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lfunc_lfunctions • Show schema
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{'Lhash': '2490438844051732253981631694388', 'a10': [2.213413666546861, 0.2845028735779972], 'a2': [-1.3082155025195337, -0.537189164975955], 'a3': [-0.9659258262890683, -0.25881904510252074], 'a4': [1.4228556020648724, 1.4055183868141354], 'a5': [-1.5242269665779147, 0.4084153847762921], 'a6': [1.1246043535168522, 0.8574759752033541], 'a7': [1.0919764580003326, -2.409893652253777], 'a8': [-1.106372507896994, -2.603063555461087], 'a9': [0.8660254037844386, 0.5], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.682973507915022, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.3082155025195337, 0.537189164975955]]], [3, [[1.0, 0], [0.9659258262890683, 0.25881904510252074]]], [7, [[1.0, 0], [-1.0919764580003326, 2.409893652253777]]]], 'bad_primes': [2, 3, 7], 'central_character': '336.37', 'coefficient_field': 'CDF', 'conductor': 336, 'conductor_radical': 42, 'conjugate': '230227111625680314510645421961', 'degree': 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'5.60675950424428807322782915223980', '6.00259349878785530520039262035089', '7.55516845583550015686134103069489', '8.241483387044301080856669770771593', '9.047633094484578117749758510100336', '10.23509435415757086135068270443529', '10.96528986886746726455691792218188', '11.86542601108588151058151580725863'], 'prelabel': '2-336-112.37-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6379784821282062, 'root_angle': 0.9863488801094784, 'root_number': '-0.9990805253791926 + 0.04287311288017895*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.493174440055', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.96460984091621975788501150283', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.94458065210107348188542466724', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.60675950424428807322782915224', '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': '112.37', 'conductor': 336, 'conductor_radical': 42, 'degree': 2, 'index': 26, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/336/2/bq/b/37/4'], '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': '2-336-112.37-c1-0-26', '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': '2-336-112.37-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6379784821282062, 'root_angle': 0.4931744400547392, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.96460984091621975788501150283', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2490438844051732253981631694388', 'Lhash_array': ['2490438844051732253981631694388'], 'label': '2-336-112.37-c1-0-26', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/336/2/bq/b/37/4'}