Properties

Label 6048.2.j.c.5615.2
Level 6048
Weight 2
Character 6048.5615
Analytic conductor 48.294
Analytic rank 0
Dimension 32
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6048.j (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(48.2935231425\)
Analytic rank: \(0\)
Dimension: \(32\)
Twist minimal: no (minimal twist has level 1512)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 5615.2
Character \(\chi\) \(=\) 6048.5615
Dual form 6048.2.j.c.5615.1

$q$-expansion

\(f(q)\) \(=\) \(q-3.61017 q^{5} -1.00000i q^{7} +O(q^{10})\) \(q-3.61017 q^{5} -1.00000i q^{7} -2.00899i q^{11} +1.59265i q^{13} -7.79257i q^{17} +5.05480 q^{19} +7.14612 q^{23} +8.03333 q^{25} -4.94298 q^{29} +2.53252i q^{31} +3.61017i q^{35} +4.76592i q^{37} +0.836835i q^{41} -0.151434 q^{43} +0.795430 q^{47} -1.00000 q^{49} -1.05980 q^{53} +7.25280i q^{55} +8.34506i q^{59} +10.2367i q^{61} -5.74974i q^{65} -0.655357 q^{67} +11.3675 q^{71} -14.3835 q^{73} -2.00899 q^{77} -3.81177i q^{79} -14.9522i q^{83} +28.1325i q^{85} +0.0444167i q^{89} +1.59265 q^{91} -18.2487 q^{95} +9.87000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + O(q^{10}) \) \( 32q + 64q^{19} - 16q^{25} + 48q^{43} - 32q^{49} - 16q^{67} - 16q^{73} - 16q^{91} + 64q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/6048\mathbb{Z}\right)^\times\).

\(n\) \(2593\) \(3781\) \(3809\) \(4159\)
\(\chi(n)\) \(1\) \(-1\) \(-1\) \(-1\)

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
\(5\) −3.61017 −1.61452 −0.807259 0.590198i \(-0.799050\pi\)
−0.807259 + 0.590198i \(0.799050\pi\)
\(6\) 0 0
\(7\) − 1.00000i − 0.377964i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) − 2.00899i − 0.605734i −0.953033 0.302867i \(-0.902056\pi\)
0.953033 0.302867i \(-0.0979438\pi\)
\(12\) 0 0
\(13\) 1.59265i 0.441722i 0.975305 + 0.220861i \(0.0708867\pi\)
−0.975305 + 0.220861i \(0.929113\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) − 7.79257i − 1.88998i −0.327106 0.944988i \(-0.606074\pi\)
0.327106 0.944988i \(-0.393926\pi\)
\(18\) 0 0
\(19\) 5.05480 1.15965 0.579825 0.814741i \(-0.303121\pi\)
0.579825 + 0.814741i \(0.303121\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 7.14612 1.49007 0.745034 0.667026i \(-0.232433\pi\)
0.745034 + 0.667026i \(0.232433\pi\)
\(24\) 0 0
\(25\) 8.03333 1.60667
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −4.94298 −0.917889 −0.458945 0.888465i \(-0.651772\pi\)
−0.458945 + 0.888465i \(0.651772\pi\)
\(30\) 0 0
\(31\) 2.53252i 0.454853i 0.973795 + 0.227427i \(0.0730312\pi\)
−0.973795 + 0.227427i \(0.926969\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 3.61017i 0.610230i
\(36\) 0 0
\(37\) 4.76592i 0.783512i 0.920069 + 0.391756i \(0.128132\pi\)
−0.920069 + 0.391756i \(0.871868\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0.836835i 0.130692i 0.997863 + 0.0653458i \(0.0208151\pi\)
−0.997863 + 0.0653458i \(0.979185\pi\)
\(42\) 0 0
\(43\) −0.151434 −0.0230934 −0.0115467 0.999933i \(-0.503676\pi\)
−0.0115467 + 0.999933i \(0.503676\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0.795430 0.116025 0.0580127 0.998316i \(-0.481524\pi\)
0.0580127 + 0.998316i \(0.481524\pi\)
\(48\) 0 0
\(49\) −1.00000 −0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −1.05980 −0.145575 −0.0727873 0.997347i \(-0.523189\pi\)
−0.0727873 + 0.997347i \(0.523189\pi\)
\(54\) 0 0
\(55\) 7.25280i 0.977968i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 8.34506i 1.08643i 0.839592 + 0.543217i \(0.182794\pi\)
−0.839592 + 0.543217i \(0.817206\pi\)
\(60\) 0 0
\(61\) 10.2367i 1.31067i 0.755336 + 0.655337i \(0.227474\pi\)
−0.755336 + 0.655337i \(0.772526\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) − 5.74974i − 0.713168i
\(66\) 0 0
\(67\) −0.655357 −0.0800646 −0.0400323 0.999198i \(-0.512746\pi\)
−0.0400323 + 0.999198i \(0.512746\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 11.3675 1.34907 0.674536 0.738242i \(-0.264344\pi\)
0.674536 + 0.738242i \(0.264344\pi\)
\(72\) 0 0
\(73\) −14.3835 −1.68346 −0.841728 0.539901i \(-0.818462\pi\)
−0.841728 + 0.539901i \(0.818462\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −2.00899 −0.228946
