Properties

Label 588.4.a.b.1.1
Level $588$
Weight $4$
Character 588.1
Self dual yes
Analytic conductor $34.693$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 588.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(34.6931230834\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 588.1

$q$-expansion

\(f(q)\) \(=\) \(q-3.00000 q^{3} +4.00000 q^{5} +9.00000 q^{9} +O(q^{10})\) \(q-3.00000 q^{3} +4.00000 q^{5} +9.00000 q^{9} -20.0000 q^{11} -4.00000 q^{13} -12.0000 q^{15} +24.0000 q^{17} +44.0000 q^{19} +72.0000 q^{23} -109.000 q^{25} -27.0000 q^{27} -38.0000 q^{29} +184.000 q^{31} +60.0000 q^{33} -30.0000 q^{37} +12.0000 q^{39} -216.000 q^{41} -164.000 q^{43} +36.0000 q^{45} +520.000 q^{47} -72.0000 q^{51} -146.000 q^{53} -80.0000 q^{55} -132.000 q^{57} +460.000 q^{59} +628.000 q^{61} -16.0000 q^{65} +556.000 q^{67} -216.000 q^{69} +592.000 q^{71} +1024.00 q^{73} +327.000 q^{75} -104.000 q^{79} +81.0000 q^{81} -324.000 q^{83} +96.0000 q^{85} +114.000 q^{87} +896.000 q^{89} -552.000 q^{93} +176.000 q^{95} -920.000 q^{97} -180.000 q^{99} +O(q^{100})\)

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
\(3\) −3.00000 −0.577350
\(4\) 0 0
\(5\) 4.00000 0.357771 0.178885 0.983870i \(-0.442751\pi\)
0.178885 + 0.983870i \(0.442751\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 9.00000 0.333333
\(10\) 0 0
\(11\) −20.0000 −0.548202 −0.274101 0.961701i \(-0.588380\pi\)
−0.274101 + 0.961701i \(0.588380\pi\)
\(12\) 0 0
\(13\) −4.00000 −0.0853385 −0.0426692 0.999089i \(-0.513586\pi\)
−0.0426692 + 0.999089i \(0.513586\pi\)
\(14\) 0 0
\(15\) −12.0000 −0.206559
\(16\) 0 0
\(17\) 24.0000 0.342403 0.171202 0.985236i \(-0.445235\pi\)
0.171202 + 0.985236i \(0.445235\pi\)
\(18\) 0 0
\(19\) 44.0000 0.531279 0.265639 0.964072i \(-0.414417\pi\)
0.265639 + 0.964072i \(0.414417\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 72.0000 0.652741 0.326370 0.945242i \(-0.394174\pi\)
0.326370 + 0.945242i \(0.394174\pi\)
\(24\) 0 0
\(25\) −109.000 −0.872000
\(26\) 0 0
\(27\) −27.0000 −0.192450
\(28\) 0 0
\(29\) −38.0000 −0.243325 −0.121662 0.992572i \(-0.538823\pi\)
−0.121662 + 0.992572i \(0.538823\pi\)
\(30\) 0 0
\(31\) 184.000 1.06604 0.533022 0.846101i \(-0.321056\pi\)
0.533022 + 0.846101i \(0.321056\pi\)
\(32\) 0 0
\(33\) 60.0000 0.316505
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −30.0000 −0.133296 −0.0666482 0.997777i \(-0.521231\pi\)
−0.0666482 + 0.997777i \(0.521231\pi\)
\(38\) 0 0
\(39\) 12.0000 0.0492702
\(40\) 0 0
\(41\) −216.000 −0.822769 −0.411385 0.911462i \(-0.634955\pi\)
−0.411385 + 0.911462i \(0.634955\pi\)
\(42\) 0 0
\(43\) −164.000 −0.581622 −0.290811 0.956780i \(-0.593925\pi\)
−0.290811 + 0.956780i \(0.593925\pi\)
\(44\) 0 0
\(45\) 36.0000 0.119257
\(46\) 0 0
\(47\) 520.000 1.61383 0.806913 0.590671i \(-0.201137\pi\)
0.806913 + 0.590671i \(0.201137\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) −72.0000 −0.197687
\(52\) 0 0
\(53\) −146.000 −0.378389 −0.189195 0.981940i \(-0.560588\pi\)
−0.189195 + 0.981940i \(0.560588\pi\)
\(54\) 0 0
\(55\) −80.0000 −0.196131
\(56\) 0 0
\(57\) −132.000 −0.306734
\(58\) 0 0
\(59\) 460.000 1.01503 0.507516 0.861642i \(-0.330564\pi\)
0.507516 + 0.861642i \(0.330564\pi\)
\(60\) 0 0
\(61\) 628.000 1.31815 0.659075 0.752077i \(-0.270948\pi\)
0.659075 + 0.752077i \(0.270948\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −16.0000 −0.0305316
\(66\) 0 0
\(67\) 556.000 1.01382 0.506912 0.861998i \(-0.330787\pi\)
0.506912 + 0.861998i \(0.330787\pi\)
\(68\) 0 0
\(69\) −216.000 −0.376860
\(70\) 0 0
\(71\) 592.000 0.989542 0.494771 0.869023i \(-0.335252\pi\)
0.494771 + 0.869023i \(0.335252\pi\)
\(72\) 0 0
\(73\) 1024.00 1.64178 0.820891 0.571084i \(-0.193477\pi\)
0.820891 + 0.571084i \(0.193477\pi\)
\(74\) 0 0
\(75\) 327.000 0.503449
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −104.000 −0.148113 −0.0740564 0.997254i \(-0.523594\pi\)
−0.0740564 + 0.997254i \(0.523594\pi\)
\(80\) 0 0
\(81\) 81.0000 0.111111
\(82\) 0 0
\(83\) −324.000 −0.428477 −0.214239 0.976781i \(-0.568727\pi\)
−0.214239 + 0.976781i \(0.568727\pi\)
\(84\) 0 0
\(85\) 96.0000 0.122502
\(86\) 0 0
