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lfunc_lfunctions • Show schema
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{'Lhash': '2415028830739970026269758276970,3598654010009238231654156216433', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 1, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': -1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.01205478892278394, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1, -1, 1]], [11, [1, 2, 1]]], 'bad_primes': [2, 5, 11], 'central_character': '220.1', 'coefficient_field': '1.1.1.1', 'conductor': 48400, 'conductor_radical': 110, 'degree': 4, 'euler_factors': [[1], [1, 0, 1, 0, 1], [1, -1, 1], [1, 0, 2, 0, 1], [1, 2, 1], [1, 0, 2, 0, 1], [1, 0, 2, 0, 1], [1, 0, -2, 0, 1], [1, 0, 1, 0, 1], [1, 0, -2, 0, 1], [1, -2, 3, -2, 1], [1, 0, 1, 0, 1], [1, 0, -2, 0, 1], [1, 0, 2, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 2, 3, 2, 1], [1, 0, -2, 0, 1], [1, 0, 1, 0, 1], [1, 2, 3, 2, 1], [1, 0, 2, 0, 1], [1, 0, -2, 0, 1], [1, 0, 2, 0, 1], [1, -2, 3, -2, 1], [1, 0, 1, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, 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2.350850457796708], 'positive_zeros': ['1.90512182955237445659925190525070', '2.83883745991311174958759578064985', '3.06636432204313608798296373661223', '4.44806780003700737466445685372104', '5.01816571985453217309847345593320', '5.48699164564002589839083031839060', '6.16819194162180967358625418537919', '6.36422800796378950164003148517366', '7.37578574256180562023732265706004', '7.940193807886545502325381459735924', '8.195590797707479658159659135352582', '8.880042955447999587174155591468505', '9.378351762009847898448380875780020', '10.00039946931955901204771160350788', '10.35125654164405097163988718077621', '10.64624087594402505418448670013574', '11.52341064033869578303731870361126', '11.53086444641975556756976949227357', '12.50076087189891172453642928628607', '12.68141026790170625600555325741021'], 'prelabel': '4-220e2-1.1-c0e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.3313522337019332, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c0e2-0', 'trace_hash': 1374262869499808628, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.90512182955237445659925190525', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.83883745991311174958759578065', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.06636432204313608798296373661', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.01205478892278394, 'bad_primes': [2, 5, 11], 'central_character': '1.1', 'conductor': 48400, 'conductor_radical': 110, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 1, 0, 0, 0, -1, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0], 'euler11': [1, 2, 1, 0, 0], 'euler13': [1, 0, 2, 0, 1], 'euler17': [1, 0, 2, 0, 1], 'euler19': [1, 0, -2, 0, 1], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 1, 0, 1], 'euler29': [1, 0, -2, 0, 1], 'euler3': [1, 0, 1, 0, 1], 'euler31': [1, -2, 3, -2, 1], 'euler37': [1, 0, 1, 0, 1], 'euler41': [1, 0, -2, 0, 1], 'euler43': [1, 0, 2, 0, 1], 'euler47': [1, 0, -2, 0, 1], 'euler5': [1, -1, 1, 0, 0], 'euler53': [1, 0, -2, 0, 1], 'euler59': [1, 2, 3, 2, 1], 'euler61': [1, 0, -2, 0, 1], 'euler67': [1, 0, 1, 0, 1], 'euler7': [1, 0, 2, 0, 1], 'euler71': [1, 2, 3, 2, 1], 'euler73': [1, 0, 2, 0, 1], 'euler79': [1, 0, -2, 0, 1], 'euler83': [1, 0, 2, 0, 1], 'euler89': [1, -2, 3, -2, 1], 'euler97': [1, 0, 1, 0, 1], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 1, 0, 1], [1, -1, 1, 0, 0], [1, 0, 2, 0, 1], [1, 2, 1, 0, 0], [1, 0, 2, 0, 1], [1, 0, 2, 0, 1], [1, 0, -2, 0, 1], [1, 0, 1, 0, 1], [1, 0, -2, 0, 1], [1, -2, 3, -2, 1], [1, 0, 1, 0, 1], [1, 0, -2, 0, 1], [1, 0, 2, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 2, 3, 2, 1], [1, 0, -2, 0, 1], [1, 0, 1, 0, 1], [1, 2, 3, 2, 1], [1, 0, 2, 0, 1], [1, 0, -2, 0, 1], [1, 0, 2, 0, 1], [1, -2, 3, -2, 1], [1, 0, 1, 0, 1]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/220/1/e/a'], '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': '4-220e2-1.1-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': '4-220e2-1.1-c0e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.3313522337019332, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0e2-0', 'trace_hash': 1374262869499808628, 'z1': {'__RealLiteral__': 0, 'data': '1.90512182955237445659925190525', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2415028830739970026269758276970,3598654010009238231654156216433', 'Lhash_array': ['2415028830739970026269758276970', '3598654010009238231654156216433'], 'factors': ['2-220-55.54-c0-0-0', '2-220-55.54-c0-0-1'], 'label': '4-220e2-1.1-c0e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/220/1/e/a'}