\(78\) 0 0
\(79\) − 3.81177i − 0.428858i −0.976740 0.214429i \(-0.931211\pi\)
0.976740 0.214429i \(-0.0687890\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) − 14.9522i − 1.64121i −0.571494 0.820606i \(-0.693636\pi\)
0.571494 0.820606i \(-0.306364\pi\)
\(84\) 0 0
\(85\) 28.1325i 3.05140i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0.0444167i 0.00470816i 0.999997 + 0.00235408i \(0.000749328\pi\)
−0.999997 + 0.00235408i \(0.999251\pi\)
\(90\) 0 0
\(91\) 1.59265 0.166955
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −18.2487 −1.87228
\(96\) 0 0
\(97\) 9.87000 1.00215 0.501073 0.865405i \(-0.332939\pi\)
0.501073 + 0.865405i \(0.332939\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 4.43029 0.440830 0.220415 0.975406i \(-0.429259\pi\)
0.220415 + 0.975406i \(0.429259\pi\)
\(102\) 0 0
\(103\) 11.2939i 1.11282i 0.830906 + 0.556412i \(0.187823\pi\)
−0.830906 + 0.556412i \(0.812177\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) − 8.60018i − 0.831411i −0.909499 0.415705i \(-0.863535\pi\)
0.909499 0.415705i \(-0.136465\pi\)
\(108\) 0 0
\(109\) − 19.9155i − 1.90756i −0.300512 0.953778i \(-0.597158\pi\)
0.300512 0.953778i \(-0.402842\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) − 3.81372i − 0.358764i −0.983779 0.179382i \(-0.942590\pi\)
0.983779 0.179382i \(-0.0574098\pi\)
\(114\) 0 0
\(115\) −25.7987 −2.40574
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −7.79257 −0.714343
\(120\) 0 0
\(121\) 6.96395 0.633086
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −10.9508 −0.979472
\(126\) 0 0
\(127\) − 15.9943i − 1.41926i −0.704574 0.709630i \(-0.748862\pi\)
0.704574 0.709630i \(-0.251138\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) − 19.8839i − 1.73726i −0.495460 0.868631i \(-0.665000\pi\)
0.495460 0.868631i \(-0.335000\pi\)
\(132\) 0 0
\(133\) − 5.05480i − 0.438307i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) − 8.93576i − 0.763433i −0.924279 0.381717i \(-0.875333\pi\)
0.924279 0.381717i \(-0.124667\pi\)
\(138\) 0 0
\(139\) −1.20344 −0.102074 −0.0510372 0.998697i \(-0.516253\pi\)
−0.0510372 + 0.998697i \(0.516253\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 3.19962 0.267566
\(144\) 0 0
\(145\) 17.8450 1.48195
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 12.6791 1.03871 0.519355 0.854559i \(-0.326172\pi\)
0.519355 + 0.854559i \(0.326172\pi\)
\(150\) 0 0
\(151\) − 17.5094i − 1.42489i −0.701727 0.712446i \(-0.747588\pi\)
0.701727 0.712446i \(-0.252412\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) − 9.14281i − 0.734368i
\(156\) 0 0
\(157\) 15.2891i 1.22020i 0.792324 + 0.610100i \(0.208871\pi\)
−0.792324 + 0.610100i \(0.791129\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) − 7.14612i − 0.563193i
\(162\) 0 0
\(163\) −17.5634 −1.37567 −0.687835 0.725867i \(-0.741439\pi\)
−0.687835 + 0.725867i \(0.741439\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −4.20290 −0.325230 −0.162615 0.986690i \(-0.551993\pi\)
−0.162615 + 0.986690i \(0.551993\pi\)
\(168\) 0 0
\(169\) 10.4635 0.804882
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −18.0074 −1.36907 −0.684537 0.728978i \(-0.739995\pi\)
−0.684537 + 0.728978i \(0.739995\pi\)
\(174\) 0 0
\(175\) − 8.03333i − 0.607263i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) − 0.886091i − 0.0662295i −0.999452 0.0331148i \(-0.989457\pi\)
0.999452 0.0331148i \(-0.0105427\pi\)
\(180\) 0 0
\(181\) − 8.47338i − 0.629821i −0.949121 0.314911i \(-0.898025\pi\)
0.949121 0.314911i \(-0.101975\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) − 17.2058i − 1.26499i
\(186\) 0 0
\(187\) −15.6552 −1.14482
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −20.6102 −1.49130 −0.745652 0.666335i \(-0.767862\pi\)
−0.745652 + 0.666335i \(0.767862\pi\)
\(192\) 0 0
\(193\) 18.2972 1.31706 0.658530 0.752555i \(-0.271179\pi\)
0.658530 + 0.752555i \(0.271179\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −10.6580 −0.759353 −0.379677 0.925119i \(-0.623965\pi\)
−0.379677 + 0.925119i \(0.623965\pi\)
\(198\) 0 0
\(199\) − 26.1305i − 1.85234i −0.377108 0.926169i \(-0.623081\pi\)
