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lfunc_lfunctions • Show schema
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{'Lhash': '929264423479493899906702787928', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': -1, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': -3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 48.549044428938494, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1, 1]], [19, [1, -1]]], 'bad_primes': [2, 5, 19], 'central_character': '6080.1', 'coefficient_field': '1.1.1.1', 'conductor': 6080, 'conductor_radical': 190, 'degree': 2, 'euler_factors': [[1], [1, 0, 3], [1, 1], [1, 0, 7], [1, -4, 11], [1, -6, 13], [1, 6, 17], [1, -1], [1, -8, 23], [1, -2, 29], [1, 0, 31], [1, 2, 37], [1, -2, 41], [1, 4, 43], [1, 8, 47], [1, -6, 53], [1, -4, 59], [1, -2, 61], [1, 8, 67], [1, -8, 71], [1, -2, 73], [1, 8, 79], [1, 4, 83], [1, 14, 89], [1, -14, 97], [1, -10, 101], [1, -4, 103], [1, -8, 107], [1, -10, 109], [1, -14, 113]], 'euler_factors_factorization': [[1], [[[1, 0, 3], 1]], [[[1, 1], 1]], [[[1, 0, 7], 1]], [[[1, -4, 11], 1]], [[[1, -6, 13], 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4.44429009568169, 4.356870496649549, 4.120141790478608, 3.7424587087082695, 3.2404450959009856, 2.6381400539273723, 1.965656387705472, 1.2574308105415344, 0.5501732041638543, -0.11935657530531445, -0.7166027978700505, -1.2113533873594895, -1.5796249860189362, -1.8051685466694587, -1.8804937666702548, -1.8073410202652014], 'positive_zeros': ['0.73306037429571521476047301200332', '1.74333899521904856200754209636775', '2.99493262394815734872603724908686', '3.56590809209375136513349937193929', '4.38056019148119516932547433378373', '5.15968148471021796410147652194533', '6.15600151629972809033939840964645', '6.55197436637470088547502867201433', '7.24716202687168129413635330491380', '8.361435156468919491742708969881487'], 'prelabel': '2-6080-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.967714433653154, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'trace_hash': 1939237719846461352, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.73306037429571521476047301200', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.74333899521904856200754209637', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.99493262394815734872603724909', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 48.549044428938494, 'bad_primes': [2, 5, 19], 'central_character': '1.1', 'conductor': 6080, 'conductor_radical': 190, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, -1, 0, 0, 0, -3, 0, 4, 0, 6, 0, 0, 0, -6, 0, 1, 0, 0, 0, 8, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, -4, 0, 3, 0, -8, 0, -7, 0, 0, 0, 6, 0, -4, 0, 0, 0, 4, 0, 2, 0, 0, 0, -6, 0, -8, 0, 0, 0, 8, 0, 2, 0, 0, 0, 0, 0, -8, 0, 9, 0, -4, 0, 6, 0, 0, 0, -14, 0, 0, 0, 0, 0, -1, 0, 14, 0, -12, 0], 'euler11': [1, -4, 11], 'euler13': [1, -6, 13], 'euler17': [1, 6, 17], 'euler19': [1, -1, 0], 'euler2': [1, 0, 0], 'euler23': [1, -8, 23], 'euler29': [1, -2, 29], 'euler3': [1, 0, 3], 'euler31': [1, 0, 31], 'euler37': [1, 2, 37], 'euler41': [1, -2, 41], 'euler43': [1, 4, 43], 'euler47': [1, 8, 47], 'euler5': [1, 1, 0], 'euler53': [1, -6, 53], 'euler59': [1, -4, 59], 'euler61': [1, -2, 61], 'euler67': [1, 8, 67], 'euler7': [1, 0, 7], 'euler71': [1, -8, 71], 'euler73': [1, -2, 73], 'euler79': [1, 8, 79], 'euler83': [1, 4, 83], 'euler89': [1, 14, 89], 'euler97': [1, -14, 97], 'euler_factors': [[1, 0, 0], [1, 0, 3], [1, 1, 0], [1, 0, 7], [1, -4, 11], [1, -6, 13], [1, 6, 17], [1, -1, 0], [1, -8, 23], [1, -2, 29], [1, 0, 31], [1, 2, 37], [1, -2, 41], [1, 4, 43], [1, 8, 47], [1, -6, 53], [1, -4, 59], [1, -2, 61], [1, 8, 67], [1, -8, 71], [1, -2, 73], [1, 8, 79], [1, 4, 83], [1, 14, 89], [1, -14, 97]], 'index': 41, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/6080/k', 'ModularForm/GL2/Q/holomorphic/6080/2/a/k/1/1', 'ModularForm/GL2/Q/holomorphic/6080/2/a/k'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-6080-1.1-c1-0-41', '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': '2-6080-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.967714433653154, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1939237719846461352, 'z1': {'__RealLiteral__': 0, 'data': '0.73306037429571521476047301200', 'prec': 103}}
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lfunc_instances • Show schema
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id: 21671554
{'Lhash': '929264423479493899906702787928', 'Lhash_array': ['929264423479493899906702787928'], 'label': '2-6080-1.1-c1-0-41', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6080/2/a/k'}
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id: 24573376
{'Lhash': '929264423479493899906702787928', 'Lhash_array': ['929264423479493899906702787928'], 'label': '2-6080-1.1-c1-0-41', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6080/2/a/k/1/1'}
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id: 90787
{'Lhash': '1939237719846461352', 'Lhash_array': ['1939237719846461352'], 'label': '2-6080-1.1-c1-0-41', 'type': 'ECQ', 'url': 'EllipticCurve/Q/6080/k'}