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nf_fields • Show schema
{'class_group': [2, 8], 'class_number': 16, 'cm': False, 'coeffs': [1296, 0, 3715, 0, 4576, 0, 3230, 0, 1486, 0, 475, 0, 106, 0, 15, 0, 1], 'conductor': 0, 'degree': 16, 'dirichlet_group': [], 'disc_abs': 540360087662636962890625, 'disc_rad': 95, 'disc_sign': 1, 'frobs': [[2, [[4, 2], [2, 4]]], [3, [[4, 2], [2, 4]]], [5, [0]], [7, [[4, 4]]], [11, [[2, 8]]], [13, [[4, 2], [2, 4]]], [17, [[4, 4]]], [19, [0]], [23, [[4, 4]]], [29, [[2, 8]]], [31, [[4, 4]]], [37, [[4, 2], [2, 4]]], [41, [[4, 4]]], [43, [[4, 4]]], [47, [[4, 4]]], [53, [[4, 2], [2, 4]]], [59, [[2, 8]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [24, 24], 'galois_label': '16T33', 'galt': 33, 'grd': 30.429351993705872, 'inessentialp': [2, 3], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 2, 'label': '16.0.540360087662636962890625.2', 'local_algs': ['5.4.3.2', '5.4.3.2', '5.4.3.2', '5.4.3.2', '19.8.6.2', '19.8.6.2'], 'minimal_sibling': [17, -46, 77, -7, -22, 9, -3, -1, 1], 'monogenic': -1, 'num_ram': 2, 'r2': 8, 'ramps': [5, 19], 'rd': 30.4293519937, 'regulator': {'__RealLiteral__': 0, 'data': '71285.5480074', 'prec': 44}, 'res': {'gal': ['1679616,-2566080,-447120,2534580,3577,-2023860,131440,1732450,-553237,-884600,395065,230195,31309,-204490,34945,31540,14810,-22040,6695,-1110,-331,265,415,-140,-317,220,30,-60,-3,10,5,-5,1'], 'sib': ['-319,796,-582,110,-29,50,-13,-3,1', '17,-46,77,-7,-22,9,-3,-1,1', '2401,-5831,2989,8988,-16929,7902,8439,-15452,9486,-2448,1021,-629,209,-27,6,-5,1', '26,-37,12,-10,16,15,8,-1,1', '49,-133,205,-171,80,-19,13,0,1', '5,50,370,950,141,-1138,196,795,-430,-738,229,22,50,-5,-4,-3,1', '8105,-21280,32730,-37120,27126,-11022,1800,934,-687,-32,8,124,-79,12,11,-6,1']}, 'subfield_mults': [1, 1, 1, 2, 1, 2, 2, 1, 2], 'subfields': ['-1.-1.1', '5.-1.1', '24.-1.1', '26.-3.4.-2.1', '36.0.7.0.1', '-4.-6.1.-1.1', '26.-37.12.-10.16.15.8.-1.1', '80.20.-15.35.6.-1.6.-1.1', '49.-133.205.-171.80.-19.13.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{59}{2520} a^{15} + \\frac{283}{840} a^{13} + \\frac{2839}{1260} a^{11} + \\frac{23813}{2520} a^{9} + \\frac{34441}{1260} a^{7} + \\frac{9503}{180} a^{5} + \\frac{18817}{315} a^{3} + \\frac{72341}{2520} a + \\frac{1}{2} \\)', '\\( \\frac{2263}{148680} a^{15} + \\frac{149}{4130} a^{14} + \\frac{10211}{49560} a^{13} + \\frac{199}{413} a^{12} + \\frac{98663}{74340} a^{11} + \\frac{2529}{826} a^{10} + \\frac{115303}{21240} a^{9} + \\frac{51427}{4130} a^{8} + \\frac{1138547}{74340} a^{7} + \\frac{72479}{2065} a^{6} + \\frac{304831}{10620} a^{5} + \\frac{38743}{590} a^{4} + \\frac{579764}{18585} a^{3} + \\frac{150939}{2065} a^{2} + \\frac{1997497}{148680} a + \\frac{147647}{4130} \\)', '\\( \\frac{1}{10620} a^{15} + \\frac{611}{24780} a^{13} + \\frac{1619}{5310} a^{11} + \\frac{131413}{74340} a^{9} + \\frac{240551}{37170} a^{7} + \\frac{17081}{1062} a^{5} + \\frac{12989}{531} a^{3} + \\frac{1273729}{74340} a \\)', '\\( \\frac{151}{18585} a^{15} + \\frac{43}{2065} a^{14} + \\frac{689}{6195} a^{13} + \\frac{564}{2065} a^{12} + \\frac{25793}{37170} a^{11} + \\frac{6891}{4130} a^{10} + \\frac{14441}{5310} a^{9} + \\frac{384}{59} a^{8} + \\frac{137419}{18585} a^{7} + \\frac{14437}{826} a^{6} + \\frac{34901}{2655} a^{5} + \\frac{17753}{590} a^{4} + \\frac{238636}{18585} a^{3} + \\frac{119143}{4130} a^{2} + \\frac{19574}{3717} a + \\frac{23743}{2065} \\)', '\\( \\frac{17}{2360} a^{15} - \\frac{5}{59} a^{14} + \\frac{2369}{16520} a^{13} - \\frac{925}{826} a^{12} + \\frac{1327}{1180} a^{11} - \\frac{815}{118} a^{10} + \\frac{84533}{16520} a^{9} - \\frac{11192}{413} a^{8} + \\frac{130821}{8260} a^{7} - \\frac{60635}{826} a^{6} + \\frac{38953}{1180} a^{5} - \\frac{15213}{118} a^{4} + \\frac{23067}{590} a^{3} - \\frac{7508}{59} a^{2} + \\frac{329141}{16520} a - \\frac{43027}{826} \\)', '\\( \\frac{431}{24780} a^{15} + \\frac{82}{2065} a^{14} + \\frac{2119}{8260} a^{13} + \\frac{2361}{4130} a^{12} + \\frac{10736}{6195} a^{11} + \\frac{15667}{4130} a^{10} + \\frac{182471}{24780} a^{9} + \\frac{65141}{4130} a^{8} + \\frac{133856}{6195} a^{7} + \\frac{187329}{4130} a^{6} + \\frac{37759}{885} a^{5} + \\frac{5111}{59} a^{4} + \\frac{625663}{12390} a^{3} + \\frac{79831}{826} a^{2} + \\frac{132973}{4956} a + \\frac{92524}{2065} \\)', '\\( \\frac{431}{24780} a^{15} - \\frac{82}{2065} a^{14} + \\frac{2119}{8260} a^{13} - \\frac{2361}{4130} a^{12} + \\frac{10736}{6195} a^{11} - \\frac{15667}{4130} a^{10} + \\frac{182471}{24780} a^{9} - \\frac{65141}{4130} a^{8} + \\frac{133856}{6195} a^{7} - \\frac{187329}{4130} a^{6} + \\frac{37759}{885} a^{5} - \\frac{5111}{59} a^{4} + \\frac{625663}{12390} a^{3} - \\frac{79831}{826} a^{2} + \\frac{132973}{4956} a - \\frac{92524}{2065} \\)'], 'used_grh': True, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', '1/2*a^8 - 1/2*a^7 - 1/2*a^5 - 1/2*a', '1/2*a^9 - 1/2*a^7 - 1/2*a^6 - 1/2*a^5 - 1/2*a^2 - 1/2*a', '1/2*a^10 - 1/2*a^6 - 1/2*a^5 - 1/2*a^3 - 1/2*a^2 - 1/2*a', '1/2*a^11 - 1/2*a^7 - 1/2*a^6 - 1/2*a^4 - 1/2*a^3 - 1/2*a^2', '1/70*a^12 + 1/10*a^10 - 8/35*a^8 + 1/70*a^6 - 1/2*a^5 - 3/10*a^4 + 1/10*a^2 + 13/35', '1/70*a^13 + 1/10*a^11 - 8/35*a^9 + 1/70*a^7 - 1/2*a^6 - 3/10*a^5 + 1/10*a^3 + 13/35*a', '1/4130*a^14 + 9/4130*a^12 - 597/4130*a^10 - 243/2065*a^8 - 867/2065*a^6 + 17/118*a^4 - 1/2*a^3 - 377/826*a^2 - 954/2065', '1/148680*a^15 - 23/9912*a^13 - 101/14868*a^11 + 7243/148680*a^9 - 3109/74340*a^7 - 2819/10620*a^5 + 10783/37170*a^3 - 1/2*a^2 + 28123/148680*a - 1/2']}
Number field data - 16.0.540360087662636962890625.2