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lfunc_lfunctions • Show schema
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{'Lhash': '2161097974066447673157711897863', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [-0.8090169943749475, -0.5877852522924731], 'a5': [0.19098300562505258, 0.5877852522924731], 'a6': [0.0, 0.0], 'a7': [-0.5, -0.36327126400268045], 'a8': [0.0, 0.0], 'a9': [0.30901699437494745, -0.9510565162951535], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.1473504640432726, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[11, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [0.8090169943749475, -0.5877852522924731]]]], 'bad_primes': [11, 19], 'central_character': '2299.493', 'coefficient_field': 'CDF', 'conductor': 2299, 'conductor_radical': 209, 'conjugate': '505333822072155682963431443200', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [0.8090169943749475, 0.5877852522924731]], [[1.0, 0], [0, 0], [-0.30901699437494745, 0.9510565162951535]], [[1.0, 0], [-0.19098300562505258, -0.5877852522924731], [-0.8090169943749475, 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[-1.0, 0]], [[1.0, 0], [0, 0], [0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [1.618033988749895, 1.1755705045849463], [0.30901699437494745, 0.9510565162951535]], [[1.0, 0], [0, 0], [0.8090169943749475, 0.5877852522924731]], [[1.0, 0], [-0.19098300562505258, -0.5877852522924731], [-0.8090169943749475, 0.5877852522924731]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [0.8090169943749475, 0.5877852522924731]], [[1.0, 0], [-0.19098300562505258, 0.5877852522924731], [-0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [0, 0], [-0.30901699437494745, -0.9510565162951535]], [[1.0, 0], [0, 0], [-0.30901699437494745, 0.9510565162951535]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-0.30901699437494745, 0.9510565162951535]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-2299-209.75-c0-0-1', 'leading_term': '0.58545312510191780423741237271307', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': 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'root_analytic_conductor': 1.0711444646000243, 'root_angle': 0.706998265656443, 'root_number': '-0.60542857085040205891344369882397 + 0.79589964543153284054081454014307*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.3534991328282215', 'prec': 60}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.70480570409335260650239137396', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.80613237758966114862270844949', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.05922477513710240919244475444', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.1473504640432726, 'bad_primes': [11, 19], 'central_character': '209.75', 'conductor': 2299, 'conductor_radical': 209, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2299/1/m/b/493/1'], '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': '2-2299-209.75-c0-0-1', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-2299-209.75-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0711444646000243, 'root_angle': 0.3534991328282215, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.70480570409335260650239137396', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2161097974066447673157711897863', 'Lhash_array': ['2161097974066447673157711897863'], 'label': '2-2299-209.75-c0-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2299/1/m/b/493/1'}