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lfunc_lfunctions • Show schema
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{'Lhash': '1540944152074696557877442883936', 'a10': [0.0, 0.0], 'a2': [0.6234898018587335, 0.2181685175319702], 'a3': [-0.4338837391175581, 0.9009688679024191], 'a4': [-0.4406894514882846, -0.3514381103230901], 'a5': [0.0, 0.0], 'a6': [-0.467085128784861, 0.467085128784861], 'a7': [0.0, 0.0], 'a8': [-0.549530757579329, -0.8745731906058427], 'a9': [-0.6234898018587335, -0.7818314824680298], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.9986290902786379, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.4338837391175581, -0.9009688679024191]]], [23, [[1.0, 0], [0.4338837391175581, -0.9009688679024191]]], [29, [[1.0, 0], [-0.7818314824680298, -0.6234898018587335]]]], 'bad_primes': [3, 23, 29], 'central_character': '2001.137', 'coefficient_field': 'CDF', 'conductor': 2001, 'conductor_radical': 2001, 'conjugate': '1255016369742907358457864067901', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.6234898018587335, 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[-0.9749279121818236, -0.2225209339563144]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 2, 'label': '2-2001-2001.137-c0-0-2', 'leading_term': '1.2267392082356258743976113251263', '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/137/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.2267392082356259, 1.237355298998703, 1.2565533806249725, 1.2828168016474522, 1.3136638292552412, 1.3459716202879717, 1.3762905855360903, 1.4010990071165037, 1.4169858345018556, 1.4207733602690085, 1.4095992385742175, 1.3809753625258454, 1.332835711032822, 1.263579919295015, 1.1721152596350084, 1.0578970275945003, 0.920965713388059, 0.7619784700394887, 0.5822320144063693, 0.3836740503143577, 0.16890048396867538, -0.05886394781888882, -0.29580353096871825, 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'4.46015617265511729932911200862054', '5.27874241710077933171054471342443', '6.19517488205074798333029889048298', '6.69243689351507808966052872905911', '7.87434394741036059009435495463965', '8.464282101476009313973701699806336', '9.000835305856390752837972334328964'], 'prelabel': '2-2001-2001.137-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9993143100539679, 'root_angle': -0.08796239897312291, 'root_number': '0.96205990789719528318807804761950 - 0.27283829206480553833205862105228*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.043981199486561456', 'prec': 70}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.21559059870066960333625837851', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.53677183602777746486504616259', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.48783870329856867173435881062', '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': '2001.137', 'conductor': 2001, 'conductor_radical': 2001, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2001/1/bf/a/137/1'], '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': '2-2001-2001.137-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': '2-2001-2001.137-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9993143100539679, 'root_angle': -0.043981199486561456, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.21559059870066960333625837851', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1540944152074696557877442883936', 'Lhash_array': ['1540944152074696557877442883936'], 'label': '2-2001-2001.137-c0-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2001/1/bf/a/137/1'}