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lfunc_lfunctions • Show schema
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{'Lhash': '767782408677674705502434185642', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.13820828399822965, 0.0], 'a4': [0.0, 0.0], 'a5': [-10.085771679410241, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [-26.980898470234266, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 46.257497444500665, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 7], 'central_character': '784.1', 'coefficient_field': 'CDF', 'conductor': 784, 'conductor_radical': 14, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.13820828399822965, 0], [27.0, 0]], [[1.0, 0], [10.085771679410241, 0], [125.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-18.67114682741555, 0], [1331.0, 0]], [[1.0, 0], [-10.084978616600381, 0], [2197.0, 0]], [[1.0, 0], [-73.63939787821302, 0], [4913.0, 0]], [[1.0, 0], [76.08011063189116, 0], [6859.0, 0]], [[1.0, 0], 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'4.21829720466458733691387742446968', '5.61411064214104715311682231146060', '6.25981022387122667658971860762533', '7.58018645773102097401355317690908', '8.066197439068803961971006857213473', '8.987778183771716825536294901211213', '9.844797162963070128838311981321928'], 'prelabel': '2-28e2-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.801286455112788, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.60567352592223929778347721083', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.25082312441583864804486466970', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.56806707885836838314432520945', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 46.257497444500665, 'bad_primes': [2, 7], 'central_character': '1.1', 'conductor': 784, 'conductor_radical': 14, 'degree': 2, 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/784/4/a/bc/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': '2-28e2-1.1-c3-0-10', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-28e2-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.801286455112788, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.60567352592223929778347721083', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '767782408677674705502434185642', 'Lhash_array': ['767782408677674705502434185642'], 'label': '2-28e2-1.1-c3-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/784/4/a/bc/1/2'}