Properties

Label 1008.4.a.c.1.1
Level $1008$
Weight $4$
Character 1008.1
Self dual yes
Analytic conductor $59.474$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1008.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(59.4739252858\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 7)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1008.1

$q$-expansion

\(f(q)\) \(=\) \(q-16.0000 q^{5} +7.00000 q^{7} +O(q^{10})\) \(q-16.0000 q^{5} +7.00000 q^{7} -8.00000 q^{11} +28.0000 q^{13} -54.0000 q^{17} +110.000 q^{19} +48.0000 q^{23} +131.000 q^{25} +110.000 q^{29} -12.0000 q^{31} -112.000 q^{35} -246.000 q^{37} -182.000 q^{41} -128.000 q^{43} +324.000 q^{47} +49.0000 q^{49} +162.000 q^{53} +128.000 q^{55} +810.000 q^{59} -488.000 q^{61} -448.000 q^{65} -244.000 q^{67} -768.000 q^{71} -702.000 q^{73} -56.0000 q^{77} -440.000 q^{79} -1302.00 q^{83} +864.000 q^{85} -730.000 q^{89} +196.000 q^{91} -1760.00 q^{95} +294.000 q^{97} +O(q^{100})\)

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
\(3\) 0 0
\(4\) 0 0
\(5\) −16.0000 −1.43108 −0.715542 0.698570i \(-0.753820\pi\)
−0.715542 + 0.698570i \(0.753820\pi\)
\(6\) 0 0
\(7\) 7.00000 0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −8.00000 −0.219281 −0.109640 0.993971i \(-0.534970\pi\)
−0.109640 + 0.993971i \(0.534970\pi\)
\(12\) 0 0
\(13\) 28.0000 0.597369 0.298685 0.954352i \(-0.403452\pi\)
0.298685 + 0.954352i \(0.403452\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −54.0000 −0.770407 −0.385204 0.922832i \(-0.625869\pi\)
−0.385204 + 0.922832i \(0.625869\pi\)
\(18\) 0 0
\(19\) 110.000 1.32820 0.664098 0.747645i \(-0.268816\pi\)
0.664098 + 0.747645i \(0.268816\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 48.0000 0.435161 0.217580 0.976042i \(-0.430184\pi\)
0.217580 + 0.976042i \(0.430184\pi\)
\(24\) 0 0
\(25\) 131.000 1.04800
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 110.000 0.704362 0.352181 0.935932i \(-0.385440\pi\)
0.352181 + 0.935932i \(0.385440\pi\)
\(30\) 0 0
\(31\) −12.0000 −0.0695246 −0.0347623 0.999396i \(-0.511067\pi\)
−0.0347623 + 0.999396i \(0.511067\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −112.000 −0.540899
\(36\) 0 0
\(37\) −246.000 −1.09303 −0.546516 0.837449i \(-0.684046\pi\)
−0.546516 + 0.837449i \(0.684046\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −182.000 −0.693259 −0.346630 0.938002i \(-0.612674\pi\)
−0.346630 + 0.938002i \(0.612674\pi\)
\(42\) 0 0
\(43\) −128.000 −0.453949 −0.226975 0.973901i \(-0.572883\pi\)
−0.226975 + 0.973901i \(0.572883\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 324.000 1.00554 0.502769 0.864421i \(-0.332315\pi\)
0.502769 + 0.864421i \(0.332315\pi\)
\(48\) 0 0
\(49\) 49.0000 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 162.000 0.419857 0.209928 0.977717i \(-0.432677\pi\)
0.209928 + 0.977717i \(0.432677\pi\)
\(54\) 0 0
\(55\) 128.000 0.313809
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 810.000 1.78734 0.893670 0.448725i \(-0.148122\pi\)
0.893670 + 0.448725i \(0.148122\pi\)
\(60\) 0 0
\(61\) −488.000 −1.02430 −0.512148 0.858898i \(-0.671150\pi\)
−0.512148 + 0.858898i \(0.671150\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −448.000 −0.854886
\(66\) 0 0
\(67\) −244.000 −0.444916 −0.222458 0.974942i \(-0.571408\pi\)
−0.222458 + 0.974942i \(0.571408\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −768.000 −1.28373 −0.641865 0.766818i \(-0.721839\pi\)
−0.641865 + 0.766818i \(0.721839\pi\)
\(72\) 0 0
\(73\) −702.000 −1.12552 −0.562759 0.826621i \(-0.690260\pi\)
−0.562759 + 0.826621i \(0.690260\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −56.0000 −0.0828804
\(78\) 0 0
\(79\) −440.000 −0.626631 −0.313316 0.949649i \(-0.601440\pi\)
−0.313316 + 0.949649i \(0.601440\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −1302.00 −1.72184 −0.860922 0.508737i \(-0.830113\pi\)
−0.860922 + 0.508737i \(0.830113\pi\)
\(84\) 0 0
\(85\) 864.000 1.10252
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −730.000 −0.869436 −0.434718 0.900567i \(-0.643152\pi\)
−0.434718 + 0.900567i \(0.643152\pi\)
