Properties

Label 6048.2.j.c.5615.30
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: \(32\)
Coefficient ring index: multiple of None
Twist minimal: no (minimal twist has level 1512)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 5615.30
Character \(\chi\) = 6048.5615
Dual form 6048.2.j.c.5615.29

$q$-expansion

\(f(q)\) \(=\) \(q+3.47003 q^{5} +1.00000i q^{7} +O(q^{10})\) \(q+3.47003 q^{5} +1.00000i q^{7} -5.11891i q^{11} +0.268602i q^{13} +1.96616i q^{17} -0.909926 q^{19} -5.86455 q^{23} +7.04110 q^{25} -7.19959 q^{29} -4.57491i q^{31} +3.47003i q^{35} -6.98312i q^{37} -8.34605i q^{41} +9.25237 q^{43} +6.49316 q^{47} -1.00000 q^{49} +4.54325 q^{53} -17.7628i q^{55} -3.50524i q^{59} -1.96254i q^{61} +0.932057i q^{65} +11.0280 q^{67} -1.20092 q^{71} -9.01697 q^{73} +5.11891 q^{77} -13.5570i q^{79} +4.96335i q^{83} +6.82263i q^{85} -18.2032i q^{89} -0.268602 q^{91} -3.15747 q^{95} +3.39139 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + O(q^{10}) \) \( 32q + 64q^{19} - 16q^{25} + 48q^{43} - 32q^{49} - 16q^{67} - 16q^{73} - 16q^{91} + 64q^{97} + O(q^{100}) \)

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
\(5\) 3.47003 1.55184 0.775922 0.630829i \(-0.217285\pi\)
0.775922 + 0.630829i \(0.217285\pi\)
\(6\) 0 0
\(7\) 1.00000i 0.377964i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) − 5.11891i − 1.54341i −0.635981 0.771705i \(-0.719404\pi\)
0.635981 0.771705i \(-0.280596\pi\)
\(12\) 0 0
\(13\) 0.268602i 0.0744968i 0.999306 + 0.0372484i \(0.0118593\pi\)
−0.999306 + 0.0372484i \(0.988141\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1.96616i 0.476864i 0.971159 + 0.238432i \(0.0766334\pi\)
−0.971159 + 0.238432i \(0.923367\pi\)
\(18\) 0 0
\(19\) −0.909926 −0.208751 −0.104376 0.994538i \(-0.533284\pi\)
−0.104376 + 0.994538i \(0.533284\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −5.86455 −1.22284 −0.611421 0.791305i \(-0.709402\pi\)
−0.611421 + 0.791305i \(0.709402\pi\)
\(24\) 0 0
\(25\) 7.04110 1.40822
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −7.19959 −1.33693 −0.668466 0.743743i \(-0.733049\pi\)
−0.668466 + 0.743743i \(0.733049\pi\)
\(30\) 0 0
\(31\) − 4.57491i − 0.821678i −0.911708 0.410839i \(-0.865236\pi\)
0.911708 0.410839i \(-0.134764\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 3.47003i 0.586542i
\(36\) 0 0
\(37\) − 6.98312i − 1.14802i −0.818849 0.574009i \(-0.805388\pi\)
0.818849 0.574009i \(-0.194612\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) − 8.34605i − 1.30343i −0.758462 0.651717i \(-0.774049\pi\)
0.758462 0.651717i \(-0.225951\pi\)
\(42\) 0 0
\(43\) 9.25237 1.41097 0.705487 0.708723i \(-0.250728\pi\)
0.705487 + 0.708723i \(0.250728\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 6.49316 0.947125 0.473562 0.880760i \(-0.342968\pi\)
0.473562 + 0.880760i \(0.342968\pi\)
\(48\) 0 0
\(49\) −1.00000 −0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 4.54325 0.624063 0.312032 0.950072i \(-0.398990\pi\)
0.312032 + 0.950072i \(0.398990\pi\)
\(54\) 0 0
\(55\) − 17.7628i − 2.39513i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) − 3.50524i − 0.456344i −0.973621 0.228172i \(-0.926725\pi\)
0.973621 0.228172i \(-0.0732748\pi\)
\(60\) 0 0
\(61\) − 1.96254i − 0.251278i −0.992076 0.125639i \(-0.959902\pi\)
0.992076 0.125639i \(-0.0400980\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0.932057i 0.115607i
\(66\) 0 0
\(67\) 11.0280 1.34728 0.673641 0.739059i \(-0.264729\pi\)
0.673641 + 0.739059i \(0.264729\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −1.20092 −0.142523 −0.0712616 0.997458i \(-0.522703\pi\)
−0.0712616 + 0.997458i \(0.522703\pi\)
\(72\) 0 0
\(73\) −9.01697 −1.05536 −0.527679 0.849444i \(-0.676937\pi\)
−0.527679 + 0.849444i \(0.676937\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 5.11891 0.583354
\(78\) 0 0
\(79\) − 13.5570i − 1.52528i −0.646825 0.762638i \(-0.723904\pi\)
0.646825 0.762638i \(-0.276096\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 4.96335i 0.544799i 0.962184 + 0.272399i \(0.0878172\pi\)
−0.962184 + 0.272399i \(0.912183\pi\)
