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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': -3, 'A8': 0, 'A9': -4, 'Lhash': '2458234240410471658627860129597', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [-1.1338934190276817, 0], 'a8': [0.0, 0], 'a9': [-1.3333333333333333, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.627967895492037, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [7, [1, 3, 9, 7]], [23, [1, 7, 29, 23]]], 'bad_primes': [2, 7, 23], 'central_character': '41216.1', 'coefficient_field': '1.1.1.1', 'conductor': 41216, 'conductor_radical': 322, 'degree': 4, 'euler_factors': [[1], [1, 0, 4, 0, 9], [1, 0, 6, 0, 25], [1, 3, 9, 7], [1, 0, -12, 0, 121], [1, 0, -22, 0, 169], [1, -4, 34, -68, 289], [1, 0, 30, 0, 361], [1, 7, 29, 23], [1, 0, 42, 0, 841], [1, 4, 62, 124, 961], [1, 0, 42, 0, 1369], [1, 0, 78, 0, 1681], [1, 0, 12, 0, 1849], [1, 14, 142, 658, 2209], [1, 0, 74, 0, 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2.335984766594353, 1.9113268333672548], 'positive_zeros': ['1.93920488813549103170007233915522', '2.96590493614543809272616014027255', '3.46515215889279553519866910128904', '4.12548383912120958514795534208151', '5.19310112614586475083982364691615', '5.67334862307047011095588887285780', '6.19320850196938924292455976243722', '6.58979855347549545962881496267449', '7.45248250543738288777765962736936', '7.989858284140712077515034529498585', '8.345575183130610167188007865710629', '9.037871427034557810662219215243902', '9.595045959251982254959930061577985', '9.926145872918632439826198575660249'], 'prelabel': '4-41216-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.2732245788913024, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1856032482743633934, 'z1': {'__RealLiteral__': 0, 'data': '1.93920488813549103170007233915522', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.96590493614543809272616014027255', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '3.46515215889279553519866910128904', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.627967895492037, 'bad_primes': [2, 7, 23], 'central_character': '1.1', 'conductor': 41216, 'conductor_radical': 322, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, -3, 0, -4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -7, 0, -6, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 2, 0, 6, 0, 0, 0, 0, 0, -4, 0, 7, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0], 'euler11': [1, 0, -12, 0, 121], 'euler13': [1, 0, -22, 0, 169], 'euler17': [1, -4, 34, -68, 289], 'euler19': [1, 0, 30, 0, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 7, 29, 23, 0], 'euler29': [1, 0, 42, 0, 841], 'euler3': [1, 0, 4, 0, 9], 'euler31': [1, 4, 62, 124, 961], 'euler37': [1, 0, 42, 0, 1369], 'euler41': [1, 0, 78, 0, 1681], 'euler43': [1, 0, 12, 0, 1849], 'euler47': [1, 14, 142, 658, 2209], 'euler5': [1, 0, 6, 0, 25], 'euler53': [1, 0, 74, 0, 2809], 'euler59': [1, 0, 80, 0, 3481], 'euler61': [1, 0, -38, 0, 3721], 'euler67': [1, 0, 56, 0, 4489], 'euler7': [1, 3, 9, 7, 0], 'euler71': [1, -2, 134, -142, 5041], 'euler73': [1, -6, 130, -438, 5329], 'euler79': [1, 4, 158, 316, 6241], 'euler83': [1, 0, 70, 0, 6889], 'euler89': [1, 8, -2, 712, 7921], 'euler97': [1, -4, 182, -388, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 4, 0, 9], [1, 0, 6, 0, 25], [1, 3, 9, 7, 0], [1, 0, -12, 0, 121], [1, 0, -22, 0, 169], [1, -4, 34, -68, 289], [1, 0, 30, 0, 361], [1, 7, 29, 23, 0], [1, 0, 42, 0, 841], [1, 4, 62, 124, 961], [1, 0, 42, 0, 1369], [1, 0, 78, 0, 1681], [1, 0, 12, 0, 1849], [1, 14, 142, 658, 2209], [1, 0, 74, 0, 2809], [1, 0, 80, 0, 3481], [1, 0, -38, 0, 3721], [1, 0, 56, 0, 4489], [1, -2, 134, -142, 5041], [1, -6, 130, -438, 5329], [1, 4, 158, 316, 6241], [1, 0, 70, 0, 6889], [1, 8, -2, 712, 7921], [1, -4, 182, -388, 9409]], 'index': 9, 'instance_types': ['ECNF', 'ECNF', 'HMF', 'HMF'], 'instance_urls': ['EllipticCurve/2.2.8.1/644.1/a', 'EllipticCurve/2.2.8.1/644.4/a', 'ModularForm/GL2/TotallyReal/2.2.8.1/holomorphic/2.2.8.1-644.1-a', 'ModularForm/GL2/TotallyReal/2.2.8.1/holomorphic/2.2.8.1-644.4-a'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': True, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': True, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-41216-1.1-c1e2-0-9', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 1, 'prelabel': '4-41216-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.2732245788913024, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1856032482743633934, 'z1': {'__RealLiteral__': 0, 'data': '1.93920488813549103170007233915522', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9566374
{'Lhash': '2458234240410471658627860129597', 'Lhash_array': ['2458234240410471658627860129597'], 'label': '4-41216-1.1-c1e2-0-9', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.8.1/holomorphic/2.2.8.1-644.4-a'}
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id: 9566219
{'Lhash': '2458234240410471658627860129597', 'Lhash_array': ['2458234240410471658627860129597'], 'label': '4-41216-1.1-c1e2-0-9', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.8.1/holomorphic/2.2.8.1-644.1-a'}
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id: 9566016
{'Lhash': '2458234240410471658627860129597', 'Lhash_array': ['2458234240410471658627860129597'], 'label': '4-41216-1.1-c1e2-0-9', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.8.1/644.4/a'}
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id: 9565843
{'Lhash': '2458234240410471658627860129597', 'Lhash_array': ['2458234240410471658627860129597'], 'label': '4-41216-1.1-c1e2-0-9', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.8.1/644.1/a'}