0.377108 0.926169i \(-0.376919\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 4.94298i 0.346929i
\(204\) 0 0
\(205\) − 3.02112i − 0.211004i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) − 10.1551i − 0.702440i
\(210\) 0 0
\(211\) 21.1542 1.45632 0.728159 0.685409i \(-0.240376\pi\)
0.728159 + 0.685409i \(0.240376\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0.546701 0.0372847
\(216\) 0 0
\(217\) 2.53252 0.171918
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 12.4108 0.834844
\(222\) 0 0
\(223\) 6.04274i 0.404652i 0.979318 + 0.202326i \(0.0648500\pi\)
−0.979318 + 0.202326i \(0.935150\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) − 20.0726i − 1.33227i −0.745832 0.666134i \(-0.767948\pi\)
0.745832 0.666134i \(-0.232052\pi\)
\(228\) 0 0
\(229\) − 18.5176i − 1.22368i −0.790983 0.611838i \(-0.790430\pi\)
0.790983 0.611838i \(-0.209570\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 17.1203i 1.12159i 0.827956 + 0.560793i \(0.189504\pi\)
−0.827956 + 0.560793i \(0.810496\pi\)
\(234\) 0 0
\(235\) −2.87164 −0.187325
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −3.95612 −0.255900 −0.127950 0.991781i \(-0.540840\pi\)
−0.127950 + 0.991781i \(0.540840\pi\)
\(240\) 0 0
\(241\) −15.3726 −0.990235 −0.495117 0.868826i \(-0.664875\pi\)
−0.495117 + 0.868826i \(0.664875\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 3.61017 0.230645
\(246\) 0 0
\(247\) 8.05054i 0.512243i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 13.1732i 0.831482i 0.909483 + 0.415741i \(0.136478\pi\)
−0.909483 + 0.415741i \(0.863522\pi\)
\(252\) 0 0
\(253\) − 14.3565i − 0.902585i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 26.9072i 1.67843i 0.543802 + 0.839213i \(0.316984\pi\)
−0.543802 + 0.839213i \(0.683016\pi\)
\(258\) 0 0
\(259\) 4.76592 0.296140
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 8.15057 0.502586 0.251293 0.967911i \(-0.419144\pi\)
0.251293 + 0.967911i \(0.419144\pi\)
\(264\) 0 0
\(265\) 3.82605 0.235033
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 3.84304 0.234314 0.117157 0.993113i \(-0.462622\pi\)
0.117157 + 0.993113i \(0.462622\pi\)
\(270\) 0 0
\(271\) 12.8705i 0.781829i 0.920427 + 0.390914i \(0.127841\pi\)
−0.920427 + 0.390914i \(0.872159\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) − 16.1389i − 0.973212i
\(276\) 0 0
\(277\) 2.72420i 0.163682i 0.996645 + 0.0818408i \(0.0260799\pi\)
−0.996645 + 0.0818408i \(0.973920\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) − 8.91234i − 0.531666i −0.964019 0.265833i \(-0.914353\pi\)
0.964019 0.265833i \(-0.0856469\pi\)
\(282\) 0 0
\(283\) −4.90080 −0.291322 −0.145661 0.989335i \(-0.546531\pi\)
−0.145661 + 0.989335i \(0.546531\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0.836835 0.0493968
\(288\) 0 0
\(289\) −43.7241 −2.57201
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −26.1386 −1.52704 −0.763518 0.645786i \(-0.776530\pi\)
−0.763518 + 0.645786i \(0.776530\pi\)
\(294\) 0 0
\(295\) − 30.1271i − 1.75407i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 11.3813i 0.658196i
\(300\) 0 0
\(301\) 0.151434i 0.00872849i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) − 36.9562i − 2.11611i
\(306\) 0 0
\(307\) 23.4257 1.33697 0.668487 0.743724i \(-0.266942\pi\)
0.668487 + 0.743724i \(0.266942\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −15.4333 −0.875143 −0.437571 0.899184i \(-0.644161\pi\)
−0.437571 + 0.899184i \(0.644161\pi\)
\(312\) 0 0
\(313\) −31.1894 −1.76293 −0.881464 0.472251i \(-0.843442\pi\)
−0.881464 + 0.472251i \(0.843442\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −30.7471 −1.72693 −0.863466 0.504407i \(-0.831711\pi\)
−0.863466 + 0.504407i \(0.831711\pi\)
\(318\) 0 0
\(319\) 9.93042i 0.555997i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) − 39.3899i − 2.19171i
\(324\) 0 0
\(325\) 12.7943i 0.709700i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) − 0.795430i − 0.0438535i
\(330\) 0 0
\(331\) −1.00125 −0.0550339 −0.0275169 0.999621i \(-0.508760\pi\)
−0.0275169 + 0.999621i \(0.508760\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 2.36595 0.129266
