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lfunc_lfunctions • Show schema
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{'Lhash': '1272142017690943780844414368557', 'a10': [-1.205877697252948, 0.0], 'a2': [-1.205877697252948, 0.0], 'a3': [0.0, 0.0], 'a4': [-0.5458589792679276, 0.0], 'a5': [1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-4.31538823919994, 0.0], 'a8': [3.069994563450349, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 43.47854390058719, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-1.0, 0]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5, 11], 'central_character': '5445.1', 'coefficient_field': 'CDF', 'conductor': 5445, 'conductor_radical': 165, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.205877697252948, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [4.31538823919994, 0], [7.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [6.182451580716731, 0], [13.0, 0]], [[1.0, 0], [-0.8039877875649498, 0], [17.0, 0]], [[1.0, 0], [-1.8738854604471997, 0], [19.0, 0]], [[1.0, 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'5.57563652885978505688782737455934', '6.69564257609370302506282591274462', '7.15896874526133432302922347437803', '7.71513009899718585785969695016218'], 'prelabel': '2-5445-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.593826195812807, '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': '1.00354310364536232533104100791', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.37137752656288858130963650090', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.07402001758763996458933035666', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 43.47854390058719, 'bad_primes': [3, 5, 11], 'central_character': '1.1', 'conductor': 5445, 'conductor_radical': 165, 'degree': 2, 'index': 81, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5445/2/a/cb/1/4'], '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': '2-5445-1.1-c1-0-81', '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': '2-5445-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.593826195812807, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.00354310364536232533104100791', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1272142017690943780844414368557', 'Lhash_array': ['1272142017690943780844414368557'], 'label': '2-5445-1.1-c1-0-81', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5445/2/a/cb/1/4'}