\(90\) 0 0
\(91\) 196.000 0.225784
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −1760.00 −1.90076
\(96\) 0 0
\(97\) 294.000 0.307744 0.153872 0.988091i \(-0.450826\pi\)
0.153872 + 0.988091i \(0.450826\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 688.000 0.677808 0.338904 0.940821i \(-0.389944\pi\)
0.338904 + 0.940821i \(0.389944\pi\)
\(102\) 0 0
\(103\) −1388.00 −1.32780 −0.663901 0.747820i \(-0.731101\pi\)
−0.663901 + 0.747820i \(0.731101\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 244.000 0.220452 0.110226 0.993907i \(-0.464843\pi\)
0.110226 + 0.993907i \(0.464843\pi\)
\(108\) 0 0
\(109\) 90.0000 0.0790866 0.0395433 0.999218i \(-0.487410\pi\)
0.0395433 + 0.999218i \(0.487410\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −1318.00 −1.09723 −0.548615 0.836075i \(-0.684845\pi\)
−0.548615 + 0.836075i \(0.684845\pi\)
\(114\) 0 0
\(115\) −768.000 −0.622751
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −378.000 −0.291187
\(120\) 0 0
\(121\) −1267.00 −0.951916
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −96.0000 −0.0686920
\(126\) 0 0
\(127\) 1776.00 1.24090 0.620451 0.784245i \(-0.286950\pi\)
0.620451 + 0.784245i \(0.286950\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −1118.00 −0.745650 −0.372825 0.927902i \(-0.621611\pi\)
−0.372825 + 0.927902i \(0.621611\pi\)
\(132\) 0 0
\(133\) 770.000 0.502011
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −2274.00 −1.41811 −0.709054 0.705154i \(-0.750878\pi\)
−0.709054 + 0.705154i \(0.750878\pi\)
\(138\) 0 0
\(139\) 210.000 0.128144 0.0640718 0.997945i \(-0.479591\pi\)
0.0640718 + 0.997945i \(0.479591\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −224.000 −0.130992
\(144\) 0 0
\(145\) −1760.00 −1.00800
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 2010.00 1.10514 0.552569 0.833467i \(-0.313648\pi\)
0.552569 + 0.833467i \(0.313648\pi\)
\(150\) 0 0
\(151\) −1112.00 −0.599293 −0.299647 0.954050i \(-0.596869\pi\)
−0.299647 + 0.954050i \(0.596869\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 192.000 0.0994956
\(156\) 0 0
\(157\) 124.000 0.0630336 0.0315168 0.999503i \(-0.489966\pi\)
0.0315168 + 0.999503i \(0.489966\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 336.000 0.164475
\(162\) 0 0
\(163\) −2008.00 −0.964900 −0.482450 0.875924i \(-0.660253\pi\)
−0.482450 + 0.875924i \(0.660253\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 2884.00 1.33635 0.668176 0.744004i \(-0.267076\pi\)
0.668176 + 0.744004i \(0.267076\pi\)
\(168\) 0 0
\(169\) −1413.00 −0.643150
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −2228.00 −0.979143 −0.489571 0.871963i \(-0.662847\pi\)
−0.489571 + 0.871963i \(0.662847\pi\)
\(174\) 0 0
\(175\) 917.000 0.396107
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −820.000 −0.342400 −0.171200 0.985236i \(-0.554764\pi\)
−0.171200 + 0.985236i \(0.554764\pi\)
\(180\) 0 0
\(181\) 3892.00 1.59829 0.799144 0.601140i \(-0.205287\pi\)
0.799144 + 0.601140i \(0.205287\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 3936.00 1.56422
\(186\) 0 0
\(187\) 432.000 0.168936
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −5048.00 −1.91236 −0.956179 0.292782i \(-0.905419\pi\)
−0.956179 + 0.292782i \(0.905419\pi\)
\(192\) 0 0
\(193\) −2962.00 −1.10471 −0.552356 0.833608i \(-0.686271\pi\)
−0.552356 + 0.833608i \(0.686271\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −3334.00 −1.20577 −0.602887 0.797826i \(-0.705983\pi\)
−0.602887 + 0.797826i \(0.705983\pi\)
\(198\) 0 0
\(199\) −1860.00 −0.662572 −0.331286 0.943530i \(-0.607483\pi\)
−0.331286 + 0.943530i \(0.607483\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 770.000 0.266224
\(204\) 0 0
\(205\) 2912.00 0.992112
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −880.000 −0.291248
\(210\) 0 0
\(211\) 4268.00 1.39252 0.696259 0.717791i \(-0.254847\pi\)
0.696259 + 0.717791i \(0.254847\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 2048.00 0.649639
\(216\) 0 0
\(217\) −84.0000 −0.0262778
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −1512.00 −0.460218
\(222\) 0 0
