Properties

Label 6048.2.a.g.1.1
Level 6048
Weight 2
Character 6048.1
Self dual yes
Analytic conductor 48.294
Analytic rank 0
Dimension 1
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6048.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(48.2935231425\)
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
Root \(0\)
Character \(\chi\) = 6048.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{5} -1.00000 q^{7} +O(q^{10})\) \(q-1.00000 q^{5} -1.00000 q^{7} +2.00000 q^{11} +4.00000 q^{13} +3.00000 q^{17} +4.00000 q^{19} -4.00000 q^{25} +8.00000 q^{29} +8.00000 q^{31} +1.00000 q^{35} -11.0000 q^{37} -7.00000 q^{41} +11.0000 q^{43} -11.0000 q^{47} +1.00000 q^{49} -2.00000 q^{53} -2.00000 q^{55} -11.0000 q^{59} -6.00000 q^{61} -4.00000 q^{65} -4.00000 q^{67} +4.00000 q^{71} +12.0000 q^{73} -2.00000 q^{77} -1.00000 q^{79} +3.00000 q^{83} -3.00000 q^{85} +10.0000 q^{89} -4.00000 q^{91} -4.00000 q^{95} +4.00000 q^{97} +O(q^{100})\)

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
\(5\) −1.00000 −0.447214 −0.223607 0.974679i \(-0.571783\pi\)
−0.223607 + 0.974679i \(0.571783\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 2.00000 0.603023 0.301511 0.953463i \(-0.402509\pi\)
0.301511 + 0.953463i \(0.402509\pi\)
\(12\) 0 0
\(13\) 4.00000 1.10940 0.554700 0.832050i \(-0.312833\pi\)
0.554700 + 0.832050i \(0.312833\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 3.00000 0.727607 0.363803 0.931476i \(-0.381478\pi\)
0.363803 + 0.931476i \(0.381478\pi\)
\(18\) 0 0
\(19\) 4.00000 0.917663 0.458831 0.888523i \(-0.348268\pi\)
0.458831 + 0.888523i \(0.348268\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) 0 0
\(25\) −4.00000 −0.800000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 8.00000 1.48556 0.742781 0.669534i \(-0.233506\pi\)
0.742781 + 0.669534i \(0.233506\pi\)
\(30\) 0 0
\(31\) 8.00000 1.43684 0.718421 0.695608i \(-0.244865\pi\)
0.718421 + 0.695608i \(0.244865\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 1.00000 0.169031
\(36\) 0 0
\(37\) −11.0000 −1.80839 −0.904194 0.427121i \(-0.859528\pi\)
−0.904194 + 0.427121i \(0.859528\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −7.00000 −1.09322 −0.546608 0.837389i \(-0.684081\pi\)
−0.546608 + 0.837389i \(0.684081\pi\)
\(42\) 0 0
\(43\) 11.0000 1.67748 0.838742 0.544529i \(-0.183292\pi\)
0.838742 + 0.544529i \(0.183292\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −11.0000 −1.60451 −0.802257 0.596978i \(-0.796368\pi\)
−0.802257 + 0.596978i \(0.796368\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −2.00000 −0.274721 −0.137361 0.990521i \(-0.543862\pi\)
−0.137361 + 0.990521i \(0.543862\pi\)
\(54\) 0 0
\(55\) −2.00000 −0.269680
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −11.0000 −1.43208 −0.716039 0.698060i \(-0.754047\pi\)
−0.716039 + 0.698060i \(0.754047\pi\)
\(60\) 0 0
\(61\) −6.00000 −0.768221 −0.384111 0.923287i \(-0.625492\pi\)
−0.384111 + 0.923287i \(0.625492\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −4.00000 −0.496139
\(66\) 0 0
\(67\) −4.00000 −0.488678 −0.244339 0.969690i \(-0.578571\pi\)
−0.244339 + 0.969690i \(0.578571\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 4.00000 0.474713 0.237356 0.971423i \(-0.423719\pi\)
0.237356 + 0.971423i \(0.423719\pi\)
\(72\) 0 0
\(73\) 12.0000 1.40449 0.702247 0.711934i \(-0.252180\pi\)
0.702247 + 0.711934i \(0.252180\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −2.00000 −0.227921
\(78\) 0 0
\(79\) −1.00000 −0.112509 −0.0562544 0.998416i \(-0.517916\pi\)
−0.0562544 + 0.998416i \(0.517916\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 3.00000 0.329293 0.164646 0.986353i \(-0.447352\pi\)
0.164646 + 0.986353i \(0.447352\pi\)
\(84\) 0 0
\(85\) −3.00000 −0.325396
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 10.0000 1.06000 0.529999 0.847998i \(-0.322192\pi\)
