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lfunc_lfunctions • Show schema
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{'Lhash': '738332051054939493833230384896,1265390357990211963493247975902', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': -4, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 147.5070039818273, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [13, [1]]], 'bad_primes': [3, 13], 'central_character': '1521.1', 'coefficient_field': '1.1.1.1', 'conductor': 2313441, 'conductor_radical': 39, 'degree': 4, 'euler_factors': [[1, 0, 4, 0, 4], [1], [1, 0, 10, 0, 25], [1, 0, -13, 0, 49], [1, 0, 22, 0, 121], [1], [1, 0, 34, 0, 289], [1, 0, 26, 0, 361], [1, 0, 46, 0, 529], [1, 0, 58, 0, 841], [1, 0, -13, 0, 961], [1, 0, 26, 0, 1369], [1, 0, 82, 0, 1681], [1, -26, 255, -1118, 1849], [1, 0, 94, 0, 2209], [1, 0, 106, 0, 2809], [1, 0, 118, 0, 3481], [1, -26, 291, -1586, 3721], [1, 0, -13, 0, 4489], [1, 0, 142, 0, 5041], [1, 0, 143, 0, 5329], [1, -26, 327, -2054, 6241], [1, 0, 166, 0, 6889], [1, 0, 178, 0, 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'2.15113593829640636363996300450576', '2.54093920856658529073826340380292', '3.59965430816273419096247497725435', '3.72835706033966006853332815738901', '4.20249564433908539379775542484639', '4.48531479108800978823334132248868', '5.24169675575209242293511872037361', '5.42673022080874236713083437174242', '5.86759524499834832980391948758029', '6.20338026813584923889916123381903', '6.90785819662818302222573672090319', '7.57777450618659838656119570440558', '7.72536714583701354336606708079181', '8.016079466379376999417096621776921', '8.728135637863489422975384731819792', '8.822791374383340678835143040773690', '9.278550982516379096278423471451782', '9.539231180083738508171994864326965'], 'prelabel': '4-39e4-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.4850030340642104, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 1786284169322408507, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 147.5070039818273, 'bad_primes': [3, 13], 'central_character': '1.1', 'conductor': 2313441, 'conductor_radical': 39, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 26, 0, 0, 0, 0, 0, 13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 26, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 26, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 40], 'euler11': [1, 0, 22, 0, 121], 'euler13': [1, 0, 0, 0, 0], 'euler17': [1, 0, 34, 0, 289], 'euler19': [1, 0, 26, 0, 361], 'euler2': [1, 0, 4, 0, 4], 'euler23': [1, 0, 46, 0, 529], 'euler29': [1, 0, 58, 0, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 0, -13, 0, 961], 'euler37': [1, 0, 26, 0, 1369], 'euler41': [1, 0, 82, 0, 1681], 'euler43': [1, -26, 255, -1118, 1849], 'euler47': [1, 0, 94, 0, 2209], 'euler5': [1, 0, 10, 0, 25], 'euler53': [1, 0, 106, 0, 2809], 'euler59': [1, 0, 118, 0, 3481], 'euler61': [1, -26, 291, -1586, 3721], 'euler67': [1, 0, -13, 0, 4489], 'euler7': [1, 0, -13, 0, 49], 'euler71': [1, 0, 142, 0, 5041], 'euler73': [1, 0, 143, 0, 5329], 'euler79': [1, -26, 327, -2054, 6241], 'euler83': [1, 0, 166, 0, 6889], 'euler89': [1, 0, 178, 0, 7921], 'euler97': [1, 0, -169, 0, 9409], 'euler_factors': [[1, 0, 4, 0, 4], [1, 0, 0, 0, 0], [1, 0, 10, 0, 25], [1, 0, -13, 0, 49], [1, 0, 22, 0, 121], [1, 0, 0, 0, 0], [1, 0, 34, 0, 289], [1, 0, 26, 0, 361], [1, 0, 46, 0, 529], [1, 0, 58, 0, 841], [1, 0, -13, 0, 961], [1, 0, 26, 0, 1369], [1, 0, 82, 0, 1681], [1, -26, 255, -1118, 1849], [1, 0, 94, 0, 2209], [1, 0, 106, 0, 2809], [1, 0, 118, 0, 3481], [1, -26, 291, -1586, 3721], [1, 0, -13, 0, 4489], [1, 0, 142, 0, 5041], [1, 0, 143, 0, 5329], [1, -26, 327, -2054, 6241], [1, 0, 166, 0, 6889], [1, 0, 178, 0, 7921], [1, 0, -169, 0, 9409]], 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1521/2/a/i'], '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': '4-39e4-1.1-c1e2-0-4', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-39e4-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.4850030340642104, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1786284169322408507, 'z1': {'__RealLiteral__': 0, 'data': '0.58244129014888587342252076828', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '738332051054939493833230384896,1265390357990211963493247975902', 'Lhash_array': ['738332051054939493833230384896', '1265390357990211963493247975902'], 'label': '4-39e4-1.1-c1e2-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1521/2/a/i'}