\(87\) 114.000 0.140484
\(88\) 0 0
\(89\) 896.000 1.06714 0.533572 0.845755i \(-0.320849\pi\)
0.533572 + 0.845755i \(0.320849\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −552.000 −0.615481
\(94\) 0 0
\(95\) 176.000 0.190076
\(96\) 0 0
\(97\) −920.000 −0.963009 −0.481504 0.876444i \(-0.659909\pi\)
−0.481504 + 0.876444i \(0.659909\pi\)
\(98\) 0 0
\(99\) −180.000 −0.182734
\(100\) 0 0
\(101\) 1108.00 1.09159 0.545793 0.837920i \(-0.316229\pi\)
0.545793 + 0.837920i \(0.316229\pi\)
\(102\) 0 0
\(103\) 1448.00 1.38520 0.692600 0.721321i \(-0.256465\pi\)
0.692600 + 0.721321i \(0.256465\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1316.00 1.18900 0.594498 0.804097i \(-0.297351\pi\)
0.594498 + 0.804097i \(0.297351\pi\)
\(108\) 0 0
\(109\) −86.0000 −0.0755716 −0.0377858 0.999286i \(-0.512030\pi\)
−0.0377858 + 0.999286i \(0.512030\pi\)
\(110\) 0 0
\(111\) 90.0000 0.0769588
\(112\) 0 0
\(113\) 1778.00 1.48018 0.740089 0.672509i \(-0.234783\pi\)
0.740089 + 0.672509i \(0.234783\pi\)
\(114\) 0 0
\(115\) 288.000 0.233532
\(116\) 0 0
\(117\) −36.0000 −0.0284462
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −931.000 −0.699474
\(122\) 0 0
\(123\) 648.000 0.475026
\(124\) 0 0
\(125\) −936.000 −0.669747
\(126\) 0 0
\(127\) −928.000 −0.648399 −0.324200 0.945989i \(-0.605095\pi\)
−0.324200 + 0.945989i \(0.605095\pi\)
\(128\) 0 0
\(129\) 492.000 0.335800
\(130\) 0 0
\(131\) 1404.00 0.936397 0.468199 0.883623i \(-0.344903\pi\)
0.468199 + 0.883623i \(0.344903\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −108.000 −0.0688530
\(136\) 0 0
\(137\) −1370.00 −0.854358 −0.427179 0.904167i \(-0.640493\pi\)
−0.427179 + 0.904167i \(0.640493\pi\)
\(138\) 0 0
\(139\) 516.000 0.314867 0.157434 0.987530i \(-0.449678\pi\)
0.157434 + 0.987530i \(0.449678\pi\)
\(140\) 0 0
\(141\) −1560.00 −0.931743
\(142\) 0 0
\(143\) 80.0000 0.0467828
\(144\) 0 0
\(145\) −152.000 −0.0870546
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 1390.00 0.764250 0.382125 0.924111i \(-0.375192\pi\)
0.382125 + 0.924111i \(0.375192\pi\)
\(150\) 0 0
\(151\) 136.000 0.0732949 0.0366474 0.999328i \(-0.488332\pi\)
0.0366474 + 0.999328i \(0.488332\pi\)
\(152\) 0 0
\(153\) 216.000 0.114134
\(154\) 0 0
\(155\) 736.000 0.381400
\(156\) 0 0
\(157\) −148.000 −0.0752337 −0.0376168 0.999292i \(-0.511977\pi\)
−0.0376168 + 0.999292i \(0.511977\pi\)
\(158\) 0 0
\(159\) 438.000 0.218463
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −1212.00 −0.582400 −0.291200 0.956662i \(-0.594054\pi\)
−0.291200 + 0.956662i \(0.594054\pi\)
\(164\) 0 0
\(165\) 240.000 0.113236
\(166\) 0 0
\(167\) 1976.00 0.915614 0.457807 0.889052i \(-0.348635\pi\)
0.457807 + 0.889052i \(0.348635\pi\)
\(168\) 0 0
\(169\) −2181.00 −0.992717
\(170\) 0 0
\(171\) 396.000 0.177093
\(172\) 0 0
\(173\) −2692.00 −1.18306 −0.591529 0.806284i \(-0.701475\pi\)
−0.591529 + 0.806284i \(0.701475\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −1380.00 −0.586029
\(178\) 0 0
\(179\) −2580.00 −1.07731 −0.538654 0.842527i \(-0.681067\pi\)
−0.538654 + 0.842527i \(0.681067\pi\)
\(180\) 0 0
\(181\) −2036.00 −0.836103 −0.418052 0.908423i \(-0.637287\pi\)
−0.418052 + 0.908423i \(0.637287\pi\)
\(182\) 0 0
\(183\) −1884.00 −0.761034
\(184\) 0 0
\(185\) −120.000 −0.0476896
\(186\) 0 0
\(187\) −480.000 −0.187706
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 3960.00 1.50019 0.750093 0.661332i \(-0.230009\pi\)
0.750093 + 0.661332i \(0.230009\pi\)
\(192\) 0 0
\(193\) 2.00000 0.000745923 0 0.000372962 1.00000i \(-0.499881\pi\)
0.000372962 1.00000i \(0.499881\pi\)
\(194\) 0 0
\(195\) 48.0000 0.0176274
\(196\) 0 0
\(197\) 3774.00 1.36491 0.682453 0.730930i \(-0.260913\pi\)
0.682453 + 0.730930i \(0.260913\pi\)
\(198\) 0 0
\(199\) −3560.00 −1.26815 −0.634075 0.773272i \(-0.718619\pi\)
−0.634075 + 0.773272i \(0.718619\pi\)
\(200\) 0 0
\(201\) −1668.00 −0.585332
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −864.000 −0.294363
\(206\) 0 0
\(207\) 648.000 0.217580
\(208\) 0 0
\(209\) −880.000 −0.291248
\(210\) 0 0
\(211\) −2692.00 −0.878317 −0.439159 0.898410i \(-0.644723\pi\)
−0.439159 + 0.898410i \(0.644723\pi\)
