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lfunc_lfunctions • Show schema
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{'Lhash': '1118871431624545367492683075899', 'a10': [0.7231234875140369, -4.8291637174650255], 'a2': [0.5651950168443727, 2.1093365190479463], 'a3': [-0.8714086763918052, -1.4968790594797838], 'a4': [-2.397804335954719, 1.3843729788275088], 'a5': [-2.050355728912074, -0.8922115135535063], 'a6': [2.6649058232272522, -2.6841227293651335], 'a7': [0.0, 0.0], 'a8': [-1.1870525378663437, -1.1870525378663437], 'a9': [-1.4812938374181643, 2.6087867998797774], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.869004548564111, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.8714086763918052, 1.4968790594797838]]], [5, [[1.0, 0], [2.050355728912074, 0.8922115135535063]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5, 7], 'central_character': '735.422', 'coefficient_field': 'CDF', 'conductor': 735, 'conductor_radical': 105, 'conjugate': '1404540622980625134372696248248', 'degree': 2, 'euler_factors': [[[1.0, 0], 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[-92.66471820493493, 53.5]], [[1.0, 0], [2.4437654654520955, -1.4109086493150784], [54.5, -94.39676901250381]], [[1.0, 0], [-2.017976254995979, -2.017976254995979], [0, 113.0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 20, 'label': '2-735-105.2-c1-0-20', '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/735/2/y/g/422/11', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.3488541806738241, 1.2548725985574718, 1.1355177460822956, 0.9867762687677579, 0.8035311335756147, 0.5815810737141048, 0.3193954048228177, 0.019411476798442528, -0.31119789036185125, -0.6603124383907787, -1.0112258751838226, -1.3435911866431518, -1.6349319937523774, -1.8626492482690835, -2.0063824447706167, -2.050509483408934, -1.9865038810302174, -1.8148270331215504, -1.546029999197626, 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'3.63940725789017452660082290712260', '4.34706933969156985442518587068183', '5.16181310768776819954825903004100', '6.57562829762928790039360800321557', '7.55935416227831741014767770989110', '9.065655713492317329211023041989935', '9.571898268598435722443257325535874', '10.45917336775239297518079250239930'], 'prelabel': '2-735-105.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.422602845817719, 'root_angle': -0.2303655335368151, 'root_number': '0.12305430034313636 - 0.9923999391208472*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.230365533537', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.882633930377268273940781735384', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.76088429247463177238643966258', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.63940725789017452660082290712', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.869004548564111, 'bad_primes': [3, 5, 7], 'central_character': '105.2', 'conductor': 735, 'conductor_radical': 105, 'degree': 2, 'index': 20, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/735/2/y/g/422/11'], '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': '2-735-105.2-c1-0-20', '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': '2-735-105.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.422602845817719, 'root_angle': -0.2303655335368151, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.882633930377268273940781735384', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1118871431624545367492683075899', 'Lhash_array': ['1118871431624545367492683075899'], 'factors': ['2-735-105.2-c1-0-20'], 'label': '2-735-105.2-c1-0-20', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/735/2/y/g/422/11'}