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  • lfunc_lfunctions • Show schema
    {'Lhash': '1888301824734977131906495405648', 'a10': [-7.652059480071777e-61, -4.243584254084118], 'a2': [-1.4797772133375875, -1.7635298102341186], 'a3': [0.0, 0.0], 'a4': [-0.5730004351373696, 3.249646950427601], 'a5': [1.4120756274374286, 1.1848721381771727], 'a6': [0.0, 0.0], 'a7': [-2.4003955890926796, -1.1126998768151315], 'a8': [2.591365364492614, -1.4961254907584833], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.5275177946066, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [2.4003955890926796, 1.1126998768151315]]]], 'bad_primes': [3, 7], 'central_character': '567.341', 'coefficient_field': 'CDF', 'conductor': 567, 'conductor_radical': 21, 'conjugate': '618530155757346138283017694411', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.4797772133375875, 1.7635298102341186], [-0.3472963553338607, 1.969615506024416]], [[1.0, 0], [0, 0]], [[1.0, 0], 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2.237620739975506, 3.8898162838850885, 4.579658912167938, 4.238106844302117], 'positive_zeros': ['1.48960748679092244087700108475320', '3.40020005391166519608166647682032', '5.20640736123708223159730725175545', '5.89059599764090986309515186579372', '6.66030293194985778362842869420614', '7.61824113463846483490418599779153', '8.613900959155349691235376599067560', '9.175529114045224138962747959936057', '9.905376757304395376151448886369606', '10.59599834401036032558171436093557'], 'prelabel': '2-567-189.131-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.1277964645629526, 'root_angle': 0.44729420935032493, 'root_number': '-0.9456657361081996 + 0.3251404551127666*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.44729420935', 'prec': 44}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.48960748679092244087700108475', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.40020005391166519608166647682', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.20640736123708223159730725176', 'prec': 103}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 4.5275177946066, 'bad_primes': [3, 7], 'central_character': '189.131', 'conductor': 567, 'conductor_radical': 21, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/567/2/ba/a/341/3'], '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': '2-567-189.131-c1-0-11', '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': '2-567-189.131-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.1277964645629526, 'root_angle': 0.44729420935032493, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.48960748679092244087700108475', 'prec': 103}}
  • lfunc_instances • Show schema
    {'Lhash': '1888301824734977131906495405648', 'Lhash_array': ['1888301824734977131906495405648'], 'factors': ['2-567-189.131-c1-0-11'], 'label': '2-567-189.131-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/567/2/ba/a/341/3'}