\(212\) 0 0
\(213\) −1776.00 −0.571312
\(214\) 0 0
\(215\) −656.000 −0.208088
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −3072.00 −0.947884
\(220\) 0 0
\(221\) −96.0000 −0.0292202
\(222\) 0 0
\(223\) 4528.00 1.35972 0.679859 0.733342i \(-0.262041\pi\)
0.679859 + 0.733342i \(0.262041\pi\)
\(224\) 0 0
\(225\) −981.000 −0.290667
\(226\) 0 0
\(227\) −3652.00 −1.06781 −0.533903 0.845546i \(-0.679275\pi\)
−0.533903 + 0.845546i \(0.679275\pi\)
\(228\) 0 0
\(229\) −4804.00 −1.38628 −0.693138 0.720805i \(-0.743772\pi\)
−0.693138 + 0.720805i \(0.743772\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 2758.00 0.775462 0.387731 0.921773i \(-0.373259\pi\)
0.387731 + 0.921773i \(0.373259\pi\)
\(234\) 0 0
\(235\) 2080.00 0.577380
\(236\) 0 0
\(237\) 312.000 0.0855130
\(238\) 0 0
\(239\) 6528.00 1.76678 0.883392 0.468635i \(-0.155254\pi\)
0.883392 + 0.468635i \(0.155254\pi\)
\(240\) 0 0
\(241\) −56.0000 −0.0149680 −0.00748398 0.999972i \(-0.502382\pi\)
−0.00748398 + 0.999972i \(0.502382\pi\)
\(242\) 0 0
\(243\) −243.000 −0.0641500
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −176.000 −0.0453385
\(248\) 0 0
\(249\) 972.000 0.247382
\(250\) 0 0
\(251\) 4900.00 1.23221 0.616106 0.787663i \(-0.288709\pi\)
0.616106 + 0.787663i \(0.288709\pi\)
\(252\) 0 0
\(253\) −1440.00 −0.357834
\(254\) 0 0
\(255\) −288.000 −0.0707265
\(256\) 0 0
\(257\) −6784.00 −1.64659 −0.823296 0.567612i \(-0.807867\pi\)
−0.823296 + 0.567612i \(0.807867\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −342.000 −0.0811083
\(262\) 0 0
\(263\) −4544.00 −1.06538 −0.532690 0.846310i \(-0.678819\pi\)
−0.532690 + 0.846310i \(0.678819\pi\)
\(264\) 0 0
\(265\) −584.000 −0.135377
\(266\) 0 0
\(267\) −2688.00 −0.616116
\(268\) 0 0
\(269\) −4052.00 −0.918419 −0.459210 0.888328i \(-0.651867\pi\)
−0.459210 + 0.888328i \(0.651867\pi\)
\(270\) 0 0
\(271\) −2752.00 −0.616871 −0.308436 0.951245i \(-0.599805\pi\)
−0.308436 + 0.951245i \(0.599805\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 2180.00 0.478033
\(276\) 0 0
\(277\) 4366.00 0.947031 0.473515 0.880786i \(-0.342985\pi\)
0.473515 + 0.880786i \(0.342985\pi\)
\(278\) 0 0
\(279\) 1656.00 0.355348
\(280\) 0 0
\(281\) 7734.00 1.64189 0.820946 0.571006i \(-0.193447\pi\)
0.820946 + 0.571006i \(0.193447\pi\)
\(282\) 0 0
\(283\) −4052.00 −0.851118 −0.425559 0.904931i \(-0.639923\pi\)
−0.425559 + 0.904931i \(0.639923\pi\)
\(284\) 0 0
\(285\) −528.000 −0.109740
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −4337.00 −0.882760
\(290\) 0 0
\(291\) 2760.00 0.555993
\(292\) 0 0
\(293\) −3420.00 −0.681906 −0.340953 0.940080i \(-0.610750\pi\)
−0.340953 + 0.940080i \(0.610750\pi\)
\(294\) 0 0
\(295\) 1840.00 0.363149
\(296\) 0 0
\(297\) 540.000 0.105502
\(298\) 0 0
\(299\) −288.000 −0.0557039
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −3324.00 −0.630227
\(304\) 0 0
\(305\) 2512.00 0.471596
\(306\) 0 0
\(307\) 7324.00 1.36157 0.680786 0.732482i \(-0.261638\pi\)
0.680786 + 0.732482i \(0.261638\pi\)
\(308\) 0 0
\(309\) −4344.00 −0.799746
\(310\) 0 0
\(311\) −4192.00 −0.764330 −0.382165 0.924094i \(-0.624821\pi\)
−0.382165 + 0.924094i \(0.624821\pi\)
\(312\) 0 0
\(313\) −6840.00 −1.23521 −0.617603 0.786490i \(-0.711896\pi\)
−0.617603 + 0.786490i \(0.711896\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 6630.00 1.17469 0.587347 0.809335i \(-0.300172\pi\)
0.587347 + 0.809335i \(0.300172\pi\)
\(318\) 0 0
\(319\) 760.000 0.133391
\(320\) 0 0
\(321\) −3948.00 −0.686467
\(322\) 0 0
\(323\) 1056.00 0.181911
\(324\) 0 0
\(325\) 436.000 0.0744152
\(326\) 0 0
\(327\) 258.000 0.0436313
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −6868.00 −1.14048 −0.570241 0.821478i \(-0.693150\pi\)
−0.570241 + 0.821478i \(0.693150\pi\)
\(332\) 0 0
\(333\) −270.000 −0.0444322
\(334\) 0 0
\(335\) 2224.00 0.362717
\(336\) 0 0
\(337\) −7378.00 −1.19260 −0.596299 0.802763i \(-0.703363\pi\)
−0.596299 + 0.802763i \(0.703363\pi\)
\(338\) 0 0
\(339\) −5334.00 −0.854581
\(340\) 0 0
\(341\) −3680.00 −0.584408
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −864.000 −0.134830
\(346\) 0 0
