 −0.556691
\(146\) 0 0
\(147\) 98.0000 0.0549857
\(148\) 0 0
\(149\) 2598.00 1.42843 0.714216 0.699925i \(-0.246783\pi\)
0.714216 + 0.699925i \(0.246783\pi\)
\(150\) 0 0
\(151\) −2648.00 −1.42709 −0.713547 0.700607i \(-0.752912\pi\)
−0.713547 + 0.700607i \(0.752912\pi\)
\(152\) 0 0
\(153\) −828.000 −0.437515
\(154\) 0 0
\(155\) 6012.00 3.11545
\(156\) 0 0
\(157\) −790.000 −0.401585 −0.200793 0.979634i \(-0.564352\pi\)
−0.200793 + 0.979634i \(0.564352\pi\)
\(158\) 0 0
\(159\) −972.000 −0.484809
\(160\) 0 0
\(161\) 1260.00 0.616782
\(162\) 0 0
\(163\) 160.000 0.0768845 0.0384422 0.999261i \(-0.487760\pi\)
0.0384422 + 0.999261i \(0.487760\pi\)
\(164\) 0 0
\(165\) 396.000 0.186840
\(166\) 0 0
\(167\) −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
\(170\) 0 0
\(171\) −644.000 −0.287999
\(172\) 0 0
\(173\) 1632.00 0.717218 0.358609 0.933488i \(-0.383251\pi\)
0.358609 + 0.933488i \(0.383251\pi\)
\(174\) 0 0
\(175\) −1393.00 −0.601719
\(176\) 0 0
\(177\) 564.000 0.239508
\(178\) 0 0
\(179\) 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 \(0.440704\pi\)
\(182\) 0 0
\(183\) 760.000 0.306999
\(184\) 0 0
\(185\) 6948.00 2.76123
\(186\) 0 0
\(187\) 396.000 0.154858
\(188\) 0 0
\(189\) 700.000 0.269405
\(190\) 0 0
\(191\) −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 \(0.372563\pi\)
\(194\) 0 0
\(195\) 2016.00 0.740353
\(196\) 0 0
\(197\) −1602.00 −0.579380 −0.289690 0.957121i \(-0.593552\pi\)
−0.289690 + 0.957121i \(0.593552\pi\)
\(198\) 0 0
\(199\) 3274.00 1.16627 0.583135 0.812375i \(-0.301826\pi\)
0.583135 + 0.812375i \(0.301826\pi\)
\(200\) 0 0
\(201\) −352.000 −0.123523
\(202\) 0 0
\(203\) 378.000 0.130692
\(204\) 0 0
\(205\) −7992.00 −2.72286
\(206\) 0 0
\(207\) 4140.00 1.39010
\(208\) 0 0
\(209\) 308.000 0.101937
\(210\) 0 0
\(211\) 4948.00 1.61438 0.807190 0.590291i \(-0.200987\pi\)
0.807190 + 0.590291i \(0.200987\pi\)
\(212\) 0 0
\(213\) 648.000 0.208452
\(214\) 0 0
\(215\) 5688.00 1.80427
\(216\) 0 0
\(217\) −2338.00 −0.731400
\(218\) 0 0
\(219\) 1600.00 0.493689
\(220\) 0 0
\(221\) 2016.00 0.613624
\(222\) 0 0
\(223\) −2342.00 −0.703282 −0.351641 0.936135i \(-0.614376\pi\)
−0.351641 + 0.936135i \(0.614376\pi\)
\(224\) 0 0
\(225\) −4577.00 −1.35615
\(226\) 0 0
\(227\) −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 \(0.577271\pi\)
\(230\) 0 0
\(231\) −154.000 −0.0438634
\(232\) 0 0
\(233\) 4158.00 1.16910 0.584549 0.811359i \(-0.301272\pi\)
0.584549 + 0.811359i \(0.301272\pi\)
\(234\) 0 0
\(235\) 7236.00 2.00862
\(236\) 0 0
\(237\) 2288.00 0.627095
\(238\) 0 0
\(239\) −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 \(0.130773\pi\)
\(242\) 0 0
\(243\) 3542.00 0.935059
\(244\) 0 0
\(245\) 882.000 0.229996
\(246\) 0 0
\(247\) 1568.00 0.403925
\(248\) 0 0
\(249\) −936.000 −0.238219
\(250\) 0 0
\(251\) 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
\(254\) 0 0
\(255\) 1296.00 0.318269
\(256\) 0 0