\(223\) 5432.00 1.63118 0.815591 0.578629i \(-0.196412\pi\)
0.815591 + 0.578629i \(0.196412\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −2046.00 −0.598228 −0.299114 0.954217i \(-0.596691\pi\)
−0.299114 + 0.954217i \(0.596691\pi\)
\(228\) 0 0
\(229\) −2980.00 −0.859930 −0.429965 0.902846i \(-0.641474\pi\)
−0.429965 + 0.902846i \(0.641474\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −4458.00 −1.25345 −0.626724 0.779241i \(-0.715605\pi\)
−0.626724 + 0.779241i \(0.715605\pi\)
\(234\) 0 0
\(235\) −5184.00 −1.43901
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 4440.00 1.20167 0.600836 0.799372i \(-0.294834\pi\)
0.600836 + 0.799372i \(0.294834\pi\)
\(240\) 0 0
\(241\) 3302.00 0.882575 0.441287 0.897366i \(-0.354522\pi\)
0.441287 + 0.897366i \(0.354522\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −784.000 −0.204441
\(246\) 0 0
\(247\) 3080.00 0.793424
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 1582.00 0.397829 0.198914 0.980017i \(-0.436258\pi\)
0.198914 + 0.980017i \(0.436258\pi\)
\(252\) 0 0
\(253\) −384.000 −0.0954224
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −2354.00 −0.571356 −0.285678 0.958326i \(-0.592219\pi\)
−0.285678 + 0.958326i \(0.592219\pi\)
\(258\) 0 0
\(259\) −1722.00 −0.413127
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −3872.00 −0.907824 −0.453912 0.891046i \(-0.649972\pi\)
−0.453912 + 0.891046i \(0.649972\pi\)
\(264\) 0 0
\(265\) −2592.00 −0.600850
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −180.000 −0.0407985 −0.0203992 0.999792i \(-0.506494\pi\)
−0.0203992 + 0.999792i \(0.506494\pi\)
\(270\) 0 0
\(271\) −2032.00 −0.455480 −0.227740 0.973722i \(-0.573134\pi\)
−0.227740 + 0.973722i \(0.573134\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −1048.00 −0.229806
\(276\) 0 0
\(277\) −5426.00 −1.17696 −0.588478 0.808513i \(-0.700273\pi\)
−0.588478 + 0.808513i \(0.700273\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −842.000 −0.178753 −0.0893764 0.995998i \(-0.528487\pi\)
−0.0893764 + 0.995998i \(0.528487\pi\)
\(282\) 0 0
\(283\) 3782.00 0.794405 0.397202 0.917731i \(-0.369981\pi\)
0.397202 + 0.917731i \(0.369981\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −1274.00 −0.262027
\(288\) 0 0
\(289\) −1997.00 −0.406473
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 4312.00 0.859760 0.429880 0.902886i \(-0.358556\pi\)
0.429880 + 0.902886i \(0.358556\pi\)
\(294\) 0 0
\(295\) −12960.0 −2.55783
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 1344.00 0.259952
\(300\) 0 0
\(301\) −896.000 −0.171577
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 7808.00 1.46585
\(306\) 0 0
\(307\) −2674.00 −0.497112 −0.248556 0.968618i \(-0.579956\pi\)
−0.248556 + 0.968618i \(0.579956\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −3768.00 −0.687021 −0.343511 0.939149i \(-0.611616\pi\)
−0.343511 + 0.939149i \(0.611616\pi\)
\(312\) 0 0
\(313\) 2438.00 0.440268 0.220134 0.975470i \(-0.429351\pi\)
0.220134 + 0.975470i \(0.429351\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 3186.00 0.564491 0.282245 0.959342i \(-0.408921\pi\)
0.282245 + 0.959342i \(0.408921\pi\)
\(318\) 0 0
\(319\) −880.000 −0.154453
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −5940.00 −1.02325
\(324\) 0 0
\(325\) 3668.00 0.626043
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 2268.00 0.380057
\(330\) 0 0
\(331\) −8672.00 −1.44005 −0.720025 0.693949i \(-0.755869\pi\)
−0.720025 + 0.693949i \(0.755869\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 3904.00 0.636711
\(336\) 0 0
\(337\) 814.000 0.131577 0.0657884 0.997834i \(-0.479044\pi\)
0.0657884 + 0.997834i \(0.479044\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 96.0000 0.0152454
\(342\) 0 0
\(343\) 343.000 0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 9344.00 1.44557 0.722784 0.691074i \(-0.242862\pi\)
0.722784 + 0.691074i \(0.242862\pi\)
\(348\) 0 0
\(349\) −5180.00 −0.794496 −0.397248 0.917711i \(-0.630035\pi\)
−0.397248 + 0.917711i \(0.630035\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −12178.0 −1.83617 −0.918087 0.396379i \(-0.870267\pi\)
