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lfunc_lfunctions • Show schema
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{'Lhash': '1954180035808118855839889102485', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.06910414199911483, 0.11969188495592122], 'a4': [0.0, 0.0], 'a5': [5.042885839705121, 8.734534491138911], 'a6': [0.0, 0.0], 'a7': [18.490449235117133, -1.0503747348238415], 'a8': [0.0, 0.0], 'a9': [13.490449235117133, 23.366143492151572], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.304106960321476, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-18.490449235117133, 1.0503747348238415]]]], 'bad_primes': [2, 7], 'central_character': '56.25', 'coefficient_field': 'CDF', 'conductor': 56, 'conductor_radical': 14, 'conjugate': '2699065569742933057854605629132', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.06910414199911483, -0.11969188495592122], [-13.5, -23.382685902179844]], [[1.0, 0], [-5.042885839705121, -8.734534491138911], [-62.5, 108.25317547305482]], [[1.0, 0], 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[1442897.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 2, 'label': '2-56-7.4-c3-0-2', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/56/4/i/a/25/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.594357910369431, 1.5448064261957852, 1.484783559875197, 1.4135398117478382, 1.3300139916544682, 1.2329260292329813, 1.1208883788236712, 0.9925320442140189, 0.8466431064660567, 0.6823055274458244, 0.49904576239600135, 0.29697425384047305, 0.07691819191407531, -0.159460910033133, -0.4095721260690869, -0.6698305150611344, -0.9356313803687342, -1.2013716563780414, -1.460525950480239, -1.7057833031931329, -1.9292484715370375, -2.122708482676022, -2.2779613993828622, -2.3871998088681887, -2.4434366891226342, -2.440956294118331, -2.375767872270301, 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'12.39468794052016522420268386440520', '13.51337710466603223866923623237157', '14.69092306143577218847992898088828'], 'prelabel': '2-56-7.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8177202645955939, 'root_angle': -0.08227816031327918, 'root_number': '0.8693212703566676 - 0.49424743692352074*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0822781603133', 'prec': 54}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.54157623201242190477892817692', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.23553283031908743570103503564', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.66533613846618373688366137702', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.304106960321476, 'bad_primes': [2, 7], 'central_character': '7.4', 'conductor': 56, 'conductor_radical': 14, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/56/4/i/a/25/2'], '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': '2-56-7.4-c3-0-2', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-56-7.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8177202645955939, 'root_angle': -0.08227816031327918, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.54157623201242190477892817692', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1954180035808118855839889102485', 'Lhash_array': ['1954180035808118855839889102485'], 'factors': ['2-56-7.4-c3-0-2'], 'label': '2-56-7.4-c3-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/56/4/i/a/25/2'}