\(257\) −2430.00 −0.589802 −0.294901 0.955528i \(-0.595287\pi\)
−0.294901 + 0.955528i \(0.595287\pi\)
\(258\) 0 0
\(259\) −2702.00 −0.648240
\(260\) 0 0
\(261\) 1242.00 0.294551
\(262\) 0 0
\(263\) −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
\(266\) 0 0
\(267\) −1740.00 −0.398825
\(268\) 0 0
\(269\) −3834.00 −0.869008 −0.434504 0.900670i \(-0.643076\pi\)
−0.434504 + 0.900670i \(0.643076\pi\)
\(270\) 0 0
\(271\) 3508.00 0.786331 0.393166 0.919468i \(-0.371380\pi\)
0.393166 + 0.919468i \(0.371380\pi\)
\(272\) 0 0
\(273\) −784.000 −0.173809
\(274\) 0 0
\(275\) 2189.00 0.480006
\(276\) 0 0
\(277\) 8294.00 1.79905 0.899527 0.436864i \(-0.143911\pi\)
0.899527 + 0.436864i \(0.143911\pi\)
\(278\) 0 0
\(279\) −7682.00 −1.64842
\(280\) 0 0
\(281\) 8022.00 1.70303 0.851517 0.524327i \(-0.175683\pi\)
0.851517 + 0.524327i \(0.175683\pi\)
\(282\) 0 0
\(283\) −392.000 −0.0823392 −0.0411696 0.999152i \(-0.513108\pi\)
−0.0411696 + 0.999152i \(0.513108\pi\)
\(284\) 0 0
\(285\) 1008.00 0.209504
\(286\) 0 0
\(287\) 3108.00 0.639231
\(288\) 0 0
\(289\) −3617.00 −0.736210
\(290\) 0 0
\(291\) −2660.00 −0.535849
\(292\) 0 0
\(293\) −2748.00 −0.547918 −0.273959 0.961741i \(-0.588333\pi\)
−0.273959 + 0.961741i \(0.588333\pi\)
\(294\) 0 0
\(295\) 5076.00 1.00182
\(296\) 0 0
\(297\) −1100.00 −0.214911
\(298\) 0 0
\(299\) −10080.0 −1.94964
\(300\) 0 0
\(301\) −2212.00 −0.423580
\(302\) 0 0
\(303\) −240.000 −0.0455038
\(304\) 0 0
\(305\) 6840.00 1.28412
\(306\) 0 0
\(307\) 3064.00 0.569615 0.284807 0.958585i \(-0.408070\pi\)
0.284807 + 0.958585i \(0.408070\pi\)
\(308\) 0 0
\(309\) 2420.00 0.445531
\(310\) 0 0
\(311\) −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 \(0.644925\pi\)
\(314\) 0 0
\(315\) 2898.00 0.518361
\(316\) 0 0
\(317\) 4806.00 0.851520 0.425760 0.904836i \(-0.360007\pi\)
0.425760 + 0.904836i \(0.360007\pi\)
\(318\) 0 0
\(319\) −594.000 −0.104256
\(320\) 0 0
\(321\) −2472.00 −0.429824
\(322\) 0 0
\(323\) 1008.00 0.173643
\(324\) 0 0
\(325\) 11144.0 1.90202
\(326\) 0 0
\(327\) −1388.00 −0.234730
\(328\) 0 0
\(329\) −2814.00 −0.471553
\(330\) 0 0
\(331\) −6620.00 −1.09930 −0.549650 0.835395i \(-0.685239\pi\)
−0.549650 + 0.835395i \(0.685239\pi\)
\(332\) 0 0
\(333\) −8878.00 −1.46100
\(334\) 0 0
\(335\) −3168.00 −0.516676
\(336\) 0 0
\(337\) 1094.00 0.176837 0.0884184 0.996083i \(-0.471819\pi\)
0.0884184 + 0.996083i \(0.471819\pi\)
\(338\) 0 0
\(339\) 1956.00 0.313379
\(340\) 0 0
\(341\) 3674.00 0.583455
\(342\) 0 0
\(343\) −343.000 −0.0539949
\(344\) 0 0
\(345\) −6480.00 −1.01122
\(346\) 0 0
\(347\) −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 \(0.716097\pi\)
\(350\) 0 0
\(351\) −5600.00 −0.851584
\(352\) 0 0
\(353\) −5070.00 −0.764444 −0.382222 0.924070i \(-0.624841\pi\)
−0.382222 + 0.924070i \(0.624841\pi\)
\(354\) 0 0
\(355\) 5832.00 0.871917
\(356\) 0 0
\(357\) −504.000 −0.0747185
\(358\) 0 0
\(359\) −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
