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lfunc_lfunctions • Show schema
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{'Lhash': '1075684480052379863326779569615', 'a10': [0.6170542470532806, -0.7121185626056603], 'a2': [-0.8184071105967161, 0.5259583134175959], 'a3': [-0.9898214418809327, -0.14231483827328514], 'a4': [-0.4376719747815895, 0.9583679435522033], 'a5': [-0.9293380118842471, 0.2728782611838857], 'a6': [0.8849285785689645, -0.4041333405699901], 'a7': [2.615087542426478, 0.4016430572608532], 'a8': [-0.42276755018999496, -2.940412898519824], 'a9': [0.9594929736144974, 0.28173255684142967], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.8567744176278445, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.9898214418809327, 0.14231483827328514]]], [7, [[1.0, 0], [-2.615087542426478, -0.4016430572608532]]], [23, [[1.0, 0], [-4.074551087827713, -2.5294334212787666]]]], 'bad_primes': [3, 7, 23], 'central_character': '483.34', 'coefficient_field': 'CDF', 'conductor': 483, 'conductor_radical': 483, 'conjugate': 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[11.242872223589526, 78.19589390859369]], [[1.0, 0], [5.97397791559048, 1.754118184246087], [69.82404322498803, 44.8731878488146]], [[1.0, 0], [1.326572213625115, -9.226512408552392], [-85.39487465169027, -25.074197558887242]], [[1.0, 0], [-14.824739325699893, 4.352936216930747], [81.60159268462458, -52.442159293192965]], [[1.0, 0], [-3.5369450632179253, 12.04572866645362], [-84.9666068159493, -54.60472256301536]], [[1.0, 0], [-12.017186448450756, -7.72297678577539], [42.7877463391943, 93.6920955215154]], [[1.0, 0], [2.1698976843839026, -0.31198418720436055], [102.66574817675122, -30.145383582032977]], [[1.0, 0], [0.148696819872306, -0.06790756226260344], [71.37982000003608, -82.37670360461415]], [[1.0, 0], [0.017242035766454434, 0.026829131344532], [-46.94189646921317, 102.78841547506057]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 10, 'label': '2-483-161.34-c1-0-10', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': 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1.9638672097745928, 'root_angle': -0.3864213087379881, 'root_number': '0.34929441440122105 - 0.937013026626689*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.193210654369', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.848565432666313795377492637830', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.20128320365436962947568010244', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.43257112560158570585836010336', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.8567744176278445, 'bad_primes': [3, 7, 23], 'central_character': '161.34', 'conductor': 483, 'conductor_radical': 483, 'degree': 2, 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/483/2/r/a/34/11'], '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': '2-483-161.34-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': '2-483-161.34-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9638672097745928, 'root_angle': -0.19321065436899404, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.848565432666313795377492637830', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1075684480052379863326779569615', 'Lhash_array': ['1075684480052379863326779569615'], 'label': '2-483-161.34-c1-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/483/2/r/a/34/11'}