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lfunc_lfunctions • Show schema
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{'Lhash': '2133014787472388673016639190870', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.7246621841757455, -0.15981348652146768], 'a4': [0.3067833097573707, -1.9763309441625188], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-0.5503810319990218, 4.852778844185473], 'a8': [0.0, 0.0], 'a9': [2.9489192990517052, 0.551248553449711], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.354222026159927, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.7246621841757455, 0.15981348652146768]]], [307, [[1.0, 0], [2.4770273826956575, -17.34544134190237]]]], 'bad_primes': [3, 307], 'central_character': '921.131', 'coefficient_field': 'CDF', 'conductor': 921, 'conductor_radical': 921, 'conjugate': '151493254549844833967562933113', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [-0.3067833097573707, 1.9763309441625188]], [[1.0, 0], [1.7246621841757455, 0.15981348652146768]], [[1.0, 0], [0, 0], [0.6653523100822683, 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'5.02734134777445918850306672376531', '6.58943102834435213612139268570475', '7.03957406625516372470400255624947', '7.56685875725349313004060884587752', '8.868044937145215664058011434412436', '9.870364663163955532887863278675392', '10.51565147145241287078534933698584'], 'prelabel': '2-921-921.131-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.7118668894619304, 'root_angle': 0.9675761045828483, 'root_number': '-0.9948164824056281 + 0.10168660843047385*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.483788052291', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.68265197609527264025684219863', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.56703089669908991439845404721', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.17986517733649230145534275591', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.354222026159927, 'bad_primes': [3, 307], 'central_character': '921.131', 'conductor': 921, 'conductor_radical': 921, 'degree': 2, 'index': 63, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/921/2/x/a/131/1'], 'is_instance_Artin': False, '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': '2-921-921.131-c1-0-63', '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': '2-921-921.131-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.7118668894619304, 'root_angle': 0.48378805229142413, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.68265197609527264025684219863', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2133014787472388673016639190870', 'Lhash_array': ['2133014787472388673016639190870'], 'label': '2-921-921.131-c1-0-63', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/921/2/x/a/131/1'}