Properties

Label 6048.2.c.f.3025.4
Level 6048
Weight 2
Character 6048.3025
Analytic conductor 48.294
Analytic rank 0
Dimension 24
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.c (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(48.2935231425\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: no (minimal twist has level 1512)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 3025.4
Character \(\chi\) \(=\) 6048.3025
Dual form 6048.2.c.f.3025.21

$q$-expansion

\(f(q)\) \(=\) \(q-3.04340i q^{5} -1.00000 q^{7} +O(q^{10})\) \(q-3.04340i q^{5} -1.00000 q^{7} +0.128573i q^{11} +6.30135i q^{13} +5.32168 q^{17} +6.68215i q^{19} -5.18212 q^{23} -4.26229 q^{25} -9.96821i q^{29} -3.27122 q^{31} +3.04340i q^{35} -0.796970i q^{37} -2.96782 q^{41} -6.99100i q^{43} -4.76595 q^{47} +1.00000 q^{49} +1.14264i q^{53} +0.391299 q^{55} -11.0999i q^{59} -14.6662i q^{61} +19.1775 q^{65} +1.05725i q^{67} -1.10582 q^{71} -12.1019 q^{73} -0.128573i q^{77} -2.62426 q^{79} +6.46403i q^{83} -16.1960i q^{85} -2.23283 q^{89} -6.30135i q^{91} +20.3365 q^{95} -7.88097 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 24q^{7} + O(q^{10}) \) \( 24q - 24q^{7} - 24q^{25} - 8q^{31} + 24q^{49} - 16q^{55} - 8q^{79} + O(q^{100}) \)

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
\(5\) − 3.04340i − 1.36105i −0.732725 0.680525i \(-0.761752\pi\)
0.732725 0.680525i \(-0.238248\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 0.128573i 0.0387662i 0.999812 + 0.0193831i \(0.00617022\pi\)
−0.999812 + 0.0193831i \(0.993830\pi\)
\(12\) 0 0
\(13\) 6.30135i 1.74768i 0.486214 + 0.873840i \(0.338378\pi\)
−0.486214 + 0.873840i \(0.661622\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 5.32168 1.29070 0.645348 0.763889i \(-0.276712\pi\)
0.645348 + 0.763889i \(0.276712\pi\)
\(18\) 0 0
\(19\) 6.68215i 1.53299i 0.642250 + 0.766495i \(0.278001\pi\)
−0.642250 + 0.766495i \(0.721999\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −5.18212 −1.08055 −0.540273 0.841490i \(-0.681679\pi\)
−0.540273 + 0.841490i \(0.681679\pi\)
\(24\) 0 0
\(25\) −4.26229 −0.852459
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) − 9.96821i − 1.85105i −0.378686 0.925525i \(-0.623624\pi\)
0.378686 0.925525i \(-0.376376\pi\)
\(30\) 0 0
\(31\) −3.27122 −0.587528 −0.293764 0.955878i \(-0.594908\pi\)
−0.293764 + 0.955878i \(0.594908\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 3.04340i 0.514429i
\(36\) 0 0
\(37\) − 0.796970i − 0.131021i −0.997852 0.0655106i \(-0.979132\pi\)
0.997852 0.0655106i \(-0.0208676\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −2.96782 −0.463496 −0.231748 0.972776i \(-0.574444\pi\)
−0.231748 + 0.972776i \(0.574444\pi\)
\(42\) 0 0
\(43\) − 6.99100i − 1.06612i −0.846078 0.533059i \(-0.821042\pi\)
0.846078 0.533059i \(-0.178958\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −4.76595 −0.695186 −0.347593 0.937646i \(-0.613001\pi\)
−0.347593 + 0.937646i \(0.613001\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 1.14264i 0.156954i 0.996916 + 0.0784772i \(0.0250058\pi\)
−0.996916 + 0.0784772i \(0.974994\pi\)
\(54\) 0 0
\(55\) 0.391299 0.0527627
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) − 11.0999i − 1.44508i −0.691329 0.722540i \(-0.742975\pi\)
0.691329 0.722540i \(-0.257025\pi\)
\(60\) 0 0
\(61\) − 14.6662i − 1.87782i −0.344165 0.938909i \(-0.611838\pi\)
0.344165 0.938909i \(-0.388162\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 19.1775 2.37868
\(66\) 0 0
\(67\) 1.05725i 0.129163i 0.997912 + 0.0645816i \(0.0205713\pi\)
−0.997912 + 0.0645816i \(0.979429\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −1.10582 −0.131237 −0.0656185 0.997845i \(-0.520902\pi\)
−0.0656185 + 0.997845i \(0.520902\pi\)
\(72\) 0 0
\(73\) −12.1019 −1.41642 −0.708212 0.706000i \(-0.750498\pi\)
−0.708212 + 0.706000i \(0.750498\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) − 0.128573i − 0.0146522i
\(78\) 0 0
\(79\) −2.62426 −0.295253 −0.147626 0.989043i \(-0.547163\pi\)
−0.147626 + 0.989043i \(0.547163\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 6.46403i 0.709520i 0.934957 + 0.354760i \(0.115437\pi\)
