Formats: - HTML - YAML - JSON - 2026-10-07T19:10:54.516927
  • lfunc_lfunctions • Show schema
    {'Lhash': '1871359198035533061980340259710', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-52.405386961116584, 0.0], 'a4': [0.0, 0.0], 'a5': [199.21616088334974, 0.0], 'a6': [0.0, 0.0], 'a7': [-343.0, 0.0], 'a8': [0.0, 0.0], 'a9': [559.3245825443679, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 34.98712285422165, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.5', 'prec': 7}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [343.0, 0]]]], 'bad_primes': [2, 7], 'central_character': '112.1', 'coefficient_field': 'CDF', 'conductor': 112, 'conductor_radical': 14, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [52.405386961116584, 0], [2187.0, 0]], [[1.0, 0], [-199.21616088334974, 0], [78125.0, 0]], [[1.0, 0], [343.0, 0]], [[1.0, 0], [1218.9737476331036, 0], [19487171.0, 0]], [[1.0, 0], [-6449.648482650049, 0], [62748517.0, 0]], [[1.0, 0], [-26786.91305363507, 0], [410338673.0, 0]], [[1.0, 0], [14910.945447950147, 0], [893871739.0, 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['1.47624211095597730836290996338413', '3.33461614675971696163153535012659', '5.17396498807482459774869503876130', '5.89743731398517553362918009103888', '6.94626605041548264089391234487013', '8.545308680119485617164219710242547', '9.845488696155923613495161358816398', '10.70675121732339552980590168191488', '11.66204482762351348452938437915482'], 'prelabel': '2-112-1.1-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.914991365523846, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'spectral_label': 'c7-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.47624211095597730836290996338', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '3.33461614675971696163153535013', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '5.17396498807482459774869503876', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 34.98712285422165, 'bad_primes': [2, 7], 'central_character': '1.1', 'conductor': 112, 'conductor_radical': 14, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/112/8/a/i/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': '2-112-1.1-c7-0-13', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [7], 'order_of_vanishing': 1, 'prelabel': '2-112-1.1-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.914991365523846, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c7-0', 'z1': {'__RealLiteral__': 0, 'data': '1.47624211095597730836290996338', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1871359198035533061980340259710', 'Lhash_array': ['1871359198035533061980340259710'], 'factors': ['2-112-1.1-c7-0-13'], 'label': '2-112-1.1-c7-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/112/8/a/i/1/1'}