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lfunc_lfunctions • Show schema
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{'Lhash': '1286453458278517499860043267872', 'a10': [0.0, 0.0], 'a2': [-0.7071067811865476, 0.7071067811865476], 'a3': [-0.7071067811865476, 0.7071067811865476], 'a4': [0.0, -1.0], 'a5': [0.0, 0.0], 'a6': [0.0, -1.0], 'a7': [0.0, 0.0], 'a8': [0.7071067811865476, 0.7071067811865476], 'a9': [0.0, -1.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.5988780151596029, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.7071067811865476, -0.7071067811865476]]], [3, [[1.0, 0], [0.7071067811865476, -0.7071067811865476]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '1200.701', 'coefficient_field': 'CDF', 'conductor': 1200, 'conductor_radical': 30, 'conjugate': '1346405126031986160395021068221', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.7071067811865476, -0.7071067811865476]], [[1.0, 0], [0.7071067811865476, -0.7071067811865476]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 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'0.59993953158798508659167638053240', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1200/1/r/a/701/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [0.5999395315879851, 0.5907868486763983, 0.5853274819137543, 0.5824149419899551, 0.5805177213767582, 0.577903716272697, 0.5728034008486312, 0.5635320987995284, 0.5485709265332216, 0.5266161826498105, 0.49660889653551915, 0.4577538723553331, 0.4095341027649025, 0.3517234539356845, 0.2843984557251581, 0.20794876899159875, 0.12308521743207093, 0.0308439608793972, -0.06741469040408418, -0.17001425220224278, -0.2749781004136364, -0.38005459581189477, -0.4827520453306261, -0.5803839142423657, -0.6701243351322992, -0.7490735612473538, -0.8143325918873635, -0.8630857659035563, -0.8926896878048702, -0.9007664329030275, 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'8.936598007806978755845485294164778', '9.963946576342807016962725960992175'], 'prelabel': '2-1200-48.29-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7738720922475515, 'root_angle': -0.375, 'root_number': '0.38268343236508977172845998403043 - 0.92387953251128675612818318939698*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.1875', 'prec': 24}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.01483283962229245839022808768', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.18684375825663080811168665870', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.35123632032944131225093329490', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.5988780151596029, 'bad_primes': [2, 3, 5], 'central_character': '48.29', 'conductor': 1200, 'conductor_radical': 30, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1200/1/r/a/701/1'], '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': '2-1200-48.29-c0-0-0', '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': '2-1200-48.29-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7738720922475515, 'root_angle': -0.1875, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.01483283962229245839022808768', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1286453458278517499860043267872', 'Lhash_array': ['1286453458278517499860043267872'], 'label': '2-1200-48.29-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1200/1/r/a/701/1'}