\(347\) −2676.00 −0.413992 −0.206996 0.978342i \(-0.566369\pi\)
−0.206996 + 0.978342i \(0.566369\pi\)
\(348\) 0 0
\(349\) −5124.00 −0.785907 −0.392953 0.919558i \(-0.628547\pi\)
−0.392953 + 0.919558i \(0.628547\pi\)
\(350\) 0 0
\(351\) 108.000 0.0164234
\(352\) 0 0
\(353\) 4560.00 0.687548 0.343774 0.939052i \(-0.388295\pi\)
0.343774 + 0.939052i \(0.388295\pi\)
\(354\) 0 0
\(355\) 2368.00 0.354029
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 3656.00 0.537483 0.268741 0.963212i \(-0.413392\pi\)
0.268741 + 0.963212i \(0.413392\pi\)
\(360\) 0 0
\(361\) −4923.00 −0.717743
\(362\) 0 0
\(363\) 2793.00 0.403842
\(364\) 0 0
\(365\) 4096.00 0.587382
\(366\) 0 0
\(367\) −1616.00 −0.229849 −0.114924 0.993374i \(-0.536663\pi\)
−0.114924 + 0.993374i \(0.536663\pi\)
\(368\) 0 0
\(369\) −1944.00 −0.274256
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 2734.00 0.379521 0.189760 0.981830i \(-0.439229\pi\)
0.189760 + 0.981830i \(0.439229\pi\)
\(374\) 0 0
\(375\) 2808.00 0.386679
\(376\) 0 0
\(377\) 152.000 0.0207650
\(378\) 0 0
\(379\) −1380.00 −0.187034 −0.0935169 0.995618i \(-0.529811\pi\)
−0.0935169 + 0.995618i \(0.529811\pi\)
\(380\) 0 0
\(381\) 2784.00 0.374353
\(382\) 0 0
\(383\) 6888.00 0.918957 0.459478 0.888189i \(-0.348036\pi\)
0.459478 + 0.888189i \(0.348036\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −1476.00 −0.193874
\(388\) 0 0
\(389\) −2046.00 −0.266674 −0.133337 0.991071i \(-0.542569\pi\)
−0.133337 + 0.991071i \(0.542569\pi\)
\(390\) 0 0
\(391\) 1728.00 0.223501
\(392\) 0 0
\(393\) −4212.00 −0.540629
\(394\) 0 0
\(395\) −416.000 −0.0529905
\(396\) 0 0
\(397\) 3116.00 0.393923 0.196962 0.980411i \(-0.436893\pi\)
0.196962 + 0.980411i \(0.436893\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 2958.00 0.368368 0.184184 0.982892i \(-0.441036\pi\)
0.184184 + 0.982892i \(0.441036\pi\)
\(402\) 0 0
\(403\) −736.000 −0.0909746
\(404\) 0 0
\(405\) 324.000 0.0397523
\(406\) 0 0
\(407\) 600.000 0.0730735
\(408\) 0 0
\(409\) 7944.00 0.960405 0.480202 0.877158i \(-0.340563\pi\)
0.480202 + 0.877158i \(0.340563\pi\)
\(410\) 0 0
\(411\) 4110.00 0.493264
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −1296.00 −0.153297
\(416\) 0 0
\(417\) −1548.00 −0.181789
\(418\) 0 0
\(419\) 4084.00 0.476173 0.238086 0.971244i \(-0.423480\pi\)
0.238086 + 0.971244i \(0.423480\pi\)
\(420\) 0 0
\(421\) −6306.00 −0.730013 −0.365007 0.931005i \(-0.618933\pi\)
−0.365007 + 0.931005i \(0.618933\pi\)
\(422\) 0 0
\(423\) 4680.00 0.537942
\(424\) 0 0
\(425\) −2616.00 −0.298576
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −240.000 −0.0270100
\(430\) 0 0
\(431\) −11824.0 −1.32144 −0.660722 0.750631i \(-0.729750\pi\)
−0.660722 + 0.750631i \(0.729750\pi\)
\(432\) 0 0
\(433\) −4504.00 −0.499881 −0.249940 0.968261i \(-0.580411\pi\)
−0.249940 + 0.968261i \(0.580411\pi\)
\(434\) 0 0
\(435\) 456.000 0.0502610
\(436\) 0 0
\(437\) 3168.00 0.346787
\(438\) 0 0
\(439\) 13056.0 1.41943 0.709714 0.704490i \(-0.248824\pi\)
0.709714 + 0.704490i \(0.248824\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 132.000 0.0141569 0.00707845 0.999975i \(-0.497747\pi\)
0.00707845 + 0.999975i \(0.497747\pi\)
\(444\) 0 0
\(445\) 3584.00 0.381793
\(446\) 0 0
\(447\) −4170.00 −0.441240
\(448\) 0 0
\(449\) 4866.00 0.511449 0.255725 0.966750i \(-0.417686\pi\)
0.255725 + 0.966750i \(0.417686\pi\)
\(450\) 0 0
\(451\) 4320.00 0.451044
\(452\) 0 0
\(453\) −408.000 −0.0423168
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 10106.0 1.03444 0.517220 0.855853i \(-0.326967\pi\)
0.517220 + 0.855853i \(0.326967\pi\)
\(458\) 0 0
\(459\) −648.000 −0.0658955
\(460\) 0 0
\(461\) −18036.0 −1.82217 −0.911085 0.412219i \(-0.864754\pi\)
−0.911085 + 0.412219i \(0.864754\pi\)
\(462\) 0 0
\(463\) 5288.00 0.530787 0.265393 0.964140i \(-0.414498\pi\)
0.265393 + 0.964140i \(0.414498\pi\)
\(464\) 0 0
\(465\) −2208.00 −0.220201
\(466\) 0 0
\(467\) 15164.0 1.50258 0.751291 0.659971i \(-0.229431\pi\)
0.751291 + 0.659971i \(0.229431\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 444.000 0.0434362
\(472\) 0 0
\(473\) 3280.00 0.318847
\(474\) 0 0
\(475\) −4796.00 −0.463275
\(476\) 0 0
