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lfunc_lfunctions • Show schema
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{'Lhash': '1591088822190709381476923225026', 'a10': [0, 0], 'a2': [0, 0], 'a3': [2.8701233705371205, -0.8731505241919281], 'a4': [0, 0], 'a5': [0, 2.23606797749979], 'a6': [0, 0], 'a7': [11.204336392247576, 0], 'a8': [0, 0], 'a9': [7.475216324206722, -5.0120994509599806], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 13.079052689294253, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-2.8701233705371205, 0.8731505241919281]]], [5, [[1.0, 0], [0, -2.23606797749979]]]], 'bad_primes': [2, 3, 5], 'central_character': '480.161', 'coefficient_field': 'CDF', 'conductor': 480, 'conductor_radical': 30, 'conjugate': '2094380091595466826700468794491', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-2.8701233705371205, 0.8731505241919281]], [[1.0, 0], [0, -2.23606797749979]], [[1.0, 0], [-11.204336392247576, 0], [49.0, 0]], [[1.0, 0], [0, -16.746135121772163], [-121.0, 0]], [[1.0, 0], 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2.512100282763094, 2.5544666855969975], 'positive_zeros': ['1.25514776856039649842666534453824', '2.57908886954554429102594569290808', '3.95319593536240268373253858959563', '4.83218901593088655823803981275109', '5.88821533146490051500545705915178', '7.50073308224829852352093821845239', '8.189673336352973977684088915898979', '8.757742557125473595892506892904959', '9.649548465865145241473825505030446', '10.97192350899440957678457017346734'], 'prelabel': '2-480-3.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.6164972956293293, 'root_angle': -0.09400466061207478, 'root_number': '0.95670779017904017592507451931130101849429362998114648974 - 0.29105017473064268529371740543994650741265829691516244029*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.047002330306037385', 'prec': 70}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.25514776856039649842666534454', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.57908886954554429102594569291', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.95319593536240268373253858960', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 13.079052689294253, 'bad_primes': [2, 3, 5], 'central_character': '3.2', 'conductor': 480, 'conductor_radical': 30, 'degree': 2, 'index': 17, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/480/3/l/a/161/15'], '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': '2-480-3.2-c2-0-17', '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': '2-480-3.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.6164972956293293, 'root_angle': -0.04700233030603739, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.25514776856039649842666534454', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1591088822190709381476923225026', 'Lhash_array': ['1591088822190709381476923225026'], 'label': '2-480-3.2-c2-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/480/3/l/a/161/15'}