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lfunc_lfunctions • Show schema
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{'Lhash': '909609131258971613063821764987', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-1.2354132725370348, 1.2139827206510536], 'a4': [0, 0], 'a5': [2.22042994438347, 3.845897478319506], 'a6': [0, 0], 'a7': [-1.4548779149712618, 2.5199224675400984], 'a8': [0, 0], 'a9': [0.05249190792133202, -2.999540731445862], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.198766312851504, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [1.2354132725370348, -1.2139827206510536]]]], 'bad_primes': [2, 3], 'central_character': '1152.385', 'coefficient_field': 'CDF', 'conductor': 1152, 'conductor_radical': 6, 'conjugate': '2576216661915071418136102130164', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.2354132725370348, -1.2139827206510536]], [[1.0, 0], [-2.22042994438347, -3.845897478319506], [-2.5, 4.330127018922194]], [[1.0, 0], [1.4548779149712618, -2.5199224675400984], [-3.5, 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'1.3524891876636783310149811811005855589798322109519210870', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1152/2/i/i/385/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.3524891876636784, 1.2238686443358564, 1.0981112152641737, 0.9750551469717369, 0.8545797780985741, 0.7366624733594047, 0.621428192291125, 0.5091891786834197, 0.4004731220812353, 0.2960389791898805, 0.19688034321270276, 0.1042167635998032, 0.01947375003948577, -0.05574761996221651, -0.11971047909323713, -0.17059027522382028, -0.2065301011688444, -0.22570208247404716, -0.22637355947013, -0.20697666985465935, -0.16617978233085404, -0.10295906240998583, -0.016668282952627265, 0.09289516015619648, 0.22543018741948387, 0.38008016530118943, 0.5553914774652046, 0.7492847365095812, 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'7.87361970574066014718717187144855', '8.515772951401929823095088341166244', '9.397376027562652629000890459853133'], 'prelabel': '2-1152-9.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.032946803498456, 'root_angle': -0.938874595801059, 'root_number': '-0.98161861455033167217136505818150626854621183740793083908 - 0.19085307324821200568567835697946258756447462643709338678*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.4694372979005295', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.71755508268225049236937556151', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.29884094125154417974441817333', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.95405137057805632185617010004', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.198766312851504, 'bad_primes': [2, 3], 'central_character': '9.7', 'conductor': 1152, 'conductor_radical': 6, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1152/2/i/i/385/2'], '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': '2-1152-9.7-c1-0-11', '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': '2-1152-9.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.032946803498456, 'root_angle': -0.4694372979005295, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.71755508268225049236937556151', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '909609131258971613063821764987', 'Lhash_array': ['909609131258971613063821764987'], 'label': '2-1152-9.7-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1152/2/i/i/385/2'}