Properties

Label 6048.2.a.bv.1.1
Level 6048
Weight 2
Character 6048.1
Self dual yes
Analytic conductor 48.294
Analytic rank 0
Dimension 4
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: \(4\)
Coefficient field: 4.4.22896.1
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-2.65924\)
Character \(\chi\) = 6048.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.83940 q^{5} +1.00000 q^{7} +O(q^{10})\) \(q-2.83940 q^{5} +1.00000 q^{7} +2.47909 q^{11} -5.31849 q^{13} +5.78284 q^{17} -4.78284 q^{19} -3.90161 q^{23} +3.06221 q^{25} -7.10133 q^{29} +10.1013 q^{31} -2.83940 q^{35} -6.31849 q^{37} +1.41688 q^{41} +3.31849 q^{43} +5.42253 q^{47} +1.00000 q^{49} +4.00000 q^{53} -7.03912 q^{55} +5.42253 q^{59} -4.72063 q^{61} +15.1013 q^{65} +1.52656 q^{67} -11.7976 q^{71} -10.8842 q^{73} +2.47909 q^{77} +8.03912 q^{79} +14.8933 q^{83} -16.4198 q^{85} +5.41688 q^{89} -5.31849 q^{91} +13.5804 q^{95} -2.84505 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{5} + 4q^{7} + O(q^{10}) \) \( 4q + 2q^{5} + 4q^{7} + 2q^{11} + 8q^{17} - 4q^{19} + 2q^{23} + 8q^{25} + 8q^{29} + 4q^{31} + 2q^{35} - 4q^{37} + 2q^{41} - 8q^{43} + 12q^{47} + 4q^{49} + 16q^{53} + 4q^{55} + 12q^{59} - 8q^{61} + 24q^{65} + 8q^{67} - 18q^{71} + 8q^{73} + 2q^{77} - 8q^{85} + 18q^{89} + 10q^{95} + 8q^{97} + O(q^{100}) \)

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
\(5\) −2.83940 −1.26982 −0.634910 0.772586i \(-0.718963\pi\)
−0.634910 + 0.772586i \(0.718963\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 2.47909 0.747472 0.373736 0.927535i \(-0.378077\pi\)
0.373736 + 0.927535i \(0.378077\pi\)
\(12\) 0 0
\(13\) −5.31849 −1.47508 −0.737542 0.675302i \(-0.764013\pi\)
−0.737542 + 0.675302i \(0.764013\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 5.78284 1.40255 0.701273 0.712893i \(-0.252616\pi\)
0.701273 + 0.712893i \(0.252616\pi\)
\(18\) 0 0
\(19\) −4.78284 −1.09726 −0.548630 0.836065i \(-0.684850\pi\)
−0.548630 + 0.836065i \(0.684850\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −3.90161 −0.813542 −0.406771 0.913530i \(-0.633345\pi\)
−0.406771 + 0.913530i \(0.633345\pi\)
\(24\) 0 0
\(25\) 3.06221 0.612442
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −7.10133 −1.31868 −0.659342 0.751843i \(-0.729165\pi\)
−0.659342 + 0.751843i \(0.729165\pi\)
\(30\) 0 0
\(31\) 10.1013 1.81425 0.907126 0.420858i \(-0.138271\pi\)
0.907126 + 0.420858i \(0.138271\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −2.83940 −0.479947
\(36\) 0 0
\(37\) −6.31849 −1.03875 −0.519377 0.854545i \(-0.673836\pi\)
−0.519377 + 0.854545i \(0.673836\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 1.41688 0.221279 0.110640 0.993861i \(-0.464710\pi\)
0.110640 + 0.993861i \(0.464710\pi\)
\(42\) 0 0
\(43\) 3.31849 0.506065 0.253032 0.967458i \(-0.418572\pi\)
0.253032 + 0.967458i \(0.418572\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 5.42253 0.790957 0.395478 0.918475i \(-0.370579\pi\)
0.395478 + 0.918475i \(0.370579\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 4.00000 0.549442 0.274721 0.961524i \(-0.411414\pi\)
0.274721 + 0.961524i \(0.411414\pi\)
\(54\) 0 0
\(55\) −7.03912 −0.949155
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 5.42253 0.705953 0.352976 0.935632i \(-0.385170\pi\)
0.352976 + 0.935632i \(0.385170\pi\)
\(60\) 0 0
\(61\) −4.72063 −0.604415 −0.302208 0.953242i \(-0.597724\pi\)
−0.302208 + 0.953242i \(0.597724\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 15.1013 1.87309
\(66\) 0 0
\(67\) 1.52656 0.186499 0.0932496 0.995643i \(-0.470275\pi\)
0.0932496 + 0.995643i \(0.470275\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −11.7976 −1.40011 −0.700057 0.714087i \(-0.746842\pi\)
−0.700057 + 0.714087i \(0.746842\pi\)
\(72\) 0 0
\(73\) −10.8842 −1.27390 −0.636948 0.770907i \(-0.719803\pi\)
−0.636948 + 0.770907i \(0.719803\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 2.47909 0.282518
\(78\) 0 0
\(79\) 8.03912 0.904472 0.452236 0.891898i \(-0.350626\pi\)
