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lfunc_lfunctions • Show schema
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{'Lhash': '2069049466940983622974887214126', 'a10': [-0.6441558512991659, 0.32159189400738586], 'a2': [0.2826854381051604, 1.3856727402540954], 'a3': [0.9441218389809675, 1.4521136157887908], 'a4': [-1.840177886166587, 0.7834190112982141], 'a5': [0.13176382099010583, 0.4917492745344854], 'a6': [-1.745264757473352, 1.7187352694122158], 'a7': [2.4051775403451607, -1.3886299003671205], 'a8': [-1.6057538600951802, -2.3284231876506962], 'a9': [-1.2172679063183924, 2.7419443546956304], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.149845789106438, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.2826854381051604, -1.3856727402540954]]], [3, [[1.0, 0], [-0.9441218389809675, -1.4521136157887908]]]], 'bad_primes': [2, 3], 'central_character': '144.13', 'coefficient_field': 'CDF', 'conductor': 144, 'conductor_radical': 6, 'conjugate': '4073531305071668631593057952844', 'degree': 2, 'euler_factors': [[[1.0, 0], 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'2.95818968819334706903213127332313', '4.72807734617566842166023883886204', '6.00905055796535592170310946207422', '7.920844517617617079812759589048731', '8.507622746978573703950137562004137', '9.730708575953472786446199929011796', '10.98687377346356108728709427579232', '11.89203112476470936839699102968190', '12.87182097048415884552856167451478'], 'prelabel': '2-12e2-144.13-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.072308625865911, 'root_angle': -0.6371295263936717, 'root_number': '-0.4176024871177314 - 0.908629827131536*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.318564763197', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.63219223543811628058494970752', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.95818968819334706903213127332', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.72807734617566842166023883886', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.149845789106438, 'bad_primes': [2, 3], 'central_character': '144.13', 'conductor': 144, 'conductor_radical': 6, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/144/2/x/e/13/9'], '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': '2-12e2-144.13-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': '2-12e2-144.13-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.072308625865911, 'root_angle': -0.31856476319683585, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.63219223543811628058494970752', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2069049466940983622974887214126', 'Lhash_array': ['2069049466940983622974887214126'], 'label': '2-12e2-144.13-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/144/2/x/e/13/9'}