\(362\) 0 0
\(363\) 242.000 0.0349909
\(364\) 0 0
\(365\) 14400.0 2.06501
\(366\) 0 0
\(367\) −10166.0 −1.44594 −0.722971 0.690878i \(-0.757224\pi\)
−0.722971 + 0.690878i \(0.757224\pi\)
\(368\) 0 0
\(369\) 10212.0 1.44069
\(370\) 0 0
\(371\) 3402.00 0.476073
\(372\) 0 0
\(373\) −2722.00 −0.377855 −0.188927 0.981991i \(-0.560501\pi\)
−0.188927 + 0.981991i \(0.560501\pi\)
\(374\) 0 0
\(375\) 2664.00 0.366849
\(376\) 0 0
\(377\) −3024.00 −0.413114
\(378\) 0 0
\(379\) 5872.00 0.795843 0.397921 0.917420i \(-0.369732\pi\)
0.397921 + 0.917420i \(0.369732\pi\)
\(380\) 0 0
\(381\) 2432.00 0.327021
\(382\) 0 0
\(383\) −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
\(386\) 0 0
\(387\) −7268.00 −0.954659
\(388\) 0 0
\(389\) −14586.0 −1.90113 −0.950565 0.310526i \(-0.899495\pi\)
−0.950565 + 0.310526i \(0.899495\pi\)
\(390\) 0 0
\(391\) −6480.00 −0.838127
\(392\) 0 0
\(393\) −3360.00 −0.431271
\(394\) 0 0
\(395\) 20592.0 2.62303
\(396\) 0 0
\(397\) 1874.00 0.236910 0.118455 0.992959i \(-0.462206\pi\)
0.118455 + 0.992959i \(0.462206\pi\)
\(398\) 0 0
\(399\) −392.000 −0.0491843
\(400\) 0 0
\(401\) 13338.0 1.66102 0.830509 0.557006i \(-0.188050\pi\)
0.830509 + 0.557006i \(0.188050\pi\)
\(402\) 0 0
\(403\) 18704.0 2.31194
\(404\) 0 0
\(405\) 7578.00 0.929763
\(406\) 0 0
\(407\) 4246.00 0.517116
\(408\) 0 0
\(409\) −8200.00 −0.991354 −0.495677 0.868507i \(-0.665080\pi\)
−0.495677 + 0.868507i \(0.665080\pi\)
\(410\) 0 0
\(411\) 2124.00 0.254913
\(412\) 0 0
\(413\) −1974.00 −0.235192
\(414\) 0 0
\(415\) −8424.00 −0.996429
\(416\) 0 0
\(417\) 1016.00 0.119314
\(418\) 0 0
\(419\) 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 \(0.737068\pi\)
\(422\) 0 0
\(423\) −9246.00 −1.06278
\(424\) 0 0
\(425\) 7164.00 0.817659
\(426\) 0 0
\(427\) −2660.00 −0.301467
\(428\) 0 0
\(429\) 1232.00 0.138652
\(430\) 0 0
\(431\) 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 \(0.332765\pi\)
\(434\) 0 0
\(435\) −1944.00 −0.214270
\(436\) 0 0
\(437\) −5040.00 −0.551707
\(438\) 0 0
\(439\) −1964.00 −0.213523 −0.106762 0.994285i \(-0.534048\pi\)
−0.106762 + 0.994285i \(0.534048\pi\)
\(440\) 0 0
\(441\) −1127.00 −0.121693
\(442\) 0 0
\(443\) −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
\(446\) 0 0
\(447\) 5196.00 0.549804
\(448\) 0 0
\(449\) 3270.00 0.343699 0.171849 0.985123i \(-0.445026\pi\)
0.171849 + 0.985123i \(0.445026\pi\)
\(450\) 0 0
\(451\) −4884.00 −0.509930
\(452\) 0 0
\(453\) −5296.00 −0.549289
\(454\) 0 0
\(455\) −7056.00 −0.727012
\(456\) 0 0
\(457\) −15526.0 −1.58922 −0.794612 0.607117i \(-0.792326\pi\)
−0.794612 + 0.607117i \(0.792326\pi\)
\(458\) 0 0
\(459\) −3600.00 −0.366086
\(460\) 0 0
\(461\) 10548.0 1.06566 0.532830 0.846222i \(-0.321128\pi\)
0.532830 + 0.846222i \(0.321128\pi\)
\(462\) 0 0
\(463\) 3796.00 0.381026 0.190513 0.981685i \(-0.438985\pi\)
0.190513 + 0.981685i \(0.438985\pi\)
\(464\) 0 0
\(465\) 12024.0 1.19914
\(466\) 0 0
