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lfunc_lfunctions • Show schema
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{'Lhash': '1602973298723684406101823620703,2878676792322677182096348499713', 'a10': 0, 'a2': 0, 'a3': 2, 'a4': 0, 'a5': -2, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.13455161871510235, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [1, -2, 1]], [5, [1, 2, 1]], [7, [1]]], 'bad_primes': [3, 5, 7], 'central_character': '735.1', 'coefficient_field': '1.1.1.1', 'conductor': 540225, 'conductor_radical': 105, 'degree': 4, 'euler_factors': [[1, 0, 0, 0, 1], [1, -2, 1], [1, 2, 1], [1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, 2, 0, 1], [1, 0, 0, 0, 1], [1, 0, 0, 0, 1], [1, 0, -2, 0, 1], [1, 0, 0, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, 2, 0, 1], [1, 0, 0, 0, 1], [1, 0, -2, 0, 1], [1, 0, 0, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, 2, 0, 1], [1, 0, 2, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, 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-1.348825992087641, -1.2417353192035288], 'positive_zeros': ['1.26452296747627704830958768689118', '2.27087558023038572895945376674229', '2.81268713147475234175828835136576', '3.32584452150696290349171029177926', '3.86403498685224914303091667554511', '4.14552515157552891623268802085893', '4.69867315682297751960105926440286', '5.05119757585646418650918676465082', '6.14663827348177540740676776082055', '6.94527195981563389294367829869263', '6.96371513771519269028208804194376', '7.43231271360043508287367320462533', '8.060314826854830759034884489991643', '8.097276034469993834674201595001100', '8.595093423959007355677406077620705', '8.978941710016274445341356389273029', '9.363250945143462697860701583681488', '9.752931178064457392572862024245427', '10.40773855280116794576302295302932', '10.77768093268297960775342011245906'], 'prelabel': '4-735e2-1.1-c0e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.6056507114544296, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c0e2-0', 'trace_hash': 1271383630834544038, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.26452296747627704830958768689', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.27087558023038572895945376674', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.81268713147475234175828835137', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.13455161871510235, 'bad_primes': [3, 5, 7], 'central_character': '1.1', 'conductor': 540225, 'conductor_radical': 105, 'degree': 4, 'dirichlet_coefficients': [1, 0, 2, 0, -2, 0, 0, 0, 3, 0, 0, 0, 0, 0, -4, -1, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 2, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler11': [1, 0, -2, 0, 1], 'euler13': [1, 0, -2, 0, 1], 'euler17': [1, 0, 2, 0, 1], 'euler19': [1, 0, 0, 0, 1], 'euler2': [1, 0, 0, 0, 1], 'euler23': [1, 0, 0, 0, 1], 'euler29': [1, 0, -2, 0, 1], 'euler3': [1, -2, 1, 0, 0], 'euler31': [1, 0, 0, 0, 1], 'euler37': [1, 0, -2, 0, 1], 'euler41': [1, 0, -2, 0, 1], 'euler43': [1, 0, -2, 0, 1], 'euler47': [1, 0, 2, 0, 1], 'euler5': [1, 2, 1, 0, 0], 'euler53': [1, 0, 0, 0, 1], 'euler59': [1, 0, -2, 0, 1], 'euler61': [1, 0, 0, 0, 1], 'euler67': [1, 0, -2, 0, 1], 'euler7': [1, 0, 0, 0, 0], 'euler71': [1, 0, -2, 0, 1], 'euler73': [1, 0, -2, 0, 1], 'euler79': [1, 0, 2, 0, 1], 'euler83': [1, 0, 2, 0, 1], 'euler89': [1, 0, -2, 0, 1], 'euler97': [1, 0, -2, 0, 1], 'euler_factors': [[1, 0, 0, 0, 1], [1, -2, 1, 0, 0], [1, 2, 1, 0, 0], [1, 0, 0, 0, 0], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, 2, 0, 1], [1, 0, 0, 0, 1], [1, 0, 0, 0, 1], [1, 0, -2, 0, 1], [1, 0, 0, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, 2, 0, 1], [1, 0, 0, 0, 1], [1, 0, -2, 0, 1], [1, 0, 0, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, 2, 0, 1], [1, 0, 2, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1]], 'index': 2, 'instance_types': ['CMF', 'Artin'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/735/1/f/d', 'ArtinRepresentation/2.735.8t6.d'], 'is_instance_Artin': True, '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': '4-735e2-1.1-c0e2-0-2', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0, 0], 'order_of_vanishing': 0, 'prelabel': '4-735e2-1.1-c0e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.6056507114544296, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0e2-0', 'trace_hash': 1271383630834544038, 'z1': {'__RealLiteral__': 0, 'data': '1.26452296747627704830958768689', 'prec': 103}}
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lfunc_instances • Show schema
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id: 24603609
{'Lhash': '1602973298723684406101823620703,2878676792322677182096348499713', 'Lhash_array': ['1602973298723684406101823620703', '2878676792322677182096348499713'], 'factors': ['2-735-15.14-c0-0-2', '2-735-15.14-c0-0-5'], 'label': '4-735e2-1.1-c0e2-0-2', 'type': 'Artin', 'url': 'ArtinRepresentation/2.735.8t6.d'}
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id: 19810513
{'Lhash': '1602973298723684406101823620703,2878676792322677182096348499713', 'Lhash_array': ['1602973298723684406101823620703', '2878676792322677182096348499713'], 'factors': ['2-735-15.14-c0-0-2', '2-735-15.14-c0-0-5'], 'label': '4-735e2-1.1-c0e2-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/735/1/f/d'}