−0.918087 + 0.396379i \(0.870267\pi\)
\(354\) 0 0
\(355\) 12288.0 1.83712
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 440.000 0.0646861 0.0323431 0.999477i \(-0.489703\pi\)
0.0323431 + 0.999477i \(0.489703\pi\)
\(360\) 0 0
\(361\) 5241.00 0.764106
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 11232.0 1.61071
\(366\) 0 0
\(367\) 9816.00 1.39616 0.698080 0.716019i \(-0.254038\pi\)
0.698080 + 0.716019i \(0.254038\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 1134.00 0.158691
\(372\) 0 0
\(373\) −442.000 −0.0613563 −0.0306781 0.999529i \(-0.509767\pi\)
−0.0306781 + 0.999529i \(0.509767\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 3080.00 0.420764
\(378\) 0 0
\(379\) 3960.00 0.536706 0.268353 0.963321i \(-0.413521\pi\)
0.268353 + 0.963321i \(0.413521\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 6708.00 0.894942 0.447471 0.894298i \(-0.352325\pi\)
0.447471 + 0.894298i \(0.352325\pi\)
\(384\) 0 0
\(385\) 896.000 0.118609
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 13350.0 1.74003 0.870015 0.493025i \(-0.164109\pi\)
0.870015 + 0.493025i \(0.164109\pi\)
\(390\) 0 0
\(391\) −2592.00 −0.335251
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 7040.00 0.896762
\(396\) 0 0
\(397\) −1356.00 −0.171425 −0.0857125 0.996320i \(-0.527317\pi\)
−0.0857125 + 0.996320i \(0.527317\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −6222.00 −0.774843 −0.387421 0.921903i \(-0.626634\pi\)
−0.387421 + 0.921903i \(0.626634\pi\)
\(402\) 0 0
\(403\) −336.000 −0.0415319
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 1968.00 0.239681
\(408\) 0 0
\(409\) 5150.00 0.622619 0.311309 0.950309i \(-0.399232\pi\)
0.311309 + 0.950309i \(0.399232\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 5670.00 0.675551
\(414\) 0 0
\(415\) 20832.0 2.46410
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 2310.00 0.269334 0.134667 0.990891i \(-0.457004\pi\)
0.134667 + 0.990891i \(0.457004\pi\)
\(420\) 0 0
\(421\) 1262.00 0.146095 0.0730476 0.997328i \(-0.476727\pi\)
0.0730476 + 0.997328i \(0.476727\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −7074.00 −0.807387
\(426\) 0 0
\(427\) −3416.00 −0.387147
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −4488.00 −0.501576 −0.250788 0.968042i \(-0.580690\pi\)
−0.250788 + 0.968042i \(0.580690\pi\)
\(432\) 0 0
\(433\) 17038.0 1.89098 0.945490 0.325652i \(-0.105584\pi\)
0.945490 + 0.325652i \(0.105584\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 5280.00 0.577979
\(438\) 0 0
\(439\) −16200.0 −1.76124 −0.880619 0.473824i \(-0.842873\pi\)
−0.880619 + 0.473824i \(0.842873\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −8772.00 −0.940791 −0.470395 0.882456i \(-0.655889\pi\)
−0.470395 + 0.882456i \(0.655889\pi\)
\(444\) 0 0
\(445\) 11680.0 1.24424
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −2130.00 −0.223877 −0.111939 0.993715i \(-0.535706\pi\)
−0.111939 + 0.993715i \(0.535706\pi\)
\(450\) 0 0
\(451\) 1456.00 0.152019
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −3136.00 −0.323116
\(456\) 0 0
\(457\) 10534.0 1.07825 0.539124 0.842226i \(-0.318755\pi\)
0.539124 + 0.842226i \(0.318755\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 9268.00 0.936342 0.468171 0.883638i \(-0.344913\pi\)
0.468171 + 0.883638i \(0.344913\pi\)
\(462\) 0 0
\(463\) 9392.00 0.942728 0.471364 0.881939i \(-0.343762\pi\)
0.471364 + 0.881939i \(0.343762\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −10806.0 −1.07075 −0.535377 0.844613i \(-0.679830\pi\)
−0.535377 + 0.844613i \(0.679830\pi\)
\(468\) 0 0
\(469\) −1708.00 −0.168162
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 1024.00 0.0995424
\(474\) 0 0
\(475\) 14410.0 1.39195
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 4940.00 0.471220 0.235610 0.971848i \(-0.424291\pi\)
0.235610 + 0.971848i \(0.424291\pi\)
\(480\) 0 0
\(481\) −6888.00 −0.652943
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −4704.00 −0.440407
\(486\) 0 0
\(487\) 5216.00 0.485338 0.242669 0.970109i \(-0.421977\pi\)
