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lfunc_lfunctions • Show schema
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{'Lhash': '2370355991045523513435229764160', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 1, 'a5': -1, 'a6': 0, 'a7': 1, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.2250783206974841, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[11, [1, 1]], [41, [1, 1]]], 'bad_primes': [11, 41], 'central_character': '451.450', 'coefficient_field': '1.1.1.1', 'conductor': 451, 'conductor_radical': 451, 'degree': 2, 'euler_factors': [[1, 0, -1], [1, 0, -1], [1, 1, 1], [1, -1, 1], [1, 1], [1, 2, 1], [1, -1, 1], [1, -1, 1], [1, 1, 1], [1, -1, 1], [1, 1, 1], [1, 1, 1], [1, 1], [1, 0, -1], [1, 0, -1], [1, 0, -1], [1, 1, 1], [1, 0, -1], [1, 0, -1], [1, 0, -1], [1, 0, -1], [1, 2, 1], [1, 0, -1], [1, 0, -1], [1, 0, -1], [1, -1, 1], [1, 1, 1], [1, 0, -1], [1, -1, 1], [1, -2, 1]], 'euler_factors_factorization': [[[[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], 2]], [[[1, 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'z1': {'__RealLiteral__': 0, 'data': '1.86988117279222023205677327092', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.21226091457868276887990528985', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.62692691740037057523082253517', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.2250783206974841, 'bad_primes': [11, 41], 'central_character': '451.450', 'conductor': 451, 'conductor_radical': 451, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 1, -1, 0, 1, 0, 1, 0, -1, 0, -2, 0, 0, 1, 1, 0, 1, -1, 0, 0, -1, 0, 0, 0, 0, 1, 1, 0, -1, 0, 0, 0, -1, 1, -1, 0, 0, 0, -1, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, -2, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1, 1, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, -2, -1, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, -2, -1, 0, 0, -1, 0, 0, 0, -1, 0], 'euler11': [1, 1, 0], 'euler13': [1, 2, 1], 'euler17': [1, -1, 1], 'euler19': [1, -1, 1], 'euler2': [1, 0, -1], 'euler23': [1, 1, 1], 'euler29': [1, -1, 1], 'euler3': [1, 0, -1], 'euler31': [1, 1, 1], 'euler37': [1, 1, 1], 'euler41': [1, 1, 0], 'euler43': [1, 0, -1], 'euler47': [1, 0, -1], 'euler5': [1, 1, 1], 'euler53': [1, 0, -1], 'euler59': [1, 1, 1], 'euler61': [1, 0, -1], 'euler67': [1, 0, -1], 'euler7': [1, -1, 1], 'euler71': [1, 0, -1], 'euler73': [1, 0, -1], 'euler79': [1, 2, 1], 'euler83': [1, 0, -1], 'euler89': [1, 0, -1], 'euler97': [1, 0, -1], 'euler_factors': [[1, 0, -1], [1, 0, -1], [1, 1, 1], [1, -1, 1], [1, 1, 0], [1, 2, 1], [1, -1, 1], [1, -1, 1], [1, 1, 1], [1, -1, 1], [1, 1, 1], [1, 1, 1], [1, 1, 0], [1, 0, -1], [1, 0, -1], [1, 0, -1], [1, 1, 1], [1, 0, -1], [1, 0, -1], [1, 0, -1], [1, 0, -1], [1, 2, 1], [1, 0, -1], [1, 0, -1], [1, 0, -1]], 'index': 1, 'instance_types': ['CMF', 'CMF', 'Artin', 'Artin'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/451/1/b/b/450/1', 'ModularForm/GL2/Q/holomorphic/451/1/b/b', 'ArtinRepresentation/2.451.6t3.b.a', 'ArtinRepresentation/2.451.6t3.b'], 'is_instance_Artin': True, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, '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': '2-451-451.450-c0-0-1', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-451-451.450-c0-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.4744241991061207, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0-0', 'trace_hash': 2184085729800457467, 'z1': {'__RealLiteral__': 0, 'data': '1.86988117279222023205677327092', 'prec': 103}}
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lfunc_instances • Show schema
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id: 24603218
{'Lhash': '2370355991045523513435229764160', 'Lhash_array': ['2370355991045523513435229764160'], 'label': '2-451-451.450-c0-0-1', 'type': 'Artin', 'url': 'ArtinRepresentation/2.451.6t3.b'}
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id: 24596785
{'Lhash': '2370355991045523513435229764160', 'Lhash_array': ['2370355991045523513435229764160'], 'label': '2-451-451.450-c0-0-1', 'type': 'Artin', 'url': 'ArtinRepresentation/2.451.6t3.b.a'}
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id: 19804165
{'Lhash': '2370355991045523513435229764160', 'Lhash_array': ['2370355991045523513435229764160'], 'label': '2-451-451.450-c0-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/451/1/b/b'}
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id: 24545924
{'Lhash': '2370355991045523513435229764160', 'Lhash_array': ['2370355991045523513435229764160'], 'label': '2-451-451.450-c0-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/451/1/b/b/450/1'}