Formats: - HTML - YAML - JSON - 2026-10-22T21:31:14.172027
  • lfunc_lfunctions • Show schema
    {'Lhash': '267324192518658873020991163405', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-4.5, 7.794228634059948], 'a4': [0, 0], 'a5': [-3.1953303150591936, -5.534474452647592], 'a6': [0, 0], 'a7': [0, 0], 'a8': [0, 0], 'a9': [-40.5, -70.14805770653953], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 94.30568605003263, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 7}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [4.5, -7.794228634059948]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 7], 'central_character': '588.361', 'coefficient_field': 'CDF', 'conductor': 588, 'conductor_radical': 42, 'conjugate': '1751884434396655834220691339106', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [4.5, -7.794228634059948]], [[1.0, 0], [3.1953303150591936, 5.534474452647592], [-1562.5, 2706.329386826371]], [[1.0, 0], [0, 0]], [[1.0, 0], [372.75797283553277, -645.6357478775221], [-80525.5, -139474.25730488764]], [[1.0, 0], 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'group': 'GL2', 'index': 4, 'label': '2-588-7.4-c5-0-4', 'leading_term': '0.830947481241251729879165552602133441395184573516756977', 'load_key': 'CMFs-workshop', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/588/6/i/j/361/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 24}, 'plot_values': [0.8309474812412517, 0.5912935536514666, 0.3560399869122452, 0.12962310234435123, -0.0836926661790993, -0.2798833565708545, -0.4552311968899679, -0.6063866778355735, -0.7304261853333944, -0.824904385951104, -0.8879005487812748, -0.9180579859431113, -0.9146158035966752, -0.8774321799316185, -0.8069984293920218, -0.7044431764786643, -0.5715260503609787, -0.41062042509482105, -0.22468487053477917, -0.017223146183603395, 0.2077672366479282, 0.44585764185718146, 0.6922616441641464, 0.9419183379631334, 1.1895846178372167, 1.4299351578183201, 1.6576685472050408, 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'7.66617921570786843706170446293847', '8.573301741540568672544748944522176', '9.253687809098283748386124346929562'], 'prelabel': '2-588-7.4-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.711111473463408, 'root_angle': 0.4798270469460539, 'root_number': '-0.99197791640852265169404803750682485961305798168199772605 + 0.1264112865127400184730959576238026966982488495928982352*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.4798270469460539', 'prec': 54}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.21088160449774527037640047312', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '1.11791852343256181328585960884', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '2.65027710115770587717027144774', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 94.30568605003263, 'bad_primes': [2, 3, 7], 'central_character': '7.4', 'conductor': 588, 'conductor_radical': 42, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/588/6/i/j/361/1'], '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': '2-588-7.4-c5-0-4', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-588-7.4-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.711111473463408, 'root_angle': 0.4798270469460539, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '0.21088160449774527037640047312', 'prec': 97}}
  • lfunc_instances • Show schema
    {'Lhash': '267324192518658873020991163405', 'Lhash_array': ['267324192518658873020991163405'], 'factors': ['2-588-7.4-c5-0-4'], 'label': '2-588-7.4-c5-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/588/6/i/j/361/1'}