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{'cm': True, 'coeffs': [262144, 0, 0, 0, 0, 0, 0, 0, 0, -2560, 0, 0, 0, 0, 0, 0, 0, 0, -487, 0, 0, 0, 0, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, 0, 0, 0, 1], 'conductor': 189, 'degree': 36, 'dirichlet_group': [1, 134, 8, 139, 13, 146, 20, 22, 155, 29, 160, 34, 167, 41, 43, 176, 50, 181, 55, 188, 62, 64, 71, 76, 83, 85, 92, 97, 104, 106, 113, 118, 169, 148, 125, 127], 'disc_abs': 14212734556341031905549296191351828189377245025195450200601, 'disc_rad': 21, 'disc_sign': 1, 'frobs': [[2, [[18, 2]]], [3, [0]], [5, [[18, 2]]], [7, [0]], [11, [[18, 2]]], [13, [[18, 2]]], [17, [[6, 6]]], [19, [[6, 6]]], [23, [[18, 2]]], [29, [[18, 2]]], [31, [[18, 2]]], [37, [[3, 12]]], [41, [[18, 2]]], [43, [[9, 4]]], [47, [[18, 2]]], [53, [[2, 18]]], [59, [[18, 2]]]], 'gal_is_abelian': True, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [90, 18], 'galois_label': '36T2', 'galt': 2, 'grd': 41.24318125460256, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '36.0.14212734556341031905549296191351828189377245025195450200601.1', 'local_algs': ['m3.18.2.90', '7.18.9.2', '7.18.9.2'], 'monogenic': 0, 'num_ram': 2, 'r2': 18, 'ramps': [3, 7], 'rd': 41.2431812546, 'res': {'ae': []}, 'subfield_mults': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'subfields': ['1.-1.1', '2.-1.1', '-5.-1.1', '-1.-3.0.1', '4.-2.-1.-1.1', '1.0.0.-1.0.0.1', '8.-12.36.-5.9.0.1', '1.30.36.-5.-12.0.1', '-1.9.0.-30.0.27.0.-9.0.1', '64.0.0.-40.0.0.17.0.0.-5.0.0.1', '1.0.0.0.0.0.0.0.0.-1.0.0.0.0.0.0.0.0.1', '512.2304.20736.9600.51840.4752.61488.468.35964.-5.12465.0.2646.0.351.0.27.0.1', '-1511.-720.20736.1200.-69120.-540.88704.90.-57024.-5.20592.0.-4368.0.540.0.-36.0.1'], 'torsion_gen': '\\( -\\frac{4049}{542572544} a^{34} - \\frac{93}{1114112} a^{25} + \\frac{4049}{1114112} a^{16} + \\frac{20245}{1059712} a^{7} \\)', 'torsion_order': 54, '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', '1/17*a^18 + 6/17*a^9 + 2/17', '1/34*a^19 - 11/34*a^10 - 15/34*a', '1/68*a^20 + 23/68*a^11 - 15/68*a^2', '1/136*a^21 - 45/136*a^12 - 15/136*a^3', '1/272*a^22 + 91/272*a^13 + 121/272*a^4', '1/544*a^23 + 91/544*a^14 + 121/544*a^5', '1/1088*a^24 - 453/1088*a^15 - 423/1088*a^6', '1/2176*a^25 + 635/2176*a^16 + 665/2176*a^7', '1/4352*a^26 - 1541/4352*a^17 - 1511/4352*a^8', '1/4238848*a^27 + 205/8704*a^18 - 2561/8704*a^9 + 1943/8279', '1/8477696*a^28 + 205/17408*a^19 - 2561/17408*a^10 - 3168/8279*a', '1/16955392*a^29 + 205/34816*a^20 - 2561/34816*a^11 + 5111/16558*a^2', '1/33910784*a^30 + 205/69632*a^21 + 32255/69632*a^12 + 5111/33116*a^3', '1/67821568*a^31 + 205/139264*a^22 - 37377/139264*a^13 - 28005/66232*a^4', '1/135643136*a^32 + 205/278528*a^23 + 101887/278528*a^14 + 38227/132464*a^5', '1/271286272*a^33 + 205/557056*a^24 - 176641/557056*a^15 - 94237/264928*a^6', '1/542572544*a^34 + 205/1114112*a^25 - 176641/1114112*a^16 + 170691/529856*a^7', '1/1085145088*a^35 + 205/2228224*a^26 + 937471/2228224*a^17 - 359165/1059712*a^8']}