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lfunc_lfunctions • Show schema
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{'Lhash': '1823950384551555526168188504589', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [-0.47594739303707356, 0.8794737512064891], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-0.8868209204669981, -0.7510990058658708], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.028572991036618, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [229, [[1.0, 0], [0.1645945902807339, 0.9863613034027223]]]], 'bad_primes': [3, 229], 'central_character': '2061.1009', 'coefficient_field': 'CDF', 'conductor': 2061, 'conductor_radical': 687, 'conjugate': '760847452208852693479789201893', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [0.47594739303707356, -0.8794737512064891]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [0.6772815716257411, -0.7357239106731316]], [[1.0, 0], [0.8868209204669981, 0.7510990058658708], [0.1645945902807339, 0.9863613034027223]], [[1.0, 0], [0, 0], 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'0.50572390433331680858674490045553 + 0.86269538806340342488898364401915*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.1656127262690562', 'prec': 60}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.43884315143555267900194424332', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.53004254603843337774620963605', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.83809058935466506615854963321', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.028572991036618, 'bad_primes': [3, 229], 'central_character': '229.93', 'conductor': 2061, 'conductor_radical': 687, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2061/1/bn/a/1009/1'], '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': '2-2061-229.93-c0-0-0', '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': '2-2061-229.93-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0141858759796538, 'root_angle': 0.1656127262690562, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.43884315143555267900194424332', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1823950384551555526168188504589', 'Lhash_array': ['1823950384551555526168188504589'], 'label': '2-2061-229.93-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2061/1/bn/a/1009/1'}