0.529999 + 0.847998i \(0.322192\pi\)
\(90\) 0 0
\(91\) −4.00000 −0.419314
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −4.00000 −0.410391
\(96\) 0 0
\(97\) 4.00000 0.406138 0.203069 0.979164i \(-0.434908\pi\)
0.203069 + 0.979164i \(0.434908\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −18.0000 −1.79107 −0.895533 0.444994i \(-0.853206\pi\)
−0.895533 + 0.444994i \(0.853206\pi\)
\(102\) 0 0
\(103\) 12.0000 1.18240 0.591198 0.806527i \(-0.298655\pi\)
0.591198 + 0.806527i \(0.298655\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 4.00000 0.386695 0.193347 0.981130i \(-0.438066\pi\)
0.193347 + 0.981130i \(0.438066\pi\)
\(108\) 0 0
\(109\) 11.0000 1.05361 0.526804 0.849987i \(-0.323390\pi\)
0.526804 + 0.849987i \(0.323390\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 14.0000 1.31701 0.658505 0.752577i \(-0.271189\pi\)
0.658505 + 0.752577i \(0.271189\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −3.00000 −0.275010
\(120\) 0 0
\(121\) −7.00000 −0.636364
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 9.00000 0.804984
\(126\) 0 0
\(127\) −7.00000 −0.621150 −0.310575 0.950549i \(-0.600522\pi\)
−0.310575 + 0.950549i \(0.600522\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 20.0000 1.74741 0.873704 0.486458i \(-0.161711\pi\)
0.873704 + 0.486458i \(0.161711\pi\)
\(132\) 0 0
\(133\) −4.00000 −0.346844
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(138\) 0 0
\(139\) 14.0000 1.18746 0.593732 0.804663i \(-0.297654\pi\)
0.593732 + 0.804663i \(0.297654\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 8.00000 0.668994
\(144\) 0 0
\(145\) −8.00000 −0.664364
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −18.0000 −1.47462 −0.737309 0.675556i \(-0.763904\pi\)
−0.737309 + 0.675556i \(0.763904\pi\)
\(150\) 0 0
\(151\) 9.00000 0.732410 0.366205 0.930534i \(-0.380657\pi\)
0.366205 + 0.930534i \(0.380657\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −8.00000 −0.642575
\(156\) 0 0
\(157\) 8.00000 0.638470 0.319235 0.947676i \(-0.396574\pi\)
0.319235 + 0.947676i \(0.396574\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 25.0000 1.95815 0.979076 0.203497i \(-0.0652307\pi\)
0.979076 + 0.203497i \(0.0652307\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 1.00000 0.0773823 0.0386912 0.999251i \(-0.487681\pi\)
0.0386912 + 0.999251i \(0.487681\pi\)
\(168\) 0 0
\(169\) 3.00000 0.230769
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −18.0000 −1.36851 −0.684257 0.729241i \(-0.739873\pi\)
−0.684257 + 0.729241i \(0.739873\pi\)
\(174\) 0 0
\(175\) 4.00000 0.302372
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −18.0000 −1.34538 −0.672692 0.739923i \(-0.734862\pi\)
−0.672692 + 0.739923i \(0.734862\pi\)
\(180\) 0 0
\(181\) 2.00000 0.148659 0.0743294 0.997234i \(-0.476318\pi\)
0.0743294 + 0.997234i \(0.476318\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 11.0000 0.808736
\(186\) 0 0
\(187\) 6.00000 0.438763
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 18.0000 1.30243 0.651217 0.758891i \(-0.274259\pi\)
0.651217 + 0.758891i \(0.274259\pi\)
\(192\) 0 0
\(193\) 15.0000 1.07972 0.539862 0.841754i \(-0.318476\pi\)
0.539862 + 0.841754i \(0.318476\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −16.0000 −1.13995 −0.569976 0.821661i \(-0.693048\pi\)
−0.569976 + 0.821661i \(0.693048\pi\)
\(198\) 0 0
\(199\) 26.0000 1.84309 0.921546 0.388270i \(-0.126927\pi\)
0.921546 + 0.388270i \(0.126927\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −8.00000 −0.561490
\(204\) 0 0
\(205\) 7.00000 0.488901
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 8.00000 0.553372
\(210\) 0 0
\(211\) −8.00000 −0.550743 −0.275371 0.961338i \(-0.588801\pi\)