\(477\) −1314.00 −0.126130
\(478\) 0 0
\(479\) 7896.00 0.753189 0.376594 0.926378i \(-0.377095\pi\)
0.376594 + 0.926378i \(0.377095\pi\)
\(480\) 0 0
\(481\) 120.000 0.0113753
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −3680.00 −0.344536
\(486\) 0 0
\(487\) 2920.00 0.271700 0.135850 0.990729i \(-0.456624\pi\)
0.135850 + 0.990729i \(0.456624\pi\)
\(488\) 0 0
\(489\) 3636.00 0.336249
\(490\) 0 0
\(491\) −7932.00 −0.729055 −0.364528 0.931193i \(-0.618770\pi\)
−0.364528 + 0.931193i \(0.618770\pi\)
\(492\) 0 0
\(493\) −912.000 −0.0833152
\(494\) 0 0
\(495\) −720.000 −0.0653770
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −2004.00 −0.179782 −0.0898911 0.995952i \(-0.528652\pi\)
−0.0898911 + 0.995952i \(0.528652\pi\)
\(500\) 0 0
\(501\) −5928.00 −0.528630
\(502\) 0 0
\(503\) 4496.00 0.398542 0.199271 0.979944i \(-0.436143\pi\)
0.199271 + 0.979944i \(0.436143\pi\)
\(504\) 0 0
\(505\) 4432.00 0.390537
\(506\) 0 0
\(507\) 6543.00 0.573146
\(508\) 0 0
\(509\) 12620.0 1.09896 0.549481 0.835506i \(-0.314825\pi\)
0.549481 + 0.835506i \(0.314825\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −1188.00 −0.102245
\(514\) 0 0
\(515\) 5792.00 0.495584
\(516\) 0 0
\(517\) −10400.0 −0.884703
\(518\) 0 0
\(519\) 8076.00 0.683039
\(520\) 0 0
\(521\) 18008.0 1.51429 0.757145 0.653247i \(-0.226594\pi\)
0.757145 + 0.653247i \(0.226594\pi\)
\(522\) 0 0
\(523\) 13292.0 1.11132 0.555658 0.831411i \(-0.312466\pi\)
0.555658 + 0.831411i \(0.312466\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 4416.00 0.365017
\(528\) 0 0
\(529\) −6983.00 −0.573929
\(530\) 0 0
\(531\) 4140.00 0.338344
\(532\) 0 0
\(533\) 864.000 0.0702139
\(534\) 0 0
\(535\) 5264.00 0.425388
\(536\) 0 0
\(537\) 7740.00 0.621984
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −8570.00 −0.681059 −0.340530 0.940234i \(-0.610606\pi\)
−0.340530 + 0.940234i \(0.610606\pi\)
\(542\) 0 0
\(543\) 6108.00 0.482724
\(544\) 0 0
\(545\) −344.000 −0.0270373
\(546\) 0 0
\(547\) −1916.00 −0.149766 −0.0748832 0.997192i \(-0.523858\pi\)
−0.0748832 + 0.997192i \(0.523858\pi\)
\(548\) 0 0
\(549\) 5652.00 0.439383
\(550\) 0 0
\(551\) −1672.00 −0.129273
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 360.000 0.0275336
\(556\) 0 0
\(557\) 19926.0 1.51578 0.757892 0.652380i \(-0.226229\pi\)
0.757892 + 0.652380i \(0.226229\pi\)
\(558\) 0 0
\(559\) 656.000 0.0496348
\(560\) 0 0
\(561\) 1440.00 0.108372
\(562\) 0 0
\(563\) 4244.00 0.317697 0.158848 0.987303i \(-0.449222\pi\)
0.158848 + 0.987303i \(0.449222\pi\)
\(564\) 0 0
\(565\) 7112.00 0.529565
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −22794.0 −1.67939 −0.839696 0.543057i \(-0.817267\pi\)
−0.839696 + 0.543057i \(0.817267\pi\)
\(570\) 0 0
\(571\) 14028.0 1.02811 0.514057 0.857756i \(-0.328142\pi\)
0.514057 + 0.857756i \(0.328142\pi\)
\(572\) 0 0
\(573\) −11880.0 −0.866133
\(574\) 0 0
\(575\) −7848.00 −0.569190
\(576\) 0 0
\(577\) 8368.00 0.603751 0.301876 0.953347i \(-0.402387\pi\)
0.301876 + 0.953347i \(0.402387\pi\)
\(578\) 0 0
\(579\) −6.00000 −0.000430659 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 2920.00 0.207434
\(584\) 0 0
\(585\) −144.000 −0.0101772
\(586\) 0 0
\(587\) 52.0000 0.00365634 0.00182817 0.999998i \(-0.499418\pi\)
0.00182817 + 0.999998i \(0.499418\pi\)
\(588\) 0 0
\(589\) 8096.00 0.566366
\(590\) 0 0
\(591\) −11322.0 −0.788029
\(592\) 0 0
\(593\) 5808.00 0.402202 0.201101 0.979570i \(-0.435548\pi\)
0.201101 + 0.979570i \(0.435548\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 10680.0 0.732166
\(598\) 0 0
\(599\) −10464.0 −0.713769 −0.356884 0.934149i \(-0.616161\pi\)
−0.356884 + 0.934149i \(0.616161\pi\)
\(600\) 0 0
\(601\) 1184.00 0.0803600 0.0401800 0.999192i \(-0.487207\pi\)
0.0401800 + 0.999192i \(0.487207\pi\)
\(602\) 0 0
\(603\) 5004.00 0.337941
\(604\) 0 0
\(605\) −3724.00 −0.250251
\(606\) 0 0
\(607\) 13152.0 0.879445 0.439723 0.898134i \(-0.355077\pi\)
0.439723 + 0.898134i \(0.355077\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −2080.00 −0.137721
\(612\) 0 0
\(613\) −18334.0 −1.20800 −0.603999 0.796985i \(-0.706427\pi\)
−0.603999 + 0.796985i \(0.706427\pi\)
\(614\) 0 0