0.242669 + 0.970109i \(0.421977\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 4412.00 0.405521 0.202760 0.979228i \(-0.435009\pi\)
0.202760 + 0.979228i \(0.435009\pi\)
\(492\) 0 0
\(493\) −5940.00 −0.542645
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −5376.00 −0.485204
\(498\) 0 0
\(499\) −19060.0 −1.70991 −0.854953 0.518706i \(-0.826414\pi\)
−0.854953 + 0.518706i \(0.826414\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 12768.0 1.13180 0.565902 0.824473i \(-0.308528\pi\)
0.565902 + 0.824473i \(0.308528\pi\)
\(504\) 0 0
\(505\) −11008.0 −0.969999
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 5500.00 0.478945 0.239473 0.970903i \(-0.423025\pi\)
0.239473 + 0.970903i \(0.423025\pi\)
\(510\) 0 0
\(511\) −4914.00 −0.425406
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 22208.0 1.90020
\(516\) 0 0
\(517\) −2592.00 −0.220495
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 7338.00 0.617051 0.308526 0.951216i \(-0.400164\pi\)
0.308526 + 0.951216i \(0.400164\pi\)
\(522\) 0 0
\(523\) 17582.0 1.46999 0.734997 0.678070i \(-0.237183\pi\)
0.734997 + 0.678070i \(0.237183\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 648.000 0.0535623
\(528\) 0 0
\(529\) −9863.00 −0.810635
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −5096.00 −0.414132
\(534\) 0 0
\(535\) −3904.00 −0.315485
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −392.000 −0.0313259
\(540\) 0 0
\(541\) −1618.00 −0.128583 −0.0642914 0.997931i \(-0.520479\pi\)
−0.0642914 + 0.997931i \(0.520479\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −1440.00 −0.113179
\(546\) 0 0
\(547\) −16144.0 −1.26192 −0.630958 0.775817i \(-0.717338\pi\)
−0.630958 + 0.775817i \(0.717338\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 12100.0 0.935531
\(552\) 0 0
\(553\) −3080.00 −0.236844
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −4654.00 −0.354033 −0.177016 0.984208i \(-0.556645\pi\)
−0.177016 + 0.984208i \(0.556645\pi\)
\(558\) 0 0
\(559\) −3584.00 −0.271175
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 10078.0 0.754418 0.377209 0.926128i \(-0.376884\pi\)
0.377209 + 0.926128i \(0.376884\pi\)
\(564\) 0 0
\(565\) 21088.0 1.57023
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 5930.00 0.436904 0.218452 0.975848i \(-0.429899\pi\)
0.218452 + 0.975848i \(0.429899\pi\)
\(570\) 0 0
\(571\) 19048.0 1.39603 0.698016 0.716082i \(-0.254067\pi\)
0.698016 + 0.716082i \(0.254067\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 6288.00 0.456048
\(576\) 0 0
\(577\) −14366.0 −1.03651 −0.518253 0.855227i \(-0.673418\pi\)
−0.518253 + 0.855227i \(0.673418\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −9114.00 −0.650796
\(582\) 0 0
\(583\) −1296.00 −0.0920666
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −3626.00 −0.254959 −0.127480 0.991841i \(-0.540689\pi\)
−0.127480 + 0.991841i \(0.540689\pi\)
\(588\) 0 0
\(589\) −1320.00 −0.0923424
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 1062.00 0.0735432 0.0367716 0.999324i \(-0.488293\pi\)
0.0367716 + 0.999324i \(0.488293\pi\)
\(594\) 0 0
\(595\) 6048.00 0.416712
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −10200.0 −0.695761 −0.347880 0.937539i \(-0.613098\pi\)
−0.347880 + 0.937539i \(0.613098\pi\)
\(600\) 0 0
\(601\) −25158.0 −1.70751 −0.853757 0.520671i \(-0.825682\pi\)
−0.853757 + 0.520671i \(0.825682\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 20272.0 1.36227
\(606\) 0 0
\(607\) −25664.0 −1.71609 −0.858047 0.513570i \(-0.828323\pi\)
−0.858047 + 0.513570i \(0.828323\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 9072.00 0.600677
\(612\) 0 0
\(613\) 19018.0 1.25307 0.626533 0.779395i \(-0.284473\pi\)
0.626533 + 0.779395i \(0.284473\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −17334.0 −1.13102 −0.565511 0.824741i \(-0.691321\pi\)
−0.565511 + 0.824741i \(0.691321\pi\)
\(618\) 0 0
\(619\) −18730.0 −1.21619 −0.608096 0.793864i \(-0.708066\pi\)
−0.608096 + 0.793864i \(0.708066\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −5110.00 −0.328616
\(624\) 0 0
\(625\) −14839.0 −0.949696
