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lfunc_lfunctions • Show schema
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{'Lhash': '350242934546768001054096650232', 'a10': [-0.07593076624502722, -0.04383864833134102], 'a2': [0.5, 0.8660254037844386], 'a3': [-0.2809878575836257, -1.7091067327380594], 'a4': [-0.5, 0.8660254037844386], 'a5': [-0.07593076624502722, 0.04383864833134102], 'a6': [1.3396359195383676, -1.0978959891914135], 'a7': [-2.620991813471897, -0.36111205146505015], 'a8': [-1.0, 0.0], 'a9': [-2.842091647781128, 0.9604764784276354], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.359831950361911, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.5, -0.8660254037844386]]], [3, [[1.0, 0], [0.2809878575836257, 1.7091067327380594]]], [7, [[1.0, 0], [2.620991813471897, 0.36111205146505015]]], [13, [[1.0, 0], [2.433014331130558, -2.660909856517752]]]], 'bad_primes': [2, 3, 7, 13], 'central_character': '546.311', 'coefficient_field': 'CDF', 'conductor': 546, 'conductor_radical': 546, 'conjugate': '2620500476393055582179370635872', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [0.2809878575836257, 1.7091067327380594]], [[1.0, 0], [0.07593076624502722, -0.04383864833134102], [2.5, -4.330127018922194]], [[1.0, 0], [2.620991813471897, 0.36111205146505015]], [[1.0, 0], [2.831312820449799, -4.9039776571401905], [-5.5, -9.526279441628825]], [[1.0, 0], [2.433014331130558, -2.660909856517752]], [[1.0, 0], [-1.3356592669357508, 2.3134297119329217], [-8.5, -14.722431864335457]], [[1.0, 0], [-3.326916970766314, -5.762389225930398], [-9.5, 16.454482671904334]], [[1.0, 0], [-1.063027060550676, 0.6137389595647894], [11.5, -19.91858428704209]], [[1.0, 0], [0, 5.847647167786417], [-29.0, 0]], [[1.0, 0], [0.44190901686164913, -0.765408869527188], [-15.5, -26.846787517317598]], [[1.0, 0], [-0.45621867684656764, 0.2633979758867007], [18.5, -32.04293994002423]], [[1.0, 0], [0, 8.993521846447633], [-41.0, 0]], [[1.0, 0], [9.697204369137854, 0], [43.0, 0]], [[1.0, 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'3.23054747020859620618774905829253', '4.78622475731496407442986695874008', '5.54211099724495126557377426395551', '6.42014667570542235694750258467271', '8.016081872445648228569479627097305', '8.959611964945410920327164652285358', '9.821875926252801627974762817755428', '10.44374469404153285068269469342013'], 'prelabel': '2-546-273.38-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0880210608042034, 'root_angle': -0.8128639633939716, 'root_number': '-0.8321043213648676 - 0.5546191471324382*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.406431981697', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.27629295839382699343345871123', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.01554700312171982135347345502', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.23054747020859620618774905829', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.359831950361911, 'bad_primes': [2, 3, 7, 13], 'central_character': '273.38', 'conductor': 546, 'conductor_radical': 546, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/546/2/bg/b/311/9'], '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': '2-546-273.38-c1-0-3', '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': '2-546-273.38-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0880210608042034, 'root_angle': -0.4064319816969858, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.27629295839382699343345871123', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '350242934546768001054096650232', 'Lhash_array': ['350242934546768001054096650232'], 'label': '2-546-273.38-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/546/2/bg/b/311/9'}