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lfunc_lfunctions • Show schema
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{'Lhash': '1729392871313016875721276163', 'a10': [2.1579982952147385, 0.5856990335063587], 'a2': [-0.5, 0.8660254037844386], 'a3': [0, 0], 'a4': [-0.5, -0.8660254037844386], 'a5': [-0.5717689056188695, -2.1617308617326536], 'a6': [0, 0], 'a7': [0.6031369289619706, 1.0446638048831938], 'a8': [1.0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.34249703648981, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.5, -0.8660254037844386]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0.5717689056188695, 2.1617308617326536]]], [13, [[1.0, 0], [-2.245107014302872, 2.8212576086433585]]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '1170.199', 'coefficient_field': 'CDF', 'conductor': 1170, 'conductor_radical': 390, 'conjugate': '1936628483861848596922702797457', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.5717689056188695, 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'6.13106945256818775082057556837916', '7.12943786476857914378902355878612', '7.63351403793453755542243773974718', '8.593596491771410750862929993101242', '9.532035885997212358308082744216485'], 'prelabel': '2-1170-65.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.0565498583353437, 'root_angle': 0.9609009868649828, 'root_number': '-0.99246548641439065963028585540837980933723081316364499209 + 0.1225245211222918798664824558518029534006754303759167544*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.48045049343249147', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.00136425042594675127161682147', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.01346154133665139958262465012', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.77594849123679850352361154004', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.34249703648981, 'bad_primes': [2, 3, 5, 13], 'central_character': '65.4', 'conductor': 1170, 'conductor_radical': 390, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1170/2/bj/c/199/3'], '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': '2-1170-65.4-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': '2-1170-65.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.0565498583353437, 'root_angle': 0.4804504934324914, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.00136425042594675127161682147', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1729392871313016875721276163', 'Lhash_array': ['1729392871313016875721276163'], 'label': '2-1170-65.4-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1170/2/bj/c/199/3'}