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lfunc_lfunctions • Show schema
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{'Lhash': '355276435427133214155862742346', 'a10': [6.9419397148247, 0.0], 'a2': [-1.7071588369497928, 0.0], 'a3': [-2.2915540634253246, 0.0], 'a4': [0.9143912945757693, 0.0], 'a5': [-4.066370137665674, 0.0], 'a6': [3.912046769724749, 0.0], 'a7': [0.0, 0.0], 'a8': [1.8533064949345999, 0.0], 'a9': [2.251220025601117, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 47.34330335841716, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [7, 11], 'central_character': '5929.1', 'coefficient_field': 'CDF', 'conductor': 5929, 'conductor_radical': 77, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.7071588369497928, 0], [2.0, 0]], [[1.0, 0], [2.2915540634253246, 0], [3.0, 0]], [[1.0, 0], [4.066370137665674, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [3.277921586338343, 0], [13.0, 0]], [[1.0, 0], [-1.3208812116089357, 0], [17.0, 0]], [[1.0, 0], 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'2.65539441552407548975087422808780', '3.86476116663956433512775388504630', '4.58051374265721322793952865129037', '5.04476803416203751093522829507915', '6.17682517106626701057833874892251', '6.97323483967608875053764876964934', '7.42190495088887570330665855851396', '8.194504992677063267735453663546013'], 'prelabel': '2-77e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.8806470159729285, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.28026369045474265528854680866', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.16726426046661253078287733455', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.65539441552407548975087422809', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 47.34330335841716, 'bad_primes': [7, 11], 'central_character': '1.1', 'conductor': 5929, 'conductor_radical': 77, 'degree': 2, 'index': 17, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5929/2/a/bt/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': '2-77e2-1.1-c1-0-17', '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': '2-77e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.8806470159729285, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.28026369045474265528854680866', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '355276435427133214155862742346', 'Lhash_array': ['355276435427133214155862742346'], 'label': '2-77e2-1.1-c1-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5929/2/a/bt/1/2'}