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lfunc_lfunctions • Show schema
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{'Lhash': '1389770425710126389211481008192', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, 11.98301511285953], 'a6': [0, 0], 'a7': [26.46242100385972, -15.278085889987617], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 27.61289388268662, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [-33.975192978711, 32.290652858982995]]]], 'bad_primes': [2, 3, 13], 'central_character': '468.433', 'coefficient_field': 'CDF', 'conductor': 468, 'conductor_radical': 78, 'conjugate': '1388867016591995277824969499112', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -11.98301511285953], [-125.0, 0]], [[1.0, 0], [-26.46242100385972, 15.278085889987617], [171.5, -297.04671349806245]], [[1.0, 0], [-36.83580715192059, -21.267163174978496], [665.5, 1152.6798124370878]], [[1.0, 0], [-33.975192978711, 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'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/468/4/t/g/433/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [2.505731380980396, 2.4814495287959257, 2.4369926647890643, 2.3728739372808247, 2.289757954605675, 2.1884663796662633, 2.0699851755187537, 1.935472851605947, 1.7862689490302568, 1.6239019205106346, 1.4500955090443737, 1.2667727103336621, 1.076056418259193, 0.8802658997313655, 0.6819083240369067, 0.48366468064627827, 0.2883695561891832, 0.09898440335203848, -0.08143588119137976, -0.24978304945099214, -0.4029420267530311, -0.5378434007850581, -0.6515211729043547, -0.7411748347934048, -0.804234604707862, -0.8384284412743824, -0.8418492561114517, -0.8130205768114112, -0.7509587764885417, -0.655229892498415, -0.5259990120181655, -0.3640702122265652, -0.17091511314378388, 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'prelabel': '2-468-13.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.2547972256488285, 'root_angle': -0.07932524181267801, 'root_number': '0.96910816115740190753274037432770452804278580362570351954 - 0.24663611247771306996017420065382328460552141688131280640*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.039662620906339006', 'prec': 70}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.09633555607508124195177276802', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.04873330578836904690069129941', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.96203553646849543080974516559', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 27.61289388268662, 'bad_primes': [2, 3, 13], 'central_character': '13.4', 'conductor': 468, 'conductor_radical': 78, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/468/4/t/g/433/4'], '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': '2-468-13.4-c3-0-9', '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': '2-468-13.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.2547972256488285, 'root_angle': -0.039662620906339006, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.09633555607508124195177276802', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1389770425710126389211481008192', 'Lhash_array': ['1389770425710126389211481008192'], 'label': '2-468-13.4-c3-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/468/4/t/g/433/4'}