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lfunc_lfunctions • Show schema
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{'Lhash': '779191587020379720028195324623', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.0, 0.0], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-1.3633282379326837, 0.0], 'a8': [0.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 62.28331357659873, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-1.0, 0]]], [5, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '7800.1', 'coefficient_field': 'CDF', 'conductor': 7800, 'conductor_radical': 390, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.3633282379326837, 0], [7.0, 0]], [[1.0, 0], [5.646000469243412, 0], [11.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-2.1413361156553643, 0], [17.0, 0]], [[1.0, 0], [-2.414679639789997, 0], [19.0, 0]], [[1.0, 0], [2.7266564758653673, 0], [23.0, 0]], [[1.0, 0], 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0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 15, 'label': '2-7800-1.1-c1-0-15', 'leading_term': '1.76947478633114277103732155046', '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/7800/2/a/bn/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [1.7694747863311429, 1.758980726698762, 1.727481420803767, 1.6749322357113752, 1.6012808243612702, 1.5064986463766594, 1.3906221604692557, 1.2538010656651477, 1.0963506106879033, 0.9188048424141841, 0.7219677040357463, 0.5069590852802146, 0.2752532291293111, 0.02870727263816032, -0.23042188818378428, -0.49947379034540823, -0.7753946010766175, -1.0547618389008457, -1.3338237119430165, -1.608552745663966, -1.8747129548253798, -2.127939402074863, -2.363828581598662, -2.5780376769179445, -2.766390375675295, 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'4.15295630319403242015120352751332', '5.32203197887047253534596418842424', '5.47864846213836003309431401786670', '6.61487731310417875338173927364207', '7.28732819317045322710340979068050', '7.961747712010711864184296710845141'], 'prelabel': '2-7800-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.8919777987902835, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.61467378067749353879409291721', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.03533605584921324542492607317', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.67104844372336206001247091008', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 62.28331357659873, 'bad_primes': [2, 3, 5, 13], 'central_character': '1.1', 'conductor': 7800, 'conductor_radical': 390, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/7800/2/a/bn/1/2'], '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': '2-7800-1.1-c1-0-15', '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': '2-7800-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.8919777987902835, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.61467378067749353879409291721', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '779191587020379720028195324623', 'Lhash_array': ['779191587020379720028195324623'], 'label': '2-7800-1.1-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7800/2/a/bn/1/2'}