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 13284.0 0.842079
\(630\) 0 0
\(631\) 6928.00 0.437083 0.218541 0.975828i \(-0.429870\pi\)
0.218541 + 0.975828i \(0.429870\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −28416.0 −1.77583
\(636\) 0 0
\(637\) 1372.00 0.0853385
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −16302.0 −1.00451 −0.502255 0.864720i \(-0.667496\pi\)
−0.502255 + 0.864720i \(0.667496\pi\)
\(642\) 0 0
\(643\) −4718.00 −0.289362 −0.144681 0.989478i \(-0.546216\pi\)
−0.144681 + 0.989478i \(0.546216\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −21436.0 −1.30253 −0.651264 0.758851i \(-0.725761\pi\)
−0.651264 + 0.758851i \(0.725761\pi\)
\(648\) 0 0
\(649\) −6480.00 −0.391930
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −4458.00 −0.267159 −0.133580 0.991038i \(-0.542647\pi\)
−0.133580 + 0.991038i \(0.542647\pi\)
\(654\) 0 0
\(655\) 17888.0 1.06709
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −26640.0 −1.57473 −0.787365 0.616487i \(-0.788555\pi\)
−0.787365 + 0.616487i \(0.788555\pi\)
\(660\) 0 0
\(661\) 7432.00 0.437324 0.218662 0.975801i \(-0.429831\pi\)
0.218662 + 0.975801i \(0.429831\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −12320.0 −0.718420
\(666\) 0 0
\(667\) 5280.00 0.306510
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 3904.00 0.224608
\(672\) 0 0
\(673\) 58.0000 0.00332204 0.00166102 0.999999i \(-0.499471\pi\)
0.00166102 + 0.999999i \(0.499471\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 21516.0 1.22146 0.610729 0.791840i \(-0.290876\pi\)
0.610729 + 0.791840i \(0.290876\pi\)
\(678\) 0 0
\(679\) 2058.00 0.116316
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 18108.0 1.01447 0.507235 0.861808i \(-0.330668\pi\)
0.507235 + 0.861808i \(0.330668\pi\)
\(684\) 0 0
\(685\) 36384.0 2.02943
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 4536.00 0.250810
\(690\) 0 0
\(691\) 10078.0 0.554827 0.277413 0.960751i \(-0.410523\pi\)
0.277413 + 0.960751i \(0.410523\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −3360.00 −0.183384
\(696\) 0 0
\(697\) 9828.00 0.534092
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −18762.0 −1.01089 −0.505443 0.862860i \(-0.668671\pi\)
−0.505443 + 0.862860i \(0.668671\pi\)
\(702\) 0 0
\(703\) −27060.0 −1.45176
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 4816.00 0.256187
\(708\) 0 0
\(709\) 6810.00 0.360726 0.180363 0.983600i \(-0.442273\pi\)
0.180363 + 0.983600i \(0.442273\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −576.000 −0.0302544
\(714\) 0 0
\(715\) 3584.00 0.187460
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 4860.00 0.252083 0.126041 0.992025i \(-0.459773\pi\)
0.126041 + 0.992025i \(0.459773\pi\)
\(720\) 0 0
\(721\) −9716.00 −0.501862
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 14410.0 0.738171
\(726\) 0 0
\(727\) 13636.0 0.695641 0.347821 0.937561i \(-0.386922\pi\)
0.347821 + 0.937561i \(0.386922\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 6912.00 0.349726
\(732\) 0 0
\(733\) 2088.00 0.105214 0.0526071 0.998615i \(-0.483247\pi\)
0.0526071 + 0.998615i \(0.483247\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 1952.00 0.0975615
\(738\) 0 0
\(739\) 5160.00 0.256852 0.128426 0.991719i \(-0.459008\pi\)
0.128426 + 0.991719i \(0.459008\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −28152.0 −1.39004 −0.695018 0.718992i \(-0.744604\pi\)
−0.695018 + 0.718992i \(0.744604\pi\)
\(744\) 0 0
\(745\) −32160.0 −1.58155
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 1708.00 0.0833230
\(750\) 0 0
\(751\) 16808.0 0.816688 0.408344 0.912828i \(-0.366106\pi\)
0.408344 + 0.912828i \(0.366106\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 17792.0 0.857639
\(756\) 0 0
\(757\) 21674.0 1.04063 0.520314 0.853975i \(-0.325815\pi\)
0.520314 + 0.853975i \(0.325815\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −7422.00 −0.353544 −0.176772 0.984252i \(-0.556566\pi\)
−0.176772 + 0.984252i \(0.556566\pi\)
\(762\) 0 0
\(763\) 630.000 0.0298919
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 22680.0 1.06770
\(768\) 0 0
