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{'cm': True, 'coeffs': [95367431640625, 0, 19073486328125, 0, 0, 0, -762939453125, 0, -152587890625, 0, 0, 0, 6103515625, 0, 1220703125, 0, 0, 0, -48828125, 0, -9765625, 0, -1953125, 0, 0, 0, 78125, 0, 15625, 0, 0, 0, -625, 0, -125, 0, 0, 0, 5, 0, 1], 'conductor': 660, 'degree': 40, 'dirichlet_group': [1, 259, 641, 521, 139, 499, 401, 19, 281, 541, 161, 419, 421, 41, 299, 301, 559, 179, 181, 439, 59, 61, 581, 199, 461, 79, 599, 601, 221, 479, 481, 101, 359, 361, 619, 239, 241, 659, 119, 379], 'disc_abs': 11302165783522556415463223790320401501047994110286233600000000000000000000, 'disc_rad': 330, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [0]], [7, [[10, 4]]], [11, [0]], [13, [[10, 4]]], [17, [[10, 4]]], [19, [[10, 4]]], [23, [[2, 20]]], [29, [[10, 4]]], [31, [[10, 4]]], [37, [[10, 4]]], [41, [[10, 4]]], [43, [[2, 20]]], [47, [[10, 4]]], [53, [[10, 4]]], [59, [[10, 4]]]], 'gal_is_abelian': True, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [40, 20, 20, 36], 'galois_label': '40T7', 'galt': 7, 'grd': 67.03923376773275, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '40.0.11302165783522556415463223790320401501047994110286233600000000000000000000.1', 'local_algs': ['m2.2.10.20', 'm2.2.10.20', '3.10.5.2', '3.10.5.2', '3.10.5.2', '3.10.5.2', 'm5.2.10.10', 'm5.2.10.10', '11.20.18.1', '11.20.18.1'], 'monogenic': 0, 'num_ram': 4, 'r2': 20, 'ramps': [2, 3, 5, 11], 'rd': 67.0392337677, 'subfield_mults': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'subfields': ['165.0.1', '5.0.1', '-8.-1.1', '3.-1.1', '-15.0.1', '-55.0.1', '1.-1.1', '174.6.-5.-2.1', '309.24.-23.-2.1', '3025.0.55.0.1', '9.-16.17.-2.1', '25.0.-5.0.1', '9.-3.-2.-1.1', '100.0.-35.0.1', '-1.3.3.-4.-1.1', '81.-144.103.-236.248.-2.-13.-2.1', '8353125.0.2784375.0.259875.0.9900.0.165.0.1', '13201.-2936.6258.-1204.1447.-242.206.-26.18.-2.1', '1.-12.12.43.-43.-34.34.10.-10.-1.1', '1.-1.1.-1.1.-1.1.-1.1.-1.1', '-390599.-71016.190938.25916.-32593.-3002.2446.134.-82.-2.1', '-34375.0.34375.0.-9625.0.1100.0.-55.0.1', '1.-3.12.1.20.-7.16.-2.5.-1.1', '261399601.-87181604.223626538.-59924902.92642076.-20925574.25267471.-4931470.5053831.-862794.776698.-115100.92914.-11788.8702.-936.618.-50.31.-2.1', '576650390625.0.38443359375.0.2562890625.0.170859375.0.11390625.0.759375.0.50625.0.3375.0.225.0.15.0.1', '1181640625.0.1181640625.0.850781250.0.255234375.0.52937500.0.6840625.0.646250.0.41250.0.1925.0.55.0.1', '9765625.0.-1953125.0.390625.0.-78125.0.15625.0.-3125.0.625.0.-125.0.25.0.-5.0.1', '3987301.-3402296.5105098.-3673930.5091018.-3514480.4192195.-2324698.2462467.-914598.876253.-211274.182026.-29002.22238.-2346.1581.-104.61.-2.1', '1.-1.0.1.-1.0.1.-1.0.1.-1.1.0.-1.1.0.-1.1.0.-1.1', '9765625.0.-78125000.0.152343750.0.-112734375.0.41640625.0.-8693750.0.1088750.0.-83250.0.3800.0.-95.0.1'], 'torsion_gen': '\\( -\\frac{1}{152587890625} a^{32} \\)', 'torsion_order': 66, 'used_grh': True, 'zk': ['1', 'a', '1/5*a^2', '1/5*a^3', '1/25*a^4', '1/25*a^5', '1/125*a^6', '1/125*a^7', '1/625*a^8', '1/625*a^9', '1/3125*a^10', '1/3125*a^11', '1/15625*a^12', '1/15625*a^13', '1/78125*a^14', '1/78125*a^15', '1/390625*a^16', '1/390625*a^17', '1/1953125*a^18', '1/1953125*a^19', '1/9765625*a^20', '1/9765625*a^21', '1/48828125*a^22', '1/48828125*a^23', '1/244140625*a^24', '1/244140625*a^25', '1/1220703125*a^26', '1/1220703125*a^27', '1/6103515625*a^28', '1/6103515625*a^29', '1/30517578125*a^30', '1/30517578125*a^31', '1/152587890625*a^32', '1/152587890625*a^33', '1/762939453125*a^34', '1/762939453125*a^35', '1/3814697265625*a^36', '1/3814697265625*a^37', '1/19073486328125*a^38', '1/19073486328125*a^39']}