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lfunc_lfunctions • Show schema
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{'Lhash': '564582679956248635931502969029', 'a10': [-0.7186593181879662, 0.0], 'a2': [-2.0664364402805306, 0.0], 'a3': [0.0, 0.0], 'a4': [2.270159561719271, 0.0], 'a5': [0.3477771220925644, 0.0], 'a6': [0.0, 0.0], 'a7': [-4.336596001999802, 0.0], 'a8': [-0.5582675630269189, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 20.769089565735037, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [17, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 17], 'central_character': '2601.1', 'coefficient_field': 'CDF', 'conductor': 2601, 'conductor_radical': 51, 'degree': 2, 'euler_factors': [[[1.0, 0], [2.0664364402805306, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.3477771220925644, 0], [5.0, 0]], [[1.0, 0], [4.336596001999802, 0], [7.0, 0]], [[1.0, 0], [-0.7298404382807289, 0], [11.0, 0]], [[1.0, 0], [5.403032442280333, 0], [13.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-3.270159561719271, 0], [19.0, 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'5.09365283102548073813281347184943', '6.10351376711060952553768321756110', '6.91592510037403480418945239184013', '7.36071441113987177309172233652079', '8.229692734629061248121743965666902', '9.104541357510620443318767628896416'], 'prelabel': '2-51e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.5573116599301216, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.44537720398239109674726359902', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.92897111751193044753882890818', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.85903743046351064886108439926', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 20.769089565735037, 'bad_primes': [3, 17], 'central_character': '1.1', 'conductor': 2601, 'conductor_radical': 51, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2601/2/a/bf/1/1'], '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': '2-51e2-1.1-c1-0-5', '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': '2-51e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.5573116599301216, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.44537720398239109674726359902', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '564582679956248635931502969029', 'Lhash_array': ['564582679956248635931502969029'], 'label': '2-51e2-1.1-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2601/2/a/bf/1/1'}