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lfunc_lfunctions • Show schema
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{'Lhash': '1756313122660677445372945699593', 'a10': [0.0, 0.0], 'a2': [-0.9009688679024191, -1.433883739117558], 'a3': [0.9749279121818236, -0.2225209339563144], 'a4': [-0.8103939372588246, 1.682800350370449], 'a5': [0.0, 0.0], 'a6': [-1.197448846138138, -1.197448846138138], 'a7': [0.0, 0.0], 'a8': [1.4602794164141346, -0.164533974922999], 'a9': [0.9009688679024191, -0.4338837391175581], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.9986290902786379, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-0.9749279121818236, 0.2225209339563144]]], [23, [[1.0, 0], [-0.9749279121818236, 0.2225209339563144]]], [29, [[1.0, 0], [0.4338837391175581, -0.9009688679024191]]]], 'bad_primes': [3, 23, 29], 'central_character': '2001.68', 'coefficient_field': 'CDF', 'conductor': 2001, 'conductor_radical': 2001, 'conjugate': '1325857878102041090239637226974', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.9009688679024191, 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[-0.7818314824680298, -0.6234898018587335]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 2, 'label': '2-2001-2001.68-c0-0-2', 'leading_term': '1.0140223192549843200034002136334', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/2001/1/bf/a/68/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.0140223192549844, 1.0587438791926196, 1.1135519532257798, 1.178159949983772, 1.2513199801031996, 1.3309776520876417, 1.414462252307069, 1.4986636746472433, 1.5801743509761828, 1.6553957811966968, 1.720619667751487, 1.772095686269403, 1.8060958332317365, 1.81898205730934, 1.8072808913238962, 1.767766458586084, 1.6975515036540034, 1.594184846817111, 1.4557527442660316, 1.2809809537867347, 1.069333801100779, 0.8211061866421556, 0.5375042578367684, 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'6.75098360553972472977521807622708', '7.43906110709513718285693864166249', '8.066174363673156350058764683868384', '8.703747417080700604326694857743226', '9.354375159977853069867328053516116'], 'prelabel': '2-2001-2001.68-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9993143100539679, 'root_angle': 0.6746512637002416, 'root_number': '-0.52156410950372506352007289043649 + 0.85321209536526513711764247701927*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.3373256318501208', 'prec': 60}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.38548675979364395157753701400', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.81714908532823150658520983667', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.00386050507714591078603173112', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.9986290902786379, 'bad_primes': [3, 23, 29], 'central_character': '2001.68', 'conductor': 2001, 'conductor_radical': 2001, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2001/1/bf/a/68/1'], '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': '2-2001-2001.68-c0-0-2', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-2001-2001.68-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9993143100539679, 'root_angle': 0.3373256318501208, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.38548675979364395157753701400', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1756313122660677445372945699593', 'Lhash_array': ['1756313122660677445372945699593'], 'label': '2-2001-2001.68-c0-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2001/1/bf/a/68/1'}