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lfunc_lfunctions • Show schema
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{'Lhash': '2414143532692237320525474388748', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, -1.0], 'a4': [0.0, 0.0], 'a5': [-0.9510565162951535, 0.30901699437494745], 'a6': [0.0, 0.0], 'a7': [-0.8090169943749475, 0.5877852522924731], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.5729266345026868, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0.8090169943749475, -0.5877852522924731]]], [41, [[1.0, 0], [-0.5877852522924731, -0.8090169943749475]]]], 'bad_primes': [2, 7, 41], 'central_character': '1148.461', 'coefficient_field': 'CDF', 'conductor': 1148, 'conductor_radical': 574, 'conjugate': '758258300345256141152028766926', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 1.0], [-1.0, 0]], [[1.0, 0], [0.9510565162951535, -0.30901699437494745], [0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [0.8090169943749475, 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'4.10348167578830668093049217838275', '4.65868719871566091936155129186765', '6.23514291079322435324272678731218', '6.95637059966711643524627930869631', '7.79963092455547717220290001972111', '8.938047867320451287952247662703580', '9.436354644017556041890509318584454', '10.26849904451374893204166795003163'], 'prelabel': '2-1148-287.174-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.756919173031498, 'root_angle': 0.6898912817230763, 'root_number': '-0.56180085690990748910154258512465 + 0.82727250478623647452797849601411*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.3449456408615382', 'prec': 60}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.90442345253304963982786053466', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.76989916261071248229868798099', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.10348167578830668093049217838', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.5729266345026868, 'bad_primes': [2, 7, 41], 'central_character': '287.174', 'conductor': 1148, 'conductor_radical': 574, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1148/1/bc/a/461/1'], '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': '2-1148-287.174-c0-0-1', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-1148-287.174-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.756919173031498, 'root_angle': 0.34494564086153817, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.90442345253304963982786053466', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2414143532692237320525474388748', 'Lhash_array': ['2414143532692237320525474388748'], 'label': '2-1148-287.174-c0-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1148/1/bc/a/461/1'}