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lfunc_lfunctions • Show schema
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{'Lhash': '678293928006824798687974316165', 'a10': [-2.4508289950867894, 0.0], 'a2': [1.127575562375462, 0.0], 'a3': [2.457306253383306, 0.0], 'a4': [-0.7285733511336605, 0.0], 'a5': [-2.1735385874483044, 0.0], 'a6': [2.7707984805874206, 0.0], 'a7': [-3.3503651955185805, 0.0], 'a8': [-3.0766726308872365, 0.0], 'a9': [3.0383540229166988, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 64.20770826531158, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[11, [[1.0, 0], [1.0, 0]]], [17, [[1.0, 0], [1.0, 0]]], [43, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [11, 17, 43], 'central_character': '8041.1', 'coefficient_field': 'CDF', 'conductor': 8041, 'conductor_radical': 8041, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.127575562375462, 0], [2.0, 0]], [[1.0, 0], [-2.457306253383306, 0], [3.0, 0]], [[1.0, 0], [2.1735385874483044, 0], [5.0, 0]], [[1.0, 0], [3.3503651955185805, 0], [7.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], 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'3.05578829101714686340822206630253', '3.34450501312466922539374705380026', '4.21067994127326262623310641183483', '4.64613144133494441109608867662111', '5.70554428146661334933082693855424', '6.43946025532362360504762758550339', '7.32571989093043437529506450588493', '7.80908657021911669134022863606487'], 'prelabel': '2-8041-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.012971250747851, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.53507956205337962249803961856', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.33822658718482274751007070921', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.05578829101714686340822206630', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 64.20770826531158, 'bad_primes': [11, 17, 43], 'central_character': '1.1', 'conductor': 8041, 'conductor_radical': 8041, 'degree': 2, 'index': 119, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8041/2/a/e/1/43'], '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': '2-8041-1.1-c1-0-119', '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': '2-8041-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.012971250747851, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.53507956205337962249803961856', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '678293928006824798687974316165', 'Lhash_array': ['678293928006824798687974316165'], 'label': '2-8041-1.1-c1-0-119', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8041/2/a/e/1/43'}