-
lfunc_lfunctions • Show schema
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{'Lhash': '1263243013978563058627230611382,1933568836833970714960230527100', 'a10': 0, 'a2': -2, 'a3': 0, 'a4': 3, 'a5': 0, 'a6': 0, 'a7': -4, 'a8': -4, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1725.4203255580962, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 2, 1]], [3, [1]], [17, [1]]], 'bad_primes': [2, 3, 17], 'central_character': '5202.1', 'coefficient_field': '1.1.1.1', 'conductor': 27060804, 'conductor_radical': 102, 'degree': 4, 'euler_factors': [[1, 2, 1], [1], [1, 0, 4, 0, 25], [1, 4, 12, 28, 49], [1, 0, -2, 0, 121], [1, -4, 6, -52, 169], [1], [1, -4, 18, -76, 361], [1, 12, 76, 276, 529], [1, 0, 52, 0, 841], [1, 4, 12, 124, 961], [1, -8, 84, -296, 1369], [1, 12, 118, 492, 1681], [1, 8, 102, 344, 1849], [1, 0, 70, 0, 2209], [1, 12, 118, 636, 2809], [1, -12, 130, -708, 3481], [1, -8, 132, -488, 3721], [1, -4, 114, -268, 4489], [1, 12, 124, 852, 5041], [1, -20, 246, -1460, 5329], [1, 4, 108, 316, 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True, 'root_analytic_conductor': 6.44501195743422, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 1033501391482752349, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.996523027521248524221400884381', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.52531686293198501246355636871', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.06148843032489325122553400852', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1725.4203255580962, 'bad_primes': [2, 3, 17], 'central_character': '1.1', 'conductor': 27060804, 'conductor_radical': 102, 'degree': 4, 'dirichlet_coefficients': [1, -2, 0, 3, 0, 0, -4, -4, 0, 0, 0, 0, 4, 8, 0, 5, 0, 0, 4, 0, 0, 0, -12, 0, -4, -8, 0, -12, 0, 0, -4, -6, 0, 0, 0, 0, 8, -8, 0, 0, -12, 0, -8, 0, 0, 24, 0, 0, 4, 8, 0, 12, -12, 0, 0, 16, 0, 0, 12, 0, 8, 8, 0, 7, 0, 0, 4, 0, 0, 0, -12, 0, 20, -16, 0, 12, 0, 0, -4, 0, 0, 24, -12, 0, 0, 16, 0, 0, -12, 0, -16, -36, 0, 0, 0, 0, 20, -8, 0, -12], 'euler11': [1, 0, -2, 0, 121], 'euler13': [1, -4, 6, -52, 169], 'euler17': [1, 0, 0, 0, 0], 'euler19': [1, -4, 18, -76, 361], 'euler2': [1, 2, 1, 0, 0], 'euler23': [1, 12, 76, 276, 529], 'euler29': [1, 0, 52, 0, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 4, 12, 124, 961], 'euler37': [1, -8, 84, -296, 1369], 'euler41': [1, 12, 118, 492, 1681], 'euler43': [1, 8, 102, 344, 1849], 'euler47': [1, 0, 70, 0, 2209], 'euler5': [1, 0, 4, 0, 25], 'euler53': [1, 12, 118, 636, 2809], 'euler59': [1, -12, 130, -708, 3481], 'euler61': [1, -8, 132, -488, 3721], 'euler67': [1, -4, 114, -268, 4489], 'euler7': [1, 4, 12, 28, 49], 'euler71': [1, 12, 124, 852, 5041], 'euler73': [1, -20, 246, -1460, 5329], 'euler79': [1, 4, 108, 316, 6241], 'euler83': [1, 12, 178, 996, 6889], 'euler89': [1, 12, 118, 1068, 7921], 'euler97': [1, -20, 270, -1940, 9409], 'euler_factors': [[1, 2, 1, 0, 0], [1, 0, 0, 0, 0], [1, 0, 4, 0, 25], [1, 4, 12, 28, 49], [1, 0, -2, 0, 121], [1, -4, 6, -52, 169], [1, 0, 0, 0, 0], [1, -4, 18, -76, 361], [1, 12, 76, 276, 529], [1, 0, 52, 0, 841], [1, 4, 12, 124, 961], [1, -8, 84, -296, 1369], [1, 12, 118, 492, 1681], [1, 8, 102, 344, 1849], [1, 0, 70, 0, 2209], [1, 12, 118, 636, 2809], [1, -12, 130, -708, 3481], [1, -8, 132, -488, 3721], [1, -4, 114, -268, 4489], [1, 12, 124, 852, 5041], [1, -20, 246, -1460, 5329], [1, 4, 108, 316, 6241], [1, 12, 178, 996, 6889], [1, 12, 118, 1068, 7921], [1, -20, 270, -1940, 9409]], 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5202/2/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': '4-5202e2-1.1-c1e2-0-11', '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': 2, 'prelabel': '4-5202e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.44501195743422, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1033501391482752349, 'z1': {'__RealLiteral__': 0, 'data': '0.996523027521248524221400884381', 'prec': 107}}
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{'Lhash': '1263243013978563058627230611382,1933568836833970714960230527100', 'Lhash_array': ['1263243013978563058627230611382', '1933568836833970714960230527100'], 'factors': ['2-5202-1.1-c1-0-43', '2-5202-1.1-c1-0-94'], 'label': '4-5202e2-1.1-c1e2-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5202/2/a/q'}