\(84\) 0 0
\(85\) 6.82263i 0.740019i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) − 18.2032i − 1.92954i −0.263100 0.964769i \(-0.584745\pi\)
0.263100 0.964769i \(-0.415255\pi\)
\(90\) 0 0
\(91\) −0.268602 −0.0281572
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −3.15747 −0.323949
\(96\) 0 0
\(97\) 3.39139 0.344344 0.172172 0.985067i \(-0.444922\pi\)
0.172172 + 0.985067i \(0.444922\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 8.18671 0.814608 0.407304 0.913293i \(-0.366469\pi\)
0.407304 + 0.913293i \(0.366469\pi\)
\(102\) 0 0
\(103\) 16.5624i 1.63194i 0.578093 + 0.815971i \(0.303797\pi\)
−0.578093 + 0.815971i \(0.696203\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) − 15.1480i − 1.46441i −0.681083 0.732206i \(-0.738491\pi\)
0.681083 0.732206i \(-0.261509\pi\)
\(108\) 0 0
\(109\) 7.70038i 0.737562i 0.929516 + 0.368781i \(0.120225\pi\)
−0.929516 + 0.368781i \(0.879775\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) − 14.5822i − 1.37178i −0.727706 0.685889i \(-0.759413\pi\)
0.727706 0.685889i \(-0.240587\pi\)
\(114\) 0 0
\(115\) −20.3501 −1.89766
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −1.96616 −0.180238
\(120\) 0 0
\(121\) −15.2033 −1.38211
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 7.08266 0.633492
\(126\) 0 0
\(127\) − 13.7782i − 1.22262i −0.791392 0.611309i \(-0.790643\pi\)
0.791392 0.611309i \(-0.209357\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 11.4226i 0.997997i 0.866603 + 0.498999i \(0.166299\pi\)
−0.866603 + 0.498999i \(0.833701\pi\)
\(132\) 0 0
\(133\) − 0.909926i − 0.0789006i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 5.89343i 0.503510i 0.967791 + 0.251755i \(0.0810077\pi\)
−0.967791 + 0.251755i \(0.918992\pi\)
\(138\) 0 0
\(139\) −3.67309 −0.311547 −0.155774 0.987793i \(-0.549787\pi\)
−0.155774 + 0.987793i \(0.549787\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 1.37495 0.114979
\(144\) 0 0
\(145\) −24.9828 −2.07471
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 23.0240 1.88620 0.943102 0.332504i \(-0.107894\pi\)
0.943102 + 0.332504i \(0.107894\pi\)
\(150\) 0 0
\(151\) − 1.33860i − 0.108934i −0.998516 0.0544669i \(-0.982654\pi\)
0.998516 0.0544669i \(-0.0173459\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) − 15.8751i − 1.27512i
\(156\) 0 0
\(157\) 21.7839i 1.73854i 0.494333 + 0.869272i \(0.335412\pi\)
−0.494333 + 0.869272i \(0.664588\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) − 5.86455i − 0.462191i
\(162\) 0 0
\(163\) 20.2710 1.58775 0.793875 0.608082i \(-0.208061\pi\)
0.793875 + 0.608082i \(0.208061\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −6.57632 −0.508891 −0.254445 0.967087i \(-0.581893\pi\)
−0.254445 + 0.967087i \(0.581893\pi\)
\(168\) 0 0
\(169\) 12.9279 0.994450
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −13.3399 −1.01421 −0.507105 0.861884i \(-0.669284\pi\)
−0.507105 + 0.861884i \(0.669284\pi\)
\(174\) 0 0
\(175\) 7.04110i 0.532257i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) − 9.82571i − 0.734408i −0.930140 0.367204i \(-0.880315\pi\)
0.930140 0.367204i \(-0.119685\pi\)
\(180\) 0 0
\(181\) 4.88753i 0.363287i 0.983364 + 0.181643i \(0.0581417\pi\)
−0.983364 + 0.181643i \(0.941858\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) − 24.2316i − 1.78154i
\(186\) 0 0
\(187\) 10.0646 0.735997
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −11.6129 −0.840281 −0.420141 0.907459i \(-0.638019\pi\)
−0.420141 + 0.907459i \(0.638019\pi\)
\(192\) 0 0
\(193\) −12.8166 −0.922562 −0.461281 0.887254i \(-0.652610\pi\)
−0.461281 + 0.887254i \(0.652610\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 4.69147 0.334253 0.167127 0.985935i \(-0.446551\pi\)
0.167127 + 0.985935i \(0.446551\pi\)
\(198\) 0 0
\(199\) − 15.3555i − 1.08852i −0.838915 0.544262i \(-0.816810\pi\)
0.838915 0.544262i \(-0.183190\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) − 7.19959i − 0.505312i
\(204\) 0 0
\(205\) − 28.9610i − 2.02273i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 4.65783i 0.322189i
\(210\) 0 0
