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lfunc_lfunctions • Show schema
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{'Lhash': '987185646141528215317184947187,1228896346087829274013336655045', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': -2, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': -1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.3637904678775588, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [1, 0, 1]], [5, [1]], [7, [1]]], 'bad_primes': [3, 5, 7], 'central_character': '3675.1', 'coefficient_field': '1.1.1.1', 'conductor': 13505625, 'conductor_radical': 105, 'degree': 4, 'euler_factors': [[1, 0, 2, 0, 1], [1, 0, 1], [1], [1], [1, 0, -2, 0, 1], [1, 0, -1, 0, 1], [1, 0, 2, 0, 1], [1, -2, 3, -2, 1], [1, 0, 2, 0, 1], [1, 0, -2, 0, 1], [1, -4, 6, -4, 1], [1, 0, -1, 0, 1], [1, 0, -2, 0, 1], [1, 0, 2, 0, 1], [1, 0, 2, 0, 1], [1, 0, 2, 0, 1], [1, 0, -2, 0, 1], [1, 2, 3, 2, 1], [1, 0, -1, 0, 1], [1, 0, -2, 0, 1], [1, 0, -1, 0, 1], [1, -2, 3, -2, 1], [1, 0, 2, 0, 1], [1, 0, -2, 0, 1], [1, 0, -1, 0, 1], [1, 0, -2, 0, 1], [1, 0, -1, 0, 1], [1, 0, 2, 0, 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'3.36205106240757318182810814674649', '3.95945095072030234037523530599555', '4.45580513022789101715444604661690', '4.85976528772197147373345262238601', '4.86721658902835951064928244183313', '5.60724870331242032306619239666725', '5.66531677893212505412912027461904', '6.36265528266144886304107768933847', '6.39454161943580176961126563382519', '7.18217574779151980930956789463976', '7.74600333965871448060914543115655', '7.85131666767761216617403301025480', '8.180876631442657523919521986529666', '8.587397658492804286930549872809492', '8.900081308112407595395009617072473'], 'prelabel': '4-3675e2-1.1-c0e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.3542761614332153, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c0e2-0', 'trace_hash': 880017547502792664, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.77875216243639538794843234557', 'prec': 103}, 'z2': 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.3637904678775588, 'bad_primes': [3, 5, 7], 'central_character': '1.1', 'conductor': 13505625, 'conductor_radical': 105, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, -2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 3, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler11': [1, 0, -2, 0, 1], 'euler13': [1, 0, -1, 0, 1], 'euler17': [1, 0, 2, 0, 1], 'euler19': [1, -2, 3, -2, 1], 'euler2': [1, 0, 2, 0, 1], 'euler23': [1, 0, 2, 0, 1], 'euler29': [1, 0, -2, 0, 1], 'euler3': [1, 0, 1, 0, 0], 'euler31': [1, -4, 6, -4, 1], 'euler37': [1, 0, -1, 0, 1], 'euler41': [1, 0, -2, 0, 1], 'euler43': [1, 0, 2, 0, 1], 'euler47': [1, 0, 2, 0, 1], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, 0, 2, 0, 1], 'euler59': [1, 0, -2, 0, 1], 'euler61': [1, 2, 3, 2, 1], 'euler67': [1, 0, -1, 0, 1], 'euler7': [1, 0, 0, 0, 0], 'euler71': [1, 0, -2, 0, 1], 'euler73': [1, 0, -1, 0, 1], 'euler79': [1, -2, 3, -2, 1], 'euler83': [1, 0, 2, 0, 1], 'euler89': [1, 0, -2, 0, 1], 'euler97': [1, 0, -1, 0, 1], 'euler_factors': [[1, 0, 2, 0, 1], [1, 0, 1, 0, 0], [1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 0, -2, 0, 1], [1, 0, -1, 0, 1], [1, 0, 2, 0, 1], [1, -2, 3, -2, 1], [1, 0, 2, 0, 1], [1, 0, -2, 0, 1], [1, -4, 6, -4, 1], [1, 0, -1, 0, 1], [1, 0, -2, 0, 1], [1, 0, 2, 0, 1], [1, 0, 2, 0, 1], [1, 0, 2, 0, 1], [1, 0, -2, 0, 1], [1, 2, 3, 2, 1], [1, 0, -1, 0, 1], [1, 0, -2, 0, 1], [1, 0, -1, 0, 1], [1, -2, 3, -2, 1], [1, 0, 2, 0, 1], [1, 0, -2, 0, 1], [1, 0, -1, 0, 1]], 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3675/1/f/b'], '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': '4-3675e2-1.1-c0e2-0-2', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0, 0], 'order_of_vanishing': 0, 'prelabel': '4-3675e2-1.1-c0e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.3542761614332153, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0e2-0', 'trace_hash': 880017547502792664, 'z1': {'__RealLiteral__': 0, 'data': '0.77875216243639538794843234557', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '987185646141528215317184947187,1228896346087829274013336655045', 'Lhash_array': ['987185646141528215317184947187', '1228896346087829274013336655045'], 'factors': ['2-3675-15.14-c0-0-5', '2-3675-15.14-c0-0-7'], 'label': '4-3675e2-1.1-c0e2-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3675/1/f/b'}