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{'class_group': [11], 'class_number': 11, 'cm': False, 'coeffs': [-15, 22, -3, -6, 0, 1], 'conductor': 0, 'degree': 5, 'dirichlet_group': [], 'disc_abs': 6223825, 'disc_rad': 1244765, 'disc_sign': 1, 'frobs': [[2, [[5, 1]]], [3, [[2, 2], [1, 1]]], [5, [0]], [7, [[2, 1], [1, 3]]], [11, [[2, 2], [1, 1]]], [13, [[5, 1]]], [17, [[4, 1], [1, 1]]], [19, [[4, 1], [1, 1]]], [23, [[3, 1], [1, 2]]], [29, [[3, 1], [2, 1]]], [31, [[3, 1], [2, 1]]], [37, [[4, 1], [1, 1]]], [41, [[5, 1]]], [43, [[3, 1], [2, 1]]], [47, [[4, 1], [1, 1]]], [53, [[4, 1], [1, 1]]], [59, [[3, 1], [2, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [80, 60, 60], 'galois_label': '5T5', 'galt': 5, 'grd': 1458.9442104703726, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '5.1.6223825.1', 'local_algs': ['5.1.0.1', '5.1.0.1', '5.3.2.1', 'm241.2.1.1', 'm241.1.3.0', 'm1033.1.1.0', 'm1033.1.2.0', 'm1033.2.1.1'], 'monogenic': 1, 'num_ram': 3, 'r2': 2, 'ramps': [5, 241, 1033], 'rd': 22.8460684966, 'regulator': {'__RealLiteral__': 0, 'data': '6.3673778095', 'prec': 40}, 'res': {'sib': ['-15953487,668173,104783,-2133,-326,-3,1', '-1819198654278263,14925040122244,-240899321215,56564477223,6654448566,54766449,10714320,-885,4877,-4,1', '-203737140000,-60558570000,233867220000,-205915910500,-137351860750,193919044375,-95586404500,-44460063500,65774241400,-34275667720,-2370160545,12753662195,-8001727261,1070051653,1396286241,-1018023938,236520670,59056373,-63040509,19417517,-1795351,-895805,491196,-150638,32599,-7027,1800,-423,84,-12,1', '-3617673,-39402608,-101191546,-120917757,-79003349,-29666778,-6686861,-971312,4736,70122,16580,719,-437,-59,-3,1', '-3982012223481103641137409,-328717280116843991310706,-1788168550894010752937705,360854807171213496089050,-254145453125775317623466,115501033436510986563060,-22960843137621902524014,7438769912291130504425,-1009719958808210574775,-341715462123504895479,27442542847455949319,-29976327720929707835,4970127609594925135,-1184515597867088610,212057878282509880,-33526482980321500,5145670464377285,-697335817916775,83210666801435,-10184817385115,968083019314,-101503090749,8318615965,-675904405,52860461,-2842010,240544,-6645,705,-6,1', '-693,-753,-775,-204,39,201,42,-3,-18,0,1', '-9876970168377617045664,-15808391941092508616544,-7727992522332233939640,-1409468794080412629000,-126645397326235659596,-8050411401410471627,-372652181407547666,-14863895288153425,2032813386991665,276221400757061,12323945881862,-163487840714,-14891022800,-164597875,-80998681,-5777057,359319,11560,-950,-4,1', '11025,-46200,130625,265780,-201830,1454760,2741154,-687456,-1217475,673848,138755,-170408,64093,-23436,11010,-3384,783,-186,44,-8,1', '1663553123448541511203575,1039641647041423595019375,5217167571577677890775,-150477931023657971375625,-35025194863688298286735,6068991123947022328785,3672988713206837391201,245165179765412923320,-162072902873855758820,-35920465513861876380,2042970691915113844,1670362872230099625,132292105334661065,-38420718672217080,-8019064264239160,211064865166575,215167875124190,14382601629420,-3169724436695,-505420141650,17452055740,8678823120,265264465,-89402025,-6822175,536010,70319,-1470,-390,0,1', '310151611484200395000,-195507104335804865625,27652768389126740000,43506926415119875,2412421120718256125,-1058013871737779250,150863115640603150,-16119088385463900,6835660272754975,-2045333581890460,296825372310160,-39226733554405,6864746580699,-859795276813,133502259983,-15662160085,1907707505,-182189593,16842431,-1381126,99800,-5140,443,-6,1', '573028914,125213387,-117087482,-16000345,7378155,727897,-212004,-25766,5840,390,-67,-6,1', '959898721789385,-287096940617205,213281379213335,-46391703789443,11013778902285,-9934812583150,1488409174918,-296366962926,183324176922,-24324482819,6308233483,-1009677851,186659312,-22567988,4223258,-311196,54046,-2437,357,-8,1', '99010415965719765026451650625,0,331408621372889523165608311875,0,149554404770331727998387294750,0,-3480944445206431682890671950,0,-327748373667115887830957175,0,6187252000138892930882540,0,-332746669306760835739589,0,224367749459115929533050,0,24053577376806317964428,0,1459148885565943224360,0,75319639811098555821,0,3116441686971655263,0,101986134248222670,0,2591433718291599,0,49476218264445,0,693107849363,0,7011955926,0,50145505,0,242648,0,720,0,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a^{4} + a^{3} - 5 a^{2} - 8 a + 14 \\)', '\\( a^{4} + a^{3} - 5 a^{2} - 8 a + 13 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4']}