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lfunc_lfunctions • Show schema
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{'Lhash': '3059865762639319412518322393791', 'a10': [5.765326183070573, 4.519774821618191], 'a2': [1.5739785212526385, 1.2339333914905446], 'a3': [0.0, -2.901178658551247], 'a4': [0.9548167707292845, 3.8843693097250807], 'a5': [3.6629001636453613, 0.0], 'a6': [3.579861221466129, -4.566392894876205], 'a7': [0.0, -1.9341432241700853], 'a8': [-3.2901919072911565, 7.292094158278251], 'a9': [0.5831623911667869, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.0708500091382565, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.5739785212526385, -1.2339333914905446]]], [19, [[1.0, 0], [0, -4.358898943540674]]]], 'bad_primes': [2, 19], 'central_character': '76.39', 'coefficient_field': 'CDF', 'conductor': 76, 'conductor_radical': 38, 'conjugate': '2948489699955926172508559153133', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.5739785212526385, -1.2339333914905446]], [[1.0, 0], [0, 2.901178658551247], [-9.0, 0]], 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'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.27969707186342805859828050863', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.0708500091382565, 'bad_primes': [2, 19], 'central_character': '4.3', 'conductor': 76, 'conductor_radical': 38, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/76/3/b/b/39/12'], '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': '2-76-4.3-c2-0-11', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-76-4.3-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4390448252706574, 'root_angle': -0.03836131496590584, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '2.41380847537043515686172382039', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3059865762639319412518322393791', 'Lhash_array': ['3059865762639319412518322393791'], 'label': '2-76-4.3-c2-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/76/3/b/b/39/12'}