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{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 'conductor': 0, 'degree': 34, 'dirichlet_group': [], 'disc_abs': 11627528865280854983574434471375691019078604726189023, 'disc_rad': 11627528865280854983574434471375691019078604726189023, 'disc_sign': -1, 'frobs': [[2, [[30, 1], [4, 1]]], [3, [[28, 1], [5, 1], [1, 1]]], [5, [[20, 1], [5, 1], [4, 1], [3, 1], [2, 1]]], [7, [[16, 1], [9, 2]]], [11, [[9, 1], [8, 1], [6, 1], [5, 1], [3, 1], [2, 1], [1, 1]]], [13, [[29, 1], [2, 2], [1, 1]]], [17, [[32, 1], [2, 1]]], [19, [[32, 1], [2, 1]]], [23, [[16, 1], [10, 1], [8, 1]]], [29, [[15, 1], [9, 1], [5, 1], [4, 1], [1, 1]]], [31, [[28, 1], [6, 1]]], [37, [[24, 1], [6, 1], [3, 1], [1, 1]]], [41, [[16, 1], [11, 1], [7, 1]]], [43, [[12, 1], [6, 1], [5, 1], [4, 2], [2, 1], [1, 1]]], [47, [[9, 1], [8, 2], [3, 1], [2, 2], [1, 2]]], [53, [[29, 1], [3, 1], [1, 2]]], [59, [[20, 1], [10, 1], [2, 1], [1, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [147616399519802070423809304821760000000, 147616399519802070423809304821760000000, 147616399519802070423809304821760000000, 147616399519802070423809304821760000000, 147616399519802070423809304821760000000, 147616399519802070423809304821760000000], 'galois_label': '34T115', 'galt': 115, 'grd': 1.0783101995845562e+26, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '34.0.11627528865280854983574434471375691019078604726189023.1', 'local_algs': ['83.2.1.1', '83.2.0.1', 'm83.1.30.0', 'm1291.1.2.0', 'm1291.2.1.1', 'm1291.1.4.0', 'm1291.1.6.0', 'm1291.1.20.0', 'm12973.1.1.0', 'm12973.1.1.0', 'm12973.1.1.0', 'm12973.1.1.0', 'm12973.2.1.1', 'm12973.1.3.0', 'm12973.1.3.0', 'm12973.1.4.0', 'm12973.1.18.0', 'm4134484433.1.2.0', 'm4134484433.2.1.1', 'm4134484433.1.3.0', 'm4134484433.1.4.0', 'm4134484433.1.5.0', 'm4134484433.1.18.0', 'm64200532307.2.1.1', 'm64200532307.1.5.0', 'm64200532307.1.13.0', 'm64200532307.1.14.0', 'm31512487292285521887257.1.1.0', 'm31512487292285521887257.2.1.1', 'm31512487292285521887257.1.8.0', 'm31512487292285521887257.1.8.0', 'm31512487292285521887257.1.15.0'], 'monogenic': 1, 'num_ram': 6, 'r2': 17, 'ramps': [83, 1291, 12973, 4134484433, 64200532307, 31512487292285521887257], 'rd': 33.9889591634, 'regulator': {'__RealLiteral__': 0, 'data': '1946991838336.107', 'prec': 57}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a \\)', '\\( a^{11} - 1 \\)', '\\( a^{28} + a^{27} + a^{26} \\)', '\\( a^{11} + a^{9} \\)', '\\( a^{6} + a^{2} \\)', '\\( a^{33} + a^{32} - a^{6} - 1 \\)', '\\( a^{33} + a^{32} + a^{31} + a^{30} + a^{29} + a^{28} - a^{10} - 1 \\)', '\\( a^{33} + a^{32} + a^{31} + a^{30} + a^{29} + a^{28} + a^{27} + a^{26} + a^{25} + a^{24} + a^{23} + a^{22} + a^{21} + a^{20} + a^{19} + a^{17} + a^{15} - 1 \\)', '\\( a^{33} + a^{32} + a^{31} + a^{30} + a^{29} + a^{28} + a^{27} + a^{26} + a^{25} + a^{24} + a^{23} + a^{22} + a^{21} + a^{20} + a^{18} + a^{16} + a^{14} - 1 \\)', '\\( a^{27} + a^{24} - a^{18} - a^{15} + a^{9} + a^{6} - 1 \\)', '\\( 2 a^{33} + 2 a^{32} + a^{31} + a^{30} + a^{29} + a^{28} + a^{26} - a^{21} - a^{18} - a^{14} + a^{13} + a^{9} + a^{6} - a^{5} + a^{4} - a - 1 \\)', '\\( a^{33} + a^{32} + a^{30} + a^{27} + a^{24} - a^{20} - a^{18} - a^{17} - a^{15} - a^{12} - a^{9} - a^{6} + a^{5} + a^{2} - a \\)', '\\( a^{33} + a^{32} - a^{28} - a^{27} - 2 a^{26} - a^{25} - a^{24} + a^{22} + a^{21} + a^{20} - a^{19} - a^{17} + a^{13} + a^{11} + a^{9} - a^{7} - a^{6} - a^{5} + a^{2} + a - 1 \\)', '\\( 3 a^{33} + a^{32} - a^{30} + a^{28} + 2 a^{27} + 3 a^{26} + 2 a^{25} + a^{24} - a^{23} - a^{22} - a^{21} + 2 a^{19} + 2 a^{18} + 2 a^{17} - a^{14} - a^{13} + a^{12} + a^{11} + 2 a^{10} - a^{7} - 2 a^{6} + 2 a^{3} + a^{2} + a - 3 \\)', '\\( a^{33} + a^{32} + a^{31} + a^{30} + a^{29} - a^{27} - 2 a^{26} - a^{25} + a^{23} - a^{17} + a^{15} + a^{14} - a^{12} + a^{9} + a^{6} - 2 a^{3} + 1 \\)', '\\( 2 a^{33} + 2 a^{32} + a^{31} - a^{28} - 2 a^{27} - 2 a^{26} - 2 a^{25} - a^{24} - a^{23} + a^{21} + a^{20} + a^{19} + a^{18} + a^{17} + a^{16} - a^{14} - a^{13} - a^{12} - 2 a^{11} - a^{10} - a^{9} + a^{5} + a^{4} + a^{3} + a^{2} - 2 \\)'], 'used_grh': True, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', 'a^11', 'a^12', 'a^13', 'a^14', 'a^15', 'a^16', 'a^17', 'a^18', 'a^19', 'a^20', 'a^21', 'a^22', 'a^23', 'a^24', 'a^25', 'a^26', 'a^27', 'a^28', 'a^29', 'a^30', 'a^31', 'a^32', 'a^33']}