−0.934957 + 0.354760i \(0.884563\pi\)
\(84\) 0 0
\(85\) − 16.1960i − 1.75670i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −2.23283 −0.236680 −0.118340 0.992973i \(-0.537757\pi\)
−0.118340 + 0.992973i \(0.537757\pi\)
\(90\) 0 0
\(91\) − 6.30135i − 0.660561i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 20.3365 2.08648
\(96\) 0 0
\(97\) −7.88097 −0.800192 −0.400096 0.916473i \(-0.631023\pi\)
−0.400096 + 0.916473i \(0.631023\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) − 16.9693i − 1.68851i −0.535945 0.844253i \(-0.680045\pi\)
0.535945 0.844253i \(-0.319955\pi\)
\(102\) 0 0
\(103\) 10.7049 1.05479 0.527393 0.849621i \(-0.323170\pi\)
0.527393 + 0.849621i \(0.323170\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1.31462i 0.127089i 0.997979 + 0.0635445i \(0.0202405\pi\)
−0.997979 + 0.0635445i \(0.979760\pi\)
\(108\) 0 0
\(109\) − 10.2677i − 0.983465i −0.870746 0.491732i \(-0.836364\pi\)
0.870746 0.491732i \(-0.163636\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −13.1796 −1.23983 −0.619916 0.784668i \(-0.712834\pi\)
−0.619916 + 0.784668i \(0.712834\pi\)
\(114\) 0 0
\(115\) 15.7713i 1.47068i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −5.32168 −0.487837
\(120\) 0 0
\(121\) 10.9835 0.998497
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) − 2.24514i − 0.200811i
\(126\) 0 0
\(127\) 0.840201 0.0745558 0.0372779 0.999305i \(-0.488131\pi\)
0.0372779 + 0.999305i \(0.488131\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 7.39979i 0.646523i 0.946310 + 0.323261i \(0.104779\pi\)
−0.946310 + 0.323261i \(0.895221\pi\)
\(132\) 0 0
\(133\) − 6.68215i − 0.579416i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 5.61682 0.479877 0.239939 0.970788i \(-0.422873\pi\)
0.239939 + 0.970788i \(0.422873\pi\)
\(138\) 0 0
\(139\) 5.19553i 0.440679i 0.975423 + 0.220339i \(0.0707165\pi\)
−0.975423 + 0.220339i \(0.929284\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −0.810183 −0.0677509
\(144\) 0 0
\(145\) −30.3373 −2.51937
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) − 11.6207i − 0.952009i −0.879443 0.476004i \(-0.842085\pi\)
0.879443 0.476004i \(-0.157915\pi\)
\(150\) 0 0
\(151\) −21.5154 −1.75090 −0.875448 0.483313i \(-0.839433\pi\)
−0.875448 + 0.483313i \(0.839433\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 9.95563i 0.799655i
\(156\) 0 0
\(157\) 18.3001i 1.46050i 0.683178 + 0.730252i \(0.260597\pi\)
−0.683178 + 0.730252i \(0.739403\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 5.18212 0.408408
\(162\) 0 0
\(163\) − 18.8550i − 1.47684i −0.674344 0.738418i \(-0.735573\pi\)
0.674344 0.738418i \(-0.264427\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −20.8283 −1.61174 −0.805872 0.592089i \(-0.798303\pi\)
−0.805872 + 0.592089i \(0.798303\pi\)
\(168\) 0 0
\(169\) −26.7070 −2.05438
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) − 5.49174i − 0.417529i −0.977966 0.208765i \(-0.933056\pi\)
0.977966 0.208765i \(-0.0669443\pi\)
\(174\) 0 0
\(175\) 4.26229 0.322199
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 7.62941i 0.570249i 0.958491 + 0.285124i \(0.0920349\pi\)
−0.958491 + 0.285124i \(0.907965\pi\)
\(180\) 0 0
\(181\) 10.0176i 0.744600i 0.928113 + 0.372300i \(0.121431\pi\)
−0.928113 + 0.372300i \(0.878569\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −2.42550 −0.178326
\(186\) 0 0
\(187\) 0.684223i 0.0500354i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 6.25601 0.452669 0.226335 0.974050i \(-0.427326\pi\)
0.226335 + 0.974050i \(0.427326\pi\)
\(192\) 0 0
\(193\) 2.46446 0.177396 0.0886980 0.996059i \(-0.471729\pi\)
0.0886980 + 0.996059i \(0.471729\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 23.8105i 1.69643i 0.529654 + 0.848214i \(0.322322\pi\)
−0.529654 + 0.848214i \(0.677678\pi\)
\(198\) 0 0
\(199\) −24.1296 −1.71050 −0.855252 0.518212i \(-0.826598\pi\)
−0.855252 + 0.518212i \(0.826598\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 9.96821i 0.699631i
\(204\) 0 0
\(205\) 9.03227i 0.630841i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −0.859144 −0.0594282
