-
nf_fields • Show schema
{'class_group': [52934], 'class_number': 52934, 'cm': True, 'coeffs': [1, 0, 360, 0, 10470, 0, 118407, 0, 691677, 0, 2413645, 0, 5490811, 0, 8624289, 0, 9725341, 0, 8084594, 0, 5038516, 0, 2375189, 0, 848161, 0, 227942, 0, 45354, 0, 6478, 0, 628, 0, 37, 0, 1], 'conductor': 228, 'degree': 36, 'dirichlet_group': [1, 7, 139, 143, 25, 155, 29, 163, 167, 41, 43, 173, 175, 49, 179, 53, 55, 185, 59, 61, 65, 71, 73, 203, 85, 89, 221, 199, 227, 107, 157, 113, 115, 187, 169, 121], 'disc_abs': 799622233646074762983150698451178476894456963777140963130998784, 'disc_rad': 114, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [[18, 2]]], [7, [[6, 6]]], [11, [[6, 6]]], [13, [[18, 2]]], [17, [[18, 2]]], [19, [0]], [23, [[18, 2]]], [29, [[9, 4]]], [31, [[6, 6]]], [37, [[2, 18]]], [41, [[9, 4]]], [43, [[18, 2]]], [47, [[18, 2]]], [53, [[9, 4]]], [59, [[18, 2]]]], 'gal_is_abelian': True, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [36, 18, 34], 'galois_label': '36T2', 'galt': 2, 'grd': 55.88591389129187, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '36.0.799622233646074762983150698451178476894456963777140963130998784.1', 'local_algs': ['2.18.18.115', '2.18.18.115', 'm3.2.18.18', 'm19.18.2.34'], 'monogenic': 1, 'num_ram': 3, 'r2': 18, 'ramps': [2, 3, 19], 'rd': 55.8859138913, 'regulator': {'__RealLiteral__': 0, 'data': '1438232971979.9597', 'prec': 60}, 'res': {'ae': []}, 'subfield_mults': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'subfields': ['1.0.1', '57.0.1', '-14.-1.1', '7.-6.-1.1', '196.0.29.0.1', '49.0.50.0.13.0.1', '513.0.342.0.57.0.1', '7.33.37.-11.-17.-1.1', '-1.5.10.-20.-15.21.7.-8.-1.1', '49.0.571.0.1857.0.1299.0.341.0.35.0.1', '1.0.45.0.330.0.924.0.1287.0.1001.0.455.0.120.0.17.0.1', '373977.0.1869885.0.2742498.0.1828332.0.660231.0.140049.0.17955.0.1368.0.57.0.1', '1.-20.20.265.-265.-989.989.1519.-1519.-1198.1198.531.-531.-134.134.18.-18.-1.1'], 'torsion_gen': '\\( -a^{19} - 19 a^{17} - 152 a^{15} - 665 a^{13} - 1729 a^{11} - 2717 a^{9} - 2508 a^{7} - 1254 a^{5} - 285 a^{3} - 19 a \\)', 'torsion_order': 4, 'units': ['\\( a^{28} + 28 a^{26} + 350 a^{24} + 2576 a^{22} + 12397 a^{20} + 40964 a^{18} + 94962 a^{16} + 155040 a^{14} + 176358 a^{12} + 136135 a^{10} + 68058 a^{8} + 20349 a^{6} + 3135 a^{4} + 171 a^{2} \\)', '\\( a^{18} + 18 a^{16} + 135 a^{14} + 546 a^{12} + 1287 a^{10} + 1782 a^{8} + 1386 a^{6} + 540 a^{4} + 81 a^{2} + 2 \\)', '\\( a^{24} + 24 a^{22} + 252 a^{20} + 1520 a^{18} + 5814 a^{16} + 14688 a^{14} + 24752 a^{12} + 27456 a^{10} + 19305 a^{8} + 