\(336\) 0 0
\(337\) 28.1818 1.53516 0.767580 0.640953i \(-0.221461\pi\)
0.767580 + 0.640953i \(0.221461\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 5.08780 0.275520
\(342\) 0 0
\(343\) 1.00000i 0.0539949i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 19.6496i 1.05485i 0.849602 + 0.527424i \(0.176842\pi\)
−0.849602 + 0.527424i \(0.823158\pi\)
\(348\) 0 0
\(349\) 11.2275i 0.600993i 0.953783 + 0.300497i \(0.0971524\pi\)
−0.953783 + 0.300497i \(0.902848\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) − 32.2047i − 1.71408i −0.515249 0.857041i \(-0.672300\pi\)
0.515249 0.857041i \(-0.327700\pi\)
\(354\) 0 0
\(355\) −41.0385 −2.17810
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −20.1918 −1.06568 −0.532842 0.846215i \(-0.678876\pi\)
−0.532842 + 0.846215i \(0.678876\pi\)
\(360\) 0 0
\(361\) 6.55100 0.344790
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 51.9267 2.71797
\(366\) 0 0
\(367\) 1.42641i 0.0744578i 0.999307 + 0.0372289i \(0.0118531\pi\)
−0.999307 + 0.0372289i \(0.988147\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 1.05980i 0.0550220i
\(372\) 0 0
\(373\) − 9.80760i − 0.507818i −0.967228 0.253909i \(-0.918284\pi\)
0.967228 0.253909i \(-0.0817165\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) − 7.87245i − 0.405452i
\(378\) 0 0
\(379\) 17.5378 0.900857 0.450428 0.892813i \(-0.351271\pi\)
0.450428 + 0.892813i \(0.351271\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −8.32355 −0.425313 −0.212657 0.977127i \(-0.568212\pi\)
−0.212657 + 0.977127i \(0.568212\pi\)
\(384\) 0 0
\(385\) 7.25280 0.369637
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 8.79829 0.446091 0.223045 0.974808i \(-0.428400\pi\)
0.223045 + 0.974808i \(0.428400\pi\)
\(390\) 0 0
\(391\) − 55.6866i − 2.81619i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 13.7611i 0.692398i
\(396\) 0 0
\(397\) − 31.5495i − 1.58342i −0.610896 0.791711i \(-0.709190\pi\)
0.610896 0.791711i \(-0.290810\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 8.99955i 0.449416i 0.974426 + 0.224708i \(0.0721428\pi\)
−0.974426 + 0.224708i \(0.927857\pi\)
\(402\) 0 0
\(403\) −4.03341 −0.200919
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 9.57470 0.474600
\(408\) 0 0
\(409\) −35.7330 −1.76688 −0.883441 0.468542i \(-0.844779\pi\)
−0.883441 + 0.468542i \(0.844779\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 8.34506 0.410633
\(414\) 0 0
\(415\) 53.9798i 2.64976i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) − 35.1521i − 1.71729i −0.512569 0.858646i \(-0.671306\pi\)
0.512569 0.858646i \(-0.328694\pi\)
\(420\) 0 0
\(421\) − 22.7156i − 1.10709i −0.832819 0.553546i \(-0.813274\pi\)
0.832819 0.553546i \(-0.186726\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) − 62.6002i − 3.03656i
\(426\) 0 0
\(427\) 10.2367 0.495388
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −1.00587 −0.0484511 −0.0242256 0.999707i \(-0.507712\pi\)
−0.0242256 + 0.999707i \(0.507712\pi\)
\(432\) 0 0
\(433\) −33.8256 −1.62555 −0.812776 0.582576i \(-0.802045\pi\)
−0.812776 + 0.582576i \(0.802045\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 36.1222 1.72796
\(438\) 0 0
\(439\) − 11.9514i − 0.570411i −0.958466 0.285206i \(-0.907938\pi\)
0.958466 0.285206i \(-0.0920619\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) − 17.6849i − 0.840234i −0.907470 0.420117i \(-0.861989\pi\)
0.907470 0.420117i \(-0.138011\pi\)
\(444\) 0 0
\(445\) − 0.160352i − 0.00760141i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 33.4546i 1.57882i 0.613867 + 0.789409i \(0.289613\pi\)
−0.613867 + 0.789409i \(0.710387\pi\)
\(450\) 0 0
\(451\) 1.68120 0.0791644
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −5.74974 −0.269552
\(456\) 0 0
\(457\) 34.7127 1.62379 0.811896 0.583802i \(-0.198436\pi\)
0.811896 + 0.583802i \(0.198436\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −9.30870 −0.433549 −0.216775 0.976222i \(-0.569554\pi\)
−0.216775 + 0.976222i \(0.569554\pi\)
\(462\) 0 0
\(463\) 1.56421i 0.0726950i 0.999339 + 0.0363475i \(0.0115723\pi\)
