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lfunc_lfunctions • Show schema
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{'Lhash': '939278839050723766147993923708', 'a10': [-1.23880726922417, -2.863242103566326e-62], 'a2': [-1.0728385655409598, 0.619403634612085], 'a3': [-1.4821885136542443, -0.8961680701695536], 'a4': [-0.23267827485867723, 0.4030105938727051], 'a5': [0.8660254037844386, 0.5], 'a6': [2.145238758736426, 0.04337071434659101], 'a7': [0.16662906883422993, -0.09620333774625933], 'a8': [0.0, -3.054101615019278], 'a9': [1.3937655800171562, 2.656580039818006], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.671248518244905, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.4821885136542443, 0.8961680701695536]]], [5, [[1.0, 0], [-0.8660254037844386, -0.5]]], [13, [[1.0, 0], [3.4547629628735503, 1.0318007900545372]]]], 'bad_primes': [3, 5, 13], 'central_character': '585.571', 'coefficient_field': 'CDF', 'conductor': 585, 'conductor_radical': 195, 'conjugate': '1269696687821105868823620609956', 'degree': 2, 'euler_factors': 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[[1.0, 0], [-1.2797497058092167, 2.216591511432887], [-56.5, -97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 16, 'label': '2-585-117.103-c1-0-16', '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/585/2/bt/b/571/18', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.6730960628436221, 0.6185354754822527, 0.5433870806473604, 0.4450800613112986, 0.3205298892669184, 0.16751339512701552, -0.014040492499041385, -0.22098943284519296, -0.44622608680745, -0.6782947611808257, -0.9014369343747656, -1.0961271806316562, -1.2401450396521552, -1.3101905468872208, -1.2839933766714164, -1.1427939879479072, -0.8739987763591768, -0.47374107660764797, 0.05097181737724254, 0.6808664405055282, 1.3840864291992674, 2.1172038681811722, 2.8276940397986454, 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'5.72535136785355837701632604873954', '6.97626580555519002610126842054545', '8.181120874528797095511014825743011', '9.201141490488225127572316708046692', '9.919915522171734403334878942273171', '10.26373244674613440092102111667430'], 'prelabel': '2-585-117.103-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.161307131863703, 'root_angle': -0.28363774800699443, 'root_number': '0.6285768822421591 - 0.7777474545832515*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.141818874003', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.74096035522849500307214772551', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.23895466189484072459518739512', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.03833465673396231525140769285', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.671248518244905, 'bad_primes': [3, 5, 13], 'central_character': '117.103', 'conductor': 585, 'conductor_radical': 195, 'degree': 2, 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/585/2/bt/b/571/18'], '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': '2-585-117.103-c1-0-16', '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': '2-585-117.103-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.161307131863703, 'root_angle': -0.14181887400349721, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.74096035522849500307214772551', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '939278839050723766147993923708', 'Lhash_array': ['939278839050723766147993923708'], 'label': '2-585-117.103-c1-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/585/2/bt/b/571/18'}