\(211\) −5.09850 −0.350995 −0.175497 0.984480i \(-0.556153\pi\)
−0.175497 + 0.984480i \(0.556153\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 32.1060 2.18961
\(216\) 0 0
\(217\) 4.57491 0.310565
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −0.528115 −0.0355249
\(222\) 0 0
\(223\) 29.5118i 1.97625i 0.153636 + 0.988127i \(0.450902\pi\)
−0.153636 + 0.988127i \(0.549098\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 14.4769i 0.960868i 0.877031 + 0.480434i \(0.159521\pi\)
−0.877031 + 0.480434i \(0.840479\pi\)
\(228\) 0 0
\(229\) 11.9120i 0.787168i 0.919289 + 0.393584i \(0.128765\pi\)
−0.919289 + 0.393584i \(0.871235\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 13.2938i 0.870904i 0.900212 + 0.435452i \(0.143411\pi\)
−0.900212 + 0.435452i \(0.856589\pi\)
\(234\) 0 0
\(235\) 22.5315 1.46979
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 11.7744 0.761624 0.380812 0.924652i \(-0.375644\pi\)
0.380812 + 0.924652i \(0.375644\pi\)
\(240\) 0 0
\(241\) −23.3009 −1.50094 −0.750471 0.660903i \(-0.770173\pi\)
−0.750471 + 0.660903i \(0.770173\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −3.47003 −0.221692
\(246\) 0 0
\(247\) − 0.244408i − 0.0155513i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) − 18.5562i − 1.17126i −0.810579 0.585629i \(-0.800847\pi\)
0.810579 0.585629i \(-0.199153\pi\)
\(252\) 0 0
\(253\) 30.0201i 1.88735i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) − 12.7179i − 0.793318i −0.917966 0.396659i \(-0.870169\pi\)
0.917966 0.396659i \(-0.129831\pi\)
\(258\) 0 0
\(259\) 6.98312 0.433910
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 4.04929 0.249690 0.124845 0.992176i \(-0.460157\pi\)
0.124845 + 0.992176i \(0.460157\pi\)
\(264\) 0 0
\(265\) 15.7652 0.968449
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −22.6641 −1.38185 −0.690926 0.722925i \(-0.742797\pi\)
−0.690926 + 0.722925i \(0.742797\pi\)
\(270\) 0 0
\(271\) 0.0619260i 0.00376174i 0.999998 + 0.00188087i \(0.000598699\pi\)
−0.999998 + 0.00188087i \(0.999401\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) − 36.0427i − 2.17346i
\(276\) 0 0
\(277\) 24.9177i 1.49716i 0.663045 + 0.748580i \(0.269264\pi\)
−0.663045 + 0.748580i \(0.730736\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 8.26290i 0.492923i 0.969153 + 0.246462i \(0.0792679\pi\)
−0.969153 + 0.246462i \(0.920732\pi\)
\(282\) 0 0
\(283\) −23.4764 −1.39553 −0.697763 0.716329i \(-0.745821\pi\)
−0.697763 + 0.716329i \(0.745821\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 8.34605 0.492652
\(288\) 0 0
\(289\) 13.1342 0.772601
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 6.18958 0.361599 0.180800 0.983520i \(-0.442131\pi\)
0.180800 + 0.983520i \(0.442131\pi\)
\(294\) 0 0
\(295\) − 12.1633i − 0.708174i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) − 1.57523i − 0.0910979i
\(300\) 0 0
\(301\) 9.25237i 0.533298i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) − 6.81007i − 0.389944i
\(306\) 0 0
\(307\) 25.4140 1.45045 0.725226 0.688511i \(-0.241735\pi\)
0.725226 + 0.688511i \(0.241735\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 7.55273 0.428276 0.214138 0.976803i \(-0.431306\pi\)
0.214138 + 0.976803i \(0.431306\pi\)
\(312\) 0 0
\(313\) 2.49790 0.141190 0.0705948 0.997505i \(-0.477510\pi\)
0.0705948 + 0.997505i \(0.477510\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 10.9643 0.615815 0.307908 0.951416i \(-0.400371\pi\)
0.307908 + 0.951416i \(0.400371\pi\)
\(318\) 0 0
\(319\) 36.8541i 2.06343i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) − 1.78906i − 0.0995460i
\(324\) 0 0
\(325\) 1.89125i 0.104908i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 6.49316i 0.357980i
\(330\) 0 0
\(331\) −35.6043 −1.95699 −0.978494 0.206275i \(-0.933866\pi\)
−0.978494 + 0.206275i \(0.933866\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 38.2674 2.09077
\(336\) 0 0
\(337\) 18.4308 1.00399 0.501995 0.864871i \(-0.332600\pi\)
0.501995 + 0.864871i \(0.332600\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −23.4185 −1.26819