0.452236 + 0.891898i \(0.350626\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 14.8933 1.63475 0.817374 0.576108i \(-0.195429\pi\)
0.817374 + 0.576108i \(0.195429\pi\)
\(84\) 0 0
\(85\) −16.4198 −1.78098
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 5.41688 0.574188 0.287094 0.957902i \(-0.407311\pi\)
0.287094 + 0.957902i \(0.407311\pi\)
\(90\) 0 0
\(91\) −5.31849 −0.557529
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 13.5804 1.39332
\(96\) 0 0
\(97\) −2.84505 −0.288871 −0.144436 0.989514i \(-0.546137\pi\)
−0.144436 + 0.989514i \(0.546137\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 13.7828 1.37144 0.685722 0.727863i \(-0.259487\pi\)
0.685722 + 0.727863i \(0.259487\pi\)
\(102\) 0 0
\(103\) −14.9464 −1.47271 −0.736355 0.676595i \(-0.763455\pi\)
−0.736355 + 0.676595i \(0.763455\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −3.17533 −0.306971 −0.153485 0.988151i \(-0.549050\pi\)
−0.153485 + 0.988151i \(0.549050\pi\)
\(108\) 0 0
\(109\) 1.38070 0.132247 0.0661234 0.997811i \(-0.478937\pi\)
0.0661234 + 0.997811i \(0.478937\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 8.95817 0.842714 0.421357 0.906895i \(-0.361554\pi\)
0.421357 + 0.906895i \(0.361554\pi\)
\(114\) 0 0
\(115\) 11.0782 1.03305
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 5.78284 0.530112
\(120\) 0 0
\(121\) −4.85413 −0.441285
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 5.50217 0.492129
\(126\) 0 0
\(127\) −20.6761 −1.83471 −0.917354 0.398073i \(-0.869679\pi\)
−0.917354 + 0.398073i \(0.869679\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −8.78014 −0.767124 −0.383562 0.923515i \(-0.625303\pi\)
−0.383562 + 0.923515i \(0.625303\pi\)
\(132\) 0 0
\(133\) −4.78284 −0.414725
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 18.1726 1.55259 0.776296 0.630369i \(-0.217096\pi\)
0.776296 + 0.630369i \(0.217096\pi\)
\(138\) 0 0
\(139\) −17.4820 −1.48281 −0.741403 0.671060i \(-0.765839\pi\)
−0.741403 + 0.671060i \(0.765839\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −13.1850 −1.10258
\(144\) 0 0
\(145\) 20.1635 1.67449
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 9.88688 0.809965 0.404982 0.914324i \(-0.367278\pi\)
0.404982 + 0.914324i \(0.367278\pi\)
\(150\) 0 0
\(151\) 6.72063 0.546917 0.273459 0.961884i \(-0.411832\pi\)
0.273459 + 0.961884i \(0.411832\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −28.6817 −2.30377
\(156\) 0 0
\(157\) 19.5212 1.55796 0.778979 0.627050i \(-0.215738\pi\)
0.778979 + 0.627050i \(0.215738\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −3.90161 −0.307490
\(162\) 0 0
\(163\) 10.2472 0.802622 0.401311 0.915942i \(-0.368555\pi\)
0.401311 + 0.915942i \(0.368555\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 12.9582 1.00273 0.501367 0.865235i \(-0.332831\pi\)
0.501367 + 0.865235i \(0.332831\pi\)
\(168\) 0 0
\(169\) 15.2863 1.17587
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 10.9434 0.832014 0.416007 0.909361i \(-0.363429\pi\)
0.416007 + 0.909361i \(0.363429\pi\)
\(174\) 0 0
\(175\) 3.06221 0.231481
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −8.10404 −0.605724 −0.302862 0.953034i \(-0.597942\pi\)
−0.302862 + 0.953034i \(0.597942\pi\)
\(180\) 0 0
\(181\) 6.28632 0.467258 0.233629 0.972326i \(-0.424940\pi\)
0.233629 + 0.972326i \(0.424940\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 17.9407 1.31903
\(186\) 0 0
\(187\) 14.3362 1.04836
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −17.1461 −1.24065 −0.620324 0.784346i \(-0.712999\pi\)
−0.620324 + 0.784346i \(0.712999\pi\)
\(192\) 0 0
\(193\) 9.79193 0.704838 0.352419 0.935842i \(-0.385359\pi\)
0.352419 + 0.935842i \(0.385359\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 10.8338 0.771873 0.385937 0.922525i \(-0.373878\pi\)
0.385937 + 0.922525i \(0.373878\pi\)
\(198\) 0 0
\(199\) 17.6761 1.25303 0.626513 0.779411i \(-0.284482\pi\)