\(467\) −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
\(470\) 0 0
\(471\) −1580.00 −0.154570
\(472\) 0 0
\(473\) 3476.00 0.337900
\(474\) 0 0
\(475\) 5572.00 0.538233
\(476\) 0 0
\(477\) 11178.0 1.07297
\(478\) 0 0
\(479\) −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
\(482\) 0 0
\(483\) 2520.00 0.237400
\(484\) 0 0
\(485\) −23940.0 −2.24136
\(486\) 0 0
\(487\) −5132.00 −0.477522 −0.238761 0.971078i \(-0.576741\pi\)
−0.238761 + 0.971078i \(0.576741\pi\)
\(488\) 0 0
\(489\) 320.000 0.0295928
\(490\) 0 0
\(491\) −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
\(494\) 0 0
\(495\) −4554.00 −0.413509
\(496\) 0 0
\(497\) −2268.00 −0.204696
\(498\) 0 0
\(499\) −3848.00 −0.345211 −0.172605 0.984991i \(-0.555219\pi\)
−0.172605 + 0.984991i \(0.555219\pi\)
\(500\) 0 0
\(501\) −528.000 −0.0470844
\(502\) 0 0
\(503\) 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
\(506\) 0 0
\(507\) 1878.00 0.164507
\(508\) 0 0
\(509\) −6162.00 −0.536593 −0.268297 0.963336i \(-0.586461\pi\)
−0.268297 + 0.963336i \(0.586461\pi\)
\(510\) 0 0
\(511\) −5600.00 −0.484793
\(512\) 0 0
\(513\) −2800.00 −0.240981
\(514\) 0 0
\(515\) 21780.0 1.86358
\(516\) 0 0
\(517\) 4422.00 0.376169
\(518\) 0 0
\(519\) 3264.00 0.276057
\(520\) 0 0
\(521\) −20946.0 −1.76135 −0.880673 0.473725i \(-0.842909\pi\)
−0.880673 + 0.473725i \(0.842909\pi\)
\(522\) 0 0
\(523\) 4696.00 0.392623 0.196311 0.980542i \(-0.437104\pi\)
0.196311 + 0.980542i \(0.437104\pi\)
\(524\) 0 0
\(525\) −2786.00 −0.231602
\(526\) 0 0
\(527\) 12024.0 0.993878
\(528\) 0 0
\(529\) 20233.0 1.66294
\(530\) 0 0
\(531\) −6486.00 −0.530072
\(532\) 0 0
\(533\) −24864.0 −2.02060
\(534\) 0 0
\(535\) −22248.0 −1.79788
\(536\) 0 0
\(537\) 1416.00 0.113789
\(538\) 0 0
\(539\) 539.000 0.0430730
\(540\) 0 0
\(541\) 19358.0 1.53838 0.769192 0.639018i \(-0.220659\pi\)
0.769192 + 0.639018i \(0.220659\pi\)
\(542\) 0 0
\(543\) 1804.00 0.142573
\(544\) 0 0
\(545\) −12492.0 −0.981832
\(546\) 0 0
\(547\) −18020.0 −1.40855 −0.704277 0.709925i \(-0.748729\pi\)
−0.704277 + 0.709925i \(0.748729\pi\)
\(548\) 0 0
\(549\) −8740.00 −0.679443
\(550\) 0 0
\(551\) −1512.00 −0.116903
\(552\) 0 0
\(553\) −8008.00 −0.615795
\(554\) 0 0
\(555\) 13896.0 1.06280
\(556\) 0 0
\(557\) 14622.0 1.11231 0.556153 0.831080i \(-0.312277\pi\)
0.556153 + 0.831080i \(0.312277\pi\)
\(558\) 0 0
\(559\) 17696.0 1.33893
\(560\) 0 0
\(561\) 792.000 0.0596048
\(562\) 0 0
\(563\) 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
\(566\) 0 0
\(567\) −2947.00 −0.218276
\(568\) 0 0
\(569\) −3258.00 −0.240039 −0.120020 0.992772i \(-0.538296\pi\)
−0.120020 + 0.992772i \(0.538296\pi\)
\(570\) 0 0
\(571\) 6604.00 0.484008 0.242004 0.970275i \(-0.422195\pi\)
0.242004 + 0.970275i \(0.422195\pi\)
\(572\) 0 0
\(573\) −3648.00 −0.265964
\(574\) 0 0
\(575\) −35820.0 −2.59791
\(576\) 0 0
\(577\) −16594.0 −1.19726 −0.598628 0.801027i \(-0.704287\pi\)
−0.598628 + 0.801027i \(0.704287\pi\)