−0.999339 + 0.0363475i \(0.988428\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) − 2.47725i − 0.114633i −0.998356 0.0573167i \(-0.981746\pi\)
0.998356 0.0573167i \(-0.0182545\pi\)
\(468\) 0 0
\(469\) 0.655357i 0.0302616i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0.304229i 0.0139885i
\(474\) 0 0
\(475\) 40.6069 1.86317
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −4.20750 −0.192245 −0.0961227 0.995369i \(-0.530644\pi\)
−0.0961227 + 0.995369i \(0.530644\pi\)
\(480\) 0 0
\(481\) −7.59045 −0.346095
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −35.6324 −1.61798
\(486\) 0 0
\(487\) 29.7159i 1.34656i 0.739389 + 0.673278i \(0.235114\pi\)
−0.739389 + 0.673278i \(0.764886\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 6.98629i 0.315287i 0.987496 + 0.157643i \(0.0503896\pi\)
−0.987496 + 0.157643i \(0.949610\pi\)
\(492\) 0 0
\(493\) 38.5185i 1.73479i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) − 11.3675i − 0.509901i
\(498\) 0 0
\(499\) −9.65859 −0.432378 −0.216189 0.976352i \(-0.569363\pi\)
−0.216189 + 0.976352i \(0.569363\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −33.8339 −1.50858 −0.754290 0.656542i \(-0.772019\pi\)
−0.754290 + 0.656542i \(0.772019\pi\)
\(504\) 0 0
\(505\) −15.9941 −0.711728
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −12.8961 −0.571611 −0.285806 0.958288i \(-0.592261\pi\)
−0.285806 + 0.958288i \(0.592261\pi\)
\(510\) 0 0
\(511\) 14.3835i 0.636287i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) − 40.7730i − 1.79667i
\(516\) 0 0
\(517\) − 1.59801i − 0.0702805i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 15.4735i 0.677905i 0.940803 + 0.338953i \(0.110073\pi\)
−0.940803 + 0.338953i \(0.889927\pi\)
\(522\) 0 0
\(523\) 20.0632 0.877301 0.438651 0.898658i \(-0.355457\pi\)
0.438651 + 0.898658i \(0.355457\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 19.7348 0.859661
\(528\) 0 0
\(529\) 28.0670 1.22031
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −1.33279 −0.0577294
\(534\) 0 0
\(535\) 31.0481i 1.34233i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 2.00899i 0.0865334i
\(540\) 0 0
\(541\) 18.5169i 0.796103i 0.917363 + 0.398052i \(0.130313\pi\)
−0.917363 + 0.398052i \(0.869687\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 71.8982i 3.07978i
\(546\) 0 0
\(547\) 24.8132 1.06094 0.530468 0.847705i \(-0.322016\pi\)
0.530468 + 0.847705i \(0.322016\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −24.9858 −1.06443
\(552\) 0 0
\(553\) −3.81177 −0.162093
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 19.4177 0.822756 0.411378 0.911465i \(-0.365048\pi\)
0.411378 + 0.911465i \(0.365048\pi\)
\(558\) 0 0
\(559\) − 0.241181i − 0.0102009i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 14.6696i 0.618252i 0.951021 + 0.309126i \(0.100036\pi\)
−0.951021 + 0.309126i \(0.899964\pi\)
\(564\) 0 0
\(565\) 13.7682i 0.579231i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 17.3133i 0.725809i 0.931826 + 0.362905i \(0.118215\pi\)
−0.931826 + 0.362905i \(0.881785\pi\)
\(570\) 0 0
\(571\) −11.7082 −0.489975 −0.244987 0.969526i \(-0.578784\pi\)
−0.244987 + 0.969526i \(0.578784\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 57.4071 2.39404
\(576\) 0 0
\(577\) 4.79465 0.199604 0.0998020 0.995007i \(-0.468179\pi\)
0.0998020 + 0.995007i \(0.468179\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −14.9522 −0.620320
\(582\) 0 0
\(583\) 2.12913i 0.0881795i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) − 30.1643i − 1.24501i −0.782615 0.622506i \(-0.786114\pi\)
0.782615 0.622506i \(-0.213886\pi\)
\(588\) 0 0
\(589\) 12.8014i 0.527471i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) − 2.60974i − 0.107169i −0.998563 0.0535847i \(-0.982935\pi\)
0.998563 0.0535847i \(-0.0170647\pi\)
\(594\) 0 0
\(595\) 28.1325 1.15332
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 27.6903 1.13139 0.565697 0.824613i \(-0.308607\pi\)
0.565697 + 0.824613i \(0.308607\pi\)
\(600\) 0 0
\(601\) 16.3291 0.666079 0.333039 0.942913i \(-0.391926\pi\)
0.333039 + 0.942913i \(0.391926\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −25.1410 −1.02213
