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lfunc_lfunctions • Show schema
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{'Lhash': '2270714581466865067680145881950', 'a10': [-2.1642479384602114, 0.0], 'a2': [-1.0, 0.0], 'a3': [0.6839691391292742, 0.0], 'a4': [1.0, 0.0], 'a5': [2.1642479384602114, 0.0], 'a6': [-0.6839691391292742, 0.0], 'a7': [0.0, 0.0], 'a8': [-1.0, 0.0], 'a9': [-2.5321862167187597, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.868144856362415, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, 0]]], [7, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 7, 19], 'central_character': '1862.1', 'coefficient_field': 'CDF', 'conductor': 1862, 'conductor_radical': 266, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 0]], [[1.0, 0], [-0.6839691391292742, 0], [3.0, 0]], [[1.0, 0], [-2.1642479384602114, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [3.644526737791148, 0], [11.0, 0]], [[1.0, 0], [4.0, 0], [13.0, 0]], [[1.0, 0], [-4.328495876920423, 0], [17.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 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[-4.735876556517097, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 51, 'label': '2-1862-1.1-c1-0-51', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/1862/2/a/o/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [-1.1911240180281092e-60, 0.1327511021904406, 0.2654080482141037, 0.3978418110810506, 0.5298555291751903, 0.6611552035036765, 0.7913255293395561, 0.9198119710300415, 1.045909791655051, 1.1687603669996174, 1.2873547807801697, 1.400544433663055, 1.5070582051352504, 1.6055255758624125, 1.6945050334539071, 1.772517029554036, 1.8380807157717665, 1.8897536488702673, 1.926173615063411, 1.9461016766042196, 1.9484654919113304, 1.9324019065484541, 1.8972977613039146, 1.8428278210763647, 1.7689887001344844, 1.6761276512268233, 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'7.60871258701898381381451743365117', '7.993804404061252811374016586931393', '8.950063718854691141463250810126440'], 'prelabel': '2-1862-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8559233467954748, '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': '1.79127796023450213402777558406', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.58766360972516234988698839381', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.41758258594709815051907820283', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 14.868144856362415, 'bad_primes': [2, 7, 19], 'central_character': '1.1', 'conductor': 1862, 'conductor_radical': 266, 'degree': 2, 'index': 51, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1862/2/a/o/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': '2-1862-1.1-c1-0-51', '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': '2-1862-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8559233467954748, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.79127796023450213402777558406', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2270714581466865067680145881950', 'Lhash_array': ['2270714581466865067680145881950'], 'label': '2-1862-1.1-c1-0-51', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1862/2/a/o/1/2'}