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lfunc_lfunctions • Show schema
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{'Lhash': '779309712338693957235302788888', 'a10': [-1.6308736248428115, -0.941585326317258], 'a2': [0.5, 0.8660254037844386], 'a3': [0.35133250673633715, 1.6960440647902877], 'a4': [-0.5, 0.8660254037844386], 'a5': [-1.6308736248428115, 0.941585326317258], 'a6': [-1.293150992678041, 1.1522849084040792], 'a7': [-1.7674472637509016, 1.9687890110063726], 'a8': [-1.0, 0.0], 'a9': [-2.753130939420723, 1.1917508256361167], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.6890885733831555, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.5, -0.8660254037844386]]], [3, [[1.0, 0], [-0.35133250673633715, -1.6960440647902877]]], [7, [[1.0, 0], [1.7674472637509016, -1.9687890110063726]]], [11, [[1.0, 0], [-3.1883928338076184, 0.9133187490269896]]]], 'bad_primes': [2, 3, 7, 11], 'central_character': '462.263', 'coefficient_field': 'CDF', 'conductor': 462, 'conductor_radical': 462, 'conjugate': 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'3.68041723136911799633643618972192', '4.32118712008935817694627817209666', '6.05814079914068797511898383365526', '6.77625182683402190448439504183267', '7.84243137508065928049711754032868', '8.746163600968273718338040647915779', '9.695181521562543389410323142105634', '10.77712912503988625901714986703357'], 'prelabel': '2-462-231.32-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9207000217064496, 'root_angle': 0.9325493939185605, 'root_number': '-0.9776325860702745 + 0.21032005765867284*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.466274696959', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.61476696512302842812154184859', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.11311513309918695704391027991', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.68041723136911799633643618972', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.6890885733831555, 'bad_primes': [2, 3, 7, 11], 'central_character': '231.32', 'conductor': 462, 'conductor_radical': 462, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/462/2/n/f/263/8'], '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': '2-462-231.32-c1-0-9', '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': '2-462-231.32-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9207000217064496, 'root_angle': 0.46627469695928025, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.61476696512302842812154184859', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '779309712338693957235302788888', 'Lhash_array': ['779309712338693957235302788888'], 'label': '2-462-231.32-c1-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/462/2/n/f/263/8'}