\(210\) 0 0
\(211\) − 14.9668i − 1.03036i −0.857083 0.515179i \(-0.827726\pi\)
0.857083 0.515179i \(-0.172274\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −21.2764 −1.45104
\(216\) 0 0
\(217\) 3.27122 0.222065
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 33.5337i 2.25572i
\(222\) 0 0
\(223\) −11.6108 −0.777518 −0.388759 0.921340i \(-0.627096\pi\)
−0.388759 + 0.921340i \(0.627096\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 0.939445i 0.0623531i 0.999514 + 0.0311766i \(0.00992542\pi\)
−0.999514 + 0.0311766i \(0.990075\pi\)
\(228\) 0 0
\(229\) 0.0137124i 0 0.000906143i 1.00000 0.000453071i \(0.000144217\pi\)
−1.00000 0.000453071i \(0.999856\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −18.2195 −1.19360 −0.596800 0.802390i \(-0.703561\pi\)
−0.596800 + 0.802390i \(0.703561\pi\)
\(234\) 0 0
\(235\) 14.5047i 0.946183i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −1.37153 −0.0887169 −0.0443585 0.999016i \(-0.514124\pi\)
−0.0443585 + 0.999016i \(0.514124\pi\)
\(240\) 0 0
\(241\) −10.5054 −0.676711 −0.338355 0.941018i \(-0.609871\pi\)
−0.338355 + 0.941018i \(0.609871\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) − 3.04340i − 0.194436i
\(246\) 0 0
\(247\) −42.1066 −2.67918
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 20.0556i 1.26590i 0.774192 + 0.632950i \(0.218156\pi\)
−0.774192 + 0.632950i \(0.781844\pi\)
\(252\) 0 0
\(253\) − 0.666280i − 0.0418887i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 24.6631 1.53844 0.769220 0.638984i \(-0.220645\pi\)
0.769220 + 0.638984i \(0.220645\pi\)
\(258\) 0 0
\(259\) 0.796970i 0.0495213i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −14.0542 −0.866616 −0.433308 0.901246i \(-0.642654\pi\)
−0.433308 + 0.901246i \(0.642654\pi\)
\(264\) 0 0
\(265\) 3.47753 0.213623
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) − 13.1276i − 0.800404i −0.916427 0.400202i \(-0.868940\pi\)
0.916427 0.400202i \(-0.131060\pi\)
\(270\) 0 0
\(271\) 15.4626 0.939285 0.469642 0.882857i \(-0.344383\pi\)
0.469642 + 0.882857i \(0.344383\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) − 0.548015i − 0.0330466i
\(276\) 0 0
\(277\) 11.1880i 0.672223i 0.941822 + 0.336112i \(0.109112\pi\)
−0.941822 + 0.336112i \(0.890888\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −0.179766 −0.0107240 −0.00536198 0.999986i \(-0.501707\pi\)
−0.00536198 + 0.999986i \(0.501707\pi\)
\(282\) 0 0
\(283\) − 29.0480i − 1.72673i −0.504583 0.863363i \(-0.668354\pi\)
0.504583 0.863363i \(-0.331646\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 2.96782 0.175185
\(288\) 0 0
\(289\) 11.3202 0.665897
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) − 4.42498i − 0.258510i −0.991611 0.129255i \(-0.958741\pi\)
0.991611 0.129255i \(-0.0412586\pi\)
\(294\) 0 0
\(295\) −33.7813 −1.96683
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) − 32.6543i − 1.88845i
\(300\) 0 0
\(301\) 6.99100i 0.402955i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −44.6352 −2.55581
\(306\) 0 0
\(307\) 8.36831i 0.477605i 0.971068 + 0.238802i \(0.0767548\pi\)
−0.971068 + 0.238802i \(0.923245\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 28.1701 1.59738 0.798690 0.601743i \(-0.205527\pi\)
0.798690 + 0.601743i \(0.205527\pi\)
\(312\) 0 0
\(313\) 14.0081 0.791784 0.395892 0.918297i \(-0.370435\pi\)
0.395892 + 0.918297i \(0.370435\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) − 14.4390i − 0.810974i −0.914101 0.405487i \(-0.867102\pi\)
0.914101 0.405487i \(-0.132898\pi\)
\(318\) 0 0
\(319\) 1.28164 0.0717582
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 35.5603i 1.97863i
\(324\) 0 0
\(325\) − 26.8582i − 1.48982i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 4.76595 0.262756
\(330\) 0 0
\(331\) − 32.5738i − 1.79042i −0.445648 0.895208i \(-0.647027\pi\)
0.445648 0.895208i \(-0.352973\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 3.21762 0.175798
\(336\) 0 0
\(337\) −2.17181 −0.118306 −0.0591529 0.998249i \(-0.518840\pi\)