\(342\) 0 0
\(343\) − 1.00000i − 0.0539949i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) − 25.2141i − 1.35356i −0.736184 0.676782i \(-0.763374\pi\)
0.736184 0.676782i \(-0.236626\pi\)
\(348\) 0 0
\(349\) 4.82396i 0.258221i 0.991630 + 0.129110i \(0.0412121\pi\)
−0.991630 + 0.129110i \(0.958788\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) − 21.2660i − 1.13187i −0.824448 0.565937i \(-0.808514\pi\)
0.824448 0.565937i \(-0.191486\pi\)
\(354\) 0 0
\(355\) −4.16723 −0.221174
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 24.9785 1.31832 0.659158 0.752004i \(-0.270913\pi\)
0.659158 + 0.752004i \(0.270913\pi\)
\(360\) 0 0
\(361\) −18.1720 −0.956423
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −31.2892 −1.63775
\(366\) 0 0
\(367\) 13.8851i 0.724795i 0.932024 + 0.362397i \(0.118042\pi\)
−0.932024 + 0.362397i \(0.881958\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 4.54325i 0.235874i
\(372\) 0 0
\(373\) 0.513970i 0.0266123i 0.999911 + 0.0133062i \(0.00423561\pi\)
−0.999911 + 0.0133062i \(0.995764\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) − 1.93383i − 0.0995972i
\(378\) 0 0
\(379\) 7.97711 0.409757 0.204878 0.978787i \(-0.434320\pi\)
0.204878 + 0.978787i \(0.434320\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 8.03401 0.410519 0.205259 0.978708i \(-0.434196\pi\)
0.205259 + 0.978708i \(0.434196\pi\)
\(384\) 0 0
\(385\) 17.7628 0.905275
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −6.60733 −0.335005 −0.167503 0.985872i \(-0.553570\pi\)
−0.167503 + 0.985872i \(0.553570\pi\)
\(390\) 0 0
\(391\) − 11.5306i − 0.583130i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) − 47.0430i − 2.36699i
\(396\) 0 0
\(397\) − 17.4642i − 0.876502i −0.898853 0.438251i \(-0.855598\pi\)
0.898853 0.438251i \(-0.144402\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 18.6133i 0.929503i 0.885441 + 0.464751i \(0.153856\pi\)
−0.885441 + 0.464751i \(0.846144\pi\)
\(402\) 0 0
\(403\) 1.22883 0.0612124
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −35.7460 −1.77186
\(408\) 0 0
\(409\) 3.72844 0.184359 0.0921797 0.995742i \(-0.470617\pi\)
0.0921797 + 0.995742i \(0.470617\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 3.50524 0.172482
\(414\) 0 0
\(415\) 17.2230i 0.845443i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) − 30.1591i − 1.47337i −0.676237 0.736684i \(-0.736391\pi\)
0.676237 0.736684i \(-0.263609\pi\)
\(420\) 0 0
\(421\) − 4.17416i − 0.203436i −0.994813 0.101718i \(-0.967566\pi\)
0.994813 0.101718i \(-0.0324340\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 13.8439i 0.671529i
\(426\) 0 0
\(427\) 1.96254 0.0949740
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −20.3147 −0.978524 −0.489262 0.872137i \(-0.662734\pi\)
−0.489262 + 0.872137i \(0.662734\pi\)
\(432\) 0 0
\(433\) 37.5740 1.80569 0.902847 0.429963i \(-0.141473\pi\)
0.902847 + 0.429963i \(0.141473\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 5.33630 0.255270
\(438\) 0 0
\(439\) 12.2219i 0.583317i 0.956522 + 0.291659i \(0.0942072\pi\)
−0.956522 + 0.291659i \(0.905793\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 2.13132i 0.101262i 0.998717 + 0.0506311i \(0.0161233\pi\)
−0.998717 + 0.0506311i \(0.983877\pi\)
\(444\) 0 0
\(445\) − 63.1657i − 2.99434i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) − 24.6873i − 1.16506i −0.812807 0.582532i \(-0.802062\pi\)
0.812807 0.582532i \(-0.197938\pi\)
\(450\) 0 0
\(451\) −42.7227 −2.01173
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −0.932057 −0.0436955
\(456\) 0 0
\(457\) −33.2814 −1.55684 −0.778419 0.627745i \(-0.783978\pi\)
−0.778419 + 0.627745i \(0.783978\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 15.2279 0.709233 0.354617 0.935012i \(-0.384611\pi\)
0.354617 + 0.935012i \(0.384611\pi\)
\(462\) 0 0
\(463\) 3.21883i 0.149592i 0.997199 + 0.0747959i \(0.0238305\pi\)
−0.997199 + 0.0747959i \(0.976169\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 22.5827i 1.04500i 0.852638 + 0.522502i \(0.175001\pi\)
−0.852638 + 0.522502i \(0.824999\pi\)
