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lfunc_lfunctions • Show schema
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{'Lhash': '2089791087438222436729098209381', 'a10': [-3.33512813843874, -0.7904398891958063], 'a2': [1.1105890446142843, 0.3091535901785388], 'a3': [0.0, 0.0], 'a4': [-0.5745017153635439, -0.34671356159280703], 'a5': [-2.9709343352268878, 0.11528578221185684], 'a6': [0.0, 0.0], 'a7': [4.356889915099126, 0.6814051484782729], 'a8': [-2.113067795555063, -2.2397210144768582], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.821094307351343, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]]], 'bad_primes': [3], 'central_character': '729.685', 'coefficient_field': 'CDF', 'conductor': 729, 'conductor_radical': 3, 'conjugate': '894350918861288593609647985057', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.1105890446142843, -0.3091535901785388], [1.712333799060533, 1.0333987423037259]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.9709343352268878, -0.11528578221185684], [4.98496470583896, 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[-74.35841521575134, -48.90629904830174]], [[1.0, 0], [-13.45338503997388, -0.5220526079423543], [96.70831529327583, 7.516764805177302]], [[1.0, 0], [-0.12126129317703047, -6.25220041083614], [-100.92404320292724, 3.9163124969384877]], [[1.0, 0], [7.424738888523022, 5.754606876346322], [25.692437837972072, 99.744165934364]], [[1.0, 0], [-2.3064173927784295, -0.8394672787652087], [81.96675541373065, 68.77827423645971]], [[1.0, 0], [12.499459804673677, -4.549431313308059], [83.49884429996861, -70.06384945583278]], [[1.0, 0], [4.12653808796232, -3.7446336516182903], [10.939628389459237, -112.46921592462773]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 19, 'label': '2-3e6-243.103-c1-0-19', '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/729/2/i/a/685/18', 'plot_delta': {'__RealLiteral__': 0, 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{'__RealLiteral__': 0, 'data': '0.180570363589', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.64855448895931878419748270619', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.39258958823643269161813833602', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.16032889863781852291340132422', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.821094307351343, 'bad_primes': [3], 'central_character': '243.103', 'conductor': 729, 'conductor_radical': 3, 'degree': 2, 'index': 19, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/729/2/i/a/685/18'], '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': '2-3e6-243.103-c1-0-19', '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': '2-3e6-243.103-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': 0.1805703635891792, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.64855448895931878419748270619', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2089791087438222436729098209381', 'Lhash_array': ['2089791087438222436729098209381'], 'label': '2-3e6-243.103-c1-0-19', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/729/2/i/a/685/18'}