−0.0591529 + 0.998249i \(0.518840\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) − 0.420590i − 0.0227762i
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) − 2.79477i − 0.150031i −0.997182 0.0750157i \(-0.976099\pi\)
0.997182 0.0750157i \(-0.0239007\pi\)
\(348\) 0 0
\(349\) 3.19085i 0.170802i 0.996347 + 0.0854011i \(0.0272172\pi\)
−0.996347 + 0.0854011i \(0.972783\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 8.10245 0.431250 0.215625 0.976476i \(-0.430821\pi\)
0.215625 + 0.976476i \(0.430821\pi\)
\(354\) 0 0
\(355\) 3.36546i 0.178620i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 17.2635 0.911134 0.455567 0.890202i \(-0.349437\pi\)
0.455567 + 0.890202i \(0.349437\pi\)
\(360\) 0 0
\(361\) −25.6511 −1.35006
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 36.8310i 1.92782i
\(366\) 0 0
\(367\) 13.5508 0.707348 0.353674 0.935369i \(-0.384932\pi\)
0.353674 + 0.935369i \(0.384932\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) − 1.14264i − 0.0593232i
\(372\) 0 0
\(373\) 16.3399i 0.846048i 0.906118 + 0.423024i \(0.139031\pi\)
−0.906118 + 0.423024i \(0.860969\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 62.8132 3.23504
\(378\) 0 0
\(379\) 2.37754i 0.122126i 0.998134 + 0.0610630i \(0.0194491\pi\)
−0.998134 + 0.0610630i \(0.980551\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 17.6210 0.900389 0.450194 0.892931i \(-0.351355\pi\)
0.450194 + 0.892931i \(0.351355\pi\)
\(384\) 0 0
\(385\) −0.391299 −0.0199424
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 12.6831i 0.643058i 0.946900 + 0.321529i \(0.104197\pi\)
−0.946900 + 0.321529i \(0.895803\pi\)
\(390\) 0 0
\(391\) −27.5776 −1.39466
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 7.98668i 0.401854i
\(396\) 0 0
\(397\) − 34.3856i − 1.72576i −0.505405 0.862882i \(-0.668657\pi\)
0.505405 0.862882i \(-0.331343\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −3.75947 −0.187739 −0.0938696 0.995585i \(-0.529924\pi\)
−0.0938696 + 0.995585i \(0.529924\pi\)
\(402\) 0 0
\(403\) − 20.6131i − 1.02681i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0.102469 0.00507919
\(408\) 0 0
\(409\) 13.0996 0.647731 0.323866 0.946103i \(-0.395017\pi\)
0.323866 + 0.946103i \(0.395017\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 11.0999i 0.546189i
\(414\) 0 0
\(415\) 19.6726 0.965692
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 24.4344i 1.19370i 0.802353 + 0.596849i \(0.203581\pi\)
−0.802353 + 0.596849i \(0.796419\pi\)
\(420\) 0 0
\(421\) 26.3907i 1.28620i 0.765781 + 0.643101i \(0.222353\pi\)
−0.765781 + 0.643101i \(0.777647\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −22.6825 −1.10027
\(426\) 0 0
\(427\) 14.6662i 0.709749i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −32.7161 −1.57588 −0.787940 0.615751i \(-0.788853\pi\)
−0.787940 + 0.615751i \(0.788853\pi\)
\(432\) 0 0
\(433\) 12.3235 0.592228 0.296114 0.955153i \(-0.404309\pi\)
0.296114 + 0.955153i \(0.404309\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) − 34.6277i − 1.65647i
\(438\) 0 0
\(439\) −4.67878 −0.223306 −0.111653 0.993747i \(-0.535615\pi\)
−0.111653 + 0.993747i \(0.535615\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) − 35.6471i − 1.69364i −0.531877 0.846821i \(-0.678513\pi\)
0.531877 0.846821i \(-0.321487\pi\)
\(444\) 0 0
\(445\) 6.79540i 0.322133i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 6.02786 0.284472 0.142236 0.989833i \(-0.454571\pi\)
0.142236 + 0.989833i \(0.454571\pi\)
\(450\) 0 0
\(451\) − 0.381581i − 0.0179680i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −19.1775 −0.899057
\(456\) 0 0
\(457\) 4.88761 0.228633 0.114316 0.993444i \(-0.463532\pi\)
0.114316 + 0.993444i \(0.463532\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) − 9.16306i − 0.426766i −0.976969 0.213383i \(-0.931552\pi\)
0.976969 0.213383i \(-0.0684483\pi\)
\(462\) 0 0
\(463\) −32.8412 −1.52626 −0.763130 0.646245i \(-0.776338\pi\)
−0.763130 + 0.646245i \(0.776338\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) − 6.40559i − 0.296415i −0.988956 0.148208i \(-0.952650\pi\)
0.988956 0.148208i \(-0.0473504\pi\)
