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lfunc_lfunctions • Show schema
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{'Lhash': '460674624634709180122013554864', 'a10': [1.7840876035471578, 5.132096318199093], 'a2': [0.12716965639136776, -2.426541596135118], 'a3': [-1.7867492350008398, 1.4468810018270737], 'a4': [-3.882888205530721, -0.40810799546442117], 'a5': [-2.0707641188306547, 0.8437629786637368], 'a6': [3.28369664931845, 4.519620700433686], 'a7': [1.5435242441731487, 2.1488445517649035], 'a8': [-0.7238452419997403, 4.570178993066183], 'a9': [0.4752731228746919, -2.235984244102129], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.3973820353724073, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [2.0707641188306547, -0.8437629786637368]]], [7, [[1.0, 0], [-1.5435242441731487, -2.1488445517649035]]]], 'bad_primes': [5, 7], 'central_character': '175.47', 'coefficient_field': 'CDF', 'conductor': 175, 'conductor_radical': 35, 'conjugate': '2934318204440958051476831915646', 'degree': 2, 'euler_factors': [[[1.0, 0], 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1.182109146979418, 'root_angle': -0.1587941495402016, 'root_number': '0.5422084740601315 - 0.840243994716644*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.15879414954', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.36340820140168650874074706712', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.37129012089105161335243993595', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.17744361668805963372606631015', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.3973820353724073, 'bad_primes': [5, 7], 'central_character': '175.47', 'conductor': 175, 'conductor_radical': 35, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/175/2/x/a/47/18'], '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': '2-175-175.47-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': '2-175-175.47-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.182109146979418, 'root_angle': -0.1587941495402016, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.36340820140168650874074706712', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '460674624634709180122013554864', 'Lhash_array': ['460674624634709180122013554864'], 'factors': ['2-175-175.47-c1-0-0'], 'label': '2-175-175.47-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/175/2/x/a/47/18'}