\(606\) 0 0
\(607\) 12.9385i 0.525159i 0.964910 + 0.262580i \(0.0845732\pi\)
−0.964910 + 0.262580i \(0.915427\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 1.26684i 0.0512509i
\(612\) 0 0
\(613\) − 21.7992i − 0.880463i −0.897884 0.440231i \(-0.854896\pi\)
0.897884 0.440231i \(-0.145104\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) − 41.8226i − 1.68371i −0.539700 0.841857i \(-0.681462\pi\)
0.539700 0.841857i \(-0.318538\pi\)
\(618\) 0 0
\(619\) 4.82763 0.194039 0.0970193 0.995282i \(-0.469069\pi\)
0.0970193 + 0.995282i \(0.469069\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0.0444167 0.00177952
\(624\) 0 0
\(625\) −0.632276 −0.0252911
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 37.1388 1.48082
\(630\) 0 0
\(631\) 20.3929i 0.811830i 0.913911 + 0.405915i \(0.133047\pi\)
−0.913911 + 0.405915i \(0.866953\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 57.7420i 2.29142i
\(636\) 0 0
\(637\) − 1.59265i − 0.0631032i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) − 9.42755i − 0.372366i −0.982515 0.186183i \(-0.940388\pi\)
0.982515 0.186183i \(-0.0596117\pi\)
\(642\) 0 0
\(643\) 27.2077 1.07297 0.536484 0.843911i \(-0.319752\pi\)
0.536484 + 0.843911i \(0.319752\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −7.24081 −0.284666 −0.142333 0.989819i \(-0.545460\pi\)
−0.142333 + 0.989819i \(0.545460\pi\)
\(648\) 0 0
\(649\) 16.7652 0.658090
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −30.0954 −1.17772 −0.588861 0.808234i \(-0.700424\pi\)
−0.588861 + 0.808234i \(0.700424\pi\)
\(654\) 0 0
\(655\) 71.7842i 2.80484i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) − 41.9316i − 1.63342i −0.577045 0.816712i \(-0.695794\pi\)
0.577045 0.816712i \(-0.304206\pi\)
\(660\) 0 0
\(661\) − 0.735053i − 0.0285903i −0.999898 0.0142951i \(-0.995450\pi\)
0.999898 0.0142951i \(-0.00455044\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 18.2487i 0.707654i
\(666\) 0 0
\(667\) −35.3232 −1.36772
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 20.5654 0.793920
\(672\) 0 0
\(673\) −21.6142 −0.833165 −0.416582 0.909098i \(-0.636772\pi\)
−0.416582 + 0.909098i \(0.636772\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 0.631879 0.0242851 0.0121425 0.999926i \(-0.496135\pi\)
0.0121425 + 0.999926i \(0.496135\pi\)
\(678\) 0 0
\(679\) − 9.87000i − 0.378776i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 22.4241i 0.858033i 0.903297 + 0.429017i \(0.141140\pi\)
−0.903297 + 0.429017i \(0.858860\pi\)
\(684\) 0 0
\(685\) 32.2596i 1.23258i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) − 1.68789i − 0.0643035i
\(690\) 0 0
\(691\) 2.69349 0.102465 0.0512325 0.998687i \(-0.483685\pi\)
0.0512325 + 0.998687i \(0.483685\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 4.34462 0.164801
\(696\) 0 0
\(697\) 6.52109 0.247004
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 28.4555 1.07475 0.537375 0.843344i \(-0.319416\pi\)
0.537375 + 0.843344i \(0.319416\pi\)
\(702\) 0 0
\(703\) 24.0908i 0.908601i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) − 4.43029i − 0.166618i
\(708\) 0 0
\(709\) − 13.4255i − 0.504204i −0.967701 0.252102i \(-0.918878\pi\)
0.967701 0.252102i \(-0.0811218\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 18.0977i 0.677763i
\(714\) 0 0
\(715\) −11.5512 −0.431990
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −49.4437 −1.84394 −0.921969 0.387264i \(-0.873420\pi\)
−0.921969 + 0.387264i \(0.873420\pi\)
\(720\) 0 0
\(721\) 11.2939 0.420608
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −39.7086 −1.47474
\(726\) 0 0
\(727\) − 5.65644i − 0.209786i −0.994484 0.104893i \(-0.966550\pi\)
0.994484 0.104893i \(-0.0334500\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 1.18006i 0.0436460i
\(732\) 0 0
\(733\) − 42.3705i − 1.56499i −0.622656 0.782495i \(-0.713946\pi\)
0.622656 0.782495i \(-0.286054\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 1.31661i 0.0484979i
\(738\) 0 0
\(739\) 41.5942 1.53007 0.765034 0.643989i \(-0.222722\pi\)
0.765034 + 0.643989i \(0.222722\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −16.5821 −0.608338 −0.304169 0.952618i \(-0.598379\pi\)