\(615\) 2592.00 0.169950
\(616\) 0 0
\(617\) −8122.00 −0.529950 −0.264975 0.964255i \(-0.585364\pi\)
−0.264975 + 0.964255i \(0.585364\pi\)
\(618\) 0 0
\(619\) 5980.00 0.388298 0.194149 0.980972i \(-0.437805\pi\)
0.194149 + 0.980972i \(0.437805\pi\)
\(620\) 0 0
\(621\) −1944.00 −0.125620
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 9881.00 0.632384
\(626\) 0 0
\(627\) 2640.00 0.168152
\(628\) 0 0
\(629\) −720.000 −0.0456411
\(630\) 0 0
\(631\) 12528.0 0.790383 0.395192 0.918599i \(-0.370678\pi\)
0.395192 + 0.918599i \(0.370678\pi\)
\(632\) 0 0
\(633\) 8076.00 0.507097
\(634\) 0 0
\(635\) −3712.00 −0.231978
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 5328.00 0.329847
\(640\) 0 0
\(641\) 20798.0 1.28155 0.640773 0.767730i \(-0.278614\pi\)
0.640773 + 0.767730i \(0.278614\pi\)
\(642\) 0 0
\(643\) −1932.00 −0.118492 −0.0592462 0.998243i \(-0.518870\pi\)
−0.0592462 + 0.998243i \(0.518870\pi\)
\(644\) 0 0
\(645\) 1968.00 0.120139
\(646\) 0 0
\(647\) −8424.00 −0.511873 −0.255936 0.966694i \(-0.582384\pi\)
−0.255936 + 0.966694i \(0.582384\pi\)
\(648\) 0 0
\(649\) −9200.00 −0.556443
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −17750.0 −1.06372 −0.531862 0.846831i \(-0.678507\pi\)
−0.531862 + 0.846831i \(0.678507\pi\)
\(654\) 0 0
\(655\) 5616.00 0.335016
\(656\) 0 0
\(657\) 9216.00 0.547261
\(658\) 0 0
\(659\) −27580.0 −1.63029 −0.815147 0.579254i \(-0.803344\pi\)
−0.815147 + 0.579254i \(0.803344\pi\)
\(660\) 0 0
\(661\) −9292.00 −0.546773 −0.273386 0.961904i \(-0.588144\pi\)
−0.273386 + 0.961904i \(0.588144\pi\)
\(662\) 0 0
\(663\) 288.000 0.0168703
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −2736.00 −0.158828
\(668\) 0 0
\(669\) −13584.0 −0.785034
\(670\) 0 0
\(671\) −12560.0 −0.722613
\(672\) 0 0
\(673\) 11486.0 0.657879 0.328940 0.944351i \(-0.393309\pi\)
0.328940 + 0.944351i \(0.393309\pi\)
\(674\) 0 0
\(675\) 2943.00 0.167816
\(676\) 0 0
\(677\) 7116.00 0.403974 0.201987 0.979388i \(-0.435260\pi\)
0.201987 + 0.979388i \(0.435260\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 10956.0 0.616498
\(682\) 0 0
\(683\) −7612.00 −0.426450 −0.213225 0.977003i \(-0.568397\pi\)
−0.213225 + 0.977003i \(0.568397\pi\)
\(684\) 0 0
\(685\) −5480.00 −0.305664
\(686\) 0 0
\(687\) 14412.0 0.800367
\(688\) 0 0
\(689\) 584.000 0.0322912
\(690\) 0 0
\(691\) −21572.0 −1.18761 −0.593804 0.804609i \(-0.702375\pi\)
−0.593804 + 0.804609i \(0.702375\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 2064.00 0.112650
\(696\) 0 0
\(697\) −5184.00 −0.281719
\(698\) 0 0
\(699\) −8274.00 −0.447713
\(700\) 0 0
\(701\) −1702.00 −0.0917028 −0.0458514 0.998948i \(-0.514600\pi\)
−0.0458514 + 0.998948i \(0.514600\pi\)
\(702\) 0 0
\(703\) −1320.00 −0.0708176
\(704\) 0 0
\(705\) −6240.00 −0.333350
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 6370.00 0.337419 0.168710 0.985666i \(-0.446040\pi\)
0.168710 + 0.985666i \(0.446040\pi\)
\(710\) 0 0
\(711\) −936.000 −0.0493709
\(712\) 0 0
\(713\) 13248.0 0.695851
\(714\) 0 0
\(715\) 320.000 0.0167375
\(716\) 0 0
\(717\) −19584.0 −1.02005
\(718\) 0 0
\(719\) −8808.00 −0.456861 −0.228430 0.973560i \(-0.573359\pi\)
−0.228430 + 0.973560i \(0.573359\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 168.000 0.00864175
\(724\) 0 0
\(725\) 4142.00 0.212179
\(726\) 0 0
\(727\) 17768.0 0.906436 0.453218 0.891400i \(-0.350276\pi\)
0.453218 + 0.891400i \(0.350276\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) 0 0
\(731\) −3936.00 −0.199149
\(732\) 0 0
\(733\) −5564.00 −0.280370 −0.140185 0.990125i \(-0.544770\pi\)
−0.140185 + 0.990125i \(0.544770\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −11120.0 −0.555781
\(738\) 0 0
\(739\) −17564.0 −0.874293 −0.437146 0.899390i \(-0.644011\pi\)
−0.437146 + 0.899390i \(0.644011\pi\)
\(740\) 0 0
\(741\) 528.000 0.0261762
\(742\) 0 0
\(743\) −38280.0 −1.89012 −0.945059 0.326901i \(-0.893996\pi\)
−0.945059 + 0.326901i \(0.893996\pi\)
\(744\) 0 0
\(745\) 5560.00 0.273426
\(746\) 0 0
\(747\) −2916.00 −0.142826
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 36192.0 1.75854 0.879271 0.476322i \(-0.158030\pi\)