0.626513 + 0.779411i \(0.284482\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −7.10133 −0.498416
\(204\) 0 0
\(205\) −4.02309 −0.280984
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −11.8571 −0.820171
\(210\) 0 0
\(211\) −16.9233 −1.16505 −0.582524 0.812814i \(-0.697935\pi\)
−0.582524 + 0.812814i \(0.697935\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −9.42253 −0.642611
\(216\) 0 0
\(217\) 10.1013 0.685723
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −30.7560 −2.06887
\(222\) 0 0
\(223\) 4.31849 0.289187 0.144594 0.989491i \(-0.453812\pi\)
0.144594 + 0.989491i \(0.453812\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 13.2445 0.879068 0.439534 0.898226i \(-0.355144\pi\)
0.439534 + 0.898226i \(0.355144\pi\)
\(228\) 0 0
\(229\) 17.9946 1.18912 0.594558 0.804053i \(-0.297327\pi\)
0.594558 + 0.804053i \(0.297327\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −3.80322 −0.249157 −0.124579 0.992210i \(-0.539758\pi\)
−0.124579 + 0.992210i \(0.539758\pi\)
\(234\) 0 0
\(235\) −15.3967 −1.00437
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 25.6643 1.66009 0.830043 0.557699i \(-0.188316\pi\)
0.830043 + 0.557699i \(0.188316\pi\)
\(240\) 0 0
\(241\) 22.1635 1.42768 0.713840 0.700309i \(-0.246955\pi\)
0.713840 + 0.700309i \(0.246955\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −2.83940 −0.181403
\(246\) 0 0
\(247\) 25.4375 1.61855
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 24.8396 1.56786 0.783932 0.620847i \(-0.213211\pi\)
0.783932 + 0.620847i \(0.213211\pi\)
\(252\) 0 0
\(253\) −9.67243 −0.608100
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 16.3660 1.02088 0.510440 0.859913i \(-0.329482\pi\)
0.510440 + 0.859913i \(0.329482\pi\)
\(258\) 0 0
\(259\) −6.31849 −0.392612
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −11.6935 −0.721054 −0.360527 0.932749i \(-0.617403\pi\)
−0.360527 + 0.932749i \(0.617403\pi\)
\(264\) 0 0
\(265\) −11.3576 −0.697693
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −10.3011 −0.628066 −0.314033 0.949412i \(-0.601680\pi\)
−0.314033 + 0.949412i \(0.601680\pi\)
\(270\) 0 0
\(271\) −7.07129 −0.429550 −0.214775 0.976664i \(-0.568902\pi\)
−0.214775 + 0.976664i \(0.568902\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 7.59148 0.457783
\(276\) 0 0
\(277\) −5.59785 −0.336342 −0.168171 0.985758i \(-0.553786\pi\)
−0.168171 + 0.985758i \(0.553786\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 12.9882 0.774812 0.387406 0.921909i \(-0.373371\pi\)
0.387406 + 0.921909i \(0.373371\pi\)
\(282\) 0 0
\(283\) 7.35761 0.437365 0.218682 0.975796i \(-0.429824\pi\)
0.218682 + 0.975796i \(0.429824\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 1.41688 0.0836356
\(288\) 0 0
\(289\) 16.4413 0.967133
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 28.9324 1.69025 0.845124 0.534571i \(-0.179527\pi\)
0.845124 + 0.534571i \(0.179527\pi\)
\(294\) 0 0
\(295\) −15.3967 −0.896433
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 20.7507 1.20004
\(300\) 0 0
\(301\) 3.31849 0.191274
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 13.4038 0.767498
\(306\) 0 0
\(307\) 30.6155 1.74732 0.873660 0.486537i \(-0.161740\pi\)
0.873660 + 0.486537i \(0.161740\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 1.41123 0.0800235 0.0400117 0.999199i \(-0.487260\pi\)
0.0400117 + 0.999199i \(0.487260\pi\)
\(312\) 0 0
\(313\) −19.7292 −1.11516 −0.557581 0.830123i \(-0.688270\pi\)
−0.557581 + 0.830123i \(0.688270\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −1.70884 −0.0959783 −0.0479891 0.998848i \(-0.515281\pi\)
−0.0479891 + 0.998848i \(0.515281\pi\)
\(318\) 0 0
\(319\) −17.6048 −0.985680
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −27.6584 −1.53896
\(324\) 0 0
\(325\) −16.2863 −0.903402
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 5.42253 0.298954
\(330\) 0 0
\(331\) 4.51256 0.248033 0.124016 0.992280i \(-0.460422\pi\)
0.124016 + 0.992280i \(0.460422\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −4.33453 −0.236820
