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lfunc_lfunctions • Show schema
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{'Lhash': '3275015049733125186264314531377', 'a10': [1.1322473170685492, 0.9810978850985471], 'a2': [-0.5406408174555976, -0.8412535328311812], 'a3': [1.2966683600145323, -1.1483253738105865], 'a4': [-0.41541501300188644, 0.9096319953545183], 'a5': [-1.4374911769542007, 0.422085492918907], 'a6': [-1.6670646196849084, -0.46999526997067903], 'a7': [3.3403699397968665, -2.8944470293525586], 'a8': [0.9898214418809327, -0.14231483827328514], 'a9': [0.3626976717255535, -2.977994358444096], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.1019355478936699, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.5406408174555976, 0.8412535328311812]]], [3, [[1.0, 0], [-1.2966683600145323, 1.1483253738105865]]], [23, [[1.0, 0], [-4.394450611292918, -1.9206258940531096]]]], 'bad_primes': [2, 3, 23], 'central_character': '138.11', 'coefficient_field': 'CDF', 'conductor': 138, 'conductor_radical': 138, 'conjugate': 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[[1.0, 0], [3.427138688008786, 1.0062987137734152], [69.82404322498803, 44.8731878488146]], [[1.0, 0], [-1.5059190629089725, 10.473897144457853], [-85.39487465169027, -25.074197558887242]], [[1.0, 0], [1.9537572231293603, 6.65388604269936], [-81.60159268462458, 52.442159293192965]], [[1.0, 0], [2.9243642077182566, -9.959469864090538], [-84.9666068159493, -54.60472256301536]], [[1.0, 0], [-10.44398821037746, 16.251162870344757], [-42.7877463391943, -93.6920955215154]], [[1.0, 0], [-0.778146137722677, -5.412125266626701], [-102.66574817675122, 30.145383582032977]], [[1.0, 0], [8.783782535149333, -4.011419073515198], [71.37982000003608, -82.37670360461415]], [[1.0, 0], [-5.055580125147157, 3.249024063379865], [46.94189646921317, -102.78841547506057]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 7, 'label': '2-138-69.11-c1-0-7', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 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0.47049078476401934, 'root_number': '0.09257319902256234 + 0.9957058816853143*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.235245392382', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.58353133674491013180686074384', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.64424647556260584316977057366', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.37069944700994717959544131447', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.1019355478936699, 'bad_primes': [2, 3, 23], 'central_character': '69.11', 'conductor': 138, 'conductor_radical': 138, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/138/2/f/a/11/3'], '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': '2-138-69.11-c1-0-7', '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': '2-138-69.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0497311788708907, 'root_angle': 0.23524539238200967, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.58353133674491013180686074384', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3275015049733125186264314531377', 'Lhash_array': ['3275015049733125186264314531377'], 'label': '2-138-69.11-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/138/2/f/a/11/3'}