−0.275371 + 0.961338i \(0.588801\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −11.0000 −0.750194
\(216\) 0 0
\(217\) −8.00000 −0.543075
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 12.0000 0.807207
\(222\) 0 0
\(223\) 16.0000 1.07144 0.535720 0.844396i \(-0.320040\pi\)
0.535720 + 0.844396i \(0.320040\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 12.0000 0.796468 0.398234 0.917284i \(-0.369623\pi\)
0.398234 + 0.917284i \(0.369623\pi\)
\(228\) 0 0
\(229\) 2.00000 0.132164 0.0660819 0.997814i \(-0.478950\pi\)
0.0660819 + 0.997814i \(0.478950\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 24.0000 1.57229 0.786146 0.618041i \(-0.212073\pi\)
0.786146 + 0.618041i \(0.212073\pi\)
\(234\) 0 0
\(235\) 11.0000 0.717561
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 6.00000 0.388108 0.194054 0.980991i \(-0.437836\pi\)
0.194054 + 0.980991i \(0.437836\pi\)
\(240\) 0 0
\(241\) −8.00000 −0.515325 −0.257663 0.966235i \(-0.582952\pi\)
−0.257663 + 0.966235i \(0.582952\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −1.00000 −0.0638877
\(246\) 0 0
\(247\) 16.0000 1.01806
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 3.00000 0.189358 0.0946792 0.995508i \(-0.469817\pi\)
0.0946792 + 0.995508i \(0.469817\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 14.0000 0.873296 0.436648 0.899632i \(-0.356166\pi\)
0.436648 + 0.899632i \(0.356166\pi\)
\(258\) 0 0
\(259\) 11.0000 0.683507
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 12.0000 0.739952 0.369976 0.929041i \(-0.379366\pi\)
0.369976 + 0.929041i \(0.379366\pi\)
\(264\) 0 0
\(265\) 2.00000 0.122859
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −9.00000 −0.548740 −0.274370 0.961624i \(-0.588469\pi\)
−0.274370 + 0.961624i \(0.588469\pi\)
\(270\) 0 0
\(271\) 6.00000 0.364474 0.182237 0.983255i \(-0.441666\pi\)
0.182237 + 0.983255i \(0.441666\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −8.00000 −0.482418
\(276\) 0 0
\(277\) 13.0000 0.781094 0.390547 0.920583i \(-0.372286\pi\)
0.390547 + 0.920583i \(0.372286\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −12.0000 −0.715860 −0.357930 0.933748i \(-0.616517\pi\)
−0.357930 + 0.933748i \(0.616517\pi\)
\(282\) 0 0
\(283\) 2.00000 0.118888 0.0594438 0.998232i \(-0.481067\pi\)
0.0594438 + 0.998232i \(0.481067\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 7.00000 0.413197
\(288\) 0 0
\(289\) −8.00000 −0.470588
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 9.00000 0.525786 0.262893 0.964825i \(-0.415323\pi\)
0.262893 + 0.964825i \(0.415323\pi\)
\(294\) 0 0
\(295\) 11.0000 0.640445
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) −11.0000 −0.634029
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 6.00000 0.343559
\(306\) 0 0
\(307\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −15.0000 −0.850572 −0.425286 0.905059i \(-0.639826\pi\)
−0.425286 + 0.905059i \(0.639826\pi\)
\(312\) 0 0
\(313\) −2.00000 −0.113047 −0.0565233 0.998401i \(-0.518002\pi\)
−0.0565233 + 0.998401i \(0.518002\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −12.0000 −0.673987 −0.336994 0.941507i \(-0.609410\pi\)
−0.336994 + 0.941507i \(0.609410\pi\)
\(318\) 0 0
\(319\) 16.0000 0.895828
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 12.0000 0.667698
\(324\) 0 0
\(325\) −16.0000 −0.887520
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 11.0000 0.606450
\(330\) 0 0
\(331\) −1.00000 −0.0549650 −0.0274825 0.999622i \(-0.508749\pi\)
−0.0274825 + 0.999622i \(0.508749\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 4.00000 0.218543
\(336\) 0 0
\(337\) 23.0000 1.25289 0.626445 0.779466i \(-0.284509\pi\)
0.626445 + 0.779466i \(0.284509\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 16.0000 0.866449
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 28.0000 1.50312 0.751559 0.659665i \(-0.229302\pi\)
