Formats: - HTML - YAML - JSON - 2026-10-16T02:14:05.583252
  • lfunc_lfunctions • Show schema
    {'Lhash': '617237507048846318182786073194', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 1.0], 'a4': [0, 0], 'a5': [0, 3.414213562373095], 'a6': [0, 0], 'a7': [-1.4142135623730951, 0], 'a8': [0, 0], 'a9': [-1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12.265021750468673, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, -1.0]]]], 'bad_primes': [2, 3], 'central_character': '1536.769', 'coefficient_field': 'CDF', 'conductor': 1536, 'conductor_radical': 6, 'conjugate': '2518673634476401249411084110095', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, -1.0]], [[1.0, 0], [0, -3.414213562373095], [-5.0, 0]], [[1.0, 0], [1.4142135623730951, 0], [7.0, 0]], [[1.0, 0], [0, -4.82842712474619], [-11.0, 0]], [[1.0, 0], [0, -0.8284271247461901], [-13.0, 0]], [[1.0, 0], [-4.82842712474619, 0], [17.0, 0]], [[1.0, 0], [0, -2.8284271247461903], [-19.0, 0]], [[1.0, 0], 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[[1.0, 0], [-3.65685424949238, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 7, 'label': '2-1536-8.5-c1-0-7', 'leading_term': '1.1950836584736335989616030035309918744951890461570254649', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1536/2/d/b/769/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 24}, 'plot_values': [1.1950836584736335, 1.0377690052031567, 0.883821962267945, 0.7332239224572425, 0.5860373307603899, 0.4424703096018409, 0.3029299587067489, 0.16806149914205626, 0.03877159312877817, -0.08376474657799507, -0.19811336072763264, -0.30260532506027743, -0.3953751618918241, -0.4744112964644781, -0.5376170417052947, -0.5828803110104662, -0.608150178188282, -0.6115183024377995, -0.591303107030863, -0.5461344490239339, -0.47503635822331586, -0.3775052758174085, -0.25358110734379957, 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'5.59351933969330532979706683902015', '6.55419877521952211605275077544320', '7.65510154907028809304158762246528', '8.259182407742600551818469106126232', '9.104677397577481342880717631772908'], 'prelabel': '2-1536-8.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.5021453068752977, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.48691453854691356156829063829', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '1.38356084350005704101408452395', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '2.95040778988887081601800938075', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 12.265021750468673, 'bad_primes': [2, 3], 'central_character': '8.5', 'conductor': 1536, 'conductor_radical': 6, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1536/2/d/b/769/4'], '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': '2-1536-8.5-c1-0-7', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-1536-8.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.5021453068752977, 'root_angle': 0.5, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.48691453854691356156829063829', 'prec': 97}}
  • lfunc_instances • Show schema
    {'Lhash': '617237507048846318182786073194', 'Lhash_array': ['617237507048846318182786073194'], 'factors': ['2-1536-8.5-c1-0-7'], 'label': '2-1536-8.5-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1536/2/d/b/769/4'}