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lfunc_lfunctions • Show schema
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{'Lhash': '875360981752731617889481484835', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, -0.33987688662318255], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [-3.8844837019393323, 0], 'a8': [0, 0], 'a9': [2.8844837019393323, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 10.380552262766455, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [-0.6601231133768174, -3.5446068153161496]]]], 'bad_primes': [2, 5, 13], 'central_character': '1300.649', 'coefficient_field': 'CDF', 'conductor': 1300, 'conductor_radical': 130, 'conjugate': '1451963499804531031566027388521', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0.33987688662318255], [-3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [3.8844837019393323, 0], [7.0, 0]], [[1.0, 0], [0, 1.5446068153161499], [-11.0, 0]], [[1.0, 0], [-0.6601231133768174, -3.5446068153161496]], [[1.0, 0], [0, 0], [-17.0, 0]], [[1.0, 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'2.46613558391985161865116519353248', '3.41350393607633713325775023120631', '4.35994846732414704451639407722839', '5.33171589161812881838131260502548', '6.48974188716872882602688234590971', '6.89879824923318715405744128210574', '7.915392574001518754132302314819381', '8.938628379663681381447105959095229', '9.640643301584127819034603664328164'], 'prelabel': '2-1300-65.64-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.221886444734894, 'root_angle': -0.10309602108468258, 'root_number': '0.7974305359577806274334390442952678270830983815661155361 - 0.6034107558886290997574518246803044821219149543734979920*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.10309602108468258', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.69053805646061346127456495378', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.46613558391985161865116519353', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.41350393607633713325775023121', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 10.380552262766455, 'bad_primes': [2, 5, 13], 'central_character': '65.64', 'conductor': 1300, 'conductor_radical': 130, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1300/2/d/d/649/3'], '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': '2-1300-65.64-c1-0-5', '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': '2-1300-65.64-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.221886444734894, 'root_angle': -0.10309602108468258, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.69053805646061346127456495378', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '875360981752731617889481484835', 'Lhash_array': ['875360981752731617889481484835'], 'factors': ['2-1300-65.64-c1-0-5'], 'label': '2-1300-65.64-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1300/2/d/d/649/3'}