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lfunc_lfunctions • Show schema
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{'Lhash': '1129010754303016680506252331584', 'a10': [0, 0], 'a2': [0, 0], 'a3': [1.5, 0.8660254037844386], 'a4': [0, 0], 'a5': [-3.207498429345325, 5.5555502448234755], 'a6': [0, 0], 'a7': [2.262812161679746, 0], 'a8': [0, 0], 'a9': [1.5, 2.598076211353316], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 24.85020010965908, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-1.5, -0.8660254037844386]]], [19, [[1.0, 0], [-18.931710389246245, 1.609453863180257]]]], 'bad_primes': [2, 3, 19], 'central_character': '912.673', 'coefficient_field': 'CDF', 'conductor': 912, 'conductor_radical': 114, 'conjugate': '1632307853691187530201548828040', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.5, -0.8660254037844386]], [[1.0, 0], [3.207498429345325, -5.5555502448234755], [-12.5, -21.650635094610966]], [[1.0, 0], [-2.262812161679746, 0], [49.0, 0]], [[1.0, 0], [-20.092805879061046, 0], 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'8.082492633407446799615856543719476', '8.966274626985197829699296530550440', '9.324679897063740506479284661686814'], 'prelabel': '2-912-19.8-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.984997503475712, 'root_angle': -0.3914891993338812, 'root_number': '0.33433235830182619386319960861719061007517441033977362362 - 0.9424552372353497138308194003650492476192352996681879378*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.1957445996669406', 'prec': 64}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.890632445643735087952025284014', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.77726468133607707783078230001', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.62529796242779277247770814157', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 24.85020010965908, 'bad_primes': [2, 3, 19], 'central_character': '19.8', 'conductor': 912, 'conductor_radical': 114, 'degree': 2, 'index': 23, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/912/3/be/f/673/1'], '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': '2-912-19.8-c2-0-23', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-912-19.8-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.984997503475712, 'root_angle': -0.1957445996669406, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.890632445643735087952025284014', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1129010754303016680506252331584', 'Lhash_array': ['1129010754303016680506252331584'], 'label': '2-912-19.8-c2-0-23', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/912/3/be/f/673/1'}