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lfunc_lfunctions • Show schema
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{'Lhash': '3550297606067986915946297574415', 'a10': [-1.256837919885295, 0.6483505557477411], 'a2': [0.06693090810734477, -1.412628844934127], 'a3': [-0.6652046229071775, -1.1521682043049273], 'a4': [-1.9910405070798523, -0.1890970628201413], 'a5': [-0.5, -0.8660254037844386], 'a6': [-1.672108789105478, 0.8625715738956702], 'a7': [0.0, -4.688775268227308], 'a8': [-0.400386114649415, 2.799944813598287], 'a9': [0.6150056193258395, -1.0652209796127179], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.034315276808656, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.06693090810734477, 1.412628844934127]]], [5, [[1.0, 0], [0.5, 0.8660254037844386]]], [19, [[1.0, 0], [-2.3092355601271124, -3.69694889440528]]]], 'bad_primes': [2, 5, 19], 'central_character': '380.31', 'coefficient_field': 'CDF', 'conductor': 380, 'conductor_radical': 190, 'conjugate': '704602207797366745885738491164', 'degree': 2, 'euler_factors': 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'9.181473348131196759590112588503115', '9.725912340529727991414380874324086', '11.10369161902910444052855015851241', '11.79089264593863200772732670379436'], 'prelabel': '2-380-76.31-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7419286084132886, 'root_angle': -0.7830894436784768, 'root_number': '-0.7766635468768706 - 0.629915657015*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.391544721839', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.80069098332678333370757891664', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.26504941032878113883645450611', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.49215707295782530397184123671', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.034315276808656, 'bad_primes': [2, 5, 19], 'central_character': '76.31', 'conductor': 380, 'conductor_radical': 190, 'degree': 2, 'index': 37, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/380/2/n/b/31/10'], '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': '2-380-76.31-c1-0-37', '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': '2-380-76.31-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7419286084132886, 'root_angle': -0.3915447218392384, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.80069098332678333370757891664', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3550297606067986915946297574415', 'Lhash_array': ['3550297606067986915946297574415'], 'label': '2-380-76.31-c1-0-37', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/380/2/n/b/31/10'}