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{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-1, 0, -4, 0, 14, 0, 43, 0, -13, 0, -112, 0, -108, 0, -34, 0, 8, 0, 7, 0, 1], 'conductor': 0, 'degree': 20, 'dirichlet_group': [], 'disc_abs': 24868623129665465017517056, 'disc_rad': 15994, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [[20, 1]]], [5, [[10, 2]]], [7, [[10, 1], [5, 2]]], [11, [0]], [13, [[5, 4]]], [17, [[5, 4]]], [19, [[20, 1]]], [23, [[4, 3], [2, 4]]], [29, [[10, 2]]], [31, [[20, 1]]], [37, [[10, 2]]], [41, [[10, 2]]], [43, [[4, 1], [2, 6], [1, 4]]], [47, [[10, 1], [5, 2]]], [53, [[10, 2]]], [59, [[20, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [317440, 131072, 81920], 'galois_label': '20T846', 'galt': 846, 'grd': 703.2778998665901, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 2, 'label': '20.6.24868623129665465017517056.2', 'local_algs': ['2.10.0.1', '2.10.10.13', '11.20.16.1', 'm727.1.1.0', 'm727.1.1.0', 'm727.1.1.0', 'm727.1.1.0', 'm727.1.1.0', 'm727.1.1.0', 'm727.1.2.0', 'm727.1.2.0', 'm727.1.2.0', 'm727.1.2.0', 'm727.1.2.0', 'm727.2.1.1', 'm727.2.1.1'], 'monogenic': 0, 'num_ram': 3, 'r2': 7, 'ramps': [2, 11, 727], 'rd': 18.611551871, 'regulator': {'__RealLiteral__': 0, 'data': '61407.6347505', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1], 'subfields': ['-1.3.3.-4.-1.1', '-1.-6.-6.16.17.-20.-7.12.-3.-2.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a \\)', '\\( \\frac{96989}{121991} a^{19} + \\frac{598521}{121991} a^{17} + \\frac{285011}{121991} a^{15} - \\frac{3496341}{121991} a^{13} - \\frac{7535178}{121991} a^{11} - \\frac{4826481}{121991} a^{9} + \\frac{2128163}{121991} a^{7} + \\frac{1950296}{121991} a^{5} + \\frac{11426}{121991} a^{3} + \\frac{130448}{121991} a \\)', '\\( \\frac{356907}{121991} a^{19} + \\frac{2283939}{121991} a^{17} + \\frac{1491036}{121991} a^{15} - \\frac{12983339}{121991} a^{13} - \\frac{30730722}{121991} a^{11} - \\frac{21800221}{121991} a^{9} + \\frac{7893048}{121991} a^{7} + \\frac{10345044}{121991} a^{5} - \\frac{997840}{121991} a^{3} - \\frac{877394}{121991} a \\)', '\\( \\frac{134008}{121991} a^{18} + \\frac{873319}{121991} a^{16} + \\frac{649786}{121991} a^{14} - \\frac{4875600}{121991} a^{12} - \\frac{12137076}{121991} a^{10} - \\frac{9143819}{121991} a^{8} + \\frac{2781726}{121991} a^{6} + \\frac{4648118}{121991} a^{4} - \\frac{31830}{121991} a^{2} - \\frac{381909}{121991} \\)', '\\( \\frac{25962}{121991} a^{18} + \\frac{133542}{121991} a^{16} - \\frac{115354}{121991} a^{14} - \\frac{1177296}{121991} a^{12} - \\frac{1116934}{121991} a^{10} + \\frac{1727180}{121991} a^{8} + \\frac{3832175}{121991} a^{6} + \\frac{1224516}{121991} a^{4} - \\frac{740971}{121991} a^{2} - \\frac{199980}{121991} \\)', '\\( \\frac{37019}{243982} a^{19} - \\frac{85271}{121991} a^{18} + \\frac{137399}{121991} a^{17} - \\frac{574982}{121991} a^{16} + \\frac{364775}{243982} a^{15} - \\frac{555600}{121991} a^{14} - \\frac{1379259}{243982} a^{13} + \\frac{5816963}{243982} a^{12} - \\frac{2300949}{121991} a^{11} + \\frac{16749365}{243982} a^{10} - \\frac{2158669}{121991} a^{9} + \\frac{16217785}{243982} a^{8} + \\frac{653563}{243982} a^{7} + \\frac{774691}{121991} a^{6} + \\frac{1348911}{121991} a^{5} - \\frac{4646621}{243982} a^{4} - \\frac{21628}{121991} a^{3} - \\frac{1097229}{243982} a^{2} - \\frac{512357}{243982} a + \\frac{146194}{121991} \\)', '\\( \\frac{37019}{243982} a^{19} + \\frac{85271}{121991} a^{18} + \\frac{137399}{121991} a^{17} + \\frac{574982}{121991} a^{16} + \\frac{364775}{243982} a^{15} + \\frac{555600}{121991} a^{14} - \\frac{1379259}{243982} a^{13} - \\frac{5816963}{243982} a^{12} - \\frac{2300949}{121991} a^{11} - \\frac{16749365}{243982} a^{10} - \\frac{2158669}{121991} a^{9} - \\frac{16217785}{243982} a^{8} + \\frac{653563}{243982} a^{7} - \\frac{774691}{121991} a^{6} + \\frac{1348911}{121991} a^{5} + \\frac{4646621}{243982} a^{4} - \\frac{21628}{121991} a^{3} + \\frac{1097229}{243982} a^{2} - \\frac{512357}{243982} a - \\frac{146194}{121991} \\)', '\\( \\frac{71111}{243982} a^{19} + \\frac{34451}{243982} a^{18} + \\frac{179886}{121991} a^{17} + \\frac{89971}{121991} a^{16} - \\frac{165230}{121991} a^{15} - \\frac{122605}{243982} a^{14} - \\frac{3110735}{243982} a^{13} - \\frac{1469801}{243982} a^{12} - \\frac{1404013}{121991} a^{11} - \\frac{1537217}{243982} a^{10} + \\frac{4454743}{243982} a^{9} + \\frac{1603617}{243982} a^{8} + \\frac{4665046}{121991} a^{7} + \\frac{1970770}{121991} a^{6} + \\frac{1017200}{121991} a^{5} + \\frac{463452}{121991} a^{4} - \\frac{2323091}{243982} a^{3} - \\frac{1156747}{243982} a^{2} - \\frac{340507}{243982} a - \\frac{47288}{121991} \\)', '\\( \\frac{176916}{121991} a^{18} + \\frac{1087458}{121991} a^{16} + \\frac{461412}{121991} a^{14} - \\frac{6591910}{121991} a^{12} - \\frac{13692314}{121991} a^{10} - \\frac{7239212}{121991} a^{8} + \\frac{6666484}{121991} a^{6} + \\frac{4773079}{121991} a^{4} - \\frac{1071739}{121991} a^{2} - \\frac{376896}{121991} \\)', '\\( \\frac{302467}{243982} a^{19} + \\frac{133523}{243982} a^{18} + \\frac{963290}{121991} a^{17} + \\frac{437583}{121991} a^{16} + \\frac{1176967}{243982} a^{15} + \\frac{746425}{243982} a^{14} - \\frac{11221001}{243982} a^{13} - \\frac{2218852}{121991} a^{12} - \\frac{25811369}{243982} a^{11} - \\frac{12147467}{243982} a^{10} - \\frac{16684021}{243982} a^{9} - \\frac{11900447}{243982} a^{8} + \\frac{4752496}{121991} a^{7} - \\frac{2202945}{243982} a^{6} + \\frac{5111570}{121991} a^{5} + \\frac{1948799}{243982} a^{4} - \\frac{1220407}{243982} a^{3} + \\frac{1140485}{243982} a^{2} - \\frac{429197}{121991} a - \\frac{24013}{243982} \\)', '\\( \\frac{26321}{243982} a^{19} + \\frac{89336}{121991} a^{18} + \\frac{106519}{243982} a^{17} + \\frac{1223387}{243982} a^{16} - \\frac{137335}{121991} a^{15} + \\frac{1263265}{243982} a^{14} - \\frac{1159603}{243982} a^{13} - \\frac{6127161}{243982} a^{12} - \\frac{56347}{243982} a^{11} - \\frac{18230235}{243982} a^{10} + \\frac{1671034}{121991} a^{9} - \\frac{8978118}{121991} a^{8} + \\frac{1988413}{121991} a^{7} - \\frac{792334}{121991} a^{6} - \\frac{478915}{243982} a^{5} + \\frac{3026220}{121991} a^{4} - \\frac{1569739}{243982} a^{3} + \\frac{1510221}{243982} a^{2} - \\frac{344415}{243982} a - \\frac{286531}{243982} \\)', '\\( \\frac{230997}{243982} a^{19} + \\frac{85271}{121991} a^{18} + \\frac{735920}{121991} a^{17} + \\frac{574982}{121991} a^{16} + \\frac{934797}{243982} a^{15} + \\frac{555600}{121991} a^{14} - \\frac{8371941}{243982} a^{13} - \\frac{5816963}{243982} a^{12} - \\frac{9836127}{121991} a^{11} - \\frac{16749365}{243982} a^{10} - \\frac{6985150}{121991} a^{9} - \\frac{16217785}{243982} a^{8} + \\frac{4909889}{243982} a^{7} - \\frac{774691}{121991} a^{6} + \\frac{3299207}{121991} a^{5} + \\frac{4646621}{243982} a^{4} - \\frac{10202}{121991} a^{3} + \\frac{1097229}{243982} a^{2} - \\frac{251461}{243982} a - \\frac{146194}{121991} \\)'], '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', '1/2*a^15 - 1/2*a^12 - 1/2*a^11 - 1/2*a^6 - 1/2*a^4 - 1/2*a - 1/2', '1/2*a^16 - 1/2*a^13 - 1/2*a^12 - 1/2*a^7 - 1/2*a^5 - 1/2*a^2 - 1/2*a', '1/2*a^17 - 1/2*a^14 - 1/2*a^13 - 1/2*a^8 - 1/2*a^6 - 1/2*a^3 - 1/2*a^2', '1/243982*a^18 + 5909/121991*a^16 - 97289/243982*a^14 + 74807/243982*a^12 - 1/2*a^11 - 17722/121991*a^10 - 1/2*a^9 + 21958/121991*a^8 - 1/2*a^7 - 13869/243982*a^6 - 47397/121991*a^4 - 1/2*a^3 + 10739/121991*a^2 - 1/2*a + 57365/243982', '1/243982*a^19 + 5909/121991*a^17 + 12351/121991*a^15 + 74807/243982*a^13 + 86547/243982*a^11 - 1/2*a^10 + 21958/121991*a^9 - 1/2*a^8 - 13869/243982*a^7 - 1/2*a^6 - 47397/121991*a^5 + 10739/121991*a^3 - 1/2*a^2 - 32313/121991*a - 1/2']}