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lfunc_lfunctions • Show schema
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{'Lhash': '1637098823262015098928835361464,1766136013444057647873856170498', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 4, 'a6': 0, 'a7': 20, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12199.550537224195, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [13, [1, 26, 169]]], 'bad_primes': [2, 3, 13], 'central_character': '1872.1', 'coefficient_field': '1.1.1.1', 'conductor': 3504384, 'conductor_radical': 78, 'degree': 4, 'euler_factors': [[1], [1], [1, -4, 226, -500, 15625], [1, -20, 534, -6860, 117649], [1, 60, 3114, 79860, 1771561], [1, 26, 169], [1, -84, 10582, -412692, 24137569], [1, -60, 6526, -411540, 47045881], [1, 72, 14430, 876024, 148035889], [1, -124, -1586, -3024236, 594823321], [1, -108, -16154, -3217428, 887503681], [1, -36, 42382, -1823508, 2565726409], [1, -52, 76666, -3583892, 4750104241], [1, -32, 150198, -2544224, 6321363049], [1, 428, 116242, 44436244, 10779215329], [1, 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['1.29144325965472644963121988851982', '1.39323565430890839190788559868912', '2.23082975137771960912342693577579', '2.57113665196715262395150298147941', '3.11533308893695196921795150547849', '3.54869564968335738168489792091175', '4.33917167591612613888005850069465', '4.58520431917712232589822190787380', '5.17585544328762991393188149535358', '5.33610701143664500506918011394661', '5.78838368201344413807248292271904', '6.16397913383407530949936006017108', '6.71003736748643046145230469162429', '7.28710042746846389443493995906568', '7.62923741148788425101860191527473', '8.030058552080768642537252782993721', '8.164890316442592924970392597250907', '8.322265584324752422589185198668069'], 'prelabel': '4-1872e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 10.509594451297657, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c3e2-0', 'trace_hash': 958736540675321533, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.29144325965472644963121988852', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.39323565430890839190788559869', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.23082975137771960912342693578', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 12199.550537224195, 'bad_primes': [2, 3, 13], 'central_character': '1.1', 'conductor': 3504384, 'conductor_radical': 78, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 4, 0, 20, 0, 0, 0, -60, 0, -26, 0, 0, 0, 84, 0, 60, 0, 0, 0, -72, 0, -210, 0, 0, 0, 124, 0, 108, 0, 0, 0, 80, 0, 36, 0, 0, 0, 52, 0, 32, 0, 0, 0, -428, 0, -134, 0, 0, 0, -380, 0, -240, 0, 0, 0, -1420, 0, 1012, 0, 0, 0, -104, 0, 844, 0, 0, 0, -868, 0, -60, 0, 0, 0, -1200, 0, -272, 0, 0, 0, -1252, 0, 336, 0, 0, 0, -572, 0, -520, 0, 0, 0, 240, 0, 708, 0, 0, 0], 'euler11': [1, 60, 3114, 79860, 1771561], 'euler13': [1, 26, 169, 0, 0], 'euler17': [1, -84, 10582, -412692, 24137569], 'euler19': [1, -60, 6526, -411540, 47045881], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 72, 14430, 876024, 148035889], 'euler29': [1, -124, -1586, -3024236, 594823321], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, -108, -16154, -3217428, 887503681], 'euler37': [1, -36, 42382, -1823508, 2565726409], 'euler41': [1, -52, 76666, -3583892, 4750104241], 'euler43': [1, -32, 150198, -2544224, 6321363049], 'euler47': [1, 428, 116242, 44436244, 10779215329], 'euler5': [1, -4, 226, -500, 15625], 'euler53': [1, 380, 258142, 56573260, 22164361129], 'euler59': [1, 1420, 882490, 291638180, 42180533641], 'euler61': [1, -1012, 708206, -229704772, 51520374361], 'euler67': [1, -844, 778238, -253843972, 90458382169], 'euler7': [1, -20, 534, -6860, 117649], 'euler71': [1, 868, 888050, 310666748, 128100283921], 'euler73': [1, 60, 114886, 23341020, 151334226289], 'euler79': [1, 272, 993374, 134106608, 243087455521], 'euler83': [1, 1252, 1118698, 715877324, 326940373369], 'euler89': [1, 572, 853306, 403242268, 496981290961], 'euler97': [1, -708, 1762390, -646172484, 832972004929], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, -4, 226, -500, 15625], [1, -20, 534, -6860, 117649], [1, 60, 3114, 79860, 1771561], [1, 26, 169, 0, 0], [1, -84, 10582, -412692, 24137569], [1, -60, 6526, -411540, 47045881], [1, 72, 14430, 876024, 148035889], [1, -124, -1586, -3024236, 594823321], [1, -108, -16154, -3217428, 887503681], [1, -36, 42382, -1823508, 2565726409], [1, -52, 76666, -3583892, 4750104241], [1, -32, 150198, -2544224, 6321363049], [1, 428, 116242, 44436244, 10779215329], [1, 380, 258142, 56573260, 22164361129], [1, 1420, 882490, 291638180, 42180533641], [1, -1012, 708206, -229704772, 51520374361], [1, -844, 778238, -253843972, 90458382169], [1, 868, 888050, 310666748, 128100283921], [1, 60, 114886, 23341020, 151334226289], [1, 272, 993374, 134106608, 243087455521], [1, 1252, 1118698, 715877324, 326940373369], [1, 572, 853306, 403242268, 496981290961], [1, -708, 1762390, -646172484, 832972004929]], 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1872/4/a/bf'], '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': '4-1872e2-1.1-c3e2-0-15', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3, 3], 'order_of_vanishing': 2, 'prelabel': '4-1872e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 10.509594451297657, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e2-0', 'trace_hash': 958736540675321533, 'z1': {'__RealLiteral__': 0, 'data': '1.29144325965472644963121988852', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1637098823262015098928835361464,1766136013444057647873856170498', 'Lhash_array': ['1637098823262015098928835361464', '1766136013444057647873856170498'], 'factors': ['2-1872-1.1-c3-0-65', '2-1872-1.1-c3-0-74'], 'label': '4-1872e2-1.1-c3e2-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1872/4/a/bf'}