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lfunc_lfunctions • Show schema
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{'Lhash': '1365014205811294074456898222487', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [1.3226764678509881, 3.1932234673175968], 'a6': [0, 0], 'a7': [2.329129981310535, 2.329129981310535], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.198766312851504, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '1152.1007', 'coefficient_field': 'CDF', 'conductor': 1152, 'conductor_radical': 6, 'conjugate': '1980647544975547681165124738746', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.3226764678509881, -3.1932234673175968], [-3.5355339059327378, 3.5355339059327378]], [[1.0, 0], [-2.329129981310535, -2.329129981310535], [0, 7.0]], [[1.0, 0], [1.4706069144837834, 3.5503591578664], [-7.7781745930520225, 7.7781745930520225]], [[1.0, 0], [-4.49745081266885, 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'2.1063806152685662272240130734945687365333164713533941054', '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/1152/2/w/b/1007/8', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [2.106380615268566, 2.0343530476864387, 1.9583281199874938, 1.8779930762910848, 1.7929045477195211, 1.7025491169053522, 1.6064083628683843, 1.50402464897166, 1.3950643197098322, 1.279375590062977, 1.1570390934558086, 1.0284096811099814, 0.8941485667047205, 0.7552452651613317, 0.6130289992550706, 0.4691693791370186, 0.3256662400450003, 0.18482859088642462, 0.0492427104781708, -0.078270451750202, -0.19470824814137236, -0.2969491427073051, -0.3818245664760291, -0.44619873486180683, -0.4870550289273224, -0.5015872179677943, -0.4872934816078726, -0.4420708912288961, -0.36430774892011936, 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'8.794947126998766463071040887691512', '9.764489598892082611870302084720360'], 'prelabel': '2-1152-96.83-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.032946803498456, 'root_angle': -0.3638090566193356, 'root_number': '0.41492144832738867183947764467154469161073178699196982707 - 0.90985723699814694188993269937871028637711546535657723791*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.1819045283096678', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.07680634203583795683621704861', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.79435897777319581041888132292', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.65211178179520080145019439181', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.198766312851504, 'bad_primes': [2, 3], 'central_character': '96.83', 'conductor': 1152, 'conductor_radical': 6, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1152/2/w/b/1007/8'], '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': '2-1152-96.83-c1-0-7', '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': '2-1152-96.83-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.032946803498456, 'root_angle': -0.1819045283096678, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.07680634203583795683621704861', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1365014205811294074456898222487', 'Lhash_array': ['1365014205811294074456898222487'], 'label': '2-1152-96.83-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1152/2/w/b/1007/8'}