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lfunc_lfunctions • Show schema
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{'Lhash': '1901279766806738405441082101623', 'a10': [5.679105794090689, 0.0], 'a2': [-2.116622652562781, 0.0], 'a3': [0.0, 0.0], 'a4': [2.4800914533419043, 0.0], 'a5': [-2.6830978999560906, 0.0], 'a6': [0.0, 0.0], 'a7': [0.972332743843107, 0.0], 'a8': [-1.0161724454452623, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.821094307351343, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]]], 'bad_primes': [3], 'central_character': '729.1', 'coefficient_field': 'CDF', 'conductor': 729, 'conductor_radical': 3, 'conjugate': '1901279766806738405441082101623', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.116622652562781, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.6830978999560906, 0], [5.0, 0]], [[1.0, 0], [-0.972332743843107, 0], [7.0, 0]], [[1.0, 0], [0.31690210004390923, 0], [11.0, 0]], [[1.0, 0], [1.5140303673064404, 0], [13.0, 0]], [[1.0, 0], [-1.1746841640096257, 0], [17.0, 0]], 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'7.14388856231166287824695764268767', '7.51735644548264790221693832422984', '8.190764938875812809500694971431052', '9.139227218070714036981462880338732', '9.739283871366419286669688923612745'], 'prelabel': '2-3e6-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.49984527792155789246925648260', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.11748094666312729388666379753', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.35960612079513948442785350673', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.821094307351343, 'bad_primes': [3], 'central_character': '1.1', 'conductor': 729, 'conductor_radical': 3, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/729/2/a/a/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': '2-3e6-1.1-c1-0-13', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-3e6-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.49984527792155789246925648260', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1901279766806738405441082101623', 'Lhash_array': ['1901279766806738405441082101623'], 'label': '2-3e6-1.1-c1-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/729/2/a/a/1/2'}