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lfunc_lfunctions • Show schema
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{'Lhash': '164978867138840922750711645923', 'a10': [-1.0356236397351444, -1.7937527615406768], 'a2': [-0.759865817130987, 1.316126202205711], 'a3': [-0.44758123464610766, 2.9664239478524754], 'a4': [0.8452078799117148, 1.4639429909646642], 'a5': [-0.6814516565867719, 1.1803088921102676], 'a6': [-3.5640866040222896, -2.8431575476251747], 'a7': [0.7360519141398916, -6.961194407548966], 'a8': [-8.647904842306554, 0.0], 'a9': [-8.599342076785332, -2.6554313861271837], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.438711217036106, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.44758123464610766, -2.9664239478524754]]], [7, [[1.0, 0], [-0.7360519141398916, 6.961194407548966]]], [13, [[1.0, 0], [13.0, 0]]]], 'bad_primes': [3, 7, 13], 'central_character': '273.233', 'coefficient_field': 'CDF', 'conductor': 273, 'conductor_radical': 273, 'conjugate': '3719054278088348203842579278320', 'degree': 2, 'euler_factors': 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'2.69055752671978665171910562492702', '4.97777306968923794054643457075762', '6.00266274276197863582660946950645', '7.00773263263764943757197304195245', '8.230373501948830702908470326324235', '9.102699727720250357562534929327195', '10.11857680364442485608103662616078', '11.17701868609049974767781157846353'], 'prelabel': '2-273-273.233-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.7274000837860415, 'root_angle': 0.5610272153853225, 'root_number': '-0.19055026500962263 + 0.9816774401527024*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.280513607693', 'prec': 47}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.13014537847348308825329840861', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.90752719284588504260447447401', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.69055752671978665171910562493', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.438711217036106, 'bad_primes': [3, 7, 13], 'central_character': '273.233', 'conductor': 273, 'conductor_radical': 273, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/273/3/w/c/233/3'], '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': '2-273-273.233-c2-0-2', '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': '2-273-273.233-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.7274000837860415, 'root_angle': 0.28051360769266126, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.13014537847348308825329840861', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '164978867138840922750711645923', 'Lhash_array': ['164978867138840922750711645923'], 'label': '2-273-273.233-c2-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/273/3/w/c/233/3'}