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  • lfunc_lfunctions • Show schema
    {'Lhash': '1425041384664985662210761320287', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.0, 0.0], 'a4': [0.0, 0.0], 'a5': [-1.381966011250105, 0.0], 'a6': [0.0, 0.0], 'a7': [-1.0, 0.0], 'a8': [0.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 61.70839068204551, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [1.0, 0]]], [7, [[1.0, 0], [1.0, 0]]], [23, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 7, 23], 'central_character': '7728.1', 'coefficient_field': 'CDF', 'conductor': 7728, 'conductor_radical': 966, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [1.381966011250105, 0], [5.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-5.47213595499958, 0], [11.0, 0]], [[1.0, 0], [2.381966011250105, 0], [13.0, 0]], [[1.0, 0], [1.0, 0], [17.0, 0]], [[1.0, 0], [-3.0, 0], [19.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [7.47213595499958, 0], 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84, 'label': '2-7728-1.1-c1-0-84', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/7728/2/a/v/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 17}, 'plot_values': [-3.269513886220014e-61, 0.151620799173189, 0.30179536021754594, 0.4490469085787631, 0.5918406015433173, 0.7285617861858147, 0.8575024193928942, 0.9768574647459839, 1.084732437634258, 1.1791626005015472, 1.2581436657351652, 1.3196732813218999, 1.3618020752649382, 1.3826926262634005, 1.3806844077113456, 1.3543625115570215, 1.302627788268359, 1.2247659305982488, 1.1205129763306099, 0.990114706229476, 0.8343774683749088, 0.6547080713302402, 0.4531405594909417, 0.23234791777502056, -0.00436294824562937, -0.2530742461853194, -0.5092992060027122, -0.7680432389304269, -1.0238841826443295, -1.271070890820536, -1.503638820230562, -1.7155406531429052, -1.900789385562207, 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'2-7728-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.855468839098371, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.12415943668422468051484352214', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.13055224009501831231306687664', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.40994181849326957461612661570', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 61.70839068204551, 'bad_primes': [2, 3, 7, 23], 'central_character': '1.1', 'conductor': 7728, 'conductor_radical': 966, 'degree': 2, 'index': 84, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/7728/2/a/v/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': '2-7728-1.1-c1-0-84', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-7728-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.855468839098371, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.12415943668422468051484352214', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1425041384664985662210761320287', 'Lhash_array': ['1425041384664985662210761320287'], 'factors': ['2-7728-1.1-c1-0-84'], 'label': '2-7728-1.1-c1-0-84', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7728/2/a/v/1/2'}