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lfunc_lfunctions • Show schema
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{'Lhash': '2394255065558045502799055824967', 'a10': [0.7016880383691804, -0.08101514571870484], 'a2': [1.297764406345312, 0.5619675663445357], 'a3': [1.2780857428214392, -1.1689725548517256], 'a4': [1.3683849087535997, 1.4586030102448722], 'a5': [0.4325489381385986, -0.2497322458720067], 'a6': [2.3155788470646503, -0.7988082392080997], 'a7': [0.0, 0.0], 'a8': [0.9561536448303742, 2.6619110066787717], 'a9': [0.26700633200685936, -2.988094312211086], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.6952036388512886, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.297764406345312, -0.5619675663445357]]], [3, [[1.0, 0], [-1.2780857428214392, 1.1689725548517256]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 7], 'central_character': '588.263', 'coefficient_field': 'CDF', 'conductor': 588, 'conductor_radical': 42, 'conjugate': '2215846921707399159372599812290', 'degree': 2, 'euler_factors': [[[1.0, 0], 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-94.39676901250381]], [[1.0, 0], [0, 10.272778333779154], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 58, 'label': '2-588-84.11-c1-0-58', '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/588/2/n/e/263/11', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [3.2404605632857204, 3.2549119815414116, 3.273930986379094, 3.289626508598307, 3.2900776461475227, 3.2612472389221905, 3.1889779684466273, 3.0608251195483116, 2.867634459812612, 2.6048397772154503, 2.273447975096272, 1.880645949801742, 1.4399377884454665, 0.97071984929702, 0.4972292044924744, 0.04685520806349332, -0.3521217141096184, -0.673214679382978, -0.8946042348154006, -1.001896270218047, -0.9904148497229937, -0.8666765619499407, -0.6487372372118151, -0.3651981724314159, -0.05280362174486627, 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'7.15907347974941592034439706813619', '7.88298949106348707453264748446111', '9.359258914481406707128726410441340', '9.908799190329302728526870186109618', '10.52163463920647761594089467087689'], 'prelabel': '2-588-84.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.166841858293145, 'root_angle': -0.016007186019422318, 'root_number': '0.9987358220586042 - 0.050266865198895685*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.00800359300971', 'prec': 57}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.88873421834611274002440338314', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.02115568650541862024549173099', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.92170767899887825969709995961', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.6952036388512886, 'bad_primes': [2, 3, 7], 'central_character': '84.11', 'conductor': 588, 'conductor_radical': 42, 'degree': 2, 'index': 58, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/588/2/n/e/263/11'], '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': '2-588-84.11-c1-0-58', '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': '2-588-84.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.166841858293145, 'root_angle': -0.008003593009711159, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.88873421834611274002440338314', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2394255065558045502799055824967', 'Lhash_array': ['2394255065558045502799055824967'], 'label': '2-588-84.11-c1-0-58', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/588/2/n/e/263/11'}