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lfunc_lfunctions • Show schema
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{'Lhash': '575824960402578104347275600550', 'a10': [0.41337246649661635, 0.0], 'a2': [-1.5051249495529495, 0.0], 'a3': [-2.1576878821384535, 0.0], 'a4': [0.26540111376676895, 0.0], 'a5': [-0.27464328899696716, 0.0], 'a6': [3.2475898647546506, 0.0], 'a7': [-3.1064001722924828, 0.0], 'a8': [2.6107880611363945, 0.0], 'a9': [1.6556169967271255, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 64.06397754167328, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[71, [[1.0, 0], [-1.0, 0]]], [113, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [71, 113], 'central_character': '8023.1', 'coefficient_field': 'CDF', 'conductor': 8023, 'conductor_radical': 8023, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.5051249495529495, 0], [2.0, 0]], [[1.0, 0], [2.1576878821384535, 0], [3.0, 0]], [[1.0, 0], [0.27464328899696716, 0], [5.0, 0]], [[1.0, 0], [3.1064001722924828, 0], [7.0, 0]], [[1.0, 0], [0.5462888445754707, 0], [11.0, 0]], [[1.0, 0], 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'2.51894301932025143967823651759087', '3.55674573088554096141145338511247', '4.35679052809601592305613024830687', '5.20383351947842222685968376514690', '6.06467961136581130549528390259265', '6.22430370373296534148867827867821', '7.39850550674577987477776315338469', '7.69200959126467396120444696405059'], 'prelabel': '2-8023-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.003997597555442, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.45424579951203104182828716283', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.17392476391832507589123958778', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.51894301932025143967823651759', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 64.06397754167328, 'bad_primes': [71, 113], 'central_character': '1.1', 'conductor': 8023, 'conductor_radical': 8023, 'degree': 2, 'index': 110, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8023/2/a/d/1/40'], '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': '2-8023-1.1-c1-0-110', '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': '2-8023-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.003997597555442, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.45424579951203104182828716283', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '575824960402578104347275600550', 'Lhash_array': ['575824960402578104347275600550'], 'label': '2-8023-1.1-c1-0-110', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8023/2/a/d/1/40'}