Formats: - HTML - YAML - JSON - 2026-08-11T05:44:30.031800
  • lfunc_lfunctions • Show schema
    {'Lhash': '5414870161098205300995155657759', 'a10': [-5.372281323269014, -1.7320508075688772], 'a2': [0.0, -2.5243377989621387], 'a3': [0.0, 0.7922869913932613], 'a4': [-4.372281323269014, 0.0], 'a5': [0.6861406616345072, -2.128194303265508], 'a6': [2.0, 0.0], 'a7': [0.0, 3.4641016151377544], 'a8': [0.0, 5.9884394140998936], 'a9': [2.3722813232690143, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.43917721111704233, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[5, [[1.0, 0], [-0.6861406616345072, 2.128194303265508]]], [11, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [5, 11], 'central_character': '55.34', 'coefficient_field': 'CDF', 'conductor': 55, 'conductor_radical': 55, 'conjugate': '2654837107351111561187403075870', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 2.5243377989621387], [-2.0, 0]], [[1.0, 0], [0, -0.7922869913932613], [-3.0, 0]], [[1.0, 0], [-0.6861406616345072, 2.128194303265508]], [[1.0, 0], [0, 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'7.72407164836328248452341648957647', '9.572150857601680511869988955595617', '10.76708718026809165163786206271554', '13.02534180515613867434447371242309', '13.73305760811598571137660315050021', '14.64086599771379449077563887432408', '15.62265946182949739567442883375968'], 'prelabel': '2-55-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6627044674038665, 'root_angle': 0.2996377367739817, 'root_number': '-0.30685143230828826 + 0.9517574262858955*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.299637736774', 'prec': 40}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '4.27157937693817625799324775125', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '6.13306182954689398397886189556', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '7.16134975081704456913463737652', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 0.43917721111704233, 'bad_primes': [5, 11], 'central_character': '5.4', 'conductor': 55, 'conductor_radical': 55, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/55/2/b/a/34/1'], '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': '2-55-5.4-c1-0-3', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-55-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6627044674038665, 'root_angle': 0.2996377367739817, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '4.27157937693817625799324775125', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '5414870161098205300995155657759', 'Lhash_array': ['5414870161098205300995155657759'], 'factors': ['2-55-5.4-c1-0-3'], 'label': '2-55-5.4-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/55/2/b/a/34/1'}