\(468\) 0 0
\(469\) − 1.05725i − 0.0488191i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0.898854 0.0413293
\(474\) 0 0
\(475\) − 28.4813i − 1.30681i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −27.3218 −1.24837 −0.624184 0.781278i \(-0.714568\pi\)
−0.624184 + 0.781278i \(0.714568\pi\)
\(480\) 0 0
\(481\) 5.02199 0.228983
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 23.9850i 1.08910i
\(486\) 0 0
\(487\) −9.05264 −0.410214 −0.205107 0.978740i \(-0.565754\pi\)
−0.205107 + 0.978740i \(0.565754\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) − 10.1183i − 0.456632i −0.973587 0.228316i \(-0.926678\pi\)
0.973587 0.228316i \(-0.0733219\pi\)
\(492\) 0 0
\(493\) − 53.0476i − 2.38914i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 1.10582 0.0496029
\(498\) 0 0
\(499\) − 19.9396i − 0.892621i −0.894878 0.446310i \(-0.852738\pi\)
0.894878 0.446310i \(-0.147262\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −24.3936 −1.08766 −0.543828 0.839197i \(-0.683026\pi\)
−0.543828 + 0.839197i \(0.683026\pi\)
\(504\) 0 0
\(505\) −51.6443 −2.29814
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 7.20394i 0.319309i 0.987173 + 0.159655i \(0.0510381\pi\)
−0.987173 + 0.159655i \(0.948962\pi\)
\(510\) 0 0
\(511\) 12.1019 0.535358
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) − 32.5793i − 1.43562i
\(516\) 0 0
\(517\) − 0.612773i − 0.0269497i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 14.8648 0.651240 0.325620 0.945501i \(-0.394427\pi\)
0.325620 + 0.945501i \(0.394427\pi\)
\(522\) 0 0
\(523\) 32.1286i 1.40489i 0.711740 + 0.702443i \(0.247907\pi\)
−0.711740 + 0.702443i \(0.752093\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −17.4084 −0.758320
\(528\) 0 0
\(529\) 3.85438 0.167582
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) − 18.7013i − 0.810042i
\(534\) 0 0
\(535\) 4.00091 0.172975
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0.128573i 0.00553803i
\(540\) 0 0
\(541\) 30.6123i 1.31612i 0.752964 + 0.658062i \(0.228624\pi\)
−0.752964 + 0.658062i \(0.771376\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −31.2487 −1.33855
\(546\) 0 0
\(547\) 7.64518i 0.326884i 0.986553 + 0.163442i \(0.0522597\pi\)
−0.986553 + 0.163442i \(0.947740\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 66.6091 2.83764
\(552\) 0 0
\(553\) 2.62426 0.111595
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 24.9682i 1.05794i 0.848641 + 0.528969i \(0.177421\pi\)
−0.848641 + 0.528969i \(0.822579\pi\)
\(558\) 0 0
\(559\) 44.0527 1.86323
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) − 33.1836i − 1.39852i −0.714865 0.699262i \(-0.753512\pi\)
0.714865 0.699262i \(-0.246488\pi\)
\(564\) 0 0
\(565\) 40.1108i 1.68748i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −17.0679 −0.715523 −0.357761 0.933813i \(-0.616460\pi\)
−0.357761 + 0.933813i \(0.616460\pi\)
\(570\) 0 0
\(571\) 5.13058i 0.214708i 0.994221 + 0.107354i \(0.0342378\pi\)
−0.994221 + 0.107354i \(0.965762\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 22.0877 0.921121
\(576\) 0 0
\(577\) −47.5819 −1.98086 −0.990429 0.138021i \(-0.955926\pi\)
−0.990429 + 0.138021i \(0.955926\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) − 6.46403i − 0.268173i
\(582\) 0 0
\(583\) −0.146913 −0.00608452
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) − 23.6803i − 0.977390i −0.872455 0.488695i \(-0.837473\pi\)
0.872455 0.488695i \(-0.162527\pi\)
\(588\) 0 0
\(589\) − 21.8588i − 0.900675i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −17.8919 −0.734734 −0.367367 0.930076i \(-0.619741\pi\)
−0.367367 + 0.930076i \(0.619741\pi\)
\(594\) 0 0
\(595\) 16.1960i 0.663971i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 32.0167 1.30817 0.654083 0.756423i \(-0.273055\pi\)
0.654083 + 0.756423i \(0.273055\pi\)
\(600\) 0 0
\(601\) 23.7187 0.967507 0.483754 0.875204i \(-0.339273\pi\)
0.483754 + 0.875204i \(0.339273\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) − 33.4271i − 1.35901i
\(606\) 0 0
\(607\) 14.4444 0.586281 0.293141 0.956069i \(-0.405300\pi\)
