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lfunc_lfunctions • Show schema
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{'Lhash': '1160252754271306272239269349753', 'a10': [98.51040599852787, -104.59329470213942], 'a2': [-2.8736080029567974, -4.9772350621577095], 'a3': [-8.304695558877263, 3.4687219079027174], 'a4': [-8.515245909314705, 14.748838553876114], 'a5': [7.19048096257032, 23.943620936001174], 'a6': [41.129083920997466, 31.366674881608507], 'a7': [41.415087256606036, -23.911011776113334], 'a8': [5.92245907398995, 0.0], 'a9': [56.93593665127146, -57.61335884707993], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.651648338772996, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [8.304695558877263, -3.4687219079027174]]], [5, [[1.0, 0], [-7.19048096257032, -23.943620936001174]]]], 'bad_primes': [3, 5], 'central_character': '45.14', 'coefficient_field': 'CDF', 'conductor': 45, 'conductor_radical': 15, 'conjugate': '1776858736641229019494723346612', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.8736080029567974, 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'5.29703442159280689533121195117230', '5.90824500678170308654517796815678', '7.74960544381038243561861354948984', '8.465022806783606274000670423741072', '10.06416450527224580032125258049562', '11.65628043641579473592466251876241', '12.77339681841763669264961945158494', '14.18336229795816836844898160081714', '15.76872882909916548624214473647043'], 'prelabel': '2-45-45.14-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.156768030821348, 'root_angle': 0.04984914172136266, 'root_number': '0.9513489971079938 + 0.3081153772560115*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0498491417214', 'prec': 50}, 'spectral_label': 'c4-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.915278038019634837406278456602', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '5.29703442159280689533121195117', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.90824500678170308654517796816', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.651648338772996, 'bad_primes': [3, 5], 'central_character': '45.14', 'conductor': 45, 'conductor_radical': 15, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/45/5/h/a/14/4'], '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': '2-45-45.14-c4-0-3', 'motivic_weight': 4, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [4], 'order_of_vanishing': 0, 'prelabel': '2-45-45.14-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.156768030821348, 'root_angle': 0.04984914172136266, 'self_dual': False, 'spectral_label': 'c4-0', 'z1': {'__RealLiteral__': 0, 'data': '0.915278038019634837406278456602', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1160252754271306272239269349753', 'Lhash_array': ['1160252754271306272239269349753'], 'factors': ['2-45-45.14-c4-0-3'], 'label': '2-45-45.14-c4-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/45/5/h/a/14/4'}