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lfunc_lfunctions • Show schema
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{'Lhash': '2916215812253127564893878503027,3816408239866308623332131496255', 'a10': 0, 'a2': 3, 'a3': 0, 'a4': 4, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 3, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.8728225087682089, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [13, [1, 5, 13]]], 'bad_primes': [3, 13], 'central_character': '117.1', 'coefficient_field': '1.1.1.1', 'conductor': 13689, 'conductor_radical': 39, 'degree': 4, 'euler_factors': [[1, -3, 5, -6, 4], [1], [1, 0, -7, 0, 25], [1, 0, 7, 0, 49], [1, 0, 11, 0, 121], [1, 5, 13], [1, 3, -8, 51, 289], [1, 6, 31, 114, 361], [1, 6, 13, 138, 529], [1, -3, -20, -87, 841], [1, 0, -50, 0, 961], [1, -15, 112, -555, 1369], [1, -9, 68, -369, 1681], [1, 8, 21, 344, 1849], [1, 0, -82, 0, 2209], [1, -6, 115, -318, 2809], [1, 12, 107, 708, 3481], [1, 1, -60, 61, 3721], [1, -6, 79, -402, 4489], [1, 6, 83, 426, 5041], [1, 0, -143, 0, 5329], [1, -8, 174, -632, 6241], [1, 0, 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-0.3103577781322812], 'positive_zeros': ['2.30048864547383042155892541730433', '3.01061525879386457489213948437798', '4.12193749243753436827426393249340', '4.49171745133503383136198757093878', '4.93028819176766711137701447128458', '5.75306601814164473145468760626911', '6.38007784589126407921637885042932', '6.79240429228524573602732606304994', '7.81619518739241434056211690148249', '8.121361817311082119247377055500695', '9.147738395607172997143644102892659', '9.578556319675191966040292762700071', '10.56540634359934074886604029253778', '10.60685065900241612146680633727847', '11.65594467670936743887824648802994', '11.87492882753469792665319424840303', '12.58913598375338648718720352897251', '12.91113829320065756769769732237389', '13.09663201674913409202885206212211', '13.82537752038117811414386352949938'], 'prelabel': '4-117e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.9665659334204683, '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': 1260473896178419383, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.30048864547383042155892541730', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.01061525879386457489213948438', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.12193749243753436827426393249', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.8728225087682089, 'bad_primes': [3, 13], 'central_character': '1.1', 'conductor': 13689, 'conductor_radical': 39, 'degree': 4, 'dirichlet_coefficients': [1, 3, 0, 4, 0, 0, 0, 3, 0, 0, 0, 0, -5, 0, 0, 3, -3, 0, -6, 0, 0, 0, -6, 0, 7, -15, 0, 0, 3, 0, 0, 6, 0, -9, 0, 0, 15, -18, 0, 0, 9, 0, -8, 0, 0, -18, 0, 0, -7, 21, 0, -20, 6, 0, 0, 0, 0, 9, -12, 0, -1, 0, 0, 5, 0, 0, 6, -12, 0, 0, -6, 0, 0, 45, 0, -24, 0, 0, 8, 0, 0, 27, 0, 0, 0, -24, 0, 0, 12, 0, 0, -24, 0, 0, 0, 0, 12, -21, 0, 28], 'euler11': [1, 0, 11, 0, 121], 'euler13': [1, 5, 13, 0, 0], 'euler17': [1, 3, -8, 51, 289], 'euler19': [1, 6, 31, 114, 361], 'euler2': [1, -3, 5, -6, 4], 'euler23': [1, 6, 13, 138, 529], 'euler29': [1, -3, -20, -87, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 0, -50, 0, 961], 'euler37': [1, -15, 112, -555, 1369], 'euler41': [1, -9, 68, -369, 1681], 'euler43': [1, 8, 21, 344, 1849], 'euler47': [1, 0, -82, 0, 2209], 'euler5': [1, 0, -7, 0, 25], 'euler53': [1, -6, 115, -318, 2809], 'euler59': [1, 12, 107, 708, 3481], 'euler61': [1, 1, -60, 61, 3721], 'euler67': [1, -6, 79, -402, 4489], 'euler7': [1, 0, 7, 0, 49], 'euler71': [1, 6, 83, 426, 5041], 'euler73': [1, 0, -143, 0, 5329], 'euler79': [1, -8, 174, -632, 6241], 'euler83': [1, 0, 26, 0, 6889], 'euler89': [1, -12, 137, -1068, 7921], 'euler97': [1, -12, 145, -1164, 9409], 'euler_factors': [[1, -3, 5, -6, 4], [1, 0, 0, 0, 0], [1, 0, -7, 0, 25], [1, 0, 7, 0, 49], [1, 0, 11, 0, 121], [1, 5, 13, 0, 0], [1, 3, -8, 51, 289], [1, 6, 31, 114, 361], [1, 6, 13, 138, 529], [1, -3, -20, -87, 841], [1, 0, -50, 0, 961], [1, -15, 112, -555, 1369], [1, -9, 68, -369, 1681], [1, 8, 21, 344, 1849], [1, 0, -82, 0, 2209], [1, -6, 115, -318, 2809], [1, 12, 107, 708, 3481], [1, 1, -60, 61, 3721], [1, -6, 79, -402, 4489], [1, 6, 83, 426, 5041], [1, 0, -143, 0, 5329], [1, -8, 174, -632, 6241], [1, 0, 26, 0, 6889], [1, -12, 137, -1068, 7921], [1, -12, 145, -1164, 9409]], 'index': 17, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/117/2/q/c'], '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': '4-117e2-1.1-c1e2-0-17', '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': '4-117e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.9665659334204683, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1260473896178419383, 'z1': {'__RealLiteral__': 0, 'data': '2.30048864547383042155892541730', 'prec': 103}}
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{'Lhash': '2916215812253127564893878503027,3816408239866308623332131496255', 'Lhash_array': ['2916215812253127564893878503027', '3816408239866308623332131496255'], 'label': '4-117e2-1.1-c1e2-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/117/2/q/c'}