0.293141 + 0.956069i \(0.405300\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) − 30.0319i − 1.21496i
\(612\) 0 0
\(613\) − 16.2817i − 0.657610i −0.944398 0.328805i \(-0.893354\pi\)
0.944398 0.328805i \(-0.106646\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −28.7753 −1.15845 −0.579225 0.815167i \(-0.696645\pi\)
−0.579225 + 0.815167i \(0.696645\pi\)
\(618\) 0 0
\(619\) 36.0871i 1.45046i 0.688506 + 0.725231i \(0.258267\pi\)
−0.688506 + 0.725231i \(0.741733\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 2.23283 0.0894564
\(624\) 0 0
\(625\) −28.1443 −1.12577
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) − 4.24122i − 0.169108i
\(630\) 0 0
\(631\) −18.0509 −0.718595 −0.359297 0.933223i \(-0.616984\pi\)
−0.359297 + 0.933223i \(0.616984\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) − 2.55707i − 0.101474i
\(636\) 0 0
\(637\) 6.30135i 0.249668i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −12.0253 −0.474971 −0.237486 0.971391i \(-0.576323\pi\)
−0.237486 + 0.971391i \(0.576323\pi\)
\(642\) 0 0
\(643\) − 9.54316i − 0.376345i −0.982136 0.188173i \(-0.939744\pi\)
0.982136 0.188173i \(-0.0602565\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 32.2201 1.26670 0.633351 0.773865i \(-0.281679\pi\)
0.633351 + 0.773865i \(0.281679\pi\)
\(648\) 0 0
\(649\) 1.42714 0.0560202
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) − 14.5245i − 0.568388i −0.958767 0.284194i \(-0.908274\pi\)
0.958767 0.284194i \(-0.0917259\pi\)
\(654\) 0 0
\(655\) 22.5205 0.879950
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) − 10.5726i − 0.411849i −0.978568 0.205924i \(-0.933980\pi\)
0.978568 0.205924i \(-0.0660201\pi\)
\(660\) 0 0
\(661\) − 27.0965i − 1.05393i −0.849887 0.526965i \(-0.823330\pi\)
0.849887 0.526965i \(-0.176670\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −20.3365 −0.788614
\(666\) 0 0
\(667\) 51.6565i 2.00015i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 1.88568 0.0727959
\(672\) 0 0
\(673\) 38.2417 1.47411 0.737055 0.675833i \(-0.236216\pi\)
0.737055 + 0.675833i \(0.236216\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 14.2289i 0.546860i 0.961892 + 0.273430i \(0.0881582\pi\)
−0.961892 + 0.273430i \(0.911842\pi\)
\(678\) 0 0
\(679\) 7.88097 0.302444
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) − 39.0552i − 1.49441i −0.664596 0.747203i \(-0.731397\pi\)
0.664596 0.747203i \(-0.268603\pi\)
\(684\) 0 0
\(685\) − 17.0942i − 0.653137i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −7.20020 −0.274306
\(690\) 0 0
\(691\) − 20.1602i − 0.766929i −0.923556 0.383464i \(-0.874731\pi\)
0.923556 0.383464i \(-0.125269\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 15.8121 0.599786
\(696\) 0 0
\(697\) −15.7938 −0.598232
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) − 22.4760i − 0.848908i −0.905449 0.424454i \(-0.860466\pi\)
0.905449 0.424454i \(-0.139534\pi\)
\(702\) 0 0
\(703\) 5.32548 0.200854
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 16.9693i 0.638195i
\(708\) 0 0
\(709\) − 20.2609i − 0.760915i −0.924798 0.380458i \(-0.875767\pi\)
0.924798 0.380458i \(-0.124233\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 16.9518 0.634852
\(714\) 0 0
\(715\) 2.46571i 0.0922124i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 21.2440 0.792269 0.396134 0.918193i \(-0.370351\pi\)
0.396134 + 0.918193i \(0.370351\pi\)
\(720\) 0 0
\(721\) −10.7049 −0.398672
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 42.4874i 1.57794i
\(726\) 0 0
\(727\) 32.9048 1.22037 0.610185 0.792259i \(-0.291095\pi\)
0.610185 + 0.792259i \(0.291095\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) − 37.2039i − 1.37603i
\(732\) 0 0
\(733\) 32.0598i 1.18415i 0.805881 + 0.592077i \(0.201692\pi\)
−0.805881 + 0.592077i \(0.798308\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −0.135933 −0.00500716
\(738\) 0 0
\(739\) − 46.3826i − 1.70621i −0.521738 0.853106i \(-0.674716\pi\)
0.521738 0.853106i \(-0.325284\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −12.1782 −0.446777 −0.223388 0.974730i \(-0.571712\pi\)
