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  • lfunc_lfunctions • Show schema
    {'Lhash': '1264869959185131218535943857468', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [0, 0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 41.394448407831774, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '5184.2593', 'coefficient_field': 'CDF', 'conductor': 5184, 'conductor_radical': 6, 'conjugate': '809237751864046381393256167037', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-5.0, 0]], [[1.0, 0], [0, 0], [7.0, 0]], [[1.0, 0], [0, 0.5505102572168219], [-11.0, 0]], [[1.0, 0], [0, 0], [-13.0, 0]], [[1.0, 0], [-7.898979485566356, 0], [17.0, 0]], [[1.0, 0], [0, 6.3484692283495345], [-19.0, 0]], [[1.0, 0], [0, 0], [23.0, 0]], [[1.0, 0], [0, 0], [-29.0, 0]], [[1.0, 0], [0, 0], [31.0, 0]], [[1.0, 0], [0, 0], 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'root_number': '0.70710678118654752440084436210484903928483593768847403659 + 0.7071067811865475244008443621048490392848359376884740366*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.997806460989646868888582719766', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '1.91629668148390267814323180266', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.13965058866266768045650602992', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 41.394448407831774, 'bad_primes': [2, 3], 'central_character': '8.5', 'conductor': 5184, 'conductor_radical': 6, 'degree': 2, 'index': 60, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5184/2/d/l/2593/2'], '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': '2-72e2-8.5-c1-0-60', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-72e2-8.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.433851755195466, 'root_angle': 0.125, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.997806460989646868888582719766', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1264869959185131218535943857468', 'Lhash_array': ['1264869959185131218535943857468'], 'factors': ['2-72e2-8.5-c1-0-60'], 'label': '2-72e2-8.5-c1-0-60', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5184/2/d/l/2593/2'}