\(468\) 0 0
\(469\) 11.0280i 0.509225i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) − 47.3621i − 2.17771i
\(474\) 0 0
\(475\) −6.40688 −0.293968
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −28.0140 −1.27999 −0.639995 0.768379i \(-0.721064\pi\)
−0.639995 + 0.768379i \(0.721064\pi\)
\(480\) 0 0
\(481\) 1.87568 0.0855237
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 11.7682 0.534368
\(486\) 0 0
\(487\) − 2.55321i − 0.115697i −0.998325 0.0578485i \(-0.981576\pi\)
0.998325 0.0578485i \(-0.0184240\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 0.803432i 0.0362584i 0.999836 + 0.0181292i \(0.00577102\pi\)
−0.999836 + 0.0181292i \(0.994229\pi\)
\(492\) 0 0
\(493\) − 14.1556i − 0.637534i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) − 1.20092i − 0.0538687i
\(498\) 0 0
\(499\) −32.6029 −1.45950 −0.729752 0.683712i \(-0.760365\pi\)
−0.729752 + 0.683712i \(0.760365\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 11.6962 0.521508 0.260754 0.965405i \(-0.416029\pi\)
0.260754 + 0.965405i \(0.416029\pi\)
\(504\) 0 0
\(505\) 28.4081 1.26414
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 40.0087 1.77335 0.886676 0.462391i \(-0.153008\pi\)
0.886676 + 0.462391i \(0.153008\pi\)
\(510\) 0 0
\(511\) − 9.01697i − 0.398887i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 57.4720i 2.53252i
\(516\) 0 0
\(517\) − 33.2379i − 1.46180i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 5.13277i 0.224871i 0.993659 + 0.112435i \(0.0358651\pi\)
−0.993659 + 0.112435i \(0.964135\pi\)
\(522\) 0 0
\(523\) −35.3652 −1.54641 −0.773207 0.634154i \(-0.781348\pi\)
−0.773207 + 0.634154i \(0.781348\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 8.99500 0.391829
\(528\) 0 0
\(529\) 11.3929 0.495344
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 2.24177 0.0971018
\(534\) 0 0
\(535\) − 52.5640i − 2.27254i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 5.11891i 0.220487i
\(540\) 0 0
\(541\) 30.7038i 1.32006i 0.751240 + 0.660029i \(0.229456\pi\)
−0.751240 + 0.660029i \(0.770544\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 26.7205i 1.14458i
\(546\) 0 0
\(547\) 2.21526 0.0947175 0.0473588 0.998878i \(-0.484920\pi\)
0.0473588 + 0.998878i \(0.484920\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 6.55110 0.279086
\(552\) 0 0
\(553\) 13.5570 0.576500
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 8.88158 0.376325 0.188162 0.982138i \(-0.439747\pi\)
0.188162 + 0.982138i \(0.439747\pi\)
\(558\) 0 0
\(559\) 2.48521i 0.105113i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 28.9398i 1.21967i 0.792529 + 0.609834i \(0.208764\pi\)
−0.792529 + 0.609834i \(0.791236\pi\)
\(564\) 0 0
\(565\) − 50.6007i − 2.12879i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 30.8816i 1.29463i 0.762224 + 0.647313i \(0.224107\pi\)
−0.762224 + 0.647313i \(0.775893\pi\)
\(570\) 0 0
\(571\) 31.5945 1.32219 0.661094 0.750303i \(-0.270092\pi\)
0.661094 + 0.750303i \(0.270092\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −41.2928 −1.72203
\(576\) 0 0
\(577\) −37.6007 −1.56534 −0.782669 0.622438i \(-0.786142\pi\)
−0.782669 + 0.622438i \(0.786142\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −4.96335 −0.205915
\(582\) 0 0
\(583\) − 23.2565i − 0.963186i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 22.0321i 0.909361i 0.890655 + 0.454680i \(0.150246\pi\)
−0.890655 + 0.454680i \(0.849754\pi\)
\(588\) 0 0
\(589\) 4.16283i 0.171526i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) − 17.8392i − 0.732569i −0.930503 0.366284i \(-0.880630\pi\)
0.930503 0.366284i \(-0.119370\pi\)
\(594\) 0 0
\(595\) −6.82263 −0.279701
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 19.5363 0.798230 0.399115 0.916901i \(-0.369317\pi\)
0.399115 + 0.916901i \(0.369317\pi\)
\(600\) 0 0
\(601\) −20.1240 −0.820877 −0.410438 0.911888i \(-0.634624\pi\)
−0.410438 + 0.911888i \(0.634624\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −52.7557 −2.14483
\(606\) 0 0
\(607\) − 15.3972i − 0.624951i −0.949926 0.312476i \(-0.898842\pi\)
