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lfunc_lfunctions • Show schema
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{'Lhash': '1482673137793865092277804673956', 'a10': [0.0, 0.0], 'a2': [-0.28173255684142967, -0.9594929736144974], 'a3': [0.0, 0.0], 'a4': [-0.8412535328311812, 0.5406408174555976], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-0.9096319953545183, 0.41541501300188644], 'a8': [0.7557495743542583, 0.6548607339452851], 'a9': [-0.9898214418809327, 0.14231483827328514], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.2855914725426143, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.28173255684142967, 0.9594929736144974]]], [7, [[1.0, 0], [0.9096319953545183, -0.41541501300188644]]], [23, [[1.0, 0], [-0.14231483827328514, 0.9898214418809327]]]], 'bad_primes': [2, 7, 23], 'central_character': '2576.1973', 'coefficient_field': 'CDF', 'conductor': 2576, 'conductor_radical': 322, 'conjugate': '668868519228685275232158109716', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.28173255684142967, 0.9594929736144974]], [[1.0, 0], 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'2.96851105867166623542024249908436', '3.72615866546180190519368919506097', '4.82669084821997006152285764606102', '5.69072058647138228473408342143301', '6.23720964551223297787356331054112', '7.13118902209111350922904069386221', '7.60167379053668554539954273618046', '8.713566715573049521797453197598828', '9.091889191687614540561938924538048'], 'prelabel': '2-2576-2576.1973-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1338392622160403, 'root_angle': 0.6631108950956655, 'root_number': '-0.49029482058798299821983382484007 + 0.87155664698549431870924511912718*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.3315554475478327', 'prec': 60}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.16962287362694638716147223229', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.96851105867166623542024249908', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.72615866546180190519368919506', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.2855914725426143, 'bad_primes': [2, 7, 23], 'central_character': '2576.1973', 'conductor': 2576, 'conductor_radical': 322, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2576/1/cq/b/1973/1'], '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': '2-2576-2576.1973-c0-0-0', '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': '2-2576-2576.1973-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1338392622160403, 'root_angle': 0.3315554475478327, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.16962287362694638716147223229', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1482673137793865092277804673956', 'Lhash_array': ['1482673137793865092277804673956'], 'label': '2-2576-2576.1973-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2576/1/cq/b/1973/1'}