Formats: - HTML - YAML - JSON - 2026-08-25T16:02:06.583855
  • lfunc_lfunctions • Show schema
    {'Lhash': '549072537457974760389638749231', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [-2.8284271247461903, -2.8284271247461903], 'a6': [0, 0], 'a7': [0, 0], 'a8': [0, 0], 'a9': [0, 3.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.176681166979115, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]]], 'bad_primes': [2], 'central_character': '1024.769', 'coefficient_field': 'CDF', 'conductor': 1024, 'conductor_radical': 2, 'conjugate': '1557162312589138431528879626041', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [0, -3.0]], [[1.0, 0], [2.8284271247461903, 2.8284271247461903], [0, 5.0]], [[1.0, 0], [0, 0], [-7.0, 0]], [[1.0, 0], [0, 0], [0, 11.0]], [[1.0, 0], [2.8284271247461903, -2.8284271247461903], [0, -13.0]], [[1.0, 0], [-2.0, 0], [17.0, 0]], [[1.0, 0], [0, 0], [0, -19.0]], [[1.0, 0], [0, 0], [-23.0, 0]], [[1.0, 0], [-2.8284271247461903, 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'9.937225204963928895232816265516429'], 'prelabel': '2-2e10-16.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.8594896689757623, 'root_angle': -0.1875, 'root_number': '0.3826834323650897717284599840303988667613445624856270415 - 0.9238795325112867561281831893967882868224166258636424861*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.1875', 'prec': 14}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.43314185893109588175371453786', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '2.63813831599139928571174717477', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.44236007021004494575513403604', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 8.176681166979115, 'bad_primes': [2], 'central_character': '16.5', 'conductor': 1024, 'conductor_radical': 2, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1024/2/e/k/769/1'], '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': '2-2e10-16.5-c1-0-3', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-2e10-16.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.8594896689757623, 'root_angle': -0.1875, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.43314185893109588175371453786', 'prec': 97}}
  • lfunc_instances • Show schema
    {'Lhash': '549072537457974760389638749231', 'Lhash_array': ['549072537457974760389638749231'], 'factors': ['2-2e10-16.5-c1-0-3'], 'label': '2-2e10-16.5-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1024/2/e/k/769/1'}