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lfunc_lfunctions • Show schema
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{'Lhash': '1968637306972775871564197097856', 'a10': [3.5251358069684127, -4.068223589475324], 'a2': [-2.183387224944393, 1.4031777675196144], 'a3': [-0.9898214418809327, -0.14231483827328514], 'a4': [1.9674419007852764, -4.308096833147603], 'a5': [-1.99005389104026, 0.5843325447845021], 'a6': [2.360856508232091, -1.0781670412556148], 'a7': [1.4916088092002717, -2.185200942777608], 'a8': [1.0106110644644128, 7.028954346194602], 'a9': [0.9594929736144974, 0.28173255684142967], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.8567744176278445, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.9898214418809327, 0.14231483827328514]]], [7, [[1.0, 0], [-1.4916088092002717, 2.185200942777608]]], [23, [[1.0, 0], [-1.5551841248034635, 4.536673047284682]]]], 'bad_primes': [3, 7, 23], 'central_character': '483.34', 'coefficient_field': 'CDF', 'conductor': 483, 'conductor_radical': 483, 'conjugate': 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'root_angle': 0.6840007057058081, 'root_number': '-0.5463962035662446 + 0.8375268286618615*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.342000352853', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.55298100803039886981923278341', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.01519025635542172754728547648', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.27832230924244765894689854067', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.8567744176278445, 'bad_primes': [3, 7, 23], 'central_character': '161.34', 'conductor': 483, 'conductor_radical': 483, 'degree': 2, 'index': 19, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/483/2/r/a/34/1'], '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': '2-483-161.34-c1-0-19', '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': '2-483-161.34-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9638672097745928, 'root_angle': 0.34200035285290403, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.55298100803039886981923278341', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1968637306972775871564197097856', 'Lhash_array': ['1968637306972775871564197097856'], 'label': '2-483-161.34-c1-0-19', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/483/2/r/a/34/1'}