\(336\) 0 0
\(337\) 20.9163 1.13939 0.569693 0.821858i \(-0.307062\pi\)
0.569693 + 0.821858i \(0.307062\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 25.0421 1.35610
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −7.10698 −0.381523 −0.190761 0.981636i \(-0.561096\pi\)
−0.190761 + 0.981636i \(0.561096\pi\)
\(348\) 0 0
\(349\) −7.36302 −0.394134 −0.197067 0.980390i \(-0.563142\pi\)
−0.197067 + 0.980390i \(0.563142\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −21.1016 −1.12312 −0.561562 0.827435i \(-0.689799\pi\)
−0.561562 + 0.827435i \(0.689799\pi\)
\(354\) 0 0
\(355\) 33.4981 1.77789
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 27.7887 1.46663 0.733316 0.679887i \(-0.237971\pi\)
0.733316 + 0.679887i \(0.237971\pi\)
\(360\) 0 0
\(361\) 3.87558 0.203978
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 30.9046 1.61762
\(366\) 0 0
\(367\) 33.4680 1.74702 0.873508 0.486809i \(-0.161839\pi\)
0.873508 + 0.486809i \(0.161839\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 4.00000 0.207670
\(372\) 0 0
\(373\) −32.1796 −1.66620 −0.833098 0.553126i \(-0.813435\pi\)
−0.833098 + 0.553126i \(0.813435\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 37.7683 1.94517
\(378\) 0 0
\(379\) −1.95547 −0.100446 −0.0502228 0.998738i \(-0.515993\pi\)
−0.0502228 + 0.998738i \(0.515993\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 23.5544 1.20357 0.601787 0.798657i \(-0.294456\pi\)
0.601787 + 0.798657i \(0.294456\pi\)
\(384\) 0 0
\(385\) −7.03912 −0.358747
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 29.5603 1.49877 0.749383 0.662137i \(-0.230350\pi\)
0.749383 + 0.662137i \(0.230350\pi\)
\(390\) 0 0
\(391\) −22.5624 −1.14103
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −22.8263 −1.14852
\(396\) 0 0
\(397\) −37.3984 −1.87697 −0.938485 0.345319i \(-0.887771\pi\)
−0.938485 + 0.345319i \(0.887771\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −20.1083 −1.00416 −0.502080 0.864821i \(-0.667432\pi\)
−0.502080 + 0.864821i \(0.667432\pi\)
\(402\) 0 0
\(403\) −53.7238 −2.67617
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −15.6641 −0.776439
\(408\) 0 0
\(409\) 25.3131 1.25165 0.625826 0.779963i \(-0.284762\pi\)
0.625826 + 0.779963i \(0.284762\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 5.42253 0.266825
\(414\) 0 0
\(415\) −42.2880 −2.07583
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 22.8338 1.11550 0.557751 0.830008i \(-0.311664\pi\)
0.557751 + 0.830008i \(0.311664\pi\)
\(420\) 0 0
\(421\) 30.2949 1.47648 0.738242 0.674536i \(-0.235656\pi\)
0.738242 + 0.674536i \(0.235656\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 17.7083 0.858977
\(426\) 0 0
\(427\) −4.72063 −0.228448
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −30.3011 −1.45955 −0.729775 0.683687i \(-0.760375\pi\)
−0.729775 + 0.683687i \(0.760375\pi\)
\(432\) 0 0
\(433\) 38.8005 1.86463 0.932317 0.361642i \(-0.117784\pi\)
0.932317 + 0.361642i \(0.117784\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 18.6608 0.892667
\(438\) 0 0
\(439\) 31.1314 1.48582 0.742910 0.669392i \(-0.233445\pi\)
0.742910 + 0.669392i \(0.233445\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 7.15094 0.339751 0.169876 0.985466i \(-0.445663\pi\)
0.169876 + 0.985466i \(0.445663\pi\)
\(444\) 0 0
\(445\) −15.3807 −0.729115
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 0.404852 0.0191061 0.00955307 0.999954i \(-0.496959\pi\)
0.00955307 + 0.999954i \(0.496959\pi\)
\(450\) 0 0
\(451\) 3.51256 0.165400
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 15.1013 0.707961
\(456\) 0 0
\(457\) 26.9946 1.26275 0.631377 0.775476i \(-0.282490\pi\)
0.631377 + 0.775476i \(0.282490\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 5.58042 0.259906 0.129953 0.991520i \(-0.458517\pi\)
0.129953 + 0.991520i \(0.458517\pi\)
\(462\) 0 0
\(463\) −8.63698 −0.401394 −0.200697 0.979653i \(-0.564321\pi\)
