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lfunc_lfunctions • Show schema
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{'Lhash': '472795079680254967308240163404', 'a10': [0.8467460949375999, -5.629116640587864], 'a2': [-2.2046745713132565, -1.2728694572232315], 'a3': [0.0, 0.0], 'a4': [2.240393310263528, 3.8804750423138534], 'a5': [0.8175444385565523, 2.0812546915227004], 'a6': [0.0, 0.0], 'a7': [-2.5448608327047726, 1.4692760868122356], 'a8': [0.0, -6.315435038313856], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.671248518244905, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-0.8175444385565523, -2.0812546915227004]]], [13, [[1.0, 0], [-3.6048388692084083, 0.07167096374575402]]]], 'bad_primes': [3, 5, 13], 'central_character': '585.334', 'coefficient_field': 'CDF', 'conductor': 585, 'conductor_radical': 195, 'conjugate': '2137063689885446514990053045721', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.2046745713132565, 1.2728694572232315], [1.0, 1.7320508075688772]], [[1.0, 0], [0, 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'group': 'GL2', 'index': 4, 'label': '2-585-65.9-c1-0-4', '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/585/2/bs/a/334/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.399406462185874, 0.2743903504296591, 0.14082119463808404, -0.0024040236895347847, -0.1547558868427231, -0.312935526901683, -0.4700791819673084, -0.6153698746447844, -0.7340831999621845, -0.8080923059294417, -0.8168601473622367, -0.7389333916209602, -0.5539153051492408, -0.2448375608244559, 0.1992191037984148, 0.7804780414389965, 1.4900801143756288, 2.306286804156012, 3.1936130587683373, 4.103198611693547, 4.974647405399085, 5.739437468756801, 6.32583458248085, 6.665046274459542, 6.698149231286539, 6.3831398041461425, 5.7013234255361755, 4.6622028381787155, 3.3060697991926604, 1.703662770943095, 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'9.319499868198401740836535340975001', '10.17235181902691206364484839740115'], 'prelabel': '2-585-65.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.161307131863703, 'root_angle': -0.5400954692099585, 'root_number': '-0.12563078829018787 - 0.9920770660758095*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.270047734605', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.37296955454060633829143896227', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.69862365798905887183173390712', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.74667919993048902514850376913', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.671248518244905, 'bad_primes': [3, 5, 13], 'central_character': '65.9', 'conductor': 585, 'conductor_radical': 195, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/585/2/bs/a/334/1'], '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': '2-585-65.9-c1-0-4', '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': '2-585-65.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.161307131863703, 'root_angle': -0.2700477346049793, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.37296955454060633829143896227', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '472795079680254967308240163404', 'Lhash_array': ['472795079680254967308240163404'], 'label': '2-585-65.9-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/585/2/bs/a/334/1'}