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lfunc_lfunctions • Show schema
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{'Lhash': '2963261186609040960917522989716', 'a10': [-1.698185103510833, -2.6676145437851213], 'a2': [1.411266311503138, 0.09125457805681579], 'a3': [0.0, 0.0], 'a4': [1.983345203967345, 0.25756902356403527], 'a5': [-1.3200117334463224, -1.8048736863182517], 'a6': [0.0, 0.0], 'a7': [1.866778495931408, 1.866778495931408], 'a8': [2.775523917874592, 0.5444878155717302], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.4373072363830477, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.411266311503138, -0.09125457805681579]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [1.3200117334463224, 1.8048736863182517]]]], 'bad_primes': [2, 3, 5], 'central_character': '180.163', 'coefficient_field': 'CDF', 'conductor': 180, 'conductor_radical': 30, 'conjugate': '2761854001095341541806191946151', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.411266311503138, -0.09125457805681579]], [[1.0, 0], [0, 0]], [[1.0, 0], 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0, 'data': '0.0081572324709', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.33760090207469763837043206504', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.92015861617883938914466347429', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.77160137102534546130446456921', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.4373072363830477, 'bad_primes': [2, 3, 5], 'central_character': '20.3', 'conductor': 180, 'conductor_radical': 30, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/180/2/k/e/163/6'], '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': '2-180-20.3-c1-0-8', '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': '2-180-20.3-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.198877490147783, 'root_angle': 0.008157232470895734, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.33760090207469763837043206504', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2963261186609040960917522989716', 'Lhash_array': ['2963261186609040960917522989716'], 'label': '2-180-20.3-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/180/2/k/e/163/6'}