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lfunc_lfunctions • Show schema
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{'Lhash': '1108513827136109191552979511110', 'a10': [0.0, 0.0], 'a2': [-0.06222952458293897, -0.08565159255547364], 'a3': [-0.5419306719471169, -0.056959208842015906], 'a4': [0.6145703071724246, -1.8914529168213097], 'a5': [0.0, 0.0], 'a6': [0.028845441124163266, 0.04996176959378749], 'a7': [0.5200049956376831, 2.4464311595562562], 'a8': [-0.4016293443654565, 0.13049728456944545], 'a9': [-2.6439983004762717, -0.5619991878106183], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.188406156649233, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [31, [[1.0, 0], [5.379636346758806, -1.435100267100374]]]], 'bad_primes': [5, 31], 'central_character': '775.524', 'coefficient_field': 'CDF', 'conductor': 775, 'conductor_radical': 155, 'conjugate': '1726773884538717742612694725600', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.06222952458293897, 0.08565159255547364], [-0.6180339887498949, 1.902113032590307]], [[1.0, 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'data': '-0.0511459750955', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.874463221124599297286518053326', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.96867121194873273225108582339', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.53719723941188772826025685194', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.188406156649233, 'bad_primes': [5, 31], 'central_character': '155.59', 'conductor': 775, 'conductor_radical': 155, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/775/2/ck/c/524/5'], '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': '2-775-155.59-c1-0-11', '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': '2-775-155.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.487650730438104, 'root_angle': -0.05114597509551, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.874463221124599297286518053326', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1108513827136109191552979511110', 'Lhash_array': ['1108513827136109191552979511110'], 'factors': ['2-775-155.59-c1-0-11'], 'label': '2-775-155.59-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/775/2/ck/c/524/5'}