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lfunc_lfunctions • Show schema
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{'Lhash': '2486489551299226236459708745525', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [1.224744871391589, -0.7071067811865476], 'a6': [0.0, 0.0], 'a7': [0.5, 0.8660254037844386], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.2515287663670332, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-0.5, -0.8660254037844386]]]], 'bad_primes': [2, 3, 7], 'central_character': '504.305', 'coefficient_field': 'CDF', 'conductor': 504, 'conductor_radical': 42, 'conjugate': '2312658943993773360950758862707', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.224744871391589, 0.7071067811865476], [0.5, -0.8660254037844386]], [[1.0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [1.224744871391589, 0.7071067811865476], [0.5, 0.8660254037844386]], [[1.0, 0], [1.0, 0], [1.0, 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-0.34524614859708364, 0.4411553876216039], 'positive_zeros': ['1.96149439826049507956339069820165', '3.00187391093175300179302104254708', '4.73803521666916912168467149619798', '5.38915805438657560386696987233117', '6.82908323287905615539422532033708', '7.27628823452008392492026722041146', '8.432619733096172378865919988009241', '9.847501068545743014491413352719144', '10.11171652615922084188038313909777', '10.89693422058892803480209888636117'], 'prelabel': '2-504-21.11-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5015264363590749, 'root_angle': 0.024709781201291546, 'root_number': '0.98797195634425140407751262240573 + 0.15463315775509661950091022089984*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.024709781201291546', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.96149439826049507956339069820', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.00187391093175300179302104255', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.73803521666916912168467149620', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.2515287663670332, 'bad_primes': [2, 3, 7], 'central_character': '21.11', 'conductor': 504, 'conductor_radical': 42, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/504/1/cu/a/305/2'], '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': '2-504-21.11-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': '2-504-21.11-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5015264363590749, 'root_angle': 0.024709781201291546, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.96149439826049507956339069820', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2486489551299226236459708745525', 'Lhash_array': ['2486489551299226236459708745525'], 'factors': ['2-504-21.11-c0-0-1'], 'label': '2-504-21.11-c0-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/504/1/cu/a/305/2'}