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lfunc_lfunctions • Show schema
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{'Lhash': '2313288952645879346289339113863', 'a10': [2.846887491179777, 1.3766741126948363], 'a2': [-0.9424896855656725, 1.0543781070386087], 'a3': [0.4382589122381559, 1.6356045273426674], 'a4': [-0.22342638520463973, -1.9874809811402945], 'a5': [-0.6158135257253181, -2.1495984977510925], 'a6': [-2.137600109795033, -1.0794497944065142], 'a7': [-0.8855843631507766, -2.4931386515279956], 'a8': [2.306133498208536, 1.6376044358881234], 'a9': [0.11494491564565729, -0.06636347798999906], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.2358112565958517, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.9424896855656725, -1.0543781070386087]]], [5, [[1.0, 0], [0.6158135257253181, 2.1495984977510925]]], [7, [[1.0, 0], [0.8855843631507766, 2.4931386515279956]]]], 'bad_primes': [2, 5, 7], 'central_character': '280.67', 'coefficient_field': 'CDF', 'conductor': 280, 'conductor_radical': 70, 'conjugate': 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9.094310185182117], 'positive_zeros': ['1.82486321722199469349788890690690', '2.78637844522795517988085096119359', '4.23557588589277677465555928958848', '6.33531221211754084826436066025535', '7.23642428325418609945532806405070', '7.87558298089095110643837554061985', '9.218356673571249033783879836208492', '9.814827479193164464562737563738517', '11.12852673835052127208201912518618', '11.78019453347314684105559642259460'], 'prelabel': '2-280-280.67-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4952629389494851, 'root_angle': 0.009728841405169874, 'root_number': '0.999532955579045 + 0.030559298280865177*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.00486442070258', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.82486321722199469349788890691', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.78637844522795517988085096119', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.23557588589277677465555928959', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.2358112565958517, 'bad_primes': [2, 5, 7], 'central_character': '280.67', 'conductor': 280, 'conductor_radical': 70, 'degree': 2, 'index': 27, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/280/2/br/a/67/13'], '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': '2-280-280.67-c1-0-27', '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': '2-280-280.67-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4952629389494851, 'root_angle': 0.004864420702584937, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.82486321722199469349788890691', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2313288952645879346289339113863', 'Lhash_array': ['2313288952645879346289339113863'], 'label': '2-280-280.67-c1-0-27', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/280/2/br/a/67/13'}