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lfunc_lfunctions • Show schema
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{'Lhash': '2214296103570095587334516187365', 'a10': [2.228241013428915, 0.0], 'a2': [-2.4478462895526025, 0.0], 'a3': [0.6674515656762904, 0.0], 'a4': [3.9919514572764445, 0.0], 'a5': [-0.9102863292270589, 0.0], 'a6': [-1.6338188384967829, 0.0], 'a7': [0.0, 0.0], 'a8': [-4.875990983663044, 0.0], 'a9': [-2.5545084074762685, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.086470608755563, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [7, 13], 'central_character': '637.1', 'coefficient_field': 'CDF', 'conductor': 637, 'conductor_radical': 91, 'conjugate': '2214296103570095587334516187365', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.4478462895526025, 0], [2.0, 0]], [[1.0, 0], [-0.6674515656762904, 0], [3.0, 0]], [[1.0, 0], [0.9102863292270589, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-3.678365382000258, 0], [11.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 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'4.36426167714966574176005306186737', '6.10222335697885023933537377020221', '6.88285217326742670782616051395261', '7.85830550016830784478718439740980', '8.496596284383703349614529315624972', '9.252775584778306557439180299937622', '9.748705149106110196372907742057865'], 'prelabel': '2-637-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2553205113144257, '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': '1.74677162868966491552739570492', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.94579331898935834227519856446', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.36426167714966574176005306187', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.086470608755563, 'bad_primes': [7, 13], 'central_character': '1.1', 'conductor': 637, 'conductor_radical': 91, 'degree': 2, 'index': 21, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/637/2/a/m/1/1'], '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': '2-637-1.1-c1-0-21', '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': '2-637-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2553205113144257, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.74677162868966491552739570492', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2214296103570095587334516187365', 'Lhash_array': ['2214296103570095587334516187365'], 'label': '2-637-1.1-c1-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/637/2/a/m/1/1'}