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lfunc_lfunctions • Show schema
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{'Lhash': '1784904126016962186846912371647,2192096292164162745969294844726', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': -2, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 428.3750897471616, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]]], 'bad_primes': [2, 3], 'central_character': '2592.1', 'coefficient_field': '1.1.1.1', 'conductor': 6718464, 'conductor_radical': 6, 'degree': 4, 'euler_factors': [[1], [1], [1, 2, 11, 10, 25], [1, 0, -10, 0, 49], [1, 0, -2, 0, 121], [1, -6, 35, -78, 169], [1, 10, 59, 170, 289], [1, 0, 14, 0, 361], [1, 0, 22, 0, 529], [1, 10, 83, 290, 841], [1, 0, 62, 0, 961], [1, 10, 99, 370, 1369], [1, -4, 86, -164, 1681], [1, 0, 62, 0, 1849], [1, 0, -2, 0, 2209], [1, 4, 110, 212, 2809], [1, 0, 22, 0, 3481], [1, 26, 291, 1586, 3721], [1, 0, 110, 0, 4489], [1, 0, 118, 0, 5041], [1, -6, 155, -438, 5329], [1, 0, -58, 0, 6241], [1, 0, 70, 0, 6889], [1, 26, 347, 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'3.62137752344738492980747789716085', '3.89955525618093693522040969849970', '4.22586106229223050916277727218973', '4.47475659220464340028771310734464', '5.31404560489571684357332779441961', '5.54997072464873009100009475867434', '6.03964430557292507596160947071569', '6.43449531214915693197831539215953', '6.75035250370432786310001011093374', '7.21907255126803469717129023629670', '7.61125333803576586827498476869274', '7.900127475677755310118239302557816', '8.362937653540424186111951539314212', '8.752319759274373161311462773208269'], 'prelabel': '4-2592e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.549420205247685, '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': 1143092139901675557, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.40804108458245971944468667846', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 428.3750897471616, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 6718464, 'conductor_radical': 6, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, -7, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -26, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, -26, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0], 'euler11': [1, 0, -2, 0, 121], 'euler13': [1, -6, 35, -78, 169], 'euler17': [1, 10, 59, 170, 289], 'euler19': [1, 0, 14, 0, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 22, 0, 529], 'euler29': [1, 10, 83, 290, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 0, 62, 0, 961], 'euler37': [1, 10, 99, 370, 1369], 'euler41': [1, -4, 86, -164, 1681], 'euler43': [1, 0, 62, 0, 1849], 'euler47': [1, 0, -2, 0, 2209], 'euler5': [1, 2, 11, 10, 25], 'euler53': [1, 4, 110, 212, 2809], 'euler59': [1, 0, 22, 0, 3481], 'euler61': [1, 26, 291, 1586, 3721], 'euler67': [1, 0, 110, 0, 4489], 'euler7': [1, 0, -10, 0, 49], 'euler71': [1, 0, 118, 0, 5041], 'euler73': [1, -6, 155, -438, 5329], 'euler79': [1, 0, -58, 0, 6241], 'euler83': [1, 0, 70, 0, 6889], 'euler89': [1, 26, 347, 2314, 7921], 'euler97': [1, 12, 230, 1164, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 2, 11, 10, 25], [1, 0, -10, 0, 49], [1, 0, -2, 0, 121], [1, -6, 35, -78, 169], [1, 10, 59, 170, 289], [1, 0, 14, 0, 361], [1, 0, 22, 0, 529], [1, 10, 83, 290, 841], [1, 0, 62, 0, 961], [1, 10, 99, 370, 1369], [1, -4, 86, -164, 1681], [1, 0, 62, 0, 1849], [1, 0, -2, 0, 2209], [1, 4, 110, 212, 2809], [1, 0, 22, 0, 3481], [1, 26, 291, 1586, 3721], [1, 0, 110, 0, 4489], [1, 0, 118, 0, 5041], [1, -6, 155, -438, 5329], [1, 0, -58, 0, 6241], [1, 0, 70, 0, 6889], [1, 26, 347, 2314, 7921], [1, 12, 230, 1164, 9409]], 'index': 35, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2592/2/a/m'], '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': '4-2592e2-1.1-c1e2-0-35', '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': '4-2592e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.549420205247685, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1143092139901675557, 'z1': {'__RealLiteral__': 0, 'data': '1.40804108458245971944468667846', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1784904126016962186846912371647,2192096292164162745969294844726', 'Lhash_array': ['1784904126016962186846912371647', '2192096292164162745969294844726'], 'factors': ['2-2592-1.1-c1-0-30', '2-2592-1.1-c1-0-42'], 'label': '4-2592e2-1.1-c1e2-0-35', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2592/2/a/m'}