0.751559 + 0.659665i \(0.229302\pi\)
\(348\) 0 0
\(349\) −32.0000 −1.71292 −0.856460 0.516213i \(-0.827341\pi\)
−0.856460 + 0.516213i \(0.827341\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −29.0000 −1.54351 −0.771757 0.635917i \(-0.780622\pi\)
−0.771757 + 0.635917i \(0.780622\pi\)
\(354\) 0 0
\(355\) −4.00000 −0.212298
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 14.0000 0.738892 0.369446 0.929252i \(-0.379548\pi\)
0.369446 + 0.929252i \(0.379548\pi\)
\(360\) 0 0
\(361\) −3.00000 −0.157895
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −12.0000 −0.628109
\(366\) 0 0
\(367\) −6.00000 −0.313197 −0.156599 0.987662i \(-0.550053\pi\)
−0.156599 + 0.987662i \(0.550053\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 2.00000 0.103835
\(372\) 0 0
\(373\) −1.00000 −0.0517780 −0.0258890 0.999665i \(-0.508242\pi\)
−0.0258890 + 0.999665i \(0.508242\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 32.0000 1.64808
\(378\) 0 0
\(379\) 25.0000 1.28416 0.642082 0.766636i \(-0.278071\pi\)
0.642082 + 0.766636i \(0.278071\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −23.0000 −1.17525 −0.587623 0.809135i \(-0.699936\pi\)
−0.587623 + 0.809135i \(0.699936\pi\)
\(384\) 0 0
\(385\) 2.00000 0.101929
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −30.0000 −1.52106 −0.760530 0.649303i \(-0.775061\pi\)
−0.760530 + 0.649303i \(0.775061\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 1.00000 0.0503155
\(396\) 0 0
\(397\) −8.00000 −0.401508 −0.200754 0.979642i \(-0.564339\pi\)
−0.200754 + 0.979642i \(0.564339\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −2.00000 −0.0998752 −0.0499376 0.998752i \(-0.515902\pi\)
−0.0499376 + 0.998752i \(0.515902\pi\)
\(402\) 0 0
\(403\) 32.0000 1.59403
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −22.0000 −1.09050
\(408\) 0 0
\(409\) 4.00000 0.197787 0.0988936 0.995098i \(-0.468470\pi\)
0.0988936 + 0.995098i \(0.468470\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 11.0000 0.541275
\(414\) 0 0
\(415\) −3.00000 −0.147264
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −13.0000 −0.635092 −0.317546 0.948243i \(-0.602859\pi\)
−0.317546 + 0.948243i \(0.602859\pi\)
\(420\) 0 0
\(421\) 38.0000 1.85201 0.926003 0.377515i \(-0.123221\pi\)
0.926003 + 0.377515i \(0.123221\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −12.0000 −0.582086
\(426\) 0 0
\(427\) 6.00000 0.290360
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −24.0000 −1.15604 −0.578020 0.816023i \(-0.696174\pi\)
−0.578020 + 0.816023i \(0.696174\pi\)
\(432\) 0 0
\(433\) 10.0000 0.480569 0.240285 0.970702i \(-0.422759\pi\)
0.240285 + 0.970702i \(0.422759\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) −26.0000 −1.24091 −0.620456 0.784241i \(-0.713053\pi\)
−0.620456 + 0.784241i \(0.713053\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −24.0000 −1.14027 −0.570137 0.821549i \(-0.693110\pi\)
−0.570137 + 0.821549i \(0.693110\pi\)
\(444\) 0 0
\(445\) −10.0000 −0.474045
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 40.0000 1.88772 0.943858 0.330350i \(-0.107167\pi\)
0.943858 + 0.330350i \(0.107167\pi\)
\(450\) 0 0
\(451\) −14.0000 −0.659234
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 4.00000 0.187523
\(456\) 0 0
\(457\) −10.0000 −0.467780 −0.233890 0.972263i \(-0.575146\pi\)
−0.233890 + 0.972263i \(0.575146\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −39.0000 −1.81641 −0.908206 0.418524i \(-0.862547\pi\)
−0.908206 + 0.418524i \(0.862547\pi\)
\(462\) 0 0
\(463\) 5.00000 0.232370 0.116185 0.993228i \(-0.462933\pi\)
0.116185 + 0.993228i \(0.462933\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −4.00000 −0.185098 −0.0925490 0.995708i \(-0.529501\pi\)
−0.0925490 + 0.995708i \(0.529501\pi\)
\(468\) 0 0