\(769\) 13790.0 0.646658 0.323329 0.946287i \(-0.395198\pi\)
0.323329 + 0.946287i \(0.395198\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 6232.00 0.289973 0.144987 0.989434i \(-0.453686\pi\)
0.144987 + 0.989434i \(0.453686\pi\)
\(774\) 0 0
\(775\) −1572.00 −0.0728618
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −20020.0 −0.920784
\(780\) 0 0
\(781\) 6144.00 0.281498
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −1984.00 −0.0902064
\(786\) 0 0
\(787\) 1766.00 0.0799887 0.0399943 0.999200i \(-0.487266\pi\)
0.0399943 + 0.999200i \(0.487266\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −9226.00 −0.414714
\(792\) 0 0
\(793\) −13664.0 −0.611883
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −1204.00 −0.0535105 −0.0267552 0.999642i \(-0.508517\pi\)
−0.0267552 + 0.999642i \(0.508517\pi\)
\(798\) 0 0
\(799\) −17496.0 −0.774673
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 5616.00 0.246805
\(804\) 0 0
\(805\) −5376.00 −0.235378
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 7050.00 0.306384 0.153192 0.988196i \(-0.451045\pi\)
0.153192 + 0.988196i \(0.451045\pi\)
\(810\) 0 0
\(811\) −23282.0 −1.00807 −0.504033 0.863684i \(-0.668151\pi\)
−0.504033 + 0.863684i \(0.668151\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 32128.0 1.38085
\(816\) 0 0
\(817\) −14080.0 −0.602934
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −10142.0 −0.431131 −0.215565 0.976489i \(-0.569159\pi\)
−0.215565 + 0.976489i \(0.569159\pi\)
\(822\) 0 0
\(823\) 9192.00 0.389323 0.194662 0.980870i \(-0.437639\pi\)
0.194662 + 0.980870i \(0.437639\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −46716.0 −1.96430 −0.982149 0.188104i \(-0.939766\pi\)
−0.982149 + 0.188104i \(0.939766\pi\)
\(828\) 0 0
\(829\) 11240.0 0.470906 0.235453 0.971886i \(-0.424343\pi\)
0.235453 + 0.971886i \(0.424343\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −2646.00 −0.110058
\(834\) 0 0
\(835\) −46144.0 −1.91243
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 700.000 0.0288042 0.0144021 0.999896i \(-0.495416\pi\)
0.0144021 + 0.999896i \(0.495416\pi\)
\(840\) 0 0
\(841\) −12289.0 −0.503875
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 22608.0 0.920401
\(846\) 0 0
\(847\) −8869.00 −0.359790
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −11808.0 −0.475644
\(852\) 0 0
\(853\) −37492.0 −1.50493 −0.752463 0.658635i \(-0.771134\pi\)
−0.752463 + 0.658635i \(0.771134\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −28894.0 −1.15169 −0.575846 0.817558i \(-0.695327\pi\)
−0.575846 + 0.817558i \(0.695327\pi\)
\(858\) 0 0
\(859\) 2770.00 0.110025 0.0550123 0.998486i \(-0.482480\pi\)
0.0550123 + 0.998486i \(0.482480\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 17688.0 0.697690 0.348845 0.937180i \(-0.386574\pi\)
0.348845 + 0.937180i \(0.386574\pi\)
\(864\) 0 0
\(865\) 35648.0 1.40124
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 3520.00 0.137408
\(870\) 0 0
\(871\) −6832.00 −0.265779
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −672.000 −0.0259631
\(876\) 0 0
\(877\) −33566.0 −1.29241 −0.646205 0.763164i \(-0.723645\pi\)
−0.646205 + 0.763164i \(0.723645\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 16758.0 0.640853 0.320426 0.947273i \(-0.396174\pi\)
0.320426 + 0.947273i \(0.396174\pi\)
\(882\) 0 0
\(883\) −11468.0 −0.437066 −0.218533 0.975830i \(-0.570127\pi\)
−0.218533 + 0.975830i \(0.570127\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −50356.0 −1.90619 −0.953094 0.302674i \(-0.902121\pi\)
−0.953094 + 0.302674i \(0.902121\pi\)
\(888\) 0 0
\(889\) 12432.0 0.469017
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 35640.0 1.33555
\(894\) 0 0
\(895\) 13120.0 0.490004
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −1320.00 −0.0489705
\(900\) 0 0
\(901\) −8748.00 −0.323461
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −62272.0 −2.28728
\(906\) 0 0
\(907\) 8716.00 0.319085 0.159542 0.987191i \(-0.448998\pi\)
0.159542 + 0.987191i \(0.448998\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 7632.00 0.277563 0.138781 0.990323i \(-0.455682\pi\)