0.949926 0.312476i \(-0.101158\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 1.74408i 0.0705578i
\(612\) 0 0
\(613\) − 37.9629i − 1.53331i −0.642061 0.766653i \(-0.721921\pi\)
0.642061 0.766653i \(-0.278079\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) − 43.0532i − 1.73326i −0.498953 0.866629i \(-0.666282\pi\)
0.498953 0.866629i \(-0.333718\pi\)
\(618\) 0 0
\(619\) 6.75463 0.271491 0.135746 0.990744i \(-0.456657\pi\)
0.135746 + 0.990744i \(0.456657\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 18.2032 0.729297
\(624\) 0 0
\(625\) −10.6285 −0.425138
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 13.7299 0.547448
\(630\) 0 0
\(631\) 1.96735i 0.0783189i 0.999233 + 0.0391594i \(0.0124680\pi\)
−0.999233 + 0.0391594i \(0.987532\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) − 47.8108i − 1.89731i
\(636\) 0 0
\(637\) − 0.268602i − 0.0106424i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) − 30.2998i − 1.19677i −0.801209 0.598385i \(-0.795809\pi\)
0.801209 0.598385i \(-0.204191\pi\)
\(642\) 0 0
\(643\) −3.85901 −0.152185 −0.0760923 0.997101i \(-0.524244\pi\)
−0.0760923 + 0.997101i \(0.524244\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −33.4004 −1.31310 −0.656552 0.754281i \(-0.727986\pi\)
−0.656552 + 0.754281i \(0.727986\pi\)
\(648\) 0 0
\(649\) −17.9430 −0.704326
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 26.9899 1.05620 0.528098 0.849184i \(-0.322905\pi\)
0.528098 + 0.849184i \(0.322905\pi\)
\(654\) 0 0
\(655\) 39.6367i 1.54874i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) − 13.1888i − 0.513763i −0.966443 0.256881i \(-0.917305\pi\)
0.966443 0.256881i \(-0.0826950\pi\)
\(660\) 0 0
\(661\) − 33.5767i − 1.30598i −0.757366 0.652990i \(-0.773514\pi\)
0.757366 0.652990i \(-0.226486\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) − 3.15747i − 0.122441i
\(666\) 0 0
\(667\) 42.2224 1.63486
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −10.0461 −0.387824
\(672\) 0 0
\(673\) 13.5269 0.521424 0.260712 0.965417i \(-0.416043\pi\)
0.260712 + 0.965417i \(0.416043\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 25.3388 0.973850 0.486925 0.873444i \(-0.338118\pi\)
0.486925 + 0.873444i \(0.338118\pi\)
\(678\) 0 0
\(679\) 3.39139i 0.130150i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) − 4.74712i − 0.181644i −0.995867 0.0908218i \(-0.971051\pi\)
0.995867 0.0908218i \(-0.0289494\pi\)
\(684\) 0 0
\(685\) 20.4504i 0.781369i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 1.22033i 0.0464908i
\(690\) 0 0
\(691\) 46.8908 1.78381 0.891904 0.452224i \(-0.149369\pi\)
0.891904 + 0.452224i \(0.149369\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −12.7457 −0.483472
\(696\) 0 0
\(697\) 16.4097 0.621561
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 11.8394 0.447166 0.223583 0.974685i \(-0.428225\pi\)
0.223583 + 0.974685i \(0.428225\pi\)
\(702\) 0 0
\(703\) 6.35412i 0.239650i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 8.18671i 0.307893i
\(708\) 0 0
\(709\) − 3.55487i − 0.133506i −0.997770 0.0667530i \(-0.978736\pi\)
0.997770 0.0667530i \(-0.0212639\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 26.8298i 1.00478i
\(714\) 0 0
\(715\) 4.77112 0.178430
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −0.174626 −0.00651246 −0.00325623 0.999995i \(-0.501036\pi\)
−0.00325623 + 0.999995i \(0.501036\pi\)
\(720\) 0 0
\(721\) −16.5624 −0.616816
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −50.6930 −1.88269
\(726\) 0 0
\(727\) 8.37928i 0.310770i 0.987854 + 0.155385i \(0.0496619\pi\)
−0.987854 + 0.155385i \(0.950338\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 18.1917i 0.672843i
\(732\) 0 0
\(733\) − 15.6312i − 0.577351i −0.957427 0.288676i \(-0.906785\pi\)
0.957427 0.288676i \(-0.0932149\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) − 56.4512i − 2.07941i
\(738\) 0 0
\(739\) 25.4382 0.935760 0.467880 0.883792i \(-0.345018\pi\)
0.467880 + 0.883792i \(0.345018\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −33.0542 −1.21264 −0.606320 0.795220i \(-0.707355\pi\)
