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lfunc_lfunctions • Show schema
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{'Lhash': '2922317044442329399049443855831', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.766044443118978, -0.6427876096865394], 'a4': [0.0, 0.0], 'a5': [0.43485849790796843, -0.15827554935621213], 'a6': [0.0, 0.0], 'a7': [-2.1205443386133798, -3.6728905341809153], 'a8': [0.0, 0.0], 'a9': [0.17364817766693036, 0.984807753012208], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.8205891660851936, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0.766044443118978, 0.6427876096865394]]], [19, [[1.0, 0], [-4.319768406383582, 0.582752876621173]]]], 'bad_primes': [2, 3, 19], 'central_character': '228.169', 'coefficient_field': 'CDF', 'conductor': 228, 'conductor_radical': 114, 'conjugate': '1074046940369774508639015772154', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.766044443118978, 0.6427876096865394]], [[1.0, 0], [-0.43485849790796843, 0.15827554935621213], 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'data': '3.90153711537805315508191602774', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.39427100140721612453571451956', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.8205891660851936, 'bad_primes': [2, 3, 19], 'central_character': '19.17', 'conductor': 228, 'conductor_radical': 114, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/228/2/q/b/169/2'], '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': '2-228-19.17-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': '2-228-19.17-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3492920981333856, 'root_angle': 0.2589515692101397, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.30530166902156775601991626276', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2922317044442329399049443855831', 'Lhash_array': ['2922317044442329399049443855831'], 'label': '2-228-19.17-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/228/2/q/b/169/2'}