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lfunc_lfunctions • Show schema
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{'Lhash': '1502757793636681110817021575770', 'a10': [3.1755705045849463, 0.0], 'a2': [1.0, 0.0], 'a3': [-1.0, 0.0], 'a4': [1.0, 0.0], 'a5': [3.1755705045849463, 0.0], 'a6': [-1.0, 0.0], 'a7': [0.38196601125010515, 0.0], 'a8': [1.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 17.29559707780934, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [3, [[1.0, 0], [1.0, 0]]], [19, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 19], 'central_character': '2166.1', 'coefficient_field': 'CDF', 'conductor': 2166, 'conductor_radical': 114, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-3.1755705045849463, 0], [5.0, 0]], [[1.0, 0], [-0.38196601125010515, 0], [7.0, 0]], [[1.0, 0], [-2.6660450550905175, 0], [11.0, 0]], [[1.0, 0], [7.040294042680404, 0], [13.0, 0]], [[1.0, 0], [-4.689153033510512, 0], [17.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], 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'5.01606015799933394506368707227136', '5.87539765226068021129552459433141', '6.52821472562418635970661971261281', '7.18289590960962294788035624583000', '8.201977283420626733633363323149225', '9.387240155422170765654729871172243'], 'prelabel': '2-2166-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.158797551914416, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.18546687341616271534370964652', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.25751955565002003201830725182', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.14680610531792933908741063349', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 17.29559707780934, 'bad_primes': [2, 3, 19], 'central_character': '1.1', 'conductor': 2166, 'conductor_radical': 114, 'degree': 2, 'index': 24, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2166/2/a/x/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': '2-2166-1.1-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': '2-2166-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.158797551914416, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.18546687341616271534370964652', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1502757793636681110817021575770', 'Lhash_array': ['1502757793636681110817021575770'], 'label': '2-2166-1.1-c1-0-24', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2166/2/a/x/1/3'}