−0.606320 + 0.795220i \(0.707355\pi\)
\(744\) 0 0
\(745\) 79.8941 2.92709
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 15.1480 0.553496
\(750\) 0 0
\(751\) 40.4075i 1.47449i 0.675625 + 0.737246i \(0.263874\pi\)
−0.675625 + 0.737246i \(0.736126\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) − 4.64498i − 0.169048i
\(756\) 0 0
\(757\) 30.0219i 1.09116i 0.838057 + 0.545582i \(0.183691\pi\)
−0.838057 + 0.545582i \(0.816309\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) − 13.9651i − 0.506234i −0.967436 0.253117i \(-0.918544\pi\)
0.967436 0.253117i \(-0.0814557\pi\)
\(762\) 0 0
\(763\) −7.70038 −0.278772
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0.941516 0.0339962
\(768\) 0 0
\(769\) 17.9999 0.649094 0.324547 0.945869i \(-0.394788\pi\)
0.324547 + 0.945869i \(0.394788\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 27.2134 0.978798 0.489399 0.872060i \(-0.337216\pi\)
0.489399 + 0.872060i \(0.337216\pi\)
\(774\) 0 0
\(775\) − 32.2124i − 1.15710i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 7.59429i 0.272094i
\(780\) 0 0
\(781\) 6.14741i 0.219972i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 75.5908i 2.69795i
\(786\) 0 0
\(787\) −3.45794 −0.123262 −0.0616312 0.998099i \(-0.519630\pi\)
−0.0616312 + 0.998099i \(0.519630\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 14.5822 0.518484
\(792\) 0 0
\(793\) 0.527143 0.0187194
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 44.2671 1.56802 0.784010 0.620748i \(-0.213171\pi\)
0.784010 + 0.620748i \(0.213171\pi\)
\(798\) 0 0
\(799\) 12.7666i 0.451650i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 46.1571i 1.62885i
\(804\) 0 0
\(805\) − 20.3501i − 0.717248i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 14.4191i 0.506949i 0.967342 + 0.253475i \(0.0815734\pi\)
−0.967342 + 0.253475i \(0.918427\pi\)
\(810\) 0 0
\(811\) −24.3314 −0.854389 −0.427195 0.904160i \(-0.640498\pi\)
−0.427195 + 0.904160i \(0.640498\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 70.3410 2.46394
\(816\) 0 0
\(817\) −8.41897 −0.294543
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −3.63626 −0.126906 −0.0634532 0.997985i \(-0.520211\pi\)
−0.0634532 + 0.997985i \(0.520211\pi\)
\(822\) 0 0
\(823\) 0.408592i 0.0142426i 0.999975 + 0.00712132i \(0.00226681\pi\)
−0.999975 + 0.00712132i \(0.997733\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) − 39.3528i − 1.36843i −0.729280 0.684215i \(-0.760145\pi\)
0.729280 0.684215i \(-0.239855\pi\)
\(828\) 0 0
\(829\) − 37.5641i − 1.30465i −0.757938 0.652327i \(-0.773793\pi\)
0.757938 0.652327i \(-0.226207\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) − 1.96616i − 0.0681234i
\(834\) 0 0
\(835\) −22.8200 −0.789719
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −35.7770 −1.23516 −0.617579 0.786509i \(-0.711887\pi\)
−0.617579 + 0.786509i \(0.711887\pi\)
\(840\) 0 0
\(841\) 22.8342 0.787385
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 44.8600 1.54323
\(846\) 0 0
\(847\) − 15.2033i − 0.522390i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 40.9528i 1.40384i
\(852\) 0 0
\(853\) 52.3988i 1.79410i 0.441929 + 0.897050i \(0.354294\pi\)
−0.441929 + 0.897050i \(0.645706\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 19.1325i 0.653553i 0.945102 + 0.326777i \(0.105963\pi\)
−0.945102 + 0.326777i \(0.894037\pi\)
\(858\) 0 0
\(859\) 12.1998 0.416253 0.208127 0.978102i \(-0.433263\pi\)
0.208127 + 0.978102i \(0.433263\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −31.3575 −1.06742 −0.533711 0.845667i \(-0.679203\pi\)
−0.533711 + 0.845667i \(0.679203\pi\)
\(864\) 0 0
\(865\) −46.2897 −1.57390
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −69.3968 −2.35413
\(870\) 0 0
\(871\) 2.96214i 0.100368i
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 7.08266i 0.239438i
\(876\) 0 0
\(877\) 4.64956i 0.157004i 0.996914 + 0.0785022i \(0.0250138\pi\)
−0.996914 + 0.0785022i \(0.974986\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 43.3414i 1.46021i 0.683336 + 0.730104i \(0.260528\pi\)
