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lfunc_lfunctions • Show schema
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{'Lhash': '1313306632307333206073405316583', 'a10': [-2.9571750141393083, 0.0], 'a2': [2.1356258868195415, 0.0], 'a3': [-2.2096088689228846, 0.0], 'a4': [2.560897928453753, 0.0], 'a5': [-1.3846877547187115, 0.0], 'a6': [-4.718897900217759, 0.0], 'a7': [5.12150676196686, 0.0], 'a8': [1.1978681358692904, 0.0], 'a9': [1.8823713536226685, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.84418973575603, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[11, [[1.0, 0], [-1.0, 0]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [11, 13], 'central_character': '1859.1', 'coefficient_field': 'CDF', 'conductor': 1859, 'conductor_radical': 143, 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.1356258868195415, 0], [2.0, 0]], [[1.0, 0], [2.2096088689228846, 0], [3.0, 0]], [[1.0, 0], [1.3846877547187115, 0], [5.0, 0]], [[1.0, 0], [-5.12150676196686, 0], [7.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.6457998605101981, 0], 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'2.43853530358166760607933408190384', '3.83287943339158845369428986348169', '4.54806076760642776096793415343832', '5.06379690482168320467928826013437', '5.73480308809142319978637079417551', '6.46959791428397762718342950617370', '7.53556280079850727748970252350026', '8.077696835388999741381660392469361', '9.257655568233209303134402890571422'], 'prelabel': '2-1859-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8528158190803814, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.03601625879472138094505889658', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.43853530358166760607933408190', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.83287943339158845369428986348', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 14.84418973575603, 'bad_primes': [11, 13], 'central_character': '1.1', 'conductor': 1859, 'conductor_radical': 143, 'degree': 2, 'index': 49, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1859/2/a/t/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': '2-1859-1.1-c1-0-49', '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': '2-1859-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8528158190803814, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.03601625879472138094505889658', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1313306632307333206073405316583', 'Lhash_array': ['1313306632307333206073405316583'], 'label': '2-1859-1.1-c1-0-49', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1859/2/a/t/1/16'}