0.879271 + 0.476322i \(0.158030\pi\)
\(752\) 0 0
\(753\) −14700.0 −0.711418
\(754\) 0 0
\(755\) 544.000 0.0262228
\(756\) 0 0
\(757\) −14.0000 −0.000672178 0 −0.000336089 1.00000i \(-0.500107\pi\)
−0.000336089 1.00000i \(0.500107\pi\)
\(758\) 0 0
\(759\) 4320.00 0.206596
\(760\) 0 0
\(761\) −26504.0 −1.26251 −0.631254 0.775576i \(-0.717460\pi\)
−0.631254 + 0.775576i \(0.717460\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 864.000 0.0408340
\(766\) 0 0
\(767\) −1840.00 −0.0866213
\(768\) 0 0
\(769\) 40184.0 1.88436 0.942180 0.335109i \(-0.108773\pi\)
0.942180 + 0.335109i \(0.108773\pi\)
\(770\) 0 0
\(771\) 20352.0 0.950661
\(772\) 0 0
\(773\) −35340.0 −1.64436 −0.822181 0.569226i \(-0.807243\pi\)
−0.822181 + 0.569226i \(0.807243\pi\)
\(774\) 0 0
\(775\) −20056.0 −0.929591
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −9504.00 −0.437120
\(780\) 0 0
\(781\) −11840.0 −0.542469
\(782\) 0 0
\(783\) 1026.00 0.0468279
\(784\) 0 0
\(785\) −592.000 −0.0269164
\(786\) 0 0
\(787\) −14852.0 −0.672702 −0.336351 0.941737i \(-0.609193\pi\)
−0.336351 + 0.941737i \(0.609193\pi\)
\(788\) 0 0
\(789\) 13632.0 0.615098
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −2512.00 −0.112489
\(794\) 0 0
\(795\) 1752.00 0.0781598
\(796\) 0 0
\(797\) 19788.0 0.879457 0.439728 0.898131i \(-0.355075\pi\)
0.439728 + 0.898131i \(0.355075\pi\)
\(798\) 0 0
\(799\) 12480.0 0.552579
\(800\) 0 0
\(801\) 8064.00 0.355715
\(802\) 0 0
\(803\) −20480.0 −0.900029
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 12156.0 0.530250
\(808\) 0 0
\(809\) 16986.0 0.738190 0.369095 0.929392i \(-0.379668\pi\)
0.369095 + 0.929392i \(0.379668\pi\)
\(810\) 0 0
\(811\) −26596.0 −1.15156 −0.575778 0.817606i \(-0.695301\pi\)
−0.575778 + 0.817606i \(0.695301\pi\)
\(812\) 0 0
\(813\) 8256.00 0.356151
\(814\) 0 0
\(815\) −4848.00 −0.208366
\(816\) 0 0
\(817\) −7216.00 −0.309004
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −34898.0 −1.48349 −0.741747 0.670680i \(-0.766002\pi\)
−0.741747 + 0.670680i \(0.766002\pi\)
\(822\) 0 0
\(823\) 12928.0 0.547560 0.273780 0.961792i \(-0.411726\pi\)
0.273780 + 0.961792i \(0.411726\pi\)
\(824\) 0 0
\(825\) −6540.00 −0.275992
\(826\) 0 0
\(827\) −43164.0 −1.81494 −0.907472 0.420112i \(-0.861991\pi\)
−0.907472 + 0.420112i \(0.861991\pi\)
\(828\) 0 0
\(829\) −41228.0 −1.72727 −0.863635 0.504117i \(-0.831818\pi\)
−0.863635 + 0.504117i \(0.831818\pi\)
\(830\) 0 0
\(831\) −13098.0 −0.546768
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 7904.00 0.327580
\(836\) 0 0
\(837\) −4968.00 −0.205160
\(838\) 0 0
\(839\) −1368.00 −0.0562915 −0.0281458 0.999604i \(-0.508960\pi\)
−0.0281458 + 0.999604i \(0.508960\pi\)
\(840\) 0 0
\(841\) −22945.0 −0.940793
\(842\) 0 0
\(843\) −23202.0 −0.947947
\(844\) 0 0
\(845\) −8724.00 −0.355165
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 12156.0 0.491393
\(850\) 0 0
\(851\) −2160.00 −0.0870080
\(852\) 0 0
\(853\) 5276.00 0.211778 0.105889 0.994378i \(-0.466231\pi\)
0.105889 + 0.994378i \(0.466231\pi\)
\(854\) 0 0
\(855\) 1584.00 0.0633587
\(856\) 0 0
\(857\) 840.000 0.0334817 0.0167409 0.999860i \(-0.494671\pi\)
0.0167409 + 0.999860i \(0.494671\pi\)
\(858\) 0 0
\(859\) −26028.0 −1.03383 −0.516917 0.856035i \(-0.672921\pi\)
−0.516917 + 0.856035i \(0.672921\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −29448.0 −1.16155 −0.580777 0.814063i \(-0.697251\pi\)
−0.580777 + 0.814063i \(0.697251\pi\)
\(864\) 0 0
\(865\) −10768.0 −0.423264
\(866\) 0 0
\(867\) 13011.0 0.509662
\(868\) 0 0
\(869\) 2080.00 0.0811958
\(870\) 0 0
\(871\) −2224.00 −0.0865182
\(872\) 0 0
\(873\) −8280.00 −0.321003
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 25866.0 0.995932 0.497966 0.867196i \(-0.334080\pi\)
0.497966 + 0.867196i \(0.334080\pi\)
\(878\) 0 0
\(879\) 10260.0 0.393699
\(880\) 0 0
\(881\) 9472.00 0.362225 0.181112 0.983462i \(-0.442030\pi\)
0.181112 + 0.983462i \(0.442030\pi\)
\(882\) 0 0
\(883\) 49372.0 1.88165 0.940827 0.338888i \(-0.110051\pi\)
0.940827 + 0.338888i \(0.110051\pi\)
\(884\) 0 0
\(885\) −5520.00 −0.209664
\(886\) 0 0
\(887\) −11160.0 −0.422453 −0.211227 0.977437i \(-0.567746\pi\)
