Formats: - HTML - YAML - JSON - 2026-07-18T21:57:44.569778
  • lfunc_lfunctions • Show schema
    {'Lhash': '2642608683315257113039767349028', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, -3.4641016151377544], 'a6': [0, 0], 'a7': [0, -3.4641016151377544], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 41.394448407831774, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '5184.5183', 'coefficient_field': 'CDF', 'conductor': 5184, 'conductor_radical': 6, 'conjugate': '1248642227625454216595481288015', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 3.4641016151377544], [-5.0, 0]], [[1.0, 0], [0, 3.4641016151377544], [-7.0, 0]], [[1.0, 0], [3.0, 0], [11.0, 0]], [[1.0, 0], [4.0, 0], [13.0, 0]], [[1.0, 0], [0, -1.7320508075688772], [-17.0, 0]], [[1.0, 0], [0, -1.7320508075688772], [-19.0, 0]], [[1.0, 0], [0, 0], [23.0, 0]], [[1.0, 0], [0, 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'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/5184/2/c/a/5183/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [-8.57563714255059e-61, -0.1691529438867328, -0.3502427318678562, -0.5428251532410553, -0.7463897533581255, -0.9603201232264797, -1.1838544511843174, -1.4160486910648027, -1.6557444856075967, -1.9015436702461763, -2.151790812154777, -2.404564849996062, -2.657680519777577, -2.9086998995024183, -3.154954087739922, -3.3935747489590815, -3.6215350068021728, -3.8356989388322495, -4.032878716363488, -4.2098982362284785, -4.363661905683475, -4.4912270676655295, -4.589878394247095, -4.657202436252077, -4.691160402806771, -4.690157163039907, -4.653104420319091, -4.579476014053946, -4.469353361118851, -4.323459163030062, -4.143177679262285, -3.930560102769309, 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'primitive': True, 'rational': False, 'root_analytic_conductor': 6.433851755195466, 'root_angle': -0.25, 'root_number': '0.e-56 - 1.00000000000000000000000000000000000000000000000000000000*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.25', 'prec': 17}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.08465067806497984259645401232', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.69308387970470332083767621438', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.07815950505512556271912172336', 'prec': 103}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 41.394448407831774, 'bad_primes': [2, 3], 'central_character': '12.11', 'conductor': 5184, 'conductor_radical': 6, 'degree': 2, 'index': 90, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5184/2/c/a/5183/1'], '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': '2-72e2-12.11-c1-0-90', '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': '2-72e2-12.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.433851755195466, 'root_angle': -0.25, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.08465067806497984259645401232', 'prec': 103}}
  • lfunc_instances • Show schema
    {'Lhash': '2642608683315257113039767349028', 'Lhash_array': ['2642608683315257113039767349028'], 'factors': ['2-72e2-12.11-c1-0-90'], 'label': '2-72e2-12.11-c1-0-90', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5184/2/c/a/5183/1'}