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{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-21, 26, 68, -106, 10, 40, -14, -2, 1], 'conductor': 0, 'degree': 8, 'dirichlet_group': [], 'disc_abs': 181912486144, 'disc_rad': 53314, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[7, 1], [1, 1]]], [5, [[6, 1], [2, 1]]], [7, [[7, 1], [1, 1]]], [11, [[7, 1], [1, 1]]], [13, [[7, 1], [1, 1]]], [17, [[6, 1], [2, 1]]], [19, [0]], [23, [0]], [29, [[3, 2], [1, 2]]], [31, [[4, 2]]], [37, [[4, 2]]], [41, [[4, 2]]], [43, [[7, 1], [1, 1]]], [47, [[7, 1], [1, 1]]], [53, [[7, 1], [1, 1]]], [59, [[6, 1], [2, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [1488, 672, 672, 672], 'galois_label': '8T48', 'galt': 48, 'grd': 351.7133437722911, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '8.8.181912486144.1', 'local_algs': ['2.8.8.13', '19.4.0.1', '19.4.2.2', '23.1.0.1', '23.1.0.1', '23.2.0.1', '23.4.2.2', '61.2.0.1', '61.2.1.1', '61.2.1.1', '61.2.0.1'], 'monogenic': 0, 'num_ram': 4, 'r2': 0, 'ramps': [2, 19, 23, 61], 'rd': 25.5554076862, 'regulator': {'__RealLiteral__': 0, 'data': '2279.4264387992516', 'prec': 60}, 'res': {'sib': ['-428747748472,2105530231888,-1611640735984,-9065848218720,23496755844992,-18320019807296,-5699211890088,17141381883344,-6387975360736,-4467220762972,3798799476008,66778793260,-860002154604,173776479644,95983150094,-36236604238,-4872020054,3553748454,-284322,-200067432,13030796,6820292,-693540,-139968,17072,1606,-208,-8,1', '-479163486423529,3299407513196542,16538270846321542,-58256601470584384,-236313821488934739,266136286241335826,1444697539499206429,71845487826009804,-3820510133069478255,-2511064927819667272,4388261831009293092,5172981441144670318,-1791399179814593090,-4683172971687557042,-641006403942321767,2199348422613621148,971095728001680488,-512343222100020528,-432209608831762915,26052501241427194,100160954401091247,15578922670477122,-12978416485335121,-4272540475707562,867450473707494,543287405879628,-9227214256628,-41187294696032,-3335792344485,1972265307014,302737725534,-59374446578,-13647530438,1050856044,372004365,-8516572,-6342958,-20256,66287,836,-391,-4,1', '1,-2,-15,34,63,-172,-61,306,-61,-172,63,34,-15,-2,1', '2942971,-19138326,33619903,-5266830,-19510395,950522,3471359,82674,-253735,-11730,8911,392,-151,-4,1', '374298534184,-33430302260112,604859735769968,-3199940051026424,3330080422999952,15088401446189720,-32353535424615712,-20676474978811280,85729051911832552,917795910636032,-117819221527992216,26599509619927328,99862165154311720,-34438749550466496,-56666413227928916,23790940255454304,22528041740061324,-10803993477128740,-6431347079682936,3473442580747632,1330097293324692,-819110669568724,-197583258453484,144232383695424,20286323411660,-19099553625772,-1267444825960,1900504933820,18905016162,-140974750612,4757140458,7675281930,-522756484,-299160614,28578530,8030884,-945992,-139400,19004,1392,-212,-6,1', '5,-56,18,2172,-9187,-6858,130226,-250646,-326773,1817822,-1781840,-2198306,5834471,-2453548,-4260292,4858156,-59189,-2374164,1025978,329632,-336997,34374,35218,-9862,-859,574,-28,-10,1', '529,25806,299082,442360,-8991961,-32589324,93147203,496327032,-435042667,-3669981628,924649434,16079673780,-360730326,-45559207364,-2332299639,87378922364,5363630238,-116685545152,-5818395631,110728484396,3816314885,-75811059088,-1630414287,37841431524,459197848,-13849189008,-74412154,3719188104,-1760171,-729701676,5204982,103521990,-1655970,-10426670,290829,722700,-31068,-32624,1983,860,-69,-10,1', '538247,716056,-28486760,-34334666,462308395,505855986,-2688018754,-2803417086,6100417711,5774369034,-6167184782,-5611352652,3081717167,2808130640,-879685708,-807054492,157532953,142443452,-18760932,-15926546,1539949,1128458,-88434,-48918,3485,1178,-86,-12,1', '60955617924653,-422604118705294,-80683331187460,5047823968163014,-3721968641941909,-22392786928448010,18333634569527307,51959090866108762,-40642267357878975,-73967735156339726,53903791613534708,70642554923189110,-47752363828119464,-47822748549116786,29954986347326341,23781169091163926,-13783488073290034,-8893100515997976,4757498858968245,2538863563236752,-1249109243873971,-558241200681778,251432077291525,94896414799008,-38908265177426,-12464191650948,4620366061550,1258788852122,-418362777867,-96818452720,28558703056,5583641298,-1444509776,-235657760,52794217,7004020,-1343858,-137484,22495,1582,-223,-8,1', '9714,26546,-138854,-13102,8660,468,-170,-4,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{39}{61} a^{7} - \\frac{27}{61} a^{6} - \\frac{586}{61} a^{5} + \\frac{789}{61} a^{4} + 24 a^{3} - \\frac{2243}{61} a^{2} - \\frac{314}{61} a + \\frac{655}{61} \\)', '\\( a - 2 \\)', '\\( \\frac{30}{61} a^{7} - \\frac{2}{61} a^{6} - \\frac{432}{61} a^{5} + \\frac{377}{61} a^{4} + 19 a^{3} - \\frac{1167}{61} a^{2} - \\frac{509}{61} a + \\frac{349}{61} \\)', '\\( a^{7} - 14 a^{5} + 12 a^{4} + 34 a^{3} - 38 a^{2} - 7 a + 11 \\)', '\\( \\frac{112}{61} a^{7} - \\frac{40}{61} a^{6} - \\frac{1625}{61} a^{5} + \\frac{1806}{61} a^{4} + 65 a^{3} - \\frac{5223}{61} a^{2} - \\frac{664}{61} a + \\frac{1490}{61} \\)', '\\( \\frac{58}{61} a^{7} - \\frac{12}{61} a^{6} - \\frac{823}{61} a^{5} + \\frac{859}{61} a^{4} + 33 a^{3} - \\frac{2549}{61} a^{2} - \\frac{431}{61} a + \\frac{752}{61} \\)', '\\( \\frac{224}{61} a^{7} - \\frac{80}{61} a^{6} - \\frac{3250}{61} a^{5} + \\frac{3612}{61} a^{4} + 130 a^{3} - \\frac{10385}{61} a^{2} - \\frac{1389}{61} a + \\frac{2675}{61} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', '1/61*a^7 + 4/61*a^6 + 10/61*a^5 - 22/61*a^4 + 16/61*a^2 - 19/61*a - 27/61']}