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lfunc_lfunctions • Show schema
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{'Lhash': '1591680867468431803118618780824', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [2.23606797749979, 0], 'a6': [0, 0], 'a7': [0, -7.745966692414834], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 58.85573710182414, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-2.23606797749979, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '2160.271', 'coefficient_field': 'CDF', 'conductor': 2160, 'conductor_radical': 30, 'conjugate': '687637507573318933588872252816', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.23606797749979, 0]], [[1.0, 0], [0, 7.745966692414834], [-49.0, 0]], [[1.0, 0], [0, -6.928203230275509], [-121.0, 0]], [[1.0, 0], [-22.0, 0], [169.0, 0]], [[1.0, 0], [6.708203932499369, 0], [289.0, 0]], [[1.0, 0], [0, 27.110883423451916], [-361.0, 0]], [[1.0, 0], [0, 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'5.72279026492969566119567566356602', '6.48531317644886442151920960883945', '7.75258800922781567141771680335253', '8.344773695375295859534147041635529', '9.175919213427991534650467254370995'], 'prelabel': '2-2160-4.3-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.671749285646928, 'root_angle': 0.5, 'root_number': '0.e-55 + 1.0000000000000000000000000000000000000000000000000000000*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.25561480993411243329743980707', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.16377751141339772657054805243', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.34257168041660878304482728432', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 58.85573710182414, 'bad_primes': [2, 3, 5], 'central_character': '4.3', 'conductor': 2160, 'conductor_radical': 30, 'degree': 2, 'index': 54, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2160/3/e/b/271/3'], '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': '2-2160-4.3-c2-0-54', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-2160-4.3-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.671749285646928, 'root_angle': 0.25, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.25561480993411243329743980707', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1591680867468431803118618780824', 'Lhash_array': ['1591680867468431803118618780824'], 'label': '2-2160-4.3-c2-0-54', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2160/3/e/b/271/3'}