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lfunc_lfunctions • Show schema
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{'Lhash': '1203309530192957618229631834655', 'a10': [0, 0], 'a2': [0, 0], 'a3': [1.1861406616345072, 1.2621688994810694], 'a4': [0, 0], 'a5': [1.0, 0], 'a6': [0, 0], 'a7': [2.0, 1.7320508075688772], 'a8': [0, 0], 'a9': [-0.18614066163450715, 2.9942197070499468], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 13.414867539575111, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-1.1861406616345072, -1.2621688994810694]]], [5, [[1.0, 0], [-1.0, 0]]], [7, [[1.0, 0], [-2.0, -1.7320508075688772]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '1680.881', 'coefficient_field': 'CDF', 'conductor': 1680, 'conductor_radical': 210, 'conjugate': '2234338228637805189491488295648', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.1861406616345072, -1.2621688994810694]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-2.0, -1.7320508075688772]], [[1.0, 0], [0, -2.5243377989621387], [-11.0, 0]], 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['0.949243845249086983080356334853635', '1.82793391029484546896910992865675', '3.19302991078330830961033496168881', '3.74834876046584214026066090216674', '5.31345107649271014879651025619210', '5.81164826170481572392949368662197', '6.94008390048820087339990649830356', '7.81067295396792885960194970918559', '8.076724171709400873716758310573804', '9.019158213140981548216300047335708'], 'prelabel': '2-1680-21.20-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.6626312317205936, 'root_angle': -0.2564665290830798, 'root_number': '-0.04061922246901388271760629706677245521077794760504346738 - 0.99917469882198916583153057489423817220288583163998252530*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.2564665290830798', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.949243845249086983080356334854', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.82793391029484546896910992866', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.19302991078330830961033496169', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 13.414867539575111, 'bad_primes': [2, 3, 5, 7], 'central_character': '21.20', 'conductor': 1680, 'conductor_radical': 210, 'degree': 2, 'index': 30, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1680/2/f/g/881/4'], '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': '2-1680-21.20-c1-0-30', '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': '2-1680-21.20-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.6626312317205936, 'root_angle': -0.2564665290830798, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.949243845249086983080356334854', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1203309530192957618229631834655', 'Lhash_array': ['1203309530192957618229631834655'], 'factors': ['2-1680-21.20-c1-0-30'], 'label': '2-1680-21.20-c1-0-30', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1680/2/f/g/881/4'}