\(469\) 4.00000 0.184703
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 22.0000 1.01156
\(474\) 0 0
\(475\) −16.0000 −0.734130
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −9.00000 −0.411220 −0.205610 0.978634i \(-0.565918\pi\)
−0.205610 + 0.978634i \(0.565918\pi\)
\(480\) 0 0
\(481\) −44.0000 −2.00623
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −4.00000 −0.181631
\(486\) 0 0
\(487\) −8.00000 −0.362515 −0.181257 0.983436i \(-0.558017\pi\)
−0.181257 + 0.983436i \(0.558017\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 20.0000 0.902587 0.451294 0.892375i \(-0.350963\pi\)
0.451294 + 0.892375i \(0.350963\pi\)
\(492\) 0 0
\(493\) 24.0000 1.08091
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −4.00000 −0.179425
\(498\) 0 0
\(499\) −15.0000 −0.671492 −0.335746 0.941953i \(-0.608988\pi\)
−0.335746 + 0.941953i \(0.608988\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 21.0000 0.936344 0.468172 0.883637i \(-0.344913\pi\)
0.468172 + 0.883637i \(0.344913\pi\)
\(504\) 0 0
\(505\) 18.0000 0.800989
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −21.0000 −0.930809 −0.465404 0.885098i \(-0.654091\pi\)
−0.465404 + 0.885098i \(0.654091\pi\)
\(510\) 0 0
\(511\) −12.0000 −0.530849
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −12.0000 −0.528783
\(516\) 0 0
\(517\) −22.0000 −0.967559
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 3.00000 0.131432 0.0657162 0.997838i \(-0.479067\pi\)
0.0657162 + 0.997838i \(0.479067\pi\)
\(522\) 0 0
\(523\) −6.00000 −0.262362 −0.131181 0.991358i \(-0.541877\pi\)
−0.131181 + 0.991358i \(0.541877\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 24.0000 1.04546
\(528\) 0 0
\(529\) −23.0000 −1.00000
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −28.0000 −1.21281
\(534\) 0 0
\(535\) −4.00000 −0.172935
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 2.00000 0.0861461
\(540\) 0 0
\(541\) 25.0000 1.07483 0.537417 0.843317i \(-0.319400\pi\)
0.537417 + 0.843317i \(0.319400\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −11.0000 −0.471188
\(546\) 0 0
\(547\) 27.0000 1.15444 0.577218 0.816590i \(-0.304138\pi\)
0.577218 + 0.816590i \(0.304138\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 32.0000 1.36325
\(552\) 0 0
\(553\) 1.00000 0.0425243
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 32.0000 1.35588 0.677942 0.735116i \(-0.262872\pi\)
0.677942 + 0.735116i \(0.262872\pi\)
\(558\) 0 0
\(559\) 44.0000 1.86100
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −12.0000 −0.505740 −0.252870 0.967500i \(-0.581374\pi\)
−0.252870 + 0.967500i \(0.581374\pi\)
\(564\) 0 0
\(565\) −14.0000 −0.588984
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 20.0000 0.838444 0.419222 0.907884i \(-0.362303\pi\)
0.419222 + 0.907884i \(0.362303\pi\)
\(570\) 0 0
\(571\) −5.00000 −0.209243 −0.104622 0.994512i \(-0.533363\pi\)
−0.104622 + 0.994512i \(0.533363\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 30.0000 1.24892 0.624458 0.781058i \(-0.285320\pi\)
0.624458 + 0.781058i \(0.285320\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −3.00000 −0.124461
\(582\) 0 0
\(583\) −4.00000 −0.165663
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −12.0000 −0.495293 −0.247647 0.968850i \(-0.579657\pi\)
−0.247647 + 0.968850i \(0.579657\pi\)
\(588\) 0 0
\(589\) 32.0000 1.31854
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −21.0000 −0.862367 −0.431183 0.902264i \(-0.641904\pi\)
−0.431183 + 0.902264i \(0.641904\pi\)
\(594\) 0 0
\(595\) 3.00000 0.122988
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 46.0000 1.87951 0.939755 0.341850i \(-0.111053\pi\)
0.939755 + 0.341850i \(0.111053\pi\)
\(600\) 0 0
\(601\) −32.0000 −1.30531 −0.652654 0.757656i \(-0.726344\pi\)
