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  • lfunc_lfunctions • Show schema
    {'Lhash': '1495411568920386508433105344037', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0.5, 0.8660254037844386], 'a6': [0, 0], 'a7': [-1.5, 2.598076211353316], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 13.798149469277257, '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': '1728.1153', 'coefficient_field': 'CDF', 'conductor': 1728, 'conductor_radical': 6, 'conjugate': '834036397792403870911021075557', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.5, -0.8660254037844386], [-2.5, 4.330127018922194]], [[1.0, 0], [1.5, -2.598076211353316], [-3.5, -6.06217782649107]], [[1.0, 0], [-2.5, 4.330127018922194], [-5.5, -9.526279441628825]], [[1.0, 0], [2.5, 4.330127018922194], [-6.5, 11.258330249197702]], [[1.0, 0], [-2.0, 0], [17.0, 0]], [[1.0, 0], [4.0, 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1.2332097051984934, 1.8598126161763158], 'positive_zeros': ['1.17967172393650958467300979696268', '2.27001762369925471968414242322737', '3.68690669879141820979525804557896', '4.42049811445718753972479674886163', '5.12762141093597702548674493332539', '6.56682407550779397664901035425769', '6.86890953461105974350371490218823', '7.65008371866623034981955284199005', '8.871480675738745095058805941502622', '9.397500391788558059738583764567735'], 'prelabel': '2-12e3-9.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.714586042788248, 'root_angle': 0.11111111111111113, 'root_number': '0.7660444431189780352023926505554166739358324570803952459 + 0.6427876096865393263226434099072634329075598842056817904*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.1111111111111111', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.17967172393650958467300979696', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.27001762369925471968414242323', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.68690669879141820979525804558', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 13.798149469277257, 'bad_primes': [2, 3], 'central_character': '9.7', 'conductor': 1728, 'conductor_radical': 6, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1728/2/i/g/1153/1'], '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': '2-12e3-9.7-c1-0-11', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-12e3-9.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.714586042788248, 'root_angle': 0.11111111111111113, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.17967172393650958467300979696', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1495411568920386508433105344037', 'Lhash_array': ['1495411568920386508433105344037'], 'factors': ['2-12e3-9.7-c1-0-11'], 'label': '2-12e3-9.7-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1728/2/i/g/1153/1'}