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lfunc_lfunctions • Show schema
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{'Lhash': '1583841740320123100574680736528', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [2.6813306436049773, 0.0], 'a4': [0.0, 0.0], 'a5': [2.9354323319700297, 0.0], 'a6': [0.0, 0.0], 'a7': [1.4272289552399249, 0.0], 'a8': [0.0, 0.0], 'a9': [4.189534020335082, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 42.41653355370416, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [83, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 83], 'central_character': '5312.1', 'coefficient_field': 'CDF', 'conductor': 5312, 'conductor_radical': 166, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-2.6813306436049773, 0], [3.0, 0]], [[1.0, 0], [-2.9354323319700297, 0], [5.0, 0]], [[1.0, 0], [-1.4272289552399249, 0], [7.0, 0]], [[1.0, 0], [0.6813306436049774, 0], [11.0, 0]], [[1.0, 0], [-3.2541016883650524, 0], [13.0, 0]], [[1.0, 0], [-4.124966352305112, 0], [17.0, 0]], [[1.0, 0], [7.633169729035217, 0], [19.0, 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'3.80015857322007611315831225414556', '4.12016787944053846864777342221643', '5.52428462396018966633493853273497', '5.88997200090046939207831160811266', '6.82816294614809845405581083772407', '7.86775064825473795844224944560318', '8.098918120259387186658883425751671'], 'prelabel': '2-5312-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.512797674863251, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.24943082899575502134535323756', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.24937978989312901191692980739', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.41023467391733472695549287926', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 42.41653355370416, 'bad_primes': [2, 83], 'central_character': '1.1', 'conductor': 5312, 'conductor_radical': 166, 'degree': 2, 'index': 107, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5312/2/a/bb/1/3'], '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': '2-5312-1.1-c1-0-107', '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': '2-5312-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.512797674863251, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.24943082899575502134535323756', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1583841740320123100574680736528', 'Lhash_array': ['1583841740320123100574680736528'], 'label': '2-5312-1.1-c1-0-107', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5312/2/a/bb/1/3'}