\(578\) 0 0
\(579\) 4180.00 0.300026
\(580\) 0 0
\(581\) 3276.00 0.233927
\(582\) 0 0
\(583\) −5346.00 −0.379775
\(584\) 0 0
\(585\) −23184.0 −1.63853
\(586\) 0 0
\(587\) 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
\(590\) 0 0
\(591\) −3204.00 −0.223003
\(592\) 0 0
\(593\) −4776.00 −0.330737 −0.165368 0.986232i \(-0.552881\pi\)
−0.165368 + 0.986232i \(0.552881\pi\)
\(594\) 0 0
\(595\) −4536.00 −0.312534
\(596\) 0 0
\(597\) 6548.00 0.448897
\(598\) 0 0
\(599\) −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 \(0.338124\pi\)
\(602\) 0 0
\(603\) 4048.00 0.273379
\(604\) 0 0
\(605\) 2178.00 0.146361
\(606\) 0 0
\(607\) −24488.0 −1.63746 −0.818729 0.574180i \(-0.805321\pi\)
−0.818729 + 0.574180i \(0.805321\pi\)
\(608\) 0 0
\(609\) 756.000 0.0503032
\(610\) 0 0
\(611\) 22512.0 1.49057
\(612\) 0 0
\(613\) −19654.0 −1.29497 −0.647486 0.762078i \(-0.724179\pi\)
−0.647486 + 0.762078i \(0.724179\pi\)
\(614\) 0 0
\(615\) −15984.0 −1.04803
\(616\) 0 0
\(617\) 2694.00 0.175780 0.0878901 0.996130i \(-0.471988\pi\)
0.0878901 + 0.996130i \(0.471988\pi\)
\(618\) 0 0
\(619\) −10178.0 −0.660886 −0.330443 0.943826i \(-0.607198\pi\)
−0.330443 + 0.943826i \(0.607198\pi\)
\(620\) 0 0
\(621\) 18000.0 1.16315
\(622\) 0 0
\(623\) 6090.00 0.391638
\(624\) 0 0
\(625\) −899.000 −0.0575360
\(626\) 0 0
\(627\) 616.000 0.0392355
\(628\) 0 0
\(629\) 13896.0 0.880874
\(630\) 0 0
\(631\) 7648.00 0.482507 0.241254 0.970462i \(-0.422441\pi\)
0.241254 + 0.970462i \(0.422441\pi\)
\(632\) 0 0
\(633\) 9896.00 0.621375
\(634\) 0 0
\(635\) 21888.0 1.36787
\(636\) 0 0
\(637\) 2744.00 0.170677
\(638\) 0 0
\(639\) −7452.00 −0.461340
\(640\) 0 0
\(641\) 270.000 0.0166371 0.00831853 0.999965i \(-0.497352\pi\)
0.00831853 + 0.999965i \(0.497352\pi\)
\(642\) 0 0
\(643\) −16250.0 −0.996637 −0.498318 0.866994i \(-0.666049\pi\)
−0.498318 + 0.866994i \(0.666049\pi\)
\(644\) 0 0
\(645\) 11376.0 0.694464
\(646\) 0 0
\(647\) −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
\(650\) 0 0
\(651\) −4676.00 −0.281516
\(652\) 0 0
\(653\) −17322.0 −1.03807 −0.519037 0.854752i \(-0.673709\pi\)
−0.519037 + 0.854752i \(0.673709\pi\)
\(654\) 0 0
\(655\) −30240.0 −1.80393
\(656\) 0 0
\(657\) −18400.0 −1.09262
\(658\) 0 0
\(659\) −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 \(0.708559\pi\)
\(662\) 0 0
\(663\) 4032.00 0.236184
\(664\) 0 0
\(665\) −3528.00 −0.205729
\(666\) 0 0
\(667\) 9720.00 0.564258
\(668\) 0 0
\(669\) −4684.00 −0.270693
\(670\) 0 0
\(671\) 4180.00 0.240487
\(672\) 0 0
\(673\) −10354.0 −0.593042 −0.296521 0.955026i \(-0.595827\pi\)
−0.296521 + 0.955026i \(0.595827\pi\)
\(674\) 0 0
\(675\) −19900.0 −1.13474
\(676\) 0 0
\(677\) −10920.0 −0.619926 −0.309963 0.950749i \(-0.600317\pi\)
−0.309963 + 0.950749i \(0.600317\pi\)
\(678\) 0 0
\(679\) 9310.00 0.526193
\(680\) 0 0
\(681\) −4128.00 −0.232284
\(682\) 0 0
\(683\) −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
\(686\) 0 0
