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lfunc_lfunctions • Show schema
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{'Lhash': '1700526255225765363039757668526', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, -1.866778495931408], 'a4': [0, 0], 'a5': [0, -1.4848619528719296], 'a6': [0, 0], 'a7': [2.552476845561595, 0], 'a8': [0, 0], 'a9': [-0.48486195287192946, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 13.287106896341061, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [0, -1.0]]]], 'bad_primes': [2, 13], 'central_character': '1664.833', 'coefficient_field': 'CDF', 'conductor': 1664, 'conductor_radical': 26, 'conjugate': '1247070403978066007114297027371', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 1.866778495931408], [-3.0, 0]], [[1.0, 0], [0, 1.4848619528719296], [-5.0, 0]], [[1.0, 0], [-2.552476845561595, 0], [7.0, 0]], [[1.0, 0], [0, -1.5908282167468129], [-11.0, 0]], [[1.0, 0], [0, -1.0]], [[1.0, 0], [-4.764908886657219, 0], [17.0, 0]], [[1.0, 0], [0, 3.5141254743763772], 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'4.60119900219469503302451664650510', '5.33324247883696388052487346532507', '6.18336561209684263026230328774012', '7.34073904029902780441761124043893', '7.984838690239413391764291525552103', '8.838997379425023881722561023638763', '9.733088762417380577911701743556419'], 'prelabel': '2-1664-8.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.645148405256096, 'root_angle': 0.25, 'root_number': '0.e-56 + 1.00000000000000000000000000000000000000000000000000000000*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.34147868104949462142268910606', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.87912147039192400376989343315', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.64211030024093452397676517727', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 13.287106896341061, 'bad_primes': [2, 13], 'central_character': '8.5', 'conductor': 1664, 'conductor_radical': 26, 'degree': 2, 'index': 33, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1664/2/b/k/833/3'], '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': '2-1664-8.5-c1-0-33', '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': '2-1664-8.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.645148405256096, 'root_angle': 0.25, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.34147868104949462142268910606', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1700526255225765363039757668526', 'Lhash_array': ['1700526255225765363039757668526'], 'factors': ['2-1664-8.5-c1-0-33'], 'label': '2-1664-8.5-c1-0-33', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1664/2/b/k/833/3'}