−0.652654 + 0.757656i \(0.726344\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 7.00000 0.284590
\(606\) 0 0
\(607\) 38.0000 1.54237 0.771186 0.636610i \(-0.219664\pi\)
0.771186 + 0.636610i \(0.219664\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −44.0000 −1.78005
\(612\) 0 0
\(613\) −6.00000 −0.242338 −0.121169 0.992632i \(-0.538664\pi\)
−0.121169 + 0.992632i \(0.538664\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 12.0000 0.483102 0.241551 0.970388i \(-0.422344\pi\)
0.241551 + 0.970388i \(0.422344\pi\)
\(618\) 0 0
\(619\) 36.0000 1.44696 0.723481 0.690344i \(-0.242541\pi\)
0.723481 + 0.690344i \(0.242541\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −10.0000 −0.400642
\(624\) 0 0
\(625\) 11.0000 0.440000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −33.0000 −1.31580
\(630\) 0 0
\(631\) 29.0000 1.15447 0.577236 0.816577i \(-0.304131\pi\)
0.577236 + 0.816577i \(0.304131\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 7.00000 0.277787
\(636\) 0 0
\(637\) 4.00000 0.158486
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 10.0000 0.394976 0.197488 0.980305i \(-0.436722\pi\)
0.197488 + 0.980305i \(0.436722\pi\)
\(642\) 0 0
\(643\) −18.0000 −0.709851 −0.354925 0.934895i \(-0.615494\pi\)
−0.354925 + 0.934895i \(0.615494\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(648\) 0 0
\(649\) −22.0000 −0.863576
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 10.0000 0.391330 0.195665 0.980671i \(-0.437313\pi\)
0.195665 + 0.980671i \(0.437313\pi\)
\(654\) 0 0
\(655\) −20.0000 −0.781465
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 6.00000 0.233727 0.116863 0.993148i \(-0.462716\pi\)
0.116863 + 0.993148i \(0.462716\pi\)
\(660\) 0 0
\(661\) 14.0000 0.544537 0.272268 0.962221i \(-0.412226\pi\)
0.272268 + 0.962221i \(0.412226\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 4.00000 0.155113
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −12.0000 −0.463255
\(672\) 0 0
\(673\) 26.0000 1.00223 0.501113 0.865382i \(-0.332924\pi\)
0.501113 + 0.865382i \(0.332924\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −26.0000 −0.999261 −0.499631 0.866239i \(-0.666531\pi\)
−0.499631 + 0.866239i \(0.666531\pi\)
\(678\) 0 0
\(679\) −4.00000 −0.153506
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −12.0000 −0.459167 −0.229584 0.973289i \(-0.573736\pi\)
−0.229584 + 0.973289i \(0.573736\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −8.00000 −0.304776
\(690\) 0 0
\(691\) 34.0000 1.29342 0.646710 0.762736i \(-0.276144\pi\)
0.646710 + 0.762736i \(0.276144\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −14.0000 −0.531050
\(696\) 0 0
\(697\) −21.0000 −0.795432
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 42.0000 1.58632 0.793159 0.609015i \(-0.208435\pi\)
0.793159 + 0.609015i \(0.208435\pi\)
\(702\) 0 0
\(703\) −44.0000 −1.65949
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 18.0000 0.676960
\(708\) 0 0
\(709\) −29.0000 −1.08912 −0.544559 0.838723i \(-0.683303\pi\)
−0.544559 + 0.838723i \(0.683303\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) −8.00000 −0.299183
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 1.00000 0.0372937 0.0186469 0.999826i \(-0.494064\pi\)
0.0186469 + 0.999826i \(0.494064\pi\)
\(720\) 0 0
\(721\) −12.0000 −0.446903
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −32.0000 −1.18845
\(726\) 0 0
\(727\) −12.0000 −0.445055 −0.222528 0.974926i \(-0.571431\pi\)
−0.222528 + 0.974926i \(0.571431\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 33.0000 1.22055
\(732\) 0 0
\(733\) 2.00000 0.0738717 0.0369358 0.999318i \(-0.488240\pi\)
0.0369358 + 0.999318i \(0.488240\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −8.00000 −0.294684
\(738\) 0 0
\(739\) −20.0000 −0.735712 −0.367856 0.929883i \(-0.619908\pi\)