−0.223388 + 0.974730i \(0.571712\pi\)
\(744\) 0 0
\(745\) −35.3666 −1.29573
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) − 1.31462i − 0.0480351i
\(750\) 0 0
\(751\) −24.4371 −0.891723 −0.445862 0.895102i \(-0.647103\pi\)
−0.445862 + 0.895102i \(0.647103\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 65.4799i 2.38306i
\(756\) 0 0
\(757\) 7.15224i 0.259953i 0.991517 + 0.129976i \(0.0414902\pi\)
−0.991517 + 0.129976i \(0.958510\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 14.7809 0.535806 0.267903 0.963446i \(-0.413669\pi\)
0.267903 + 0.963446i \(0.413669\pi\)
\(762\) 0 0
\(763\) 10.2677i 0.371715i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 69.9441 2.52554
\(768\) 0 0
\(769\) −1.90576 −0.0687235 −0.0343618 0.999409i \(-0.510940\pi\)
−0.0343618 + 0.999409i \(0.510940\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 6.63435i 0.238621i 0.992857 + 0.119310i \(0.0380684\pi\)
−0.992857 + 0.119310i \(0.961932\pi\)
\(774\) 0 0
\(775\) 13.9429 0.500843
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) − 19.8314i − 0.710534i
\(780\) 0 0
\(781\) − 0.142179i − 0.00508756i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 55.6944 1.98782
\(786\) 0 0
\(787\) 2.91096i 0.103765i 0.998653 + 0.0518823i \(0.0165221\pi\)
−0.998653 + 0.0518823i \(0.983478\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 13.1796 0.468613
\(792\) 0 0
\(793\) 92.4170 3.28182
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 6.96910i 0.246858i 0.992353 + 0.123429i \(0.0393891\pi\)
−0.992353 + 0.123429i \(0.960611\pi\)
\(798\) 0 0
\(799\) −25.3629 −0.897274
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) − 1.55598i − 0.0549094i
\(804\) 0 0
\(805\) − 15.7713i − 0.555864i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −21.3012 −0.748909 −0.374454 0.927245i \(-0.622170\pi\)
−0.374454 + 0.927245i \(0.622170\pi\)
\(810\) 0 0
\(811\) − 18.1357i − 0.636832i −0.947951 0.318416i \(-0.896849\pi\)
0.947951 0.318416i \(-0.103151\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −57.3832 −2.01005
\(816\) 0 0
\(817\) 46.7149 1.63435
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 24.3030i 0.848180i 0.905620 + 0.424090i \(0.139406\pi\)
−0.905620 + 0.424090i \(0.860594\pi\)
\(822\) 0 0
\(823\) −1.29306 −0.0450734 −0.0225367 0.999746i \(-0.507174\pi\)
−0.0225367 + 0.999746i \(0.507174\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) − 23.6268i − 0.821585i −0.911729 0.410792i \(-0.865252\pi\)
0.911729 0.410792i \(-0.134748\pi\)
\(828\) 0 0
\(829\) 5.66492i 0.196751i 0.995149 + 0.0983754i \(0.0313646\pi\)
−0.995149 + 0.0983754i \(0.968635\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 5.32168 0.184385
\(834\) 0 0
\(835\) 63.3890i 2.19367i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 21.1554 0.730366 0.365183 0.930936i \(-0.381006\pi\)
0.365183 + 0.930936i \(0.381006\pi\)
\(840\) 0 0
\(841\) −70.3652 −2.42639
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 81.2801i 2.79612i
\(846\) 0 0
\(847\) −10.9835 −0.377396
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 4.13000i 0.141574i
\(852\) 0 0
\(853\) 4.41255i 0.151083i 0.997143 + 0.0755413i \(0.0240685\pi\)
−0.997143 + 0.0755413i \(0.975932\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 20.9783 0.716606 0.358303 0.933605i \(-0.383356\pi\)
0.358303 + 0.933605i \(0.383356\pi\)
\(858\) 0 0
\(859\) 15.6318i 0.533351i 0.963786 + 0.266676i \(0.0859253\pi\)
−0.963786 + 0.266676i \(0.914075\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −16.1880 −0.551047 −0.275523 0.961294i \(-0.588851\pi\)
−0.275523 + 0.961294i \(0.588851\pi\)
\(864\) 0 0
\(865\) −16.7136 −0.568278
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) − 0.337409i − 0.0114458i
\(870\) 0 0
\(871\) −6.66208 −0.225736
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 2.24514i 0.0758995i
\(876\) 0 0
\(877\) 38.1001i 1.28655i 0.765636 + 0.643274i \(0.222424\pi\)
−0.765636 + 0.643274i \(0.777576\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −46.4289 −1.56423 −0.782114 0.623135i \(-0.785859\pi\)
