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lfunc_lfunctions • Show schema
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{'Lhash': '494236184047780067392586272409', 'a10': [-1.7192935194692556, -0.6218593465067874], 'a2': [0.24837563436218082, 1.3922318572188987], 'a3': [-1.648444199056123, 0.5316311903925667], 'a4': [-1.8766190885103686, 0.6915929414319623], 'a5': [-0.6464015057345192, 1.119600250021212], 'a6': [-1.1495872532069586, -2.162972294613151], 'a7': [-2.4274187002655716, -1.0524440382276876], 'a8': [-1.4289641818542422, -2.440914043340657], 'a9': [2.4347365548035653, -1.7527287036798553], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.341486753957511, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.24837563436218082, -1.3922318572188987]]], [3, [[1.0, 0], [1.648444199056123, -0.5316311903925667]]], [7, [[1.0, 0], [2.4274187002655716, 1.0524440382276876]]]], 'bad_primes': [2, 3, 7], 'central_character': '168.107', 'coefficient_field': 'CDF', 'conductor': 168, 'conductor_radical': 42, 'conjugate': 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'4.44164623139874484561473699599442', '5.45921869468200133511657284401476', '6.66697376052375133375587455034543', '8.321146753444575451317294328158353', '9.420873809649680975923662322830157', '10.49960689166485962972974380800106', '11.32423951604989180362821353116354', '12.23456972348416349873068801163498'], 'prelabel': '2-168-168.107-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1582256921505028, 'root_angle': 0.8421574712394251, 'root_number': '-0.8795518026142686 + 0.475803138407042*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.42107873562', 'prec': 44}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.38988360354091037854047983105', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.66155589498659644139504503803', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.44164623139874484561473699599', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.341486753957511, 'bad_primes': [2, 3, 7], 'central_character': '168.107', 'conductor': 168, 'conductor_radical': 42, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/168/2/v/a/107/16'], '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': '2-168-168.107-c1-0-1', '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': '2-168-168.107-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1582256921505028, 'root_angle': 0.42107873561971254, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.38988360354091037854047983105', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '494236184047780067392586272409', 'Lhash_array': ['494236184047780067392586272409'], 'label': '2-168-168.107-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/168/2/v/a/107/16'}