8008 a^{6} + 1716 a^{4} + 144 a^{2} + 2 \\)', '\\( a^{34} + 34 a^{32} + 526 a^{30} + 4899 a^{28} + 30626 a^{26} + 135631 a^{24} + 437669 a^{22} + 1042381 a^{20} + 1835494 a^{18} + 2370631 a^{16} + 2205633 a^{14} + 1434576 a^{12} + 622921 a^{10} + 168363 a^{8} + 25271 a^{6} + 1644 a^{4} - 3 \\)', '\\( a^{34} + 34 a^{32} + 526 a^{30} + 4899 a^{28} + 30626 a^{26} + 135631 a^{24} + 437669 a^{22} + 1042381 a^{20} + 1835494 a^{18} + 2370631 a^{16} + 2205633 a^{14} + 1434577 a^{12} + 622933 a^{10} + 168417 a^{8} + 25383 a^{6} + 1749 a^{4} + 36 a^{2} - 1 \\)', '\\( a^{12} + 12 a^{10} + 54 a^{8} + 112 a^{6} + 105 a^{4} + 36 a^{2} + 3 \\)', '\\( a^{18} + 18 a^{16} + 135 a^{14} + 546 a^{12} + 1287 a^{10} + 1782 a^{8} + 1386 a^{6} + 540 a^{4} + 81 a^{2} + 1 \\)', '\\( a^{6} + 6 a^{4} + 9 a^{2} + 1 \\)', '\\( a^{35} + 35 a^{33} + 560 a^{31} + 5425 a^{29} + 35525 a^{27} + 166257 a^{25} + 573300 a^{23} + 1480050 a^{21} + 2877875 a^{19} + 4206125 a^{17} + 4576264 a^{15} + 3640210 a^{13} + 2057510 a^{11} + 791350 a^{9} + 193800 a^{7} + 27132 a^{5} + 1786 a^{3} + 38 a \\)', '\\( a^{20} + 20 a^{18} + 170 a^{16} + 800 a^{14} + 2275 a^{12} + 4004 a^{10} + 4290 a^{8} + 2640 a^{6} + 825 a^{4} + 100 a^{2} + 2 \\)', '\\( a^{29} + 29 a^{27} + 377 a^{25} + 2900 a^{23} + 14674 a^{21} + 51359 a^{19} + 127281 a^{17} + 224808 a^{15} + 281010 a^{13} + 243542 a^{11} + 140999 a^{9} + 51281 a^{7} + 10583 a^{5} + 1045 a^{3} + 38 a \\)', '\\( a^{33} + 33 a^{31} + 495 a^{29} + 4466 a^{27} + 27027 a^{25} + 115830 a^{23} + 361790 a^{21} + 834900 a^{19} + 1427679 a^{17} + 1797818 a^{15} + 1641486 a^{13} + 1058148 a^{11} + 461890 a^{9} + 127908 a^{7} + 20196 a^{5} + 1496 a^{3} + 32 a \\)', '\\( a^{13} + 13 a^{11} + 65 a^{9} + 156 a^{7} + 182 a^{5} + 91 a^{3} + 13 a \\)', '\\( a^{8} + 8 a^{6} + 20 a^{4} + 16 a^{2} + 2 \\)', '\\( a^{4} + 4 a^{2} + 2 \\)', '\\( a^{28} + 28 a^{26} + 350 a^{24} + 2576 a^{22} + 12397 a^{20} + 40964 a^{18} + 94962 a^{16} + 155040 a^{14} + 176358 a^{12} + 136136 a^{10} + 68068 a^{8} + 20384 a^{6} + 3185 a^{4} + 196 a^{2} + 1 \\)', '\\( a^{26} + 25 a^{24} + 275 a^{22} + 1750 a^{20} + 7125 a^{18} + 19380 a^{16} + 35700 a^{14} + 44199 a^{12} + 35738 a^{10} + 17821 a^{8} + 4893 a^{6} + 545 a^{4} - 11 a^{2} - 2 \\)'], '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', 'a^15', 'a^16', 'a^17', 'a^18', 'a^19', 'a^20', 'a^21', 'a^22', 'a^23', 'a^24', 'a^25', 'a^26', 'a^27', 'a^28', 'a^29', 'a^30', 'a^31', 'a^32', 'a^33', 'a^34', 'a^35']}
Number field data - 36.0.799622233646074762983150698451178476894456963777140963130998784.1