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lfunc_lfunctions • Show schema
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{'Lhash': '7014262104801137330658011663', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0.5856900376820378, 0], 'a6': [0, 0], 'a7': [5.159011729346286, 0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 74.55060032897724, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [18.480624283524246, 4.4120886313869425]]]], 'bad_primes': [2, 3, 19], 'central_character': '2736.721', 'coefficient_field': 'CDF', 'conductor': 2736, 'conductor_radical': 114, 'conjugate': '1761309092571477646090272135490', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.5856900376820378, 0], [25.0, 0]], [[1.0, 0], [-5.159011729346286, 0], [49.0, 0]], [[1.0, 0], [-11.817351183272384, 0], [121.0, 0]], [[1.0, 0], [0, 14.904798751161984], [-169.0, 0]], [[1.0, 0], [8.919333541653188, 0], [289.0, 0]], [[1.0, 0], 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['0.00553327715345086477110533392640', '1.70484825712870040870977998932450', '2.06171954276976086514149482991720', '3.75236283434337405671026983582696', '4.18836430123310532562569191428351', '5.10923810211602875344146293530572', '6.18292511626590267175004398713505', '6.62906759942337335430909783805246', '7.57950391282363913673759312853462', '8.391997831982167677821015417285617'], 'prelabel': '2-2736-19.18-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.634268951623945, 'root_angle': -0.9254026418230256, 'root_number': '-0.97266443597496038603796734186930036942514995105114180411 - 0.2322151911256285317002946017946259045855977530883623419*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.4627013209115128', 'prec': 64}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.00553327715345086477110533393', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.70484825712870040870977998932', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.06171954276976086514149482992', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 74.55060032897724, 'bad_primes': [2, 3, 19], 'central_character': '19.18', 'conductor': 2736, 'conductor_radical': 114, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2736/3/o/q/721/13'], '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': '2-2736-19.18-c2-0-1', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-2736-19.18-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.634268951623945, 'root_angle': -0.4627013209115128, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.00553327715345086477110533393', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '7014262104801137330658011663', 'Lhash_array': ['7014262104801137330658011663'], 'label': '2-2736-19.18-c2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2736/3/o/q/721/13'}