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lfunc_lfunctions • Show schema
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{'Lhash': '1613697366498305624002604343923', 'a10': [1682.7930565142594, -349.28566080137904], 'a2': [2.299300413479937, 11.077599812620557], 'a3': [17.51807002481427, 43.36031852518733], 'a4': [-117.42643521714199, 50.94145965904744], 'a5': [0.0, -151.90953681113092], 'a6': [-440.0489507183569, 293.75656753794135], 'a7': [0.0, 893.2778784832404], 'a8': [-834.3077550219311, -1183.6733375007925], 'a9': [-1573.2344452114075, 1519.1781924449663], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.748620305809463, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-2.299300413479937, -11.077599812620557]]], [3, [[1.0, 0], [-17.51807002481427, -43.36031852518733]]]], 'bad_primes': [2, 3], 'central_character': '12.11', 'coefficient_field': 'CDF', 'conductor': 12, 'conductor_radical': 6, 'conjugate': '5156920014341960789740966163119', 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.299300413479937, -11.077599812620557]], [[1.0, 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'-0.7126537802002595 - 0.7015159225322546*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.376253462331', 'prec': 50}, 'spectral_label': 'c7-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.27298276528861622387522654202', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.58888682966595410436067759997', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.73010153761778223638224265107', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.748620305809463, 'bad_primes': [2, 3], 'central_character': '12.11', 'conductor': 12, 'conductor_radical': 6, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/12/8/b/b/11/6'], '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': '2-12-12.11-c7-0-3', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [7], 'order_of_vanishing': 0, 'prelabel': '2-12-12.11-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.936135404823088, 'root_angle': -0.3762534623312828, 'self_dual': False, 'spectral_label': 'c7-0', 'z1': {'__RealLiteral__': 0, 'data': '1.27298276528861622387522654202', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1613697366498305624002604343923', 'Lhash_array': ['1613697366498305624002604343923'], 'label': '2-12-12.11-c7-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/12/8/b/b/11/6'}