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nf_fields • Show schema
{'class_group': [2], 'class_number': 2, 'cm': False, 'coeffs': [194481, 0, -1166886, 0, 1694763, 0, -981666, 0, 268128, 0, -37044, 0, 2583, 0, -84, 0, 1], 'conductor': 0, 'degree': 16, 'dirichlet_group': [], 'disc_abs': 12341030701727613557145600000000, 'disc_rad': 210, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [0]], [7, [0]], [11, [[4, 4]]], [13, [[2, 8]]], [17, [[2, 8]]], [19, [[4, 4]]], [23, [[4, 4]]], [29, [[4, 4]]], [31, [[4, 4]]], [37, [[4, 4]]], [41, [[4, 4]]], [43, [[4, 4]]], [47, [[2, 8]]], [53, [[4, 4]]], [59, [[2, 4], [1, 8]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [80, 24, 16, 24], 'galois_label': '16T20', 'galt': 20, 'grd': 124.08647925963417, 'inessentialp': [2], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 1, 'label': '16.16.12341030701727613557145600000000.1', 'local_algs': ['2.8.16.22', '2.8.16.22', '3.8.6.1', '3.8.6.1', '5.8.4.1', '5.8.4.1', '7.8.6.2', '7.8.6.2'], 'minimal_sibling': [16857, 305568, 1229976, 1605240, -380520, -2383248, -1289736, 453156, 446455, -9328, -56336, -3220, 3304, 224, -92, -4, 1], 'monogenic': -1, 'num_ram': 4, 'r2': 0, 'ramps': [2, 3, 5, 7], 'rd': 87.7423909381, 'regulator': {'__RealLiteral__': 0, 'data': '16027729714.4', 'prec': 44}, 'res': {'gal': ['1156,-26112,-695360,1526752,96056428,527491592,-446213456,-12022490168,-38867736246,-39594012184,40575041224,126131461344,70918539842,-58295796808,-70935023092,4743625896,27877239275,3205827972,-6335204800,-1135727844,938280858,179287960,-94673896,-16384888,6539787,910528,-301736,-30112,8784,540,-144,-4,1'], 'sib': ['-72176,-303424,1025504,3082464,-1213048,-7020896,-2975840,2807688,2041078,66360,-185768,-21040,6722,756,-124,-8,1', '1156,-10064,13176,105944,-353748,142080,679084,-760588,-31227,274516,-39224,-26280,4896,700,-144,-4,1', '14161,-273224,1420412,-833784,-2892148,3280592,188272,-1303596,242335,188184,-51632,-11900,3836,336,-112,-4,1', '16857,305568,1229976,1605240,-380520,-2383248,-1289736,453156,446455,-9328,-56336,-3220,3304,224,-92,-4,1']}, 'subfield_mults': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'subfields': ['-3.0.1', '-7.0.1', '-26.-1.1', '-1.-1.1', '-5.-1.1', '-35.0.1', '-15.0.1', '25.0.-25.0.1', '1.0.-5.0.1', '16.0.-13.0.1', '64.0.-19.0.1', '29.16.-15.-2.1', '1.8.-7.-2.1', '4.0.-11.0.1', '1.0.-15.0.32.0.-15.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{187278} a^{14} - \\frac{55}{120393} a^{12} + \\frac{64}{4459} a^{10} - \\frac{19}{91} a^{8} + \\frac{934}{637} a^{6} - \\frac{59}{13} a^{4} + \\frac{771}{182} a^{2} + \\frac{11}{13} \\)', '\\( \\frac{1268}{149166927} a^{14} - \\frac{10237}{14206374} a^{12} + \\frac{159119}{7103187} a^{10} - \\frac{12171}{37583} a^{8} + \\frac{783596}{338247} a^{6} - \\frac{127222}{16107} a^{4} + \\frac{170930}{16107} a^{2} - \\frac{3943}{