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lfunc_lfunctions • Show schema
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{'Lhash': '96835608403505366446335850502', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0.5553121645811667, 4.9690671559024215], 'a6': [0, 0], 'a7': [3.2346930702214136, 3.2346930702214136], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 44.1418028263681, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-0.5553121645811667, -4.9690671559024215]]]], 'bad_primes': [2, 3, 5], 'central_character': '1620.1297', 'coefficient_field': 'CDF', 'conductor': 1620, 'conductor_radical': 30, 'conjugate': '2511875781359271869580039421620', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.5553121645811667, -4.9690671559024215]], [[1.0, 0], [-3.2346930702214136, -3.2346930702214136], [0, 49.0]], [[1.0, 0], [6.140543516530305, 0], [121.0, 0]], [[1.0, 0], [16.32636770896051, -16.32636770896051], [0, 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{'__RealLiteral__': 0, 'data': '0.39418322723608984', 'prec': 64}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.07638982570281666118861500844', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.23819092823455484381387624938', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.46059526996956512157716477106', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 44.1418028263681, 'bad_primes': [2, 3, 5], 'central_character': '5.2', 'conductor': 1620, 'conductor_radical': 30, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1620/3/l/f/1297/7'], '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': '2-1620-5.2-c2-0-5', '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': '2-1620-5.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.643929772835358, 'root_angle': 0.39418322723608984, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.07638982570281666118861500844', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '96835608403505366446335850502', 'Lhash_array': ['96835608403505366446335850502'], 'label': '2-1620-5.2-c2-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1620/3/l/f/1297/7'}