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lfunc_lfunctions • Show schema
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{'Lhash': '570100416606240050644566068017', 'a10': [0.05495813208737119, -0.0951902770644083], 'a2': [-0.2225209339563144, 0.38541756336001515], 'a3': [-0.5, 0.8660254037844386], 'a4': [0.9009688679024191, 1.5605238552448022], 'a5': [-0.24697960371746705, 0.0], 'a6': [-0.2225209339563144, -0.38541756336001515], 'a7': [-0.8765101981412665, -1.5181601965329372], 'a8': [-1.6920214716300959, 0.0], 'a9': [-0.5, -0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.048415382478917, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.5, -0.8660254037844386]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 13], 'central_character': '507.22', 'coefficient_field': 'CDF', 'conductor': 507, 'conductor_radical': 39, 'conjugate': '2927138073080154930783864716643', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.2225209339563144, -0.38541756336001515], [-1.0, -1.7320508075688772]], [[1.0, 0], [0.5, 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[0]], 'group': 'GL2', 'index': 2, 'label': '2-507-13.9-c1-0-2', '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/507/2/e/j/22/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.7500538821125665, 0.540577699907005, 0.3341593371878155, 0.12621400942656086, -0.0857953365415783, -0.3013982659441763, -0.5166670294464131, -0.7242405129429532, -0.9137535289606146, -1.0726180284135087, -1.1871208110536478, -1.2438004503373967, -1.2310420579523325, -1.140789685196131, -0.9702326804548167, -0.723284069832078, -0.41164493983253786, -0.05524652930684096, 0.31811294320183703, 0.6740637457406896, 0.9739334842300106, 1.177919542891079, 1.248969242165257, 1.1570447286856502, 0.8833389120620473, 0.4239333652438335, -0.20763319620847445, -0.9793726810643034, -1.8418002664450541, 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'9.853702969945341046877987159111085', '10.53438284102927230206595023200669'], 'prelabel': '2-507-13.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0120674398436345, 'root_angle': -0.9571820145637041, 'root_number': '-0.9909662671986046 - 0.13411136146674463*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.478591007282', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.44972993071087447733884193620', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.14359875952005769838066149262', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.21219233542648758830026458624', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.048415382478917, 'bad_primes': [3, 13], 'central_character': '13.9', 'conductor': 507, 'conductor_radical': 39, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/507/2/e/j/22/2'], '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': '2-507-13.9-c1-0-2', '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': '2-507-13.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0120674398436345, 'root_angle': -0.47859100728185205, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.44972993071087447733884193620', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '570100416606240050644566068017', 'Lhash_array': ['570100416606240050644566068017'], 'label': '2-507-13.9-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/507/2/e/j/22/2'}