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lfunc_lfunctions • Show schema
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{'Lhash': '2547295496320723365535733989719,4162916578406951986772062330497', 'a10': 0, 'a2': -1, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': -1, 'a8': 0, 'a9': 2, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.0026423399934259258, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[103, [1, -2, 1]]], 'bad_primes': [103], 'central_character': '103.1', 'coefficient_field': '1.1.1.1', 'conductor': 10609, 'conductor_radical': 103, 'degree': 4, 'euler_factors': [[1, 1, 1, 1, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 1, 1, 1, 1], [1, 0, -2, 0, 1], [1, 1, 1, 1, 1], [1, 1, 1, 1, 1], [1, 1, 1, 1, 1], [1, 1, 1, 1, 1], [1, 1, 1, 1, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 1, 1, 1, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 1, 1, 1, 1], [1, 1, 1, 1, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 1, 1, 1, 1], [1, 1, 1, 1, 1], [1, 0, -2, 0, 1], [1, 1, 1, 1, 1], [1, 0, -2, 0, 1], [1, -2, 1], [1, -4, 6, -4, 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'10.91161638857600902781983446815478', '11.72604188680177212338039429439052', '12.51791807552834908624905200910991', '12.70894104994314844385392810633368', '13.06999783634067273401280863881848', '13.68380576693065448866038657734555', '14.35488539200342705454252134632551'], 'prelabel': '4-103e2-1.1-c0e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.22672383267137852, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c0e2-0', 'trace_hash': 1619066268445811528, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.00946183109297238095017317494', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.28396214040166531134869327212', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.46895357445124374556423870030', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.0026423399934259258, 'bad_primes': [103], 'central_character': '1.1', 'conductor': 10609, 'conductor_radical': 103, 'degree': 4, 'dirichlet_coefficients': [1, -1, 0, 0, 0, 0, -1, 0, 2, 0, 0, 0, -1, 1, 0, 0, -1, -2, -1, 0, 0, 0, -1, 0, 2, 1, 0, 0, -1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, -1, 0, -2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 3, 1, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0], 'euler11': [1, 0, -2, 0, 1], 'euler13': [1, 1, 1, 1, 1], 'euler17': [1, 1, 1, 1, 1], 'euler19': [1, 1, 1, 1, 1], 'euler2': [1, 1, 1, 1, 1], 'euler23': [1, 1, 1, 1, 1], 'euler29': [1, 1, 1, 1, 1], 'euler3': [1, 0, -2, 0, 1], 'euler31': [1, 0, -2, 0, 1], 'euler37': [1, 0, -2, 0, 1], 'euler41': [1, 1, 1, 1, 1], 'euler43': [1, 0, -2, 0, 1], 'euler47': [1, 0, -2, 0, 1], 'euler5': [1, 0, -2, 0, 1], 'euler53': [1, 0, -2, 0, 1], 'euler59': [1, 1, 1, 1, 1], 'euler61': [1, 1, 1, 1, 1], 'euler67': [1, 0, -2, 0, 1], 'euler7': [1, 1, 1, 1, 1], 'euler71': [1, 0, -2, 0, 1], 'euler73': [1, 0, -2, 0, 1], 'euler79': [1, 1, 1, 1, 1], 'euler83': [1, 1, 1, 1, 1], 'euler89': [1, 0, -2, 0, 1], 'euler97': [1, 1, 1, 1, 1], 'euler_factors': [[1, 1, 1, 1, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 1, 1, 1, 1], [1, 0, -2, 0, 1], [1, 1, 1, 1, 1], [1, 1, 1, 1, 1], [1, 1, 1, 1, 1], [1, 1, 1, 1, 1], [1, 1, 1, 1, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 1, 1, 1, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 1, 1, 1, 1], [1, 1, 1, 1, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 1, 1, 1, 1], [1, 1, 1, 1, 1], [1, 0, -2, 0, 1], [1, 1, 1, 1, 1]], 'index': 0, 'instance_types': ['CMF', 'Artin'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/103/1/b/a', 'ArtinRepresentation/2.103.5t2.a'], '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': '4-103e2-1.1-c0e2-0-0', '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': '4-103e2-1.1-c0e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.22672383267137852, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0e2-0', 'trace_hash': 1619066268445811528, 'z1': {'__RealLiteral__': 0, 'data': '2.00946183109297238095017317494', 'prec': 103}}
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lfunc_instances • Show schema
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id: 24602852
{'Lhash': '2547295496320723365535733989719,4162916578406951986772062330497', 'Lhash_array': ['2547295496320723365535733989719', '4162916578406951986772062330497'], 'factors': ['2-103-103.102-c0-0-0', '2-103-103.102-c0-0-1'], 'label': '4-103e2-1.1-c0e2-0-0', 'type': 'Artin', 'url': 'ArtinRepresentation/2.103.5t2.a'}
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id: 19801825
{'Lhash': '2547295496320723365535733989719,4162916578406951986772062330497', 'Lhash_array': ['2547295496320723365535733989719', '4162916578406951986772062330497'], 'factors': ['2-103-103.102-c0-0-0', '2-103-103.102-c0-0-1'], 'label': '4-103e2-1.1-c0e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/103/1/b/a'}