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lfunc_lfunctions • Show schema
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{'Lhash': '3038139803605406683930880867879', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.8651900058217911, -1.1908318817854626], 'a4': [0.0, 0.0], 'a5': [0.10766584719974404, -2.2334744380329856], 'a6': [0.0, 0.0], 'a7': [0.0, -3.2608556170799923], 'a8': [0.0, 0.0], 'a9': [0.2575241586220471, 0.7925778634159829], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.194016080851217, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-0.10766584719974404, 2.2334744380329856]]]], 'bad_primes': [2, 5], 'central_character': '400.129', 'coefficient_field': 'CDF', 'conductor': 400, 'conductor_radical': 10, 'conjugate': '1293239485437882952845046218878', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.8651900058217911, 1.1908318817854626], [-0.9270509831248422, -2.853169548885461]], [[1.0, 0], [-0.10766584719974404, 2.2334744380329856]], [[1.0, 0], [0, 3.2608556170799923], [-7.0, 0]], 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'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.48818165847184404110438957205', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.194016080851217, 'bad_primes': [2, 5], 'central_character': '25.4', 'conductor': 400, 'conductor_radical': 10, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/400/2/y/c/129/2'], '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': '2-20e2-25.4-c1-0-12', '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': '2-20e2-25.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7871810431098514, 'root_angle': 0.2753324317629009, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.39666971566014814266682902032', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3038139803605406683930880867879', 'Lhash_array': ['3038139803605406683930880867879'], 'label': '2-20e2-25.4-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/400/2/y/c/129/2'}