\(687\) −3332.00 −0.185042
\(688\) 0 0
\(689\) −27216.0 −1.50486
\(690\) 0 0
\(691\) 25834.0 1.42225 0.711123 0.703068i \(-0.248187\pi\)
0.711123 + 0.703068i \(0.248187\pi\)
\(692\) 0 0
\(693\) 1771.00 0.0970775
\(694\) 0 0
\(695\) 9144.00 0.499067
\(696\) 0 0
\(697\) −15984.0 −0.868633
\(698\) 0 0
\(699\) 8316.00 0.449986
\(700\) 0 0
\(701\) −10590.0 −0.570583 −0.285292 0.958441i \(-0.592090\pi\)
−0.285292 + 0.958441i \(0.592090\pi\)
\(702\) 0 0
\(703\) 10808.0 0.579846
\(704\) 0 0
\(705\) 14472.0 0.773116
\(706\) 0 0
\(707\) 840.000 0.0446838
\(708\) 0 0
\(709\) −6802.00 −0.360302 −0.180151 0.983639i \(-0.557659\pi\)
−0.180151 + 0.983639i \(0.557659\pi\)
\(710\) 0 0
\(711\) −26312.0 −1.38787
\(712\) 0 0
\(713\) −60120.0 −3.15780
\(714\) 0 0
\(715\) 11088.0 0.579955
\(716\) 0 0
\(717\) −144.000 −0.00750039
\(718\) 0 0
\(719\) −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
\(722\) 0 0
\(723\) 13720.0 0.705743
\(724\) 0 0
\(725\) −10746.0 −0.550478
\(726\) 0 0
\(727\) −4682.00 −0.238853 −0.119426 0.992843i \(-0.538106\pi\)
−0.119426 + 0.992843i \(0.538106\pi\)
\(728\) 0 0
\(729\) −4283.00 −0.217599
\(730\) 0 0
\(731\) 11376.0 0.575590
\(732\) 0 0
\(733\) −17860.0 −0.899965 −0.449982 0.893037i \(-0.648570\pi\)
−0.449982 + 0.893037i \(0.648570\pi\)
\(734\) 0 0
\(735\) 1764.00 0.0885253
\(736\) 0 0
\(737\) −1936.00 −0.0967618
\(738\) 0 0
\(739\) −6860.00 −0.341474 −0.170737 0.985317i \(-0.554615\pi\)
−0.170737 + 0.985317i \(0.554615\pi\)
\(740\) 0 0
\(741\) 3136.00 0.155471
\(742\) 0 0
\(743\) 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
\(746\) 0 0
\(747\) 10764.0 0.527221
\(748\) 0 0
\(749\) 8652.00 0.422079
\(750\) 0 0
\(751\) −7364.00 −0.357811 −0.178906 0.983866i \(-0.557256\pi\)
−0.178906 + 0.983866i \(0.557256\pi\)
\(752\) 0 0
\(753\) 300.000 0.0145187
\(754\) 0 0
\(755\) −47664.0 −2.29758
\(756\) 0 0
\(757\) −34378.0 −1.65058 −0.825290 0.564709i \(-0.808989\pi\)
−0.825290 + 0.564709i \(0.808989\pi\)
\(758\) 0 0
\(759\) −3960.00 −0.189379
\(760\) 0 0
\(761\) 27456.0 1.30786 0.653929 0.756556i \(-0.273120\pi\)
0.653929 + 0.756556i \(0.273120\pi\)
\(762\) 0 0
\(763\) 4858.00 0.230500
\(764\) 0 0
\(765\) −14904.0 −0.704386
\(766\) 0 0
\(767\) 15792.0 0.743437
\(768\) 0 0
\(769\) 7952.00 0.372895 0.186448 0.982465i \(-0.440303\pi\)
0.186448 + 0.982465i \(0.440303\pi\)
\(770\) 0 0
\(771\) −4860.00 −0.227015
\(772\) 0 0
\(773\) −4986.00 −0.231997 −0.115999 0.993249i \(-0.537007\pi\)
−0.115999 + 0.993249i \(0.537007\pi\)
\(774\) 0 0
\(775\) 66466.0 3.08068
\(776\) 0 0
\(777\) −5404.00 −0.249508
\(778\) 0 0
\(779\) −12432.0 −0.571788
\(780\) 0 0
\(781\) 3564.00 0.163291
\(782\) 0 0
\(783\) 5400.00 0.246463
\(784\) 0 0
\(785\) −14220.0 −0.646540
\(786\) 0 0
\(787\) 42748.0 1.93622 0.968108 0.250534i \(-0.0806062\pi\)
0.968108 + 0.250534i \(0.0806062\pi\)
\(788\) 0 0
\(789\) −6096.00 −0.275061
\(790\) 0 0
\(791\) −6846.00 −0.307732
\(792\) 0 0
