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lfunc_lfunctions • Show schema
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{'Lhash': '1678321014101832033634187196873', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.708716959448667, 0.0], 'a4': [0.0, 0.0], 'a5': [3.668162619581909, 0.0], 'a6': [0.0, 0.0], 'a7': [1.0, 0.0], 'a8': [0.0, 0.0], 'a9': [-0.08028635249250185, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 57.23676816885381, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 7], 'central_character': '7168.1', 'coefficient_field': 'CDF', 'conductor': 7168, 'conductor_radical': 14, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.708716959448667, 0], [3.0, 0]], [[1.0, 0], [-3.668162619581909, 0], [5.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-1.527755610941458, 0], [11.0, 0]], [[1.0, 0], [4.213394717342056, 0], [13.0, 0]], [[1.0, 0], [7.187565325602756, 0], [17.0, 0]], [[1.0, 0], [3.192697873999128, 0], [19.0, 0]], [[1.0, 0], [-3.496777050801725, 0], 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'5.58463571182856550391044609949360', '6.09351996145136952264712803789550', '6.75074892218278893208934061981910', '7.20327312201593458675745256066700'], 'prelabel': '2-7168-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.565498540668275, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.32396183443581773759774440585', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.23008932478638475160697870623', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.80212961564441690164004595245', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 57.23676816885381, 'bad_primes': [2, 7], 'central_character': '1.1', 'conductor': 7168, 'conductor_radical': 14, 'degree': 2, 'index': 148, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/7168/2/a/bd/1/3'], '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': '2-7168-1.1-c1-0-148', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-7168-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.565498540668275, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.32396183443581773759774440585', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1678321014101832033634187196873', 'Lhash_array': ['1678321014101832033634187196873'], 'label': '2-7168-1.1-c1-0-148', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7168/2/a/bd/1/3'}