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lfunc_lfunctions • Show schema
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{'Lhash': '593266690163779718902392392247', 'a10': [-0.5547897216124628, 0.3203079951165929], 'a2': [-0.40439034028745, -0.40439034028745], 'a3': [0.20052373112586994, 1.720404090106554], 'a4': [0.0, -1.6729369053644008], 'a5': [0.28992003905087693, -1.0819963158702257], 'a6': [0.6146249355644106, -0.7768046552958099], 'a7': [-0.25881904510252074, 0.9659258262890683], 'a8': [-1.4853002050146438, 1.4853002050146438], 'a9': [-2.9195804665107197, 0.689963694384747], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.5397479255428665, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-0.20052373112586994, -1.720404090106554]]], [7, [[1.0, 0], [0.25881904510252074, -0.9659258262890683]]], [13, [[1.0, 0], [2.476400735466469, -2.6205799734755533]]]], 'bad_primes': [3, 7, 13], 'central_character': '819.470', 'coefficient_field': 'CDF', 'conductor': 819, 'conductor_radical': 273, 'conjugate': '2019351207669388146332956948458', 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'2.52167402484393795896668055203973', '3.11558437726163626394388610905084', '4.59096404266035273982104720864375', '5.96507080750669744630990507930819', '6.88514973703700087837677879721636', '7.37693671019273842329367734489171', '8.100831413040131546850675723076565', '8.973922980146725072595232435097403', '9.846409607472965336468443964789809'], 'prelabel': '2-819-117.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.5572930855775735, 'root_angle': -0.519105561138523, 'root_number': '-0.059985857589461705 - 0.9981992270530251*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.259552780569', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.46800489824007280955772441368', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.52167402484393795896668055204', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.11558437726163626394388610905', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.5397479255428665, 'bad_primes': [3, 7, 13], 'central_character': '117.2', 'conductor': 819, 'conductor_radical': 273, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/819/2/ew/a/470/34'], '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': '2-819-117.2-c1-0-12', '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': '2-819-117.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.5572930855775735, 'root_angle': -0.2595527805692615, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.46800489824007280955772441368', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '593266690163779718902392392247', 'Lhash_array': ['593266690163779718902392392247'], 'label': '2-819-117.2-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/819/2/ew/a/470/34'}