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lfunc_lfunctions • Show schema
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{'Lhash': '243334218590420213292628594612', 'a10': [-1.2475530634860794, -7.130284410137185e-61], 'a2': [-2.382792202974367, 0.6384672465181573], 'a3': [0.0, 1.0], 'a4': [3.5380074501100807, -2.0426695537159567], 'a5': [0.48849532622445974, 0.13089192816822182], 'a6': [-0.6384672465181573, -2.382792202974367], 'a7': [-2.1517654912564472, -1.5394496648601088], 'a8': [-3.637509047767602, 3.637509047767602], 'a9': [-1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.1799159751809554, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, -1.0]]], [7, [[1.0, 0], [2.1517654912564472, 1.5394496648601088]]], [13, [[1.0, 0], [-3.5078177554282104, 0.8337952954428265]]]], 'bad_primes': [3, 7, 13], 'central_character': '273.115', 'coefficient_field': 'CDF', 'conductor': 273, 'conductor_radical': 273, 'conjugate': '2692208826833541041947289512389', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.382792202974367, 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['0.19195685194848644875743699872723', '2.07872391033040046721571175456975', '3.19576489897110192686831496764001', '5.76957283128909515569521065501575', '6.62789764660312530226573455326107', '7.931123494328153280761278706680668', '8.543193910864734479616568492546625', '9.362943785896986169834196448402362', '10.37889804489904501493044709149771', '11.18097452241988350773003183921472'], 'prelabel': '2-273-91.24-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4764538513549808, 'root_angle': 0.9040874866539067, 'root_number': '-0.9549461497949139 + 0.2967791282955558*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.452043743327', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.19195685194848644875743699873', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.07872391033040046721571175457', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.19576489897110192686831496764', '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': '91.24', 'conductor': 273, 'conductor_radical': 273, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/273/2/cg/a/115/1'], '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': '2-273-91.24-c1-0-0', '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': '2-273-91.24-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4764538513549808, 'root_angle': 0.45204374332695335, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.19195685194848644875743699873', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '243334218590420213292628594612', 'Lhash_array': ['243334218590420213292628594612'], 'label': '2-273-91.24-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/273/2/cg/a/115/1'}