−0.200697 + 0.979653i \(0.564321\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −18.4295 −0.852815 −0.426407 0.904531i \(-0.640221\pi\)
−0.426407 + 0.904531i \(0.640221\pi\)
\(468\) 0 0
\(469\) 1.52656 0.0704901
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 8.22682 0.378269
\(474\) 0 0
\(475\) −14.6461 −0.672007
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −40.6316 −1.85650 −0.928252 0.371952i \(-0.878688\pi\)
−0.928252 + 0.371952i \(0.878688\pi\)
\(480\) 0 0
\(481\) 33.6048 1.53225
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 8.07825 0.366814
\(486\) 0 0
\(487\) 1.87722 0.0850650 0.0425325 0.999095i \(-0.486457\pi\)
0.0425325 + 0.999095i \(0.486457\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −30.9772 −1.39798 −0.698990 0.715132i \(-0.746367\pi\)
−0.698990 + 0.715132i \(0.746367\pi\)
\(492\) 0 0
\(493\) −41.0659 −1.84951
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −11.7976 −0.529194
\(498\) 0 0
\(499\) 18.5979 0.832554 0.416277 0.909238i \(-0.363335\pi\)
0.416277 + 0.909238i \(0.363335\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −36.1672 −1.61262 −0.806308 0.591496i \(-0.798538\pi\)
−0.806308 + 0.591496i \(0.798538\pi\)
\(504\) 0 0
\(505\) −39.1350 −1.74149
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −29.9018 −1.32538 −0.662688 0.748896i \(-0.730584\pi\)
−0.662688 + 0.748896i \(0.730584\pi\)
\(510\) 0 0
\(511\) −10.8842 −0.481487
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 42.4388 1.87008
\(516\) 0 0
\(517\) 13.4429 0.591218
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −21.0866 −0.923821 −0.461910 0.886927i \(-0.652836\pi\)
−0.461910 + 0.886927i \(0.652836\pi\)
\(522\) 0 0
\(523\) 25.9233 1.13355 0.566773 0.823874i \(-0.308192\pi\)
0.566773 + 0.823874i \(0.308192\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 58.4144 2.54457
\(528\) 0 0
\(529\) −7.77743 −0.338149
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −7.53565 −0.326405
\(534\) 0 0
\(535\) 9.01604 0.389797
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 2.47909 0.106782
\(540\) 0 0
\(541\) −0.836461 −0.0359623 −0.0179811 0.999838i \(-0.505724\pi\)
−0.0179811 + 0.999838i \(0.505724\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −3.92035 −0.167930
\(546\) 0 0
\(547\) −4.94688 −0.211513 −0.105757 0.994392i \(-0.533726\pi\)
−0.105757 + 0.994392i \(0.533726\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 33.9645 1.44694
\(552\) 0 0
\(553\) 8.03912 0.341858
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 34.4777 1.46087 0.730433 0.682984i \(-0.239318\pi\)
0.730433 + 0.682984i \(0.239318\pi\)
\(558\) 0 0
\(559\) −17.6493 −0.746488
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 9.22575 0.388819 0.194409 0.980920i \(-0.437721\pi\)
0.194409 + 0.980920i \(0.437721\pi\)
\(564\) 0 0
\(565\) −25.4359 −1.07009
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 28.0895 1.17757 0.588787 0.808288i \(-0.299606\pi\)
0.588787 + 0.808288i \(0.299606\pi\)
\(570\) 0 0
\(571\) −4.35066 −0.182069 −0.0910347 0.995848i \(-0.529017\pi\)
−0.0910347 + 0.995848i \(0.529017\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −11.9475 −0.498247
\(576\) 0 0
\(577\) 10.9287 0.454968 0.227484 0.973782i \(-0.426950\pi\)
0.227484 + 0.973782i \(0.426950\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 14.8933 0.617876
\(582\) 0 0
\(583\) 9.91634 0.410693
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −2.87451 −0.118644 −0.0593219 0.998239i \(-0.518894\pi\)
−0.0593219 + 0.998239i \(0.518894\pi\)
\(588\) 0 0
\(589\) −48.3131 −1.99071
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −39.8018 −1.63446 −0.817232 0.576308i \(-0.804493\pi\)
−0.817232 + 0.576308i \(0.804493\pi\)
\(594\) 0 0
\(595\) −16.4198 −0.673147
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −6.09298 −0.248952 −0.124476 0.992223i \(-0.539725\pi\)
−0.124476 + 0.992223i \(0.539725\pi\)
\(600\) 0 0
