Formats: - HTML - YAML - JSON - 2026-09-11T01:34:30.010895
  • lfunc_lfunctions • Show schema
    {'Lhash': '1100722238865797871590053995122', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [1.4142135623730951, 0.0], 'a6': [0.0, 0.0], 'a7': [3.1622776601683795, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 36.795065251406015, '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': '4608.1', 'coefficient_field': 'CDF', 'conductor': 4608, 'conductor_radical': 6, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.4142135623730951, 0], [5.0, 0]], [[1.0, 0], [-3.1622776601683795, 0], [7.0, 0]], [[1.0, 0], [4.47213595499958, 0], [11.0, 0]], [[1.0, 0], [4.47213595499958, 0], [13.0, 0]], [[1.0, 0], [-6.324555320336759, 0], [17.0, 0]], [[1.0, 0], [-2.8284271247461903, 0], [19.0, 0]], [[1.0, 0], [-4.0, 0], [23.0, 0]], [[1.0, 0], 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'2.36935748825341515347819439348', '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/4608/2/a/y/1/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 24}, 'plot_values': [2.369357488253415, 2.3613285563178477, 2.3371805778851167, 2.2967382795119176, 2.2397365367757422, 2.1658588948507864, 2.074787767400398, 1.9662630578490106, 1.8401455897697783, 1.6964816566803416, 1.5355651559280177, 1.3579940895199059, 1.1647186296601317, 0.9570784034360372, 0.7368271124208498, 0.506143049778256, 0.2676245050579574, 0.024269459900952542, -0.2205606147485642, -0.4631926384951206, -0.6997088362024437, -0.9260276123314113, -1.1379968668479288, -1.3314977891005209, -1.502556728964304, -1.647462330295722, -1.7628847370652099, -1.8459933654762009, -1.894569494298742, -1.907109778234637, -1.8829167514547995, -1.8221724740446534, -1.725991693126301, 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'prelabel': '2-4608-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.065893606996912, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.868316741748572091798173712139', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.05861198590112527805779050981', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '2.65370257639411034436113204450', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 36.795065251406015, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 4608, 'conductor_radical': 6, 'degree': 2, 'index': 23, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4608/2/a/y/1/4'], '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': '2-4608-1.1-c1-0-23', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-4608-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.065893606996912, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.868316741748572091798173712139', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1100722238865797871590053995122', 'Lhash_array': ['1100722238865797871590053995122'], 'factors': ['2-4608-1.1-c1-0-23'], 'label': '2-4608-1.1-c1-0-23', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4608/2/a/y/1/4'}