Formats: - HTML - YAML - JSON - 2026-08-09T10:33:07.732122
  • lfunc_lfunctions • Show schema
    {'Lhash': '1201867285886859758816852894530', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [3.3722813232690143, 0.0], 'a6': [0.0, 0.0], 'a7': [1.3722813232690143, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 41.394448407831774, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '5184.1', 'coefficient_field': 'CDF', 'conductor': 5184, 'conductor_radical': 6, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-3.3722813232690143, 0], [5.0, 0]], [[1.0, 0], [-1.3722813232690143, 0], [7.0, 0]], [[1.0, 0], [-1.0, 0], [11.0, 0]], [[1.0, 0], [5.372281323269014, 0], [13.0, 0]], [[1.0, 0], [-0.3722813232690143, 0], [17.0, 0]], [[1.0, 0], [-6.372281323269014, 0], [19.0, 0]], [[1.0, 0], [5.372281323269014, 0], [23.0, 0]], [[1.0, 0], 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'group': 'GL2', 'index': 34, 'label': '2-72e2-1.1-c1-0-34', 'leading_term': '2.87693857958675113535896477066', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/5184/2/a/bs/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 24}, 'plot_values': [2.876938579586751, 2.868566440874677, 2.843382769724928, 2.8011948799294366, 2.7417112339995273, 2.664583628796944, 2.5694620603769116, 2.4560586096447103, 2.324216294264293, 2.1739787549546916, 2.005656829717827, 1.819888442206897, 1.6176887147340024, 1.4004877501259465, 1.1701540674462731, 0.9290022022187758, 0.6797834859848498, 0.4256595069082399, 0.17015823146561967, -0.0828867541308167, -0.3294129394265219, -0.5652200868847874, -0.7860740005870962, -0.9878204477830791, -1.1665063460177547, -1.3185048970014361, -1.440640973109976, -1.5303127637077363, -1.5856054865084817, 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'6.79010531190910557146903464270833', '7.46624840873072606194571742725088', '8.138629231776818740532688947296117'], 'prelabel': '2-72e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.433851755195466, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.948106115100228775667493297987', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.05473703962203636975436807099', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '2.51315983834014644421953462582', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 41.394448407831774, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 5184, 'conductor_radical': 6, 'degree': 2, 'index': 34, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5184/2/a/bs/1/2'], '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': '2-72e2-1.1-c1-0-34', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-72e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.433851755195466, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.948106115100228775667493297987', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1201867285886859758816852894530', 'Lhash_array': ['1201867285886859758816852894530'], 'factors': ['2-72e2-1.1-c1-0-34'], 'label': '2-72e2-1.1-c1-0-34', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5184/2/a/bs/1/2'}