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lfunc_lfunctions • Show schema
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{'Lhash': '329277367751306394051439500859,1338042058736616194445165515959', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': -4, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8053.60953433941, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', '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, 64], [1], [1, 0, 58, 0, 15625], [1, 0, 179, 0, 117649], [1, 0, 2155, 0, 1771561], [1], [1, -54, 10555, -265302, 24137569], [1, 0, 5915, 0, 47045881], [1, -114, 27583, -1387038, 148035889], [1, -138, 53539, -3365682, 594823321], [1, 0, 54290, 0, 887503681], [1, 0, 99719, 0, 2565726409], [1, 0, -16745, 0, 4750104241], [1, -170, 166239, -13516190, 6321363049], [1, 0, 90034, 0, 10779215329], [1, 852, 479230, 126843204, 22164361129], [1, 0, 410395, 0, 42180533641], [1, 34, 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'4-39e4-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 9.473220419621383, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3e2-0', 'trace_hash': 227195072658907131, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.25975404239308756247164309666', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.05552906967875329890587494365', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.51608997029439906082986117727', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8053.60953433941, '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, -48, 54, 0, 0, 0, 0, 0, 114, 0, -58, 0, 0, 0, 138, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 170, 0, 0, 0, 0, 0, -179, 0, 0, 0, -852, 0, 0, 0, 0, 0, 0, 0, -34, 0, 0, 448, 0, 0, 0, -216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2488, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -456, 0, 0, 0, 0, 0, 0, 0, 232], 'euler11': [1, 0, 2155, 0, 1771561], 'euler13': [1, 0, 0, 0, 0], 'euler17': [1, -54, 10555, -265302, 24137569], 'euler19': [1, 0, 5915, 0, 47045881], 'euler2': [1, 0, 4, 0, 64], 'euler23': [1, -114, 27583, -1387038, 148035889], 'euler29': [1, -138, 53539, -3365682, 594823321], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 0, 54290, 0, 887503681], 'euler37': [1, 0, 99719, 0, 2565726409], 'euler41': [1, 0, -16745, 0, 4750104241], 'euler43': [1, -170, 166239, -13516190, 6321363049], 'euler47': [1, 0, 90034, 0, 10779215329], 'euler5': [1, 0, 58, 0, 15625], 'euler53': [1, 852, 479230, 126843204, 22164361129], 'euler59': [1, 0, 410395, 0, 42180533641], 'euler61': [1, 34, 454251, 7717354, 51520374361], 'euler67': [1, 0, 574451, 0, 90458382169], 'euler7': [1, 0, 179, 0, 117649], 'euler71': [1, 0, 375115, 0, 128100283921], 'euler73': [1, 0, -231166, 0, 151334226289], 'euler79': [1, 2488, 2533614, 1226681032, 243087455521], 'euler83': [1, 0, 962026, 0, 326940373369], 'euler89': [1, 0, 1315951, 0, 496981290961], 'euler97': [1, 0, 300239, 0, 832972004929], 'euler_factors': [[1, 0, 4, 0, 64], [1, 0, 0, 0, 0], [1, 0, 58, 0, 15625], [1, 0, 179, 0, 117649], [1, 0, 2155, 0, 1771561], [1, 0, 0, 0, 0], [1, -54, 10555, -265302, 24137569], [1, 0, 5915, 0, 47045881], [1, -114, 27583, -1387038, 148035889], [1, -138, 53539, -3365682, 594823321], [1, 0, 54290, 0, 887503681], [1, 0, 99719, 0, 2565726409], [1, 0, -16745, 0, 4750104241], [1, -170, 166239, -13516190, 6321363049], [1, 0, 90034, 0, 10779215329], [1, 852, 479230, 126843204, 22164361129], [1, 0, 410395, 0, 42180533641], [1, 34, 454251, 7717354, 51520374361], [1, 0, 574451, 0, 90458382169], [1, 0, 375115, 0, 128100283921], [1, 0, -231166, 0, 151334226289], [1, 2488, 2533614, 1226681032, 243087455521], [1, 0, 962026, 0, 326940373369], [1, 0, 1315951, 0, 496981290961], [1, 0, 300239, 0, 832972004929]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1521/4/a/q'], '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-c3e2-0-0', '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': 0, 'prelabel': '4-39e4-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 9.473220419621383, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e2-0', 'trace_hash': 227195072658907131, 'z1': {'__RealLiteral__': 0, 'data': '0.25975404239308756247164309666', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '329277367751306394051439500859,1338042058736616194445165515959', 'Lhash_array': ['329277367751306394051439500859', '1338042058736616194445165515959'], 'label': '4-39e4-1.1-c3e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1521/4/a/q'}