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lfunc_lfunctions • Show schema
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{'Lhash': '4053259534873396145043000679987', 'a10': [0.8271228151099318, 1.4326187398698005], 'a2': [1.2761107082137368, -2.210288582708895], 'a3': [-0.5, -0.8660254037844386], 'a4': [-2.2569170792355306, -3.9090950497058925], 'a5': [-0.32407956840504637, 0.5613222781725338], 'a6': [-2.5522214164274737, 8.511001888722816e-61], 'a7': [-2.3847796894654953, -1.1457861199686683], 'a8': [-6.415861376596777, 0.0], 'a9': [-0.5, 0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.8567744176278445, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.5, 0.8660254037844386]]], [7, [[1.0, 0], [2.3847796894654953, 1.1457861199686683]]], [23, [[1.0, 0], [-0.5, 0.8660254037844386]]]], 'bad_primes': [3, 7, 23], 'central_character': '483.415', 'coefficient_field': 'CDF', 'conductor': 483, 'conductor_radical': 483, 'conjugate': '743632758970547519851046658087', 'degree': 2, 'euler_factors': [[[1.0, 0], 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14.004556142356867], [-54.5, 94.39676901250381]], [[1.0, 0], [4.704672843474666, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 29, 'label': '2-483-7.2-c1-0-29', '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/483/2/i/g/415/8', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.2659474232586887, 1.5971433951938305, 1.97108707795338, 2.3959293778914614, 2.8762490753147048, 3.411946834227564, 3.997579079965029, 4.622050148156674, 5.2686111191761675, 5.9151751311906136, 6.535000711748496, 7.097800431170876, 7.571306058583811, 7.923273273846092, 8.123848428590284, 8.148155396537485, 7.97890045959393, 7.608745854602517, 7.042176385738308, 6.2965858188157116, 5.402345989989767, 4.4016937591974274, 3.346376820752473, 2.2941316067487953, 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'6.51440442440706716972622606237715', '7.81851213892711664419995244638140', '8.618074099873188055734498972707039', '9.490818885792182500591036628664375', '10.59158311619615529487519658810141', '12.14997182839883506028190038405319'], 'prelabel': '2-483-7.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9638672097745928, 'root_angle': -0.7109378276370049, 'root_number': '-0.6152324020268615 - 0.7883457943670774*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.355468913819', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.19745798577592455100680524184', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.13228386297394765128720579758', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.11434456975839068527414538119', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.8567744176278445, 'bad_primes': [3, 7, 23], 'central_character': '7.2', 'conductor': 483, 'conductor_radical': 483, 'degree': 2, 'index': 29, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/483/2/i/g/415/8'], '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': '2-483-7.2-c1-0-29', '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': '2-483-7.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9638672097745928, 'root_angle': -0.35546891381850243, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '3.19745798577592455100680524184', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '4053259534873396145043000679987', 'Lhash_array': ['4053259534873396145043000679987'], 'label': '2-483-7.2-c1-0-29', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/483/2/i/g/415/8'}