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lfunc_lfunctions • Show schema
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{'Lhash': '428328217830386415426063169624', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.6675660126077214, -0.4682131924621356], 'a4': [0.0, 0.0], 'a5': [-0.9364263849242712, 0.0], 'a6': [0.0, 0.0], 'a7': [-1.5615528128088303, -2.135779205069857], 'a8': [0.0, 0.0], 'a9': [2.5615528128088303, 1.5615528128088303], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.682973507915022, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [1.6675660126077214, 0.4682131924621356]]], [7, [[1.0, 0], [1.5615528128088303, 2.135779205069857]]]], 'bad_primes': [2, 3, 7], 'central_character': '336.209', 'coefficient_field': 'CDF', 'conductor': 336, 'conductor_radical': 42, 'conjugate': '2280893484282857227040452387184', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.6675660126077214, 0.4682131924621356]], [[1.0, 0], [0.9364263849242712, 0], [5.0, 0]], [[1.0, 0], [1.5615528128088303, 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['0.33789138564938135690419200069499', '2.89131311290160942616358338992451', '4.18698246745623218711546618448892', '5.57757633980518531089908001226437', '6.09673460847483120623364958791164', '7.31729778640392544401321399702778', '8.615221690366633421121445953205027', '9.398304647832427662803812011711216', '10.60004236166578583956985073343862', '11.30713005049328599916631116650383'], 'prelabel': '2-336-21.20-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6379784821282062, 'root_angle': -0.6138251579737688, 'root_number': '-0.35001983694400235 - 0.9367422877962188*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.306912578987', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.33789138564938135690419200069', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.89131311290160942616358338992', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.18698246745623218711546618449', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.682973507915022, 'bad_primes': [2, 3, 7], 'central_character': '21.20', 'conductor': 336, 'conductor_radical': 42, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/336/2/k/c/209/1'], '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': '2-336-21.20-c1-0-0', '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': '2-336-21.20-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6379784821282062, 'root_angle': -0.3069125789868844, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.33789138564938135690419200069', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '428328217830386415426063169624', 'Lhash_array': ['428328217830386415426063169624'], 'label': '2-336-21.20-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/336/2/k/c/209/1'}