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lfunc_lfunctions • Show schema
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{'Lhash': '3392543407420992464072200301818', 'a10': [-0.5248272489843956, -0.30300915347919155], 'a2': [0.25881904510252074, 0.9659258262890683], 'a3': [1.4586457657319003, -0.9339981424566101], 'a4': [-0.8660254037844386, 0.5], 'a5': [-0.42851965437346334, 0.42851965437346334], 'a6': [1.2796982317344217, 1.1672071091694887], 'a7': [-0.73517984784166, -0.19699084652080848], 'a8': [-0.7071067811865476, -0.7071067811865476], 'a9': [1.255294939775204, -2.724744871391589], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.6228331357659873, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.25881904510252074, -0.9659258262890683]]], [3, [[1.0, 0], [-1.4586457657319003, 0.9339981424566101]]], [13, [[1.0, 0], [-0.6012052516260986, -3.55507415470018]]]], 'bad_primes': [2, 3, 13], 'central_character': '78.59', 'coefficient_field': 'CDF', 'conductor': 78, 'conductor_radical': 78, 'conjugate': 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['2.67624486337969997461794688460644', '4.06253920901433811902486824668516', '5.59933010440160890229430976756883', '7.889213641449688999845529884395463', '8.744644352014627120117458838396351', '10.19540028388725989548926704064352', '10.71920235471392624735159681339984', '12.44620051228390867603081973909763', '13.22984654472457049492835356662627', '14.22766218476589071952346534602325'], 'prelabel': '2-78-39.20-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7891977798790284, 'root_angle': -0.1594913268525917, 'root_number': '0.8770754242680342 - 0.4803526830830111*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0797456634263', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.67624486337969997461794688461', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.06253920901433811902486824669', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.59933010440160890229430976757', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.6228331357659873, 'bad_primes': [2, 3, 13], 'central_character': '39.20', 'conductor': 78, 'conductor_radical': 78, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/78/2/k/a/59/4'], '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': '2-78-39.20-c1-0-2', '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': '2-78-39.20-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7891977798790284, 'root_angle': -0.07974566342629585, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.67624486337969997461794688461', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3392543407420992464072200301818', 'Lhash_array': ['3392543407420992464072200301818'], 'label': '2-78-39.20-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/78/2/k/a/59/4'}