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lfunc_lfunctions • Show schema
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{'Lhash': '2187543825472820208398780757450', 'a10': [-0.17181470586822647, -0.2975918000512708], 'a2': [0.05782322925002234, -0.2157992294187862], 'a3': [-0.8660254037844386, 0.5], 'a4': [1.688825025992036, 0.9750435833706788], 'a5': [1.0876000511766275, -1.0876000511766275], 'a6': [0.05782322925002234, 0.2157992294187862], 'a7': [-0.7259429497717277, -2.544210453888735], 'a8': [0.6240189709197647, -0.6240189709197647], 'a9': [0.5, -0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.1799159751809554, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.8660254037844386, -0.5]]], [7, [[1.0, 0], [0.7259429497717277, 2.544210453888735]]], [13, [[1.0, 0], [3.010960671127194, -1.983460571053853]]]], 'bad_primes': [3, 7, 13], 'central_character': '273.76', 'coefficient_field': 'CDF', 'conductor': 273, 'conductor_radical': 273, 'conjugate': '1941956432778486021900628550592', 'degree': 2, 'euler_factors': 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'6.16487797148387920434759996634282', '6.57476850976317102337058388116885', '7.84563966726000858568390561600362', '9.209885915690839241882561620707577', '10.21282366287693205635106625059103', '10.96666511456079263540573968612694', '12.03232138803184285768350061019744'], 'prelabel': '2-273-91.76-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4764538513549808, 'root_angle': 0.047154013744432344, 'root_number': '0.9890475137366014 + 0.14759747820151714*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0235770068722', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.72566780237312401278477804267', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.07990985947668178752158287212', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.16616986649935521953543938079', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.1799159751809554, 'bad_primes': [3, 7, 13], 'central_character': '91.76', 'conductor': 273, 'conductor_radical': 273, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/273/2/by/d/76/6'], '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': '2-273-91.76-c1-0-8', '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': '2-273-91.76-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4764538513549808, 'root_angle': 0.023577006872216172, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.72566780237312401278477804267', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2187543825472820208398780757450', 'Lhash_array': ['2187543825472820208398780757450'], 'label': '2-273-91.76-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/273/2/by/d/76/6'}