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lfunc_lfunctions • Show schema
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{'Lhash': '1469382006830787481700231226692', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [0.4736257582079006, 0.0], 'a6': [0.0, 0.0], 'a7': [-4.557647291327849, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 73.59013050281203, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '9216.1', 'coefficient_field': 'CDF', 'conductor': 9216, 'conductor_radical': 6, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.4736257582079006, 0], [5.0, 0]], [[1.0, 0], [4.557647291327849, 0], [7.0, 0]], [[1.0, 0], [-3.4982350954930435, 0], [11.0, 0]], [[1.0, 0], [0.08402153311994831, 0], [13.0, 0]], [[1.0, 0], [-3.6170594871626545, 0], [17.0, 0]], [[1.0, 0], [3.6170594871626545, 0], [19.0, 0]], [[1.0, 0], [-2.8284271247461903, 0], [23.0, 0]], [[1.0, 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0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 105, 'label': '2-96e2-1.1-c1-0-105', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/9216/2/a/x/1/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [-2.9170384114974102e-61, 0.1879940107459286, 0.37429779955410497, 0.5571844315677859, 0.7348571363812539, 0.9054230980158292, 1.0668769766803448, 1.2170963017919314, 1.3538500920243002, 1.4748212437392658, 1.5776424469401924, 1.6599446835281504, 1.7194167626855479, 1.7538738622877634, 1.7613326707315733, 1.7400904509773383, 1.6888051663140558, 1.606573705023375, 1.4930052115091772, 1.3482865709680765, 1.173237202863748, 0.9693504970301614, 0.7388194777300607, 0.4845446076043293, 0.21012204582325933, -0.0801888488521231, -0.3815194337586424, -0.6884671737814583, 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'6.63418263904630783378391319723730', '7.25462829694771830514665434110573'], 'prelabel': '2-96e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.578469006927287, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.15913802002400196484589656062', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.27534018618167788497511261890', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.14157221243803111160534895048', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 73.59013050281203, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 9216, 'conductor_radical': 6, 'degree': 2, 'index': 105, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/9216/2/a/x/1/3'], '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': '2-96e2-1.1-c1-0-105', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-96e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.578469006927287, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.15913802002400196484589656062', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1469382006830787481700231226692', 'Lhash_array': ['1469382006830787481700231226692'], 'factors': ['2-96e2-1.1-c1-0-105'], 'label': '2-96e2-1.1-c1-0-105', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9216/2/a/x/1/3'}