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lfunc_lfunctions • Show schema
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{'Lhash': '1382967008155349351196282161941', 'a10': [-13295.040722163276, 23027.686019484012], 'a2': [8.0, 13.856406460551018], 'a3': [9.292944193973867, 16.095851495864945], 'a4': [-128.0, 221.70250336881628], 'a5': [830.9400451352047, 1439.2303762177507], 'a6': [-148.68710710358187, 257.5336239338391], 'a7': [10512.553063450767, 0.0], 'a8': [-4096.0, 0.0], 'a9': [9668.782376415375, -16746.82232327798], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 19.571361774227185, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '4.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-8.0, -13.856406460551018]]], [19, [[1.0, 0], [-234882.93055147756, -517221.139083226]]]], 'bad_primes': [2, 19], 'central_character': '38.7', 'coefficient_field': 'CDF', 'conductor': 38, 'conductor_radical': 38, 'conjugate': '2266988461439395443895151809188', 'degree': 2, 'euler_factors': [[[1.0, 0], [-8.0, -13.856406460551018]], [[1.0, 0], [-9.292944193973867, -16.095851495864945], [-9841.5, 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-2.0681193224838705, -1.5161413142664664, -0.7627493480177797], 'positive_zeros': ['1.09096860594422330507313248151883', '2.16330331409301756283520941982997', '4.63623173889208259164771930915354', '5.30156512053900290322794205950260', '7.71654291306224930152048125992828', '8.964303158879863629451130756231924', '10.43426385694038545969211139438354', '11.58255900638057193312496029586827', '12.84709691788718157531607976416899', '13.73568140216287165770747503676150'], 'prelabel': '2-38-19.7-c9-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.423953184000389, 'root_angle': -0.5679354644030533, 'root_number': '-0.21180896977305838 - 0.97731108677006*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.283967732202', 'prec': 50}, 'spectral_label': 'c9-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.09096860594422330507313248152', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.16330331409301756283520941983', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.63623173889208259164771930915', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 19.571361774227185, 'bad_primes': [2, 19], 'central_character': '19.7', 'conductor': 38, 'conductor_radical': 38, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/38/10/c/a/7/4'], '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': '2-38-19.7-c9-0-6', 'motivic_weight': 9, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [9], 'order_of_vanishing': 0, 'prelabel': '2-38-19.7-c9-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.423953184000389, 'root_angle': -0.28396773220152666, 'self_dual': False, 'spectral_label': 'c9-0', 'z1': {'__RealLiteral__': 0, 'data': '1.09096860594422330507313248152', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1382967008155349351196282161941', 'Lhash_array': ['1382967008155349351196282161941'], 'label': '2-38-19.7-c9-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/38/10/c/a/7/4'}