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lfunc_lfunctions • Show schema
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{'Lhash': '1638098572882497237244470331304', 'a10': [0.0, 0.0], 'a2': [0.6234898018587335, 0.7818314824680298], 'a3': [1.6234898018587336, -0.7818314824680298], 'a4': [-0.2225209339563144, 0.9749279121818236], 'a5': [0.0, 0.0], 'a6': [1.6234898018587336, 0.7818314824680298], 'a7': [-0.9009688679024191, 0.4338837391175581], 'a8': [-0.9009688679024191, 0.4338837391175581], 'a9': [1.400968867902419, -1.7567593946498534], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.6628846220931641, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.6234898018587335, -0.7818314824680298]]], [7, [[1.0, 0], [0.9009688679024191, -0.4338837391175581]]], [17, [[1.0, 0], [0.2225209339563144, 0.9749279121818236]]]], 'bad_primes': [2, 7, 17], 'central_character': '3332.2311', 'coefficient_field': 'CDF', 'conductor': 3332, 'conductor_radical': 238, 'conjugate': '2258544694661433520375295680611', 'degree': 2, 'euler_factors': [[[1.0, 0], 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-0.9749279121818236]], [[1.0, 0], [0, 0], [0.2225209339563144, 0.9749279121818236]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 2, 'label': '2-3332-3332.2311-c0-0-2', 'leading_term': '2.7944726369871329233481779854937', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/3332/1/be/b/2311/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [2.794472636987133, 2.7537891520256768, 2.731700877239233, 2.7250533879013696, 2.7298192819285645, 2.74145767138398, 2.755254842459776, 2.766600825104566, 2.7711869222325656, 2.7651314496517028, 2.745051208695734, 2.708097310081085, 2.6519703735610123, 2.574925271004363, 2.4757712506900122, 2.35387007286426, 2.2091326823717985, 2.0420137073943256, 1.853502447173855, 1.6451087893369825, 1.4188425332816557, 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'3.73745350884794681555926611202211', '4.29502192060727304995159696964233', '5.53402952251152962625524970096580', '6.26884828633074220788346536416818', '7.24447633704381236107552869306897', '8.385251299017871601771258033437913', '8.816847783384506408862439114888834'], 'prelabel': '2-3332-3332.2311-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2895288372476066, 'root_angle': -0.32653061224489793, 'root_number': '0.51839256831052503153847431467515 - 0.85514276300534616571883696203789*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.16326530612244897', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.29223192304533435226780931431', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.54755603560408072253024734036', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.30978354497273307790501486054', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.6628846220931641, 'bad_primes': [2, 7, 17], 'central_character': '3332.2311', 'conductor': 3332, 'conductor_radical': 238, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3332/1/be/b/2311/1'], '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': '2-3332-3332.2311-c0-0-2', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-3332-3332.2311-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2895288372476066, 'root_angle': -0.16326530612244897, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.29223192304533435226780931431', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1638098572882497237244470331304', 'Lhash_array': ['1638098572882497237244470331304'], 'label': '2-3332-3332.2311-c0-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3332/1/be/b/2311/1'}