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lfunc_lfunctions • Show schema
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{'Lhash': '3141123612922254550134106375419', 'a10': [-0.5495771722840682, -0.9518955850760404], 'a2': [0.766044443118978, -0.6427876096865394], 'a3': [0.6544373609013495, -1.603655742563371], 'a4': [0.17364817766693036, -0.984807753012208], 'a5': [0.19086614890894615, -1.0824557202877527], 'a6': [-0.5294819378344735, -1.6491357971698544], 'a7': [2.536722298327327, 0.7516914135261383], 'a8': [-0.5, -0.8660254037844386], 'a9': [-2.1434234813129533, -2.098984463914933], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.0183451964044, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.766044443118978, 0.6427876096865394]]], [3, [[1.0, 0], [-0.6544373609013495, 1.603655742563371]]], [7, [[1.0, 0], [-2.536722298327327, -0.7516914135261383]]]], 'bad_primes': [2, 3, 7], 'central_character': '378.67', 'coefficient_field': 'CDF', 'conductor': 378, 'conductor_radical': 42, 'conjugate': '1761616127368857280933799748607', 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'0.287231638979', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.47790961670094481977251814800', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.72054977239115800660680733252', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.73417004050267003611386373403', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.0183451964044, 'bad_primes': [2, 3, 7], 'central_character': '189.67', 'conductor': 378, 'conductor_radical': 42, 'degree': 2, 'index': 19, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/378/2/v/b/67/8'], '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': '2-378-189.67-c1-0-19', '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': '2-378-189.67-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.737338538225754, 'root_angle': 0.28723163897857196, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.47790961670094481977251814800', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3141123612922254550134106375419', 'Lhash_array': ['3141123612922254550134106375419'], 'label': '2-378-189.67-c1-0-19', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/378/2/v/b/67/8'}