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lfunc_lfunctions • Show schema
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{'Lhash': '3102903343392393804352621717967', 'a10': [-2.0595276377251452, -3.56720650813226], 'a2': [1.8583656656257541, -1.0729279173017872], 'a3': [0.5, 0.8660254037844386], 'a4': [1.3023486314511015, -2.2557339988411025], 'a5': [0.0, -1.9195396116679222], 'a6': [1.8583656656257541, 1.0729279173017872], 'a7': [0.8660254037844386, 0.5], 'a8': [0.0, -1.2975931497675037], 'a9': [-0.5, 0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.1799159751809554, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-0.5, -0.8660254037844386]]], [7, [[1.0, 0], [-0.8660254037844386, -0.5]]], [13, [[1.0, 0], [-1.0548086398466383, 3.447807815598904]]]], 'bad_primes': [3, 7, 13], 'central_character': '273.127', 'coefficient_field': 'CDF', 'conductor': 273, 'conductor_radical': 273, 'conjugate': '2519480909039099302874245105037', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.8583656656257541, 1.0729279173017872], 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 12, 'label': '2-273-13.10-c1-0-12', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/273/2/bd/b/127/7', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [2.6034547512537136, 2.682660201157785, 2.7852291242248177, 2.9077570343530477, 3.043382883759381, 3.1825160980688265, 3.3136570879233296, 3.4241881078028715, 3.5011166334649086, 3.531807981023771, 3.50474696305782, 3.4103432400143774, 3.241762053080341, 2.9957321156765806, 2.6732599664796473, 2.2801666488007366, 1.8273590402293287, 1.3307552231818547, 0.8108013952771578, 0.29154676279649155, -0.20071856502976604, -0.6392119131320851, -0.9986926974670312, -1.2576359368941399, -1.4003570391569773, -1.4188737578814787, -1.3142840319549278, -1.0974550633799784, 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'10.33045231296767621389099998938410', '11.43053150144218801145430929379257', '12.22639795817328552870667100173822'], 'prelabel': '2-273-13.10-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4764538513549808, 'root_angle': 0.2652527878833934, 'root_number': '0.6724249184580768 + 0.7401653389862624*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.132626393942', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.44775914028182781655924382732', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.75586862618827002313314807185', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.86430925450513092523331685465', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.1799159751809554, 'bad_primes': [3, 7, 13], 'central_character': '13.10', 'conductor': 273, 'conductor_radical': 273, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/273/2/bd/b/127/7'], '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': '2-273-13.10-c1-0-12', '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': '2-273-13.10-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4764538513549808, 'root_angle': 0.1326263939416967, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.44775914028182781655924382732', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3102903343392393804352621717967', 'Lhash_array': ['3102903343392393804352621717967'], 'label': '2-273-13.10-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/273/2/bd/b/127/7'}