Formats: - HTML - YAML - JSON - 2026-10-07T18:19:44.251080
  • lfunc_lfunctions • Show schema
    {'Lhash': '2236846398191289878230686983040', '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': 8.746780713555413, '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': '28.1', 'coefficient_field': 'CDF', 'conductor': 28, 'conductor_radical': 14, 'conjugate': '2236846398191289878230686983040', '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]], 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-0.5328484172141733], 'positive_zeros': ['1.76456067451754075735137880176392', '3.51915384741544475741790919463012', '5.76430981346213732480806593772948', '7.76717219542702270248161217236380', '8.962201325185025528391773777485689', '10.17678349432128532339976530841576', '11.93850083991008694361766843337731', '13.66650631025782096548867400247425', '14.14500261212495231940646383532019', '15.42109138499016762990100591992089'], 'prelabel': '2-28-1.1-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.957495682761923, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c7-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.76456067451754075735137880176', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '3.51915384741544475741790919463', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '5.76430981346213732480806593773', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 8.746780713555413, 'bad_primes': [2, 7], 'central_character': '1.1', 'conductor': 28, 'conductor_radical': 14, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/28/8/a/a/1/2'], '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': '2-28-1.1-c7-0-1', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [7], 'order_of_vanishing': 0, 'prelabel': '2-28-1.1-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.957495682761923, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c7-0', 'z1': {'__RealLiteral__': 0, 'data': '1.76456067451754075735137880176', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '2236846398191289878230686983040', 'Lhash_array': ['2236846398191289878230686983040'], 'factors': ['2-28-1.1-c7-0-1'], 'label': '2-28-1.1-c7-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/28/8/a/a/1/2'}