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lfunc_lfunctions • Show schema
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{'Lhash': '3392402595055361129286817540061', 'a10': [-2.2057676568466067, 0.3668637949013649], 'a2': [-0.5406408174555976, -0.8412535328311812], 'a3': [-1.5990075907654482, -0.2299025834852686], 'a4': [-0.41541501300188644, 0.9096319953545183], 'a5': [0.8839025655860403, -2.053951375897301], 'a6': [0.6710824104251398, 1.4694655054259382], 'a7': [-1.3524609306948776, 1.171914067518893], 'a8': [0.9898214418809327, -0.14231483827328514], 'a9': [-0.3745088434111698, -0.10996571826522573], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.8365592464894498, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.5406408174555976, 0.8412535328311812]]], [5, [[1.0, 0], [-0.8839025655860403, 2.053951375897301]]], [23, [[1.0, 0], [4.173629940449601, 2.3623744665447655]]]], 'bad_primes': [2, 5, 23], 'central_character': '230.219', 'coefficient_field': 'CDF', 'conductor': 230, 'conductor_radical': 230, 'conjugate': 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0], [4.324689631557567, -14.72854029035226], [-69.82404322498803, -44.8731878488146]], [[1.0, 0], [-0.03313884290425285, 0.23048571507887988], [-85.39487465169027, -25.074197558887242]], [[1.0, 0], [3.2971606227840997, 11.229097857583941], [-81.60159268462458, 52.442159293192965]], [[1.0, 0], [-3.2631296950609348, -0.9581413283637843], [84.9666068159493, 54.60472256301536]], [[1.0, 0], [-9.976436771789412, 15.523638630973391], [-42.7877463391943, -93.6920955215154]], [[1.0, 0], [0.5408368362739412, -0.07776059764910596], [102.66574817675122, -30.145383582032977]], [[1.0, 0], [-4.675287194437337, -10.237450950074717], [-71.37982000003608, 82.37670360461415]], [[1.0, 0], [1.7103389391743775, 2.6613393374379277], [-46.94189646921317, 102.78841547506057]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 10, 'label': '2-230-115.104-c1-0-10', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 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-0.4378125933526454, 'root_number': '-0.9246293716675583 - 0.380868120285298*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.437812593353', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.67613378200948172776763938066', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.70805385210310539975909073814', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.74885498648332823881927829953', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.8365592464894498, 'bad_primes': [2, 5, 23], 'central_character': '115.104', 'conductor': 230, 'conductor_radical': 230, 'degree': 2, 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/230/2/j/a/219/3'], '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': '2-230-115.104-c1-0-10', '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': '2-230-115.104-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.355197124587213, 'root_angle': -0.4378125933526454, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.67613378200948172776763938066', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3392402595055361129286817540061', 'Lhash_array': ['3392402595055361129286817540061'], 'factors': ['2-230-115.104-c1-0-10'], 'label': '2-230-115.104-c1-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/230/2/j/a/219/3'}