\(601\) 9.31849 0.380109 0.190055 0.981774i \(-0.439134\pi\)
0.190055 + 0.981774i \(0.439134\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 13.7828 0.560352
\(606\) 0 0
\(607\) 4.20807 0.170800 0.0854002 0.996347i \(-0.472783\pi\)
0.0854002 + 0.996347i \(0.472783\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −28.8396 −1.16673
\(612\) 0 0
\(613\) −10.1013 −0.407989 −0.203994 0.978972i \(-0.565392\pi\)
−0.203994 + 0.978972i \(0.565392\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −14.9046 −0.600035 −0.300017 0.953934i \(-0.596992\pi\)
−0.300017 + 0.953934i \(0.596992\pi\)
\(618\) 0 0
\(619\) −27.5126 −1.10582 −0.552912 0.833240i \(-0.686483\pi\)
−0.552912 + 0.833240i \(0.686483\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 5.41688 0.217023
\(624\) 0 0
\(625\) −30.9339 −1.23736
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −36.5388 −1.45690
\(630\) 0 0
\(631\) −7.24024 −0.288230 −0.144115 0.989561i \(-0.546033\pi\)
−0.144115 + 0.989561i \(0.546033\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 58.7078 2.32975
\(636\) 0 0
\(637\) −5.31849 −0.210726
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −15.7625 −0.622580 −0.311290 0.950315i \(-0.600761\pi\)
−0.311290 + 0.950315i \(0.600761\pi\)
\(642\) 0 0
\(643\) 18.0622 0.712304 0.356152 0.934428i \(-0.384089\pi\)
0.356152 + 0.934428i \(0.384089\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −31.0900 −1.22228 −0.611138 0.791524i \(-0.709288\pi\)
−0.611138 + 0.791524i \(0.709288\pi\)
\(648\) 0 0
\(649\) 13.4429 0.527680
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 13.7088 0.536469 0.268234 0.963354i \(-0.413560\pi\)
0.268234 + 0.963354i \(0.413560\pi\)
\(654\) 0 0
\(655\) 24.9303 0.974109
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 16.0394 0.624805 0.312402 0.949950i \(-0.398866\pi\)
0.312402 + 0.949950i \(0.398866\pi\)
\(660\) 0 0
\(661\) −36.4906 −1.41932 −0.709660 0.704544i \(-0.751152\pi\)
−0.709660 + 0.704544i \(0.751152\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 13.5804 0.526626
\(666\) 0 0
\(667\) 27.7066 1.07281
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −11.7029 −0.451784
\(672\) 0 0
\(673\) 13.7919 0.531640 0.265820 0.964023i \(-0.414357\pi\)
0.265820 + 0.964023i \(0.414357\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 10.6313 0.408595 0.204298 0.978909i \(-0.434509\pi\)
0.204298 + 0.978909i \(0.434509\pi\)
\(678\) 0 0
\(679\) −2.84505 −0.109183
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −27.6340 −1.05739 −0.528693 0.848813i \(-0.677318\pi\)
−0.528693 + 0.848813i \(0.677318\pi\)
\(684\) 0 0
\(685\) −51.5994 −1.97151
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −21.2740 −0.810473
\(690\) 0 0
\(691\) −44.1190 −1.67837 −0.839183 0.543849i \(-0.816966\pi\)
−0.839183 + 0.543849i \(0.816966\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 49.6385 1.88290
\(696\) 0 0
\(697\) 8.19358 0.310354
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 5.43382 0.205233 0.102616 0.994721i \(-0.467279\pi\)
0.102616 + 0.994721i \(0.467279\pi\)
\(702\) 0 0
\(703\) 30.2203 1.13978
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 13.7828 0.518357
\(708\) 0 0
\(709\) 25.4771 0.956813 0.478406 0.878139i \(-0.341215\pi\)
0.478406 + 0.878139i \(0.341215\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −39.4115 −1.47597
\(714\) 0 0
\(715\) 37.4375 1.40008
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 7.07187 0.263736 0.131868 0.991267i \(-0.457902\pi\)
0.131868 + 0.991267i \(0.457902\pi\)
\(720\) 0 0
\(721\) −14.9464 −0.556632
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −21.7458 −0.807617
\(726\) 0 0
\(727\) −39.7629 −1.47473 −0.737363 0.675497i \(-0.763929\pi\)
−0.737363 + 0.675497i \(0.763929\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 19.1903 0.709779
\(732\) 0 0
\(733\) −11.9609 −0.441785 −0.220893 0.975298i \(-0.570897\pi\)
−0.220893 + 0.975298i \(0.570897\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 3.78448 0.139403
