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lfunc_lfunctions • Show schema
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{'Lhash': '1269617240561500168182095182000', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-2.9032119259115534, 0.0], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-3.525427560843517, 0.0], 'a8': [0.0, 0.0], 'a9': [5.4286394867550705, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 25.552128646809734, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 5], 'central_character': '3200.1', 'coefficient_field': 'CDF', 'conductor': 3200, 'conductor_radical': 10, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [2.9032119259115534, 0], [3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [3.525427560843517, 0], [7.0, 0]], [[1.0, 0], [3.8064238518231064, 0], [11.0, 0]], [[1.0, 0], [2.6222156349319636, 0], [13.0, 0]], [[1.0, 0], [-5.806423851823107, 0], [17.0, 0]], [[1.0, 0], [-5.050855121687034, 0], [19.0, 0]], [[1.0, 0], [0.4745724391564829, 0], [23.0, 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0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 27, 'label': '2-3200-1.1-c1-0-27', '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': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/3200/2/a/bp/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [-4.478869394319982e-61, 0.08776624796369883, 0.17449633568850767, 0.25912002724743627, 0.34050156922980707, 0.4174133169274489, 0.48851649279371756, 0.5523506536057734, 0.6073328983081411, 0.6517673052450673, 0.6838645894688361, 0.701771543720336, 0.7036094784052638, 0.6875206008110667, 0.6517210585960936, 0.5945592016847547, 0.5145774764288907, 0.41057624674110427, 0.28167773433758814, 0.12738818437199406, -0.052343702554613784, -0.2570740693750123, -0.4858189335641444, -0.7370189121509911, -1.0085155134440664, -1.2975407224819027, -1.6007214006456283, 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'6.75599148957352270341634295760775', '7.28848271779358453382459274823180', '8.061916963971535515451910583893048'], 'prelabel': '2-3200-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.054911339164094, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.00155140567354812934813386066', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.66639596194841814838482813479', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.53213132492645684856537405150', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 25.552128646809734, 'bad_primes': [2, 5], 'central_character': '1.1', 'conductor': 3200, 'conductor_radical': 10, 'degree': 2, 'index': 27, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3200/2/a/bp/1/1'], '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': '2-3200-1.1-c1-0-27', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-3200-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.054911339164094, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.00155140567354812934813386066', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1269617240561500168182095182000', 'Lhash_array': ['1269617240561500168182095182000'], 'label': '2-3200-1.1-c1-0-27', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3200/2/a/bp/1/1'}