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lfunc_lfunctions • Show schema
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{'Lhash': '1061769135583953245437573472593', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.618033988749895, 0.0], 'a4': [0.0, 0.0], 'a5': [-1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.6180339887498949, 0.0], 'a8': [0.0, 0.0], 'a9': [-0.38196601125010515, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 58.76989588766239, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [1.0, 0]]], [23, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 5, 23], 'central_character': '7360.1', 'coefficient_field': 'CDF', 'conductor': 7360, 'conductor_radical': 230, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.618033988749895, 0], [3.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-0.6180339887498949, 0], [7.0, 0]], [[1.0, 0], [2.8541019662496847, 0], [11.0, 0]], [[1.0, 0], [-7.0901699437494745, 0], [13.0, 0]], [[1.0, 0], [-6.0901699437494745, 0], [17.0, 0]], [[1.0, 0], [-1.8541019662496845, 0], [19.0, 0]], 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0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 65, 'label': '2-7360-1.1-c1-0-65', 'leading_term': '2.8644493141145650639705095004103', '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': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/7360/2/a/bn/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [2.864449314114565, 2.8533318431044976, 2.819932846642293, 2.764123833827149, 2.685727317789839, 2.58456887566576, 2.460544486158879, 2.3136982969519635, 2.1443054386235016, 1.952954390334099, 1.7406236476349966, 1.5087479508032768, 1.2592700076952075, 0.9946744080592699, 0.7180012199301687, 0.43283755046215966, 0.1432861298921758, -0.14608926299615288, -0.4303409684961169, -0.7042359031958343, -0.9623732745459304, -1.1993188074636434, -1.409752053071819, -1.5886227122295906, -1.7313113394953852, 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'5.23925111121201693835090570712588', '5.65729697233838068584139532939679', '6.59111876934830152893849690709551', '7.47262979578302811213487256580375', '8.092545752927417875603902820626792'], 'prelabel': '2-7360-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.66615261312103, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.837588161432488574259431249259', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.84583387825285221848584750045', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.92938579063873202036819007700', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 58.76989588766239, 'bad_primes': [2, 5, 23], 'central_character': '1.1', 'conductor': 7360, 'conductor_radical': 230, 'degree': 2, 'index': 65, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/7360/2/a/bn/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': '2-7360-1.1-c1-0-65', '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': '2-7360-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.66615261312103, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.837588161432488574259431249259', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1061769135583953245437573472593', 'Lhash_array': ['1061769135583953245437573472593'], 'label': '2-7360-1.1-c1-0-65', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7360/2/a/bn/1/2'}