\(793\) 21280.0 0.952932
\(794\) 0 0
\(795\) −17496.0 −0.780527
\(796\) 0 0
\(797\) 35610.0 1.58265 0.791324 0.611397i \(-0.209392\pi\)
0.791324 + 0.611397i \(0.209392\pi\)
\(798\) 0 0
\(799\) 14472.0 0.640779
\(800\) 0 0
\(801\) 20010.0 0.882670
\(802\) 0 0
\(803\) 8800.00 0.386731
\(804\) 0 0
\(805\) 22680.0 0.993000
\(806\) 0 0
\(807\) −7668.00 −0.334481
\(808\) 0 0
\(809\) −17046.0 −0.740798 −0.370399 0.928873i \(-0.620779\pi\)
−0.370399 + 0.928873i \(0.620779\pi\)
\(810\) 0 0
\(811\) 2176.00 0.0942166 0.0471083 0.998890i \(-0.484999\pi\)
0.0471083 + 0.998890i \(0.484999\pi\)
\(812\) 0 0
\(813\) 7016.00 0.302659
\(814\) 0 0
\(815\) 2880.00 0.123782
\(816\) 0 0
\(817\) 8848.00 0.378889
\(818\) 0 0
\(819\) 9016.00 0.384670
\(820\) 0 0
\(821\) 2094.00 0.0890147 0.0445074 0.999009i \(-0.485828\pi\)
0.0445074 + 0.999009i \(0.485828\pi\)
\(822\) 0 0
\(823\) −7328.00 −0.310374 −0.155187 0.987885i \(-0.549598\pi\)
−0.155187 + 0.987885i \(0.549598\pi\)
\(824\) 0 0
\(825\) 4378.00 0.184754
\(826\) 0 0
\(827\) 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 \(0.787465\pi\)
\(830\) 0 0
\(831\) 16588.0 0.692456
\(832\) 0 0
\(833\) 1764.00 0.0733721
\(834\) 0 0
\(835\) −4752.00 −0.196946
\(836\) 0 0
\(837\) −33400.0 −1.37930
\(838\) 0 0
\(839\) 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
\(842\) 0 0
\(843\) 16044.0 0.655498
\(844\) 0 0
\(845\) 16902.0 0.688102
\(846\) 0 0
\(847\) −847.000 −0.0343604
\(848\) 0 0
\(849\) −784.000 −0.0316924
\(850\) 0 0
\(851\) −69480.0 −2.79876
\(852\) 0 0
\(853\) 9440.00 0.378921 0.189460 0.981888i \(-0.439326\pi\)
0.189460 + 0.981888i \(0.439326\pi\)
\(854\) 0 0
\(855\) −11592.0 −0.463670
\(856\) 0 0
\(857\) −28440.0 −1.13360 −0.566798 0.823857i \(-0.691818\pi\)
−0.566798 + 0.823857i \(0.691818\pi\)
\(858\) 0 0
\(859\) 24334.0 0.966549 0.483274 0.875469i \(-0.339447\pi\)
0.483274 + 0.875469i \(0.339447\pi\)
\(860\) 0 0
\(861\) 6216.00 0.246040
\(862\) 0 0
\(863\) −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
\(866\) 0 0
\(867\) −7234.00 −0.283367
\(868\) 0 0
\(869\) 12584.0 0.491235
\(870\) 0 0
\(871\) −9856.00 −0.383419
\(872\) 0 0
\(873\) 30590.0 1.18593
\(874\) 0 0
\(875\) −9324.00 −0.360239
\(876\) 0 0
\(877\) 32114.0 1.23650 0.618251 0.785981i \(-0.287841\pi\)
0.618251 + 0.785981i \(0.287841\pi\)
\(878\) 0 0
\(879\) −5496.00 −0.210894
\(880\) 0 0
\(881\) 41454.0 1.58527 0.792634 0.609698i \(-0.208709\pi\)
0.792634 + 0.609698i \(0.208709\pi\)
\(882\) 0 0
\(883\) −2876.00 −0.109609 −0.0548047 0.998497i \(-0.517454\pi\)
−0.0548047 + 0.998497i \(0.517454\pi\)
\(884\) 0 0
\(885\) 10152.0 0.385600
\(886\) 0 0
\(887\) −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
\(890\) 0 0
\(891\) 4631.00 0.174124
\(892\) 0 0
\(893\) 11256.0 0.421800
\(894\) 0 0
\(895\) 12744.0 0.475961
\(896\) 0 0
\(897\) −20160.0 −0.750416
\(898\) 0 0
\(899\) −18036.0 −0.669115
\(900\) 0 0
\(901\) −17496.0 −0.646921
\(902\) 0 0