−0.367856 + 0.929883i \(0.619908\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −36.0000 −1.32071 −0.660356 0.750953i \(-0.729595\pi\)
−0.660356 + 0.750953i \(0.729595\pi\)
\(744\) 0 0
\(745\) 18.0000 0.659469
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −4.00000 −0.146157
\(750\) 0 0
\(751\) −16.0000 −0.583848 −0.291924 0.956441i \(-0.594295\pi\)
−0.291924 + 0.956441i \(0.594295\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −9.00000 −0.327544
\(756\) 0 0
\(757\) 27.0000 0.981332 0.490666 0.871348i \(-0.336754\pi\)
0.490666 + 0.871348i \(0.336754\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 21.0000 0.761249 0.380625 0.924730i \(-0.375709\pi\)
0.380625 + 0.924730i \(0.375709\pi\)
\(762\) 0 0
\(763\) −11.0000 −0.398227
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −44.0000 −1.58875
\(768\) 0 0
\(769\) −50.0000 −1.80305 −0.901523 0.432731i \(-0.857550\pi\)
−0.901523 + 0.432731i \(0.857550\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 21.0000 0.755318 0.377659 0.925945i \(-0.376729\pi\)
0.377659 + 0.925945i \(0.376729\pi\)
\(774\) 0 0
\(775\) −32.0000 −1.14947
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −28.0000 −1.00320
\(780\) 0 0
\(781\) 8.00000 0.286263
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −8.00000 −0.285532
\(786\) 0 0
\(787\) −12.0000 −0.427754 −0.213877 0.976861i \(-0.568609\pi\)
−0.213877 + 0.976861i \(0.568609\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −14.0000 −0.497783
\(792\) 0 0
\(793\) −24.0000 −0.852265
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 18.0000 0.637593 0.318796 0.947823i \(-0.396721\pi\)
0.318796 + 0.947823i \(0.396721\pi\)
\(798\) 0 0
\(799\) −33.0000 −1.16746
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 24.0000 0.846942
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 46.0000 1.61727 0.808637 0.588308i \(-0.200206\pi\)
0.808637 + 0.588308i \(0.200206\pi\)
\(810\) 0 0
\(811\) −2.00000 −0.0702295 −0.0351147 0.999383i \(-0.511180\pi\)
−0.0351147 + 0.999383i \(0.511180\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −25.0000 −0.875712
\(816\) 0 0
\(817\) 44.0000 1.53937
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −16.0000 −0.558404 −0.279202 0.960232i \(-0.590070\pi\)
−0.279202 + 0.960232i \(0.590070\pi\)
\(822\) 0 0
\(823\) 37.0000 1.28974 0.644869 0.764293i \(-0.276912\pi\)
0.644869 + 0.764293i \(0.276912\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −22.0000 −0.765015 −0.382507 0.923952i \(-0.624939\pi\)
−0.382507 + 0.923952i \(0.624939\pi\)
\(828\) 0 0
\(829\) −4.00000 −0.138926 −0.0694629 0.997585i \(-0.522129\pi\)
−0.0694629 + 0.997585i \(0.522129\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 3.00000 0.103944
\(834\) 0 0
\(835\) −1.00000 −0.0346064
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −11.0000 −0.379762 −0.189881 0.981807i \(-0.560810\pi\)
−0.189881 + 0.981807i \(0.560810\pi\)
\(840\) 0 0
\(841\) 35.0000 1.20690
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −3.00000 −0.103203
\(846\) 0 0
\(847\) 7.00000 0.240523
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) −30.0000 −1.02718 −0.513590 0.858036i \(-0.671685\pi\)
−0.513590 + 0.858036i \(0.671685\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 37.0000 1.26390 0.631948 0.775011i \(-0.282256\pi\)
0.631948 + 0.775011i \(0.282256\pi\)
\(858\) 0 0
\(859\) 14.0000 0.477674 0.238837 0.971060i \(-0.423234\pi\)
0.238837 + 0.971060i \(0.423234\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 10.0000 0.340404 0.170202 0.985409i \(-0.445558\pi\)
0.170202 + 0.985409i \(0.445558\pi\)
\(864\) 0 0
\(865\) 18.0000 0.612018
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −2.00000 −0.0678454
\(870\) 0 0
\(871\) −16.0000 −0.542139
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −9.00000 −0.304256
