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lfunc_lfunctions • Show schema
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{'Lhash': '1392461830804614939058019203066', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.3109127844683253, 0.0], 'a4': [0.0, 0.0], 'a5': [-1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [4.66211639931327, 0.0], 'a8': [0.0, 0.0], 'a9': [-1.2815076715175024, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.692473971915598, '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': '1840.1', 'coefficient_field': 'CDF', 'conductor': 1840, 'conductor_radical': 230, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.3109127844683253, 0], [3.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-4.66211639931327, 0], [7.0, 0]], [[1.0, 0], [2.2301986543258634, 0], [11.0, 0]], [[1.0, 0], [2.800715206070875, 0], [13.0, 0]], [[1.0, 0], [-7.632711286362447, 0], [17.0, 0]], [[1.0, 0], [-1.362221801659964, 0], [19.0, 0]], 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0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 15, 'label': '2-1840-1.1-c1-0-15', 'leading_term': '2.4508534634807016143323632139893', '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/1840/2/a/v/1/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [2.4508534634807018, 2.4455203947280144, 2.4293715993041607, 2.4019701464985506, 2.3626263193284327, 2.3104521782604768, 2.244432088910346, 2.1635044039794034, 2.0666493003073705, 1.9529780475534824, 1.8218195525094516, 1.6728007062874208, 1.5059177240591906, 1.3215962295813473, 1.1207382748912211, 0.9047548145103574, 0.6755824103616004, 0.4356831721991741, 0.18802717881333106, -0.06394309151047654, -0.3163664472335766, -0.5650344961166561, -0.8054802080544055, -1.033082207044307, 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'5.82520055560519167698584789344176', '7.42892889986029071243694209985200', '7.72915346197858723845644383251353', '8.311455487006037228373533695297242', '9.016582168823071839985359932098535'], 'prelabel': '2-1840-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.833076306560515, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.09845870033423592219487773786', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.40917653730055886239035235130', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.15386255094323939197696483215', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 14.692473971915598, 'bad_primes': [2, 5, 23], 'central_character': '1.1', 'conductor': 1840, 'conductor_radical': 230, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1840/2/a/v/1/4'], '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': '2-1840-1.1-c1-0-15', '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': '2-1840-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.833076306560515, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.09845870033423592219487773786', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1392461830804614939058019203066', 'Lhash_array': ['1392461830804614939058019203066'], 'label': '2-1840-1.1-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1840/2/a/v/1/4'}