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lfunc_lfunctions • Show schema
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{'Lhash': '776252090182410084667755558451', 'a10': [-0.010950660845953841, 0.0], 'a2': [2.0086359345703553, 0.0], 'a3': [0.0, 0.0], 'a4': [2.0346183176473245, 0.0], 'a5': [-0.005451789773091047, 0.0], 'a6': [0.0, 0.0], 'a7': [-3.8278050641675376, 0.0], 'a8': [0.06953559682078687, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 78.26137902105694, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 11], 'central_character': '9801.1', 'coefficient_field': 'CDF', 'conductor': 9801, 'conductor_radical': 33, 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.0086359345703553, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.005451789773091047, 0], [5.0, 0]], [[1.0, 0], [3.8278050641675376, 0], [7.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [3.53346562988113, 0], [13.0, 0]], [[1.0, 0], [-4.573603696308888, 0], [17.0, 0]], [[1.0, 0], [0.6849594912628001, 0], 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'3.46271465507936385334118354088463', '4.16819531086776355371712058783807', '4.87182221798370994104410934358429', '5.66656580022969438495892228942238', '6.10562686464962916000696424536082', '6.73917283072953506281251873856770', '7.41472411830774317881141043516395'], 'prelabel': '2-99e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.846546163393764, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.61235492654099851037797466561', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.21339351800525989277827704523', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.89709498096031253542130712250', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 78.26137902105694, 'bad_primes': [3, 11], 'central_character': '1.1', 'conductor': 9801, 'conductor_radical': 33, 'degree': 2, 'index': 102, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/9801/2/a/cp/1/16'], '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': '2-99e2-1.1-c1-0-102', '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': '2-99e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.846546163393764, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.61235492654099851037797466561', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '776252090182410084667755558451', 'Lhash_array': ['776252090182410084667755558451'], 'label': '2-99e2-1.1-c1-0-102', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9801/2/a/cp/1/16'}