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lfunc_lfunctions • Show schema
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{'Lhash': '1530659991155492539446615551232', 'a10': [-3.0359593895661745, 0.0], 'a2': [-0.6071918779132348, 0.0], 'a3': [3.0, 0.0], 'a4': [-7.631318023396199, 0.0], 'a5': [5.0, 0.0], 'a6': [-1.8215756337397047, 0.0], 'a7': [8.950799388600917, 0.0], 'a8': [9.491209344884933, 0.0], 'a9': [9.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.735315150947207, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-3.0, 0]]], [5, [[1.0, 0], [-5.0, 0]]], [11, [[1.0, 0], [11.0, 0]]]], 'bad_primes': [3, 5, 11], 'central_character': '165.1', 'coefficient_field': 'CDF', 'conductor': 165, 'conductor_radical': 165, 'conjugate': '1530659991155492539446615551232', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.6071918779132348, 0], [8.0, 0]], [[1.0, 0], [-3.0, 0]], [[1.0, 0], [-5.0, 0]], [[1.0, 0], [-8.950799388600917, 0], [343.0, 0]], [[1.0, 0], [11.0, 0]], [[1.0, 0], [0.46038681282188876, 0], [2197.0, 0]], [[1.0, 0], 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'3.12791487994090885759162751115988', '4.61749048961360917943542706485610', '5.69102629869008333045958502836637', '7.50139287119856281710070420224250', '8.277180068951443661438294092647586', '9.388079821420692639793492986242754', '10.00212734113146905023655586956338', '11.24903380010802816436380458650711', '12.73571293142000328895449976337012'], 'prelabel': '2-165-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.12014665535888, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.20747782620850776850538122683', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.12791487994090885759162751116', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.61749048961360917943542706486', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.735315150947207, 'bad_primes': [3, 5, 11], 'central_character': '1.1', 'conductor': 165, 'conductor_radical': 165, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/165/4/a/h/1/2'], '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': '2-165-1.1-c3-0-6', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-165-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.12014665535888, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.20747782620850776850538122683', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1530659991155492539446615551232', 'Lhash_array': ['1530659991155492539446615551232'], 'label': '2-165-1.1-c3-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/165/4/a/h/1/2'}