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lfunc_lfunctions • Show schema
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{'Lhash': '4878494632581260744935829779921', 'a10': [-1.0, 0.0], 'a2': [0.6180339887498949, 0.0], 'a3': [0.0, 0.0], 'a4': [-0.6180339887498949, 0.0], 'a5': [-1.618033988749895, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [-1.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.03942613599800719, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[79, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [79], 'central_character': '79.78', 'coefficient_field': 'CDF', 'conductor': 79, 'conductor_radical': 79, 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.6180339887498949, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [1.618033988749895, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-0.6180339887498949, 0], [1.0, 0]], [[1.0, 0], [-0.6180339887498949, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [1.618033988749895, 0], [1.0, 0]], [[1.0, 0], [1.618033988749895, 0], [1.0, 0]], [[1.0, 0], [0, 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'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/79/1/b/a/78/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0859375', 'prec': 30}, 'plot_values': [0.5273458988906156, 0.5357743052696331, 0.5605166455003816, 0.6001568010032665, 0.6528753079868937, 0.7168724462403656, 0.790588835691737, 0.8727464716220001, 0.9622940660168984, 1.0583223207876447, 1.15998231442546, 1.2664186895048808, 1.3767192922985168, 1.489879426468376, 1.6047782663735055, 1.7201653572236113, 1.8346557198276436, 1.946732597059559, 2.054757254712134, 2.1569854823020176, 2.251590551709724, 2.336692407522415, 2.4103928035841213, 2.470815982679003, 2.516154334594449, 2.5447182742151546, 2.554989366964533, 2.545675504686199, 2.5157667119001745, 2.4645899515489242, 2.3918611124910263, 2.2977322099556754, 2.18283172676295, 2.0482959787770048, 1.8957894133865552, 1.7275118540382264, 1.546190894309081, 1.3550579265334797, 1.1578066643872529, 0.9585334843063517, 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'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.84845369197390074372926468934', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.39037048839329186211077735661', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.38007356073625378647747108423', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.03942613599800719, 'bad_primes': [79], 'central_character': '79.78', 'conductor': 79, 'conductor_radical': 79, 'degree': 2, 'index': 1, 'instance_types': ['CMF', 'Artin'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/79/1/b/a/78/2', 'ArtinRepresentation/2.79.5t2.a.b'], 'is_instance_Artin': True, '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': '2-79-79.78-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': '2-79-79.78-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.19856015712626537, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '3.84845369197390074372926468934', 'prec': 103}}
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lfunc_instances • Show schema
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id: 24596367
{'Lhash': '4878494632581260744935829779921', 'Lhash_array': ['4878494632581260744935829779921'], 'label': '2-79-79.78-c0-0-1', 'type': 'Artin', 'url': 'ArtinRepresentation/2.79.5t2.a.b'}
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id: 19806119
{'Lhash': '4878494632581260744935829779921', 'Lhash_array': ['4878494632581260744935829779921'], 'label': '2-79-79.78-c0-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/79/1/b/a/78/2'}