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lfunc_lfunctions • Show schema
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{'Lhash': '2539422544918404705542360469010', 'a10': [1.0, 0.0], 'a2': [-0.8660254037844386, -0.5], 'a3': [0.8660254037844386, -0.5], 'a4': [0.5, 0.8660254037844386], 'a5': [-0.8660254037844386, 0.5], 'a6': [-1.0, 0.0], 'a7': [-0.5, -0.8660254037844386], 'a8': [-3.9689140359382235e-80, -1.0], 'a9': [0.5, -0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.41921461061172205, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.8660254037844386, 0.5]]], [3, [[1.0, 0], [-0.8660254037844386, 0.5]]], [5, [[1.0, 0], [0.8660254037844386, -0.5]]], [7, [[1.0, 0], [0.5, 0.8660254037844386]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '840.149', 'coefficient_field': 'CDF', 'conductor': 840, 'conductor_radical': 210, 'conjugate': '989787884980282733741535033351', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.8660254037844386, 0.5]], [[1.0, 0], [-0.8660254037844386, 0.5]], [[1.0, 0], [0.8660254037844386, 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-0.023835894774862663, -0.1798699758281653, -0.33852118490777955], 'positive_zeros': ['2.00325116752297824852606799817788', '3.09985963295911593686661986388041', '4.62842248268027809634048145413819', '5.22899022101729665070302856865740', '6.72111745596697213266417962639309', '7.53749228545587394862456934963081', '8.293252034786180950949521422061292', '8.853721284362381483867225216819983', '9.734211731518223675409328245262177', '10.22590914524953154160621070650889'], 'prelabel': '2-840-840.149-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6474678452338171, 'root_angle': 0.3232468568063602, 'root_number': '-0.44414843034206066891807967048929 + 0.89595321966310477774725020770463*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.3232468568063603', 'prec': 60}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.00325116752297824852606799818', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.41921461061172205, 'bad_primes': [2, 3, 5, 7], 'central_character': '840.149', 'conductor': 840, 'conductor_radical': 210, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/840/1/cg/a/149/1'], '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': '2-840-840.149-c0-0-3', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-840-840.149-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6474678452338171, 'root_angle': 0.3232468568063602, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.00325116752297824852606799818', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2539422544918404705542360469010', 'Lhash_array': ['2539422544918404705542360469010'], 'factors': ['2-840-840.149-c0-0-3'], 'label': '2-840-840.149-c0-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/840/1/cg/a/149/1'}