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lfunc_lfunctions • Show schema
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{'Lhash': '433209036557564426840219118466', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [-4.046818863181626, 0], 'a6': [0, 0], 'a7': [0, -3.8962277254667748], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 41.394448407831774, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '5184.2591', 'coefficient_field': 'CDF', 'conductor': 5184, 'conductor_radical': 6, 'conjugate': '705076068486018896724913142420', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [4.046818863181626, 0], [5.0, 0]], [[1.0, 0], [0, 3.8962277254667748], [-7.0, 0]], [[1.0, 0], [0, 0.4685724243105738], [-11.0, 0]], [[1.0, 0], [0, -4.896227725466775], [-13.0, 0]], [[1.0, 0], [0, 3.5782464388710524], [-17.0, 0]], [[1.0, 0], [1.8962277254667748, 0], [19.0, 0]], [[1.0, 0], [8.562210150673826, 0], 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'2.93691507790334697603823523722147', '3.68101023755143711281551004170414', '4.37853673370347498449891352685847', '5.29040131962210554632162387476369', '5.98755543480053608821769408744750', '6.73187748041569203422344398552782', '7.88230616264891481987340351844314', '8.136500401716218255227990871659346'], 'prelabel': '2-72e2-24.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.433851755195466, 'root_angle': -0.08333333333333333, 'root_number': '0.96592582628906828674974319972889736763390483900840455040 - 0.2588190451025207623488988376240483283490689013199305138*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.04166666666666667', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.34174167272872266964324437966', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.96933485590991223777156987876', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.93691507790334697603823523722', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 41.394448407831774, 'bad_primes': [2, 3], 'central_character': '24.11', 'conductor': 5184, 'conductor_radical': 6, 'degree': 2, 'index': 19, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5184/2/f/e/2591/1'], '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': '2-72e2-24.11-c1-0-19', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-72e2-24.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.433851755195466, 'root_angle': -0.041666666666666664, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.34174167272872266964324437966', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '433209036557564426840219118466', 'Lhash_array': ['433209036557564426840219118466'], 'label': '2-72e2-24.11-c1-0-19', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5184/2/f/e/2591/1'}