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lfunc_lfunctions • Show schema
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{'Lhash': '3180679183707328904956130645772', 'a10': [10.196152422706632, 0.0], 'a2': [-2.732050807568877, 0.0], 'a3': [1.7320508075688772, 0.0], 'a4': [5.464101615137754, 0.0], 'a5': [-3.732050807568877, 0.0], 'a6': [-4.732050807568878, 0.0], 'a7': [-2.0, 0.0], 'a8': [-9.464101615137755, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.493202517797944, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[11, [[1.0, 0], [-1.0, 0]]], [17, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [11, 17], 'central_character': '187.1', 'coefficient_field': 'CDF', 'conductor': 187, 'conductor_radical': 187, 'conjugate': '3180679183707328904956130645772', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.732050807568877, 0], [2.0, 0]], [[1.0, 0], [-1.7320508075688772, 0], [3.0, 0]], [[1.0, 0], [3.732050807568877, 0], [5.0, 0]], [[1.0, 0], [2.0, 0], [7.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [3.267949192431123, 0], [13.0, 0]], [[1.0, 0], 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'8.914592410369310008235797861060485', '9.799025126566522876008329274842978', '10.87411142962362185284498662498864', '11.82544775901667069597481524111328'], 'prelabel': '2-187-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2219666598553105, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.50911346007699238392301203647', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.71599331035951613782649292105', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.50059977075890955087394229485', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.493202517797944, 'bad_primes': [11, 17], 'central_character': '1.1', 'conductor': 187, 'conductor_radical': 187, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/187/2/a/c/1/1'], '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': '2-187-1.1-c1-0-6', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-187-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2219666598553105, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.50911346007699238392301203647', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3180679183707328904956130645772', 'Lhash_array': ['3180679183707328904956130645772'], 'label': '2-187-1.1-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/187/2/a/c/1/1'}