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lfunc_lfunctions • Show schema
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'8-133e4-1.1-c0e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.25763471559591755, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c0e4-0', 'trace_hash': 1146412442866144201, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.69683603271289636518353803388', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.33705050726053221832002406374', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.71044367256582579166473223063', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.9410425747961305e-05, 'bad_primes': [7, 19], 'central_character': '1.1', 'conductor': 312900721, 'conductor_radical': 133, 'degree': 8, 'dirichlet_coefficients': [1, -2, 0, 3, 0, 0, 0, -6, -1, 0, 0, 0, 0, 0, 0, 9, 0, 2, 0, 0, 0, 0, -2, 0, -1, 0, 0, 0, 2, 0, 0, -12, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, -2, 0, 0, 4, 0, 0, -2, 2, 0, 0, 2, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 18, 0, 0, -2, 0, 0, 0, 2, 6, 0, 0, 0, 0, 0, 0, -2, 0, 1, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 4, 0, -3], 'euler11': [1, 0, 4, 0, 6, 0, 4, 0, 1], 'euler13': [1, 0, 1, 0, 0, 0, 1, 0, 1], 'euler17': [1, 0, 1, 0, 0, 0, 1, 0, 1], 'euler19': [1, 0, 2, 0, 1, 0, 0, 0, 0], 'euler2': [1, 2, 1, 2, 4, 2, 1, 2, 1], 'euler23': [1, 2, 1, 2, 4, 2, 1, 2, 1], 'euler29': [1, -2, 1, -2, 4, -2, 1, -2, 1], 'euler3': [1, 0, 1, 0, 0, 0, 1, 0, 1], 'euler31': [1, 0, -4, 0, 6, 0, -4, 0, 1], 'euler37': [1, 0, 4, 0, 6, 0, 4, 0, 1], 'euler41': [1, 0, 1, 0, 0, 0, 1, 0, 1], 'euler43': [1, 2, 1, 2, 4, 2, 1, 2, 1], 'euler47': [1, 0, 1, 0, 0, 0, 1, 0, 1], 'euler5': [1, 0, 1, 0, 0, 0, 1, 0, 1], 'euler53': [1, -2, 1, -2, 4, -2, 1, -2, 1], 'euler59': [1, 0, 1, 0, 0, 0, 1, 0, 1], 'euler61': [1, 0, 1, 0, 0, 0, 1, 0, 1], 'euler67': [1, 2, 1, 2, 4, 2, 1, 2, 1], 'euler7': [1, 0, 2, 0, 1, 0, 0, 0, 0], 'euler71': [1, -2, 1, -2, 4, -2, 1, -2, 1], 'euler73': [1, 0, 1, 0, 0, 0, 1, 0, 1], 'euler79': [1, 2, 1, 2, 4, 2, 1, 2, 1], 'euler83': [1, 0, -4, 0, 6, 0, -4, 0, 1], 'euler89': [1, 0, 1, 0, 0, 0, 1, 0, 1], 'euler97': [1, 0, 1, 0, 0, 0, 1, 0, 1], 'euler_factors': [[1, 2, 1, 2, 4, 2, 1, 2, 1], [1, 0, 1, 0, 0, 0, 1, 0, 1], [1, 0, 1, 0, 0, 0, 1, 0, 1], [1, 0, 2, 0, 1, 0, 0, 0, 0], [1, 0, 4, 0, 6, 0, 4, 0, 1], [1, 0, 1, 0, 0, 0, 1, 0, 1], [1, 0, 1, 0, 0, 0, 1, 0, 1], [1, 0, 2, 0, 1, 0, 0, 0, 0], [1, 2, 1, 2, 4, 2, 1, 2, 1], [1, -2, 1, -2, 4, -2, 1, -2, 1], [1, 0, -4, 0, 6, 0, -4, 0, 1], [1, 0, 4, 0, 6, 0, 4, 0, 1], [1, 0, 1, 0, 0, 0, 1, 0, 1], [1, 2, 1, 2, 4, 2, 1, 2, 1], [1, 0, 1, 0, 0, 0, 1, 0, 1], [1, -2, 1, -2, 4, -2, 1, -2, 1], [1, 0, 1, 0, 0, 0, 1, 0, 1], [1, 0, 1, 0, 0, 0, 1, 0, 1], [1, 2, 1, 2, 4, 2, 1, 2, 1], [1, -2, 1, -2, 4, -2, 1, -2, 1], [1, 0, 1, 0, 0, 0, 1, 0, 1], [1, 2, 1, 2, 4, 2, 1, 2, 1], [1, 0, -4, 0, 6, 0, -4, 0, 1], [1, 0, 1, 0, 0, 0, 1, 0, 1], [1, 0, 1, 0, 0, 0, 1, 0, 1]], 'index': 0, 'instance_types': ['CMF', 'Artin'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/133/1/m/a', 'ArtinRepresentation/2.133.16t60.a'], 'is_instance_Artin': True, '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': '8-133e4-1.1-c0e4-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0, 0, 0, 0], 'order_of_vanishing': 0, 'prelabel': '8-133e4-1.1-c0e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.25763471559591755, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0e4-0', 'trace_hash': 1146412442866144201, 'z1': {'__RealLiteral__': 0, 'data': '1.69683603271289636518353803388', 'prec': 103}}
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lfunc_instances • Show schema
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id: 24602873
{'Lhash': '2150995215357390577246835737621,2962563478292501661412347393626,3435895548412875541479497424653,4222108554233936012882888773619', 'Lhash_array': ['2150995215357390577246835737621', '2962563478292501661412347393626', '3435895548412875541479497424653', '4222108554233936012882888773619'], 'label': '8-133e4-1.1-c0e4-0-0', 'type': 'Artin', 'url': 'ArtinRepresentation/2.133.16t60.a'}
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id: 19804696
{'Lhash': '2150995215357390577246835737621,2962563478292501661412347393626,3435895548412875541479497424653,4222108554233936012882888773619', 'Lhash_array': ['2150995215357390577246835737621', '2962563478292501661412347393626', '3435895548412875541479497424653', '4222108554233936012882888773619'], 'label': '8-133e4-1.1-c0e4-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/133/1/m/a'}