\(738\) 0 0
\(739\) 16.9415 0.623202 0.311601 0.950213i \(-0.399135\pi\)
0.311601 + 0.950213i \(0.399135\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −32.2920 −1.18468 −0.592339 0.805689i \(-0.701795\pi\)
−0.592339 + 0.805689i \(0.701795\pi\)
\(744\) 0 0
\(745\) −28.0728 −1.02851
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −3.17533 −0.116024
\(750\) 0 0
\(751\) −26.1635 −0.954721 −0.477361 0.878708i \(-0.658406\pi\)
−0.477361 + 0.878708i \(0.658406\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −19.0826 −0.694486
\(756\) 0 0
\(757\) 41.9109 1.52328 0.761639 0.648001i \(-0.224395\pi\)
0.761639 + 0.648001i \(0.224395\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −16.1335 −0.584839 −0.292419 0.956290i \(-0.594460\pi\)
−0.292419 + 0.956290i \(0.594460\pi\)
\(762\) 0 0
\(763\) 1.38070 0.0499846
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −28.8396 −1.04134
\(768\) 0 0
\(769\) −36.7951 −1.32687 −0.663433 0.748236i \(-0.730901\pi\)
−0.663433 + 0.748236i \(0.730901\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −14.3155 −0.514894 −0.257447 0.966292i \(-0.582881\pi\)
−0.257447 + 0.966292i \(0.582881\pi\)
\(774\) 0 0
\(775\) 30.9324 1.11112
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −6.77670 −0.242801
\(780\) 0 0
\(781\) −29.2472 −1.04655
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −55.4284 −1.97832
\(786\) 0 0
\(787\) 2.42890 0.0865810 0.0432905 0.999063i \(-0.486216\pi\)
0.0432905 + 0.999063i \(0.486216\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 8.95817 0.318516
\(792\) 0 0
\(793\) 25.1066 0.891563
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 41.8035 1.48075 0.740377 0.672192i \(-0.234647\pi\)
0.740377 + 0.672192i \(0.234647\pi\)
\(798\) 0 0
\(799\) 31.3576 1.10935
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −26.9828 −0.952202
\(804\) 0 0
\(805\) 11.0782 0.390457
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −14.6670 −0.515665 −0.257832 0.966190i \(-0.583008\pi\)
−0.257832 + 0.966190i \(0.583008\pi\)
\(810\) 0 0
\(811\) 14.3630 0.504354 0.252177 0.967681i \(-0.418853\pi\)
0.252177 + 0.967681i \(0.418853\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −29.0959 −1.01919
\(816\) 0 0
\(817\) −15.8718 −0.555284
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −33.7496 −1.17787 −0.588935 0.808181i \(-0.700452\pi\)
−0.588935 + 0.808181i \(0.700452\pi\)
\(822\) 0 0
\(823\) −38.4053 −1.33873 −0.669363 0.742936i \(-0.733433\pi\)
−0.669363 + 0.742936i \(0.733433\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −25.6137 −0.890674 −0.445337 0.895363i \(-0.646916\pi\)
−0.445337 + 0.895363i \(0.646916\pi\)
\(828\) 0 0
\(829\) 17.0868 0.593450 0.296725 0.954963i \(-0.404105\pi\)
0.296725 + 0.954963i \(0.404105\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 5.78284 0.200364
\(834\) 0 0
\(835\) −36.7935 −1.27329
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −20.8697 −0.720501 −0.360251 0.932856i \(-0.617309\pi\)
−0.360251 + 0.932856i \(0.617309\pi\)
\(840\) 0 0
\(841\) 21.4289 0.738928
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −43.4040 −1.49314
\(846\) 0 0
\(847\) −4.85413 −0.166790
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 24.6523 0.845069
\(852\) 0 0
\(853\) 10.4289 0.357079 0.178539 0.983933i \(-0.442863\pi\)
0.178539 + 0.983933i \(0.442863\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 38.8989 1.32876 0.664381 0.747394i \(-0.268695\pi\)
0.664381 + 0.747394i \(0.268695\pi\)
\(858\) 0 0
\(859\) −19.3791 −0.661205 −0.330603 0.943770i \(-0.607252\pi\)
−0.330603 + 0.943770i \(0.607252\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −19.1572 −0.652117 −0.326059 0.945350i \(-0.605721\pi\)
−0.326059 + 0.945350i \(0.605721\pi\)
\(864\) 0 0
\(865\) −31.0728 −1.05651
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 19.9297 0.676068
\(870\) 0 0
\(871\) −8.11900 −0.275102
