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lfunc_lfunctions • Show schema
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{'Lhash': '1586850976533876585693418481222', 'a10': [2.1213203435596424, -0.7071067811865476], 'a2': [1.0, 0], 'a3': [0, 0], 'a4': [1.0, 0], 'a5': [2.1213203435596424, -0.7071067811865476], 'a6': [0, 0], 'a7': [1.0, 1.0], 'a8': [1.0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12.217111509255904, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-2.1213203435596424, 0.7071067811865476]]], [17, [[1.0, 0], [-2.1213203435596424, -3.5355339059327378]]]], 'bad_primes': [2, 3, 5, 17], 'central_character': '1530.829', 'coefficient_field': 'CDF', 'conductor': 1530, 'conductor_radical': 510, 'conjugate': '1919276827121631836067604454591', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.1213203435596424, 0.7071067811865476]], [[1.0, 0], [-1.0, -1.0], [0, 7.0]], [[1.0, 0], [-1.5857864376269049, 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'prec': 70}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.25180469779936044579153673938', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.47418789283766730793330171467', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.32187677505830848092071676884', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 12.217111509255904, 'bad_primes': [2, 3, 5, 17], 'central_character': '85.64', 'conductor': 1530, 'conductor_radical': 510, 'degree': 2, 'index': 24, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1530/2/n/o/829/2'], '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': '2-1530-85.64-c1-0-24', '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': '2-1530-85.64-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.4952984864322967, 'root_angle': -0.03171340858044103, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.25180469779936044579153673938', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1586850976533876585693418481222', 'Lhash_array': ['1586850976533876585693418481222'], 'label': '2-1530-85.64-c1-0-24', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1530/2/n/o/829/2'}