−0.211227 + 0.977437i \(0.567746\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −1620.00 −0.0609114
\(892\) 0 0
\(893\) 22880.0 0.857391
\(894\) 0 0
\(895\) −10320.0 −0.385430
\(896\) 0 0
\(897\) 864.000 0.0321607
\(898\) 0 0
\(899\) −6992.00 −0.259395
\(900\) 0 0
\(901\) −3504.00 −0.129562
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −8144.00 −0.299133
\(906\) 0 0
\(907\) 22708.0 0.831319 0.415660 0.909520i \(-0.363551\pi\)
0.415660 + 0.909520i \(0.363551\pi\)
\(908\) 0 0
\(909\) 9972.00 0.363862
\(910\) 0 0
\(911\) −16192.0 −0.588875 −0.294437 0.955671i \(-0.595132\pi\)
−0.294437 + 0.955671i \(0.595132\pi\)
\(912\) 0 0
\(913\) 6480.00 0.234892
\(914\) 0 0
\(915\) −7536.00 −0.272276
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −46320.0 −1.66263 −0.831314 0.555802i \(-0.812411\pi\)
−0.831314 + 0.555802i \(0.812411\pi\)
\(920\) 0 0
\(921\) −21972.0 −0.786104
\(922\) 0 0
\(923\) −2368.00 −0.0844460
\(924\) 0 0
\(925\) 3270.00 0.116235
\(926\) 0 0
\(927\) 13032.0 0.461734
\(928\) 0 0
\(929\) −2280.00 −0.0805214 −0.0402607 0.999189i \(-0.512819\pi\)
−0.0402607 + 0.999189i \(0.512819\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 12576.0 0.441286
\(934\) 0 0
\(935\) −1920.00 −0.0671558
\(936\) 0 0
\(937\) 49056.0 1.71034 0.855171 0.518347i \(-0.173452\pi\)
0.855171 + 0.518347i \(0.173452\pi\)
\(938\) 0 0
\(939\) 20520.0 0.713147
\(940\) 0 0
\(941\) −24876.0 −0.861779 −0.430890 0.902405i \(-0.641800\pi\)
−0.430890 + 0.902405i \(0.641800\pi\)
\(942\) 0 0
\(943\) −15552.0 −0.537055
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 23428.0 0.803915 0.401958 0.915658i \(-0.368330\pi\)
0.401958 + 0.915658i \(0.368330\pi\)
\(948\) 0 0
\(949\) −4096.00 −0.140107
\(950\) 0 0
\(951\) −19890.0 −0.678210
\(952\) 0 0
\(953\) −6678.00 −0.226990 −0.113495 0.993539i \(-0.536205\pi\)
−0.113495 + 0.993539i \(0.536205\pi\)
\(954\) 0 0
\(955\) 15840.0 0.536723
\(956\) 0 0
\(957\) −2280.00 −0.0770135
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 4065.00 0.136451
\(962\) 0 0
\(963\) 11844.0 0.396332
\(964\) 0 0
\(965\) 8.00000 0.000266870 0
\(966\) 0 0
\(967\) 15544.0 0.516920 0.258460 0.966022i \(-0.416785\pi\)
0.258460 + 0.966022i \(0.416785\pi\)
\(968\) 0 0
\(969\) −3168.00 −0.105027
\(970\) 0 0
\(971\) −31124.0 −1.02865 −0.514324 0.857596i \(-0.671957\pi\)
−0.514324 + 0.857596i \(0.671957\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) −1308.00 −0.0429636
\(976\) 0 0
\(977\) 50062.0 1.63933 0.819665 0.572843i \(-0.194160\pi\)
0.819665 + 0.572843i \(0.194160\pi\)
\(978\) 0 0
\(979\) −17920.0 −0.585011
\(980\) 0 0
\(981\) −774.000 −0.0251905
\(982\) 0 0
\(983\) 328.000 0.0106425 0.00532125 0.999986i \(-0.498306\pi\)
0.00532125 + 0.999986i \(0.498306\pi\)
\(984\) 0 0
\(985\) 15096.0 0.488323
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −11808.0 −0.379649
\(990\) 0 0
\(991\) −20872.0 −0.669042 −0.334521 0.942388i \(-0.608575\pi\)
−0.334521 + 0.942388i \(0.608575\pi\)
\(992\) 0 0
\(993\) 20604.0 0.658457
\(994\) 0 0
\(995\) −14240.0 −0.453707
\(996\) 0 0
\(997\) −46924.0 −1.49057 −0.745285 0.666746i \(-0.767687\pi\)
−0.745285 + 0.666746i \(0.767687\pi\)
\(998\) 0 0
\(999\) 810.000 0.0256529
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 588.4.a.b.1.1 1
3.2 odd 2 1764.4.a.d.1.1 1
4.3 odd 2 2352.4.a.be.1.1 1
7.2 even 3 588.4.i.g.361.1 2
7.3 odd 6 588.4.i.b.373.1 2
7.4 even 3 588.4.i.g.373.1 2
7.5 odd 6 588.4.i.b.361.1 2
7.6 odd 2 588.4.a.e.1.1 yes 1
21.2 odd 6 1764.4.k.j.361.1 2
21.5 even 6 1764.4.k.g.361.1 2
21.11 odd 6 1764.4.k.j.1549.1 2
21.17 even 6 1764.4.k.g.1549.1 2
21.20 even 2 1764.4.a.i.1.1 1
28.27 even 2 2352.4.a.g.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
588.4.a.b.1.1 1 1.1 even 1 trivial
588.4.a.e.1.1 yes 1 7.6 odd 2
588.4.i.b.361.1 2 7.5 odd 6
588.4.i.b.373.1 2 7.3 odd 6
588.4.i.g.361.1 2 7.2 even 3
588.4.i.g.373.1 2 7.4 even 3
1764.4.a.d.1.1 1 3.2 odd 2
1764.4.a.i.1.1 1 21.20 even 2
1764.4.k.g.361.1 2 21.5 even 6
1764.4.k.g.1549.1 2 21.17 even 6
1764.4.k.j.361.1 2 21.2 odd 6
1764.4.k.j.1549.1 2 21.11 odd 6
2352.4.a.g.1.1 1 28.27 even 2
2352.4.a.be.1.1 1 4.3 odd 2