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{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-4, 8, 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': 23, 'dirichlet_group': [], 'disc_abs': 28585240626865948858207093238982844088320, 'disc_rad': 13630504907067274502852961177340910, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [[9, 1], [7, 1], [5, 1], [2, 1]]], [5, [0]], [7, [[19, 1], [2, 2]]], [11, [[22, 1], [1, 1]]], [13, [[13, 1], [4, 2], [1, 2]]], [17, [[17, 1], [3, 2]]], [19, [[18, 1], [2, 2], [1, 1]]], [23, [[22, 1], [1, 1]]], [29, [[16, 1], [4, 1], [2, 1], [1, 1]]], [31, [[10, 1], [8, 1], [2, 1], [1, 3]]], [37, [[13, 1], [4, 2], [1, 2]]], [41, [[18, 1], [3, 1], [1, 2]]], [43, [[20, 1], [3, 1]]], [47, [[11, 1], [8, 1], [2, 1], [1, 2]]], [53, [[14, 1], [6, 1], [1, 3]]], [59, [[12, 1], [6, 1], [3, 1], [1, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [24728016011107368960000, 12926008369442488320000, 12926008369442488320000, 12926008369442488320000], 'galois_label': '23T7', 'galt': 7, 'grd': 1.6020745037248333e+17, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '23.1.28585240626865948858207093238982844088320.1', 'local_algs': ['2.23.22.1', '5.1.0.1', '5.2.1.1', '5.8.0.1', '5.12.0.1', 'm24986142523.2.1.1', 'm24986142523.1.5.0', 'm24986142523.1.16.0', 'm54552257894632015274417.1.1.0', 'm54552257894632015274417.2.1.1', 'm54552257894632015274417.1.5.0', 'm54552257894632015274417.1.15.0'], 'monogenic': 0, 'num_ram': 4, 'r2': 11, 'ramps': [2, 5, 24986142523, 54552257894632015274417], 'rd': 57.4067141285, 'regulator': 281108277991, 'res': {}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{41} a^{22} - \\frac{6}{41} a^{21} - \\frac{5}{41} a^{20} + \\frac{19}{82} a^{19} + \\frac{9}{82} a^{18} - \\frac{13}{82} a^{17} - \\frac{2}{41} a^{16} - \\frac{17}{82} a^{15} + \\frac{10}{41} a^{14} + \\frac{3}{82} a^{13} + \\frac{23}{82} a^{12} - \\frac{28}{41} a^{11} + \\frac{4}{41} a^{10} + \\frac{17}{41} a^{9} + \\frac{21}{41} a^{8} - \\frac{44}{41} a^{7} + \\frac{18}{41} a^{6} - \\frac{26}{41} a^{5} + \\frac{33}{41} a^{4} + \\frac{7}{41} a^{3} - \\frac{1}{41} a^{2} - \\frac{35}{41} a + \\frac{13}{41} \\)', '\\( \\frac{32}{41} a^{22} + \\frac{13}{41} a^{21} + \\frac{4}{41} a^{20} - \\frac{7}{82} a^{19} + \\frac{1}{82} a^{18} - \\frac{3}{41} a^{17} - \\frac{5}{82} a^{16} - \\frac{11}{82} a^{15} - \\frac{8}{41} a^{14} - \\frac{27}{82} a^{13} - \\frac{1}{41} a^{12} + \\frac{6}{41} a^{11} + \\frac{5}{41} a^{10} + \\frac{11}{41} a^{9} + \\frac{16}{41} a^{8} + \\frac{27}{41} a^{7} + \\frac{2}{41} a^{6} + \\frac{29}{41} a^{5} - \\frac{10}{41} a^{4} - \\frac{22}{41} a^{3} - \\frac{73}{41} a^{2} - \\frac{13}{41} a + \\frac{211}{41} \\)', '\\( \\frac{8}{41} a^{22} + \\frac{27}{82} a^{21} + \\frac{1}{41} a^{20} - \\frac{6}{41} a^{19} - \\frac{5}{41} a^{18} + \\frac{19}{82} a^{17} + \\frac{9}{82} a^{16} - \\frac{13}{82} a^{15} + \\frac{37}{82} a^{14} + \\frac{12}{41} a^{13} - \\frac{21}{82} a^{12} - \\frac{19}{41} a^{11} - \\frac{9}{41} a^{10} + \\frac{13}{41} a^{9} - \\frac{37}{41} a^{8} - \\frac{65}{41} a^{7} - \\frac{20}{41} a^{6} - \\frac{44}{41} a^{5} - \\frac{64}{41} a^{4} - \\frac{67}{41} a^{3} - \\frac{8}{41} a^{2} + \\frac{48}{41} a - \\frac{19}{41} \\)', '\\( \\frac{400}{41} a^{22} + \\frac{407}{82} a^{21} + \\frac{91}{41} a^{20} + \\frac{28}{41} a^{19} + \\frac{33}{82} a^{18} + \\frac{24}{41} a^{17} + \\frac{20}{41} a^{16} + \\frac{3}{41} a^{15} + \\frac{5}{82} a^{14} - \\frac{15}{41} a^{13} - \\frac{25}{82} a^{12} - \\frac{7}{41} a^{11} + \\frac{42}{41} a^{10} + \\frac{35}{41} a^{9} - \\frac{5}{41} a^{8} - \\frac{52}{41} a^{7} - \\frac{16}{41} a^{6} + \\frac{14}{41} a^{5} + \\frac{39}{41} a^{4} + \\frac{12}{41} a^{3} + \\frac{10}{41} a^{2} - \\frac{19}{41} a + \\frac{3109}{41} \\)', '\\( \\frac{156}{41} a^{22} + \\frac{301}{82} a^{21} + \\frac{122}{41} a^{20} + \\frac{47}{41} a^{19} - \\frac{36}{41} a^{18} - \\frac{265}{82} a^{17} - \\frac{419}{82} a^{16} - \\frac{260}{41} a^{15} - \\frac{529}{82} a^{14} - \\frac{393}{82} a^{13} - \\frac{92}{41} a^{12} + \\frac{60}{41} a^{11} + \\frac{214}{41} a^{10} + \\frac{356}{41} a^{9} + \\frac{447}{41} a^{8} + \\frac{434}{41} a^{7} + \\frac{348}{41} a^{6} + \\frac{167}{41} a^{5} - \\frac{59}{41} a^{4} - \\frac{343}{41} a^{3} - \\frac{566}{41} a^{2} - \\frac{704}{41} a + \\frac{511}{41} \\)', '\\( \\frac{1457}{82} a^{22} + \\frac{385}{41} a^{21} + \\frac{191}{41} a^{20} + \\frac{84}{41} a^{19} + \\frac{17}{82} a^{18} - \\frac{10}{41} a^{17} - \\frac{22}{41} a^{16} + \\frac{9}{41} a^{15} + \\frac{28}{41} a^{14} + \\frac{115}{82} a^{13} + \\frac{89}{82} a^{12} + \\frac{20}{41} a^{11} - \\frac{38}{41} a^{10} - \\frac{59}{41} a^{9} - \\frac{56}{41} a^{8} - \\frac{33}{41} a^{7} + \\frac{34}{41} a^{6} + \\frac{83}{41} a^{5} + \\frac{117}{41} a^{4} + \\frac{36}{41} a^{3} - \\frac{11}{41} a^{2} - \\frac{139}{41} a + \\frac{5719}{41} \\)', '\\( \\frac{5}{82} a^{22} + \\frac{11}{82} a^{21} + \\frac{8}{41} a^{20} + \\frac{27}{82} a^{19} + \\frac{1}{41} a^{18} - \\frac{6}{41} a^{17} - \\frac{5}{41} a^{16} - \\frac{11}{41} a^{15} + \\frac{9}{82} a^{14} - \\frac{27}{41} a^{13} - \\frac{2}{41} a^{12} - \\frac{29}{41} a^{11} + \\frac{10}{41} a^{10} + \\frac{22}{41} a^{9} - \\frac{9}{41} a^{8} + \\frac{54}{41} a^{7} - \\frac{37}{41} a^{6} + \\frac{99}{41} a^{5} - \\frac{61}{41} a^{4} + \\frac{79}{41} a^{3} - \\frac{105}{41} a^{2} + \\frac{56}{41} a - \\frac{29}{41} \\)', '\\( \\frac{7}{41} a^{22} + \\frac{39}{82} a^{21} - \\frac{29}{82} a^{20} - \\frac{31}{82} a^{19} + \\frac{11}{41} a^{18} + \\frac{73}{82} a^{17} - \\frac{14}{41} a^{16} - \\frac{39}{41} a^{15} + \\frac{29}{41} a^{14} + \\frac{103}{82} a^{13} - \\frac{22}{41} a^{12} - \\frac{73}{41} a^{11} + \\frac{69}{41} a^{10} + \\frac{78}{41} a^{9} - \\frac{58}{41} a^{8} - \\frac{62}{41} a^{7} + \\frac{85}{41} a^{6} + \\frac{105}{41} a^{5} - \\frac{138}{41} a^{4} - \\frac{74}{41} a^{3} + \\frac{116}{41} a^{2} + \\frac{124}{41} a - \\frac{73}{41} \\)', '\\( \\frac{24}{41} a^{22} + \\frac{20}{41} a^{21} + \\frac{47}{82} a^{20} + \\frac{23}{41} a^{19} + \\frac{26}{41} a^{18} + \\frac{49}{41} a^{17} + \\frac{109}{82} a^{16} + \\frac{42}{41} a^{15} + \\frac{111}{82} a^{14} + \\frac{113}{82} a^{13} + \\frac{101}{82} a^{12} + \\frac{66}{41} a^{11} + \\frac{55}{41} a^{10} + \\frac{39}{41} a^{9} + \\frac{53}{41} a^{8} + \\frac{10}{41} a^{7} - \\frac{19}{41} a^{6} + \\frac{32}{41} a^{5} + \\frac{13}{41} a^{4} - \\frac{37}{41} a^{3} - \\frac{24}{41} a^{2} - \\frac{61}{41} a + \\frac{107}{41} \\)', '\\( \\frac{39}{82} a^{22} + \\frac{6}{41} a^{21} - \\frac{31}{82} a^{20} - \\frac{19}{82} a^{19} - \\frac{9}{82} a^{18} - \\frac{14}{41} a^{17} + \\frac{45}{82} a^{16} + \\frac{29}{41} a^{15} - \\frac{10}{41} a^{14} - \\frac{3}{82} a^{13} + \\frac{59}{82} a^{12} - \\frac{13}{41} a^{11} - \\frac{86}{41} a^{10} - \\frac{17}{41} a^{9} + \\frac{20}{41} a^{8} + \\frac{3}{41} a^{7} + \\frac{64}{41} a^{6} + \\frac{67}{41} a^{5} - \\frac{33}{41} a^{4} - \\frac{48}{41} a^{3} + \\frac{83}{41} a^{2} - \\frac{47}{41} a - \\frac{13}{41} \\)', '\\( \\frac{91}{41} a^{22} - \\frac{313}{82} a^{21} - \\frac{86}{41} a^{20} + \\frac{417}{82} a^{19} + \\frac{102}{41} a^{18} - \\frac{527}{82} a^{17} - \\frac{241}{82} a^{16} + \\frac{313}{41} a^{15} + \\frac{221}{82} a^{14} - \\frac{793}{82} a^{13} - \\frac{285}{82} a^{12} + \\frac{486}{41} a^{11} + \\frac{159}{41} a^{10} - \\frac{585}{41} a^{9} - \\frac{139}{41} a^{8} + \\frac{752}{41} a^{7} + \\frac{162}{41} a^{6} - \\frac{890}{41} a^{5} - \\frac{154}{41} a^{4} + \\frac{1088}{41} a^{3} + \\frac{114}{41} a^{2} - \\frac{1381}{41} a + \\frac{609}{41} \\)'], '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', '1/2*a^12', '1/2*a^13', '1/2*a^14', '1/2*a^15', '1/2*a^16', '1/2*a^17', '1/2*a^18', '1/2*a^19', '1/2*a^20', '1/2*a^21', '1/82*a^22 - 3/41*a^21 - 5/82*a^20 - 11/82*a^19 - 8/41*a^18 + 7/41*a^17 - 1/41*a^16 + 6/41*a^15 + 5/41*a^14 - 19/82*a^13 - 9/82*a^12 - 14/41*a^11 + 2/41*a^10 - 12/41*a^9 - 10/41*a^8 + 19/41*a^7 + 9/41*a^6 - 13/41*a^5 - 4/41*a^4 - 17/41*a^3 + 20/41*a^2 + 3/41*a - 14/41']}