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lfunc_lfunctions • Show schema
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{'Lhash': '945592009238143595324786757657', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.7516896584148686, -1.5604366880563076], 'a4': [0.0, 0.0], 'a5': [1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 4.285909862345988], 'a8': [0.0, 0.0], 'a9': [-1.8699253148642763, 2.3459282420461496], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.8328192970214605, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0.7516896584148686, 1.5604366880563076]]], [5, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '480.431', 'coefficient_field': 'CDF', 'conductor': 480, 'conductor_radical': 30, 'conjugate': '2288245093903070349456242468903', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.7516896584148686, 1.5604366880563076]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, -4.285909862345988], [-7.0, 0]], [[1.0, 0], [0, -2.4467289863573063], [-11.0, 0]], [[1.0, 0], [0, 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'4.11775574275003069359570439052265', '5.04953146476661070575566208662596', '6.15201828121621944795778279250386', '7.05569967445951754007186960918881', '8.283683674953069799068260202488310', '9.254026787459650618844650810070401', '10.24057392596262651046329887852987', '10.74129313562626529514124108953921'], 'prelabel': '2-480-24.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9577587433137569, 'root_angle': -0.2770739904134884, 'root_number': '0.6444797715337864 - 0.7646213599447497*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.138536995207', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.74594056837735731427249108274', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.07301379258703542300534998112', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.11775574275003069359570439052', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.8328192970214605, 'bad_primes': [2, 3, 5], 'central_character': '24.11', 'conductor': 480, 'conductor_radical': 30, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/480/2/b/b/431/3'], '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': '2-480-24.11-c1-0-2', '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': '2-480-24.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9577587433137569, 'root_angle': -0.1385369952067442, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.74594056837735731427249108274', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '945592009238143595324786757657', 'Lhash_array': ['945592009238143595324786757657'], 'label': '2-480-24.11-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/480/2/b/b/431/3'}