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lfunc_lfunctions • Show schema
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{'Lhash': '1054623248888850977949387550202', 'a10': [-0.9135835829431791, 0.25213304835443207], 'a2': [-0.7667356020847637, 0.5570660226503766], 'a3': [-0.2429028279916281, 0.7475780348431461], 'a4': [-0.031456064462172334, 0.09681181173955135], 'a5': [0.9362348706397372, 0.3513748240813427], 'a6': [-0.23020807642260332, -0.7085076069306289], 'a7': [0.0, 0.0], 'a8': [-0.32267902599847303, -0.9931039261072461], 'a9': [0.3091458600413377, 0.22460761467682497], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.8858403974235793, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [-0.9362348706397372, -0.3513748240813427]]], [71, [[1.0, 0], [-0.30901699437494745, 0.9510565162951535]]]], 'bad_primes': [5, 71], 'central_character': '1775.1561', 'coefficient_field': 'CDF', 'conductor': 1775, 'conductor_radical': 355, 'conjugate': '2054866869508907885914657261557', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.7667356020847637, 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['0.831951050785583415141396623239569', '1.80448509490531286870107069437910', '2.57982265425004249575707229182568', '4.17968568617973246841676421543076', '5.33081953449651350211078681772125', '5.97023470712367842808221688963962', '6.74421082065537831778671150803157', '7.74108063800905653871373548090700', '8.537870701930884385960813269278618', '9.392221631442647354571902220533366'], 'prelabel': '2-1775-1775.1561-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9411909463140725, 'root_angle': -0.8114285714285715, 'root_number': '-0.82959486057183116853900916138701 - 0.55836580062966249263567256491695*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.4057142857142857', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.831951050785583415141396623240', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.80448509490531286870107069438', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.57982265425004249575707229183', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.8858403974235793, 'bad_primes': [5, 71], 'central_character': '1775.1561', 'conductor': 1775, 'conductor_radical': 355, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1775/1/p/b/1561/3'], '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': '2-1775-1775.1561-c0-0-1', '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': '2-1775-1775.1561-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9411909463140725, 'root_angle': -0.40571428571428575, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.831951050785583415141396623240', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1054623248888850977949387550202', 'Lhash_array': ['1054623248888850977949387550202'], 'label': '2-1775-1775.1561-c0-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1775/1/p/b/1561/3'}