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lfunc_lfunctions • Show schema
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{'Lhash': '776153189566406212536705543403', 'a10': [-5.083502805572695, 0.0], 'a2': [1.552048223200346, 0.0], 'a3': [-1.0, 0.0], 'a4': [0.4088536871393512, 0.0], 'a5': [-3.275351068081144, 0.0], 'a6': [-1.552048223200346, 0.0], 'a7': [2.821779274422298, 0.0], 'a8': [-2.469535807727152, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 24.02698596820328, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.0, 0]]], [17, [[1.0, 0], [-1.0, 0]]], [59, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [3, 17, 59], 'central_character': '3009.1', 'coefficient_field': 'CDF', 'conductor': 3009, 'conductor_radical': 3009, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.552048223200346, 0], [2.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [3.275351068081144, 0], [5.0, 0]], [[1.0, 0], [-2.821779274422298, 0], [7.0, 0]], [[1.0, 0], [1.9564715248005629, 0], [11.0, 0]], [[1.0, 0], [4.410537984648812, 0], [13.0, 0]], [[1.0, 0], 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'4.31680568476276913577144474268035', '4.80971156747084537228016152856401', '5.23578656515859831507037966401310', '6.31519906745011593100171546131949', '7.28418083474030531551576809919846', '7.75553931402316934607684170351470', '8.558347310674620180097555119398571'], 'prelabel': '2-3009-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.901732955619194, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.61227690771153078012147092426', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.38926108975777361393216283430', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.37151979021854658969174366667', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 24.02698596820328, 'bad_primes': [3, 17, 59], 'central_character': '1.1', 'conductor': 3009, 'conductor_radical': 3009, 'degree': 2, 'index': 20, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3009/2/a/h/1/12'], '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': '2-3009-1.1-c1-0-20', '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': '2-3009-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.901732955619194, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.61227690771153078012147092426', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '776153189566406212536705543403', 'Lhash_array': ['776153189566406212536705543403'], 'label': '2-3009-1.1-c1-0-20', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3009/2/a/h/1/12'}