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lfunc_lfunctions • Show schema
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{'Lhash': '2880144907351544340827009922152,3893484791432041836001209150870', 'a10': 0, 'a2': 1, 'a3': -1, 'a4': 0, 'a5': 0, 'a6': -1, 'a7': 1, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.0050931483198762145, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[11, [1, 2, 1]], [13, [1, 2, 1]]], 'bad_primes': [11, 13], 'central_character': '143.1', 'coefficient_field': '1.1.1.1', 'conductor': 20449, 'conductor_radical': 143, 'degree': 4, 'euler_factors': [[1, -1, 1, -1, 1], [1, 1, 1, 1, 1], [1, 0, -2, 0, 1], [1, -1, 1, -1, 1], [1, 2, 1], [1, 2, 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, 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, 0, -2, 0, 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, 0, -2, 0, 1], [1, 1, 1, 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['2.27203371878102644767358401044689', '3.07141793703332287184327843998639', '4.38802451253424855324823205856079', '4.86221255192137125487916254235871', '5.31421961759558757154414127899019', '5.40644236408523558557252902644401', '6.44399786173049336138211999785876', '7.34040097683464702793451134111023', '7.66026602909536586139046396552051', '8.129979544218070959974762466047851', '9.004257973228336367496572581078589', '9.724324737236978039854594585250144', '10.21318557697500063287799539774542', '10.82066324397992018341842346619053', '11.09964703010420586370456732130609', '11.67030199132299516852202375699998', '12.36739753161912299402971421224257', '12.49653956081239081415209781238431', '13.01428957171829116532910775373941', '13.60486632803815923946613303661787'], 'prelabel': '4-143e2-1.1-c0e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.26714471135794426, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c0e2-0', 'trace_hash': 1209999580595804389, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.27203371878102644767358401045', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.07141793703332287184327843999', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.38802451253424855324823205856', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.0050931483198762145, 'bad_primes': [11, 13], 'central_character': '1.1', 'conductor': 20449, 'conductor_radical': 143, 'degree': 4, 'dirichlet_coefficients': [1, 1, -1, 0, 0, -1, 1, 0, 0, 0, -2, 0, -2, 1, 0, 0, 0, 0, 1, 0, -1, -2, -1, 0, 2, -2, 0, 0, 0, 0, 0, -1, 2, 0, 0, 0, 0, 1, 2, 0, 1, -1, 0, 0, 0, -1, 0, 0, 0, 2, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 2, 0, 0, 1, 0, 0, 0, 1, 0, -2, 0, -2, 2, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 1, 0, 0, 0, 0], 'euler11': [1, 2, 1, 0, 0], 'euler13': [1, 2, 1, 0, 0], 'euler17': [1, 0, -2, 0, 1], 'euler19': [1, -1, 1, -1, 1], 'euler2': [1, -1, 1, -1, 1], 'euler23': [1, 1, 1, 1, 1], 'euler29': [1, 0, -2, 0, 1], 'euler3': [1, 1, 1, 1, 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, 1, 1, 1, 1], '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, 0, -2, 0, 1], 'euler73': [1, -1, 1, -1, 1], 'euler79': [1, 0, -2, 0, 1], 'euler83': [1, -1, 1, -1, 1], 'euler89': [1, 0, -2, 0, 1], 'euler97': [1, 0, -2, 0, 1], 'euler_factors': [[1, -1, 1, -1, 1], [1, 1, 1, 1, 1], [1, 0, -2, 0, 1], [1, -1, 1, -1, 1], [1, 2, 1, 0, 0], [1, 2, 1, 0, 0], [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, 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, 0, -2, 0, 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]], 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/143/1/d/b'], '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': '4-143e2-1.1-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': '4-143e2-1.1-c0e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.26714471135794426, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0e2-0', 'trace_hash': 1209999580595804389, 'z1': {'__RealLiteral__': 0, 'data': '2.27203371878102644767358401045', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2880144907351544340827009922152,3893484791432041836001209150870', 'Lhash_array': ['2880144907351544340827009922152', '3893484791432041836001209150870'], 'label': '4-143e2-1.1-c0e2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/143/1/d/b'}