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lfunc_lfunctions • Show schema
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{'Lhash': '2714228904607102572021039075461', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.778508874707938, -1.778508874707938], 'a4': [0.0, 0.0], 'a5': [-2.2330842092925938, -0.11547689902344639], 'a6': [0.0, 0.0], 'a7': [0.7071067811865476, 0.7071067811865476], 'a8': [0.0, 0.0], 'a9': [0.0, -3.326187634829792], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.471622513191703, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [2.2330842092925938, 0.11547689902344639]]], [7, [[1.0, 0], [-0.7071067811865476, -0.7071067811865476]]]], 'bad_primes': [2, 5, 7], 'central_character': '560.463', 'coefficient_field': 'CDF', 'conductor': 560, 'conductor_radical': 70, 'conjugate': '1046197468951189555374614813396', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.778508874707938, 1.778508874707938], [0, -3.0]], [[1.0, 0], [2.2330842092925938, 0.11547689902344639]], [[1.0, 0], 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['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.14114907066539423490025869211', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.53622995094193704345872111939', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.24448387907881834352339535835', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.471622513191703, 'bad_primes': [2, 5, 7], 'central_character': '20.3', 'conductor': 560, 'conductor_radical': 70, 'degree': 2, 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/560/2/x/b/463/11'], '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': '2-560-20.3-c1-0-14', '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': '2-560-20.3-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.114621127576215, 'root_angle': 0.30466029986453774, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.14114907066539423490025869211', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2714228904607102572021039075461', 'Lhash_array': ['2714228904607102572021039075461'], 'label': '2-560-20.3-c1-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/560/2/x/b/463/11'}