−0.304169 + 0.952618i \(0.598379\pi\)
\(744\) 0 0
\(745\) −45.7736 −1.67702
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −8.60018 −0.314244
\(750\) 0 0
\(751\) − 4.26395i − 0.155594i −0.996969 0.0777968i \(-0.975211\pi\)
0.996969 0.0777968i \(-0.0247886\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 63.2118i 2.30051i
\(756\) 0 0
\(757\) − 19.5706i − 0.711305i −0.934618 0.355653i \(-0.884259\pi\)
0.934618 0.355653i \(-0.115741\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) − 22.1256i − 0.802053i −0.916066 0.401027i \(-0.868653\pi\)
0.916066 0.401027i \(-0.131347\pi\)
\(762\) 0 0
\(763\) −19.9155 −0.720988
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −13.2908 −0.479902
\(768\) 0 0
\(769\) −16.1961 −0.584046 −0.292023 0.956411i \(-0.594328\pi\)
−0.292023 + 0.956411i \(0.594328\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 2.34825 0.0844608 0.0422304 0.999108i \(-0.486554\pi\)
0.0422304 + 0.999108i \(0.486554\pi\)
\(774\) 0 0
\(775\) 20.3445i 0.730797i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 4.23003i 0.151557i
\(780\) 0 0
\(781\) − 22.8372i − 0.817179i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) − 55.1962i − 1.97004i
\(786\) 0 0
\(787\) −10.9012 −0.388586 −0.194293 0.980943i \(-0.562241\pi\)
−0.194293 + 0.980943i \(0.562241\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −3.81372 −0.135600
\(792\) 0 0
\(793\) −16.3035 −0.578954
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −5.08600 −0.180155 −0.0900776 0.995935i \(-0.528712\pi\)
−0.0900776 + 0.995935i \(0.528712\pi\)
\(798\) 0 0
\(799\) − 6.19844i − 0.219285i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 28.8963i 1.01973i
\(804\) 0 0
\(805\) 25.7987i 0.909285i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 26.8140i 0.942729i 0.881938 + 0.471365i \(0.156238\pi\)
−0.881938 + 0.471365i \(0.843762\pi\)
\(810\) 0 0
\(811\) −38.8383 −1.36380 −0.681899 0.731446i \(-0.738846\pi\)
−0.681899 + 0.731446i \(0.738846\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 63.4068 2.22104
\(816\) 0 0
\(817\) −0.765467 −0.0267803
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 29.3421 1.02405 0.512023 0.858972i \(-0.328896\pi\)
0.512023 + 0.858972i \(0.328896\pi\)
\(822\) 0 0
\(823\) − 23.9770i − 0.835784i −0.908497 0.417892i \(-0.862769\pi\)
0.908497 0.417892i \(-0.137231\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) − 4.92468i − 0.171248i −0.996328 0.0856239i \(-0.972712\pi\)
0.996328 0.0856239i \(-0.0272883\pi\)
\(828\) 0 0
\(829\) 8.00324i 0.277964i 0.990295 + 0.138982i \(0.0443830\pi\)
−0.990295 + 0.138982i \(0.955617\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 7.79257i 0.269996i
\(834\) 0 0
\(835\) 15.1732 0.525089
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −31.4595 −1.08610 −0.543051 0.839700i \(-0.682731\pi\)
−0.543051 + 0.839700i \(0.682731\pi\)
\(840\) 0 0
\(841\) −4.56691 −0.157479
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −37.7749 −1.29950
\(846\) 0 0
\(847\) − 6.96395i − 0.239284i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 34.0578i 1.16749i
\(852\) 0 0
\(853\) 1.31213i 0.0449263i 0.999748 + 0.0224632i \(0.00715085\pi\)
−0.999748 + 0.0224632i \(0.992849\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 24.2200i 0.827341i 0.910427 + 0.413670i \(0.135753\pi\)
−0.910427 + 0.413670i \(0.864247\pi\)
\(858\) 0 0
\(859\) −8.49401 −0.289812 −0.144906 0.989445i \(-0.546288\pi\)
−0.144906 + 0.989445i \(0.546288\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 30.8759 1.05103 0.525513 0.850785i \(-0.323873\pi\)
0.525513 + 0.850785i \(0.323873\pi\)
\(864\) 0 0
\(865\) 65.0096 2.21039
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −7.65782 −0.259774
\(870\) 0 0
\(871\) − 1.04376i − 0.0353663i
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 10.9508i 0.370206i
\(876\) 0 0
\(877\) − 33.4689i − 1.13016i −0.825035 0.565082i \(-0.808845\pi\)
0.825035 0.565082i \(-0.191155\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) − 33.7535i − 1.13719i −0.822619 0.568593i \(-0.807488\pi\)
