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lfunc_lfunctions • Show schema
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{'Lhash': '363473304186661327993301693393', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-3.0, 0.0], 'a4': [0.0, 0.0], 'a5': [-9.154860836431586, 0.0], 'a6': [0.0, 0.0], 'a7': [-27.417451742901967, 0.0], 'a8': [0.0, 0.0], 'a9': [9.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 45.31346688440881, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [3.0, 0]]]], 'bad_primes': [2, 3], 'central_character': '768.1', 'coefficient_field': 'CDF', 'conductor': 768, 'conductor_radical': 6, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [3.0, 0]], [[1.0, 0], [9.154860836431586, 0], [125.0, 0]], [[1.0, 0], [27.417451742901967, 0], [343.0, 0]], [[1.0, 0], [20.52518181294076, 0], [1331.0, 0]], [[1.0, 0], [-32.04713076639279, 0], [2197.0, 0]], [[1.0, 0], [111.76406850439345, 0], [4913.0, 0]], [[1.0, 0], [129.76406850439344, 0], [6859.0, 0]], [[1.0, 0], [9.165096514196067, 0], [12167.0, 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'4.29440452054830276877880971358073', '5.60809225204336433473199396236716', '6.55033827306527699334108003037120', '7.03644172193551899252486464756703', '8.329736859469994866281438536553487', '9.000151447124826008932421458527915', '10.12194775151595875939405726306399'], 'prelabel': '2-768-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.731527826905926, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.28672987976436183530655822686', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.25186256394296764612958826381', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.61032357154715816646710094597', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 45.31346688440881, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 768, 'conductor_radical': 6, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/768/4/a/r/1/1'], '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': '2-768-1.1-c3-0-0', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-768-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.731527826905926, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.28672987976436183530655822686', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '363473304186661327993301693393', 'Lhash_array': ['363473304186661327993301693393'], 'label': '2-768-1.1-c3-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/768/4/a/r/1/1'}