−0.683336 + 0.730104i \(0.739472\pi\)
\(882\) 0 0
\(883\) −0.420653 −0.0141561 −0.00707805 0.999975i \(-0.502253\pi\)
−0.00707805 + 0.999975i \(0.502253\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 14.5102 0.487204 0.243602 0.969875i \(-0.421671\pi\)
0.243602 + 0.969875i \(0.421671\pi\)
\(888\) 0 0
\(889\) 13.7782 0.462106
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −5.90830 −0.197714
\(894\) 0 0
\(895\) − 34.0955i − 1.13969i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 32.9375i 1.09853i
\(900\) 0 0
\(901\) 8.93276i 0.297593i
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 16.9599i 0.563765i
\(906\) 0 0
\(907\) 30.1284 1.00040 0.500198 0.865911i \(-0.333260\pi\)
0.500198 + 0.865911i \(0.333260\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −15.1934 −0.503379 −0.251689 0.967808i \(-0.580986\pi\)
−0.251689 + 0.967808i \(0.580986\pi\)
\(912\) 0 0
\(913\) 25.4070 0.840848
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −11.4226 −0.377207
\(918\) 0 0
\(919\) 38.7985i 1.27984i 0.768440 + 0.639922i \(0.221033\pi\)
−0.768440 + 0.639922i \(0.778967\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) − 0.322570i − 0.0106175i
\(924\) 0 0
\(925\) − 49.1688i − 1.61666i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 43.7700i 1.43605i 0.696019 + 0.718023i \(0.254953\pi\)
−0.696019 + 0.718023i \(0.745047\pi\)
\(930\) 0 0
\(931\) 0.909926 0.0298216
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 34.9245 1.14215
\(936\) 0 0
\(937\) 17.7605 0.580209 0.290104 0.956995i \(-0.406310\pi\)
0.290104 + 0.956995i \(0.406310\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −32.6364 −1.06392 −0.531958 0.846771i \(-0.678544\pi\)
−0.531958 + 0.846771i \(0.678544\pi\)
\(942\) 0 0
\(943\) 48.9458i 1.59390i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) − 14.9843i − 0.486925i −0.969910 0.243462i \(-0.921717\pi\)
0.969910 0.243462i \(-0.0782832\pi\)
\(948\) 0 0
\(949\) − 2.42198i − 0.0786208i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 23.1053i 0.748453i 0.927337 + 0.374226i \(0.122092\pi\)
−0.927337 + 0.374226i \(0.877908\pi\)
\(954\) 0 0
\(955\) −40.2971 −1.30398
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −5.89343 −0.190309
\(960\) 0 0
\(961\) 10.0702 0.324846
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −44.4741 −1.43167
\(966\) 0 0
\(967\) 25.1604i 0.809103i 0.914515 + 0.404552i \(0.132572\pi\)
−0.914515 + 0.404552i \(0.867428\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 24.0973i 0.773318i 0.922223 + 0.386659i \(0.126371\pi\)
−0.922223 + 0.386659i \(0.873629\pi\)
\(972\) 0 0
\(973\) − 3.67309i − 0.117754i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 30.9215i 0.989267i 0.869102 + 0.494634i \(0.164698\pi\)
−0.869102 + 0.494634i \(0.835302\pi\)
\(978\) 0 0
\(979\) −93.1807 −2.97807
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 1.67927 0.0535602 0.0267801 0.999641i \(-0.491475\pi\)
0.0267801 + 0.999641i \(0.491475\pi\)
\(984\) 0 0
\(985\) 16.2795 0.518709
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −54.2610 −1.72540
\(990\) 0 0
\(991\) 7.63921i 0.242667i 0.992612 + 0.121334i \(0.0387171\pi\)
−0.992612 + 0.121334i \(0.961283\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) − 53.2841i − 1.68922i
\(996\) 0 0
\(997\) 57.4039i 1.81800i 0.416798 + 0.908999i \(0.363152\pi\)
−0.416798 + 0.908999i \(0.636848\pi\)
\(998\) 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.5615.30 32
3.2 odd 2 inner 6048.2.j.c.5615.3 32
4.3 odd 2 1512.2.j.c.323.29 yes 32
8.3 odd 2 inner 6048.2.j.c.5615.4 32
8.5 even 2 1512.2.j.c.323.3 32
12.11 even 2 1512.2.j.c.323.4 yes 32
24.5 odd 2 1512.2.j.c.323.30 yes 32
24.11 even 2 inner 6048.2.j.c.5615.29 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1512.2.j.c.323.3 32 8.5 even 2
1512.2.j.c.323.4 yes 32 12.11 even 2
1512.2.j.c.323.29 yes 32 4.3 odd 2
1512.2.j.c.323.30 yes 32 24.5 odd 2
6048.2.j.c.5615.3 32 3.2 odd 2 inner
6048.2.j.c.5615.4 32 8.3 odd 2 inner
6048.2.j.c.5615.29 32 24.11 even 2 inner
6048.2.j.c.5615.30 32 1.1 even 1 trivial