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lfunc_lfunctions • Show schema
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{'Lhash': '2338754708713271411480691639718', 'a10': [-2.365708573015273, 0.0], 'a2': [-1.0, 0.0], 'a3': [-1.3232411320539659, 0.0], 'a4': [1.0, 0.0], 'a5': [2.365708573015273, 0.0], 'a6': [1.3232411320539659, 0.0], 'a7': [2.1825783146242315, 0.0], 'a8': [-1.0, 0.0], 'a9': [-1.249032906440539, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.883104654234373, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, 0]]], [431, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 431], 'central_character': '862.1', 'coefficient_field': 'CDF', 'conductor': 862, 'conductor_radical': 862, 'conjugate': '2338754708713271411480691639718', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 0]], [[1.0, 0], [1.3232411320539659, 0], [3.0, 0]], [[1.0, 0], [-2.365708573015273, 0], [5.0, 0]], [[1.0, 0], [-2.1825783146242315, 0], [7.0, 0]], [[1.0, 0], [5.723427431555071, 0], [11.0, 0]], [[1.0, 0], [-0.593024541288569, 0], [13.0, 0]], [[1.0, 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'5.38280750115608869363478336265344', '6.28153891949457198481846618302823', '7.08444357024991670251947482115700', '8.407115717887632952624664244945628', '8.667009705040072003209182771104588', '9.991198570023228661182429232030227'], 'prelabel': '2-862-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.623567162135243, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.84495215660545507175918725981', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.72382706081070357360295950535', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.76405810025956420729923963557', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.883104654234373, 'bad_primes': [2, 431], 'central_character': '1.1', 'conductor': 862, 'conductor_radical': 862, 'degree': 2, 'index': 24, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/862/2/a/i/1/3'], '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': '2-862-1.1-c1-0-24', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-862-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.623567162135243, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.84495215660545507175918725981', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2338754708713271411480691639718', 'Lhash_array': ['2338754708713271411480691639718'], 'label': '2-862-1.1-c1-0-24', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/862/2/a/i/1/3'}