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lfunc_lfunctions • Show schema
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{'Lhash': '1063271150388476283864693957118', 'a10': -1, 'a2': 1, 'a3': 1, 'a4': -1, 'a5': -1, 'a6': 1, 'a7': 0, 'a8': -3, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 19.523423294203063, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, -1]], [5, [1, 1]], [163, [1, 1]]], 'bad_primes': [3, 5, 163], 'central_character': '2445.1', 'coefficient_field': '1.1.1.1', 'conductor': 2445, 'conductor_radical': 2445, 'degree': 2, 'euler_factors': [[1, -1, 2], [1, -1], [1, 1], [1, 0, 7], [1, 4, 11], [1, -2, 13], [1, 2, 17], [1, 0, 19], [1, -8, 23], [1, -10, 29], [1, -4, 31], [1, -10, 37], [1, -2, 41], [1, 4, 43], [1, -12, 47], [1, -2, 53], [1, -4, 59], [1, 2, 61], [1, 4, 67], [1, 0, 71], [1, 10, 73], [1, 12, 79], [1, 0, 83], [1, 2, 89], [1, -2, 97], [1, -10, 101], [1, 0, 103], [1, 4, 107], [1, 18, 109], [1, -6, 113]], 'euler_factors_factorization': [[[[1, -1, 2], 1]], [[[1, -1], 1]], [[[1, 1], 1]], [[[1, 0, 7], 1]], [[[1, 4, 11], 1]], [[[1, -2, 13], 1]], [[[1, 2, 17], 1]], [[[1, 0, 19], 1]], [[[1, -8, 23], 1]], [[[1, -10, 29], 1]], [[[1, -4, 31], 1]], [[[1, -10, 37], 1]], [[[1, -2, 41], 1]], [[[1, 4, 43], 1]], [[[1, -12, 47], 1]], [[[1, -2, 53], 1]], [[[1, -4, 59], 1]], [[[1, 2, 61], 1]], [[[1, 4, 67], 1]], [[[1, 0, 71], 1]], [[[1, 10, 73], 1]], [[[1, 12, 79], 1]], [[[1, 0, 83], 1]], [[[1, 2, 89], 1]], [[[1, -2, 97], 1]], [[[1, -10, 101], 1]], [[[1, 0, 103], 1]], [[[1, 4, 107], 1]], [[[1, 18, 109], 1]], [[[1, -6, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 25, 'label': '2-2445-1.1-c1-0-25', 'leading_term': '2.22136806218993681762048218571000000000000000000000000000000000000000000000000000000000000', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/2445/2/a/c', 'plot_delta': {'__RealLiteral__': 0, 'data': 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{'__RealLiteral__': 0, 'data': '0.838773042190839979450102072513', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.69411041556594394393594930744', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.10223838202310795165601485529', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 19.523423294203063, 'bad_primes': [3, 5, 163], 'central_character': '1.1', 'conductor': 2445, 'conductor_radical': 2445, 'degree': 2, 'dirichlet_coefficients': [1, 1, 1, -1, -1, 1, 0, -3, 1, -1, -4, -1, 2, 0, -1, -1, -2, 1, 0, 1, 0, -4, 8, -3, 1, 2, 1, 0, 10, -1, 4, 5, -4, -2, 0, -1, 10, 0, 2, 3, 2, 0, -4, 4, -1, 8, 12, -1, -7, 1, -2, -2, 2, 1, 4, 0, 0, 10, 4, 1, -2, 4, 0, 7, -2, -4, -4, 2, 8, 0, 0, -3, -10, 10, 1, 0, 0, 2, -12, 1, 1, 2, 0, 0, 2, -4, 10, 12, -2, -1, 0, -8, 4, 12, 0, 5, 2, -7, -4, -1], 'euler11': [1, 4, 11], 'euler13': [1, -2, 13], 'euler17': [1, 2, 17], 'euler19': [1, 0, 19], 'euler2': [1, -1, 2], 'euler23': [1, -8, 23], 'euler29': [1, -10, 29], 'euler3': [1, -1, 0], 'euler31': [1, -4, 31], 'euler37': [1, -10, 37], 'euler41': [1, -2, 41], 'euler43': [1, 4, 43], 'euler47': [1, -12, 47], 'euler5': [1, 1, 0], 'euler53': [1, -2, 53], 'euler59': [1, -4, 59], 'euler61': [1, 2, 61], 'euler67': [1, 4, 67], 'euler7': [1, 0, 7], 'euler71': [1, 0, 71], 'euler73': [1, 10, 73], 'euler79': [1, 12, 79], 'euler83': [1, 0, 83], 'euler89': [1, 2, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, -1, 2], [1, -1, 0], [1, 1, 0], [1, 0, 7], [1, 4, 11], [1, -2, 13], [1, 2, 17], [1, 0, 19], [1, -8, 23], [1, -10, 29], [1, -4, 31], [1, -10, 37], [1, -2, 41], [1, 4, 43], [1, -12, 47], [1, -2, 53], [1, -4, 59], [1, 2, 61], [1, 4, 67], [1, 0, 71], [1, 10, 73], [1, 12, 79], [1, 0, 83], [1, 2, 89], [1, -2, 97]], 'index': 25, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/2445/c', 'ModularForm/GL2/Q/holomorphic/2445/2/a/c/1/1', 'ModularForm/GL2/Q/holomorphic/2445/2/a/c'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-2445-1.1-c1-0-25', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-2445-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.418531803009125, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1176144819894271386, 'z1': {'__RealLiteral__': 0, 'data': '0.838773042190839979450102072513', 'prec': 107}}
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lfunc_instances • Show schema
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id: 20649400
{'Lhash': '1063271150388476283864693957118', 'Lhash_array': ['1063271150388476283864693957118'], 'factors': ['2-2445-1.1-c1-0-25'], 'label': '2-2445-1.1-c1-0-25', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2445/2/a/c'}
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id: 24557245
{'Lhash': '1063271150388476283864693957118', 'Lhash_array': ['1063271150388476283864693957118'], 'factors': ['2-2445-1.1-c1-0-25'], 'label': '2-2445-1.1-c1-0-25', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2445/2/a/c/1/1'}
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id: 23225
{'Lhash': '1176144819894271386', 'Lhash_array': ['1176144819894271386'], 'factors': ['2-2445-1.1-c1-0-25'], 'label': '2-2445-1.1-c1-0-25', 'type': 'ECQ', 'url': 'EllipticCurve/Q/2445/c'}