Formats: - HTML - YAML - JSON - 2026-10-15T06:15:38.525073
  • lfunc_lfunctions • Show schema
    {'Lhash': '276991730858587258007900726145', 'a10': [0, 0], 'a2': [-1024.0, 0], 'a3': [-12234.542831936957, 0], 'a4': [1048576.0, 0], 'a5': [0, 0], 'a6': [12528171.859903444, 0], 'a7': [-906115293.7796264, 0], 'a8': [-1073741824.0, 0], 'a9': [-10310669164.6935, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 139.73867214353106, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '10.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1024.0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 5], 'central_character': '50.1', 'coefficient_field': 'CDF', 'conductor': 50, 'conductor_radical': 10, 'degree': 2, 'euler_factors': [[[1.0, 0], [1024.0, 0]], [[1.0, 0], [12234.542831936957, 0], [10460353203.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [906115293.7796264, 0], [558545864083284030, 0]], [[1.0, 0], [-87557511113.63313, 0], [7400249944258161000000, 0]], [[1.0, 0], [37829873122.5831, 0], [247064529073450400000000, 0]], [[1.0, 0], [10319718874384.64, 0], 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'group': 'GL2', 'index': 0, 'label': '2-50-1.1-c21-0-0', 'leading_term': '0.210247983286397684602743384142300580770860957187455641', 'load_key': 'CMFs-workshop', 'motivic_weight': 21, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [21], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/50/22/a/i/1/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0703125', 'prec': 20}, 'plot_values': [0.21024798328639768, 0.18791555732339368, 0.12170228390624345, 0.013935115123573535, -0.13159046871818963, -0.3097319653147619, -0.5141647323299858, -0.7375852035054726, -0.9719462154239282, -1.2087172233003436, -1.4391613996634576, -1.6546210626705862, -1.8468025880396846, -2.0080519298409194, -2.131612112706374, -2.2118545557184457, -2.244476833060211, -2.2266604479310974, -2.157183367006588, -2.036483399623492, -1.8666699705958436, -1.6514833857829345, -1.3962022800723306, -1.1075015215708188, -0.7932643765404224, -0.4623541711119148, -0.12435197463721288, 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'9.116564193357726586171272056387229', '10.13761089718158929617653657014074', '11.30097048887196223122799475811073'], 'prelabel': '2-50-1.1-c21-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.821111290548409, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c21-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.21850794754384001389475704156', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '1.85403423575163878546077054850', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '2.97277030419882054142181476157', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 139.73867214353106, 'bad_primes': [2, 5], 'central_character': '1.1', 'conductor': 50, 'conductor_radical': 10, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/50/22/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': '2-50-1.1-c21-0-0', 'motivic_weight': 21, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [21], 'order_of_vanishing': 0, 'prelabel': '2-50-1.1-c21-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.821111290548409, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c21-0', 'z1': {'__RealLiteral__': 0, 'data': '0.21850794754384001389475704156', 'prec': 97}}
  • lfunc_instances • Show schema
    {'Lhash': '276991730858587258007900726145', 'Lhash_array': ['276991730858587258007900726145'], 'factors': ['2-50-1.1-c21-0-0'], 'label': '2-50-1.1-c21-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/50/22/a/i/1/3'}