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lfunc_lfunctions • Show schema
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{'Lhash': '2614020532770208159913854099803,3796938324892724838298007737716', 'a10': 1, 'a2': -1, 'a3': 2, 'a4': 0, 'a5': -1, 'a6': -2, 'a7': -1, 'a8': 0, 'a9': 3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.006296634685059933, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [1, -2, 1]], [53, [1, -2, 1]]], 'bad_primes': [3, 53], 'central_character': '159.1', 'coefficient_field': '1.1.1.1', 'conductor': 25281, 'conductor_radical': 159, 'degree': 4, 'euler_factors': [[1, 1, 1, 1, 1], [1, -2, 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, 0, -2, 0, 1], [1, 1, 1, 1, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 1, 1, 1, 1], [1, 1, 1, 1, 1], [1, 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, 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, -4, 6, -4, 1], [1, 0, -2, 0, 1], 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['2.06209860374741796339889994643407', '2.99525620404322713807727056052753', '3.56732910811294467104717462395313', '4.19516455922442619181815882043606', '4.92042080695935339238281285710958', '6.18693376072904024118256695994772', '7.12455000812335815902247706939227', '7.16533614001499362983021333869135', '7.985342886408146721932302617207700', '8.319312957477228354448347977820551', '8.827944736570786066227315986208578', '9.140744998868018239527572375950567', '9.929638345352002043042230505656618', '9.976018845523336640746641565714730', '10.37181457340143541192994701428062', '11.50962232126074463883831350212716', '12.08075452607637885321168741454836', '12.31912059848638155757535555551619', '13.12971081393997962784196767073790', '13.29794649973420546914448632558663'], 'prelabel': '4-159e2-1.1-c0e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.2816936935904803, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c0e2-0', 'trace_hash': 1382489676216534128, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.06209860374741796339889994643', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.99525620404322713807727056053', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.56732910811294467104717462395', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.006296634685059933, 'bad_primes': [3, 53], 'central_character': '1.1', 'conductor': 25281, 'conductor_radical': 159, 'degree': 4, 'dirichlet_coefficients': [1, -1, 2, 0, -1, -2, -1, 0, 3, 1, 0, 0, -1, 1, -2, 0, 0, -3, 0, 0, -2, 0, -1, 0, 0, 1, 4, 0, 0, 2, 0, 1, 0, 0, 1, 0, -1, 0, -2, 0, -1, 2, -1, 0, -3, 1, 0, 0, 0, 0, 0, 0, 2, -4, 0, 0, 0, 0, 0, 0, 0, 0, -3, -1, 1, 0, 0, 0, -2, -1, -1, 0, 0, 1, 0, 0, 0, 2, 0, 0, 5, 1, -1, 0, 0, 1, 0, 0, 0, 3, 1, 0, 0, 0, 0, 2, -1, 0, 0, 0], 'euler11': [1, 0, -2, 0, 1], 'euler13': [1, 1, 1, 1, 1], 'euler17': [1, 0, -2, 0, 1], 'euler19': [1, 0, -2, 0, 1], 'euler2': [1, 1, 1, 1, 1], 'euler23': [1, 1, 1, 1, 1], 'euler29': [1, 0, -2, 0, 1], 'euler3': [1, -2, 1, 0, 0], 'euler31': [1, 0, -2, 0, 1], 'euler37': [1, 1, 1, 1, 1], 'euler41': [1, 1, 1, 1, 1], 'euler43': [1, 1, 1, 1, 1], 'euler47': [1, 0, -2, 0, 1], 'euler5': [1, 1, 1, 1, 1], 'euler53': [1, -2, 1, 0, 0], 'euler59': [1, 0, -2, 0, 1], 'euler61': [1, 0, -2, 0, 1], 'euler67': [1, 0, -2, 0, 1], 'euler7': [1, 1, 1, 1, 1], 'euler71': [1, 1, 1, 1, 1], 'euler73': [1, 0, -2, 0, 1], 'euler79': [1, 0, -2, 0, 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, -2, 1, 0, 0], [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, 0, -2, 0, 1], [1, 1, 1, 1, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 1, 1, 1, 1], [1, 1, 1, 1, 1], [1, 1, 1, 1, 1], [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, 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]], 'index': 1, 'instance_types': ['CMF', 'Artin'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/159/1/d/a', 'ArtinRepresentation/2.159.5t2.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': '4-159e2-1.1-c0e2-0-1', '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': '4-159e2-1.1-c0e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.2816936935904803, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0e2-0', 'trace_hash': 1382489676216534128, 'z1': {'__RealLiteral__': 0, 'data': '2.06209860374741796339889994643', 'prec': 103}}
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id: 24602897
{'Lhash': '2614020532770208159913854099803,3796938324892724838298007737716', 'Lhash_array': ['2614020532770208159913854099803', '3796938324892724838298007737716'], 'label': '4-159e2-1.1-c0e2-0-1', 'type': 'Artin', 'url': 'ArtinRepresentation/2.159.5t2.a'}
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id: 19804107
{'Lhash': '2614020532770208159913854099803,3796938324892724838298007737716', 'Lhash_array': ['2614020532770208159913854099803', '3796938324892724838298007737716'], 'label': '4-159e2-1.1-c0e2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/159/1/d/a'}