0.822619 0.568593i \(-0.192512\pi\)
\(882\) 0 0
\(883\) −1.59496 −0.0536746 −0.0268373 0.999640i \(-0.508544\pi\)
−0.0268373 + 0.999640i \(0.508544\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 17.9639 0.603167 0.301584 0.953440i \(-0.402485\pi\)
0.301584 + 0.953440i \(0.402485\pi\)
\(888\) 0 0
\(889\) −15.9943 −0.536430
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 4.02074 0.134549
\(894\) 0 0
\(895\) 3.19894i 0.106929i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) − 12.5182i − 0.417505i
\(900\) 0 0
\(901\) 8.25855i 0.275132i
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 30.5903i 1.01686i
\(906\) 0 0
\(907\) −52.9653 −1.75868 −0.879342 0.476190i \(-0.842017\pi\)
−0.879342 + 0.476190i \(0.842017\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 52.6435 1.74416 0.872079 0.489365i \(-0.162771\pi\)
0.872079 + 0.489365i \(0.162771\pi\)
\(912\) 0 0
\(913\) −30.0388 −0.994138
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −19.8839 −0.656623
\(918\) 0 0
\(919\) − 36.5794i − 1.20664i −0.797498 0.603322i \(-0.793843\pi\)
0.797498 0.603322i \(-0.206157\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 18.1044i 0.595915i
\(924\) 0 0
\(925\) 38.2862i 1.25884i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 24.8413i 0.815018i 0.913201 + 0.407509i \(0.133602\pi\)
−0.913201 + 0.407509i \(0.866398\pi\)
\(930\) 0 0
\(931\) −5.05480 −0.165664
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 56.5180 1.84833
\(936\) 0 0
\(937\) 0.904448 0.0295470 0.0147735 0.999891i \(-0.495297\pi\)
0.0147735 + 0.999891i \(0.495297\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 8.11337 0.264488 0.132244 0.991217i \(-0.457782\pi\)
0.132244 + 0.991217i \(0.457782\pi\)
\(942\) 0 0
\(943\) 5.98012i 0.194740i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) − 34.2396i − 1.11264i −0.830969 0.556319i \(-0.812213\pi\)
0.830969 0.556319i \(-0.187787\pi\)
\(948\) 0 0
\(949\) − 22.9078i − 0.743620i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 5.47739i 0.177430i 0.996057 + 0.0887151i \(0.0282761\pi\)
−0.996057 + 0.0887151i \(0.971724\pi\)
\(954\) 0 0
\(955\) 74.4065 2.40774
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −8.93576 −0.288551
\(960\) 0 0
\(961\) 24.5864 0.793109
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −66.0559 −2.12641
\(966\) 0 0
\(967\) − 45.0597i − 1.44902i −0.689262 0.724512i \(-0.742065\pi\)
0.689262 0.724512i \(-0.257935\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 28.4013i 0.911442i 0.890123 + 0.455721i \(0.150618\pi\)
−0.890123 + 0.455721i \(0.849382\pi\)
\(972\) 0 0
\(973\) 1.20344i 0.0385805i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) − 4.06448i − 0.130034i −0.997884 0.0650171i \(-0.979290\pi\)
0.997884 0.0650171i \(-0.0207102\pi\)
\(978\) 0 0
\(979\) 0.0892328 0.00285189
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 13.0487 0.416189 0.208094 0.978109i \(-0.433274\pi\)
0.208094 + 0.978109i \(0.433274\pi\)
\(984\) 0 0
\(985\) 38.4773 1.22599
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −1.08216 −0.0344108
\(990\) 0 0
\(991\) − 0.598647i − 0.0190166i −0.999955 0.00950832i \(-0.996973\pi\)
0.999955 0.00950832i \(-0.00302664\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 94.3354i 2.99063i
\(996\) 0 0
\(997\) 4.04553i 0.128123i 0.997946 + 0.0640616i \(0.0204054\pi\)
−0.997946 + 0.0640616i \(0.979595\pi\)
\(998\) 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.j.c.5615.2 32
3.2 odd 2 inner 6048.2.j.c.5615.31 32
4.3 odd 2 1512.2.j.c.323.28 yes 32
8.3 odd 2 inner 6048.2.j.c.5615.32 32
8.5 even 2 1512.2.j.c.323.6 yes 32
12.11 even 2 1512.2.j.c.323.5 32
24.5 odd 2 1512.2.j.c.323.27 yes 32
24.11 even 2 inner 6048.2.j.c.5615.1 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1512.2.j.c.323.5 32 12.11 even 2
1512.2.j.c.323.6 yes 32 8.5 even 2
1512.2.j.c.323.27 yes 32 24.5 odd 2
1512.2.j.c.323.28 yes 32 4.3 odd 2
6048.2.j.c.5615.1 32 24.11 even 2 inner
6048.2.j.c.5615.2 32 1.1 even 1 trivial
6048.2.j.c.5615.31 32 3.2 odd 2 inner
6048.2.j.c.5615.32 32 8.3 odd 2 inner