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lfunc_lfunctions • Show schema
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{'Lhash': '1657142419766380631101905265292', 'a10': [-0.2606118103373942, 0.4513928965568707], 'a2': [0.0, 0.4999866260092949], 'a3': [0.0, 0.0], 'a4': [1.7500133738118415, 0.0], 'a5': [0.9028099414572724, 0.5212375627274265], 'a6': [0.0, 0.0], 'a7': [2.634907079128189, 0.23930040610111034], 'a8': [0.0, 1.8749565342619154], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.5397479255428665, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-2.634907079128189, -0.23930040610111034]]], [13, [[1.0, 0], [3.5750364856214603, 0.4680962790659202]]]], 'bad_primes': [3, 7, 13], 'central_character': '819.478', 'coefficient_field': 'CDF', 'conductor': 819, 'conductor_radical': 273, 'conjugate': '2185002782420686581086778770439', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -0.4999866260092949], [-2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.9028099414572724, -0.5212375627274265], 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'10.33679718251333668209165829717898'], 'prelabel': '2-819-91.23-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.5572930855775735, 'root_angle': -0.2791527417558728, 'root_number': '0.6394726354290753 - 0.7688138581850571*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.139576370878', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.30725486933704495124244846736', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.25482742446617083838257937533', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.52923126661019591506768901975', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.5397479255428665, 'bad_primes': [3, 7, 13], 'central_character': '91.23', 'conductor': 819, 'conductor_radical': 273, 'degree': 2, 'index': 23, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/819/2/bm/f/478/4'], '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': '2-819-91.23-c1-0-23', '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': '2-819-91.23-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.5572930855775735, 'root_angle': -0.1395763708779364, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.30725486933704495124244846736', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1657142419766380631101905265292', 'Lhash_array': ['1657142419766380631101905265292'], 'label': '2-819-91.23-c1-0-23', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/819/2/bm/f/478/4'}