−0.782114 + 0.623135i \(0.785859\pi\)
\(882\) 0 0
\(883\) 17.8873i 0.601956i 0.953631 + 0.300978i \(0.0973131\pi\)
−0.953631 + 0.300978i \(0.902687\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −35.5228 −1.19274 −0.596369 0.802711i \(-0.703390\pi\)
−0.596369 + 0.802711i \(0.703390\pi\)
\(888\) 0 0
\(889\) −0.840201 −0.0281795
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) − 31.8468i − 1.06571i
\(894\) 0 0
\(895\) 23.2194 0.776137
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 32.6082i 1.08754i
\(900\) 0 0
\(901\) 6.08079i 0.202580i
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 30.4875 1.01344
\(906\) 0 0
\(907\) 41.8996i 1.39125i 0.718404 + 0.695627i \(0.244873\pi\)
−0.718404 + 0.695627i \(0.755127\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −5.35427 −0.177395 −0.0886974 0.996059i \(-0.528270\pi\)
−0.0886974 + 0.996059i \(0.528270\pi\)
\(912\) 0 0
\(913\) −0.831099 −0.0275054
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) − 7.39979i − 0.244363i
\(918\) 0 0
\(919\) 54.8843 1.81047 0.905234 0.424914i \(-0.139696\pi\)
0.905234 + 0.424914i \(0.139696\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) − 6.96817i − 0.229360i
\(924\) 0 0
\(925\) 3.39692i 0.111690i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −10.4091 −0.341512 −0.170756 0.985313i \(-0.554621\pi\)
−0.170756 + 0.985313i \(0.554621\pi\)
\(930\) 0 0
\(931\) 6.68215i 0.218999i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 2.08237 0.0681007
\(936\) 0 0
\(937\) 49.8177 1.62747 0.813737 0.581233i \(-0.197430\pi\)
0.813737 + 0.581233i \(0.197430\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 5.61503i 0.183045i 0.995803 + 0.0915224i \(0.0291733\pi\)
−0.995803 + 0.0915224i \(0.970827\pi\)
\(942\) 0 0
\(943\) 15.3796 0.500829
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 22.3495i 0.726262i 0.931738 + 0.363131i \(0.118292\pi\)
−0.931738 + 0.363131i \(0.881708\pi\)
\(948\) 0 0
\(949\) − 76.2585i − 2.47545i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −19.9449 −0.646080 −0.323040 0.946385i \(-0.604705\pi\)
−0.323040 + 0.946385i \(0.604705\pi\)
\(954\) 0 0
\(955\) − 19.0396i − 0.616106i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −5.61682 −0.181376
\(960\) 0 0
\(961\) −20.2991 −0.654811
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) − 7.50035i − 0.241445i
\(966\) 0 0
\(967\) −32.6951 −1.05140 −0.525702 0.850669i \(-0.676197\pi\)
−0.525702 + 0.850669i \(0.676197\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) − 33.7391i − 1.08274i −0.840785 0.541369i \(-0.817906\pi\)
0.840785 0.541369i \(-0.182094\pi\)
\(972\) 0 0
\(973\) − 5.19553i − 0.166561i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −45.8374 −1.46647 −0.733235 0.679976i \(-0.761990\pi\)
−0.733235 + 0.679976i \(0.761990\pi\)
\(978\) 0 0
\(979\) − 0.287081i − 0.00917516i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −14.0557 −0.448307 −0.224154 0.974554i \(-0.571962\pi\)
−0.224154 + 0.974554i \(0.571962\pi\)
\(984\) 0 0
\(985\) 72.4649 2.30892
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 36.2282i 1.15199i
\(990\) 0 0
\(991\) −18.3875 −0.584099 −0.292050 0.956403i \(-0.594337\pi\)
−0.292050 + 0.956403i \(0.594337\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 73.4362i 2.32808i
\(996\) 0 0
\(997\) 20.8011i 0.658776i 0.944195 + 0.329388i \(0.106842\pi\)
−0.944195 + 0.329388i \(0.893158\pi\)
\(998\) 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.c.f.3025.4 24
3.2 odd 2 inner 6048.2.c.f.3025.22 24
4.3 odd 2 1512.2.c.g.757.11 24
8.3 odd 2 1512.2.c.g.757.12 yes 24
8.5 even 2 inner 6048.2.c.f.3025.21 24
12.11 even 2 1512.2.c.g.757.14 yes 24
24.5 odd 2 inner 6048.2.c.f.3025.3 24
24.11 even 2 1512.2.c.g.757.13 yes 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1512.2.c.g.757.11 24 4.3 odd 2
1512.2.c.g.757.12 yes 24 8.3 odd 2
1512.2.c.g.757.13 yes 24 24.11 even 2
1512.2.c.g.757.14 yes 24 12.11 even 2
6048.2.c.f.3025.3 24 24.5 odd 2 inner
6048.2.c.f.3025.4 24 1.1 even 1 trivial
6048.2.c.f.3025.21 24 8.5 even 2 inner
6048.2.c.f.3025.22 24 3.2 odd 2 inner