\(903\) −4424.00 −0.163036
\(904\) 0 0
\(905\) 16236.0 0.596357
\(906\) 0 0
\(907\) 19768.0 0.723689 0.361844 0.932239i \(-0.382147\pi\)
0.361844 + 0.932239i \(0.382147\pi\)
\(908\) 0 0
\(909\) 2760.00 0.100708
\(910\) 0 0
\(911\) −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
\(914\) 0 0
\(915\) 13680.0 0.494259
\(916\) 0 0
\(917\) 11760.0 0.423500
\(918\) 0 0
\(919\) −31544.0 −1.13225 −0.566127 0.824318i \(-0.691559\pi\)
−0.566127 + 0.824318i \(0.691559\pi\)
\(920\) 0 0
\(921\) 6128.00 0.219245
\(922\) 0 0
\(923\) 18144.0 0.647039
\(924\) 0 0
\(925\) 76814.0 2.73041
\(926\) 0 0
\(927\) −27830.0 −0.986038
\(928\) 0 0
\(929\) 11118.0 0.392648 0.196324 0.980539i \(-0.437100\pi\)
0.196324 + 0.980539i \(0.437100\pi\)
\(930\) 0 0
\(931\) 1372.00 0.0482980
\(932\) 0 0
\(933\) −8124.00 −0.285067
\(934\) 0 0
\(935\) 7128.00 0.249316
\(936\) 0 0
\(937\) 10568.0 0.368454 0.184227 0.982884i \(-0.441022\pi\)
0.184227 + 0.982884i \(0.441022\pi\)
\(938\) 0 0
\(939\) −9740.00 −0.338501
\(940\) 0 0
\(941\) 14964.0 0.518398 0.259199 0.965824i \(-0.416541\pi\)
0.259199 + 0.965824i \(0.416541\pi\)
\(942\) 0 0
\(943\) 79920.0 2.75987
\(944\) 0 0
\(945\) 12600.0 0.433733
\(946\) 0 0
\(947\) −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
\(950\) 0 0
\(951\) 9612.00 0.327750
\(952\) 0 0
\(953\) 3906.00 0.132768 0.0663839 0.997794i \(-0.478854\pi\)
0.0663839 + 0.997794i \(0.478854\pi\)
\(954\) 0 0
\(955\) −32832.0 −1.11248
\(956\) 0 0
\(957\) −1188.00 −0.0401281
\(958\) 0 0
\(959\) −7434.00 −0.250319
\(960\) 0 0
\(961\) 81765.0 2.74462
\(962\) 0 0
\(963\) 28428.0 0.951277
\(964\) 0 0
\(965\) 37620.0 1.25495
\(966\) 0 0
\(967\) 36448.0 1.21209 0.606044 0.795431i \(-0.292756\pi\)
0.606044 + 0.795431i \(0.292756\pi\)
\(968\) 0 0
\(969\) 2016.00 0.0668351
\(970\) 0 0
\(971\) 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
\(974\) 0 0
\(975\) 22288.0 0.732089
\(976\) 0 0
\(977\) 37434.0 1.22581 0.612907 0.790155i \(-0.290000\pi\)
0.612907 + 0.790155i \(0.290000\pi\)
\(978\) 0 0
\(979\) −9570.00 −0.312419
\(980\) 0 0
\(981\) 15962.0 0.519498
\(982\) 0 0
\(983\) 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
\(986\) 0 0
\(987\) −5628.00 −0.181501
\(988\) 0 0
\(989\) −56880.0 −1.82880
\(990\) 0 0
\(991\) 15220.0 0.487870 0.243935 0.969792i \(-0.421562\pi\)
0.243935 + 0.969792i \(0.421562\pi\)
\(992\) 0 0
\(993\) −13240.0 −0.423121
\(994\) 0 0
\(995\) 58932.0 1.87766
\(996\) 0 0
\(997\) 37664.0 1.19642 0.598210 0.801339i \(-0.295879\pi\)
0.598210 + 0.801339i \(0.295879\pi\)
\(998\) 0 0
\(999\) −38600.0 −1.22247
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 1232.4.a.f.1.1 1
4.3 odd 2 154.4.a.d.1.1 1
12.11 even 2 1386.4.a.a.1.1 1
28.27 even 2 1078.4.a.g.1.1 1
44.43 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 4.3 odd 2
1078.4.a.g.1.1 1 28.27 even 2
1232.4.a.f.1.1 1 1.1 even 1 trivial
1386.4.a.a.1.1 1 12.11 even 2
1694.4.a.c.1.1 1 44.43 even 2