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 5.50217 0.186007
\(876\) 0 0
\(877\) −16.1801 −0.546362 −0.273181 0.961963i \(-0.588076\pi\)
−0.273181 + 0.961963i \(0.588076\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −7.95744 −0.268093 −0.134047 0.990975i \(-0.542797\pi\)
−0.134047 + 0.990975i \(0.542797\pi\)
\(882\) 0 0
\(883\) 14.4107 0.484960 0.242480 0.970156i \(-0.422039\pi\)
0.242480 + 0.970156i \(0.422039\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 47.8627 1.60707 0.803537 0.595255i \(-0.202949\pi\)
0.803537 + 0.595255i \(0.202949\pi\)
\(888\) 0 0
\(889\) −20.6761 −0.693454
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −25.9351 −0.867885
\(894\) 0 0
\(895\) 23.0106 0.769160
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −71.7329 −2.39243
\(900\) 0 0
\(901\) 23.1314 0.770618
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −17.8494 −0.593334
\(906\) 0 0
\(907\) −26.9287 −0.894153 −0.447077 0.894496i \(-0.647535\pi\)
−0.447077 + 0.894496i \(0.647535\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 21.7833 0.721713 0.360857 0.932621i \(-0.382484\pi\)
0.360857 + 0.932621i \(0.382484\pi\)
\(912\) 0 0
\(913\) 36.9217 1.22193
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −8.78014 −0.289946
\(918\) 0 0
\(919\) 0.535153 0.0176531 0.00882653 0.999961i \(-0.497190\pi\)
0.00882653 + 0.999961i \(0.497190\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 62.7453 2.06529
\(924\) 0 0
\(925\) −19.3485 −0.636176
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 15.4729 0.507651 0.253825 0.967250i \(-0.418311\pi\)
0.253825 + 0.967250i \(0.418311\pi\)
\(930\) 0 0
\(931\) −4.78284 −0.156751
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −40.7061 −1.33123
\(936\) 0 0
\(937\) 27.4359 0.896290 0.448145 0.893961i \(-0.352085\pi\)
0.448145 + 0.893961i \(0.352085\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −5.79169 −0.188804 −0.0944018 0.995534i \(-0.530094\pi\)
−0.0944018 + 0.995534i \(0.530094\pi\)
\(942\) 0 0
\(943\) −5.52810 −0.180020
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −4.57771 −0.148756 −0.0743778 0.997230i \(-0.523697\pi\)
−0.0743778 + 0.997230i \(0.523697\pi\)
\(948\) 0 0
\(949\) 57.8874 1.87910
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 36.1672 1.17157 0.585785 0.810466i \(-0.300786\pi\)
0.585785 + 0.810466i \(0.300786\pi\)
\(954\) 0 0
\(955\) 48.6847 1.57540
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 18.1726 0.586825
\(960\) 0 0
\(961\) 71.0369 2.29151
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −27.8032 −0.895017
\(966\) 0 0
\(967\) 19.0885 0.613844 0.306922 0.951735i \(-0.400701\pi\)
0.306922 + 0.951735i \(0.400701\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 44.6616 1.43326 0.716630 0.697454i \(-0.245684\pi\)
0.716630 + 0.697454i \(0.245684\pi\)
\(972\) 0 0
\(973\) −17.4820 −0.560448
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 36.9179 1.18111 0.590554 0.806998i \(-0.298909\pi\)
0.590554 + 0.806998i \(0.298909\pi\)
\(978\) 0 0
\(979\) 13.4289 0.429190
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 47.0610 1.50101 0.750507 0.660862i \(-0.229809\pi\)
0.750507 + 0.660862i \(0.229809\pi\)
\(984\) 0 0
\(985\) −30.7614 −0.980139
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −12.9475 −0.411705
\(990\) 0 0
\(991\) 30.6525 0.973709 0.486855 0.873483i \(-0.338144\pi\)
0.486855 + 0.873483i \(0.338144\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −50.1896 −1.59112
\(996\) 0 0
\(997\) −5.13137 −0.162512 −0.0812561 0.996693i \(-0.525893\pi\)
−0.0812561 + 0.996693i \(0.525893\pi\)
\(998\) 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.bv.1.1 yes 4
3.2 odd 2 6048.2.a.bo.1.4 yes 4
4.3 odd 2 6048.2.a.br.1.1 yes 4
12.11 even 2 6048.2.a.bm.1.4 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6048.2.a.bm.1.4 4 12.11 even 2
6048.2.a.bo.1.4 yes 4 3.2 odd 2
6048.2.a.br.1.1 yes 4 4.3 odd 2
6048.2.a.bv.1.1 yes 4 1.1 even 1 trivial