1534} \\)', '\\( \\frac{397}{16574103} a^{14} - \\frac{1991}{1014741} a^{12} + \\frac{45538}{789243} a^{10} - \\frac{28614}{37583} a^{8} + \\frac{530567}{112749} a^{6} - \\frac{9670}{767} a^{4} + \\frac{59259}{5369} a^{2} - \\frac{2631}{767} \\)', '\\( \\frac{353}{33148206} a^{14} - \\frac{12601}{14206374} a^{12} + \\frac{63590}{2367729} a^{10} - \\frac{42113}{112749} a^{8} + \\frac{95007}{37583} a^{6} - \\frac{41767}{5369} a^{4} + \\frac{77981}{10738} a^{2} + \\frac{6285}{1534} \\)', '\\( \\frac{6619}{298333854} a^{14} - \\frac{26987}{14206374} a^{12} + \\frac{426437}{7103187} a^{10} - \\frac{301459}{338247} a^{8} + \\frac{2238863}{338247} a^{6} - \\frac{376930}{16107} a^{4} + \\frac{1000309}{32214} a^{2} - \\frac{10317}{1534} \\)', '\\( \\frac{541}{21309561} a^{14} - \\frac{3329}{1578486} a^{12} + \\frac{64685}{1014741} a^{10} - \\frac{301192}{338247} a^{8} + \\frac{299557}{48321} a^{6} - \\frac{48905}{2301} a^{4} + \\frac{74495}{2301} a^{2} - \\frac{26357}{1534} \\)', '\\( \\frac{997}{298333854} a^{14} - \\frac{620}{2367729} a^{12} + \\frac{5563}{789243} a^{10} - \\frac{25580}{338247} a^{8} + \\frac{77864}{338247} a^{6} + \\frac{5864}{5369} a^{4} - \\frac{71893}{10738} a^{2} + \\frac{5104}{767} \\)', '\\( \\frac{1151}{298333854} a^{15} - \\frac{2269}{16574103} a^{14} - \\frac{2972}{7103187} a^{13} + \\frac{162125}{14206374} a^{12} + \\frac{126262}{7103187} a^{11} - \\frac{2459825}{7103187} a^{10} - \\frac{127511}{338247} a^{9} + \\frac{234278}{48321} a^{8} + \\frac{1431538}{338247} a^{7} - \\frac{3784220}{112749} a^{6} - \\frac{400129}{16107} a^{5} + \\frac{1810871}{16107} a^{4} + \\frac{2241167}{32214} a^{3} - \\frac{2545103}{16107} a^{2} - \\frac{53132}{767} a + \\frac{89879}{1534} \\)', '\\( \\frac{2911}{33148206} a^{15} + \\frac{4894}{49722309} a^{14} - \\frac{51167}{7103187} a^{13} - \\frac{114941}{14206374} a^{12} + \\frac{503038}{2367729} a^{11} + \\frac{1698479}{7103187} a^{10} - \\frac{318211}{112749} a^{9} - \\frac{358045}{112749} a^{8} + \\frac{665475}{37583} a^{7} + \\frac{2225995}{112749} a^{6} - \\frac{262237}{5369} a^{5} - \\frac{852697}{16107} a^{4} + \\frac{466027}{10738} a^{3} + \\frac{704114}{16107} a^{2} - \\frac{2257}{767} a - \\frac{8139}{1534} \\)', '\\( \\frac{2395}{298333854} a^{15} + \\frac{5168}{149166927} a^{14} - \\frac{10691}{14206374} a^{13} - \\frac{18892}{7103187} a^{12} + \\frac{189589}{7103187} a^{11} + \\frac{165962}{2367729} a^{10} - \\frac{16987}{37583} a^{9} - \\frac{258389}{338247} a^{8} + \\frac{1281239}{338247} a^{7} + \\frac{1157216}{338247} a^{6} - \\frac{237730}{16107} a^{5} - \\frac{84998}{16107} a^{4} + \\frac{729635}{32214} a^{3} + \\frac{3239}{5369} a^{2} - \\frac{13389}{1534} a + \\frac{1597}{767} \\)', '\\( \\frac{176}{5524701} a^{15} - \\frac{211}{2528253} a^{14} - \\frac{35899}{14206374} a^{13} + \\frac{1609}{240786} a^{12} + \\frac{166898}{2367729} a^{11} - \\frac{22822}{120393} a^{10} - \\frac{96092}{112749} a^{9} + \\frac{13565}{5733} a^{8} + \\frac{519565}{112749} a^{7} - \\frac{77905}{5733} a^{6} - \\frac{55312}{5369} a^{5} + \\frac{9332}{273} a^{4} + \\frac{43786}{5369} a^{3} - \\frac{9097}{273} a^{2} - \\frac{1525}{1534} a + \\frac{167}{26} \\)', '\\( \\frac{10670}{49722309} a^{15} - \\frac{671}{3683134} a^{14} - \\frac{4691}{263081} a^{13} + \\frac{35930}{2367729} a^{12} + \\frac{3823279}{7103187} a^{11} - \\frac{3264341}{7103187} a^{10} - \\frac{2527208}{338247} a^{9} + \\frac{2165057}{338247} a^{8} + \\frac{1918251}{37583} a^{7} - \\frac{4930444}{112749} a^{6} - \\frac{899602}{5369} a^{5} + \\frac{326492}{2301} a^{4} + \\frac{3674485}{16107} a^{3} - \\frac{5952637}{32214} a^{2} - \\frac{62624}{767} a + \\frac{41596}{767} \\)', '\\( \\frac{57599}{298333854} a^{15} + \\frac{12440}{49722309} a^{14} - \\frac{4161}{263081} a^{13} - \\frac{145478}{7103187} a^{12} + \\frac{1103320}{2367729} a^{11} + \\frac{4277461}{7103187} a^{10} - \\frac{2095804}{338247} a^{9} - \\frac{299281}{37583} a^{8} + \\frac{13268314}{338247} a^{7} + \\frac{5600527}{112749} a^{6} - \\frac{1802239}{16107} a^{5} - \\frac{2194415}{16107} a^{4} + \\frac{1238871}{10738} a^{3} + \\frac{1987144}{16107} a^{2} - \\frac{24796}{767} a - \\frac{17135}{767} \\)', '\\( \\frac{12937}{149166927} a^{15} - \\frac{16511}{298333854} a^{14} - \\frac{51440}{7103187} a^{13} + \\frac{66527}{14206374} a^{12} + \\frac{521524}{2367729} a^{11} - \\frac{1033408}{7103187} a^{10} - \\frac{348592}{112749} a^{9} + \\frac{238052}{112749} a^{8} + \\frac{7238107}{338247} a^{7} - \\frac{5181769}{338247} a^{6} - \\frac{379237}{5369} a^{5} + \\frac{287089}{5369} a^{4} + \\frac{492890}{5369} a^{3} - \\frac{2306849}{32214} a^{2} - \\frac{16739}{767} a + \\frac{19439}{1534} \\)', '\\( \\frac{8914}{149166927} a^{15} + \\frac{6658}{149166927} a^{14} - \\frac{71621}{14206374} a^{13} - \\frac{17467}{4735458} a^{12} + \\frac{1108414}{7103187} a^{11} + \\frac{784156}{7103187} a^{10} - \\frac{764054}{338247} a^{9} - \\frac{56887}{37583} a^{8} + \\frac{5588428}{338247} a^{7} + \\frac{3457057}{338247} a^{6} - \\frac{979102}{16107} a^{5} - \\frac{182300}{5369} a^{4} + \\frac{1649275}{16107} a^{3} + \\frac{836392}{16107} a^{2} - \\frac{92671}{1534} a - \\frac{45191}{1534} \\)'], 'used_grh': True, 'zk': ['1', 'a', 'a^2', 'a^3', '1/21*a^4', '1/21*a^5', '1/21*a^6', '1/21*a^7', '1/441*a^8', '1/441*a^9', '1/1323*a^10 + 1/3*a^2', '1/1323*a^11 + 1/3*a^3', '1/18522*a^12 - 1/2', '1/18522*a^13 - 1/2*a', '1/298333854*a^14 - 383/14206374*a^12 - 2120/7103187*a^10 - 6/5369*a^8 - 6271/338247*a^6 - 277/16107*a^4 - 9985/32214*a^2 - 69/1534', '1/298333854*a^15 - 383/14206374*a^13 - 2120/7103187*a^11 - 6/5369*a^9 - 6271/338247*a^7 - 277/16107*a^5 - 9985/32214*a^3 - 69/1534*a']}
Number field data - 16.16.12341030701727613557145600000000.1