\(876\) 0 0
\(877\) −47.0000 −1.58708 −0.793539 0.608520i \(-0.791764\pi\)
−0.793539 + 0.608520i \(0.791764\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 30.0000 1.01073 0.505363 0.862907i \(-0.331359\pi\)
0.505363 + 0.862907i \(0.331359\pi\)
\(882\) 0 0
\(883\) −43.0000 −1.44707 −0.723533 0.690290i \(-0.757483\pi\)
−0.723533 + 0.690290i \(0.757483\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −27.0000 −0.906571 −0.453286 0.891365i \(-0.649748\pi\)
−0.453286 + 0.891365i \(0.649748\pi\)
\(888\) 0 0
\(889\) 7.00000 0.234772
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −44.0000 −1.47240
\(894\) 0 0
\(895\) 18.0000 0.601674
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 64.0000 2.13452
\(900\) 0 0
\(901\) −6.00000 −0.199889
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −2.00000 −0.0664822
\(906\) 0 0
\(907\) −47.0000 −1.56061 −0.780305 0.625400i \(-0.784936\pi\)
−0.780305 + 0.625400i \(0.784936\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 42.0000 1.39152 0.695761 0.718273i \(-0.255067\pi\)
0.695761 + 0.718273i \(0.255067\pi\)
\(912\) 0 0
\(913\) 6.00000 0.198571
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −20.0000 −0.660458
\(918\) 0 0
\(919\) −3.00000 −0.0989609 −0.0494804 0.998775i \(-0.515757\pi\)
−0.0494804 + 0.998775i \(0.515757\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 16.0000 0.526646
\(924\) 0 0
\(925\) 44.0000 1.44671
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −3.00000 −0.0984268 −0.0492134 0.998788i \(-0.515671\pi\)
−0.0492134 + 0.998788i \(0.515671\pi\)
\(930\) 0 0
\(931\) 4.00000 0.131095
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −6.00000 −0.196221
\(936\) 0 0
\(937\) −52.0000 −1.69877 −0.849383 0.527777i \(-0.823026\pi\)
−0.849383 + 0.527777i \(0.823026\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −41.0000 −1.33656 −0.668281 0.743909i \(-0.732970\pi\)
−0.668281 + 0.743909i \(0.732970\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 48.0000 1.55979 0.779895 0.625910i \(-0.215272\pi\)
0.779895 + 0.625910i \(0.215272\pi\)
\(948\) 0 0
\(949\) 48.0000 1.55815
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 36.0000 1.16615 0.583077 0.812417i \(-0.301849\pi\)
0.583077 + 0.812417i \(0.301849\pi\)
\(954\) 0 0
\(955\) −18.0000 −0.582466
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 33.0000 1.06452
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −15.0000 −0.482867
\(966\) 0 0
\(967\) −24.0000 −0.771788 −0.385894 0.922543i \(-0.626107\pi\)
−0.385894 + 0.922543i \(0.626107\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 11.0000 0.353007 0.176503 0.984300i \(-0.443521\pi\)
0.176503 + 0.984300i \(0.443521\pi\)
\(972\) 0 0
\(973\) −14.0000 −0.448819
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 2.00000 0.0639857 0.0319928 0.999488i \(-0.489815\pi\)
0.0319928 + 0.999488i \(0.489815\pi\)
\(978\) 0 0
\(979\) 20.0000 0.639203
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 33.0000 1.05254 0.526268 0.850319i \(-0.323591\pi\)
0.526268 + 0.850319i \(0.323591\pi\)
\(984\) 0 0
\(985\) 16.0000 0.509802
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) −25.0000 −0.794151 −0.397076 0.917786i \(-0.629975\pi\)
−0.397076 + 0.917786i \(0.629975\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −26.0000 −0.824255
\(996\) 0 0
\(997\) 24.0000 0.760088 0.380044 0.924968i \(-0.375909\pi\)
0.380044 + 0.924968i \(0.375909\pi\)
\(998\) 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 6048.2.a.g.1.1 1
3.2 odd 2 6048.2.a.o.1.1 yes 1
4.3 odd 2 6048.2.a.h.1.1 yes 1
12.11 even 2 6048.2.a.t.1.1 yes 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6048.2.a.g.1.1 1 1.1 even 1 trivial
6048.2.a.h.1.1 yes 1 4.3 odd 2
6048.2.a.o.1.1 yes 1 3.2 odd 2
6048.2.a.t.1.1 yes 1 12.11 even 2