-
nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-1, 4, -6, 24, -41, 8, 34, 20, -58, 12, 34, -40, 35, -24, 10, -4, 1], 'conductor': 0, 'degree': 16, 'dirichlet_group': [], 'disc_abs': 134166736498994446336, 'disc_rad': 62, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[8, 2]]], [5, [[4, 4]]], [7, [[8, 1], [4, 2]]], [11, [[8, 2]]], [13, [[16, 1]]], [17, [[4, 3], [1, 4]]], [19, [[8, 1], [4, 2]]], [23, [[8, 1], [4, 1], [2, 2]]], [29, [[16, 1]]], [31, [0]], [37, [[16, 1]]], [41, [[8, 2]]], [43, [[8, 2]]], [47, [[2, 7], [1, 2]]], [53, [[16, 1]]], [59, [[8, 1], [4, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_label': '16T1771', 'galt': 1771, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 2, 'label': '16.4.134166736498994446336.2', 'local_algs': ['2.8.30.39', '2.8.22.2', '31.1.0.1', '31.1.0.1', '31.2.0.1', '31.2.0.1', '31.2.0.1', '31.2.0.1', '31.2.1.1', '31.4.2.1'], 'monogenic': 0, 'num_ram': 2, 'r2': 6, 'ramps': [2, 31], 'rd': 18.112475186145325, 'regulator': {'__RealLiteral__': 0, 'data': '11833.084314328344', 'prec': 60}, 'subfield_mults': [1, 1, 1], 'subfields': ['-2.0.1', '2.0.-4.0.1', '-1.0.4.-8.-4.-8.0.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a \\)', '\\( -\\frac{2973914350}{11300378777} a^{15} + \\frac{22045088791}{22600757554} a^{14} - \\frac{25220440699}{11300378777} a^{13} + \\frac{119788717549}{22600757554} a^{12} - \\frac{77565404914}{11300378777} a^{11} + \\frac{74720945078}{11300378777} a^{10} - \\frac{56813624911}{11300378777} a^{9} - \\frac{73387553031}{11300378777} a^{8} + \\frac{161097407666}{11300378777} a^{7} + \\frac{30398694006}{11300378777} a^{6} - \\frac{145644753226}{11300378777} a^{5} - \\frac{97996293975}{11300378777} a^{4} + \\frac{145961824466}{11300378777} a^{3} + \\frac{5687035157}{22600757554} a^{2} + \\frac{1191531769}{11300378777} a - \\frac{35864449481}{22600757554} \\)', '\\( -\\frac{7431029326}{11300378777} a^{15} + \\frac{112903881381}{45201515108} a^{14} - \\frac{135650211151}{22600757554} a^{13} + \\frac{649901382393}{45201515108} a^{12} - \\frac{222580775887}{11300378777} a^{11} + \\frac{481115134549}{22600757554} a^{10} - \\frac{193663035155}{11300378777} a^{9} - \\frac{140802951890}{11300378777} a^{8} + \\frac{410078808345}{11300378777} a^{7} - \\frac{92429021755}{22600757554} a^{6} - \\frac{278110137973}{11300378777} a^{5} - \\frac{144318786337}{11300378777} a^{4} + \\frac{287271169672}{11300378777} a^{3} - \\frac{315716012385}{45201515108} a^{2} + \\frac{27425278415}{22600757554} a - \\frac{112122420393}{45201515108} \\)', '\\( \\frac{16177053593}{22600757554} a^{15} - \\frac{58338443049}{22600757554} a^{14} + \\frac{139032875785}{22600757554} a^{13} - \\frac{167362992540}{11300378777} a^{12} + \\frac{436823509535}{22600757554} a^{11} - \\frac{480715274403}{22600757554} a^{10} + \\frac{368974901925}{22600757554} a^{9} + \\frac{337751868815}{22600757554} a^{8} - \\frac{803998871817}{22600757554} a^{7} + \\frac{28593993349}{22600757554} a^{6} + \\frac{522654263067}{22600757554} a^{5} + \\frac{339488801739}{22600757554} a^{4} - \\frac{257928468905}{11300378777} a^{3} + \\frac{92751877856}{11300378777} a^{2} - \\frac{13091292836}{11300378777} a + \\frac{46761709669}{22600757554} \\)', '\\( -\\frac{1611954979}{11300378777} a^{15} + \\frac{24532881539}{45201515108} a^{14} - \\frac{30609241743}{22600757554} a^{13} + \\frac{149382497865}{45201515108} a^{12} - \\frac{106380901577}{22600757554} a^{11} + \\frac{63771542554}{11300378777} a^{10} - \\frac{114670019525}{22600757554} a^{9} - \\frac{27135723573}{22600757554} a^{8} + \\frac{147506015531}{22600757554} a^{7} - \\frac{15106151097}{11300378777} a^{6} - \\frac{86401816295}{22600757554} a^{5} - \\frac{35631734161}{22600757554} a^{4} + \\frac{64797172093}{22600757554} a^{3} - \\frac{172194378297}{45201515108} a^{2} + \\frac{37896039578}{11300378777} a - \\frac{70332596795}{45201515108} \\)', '\\( -\\frac{4504524825}{11300378777} a^{15} + \\frac{65937993503}{45201515108} a^{14} - \\frac{76782717283}{22600757554} a^{13} + \\frac{365214412209}{45201515108} a^{12} - \\frac{235264025433}{22600757554} a^{11} + \\frac{118820477994}{11300378777} a^{10} - \\frac{170677243099}{22600757554} a^{9} - \\frac{225700320365}{22600757554} a^{8} + \\frac{485790032471}{22600757554} a^{7} + \\frac{17784542883}{11300378777} a^{6} - \\frac{406133451923}{22600757554} a^{5} - \\frac{198781144783}{22600757554} a^{4} + \\frac{381673171355}{22600757554} a^{3} - \\frac{110525246049}{45201515108} a^{2} - \\frac{16766760720}{11300378777} a - \\frac{65025555307}{45201515108} \\)', '\\( -\\frac{9593269777}{11300378777} a^{15} + \\frac{36858720718}{11300378777} a^{14} - \\frac{181360816979}{22600757554} a^{13} + \\frac{435623815715}{22600757554} a^{12} - \\frac{305488968322}{11300378777} a^{11} + \\frac{344985417798}{11300378777} a^{10} - \\frac{281470463435}{11300378777} a^{9} - \\frac{152377923483}{11300378777} a^{8} + \\frac{532573641078}{11300378777} a^{7} - \\frac{132689753216}{11300378777} a^{6} - \\frac{313451414670}{11300378777} a^{5} - \\frac{120089715573}{11300378777} a^{4} + \\frac{344748281475}{11300378777} a^{3} - \\frac{189512564632}{11300378777} a^{2} + \\frac{95712357221}{22600757554} a - \\frac{63685124961}{22600757554} \\)', '\\( \\frac{1016333}{1208209} a^{15} - \\frac{3759844}{1208209} a^{14} + \\frac{8983663}{1208209} a^{13} - \\frac{42991567}{2416418} a^{12} + \\frac{28579644}{1208209} a^{11} - \\frac{30763016}{1208209} a^{10} + \\frac{23317522}{1208209} a^{9} + \\frac{21845700}{1208209} a^{8} - \\frac{54741610}{1208209} a^{7} + \\frac{4065128}{1208209} a^{6} + \\frac{38406396}{1208209} a^{5} + \\frac{17606536}{1208209} a^{4} - \\frac{36252001}{1208209} a^{3} + \\frac{13855325}{1208209} a^{2} - \\frac{2001155}{1208209} a + \\frac{6038323}{2416418} \\)', '\\( -\\frac{10637259275}{45201515108} a^{15} + \\frac{10207615477}{11300378777} a^{14} - \\frac{95516582677}{45201515108} a^{13} + \\frac{56666385298}{11300378777} a^{12} - \\frac{76858748308}{11300378777} a^{11} + \\frac{154498971109}{22600757554} a^{10} - \\frac{125178445745}{22600757554} a^{9} - \\frac{107294344029}{22600757554} a^{8} + \\frac{143964459183}{11300378777} a^{7} + \\frac{37586265735}{22600757554} a^{6} - \\frac{281449051955}{22600757554} a^{5} - \\frac{128609451765}{22600757554} a^{4} + \\frac{601293998177}{45201515108} a^{3} - \\frac{50761584251}{22600757554} a^{2} + \\frac{4105929099}{45201515108} a - \\frac{32640539523}{22600757554} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', '1/2*a^11 - 1/2*a^10 - 1/2*a^9 - 1/2*a^8 - 1/2*a^7 - 1/2*a^6 - 1/2*a^5 - 1/2*a^4 - 1/2*a^3 - 1/2*a^2 - 1/2*a - 1/2', '1/2*a^12 - 1/2', '1/2*a^13 - 1/2*a', '1/4*a^14 - 1/4*a^12 - 1/2*a^10 - 1/2*a^6 - 1/4*a^2 + 1/4', '1/45201515108*a^15 - 339909727/11300378777*a^14 + 8448754417/45201515108*a^13 + 904573711/22600757554*a^12 + 1799812250/11300378777*a^11 + 6875262403/22600757554*a^10 + 6741728765/22600757554*a^9 - 10961867771/22600757554*a^8 - 747300824/11300378777*a^7 + 9793330835/22600757554*a^6 + 11202871017/22600757554*a^5 - 10550763559/22600757554*a^4 - 3985360939/45201515108*a^3 - 6326521869/22600757554*a^2 + 16221870797/45201515108*a + 4207130805/11300378777']}
Number field data - 16.4.134166736498994446336.2