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lfunc_lfunctions • Show schema
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{'Lhash': '664987134130298107454676920100', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-2.696392779347098, 0.0], 'a4': [0.0, 0.0], 'a5': [-1.4258587588319314, 0.0], 'a6': [0.0, 0.0], 'a7': [-1.0, 0.0], 'a8': [0.0, 0.0], 'a9': [4.270534020515166, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 67.96866220051389, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [1.0, 0]]], [19, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 7, 19], 'central_character': '8512.1', 'coefficient_field': 'CDF', 'conductor': 8512, 'conductor_radical': 266, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [2.696392779347098, 0], [3.0, 0]], [[1.0, 0], [1.4258587588319314, 0], [5.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-3.270534020515166, 0], [11.0, 0]], [[1.0, 0], [3.4258587588319314, 0], [13.0, 0]], [[1.0, 0], [-5.270534020515166, 0], [17.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], 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'4.35055237876135894059879165029875', '5.07091069185580242922509838650524', '5.83736391754173069462216679332845', '6.21304288510182901975075719129959', '7.19181693558475457057465620794751', '7.40802127238230014619776955461638'], 'prelabel': '2-8512-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.244310899069363, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.52458235259035336005619217026', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.34979862011024683108000362082', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.71557733646255377679495739498', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 67.96866220051389, 'bad_primes': [2, 7, 19], 'central_character': '1.1', 'conductor': 8512, 'conductor_radical': 266, 'degree': 2, 'index': 33, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8512/2/a/bn/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': '2-8512-1.1-c1-0-33', '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': '2-8512-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.244310899069363, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.52458235259035336005619217026', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '664987134130298107454676920100', 'Lhash_array': ['664987134130298107454676920100'], 'label': '2-8512-1.1-c1-0-33', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8512/2/a/bn/1/1'}