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lfunc_lfunctions • Show schema
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{'Lhash': '1070193266951357114220290330765', 'a10': [0.0, 0.0], 'a2': [-0.33642769802418476, 2.339906036414278], 'a3': [1.1064634105929603, 2.422816914322424], 'a4': [-3.442990716021128, -1.01095328916464], 'a5': [0.0, 0.0], 'a6': [-6.041408861123432, 1.7739176962984453], 'a7': [2.96780258052457, 1.9072909064426147], 'a8': [1.559797699176447, -3.41548054125048], 'a9': [-2.681198319509971, 3.094267809464227], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.591398116223624, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [23, [[1.0, 0], [-1.3506607873874972, 4.601707882668541]]]], 'bad_primes': [5, 23], 'central_character': '575.376', 'coefficient_field': 'CDF', 'conductor': 575, 'conductor_radical': 115, 'conjugate': '3309368690388142312390673877175', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.33642769802418476, -2.339906036414278], [-1.9189859472289947, -0.5634651136828593]], [[1.0, 0], 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[-58.28260532113037, 67.26171211752899]], [[1.0, 0], [6.128789175157684, 7.072999754508726], [-13.804539312508659, 96.01267986245047]], [[1.0, 0], [-11.5966149388269, 13.383207069338384], [-14.373798665601798, -99.9719656299742]], [[1.0, 0], [-0.28309615818678524, -1.9689770292912412], [-98.82777628229323, 29.01845335466726]], [[1.0, 0], [6.093359925618939, -13.342597099467], [-70.07009853214551, -80.86520445590564]], [[1.0, 0], [12.989641331155156, -3.8141028285943457], [91.69663507859875, -58.929849102660135]], [[1.0, 0], [-0.3061964954274067, 2.1296434038792516], [-108.4227060184382, -31.835778923081556]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 4, 'label': '2-575-23.8-c1-0-4', '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/575/2/k/g/376/1', 'plot_delta': {'__RealLiteral__': 0, 'data': 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'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.335039310608', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.844233629328679510170402021081', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.94943137639509041542173193550', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.64824714742357195903013269595', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.591398116223624, 'bad_primes': [5, 23], 'central_character': '23.8', 'conductor': 575, 'conductor_radical': 115, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/575/2/k/g/376/1'], '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': '2-575-23.8-c1-0-4', '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': '2-575-23.8-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.142754796103284, 'root_angle': 0.33503931060766806, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.844233629328679510170402021081', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1070193266951357114220290330765', 'Lhash_array': ['1070193266951357114220290330765'], 'label': '2-575-23.8-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/575/2/k/g/376/1'}