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lfunc_lfunctions • Show schema
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{'Lhash': '672973482171887287609432667893', 'a10': [-1.6154408755455913, 3.278273671959763e-61], 'a2': [1.3990128365342578, -0.8077204377727957], 'a3': [0.051700073546916456, 1.7312790365493493], 'a4': [0.3048246111917534, -0.5279717139815455], 'a5': [-0.8660254037844386, -0.5], 'a6': [1.4707185278504058, 2.3803223897170014], 'a7': [-1.6732846962682104, 0.9660713698213325], 'a8': [0.0, 2.2460294775082814], 'a9': [-2.994654204790487, 0.17901450703967206], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.671248518244905, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-0.051700073546916456, -1.7312790365493493]]], [5, [[1.0, 0], [0.8660254037844386, 0.5]]], [13, [[1.0, 0], [3.4614125172815466, 1.009268737852623]]]], 'bad_primes': [3, 5, 13], 'central_character': '585.571', 'coefficient_field': 'CDF', 'conductor': 585, 'conductor_radical': 195, 'conjugate': '3468645204140394814229462810228', 'degree': 2, 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'5.18092208216606617840517697792203', '5.74988021603274173428372453582731', '6.75798882294860241288839868907219', '7.56859141409228438825235812969568', '8.109118823786590453456706502651913', '9.663088045147536455903074418070951', '10.42502888957468319159601688165503'], 'prelabel': '2-585-117.103-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.161307131863703, 'root_angle': -0.6509193365415835, 'root_number': '-0.45656199070948444 - 0.8896916031071624*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.325459668271', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.53088247033585145555059887691', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.77279042822773551257342839866', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.60362405435991557243311088786', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.671248518244905, 'bad_primes': [3, 5, 13], 'central_character': '117.103', 'conductor': 585, 'conductor_radical': 195, 'degree': 2, 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/585/2/bt/b/571/42'], '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': '2-585-117.103-c1-0-10', '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': '2-585-117.103-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.161307131863703, 'root_angle': -0.32545966827079176, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.53088247033585145555059887691', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '672973482171887287609432667893', 'Lhash_array': ['672973482171887287609432667893'], 'label': '2-585-117.103-c1-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/585/2/bt/b/571/42'}