Formats: - HTML - YAML - JSON - 2026-07-18T19:04:55.845196
  • lfunc_lfunctions • Show schema
    {'Lhash': '2269196138314587425691866840780', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [2.23606797749979, 0.0], 'a4': [0.0, 0.0], 'a5': [-2.288245611270737, 0.0], 'a6': [0.0, 0.0], 'a7': [3.7024591736438324, 0.0], 'a8': [0.0, 0.0], 'a9': [2.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 33.79269013540588, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [23, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 23], 'central_character': '4232.1', 'coefficient_field': 'CDF', 'conductor': 4232, 'conductor_radical': 46, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-2.23606797749979, 0], [3.0, 0]], [[1.0, 0], [2.288245611270737, 0], [5.0, 0]], [[1.0, 0], [-3.7024591736438324, 0], [7.0, 0]], [[1.0, 0], [-0.540181513475453, 0], [11.0, 0]], [[1.0, 0], [6.23606797749979, 0], [13.0, 0]], [[1.0, 0], [3.7024591736438324, 0], [17.0, 0]], [[1.0, 0], [-0.33385053542218923, 0], [19.0, 0]], [[1.0, 0], 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[113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 119, 'label': '2-4232-1.1-c1-0-119', '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/4232/2/a/t/1/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [-8.878735664995242e-61, 0.2290103001552466, 0.4575667474510869, 0.6851722664021596, 0.9112457958138566, 1.1350862712415317, 1.3558433153663922, 1.572496166579993, 1.7838418864109347, 1.9884933894573724, 2.1848873766425245, 2.3713018516423845, 2.5458825742513858, 2.7066775535370424, 2.851678499282703, 2.9788680192280377, 3.086271257944184, 3.172010608602515, 3.234362082493515, 3.2718118877713067, 3.283111746894366, 3.267331472793693, 3.2239073301085046, 3.152684734215598, 3.0539538919627995, 2.928477068488219, 2.777506278034754, 2.6027903459407336, 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'7.997494096223462751568821935675971'], 'prelabel': '2-4232-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.813148040038708, 'root_angle': 0.5, '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': '1.79008011979486974669513582231', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.37369517441538133818800001219', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.40923305384672370564399850570', 'prec': 103}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 33.79269013540588, 'bad_primes': [2, 23], 'central_character': '1.1', 'conductor': 4232, 'conductor_radical': 46, 'degree': 2, 'index': 119, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4232/2/a/t/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': '2-4232-1.1-c1-0-119', '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': '2-4232-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.813148040038708, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.79008011979486974669513582231', 'prec': 103}}
  • lfunc_instances • Show schema
    {'Lhash': '2269196138314587425691866840780', 'Lhash_array': ['2269196138314587425691866840780'], 'factors': ['2-4232-1.1-c1-0-119'], 'label': '2-4232-1.1-c1-0-119', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4232/2/a/t/1/3'}