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lfunc_lfunctions • Show schema
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{'Lhash': '3151045993727300449126622020181', 'a10': [-5.836803674298185, -18.47406060769739], 'a2': [1.5007182129950523, 0.8664400642504676], 'a3': [2.598076211353316, -1.5], 'a4': [-2.4985632301232914, -4.327638460496949], 'a5': [-8.247454816771858, -7.548475941890963], 'a6': [5.198640385502806, 5.5731301480559415e-61], 'a7': [14.915857435179786, 10.978032472779075], 'a8': [0.0, -22.522462170575004], 'a9': [4.5, -7.794228634059948], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.195200550602768, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-2.598076211353316, 1.5]]], [5, [[1.0, 0], [8.247454816771858, 7.548475941890963]]], [7, [[1.0, 0], [-14.915857435179786, -10.978032472779075]]]], 'bad_primes': [3, 5, 7], 'central_character': '105.79', 'coefficient_field': 'CDF', 'conductor': 105, 'conductor_radical': 105, 'conjugate': '1232099577569292666695077670812', 'degree': 2, 'euler_factors': [[[1.0, 0], 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'4.67802540169332197402874919208563', '7.05912014758576913892343736339340', '7.933388954501905062617351820696748', '9.049255255107502942940807275330736', '10.63216185333588571607393844359528', '11.41140065069492537937589043215331', '12.48224552946606452893104905369640', '13.58706163909250510499759471843615'], 'prelabel': '2-105-35.9-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.489015980383165, 'root_angle': 0.417711793372606, 'root_number': '0.25564617118552607 + 0.9667704149166857*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.208855896686', 'prec': 47}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.48573699500476091951399850261', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.01486875034113811312054574159', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.67802540169332197402874919209', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.195200550602768, 'bad_primes': [3, 5, 7], 'central_character': '35.9', 'conductor': 105, 'conductor_radical': 105, 'degree': 2, 'index': 20, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/105/4/q/b/79/14'], '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': '2-105-35.9-c3-0-20', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-105-35.9-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.489015980383165, 'root_angle': 0.208855896686303, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '2.48573699500476091951399850261', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3151045993727300449126622020181', 'Lhash_array': ['3151045993727300449126622020181'], 'label': '2-105-35.9-c3-0-20', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/105/4/q/b/79/14'}