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lfunc_lfunctions • Show schema
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{'Lhash': '1293316977904865774947530631086', 'a10': [-3.9008474675123503, 2.2521553354359254], 'a2': [1.611969751906433, 1.611969751906433], 'a3': [-1.3718640952141605, -1.057349944087686], 'a4': [0.0, 3.196892962122575], 'a5': [-0.5113905301655199, 1.908535441087305], 'a6': [-0.506987298162406, -3.9158195522610217], 'a7': [-1.4801767688923704, 2.192960723048031], 'a8': [-1.929355251211283, 1.929355251211283], 'a9': [0.7640221914755352, 2.9010808487411928], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.1799159751809554, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.3718640952141605, 1.057349944087686]]], [7, [[1.0, 0], [1.4801767688923704, -2.192960723048031]]], [13, [[1.0, 0], [3.190486211417923, -1.6795230676451303]]]], 'bad_primes': [3, 7, 13], 'central_character': '273.32', 'coefficient_field': 'CDF', 'conductor': 273, 'conductor_radical': 273, 'conjugate': '3445347752957037377687853445234', 'degree': 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['1.02024720192773573938503038812624', '3.30446453932887491782196649325184', '4.16922333776625917085480904306607', '5.06676959926116452347541367754180', '5.95831006967552392768353267777705', '7.47828311541927808522292870971478', '9.190121008691176149259620341855843', '10.17839690342584031790243241327911', '10.67957319390527955854638885167258', '11.83046729529394586506339798310726'], 'prelabel': '2-273-273.32-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4764538513549808, 'root_angle': -0.7237698601247712, 'root_number': '-0.6465045421844491 - 0.7629101368672957*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.361884930062', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.02024720192773573938503038813', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.30446453932887491782196649325', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.16922333776625917085480904307', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.1799159751809554, 'bad_primes': [3, 7, 13], 'central_character': '273.32', 'conductor': 273, 'conductor_radical': 273, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/273/2/bv/b/32/29'], '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': '2-273-273.32-c1-0-6', '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': '2-273-273.32-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4764538513549808, 'root_angle': -0.3618849300623856, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.02024720192773573938503038813', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1293316977904865774947530631086', 'Lhash_array': ['1293316977904865774947530631086'], 'label': '2-273-273.32-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/273/2/bv/b/32/29'}