0.138781 + 0.990323i \(0.455682\pi\)
\(912\) 0 0
\(913\) 10416.0 0.377568
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −7826.00 −0.281829
\(918\) 0 0
\(919\) 23080.0 0.828443 0.414221 0.910176i \(-0.364054\pi\)
0.414221 + 0.910176i \(0.364054\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −21504.0 −0.766861
\(924\) 0 0
\(925\) −32226.0 −1.14550
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −45110.0 −1.59312 −0.796561 0.604558i \(-0.793350\pi\)
−0.796561 + 0.604558i \(0.793350\pi\)
\(930\) 0 0
\(931\) 5390.00 0.189742
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −6912.00 −0.241761
\(936\) 0 0
\(937\) 16674.0 0.581340 0.290670 0.956823i \(-0.406122\pi\)
0.290670 + 0.956823i \(0.406122\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −43832.0 −1.51847 −0.759236 0.650815i \(-0.774427\pi\)
−0.759236 + 0.650815i \(0.774427\pi\)
\(942\) 0 0
\(943\) −8736.00 −0.301679
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −736.000 −0.0252553 −0.0126277 0.999920i \(-0.504020\pi\)
−0.0126277 + 0.999920i \(0.504020\pi\)
\(948\) 0 0
\(949\) −19656.0 −0.672351
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −38138.0 −1.29634 −0.648169 0.761496i \(-0.724465\pi\)
−0.648169 + 0.761496i \(0.724465\pi\)
\(954\) 0 0
\(955\) 80768.0 2.73674
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −15918.0 −0.535995
\(960\) 0 0
\(961\) −29647.0 −0.995166
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 47392.0 1.58094
\(966\) 0 0
\(967\) −26224.0 −0.872086 −0.436043 0.899926i \(-0.643620\pi\)
−0.436043 + 0.899926i \(0.643620\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 18762.0 0.620084 0.310042 0.950723i \(-0.399657\pi\)
0.310042 + 0.950723i \(0.399657\pi\)
\(972\) 0 0
\(973\) 1470.00 0.0484337
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −38394.0 −1.25725 −0.628625 0.777709i \(-0.716382\pi\)
−0.628625 + 0.777709i \(0.716382\pi\)
\(978\) 0 0
\(979\) 5840.00 0.190651
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 5388.00 0.174822 0.0874112 0.996172i \(-0.472141\pi\)
0.0874112 + 0.996172i \(0.472141\pi\)
\(984\) 0 0
\(985\) 53344.0 1.72556
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −6144.00 −0.197541
\(990\) 0 0
\(991\) −25472.0 −0.816493 −0.408247 0.912872i \(-0.633860\pi\)
−0.408247 + 0.912872i \(0.633860\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 29760.0 0.948196
\(996\) 0 0
\(997\) −17096.0 −0.543065 −0.271532 0.962429i \(-0.587530\pi\)
−0.271532 + 0.962429i \(0.587530\pi\)
\(998\) 0 0
\(999\) 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 1008.4.a.c.1.1 1
3.2 odd 2 112.4.a.f.1.1 1
4.3 odd 2 63.4.a.b.1.1 1
12.11 even 2 7.4.a.a.1.1 1
20.19 odd 2 1575.4.a.e.1.1 1
21.20 even 2 784.4.a.g.1.1 1
24.5 odd 2 448.4.a.e.1.1 1
24.11 even 2 448.4.a.i.1.1 1
28.3 even 6 441.4.e.e.226.1 2
28.11 odd 6 441.4.e.h.226.1 2
28.19 even 6 441.4.e.e.361.1 2
28.23 odd 6 441.4.e.h.361.1 2
28.27 even 2 441.4.a.i.1.1 1
60.23 odd 4 175.4.b.b.99.2 2
60.47 odd 4 175.4.b.b.99.1 2
60.59 even 2 175.4.a.b.1.1 1
84.11 even 6 49.4.c.c.30.1 2
84.23 even 6 49.4.c.c.18.1 2
84.47 odd 6 49.4.c.b.18.1 2
84.59 odd 6 49.4.c.b.30.1 2
84.83 odd 2 49.4.a.b.1.1 1
132.131 odd 2 847.4.a.b.1.1 1
156.155 even 2 1183.4.a.b.1.1 1
204.203 even 2 2023.4.a.a.1.1 1
420.419 odd 2 1225.4.a.j.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
7.4.a.a.1.1 1 12.11 even 2
49.4.a.b.1.1 1 84.83 odd 2
49.4.c.b.18.1 2 84.47 odd 6
49.4.c.b.30.1 2 84.59 odd 6
49.4.c.c.18.1 2 84.23 even 6
49.4.c.c.30.1 2 84.11 even 6
63.4.a.b.1.1 1 4.3 odd 2
112.4.a.f.1.1 1 3.2 odd 2
175.4.a.b.1.1 1 60.59 even 2
175.4.b.b.99.1 2 60.47 odd 4
175.4.b.b.99.2 2 60.23 odd 4
441.4.a.i.1.1 1 28.27 even 2
441.4.e.e.226.1 2 28.3 even 6
441.4.e.e.361.1 2 28.19 even 6
441.4.e.h.226.1 2 28.11 odd 6
441.4.e.h.361.1 2 28.23 odd 6
448.4.a.e.1.1 1 24.5 odd 2
448.4.a.i.1.1 1 24.11 even 2
784.4.a.g.1.1 1 21.20 even 2
847.4.a.b.1.1 1 132.131 odd 2
1008.4.a.c.1.1 1 1.1 even 1 trivial
1183.4.a.b.1.1 1 156.155 even 2
1225.4.a.j.1.1 1 420.419 odd 2
1575.4.a.e.1.1 1 20.19 odd 2
2023.4.a.a.1.1 1 204.203 even 2