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lfunc_lfunctions • Show schema
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{'Lhash': '1155613023109465178131115937306', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.08056746729191024, 1.7301759688581295], 'a4': [0.0, 0.0], 'a5': [1.900167732829384, 3.2911870561634573], 'a6': [0.0, 0.0], 'a7': [-2.2349496570720953, 1.4159802365687608], 'a8': [0.0, 0.0], 'a9': [-2.987017766428334, -0.2787917915604529], '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], [0.08056746729191024, -1.7301759688581295]]], [7, [[1.0, 0], [2.2349496570720953, -1.4159802365687608]]]], 'bad_primes': [2, 3, 7], 'central_character': '336.17', 'coefficient_field': 'CDF', 'conductor': 336, 'conductor_radical': 42, 'conjugate': '3577566344414290428321072549829', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.08056746729191024, -1.7301759688581295]], [[1.0, 0], [-1.900167732829384, -3.2911870561634573], [-2.5, 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'label': '2-336-21.17-c1-0-1', '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/336/2/bc/f/17/5', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.2507453570928806, 1.0917730545820674, 0.9377625157638353, 0.7822834933142406, 0.6195577702203979, 0.4455031827206017, 0.25849487421711453, 0.05983789499630682, -0.1460113856011641, -0.35144642031496204, -0.5459324292305077, -0.7164672263514996, -0.8483023916968218, -0.9259334058433871, -0.9343420022346914, -0.8604405668302436, -0.6946314699162135, -0.4323584827247527, -0.0754979115078887, 0.36658112420896244, 0.8764599555472549, 1.4287720371674835, 1.9910779488355317, 2.525566700609375, 2.991555358138133, 3.3486651260633855, 3.5604543073420523, 3.598198479338442, 3.444438633402926, 3.0958816301655414, 2.5652449420826144, 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'11.56932457425932665368284003257104'], 'prelabel': '2-336-21.17-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6379784821282062, 'root_angle': -0.7052942419217096, 'root_number': '-0.6011591878026943 - 0.7991292954962951*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.352647120961', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.911617935495322735081226830594', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.27304387694422676313683341942', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.16133336571614857754587701062', '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': '21.17', 'conductor': 336, 'conductor_radical': 42, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/336/2/bc/f/17/5'], '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': '2-336-21.17-c1-0-1', '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': '2-336-21.17-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6379784821282062, 'root_angle': -0.3526471209608548, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.911617935495322735081226830594', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1155613023109465178131115937306', 'Lhash_array': ['1155613023109465178131115937306'], 'label': '2-336-21.17-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/336/2/bc/f/17/5'}