Formats: - HTML - YAML - JSON - 2026-10-12T03:57:26.445270
  • lfunc_lfunctions • Show schema
    {'Lhash': '1242872441995254246473528676668', 'a10': [0.0, 0.0], 'a2': [-2.7040488011036468, 0.0], 'a3': [0.20525811457925752, 0.0], 'a4': [5.311879918750069, 0.0], 'a5': [0.0, 0.0], 'a6': [-0.5550279586448362, 0.0], 'a7': [-2.5526513983698957, 0.0], 'a8': [-8.955484923695368, 0.0], 'a9': [-2.9578691063993685, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 41.72183505611902, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [1.0, 0]]], [19, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [5, 11, 19], 'central_character': '5225.1', 'coefficient_field': 'CDF', 'conductor': 5225, 'conductor_radical': 1045, 'degree': 2, 'euler_factors': [[[1.0, 0], [2.7040488011036468, 0], [2.0, 0]], [[1.0, 0], [-0.20525811457925752, 0], [3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.5526513983698957, 0], [7.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0.7276023733959266, 0], [13.0, 0]], [[1.0, 0], 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'5.30911303895964068280225525460489', '6.03921030130057258363974234409318', '6.60694443233227980901564196921644', '7.39843528058669559711124318007081', '8.070398661114127615377608519652217'], 'prelabel': '2-5225-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.459244155171642, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.980453479666625752880055920239', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.26222089836759792475795270645', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '2.89873325125029541981637100318', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 41.72183505611902, 'bad_primes': [5, 11, 19], 'central_character': '1.1', 'conductor': 5225, 'conductor_radical': 1045, 'degree': 2, 'index': 141, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5225/2/a/v/1/1'], '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': '2-5225-1.1-c1-0-141', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-5225-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.459244155171642, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.980453479666625752880055920239', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1242872441995254246473528676668', 'Lhash_array': ['1242872441995254246473528676668'], 'factors': ['2-5225-1.1-c1-0-141'], 'label': '2-5225-1.1-c1-0-141', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5225/2/a/v/1/1'}