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lfunc_lfunctions • Show schema
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{'Lhash': '680756342699883489876472355800', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.4142135623730951, 0.0], 'a4': [0.0, 0.0], 'a5': [0.0, 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': 57.23676816885381, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 7], 'central_character': '7168.1', 'coefficient_field': 'CDF', 'conductor': 7168, 'conductor_radical': 14, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.4142135623730951, 0], [3.0, 0]], [[1.0, 0], [0, 0], [5.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-2.8284271247461903, 0], [11.0, 0]], [[1.0, 0], [2.8284271247461903, 0], [13.0, 0]], [[1.0, 0], [-6.0, 0], [17.0, 0]], [[1.0, 0], [4.242640687119285, 0], [19.0, 0]], [[1.0, 0], [0, 0], [23.0, 0]], [[1.0, 0], [-1.4142135623730951, 0], [29.0, 0]], [[1.0, 0], [-10.0, 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[{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/7168/2/a/e/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [1.02232468882513, 1.0128073773766404, 0.9842695301424041, 0.9367619682894905, 0.8703972275415333, 0.785388936385288, 0.6821024526850384, 0.5611128053080447, 0.42326551819091174, 0.26973576183290715, 0.1020814348518431, -0.07771384100556167, -0.2672112948978718, -0.463504004766658, -0.6632224960223273, -0.8625604166506371, -1.0573210525866403, -1.2429847296721128, -1.4147964265145017, -1.5678721981856432, -1.6973222895860318, -1.7983881100949235, -1.866589563763164, -1.8978786024888488, -1.8887943177321425, -1.836614436009756, -1.7394977619246998, -1.5966119460286146, -1.4082409668230644, -1.175866925753389, -0.9022211743489531, -0.5913004297728977, -0.24834438679317145, 0.12022761059994892, 0.5069220366492393, 0.9033185983164975, 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False, 'root_analytic_conductor': 7.565498540668275, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.53702206473717542156409897648', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.65954024996262978691308087413', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.80534241518548287374684282768', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 57.23676816885381, 'bad_primes': [2, 7], 'central_character': '1.1', 'conductor': 7168, 'conductor_radical': 14, 'degree': 2, 'index': 31, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/7168/2/a/e/1/1'], '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': '2-7168-1.1-c1-0-31', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-7168-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.565498540668275, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.53702206473717542156409897648', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '680756342699883489876472355800', 'Lhash_array': ['680756342699883489876472355800'], 'label': '2-7168-1.1-c1-0-31', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7168/2/a/e/1/1'}