Formats: - HTML - YAML - JSON - 2026-09-22T23:37:19.868685
  • lfunc_lfunctions • Show schema
    {'Lhash': '2868575080667843878223758720299', 'a10': [0.0, 0.0], 'a2': [7.135528725660044, 0.0], 'a3': [27.0, 0.0], 'a4': [-77.08422980528034, 0.0], 'a5': [0.0, 0.0], 'a6': [192.6592755928212, 0.0], 'a7': [112.89740215924061, 0.0], 'a8': [-1463.3844129554436, 0.0], 'a9': [729.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 23.428876911309143, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.5', 'prec': 7}, 'bad_lfactors': [[3, [[1.0, 0], [-27.0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '75.1', 'coefficient_field': 'CDF', 'conductor': 75, 'conductor_radical': 15, 'degree': 2, 'euler_factors': [[[1.0, 0], [-7.135528725660044, 0], [128.0, 0]], [[1.0, 0], [-27.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-112.89740215924061, 0], [823543.0, 0]], [[1.0, 0], [-656.0506410255716, 0], [19487171.0, 0]], [[1.0, 0], [7805.116502795373, 0], [62748517.0, 0]], [[1.0, 0], [14635.518483708696, 0], [410338673.0, 0]], [[1.0, 0], 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'positive_zeros': ['2.26290673483007228371179917995047', '3.84313931145968140498812204119825', '4.88479577188490182659343609433736', '6.43225729300978571403629594815640', '8.028500625939717141575204089163354', '9.077702120540965566695246899454241', '10.13674727801174657776992274864138', '11.74476451547060353048354266781691', '12.84941829857426625178435627890593'], 'prelabel': '2-75-1.1-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.84033851205772, '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': '2.26290673483007228371179917995', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '3.84313931145968140498812204120', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '4.88479577188490182659343609434', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 23.428876911309143, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 75, 'conductor_radical': 15, 'degree': 2, 'index': 19, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/75/8/a/d/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': '2-75-1.1-c7-0-19', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [7], 'order_of_vanishing': 1, 'prelabel': '2-75-1.1-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.84033851205772, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c7-0', 'z1': {'__RealLiteral__': 0, 'data': '2.26290673483007228371179917995', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '2868575080667843878223758720299', 'Lhash_array': ['2868575080667843878223758720299'], 'factors': ['2-75-1.1-c7-0-19'], 'label': '2-75-1.1-c7-0-19', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/75/8/a/d/1/2'}