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lfunc_lfunctions • Show schema
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{'Lhash': '1326787238277026245911534646740', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, -2.7544057079459154], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [0, 3.8499679278027856], 'a8': [0, 0], 'a9': [1.4132491960349605, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 21.798421148823756, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 5], 'central_character': '800.351', 'coefficient_field': 'CDF', 'conductor': 800, 'conductor_radical': 10, 'conjugate': '1207712131798150824447325117568', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 2.7544057079459154], [-9.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -3.8499679278027856], [-49.0, 0]], [[1.0, 0], [0, 6.19112443971374], [-121.0, 0]], [[1.0, 0], [-16.11318505164053, 0], [169.0, 0]], [[1.0, 0], [5.208747271497402, 0], [289.0, 0]], [[1.0, 0], [0, -36.22637010328106], [-361.0, 0]], [[1.0, 0], [0, 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'4.03952535439498710256315709126842', '4.47824046182685693043400685853298', '5.64128532399189099088698549713636', '6.76804226275593960312021754749265', '7.53315944194217920217168361584299', '8.702510708851886544724216027751602', '9.446910645135695683066234755206956', '10.08520175886183248985261589868632'], 'prelabel': '2-800-4.3-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.668877932525518, 'root_angle': 0.25, 'root_number': '0.7071067811865475244008443621048490392848359376884740366 + 0.7071067811865475244008443621048490392848359376884740366*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.04665058182290120798737263806', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.72951988459881387882698495541', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.03952535439498710256315709127', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 21.798421148823756, 'bad_primes': [2, 5], 'central_character': '4.3', 'conductor': 800, 'conductor_radical': 10, 'degree': 2, 'index': 20, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/800/3/b/i/351/2'], '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': '2-800-4.3-c2-0-20', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-800-4.3-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.668877932525518, 'root_angle': 0.125, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.04665058182290120798737263806', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1326787238277026245911534646740', 'Lhash_array': ['1326787238277026245911534646740'], 'label': '2-800-4.3-c2-0-20', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/800/3/b/i/351/2'}