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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': -1, 'A8': 0, 'A9': -4, 'Lhash': '844331273118422623721075654687', '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': [-0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [-1.3333333333333333, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 89.57942739416335, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [7, [1, 1]]], 'bad_primes': [2, 7], 'central_character': '1404928.1', 'coefficient_field': '1.1.1.1', 'conductor': 1404928, 'conductor_radical': 14, 'degree': 4, 'euler_factors': [[1], [1, 0, 4, 0, 9], [1, 0, -2, 0, 25], [1, 1], [1, -6, 30, -66, 121], [1, 0, -6, 0, 169], [1, 0, 26, 0, 289], [1, 0, -20, 0, 361], [1, 2, 22, 46, 529], [1, -6, 58, -174, 841], [1, 0, 34, 0, 961], [1, -6, 34, -222, 1369], [1, 0, 50, 0, 1681], [1, -14, 126, -602, 1849], [1, 0, 70, 0, 2209], [1, -4, 94, -212, 2809], [1, 0, 68, 0, 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0.38663095296557426, -0.03256075797944717, -0.455533414811248, -0.7960629513339479, -0.9804158151345557], 'positive_zeros': ['0.66605993241860822215856807505572', '1.33728408232782050400274817279888', '2.32529761773487740473529909758157', '2.71893794562589817047343582243170', '3.32222335300377067084853089644567', '3.86148798444796531892510686273152', '4.27065933609661481678911430733308', '4.75753626262456766060320377777629', '5.42294687986564573940240116382144', '5.93714354268193916935828673496023', '6.13891864417063180016649951746752', '6.58417639129110548206174139221640', '6.98524175315750446329803899079057', '7.52524187274780758002045715057615', '7.971546368458368402477222584228345'], 'prelabel': '4-112e3-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.076465650952455, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1588359829701072412, 'z1': {'__RealLiteral__': 0, 'data': '0.66605993241860822215856807505572', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '1.33728408232782050400274817279888', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.32529761773487740473529909758157', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 89.57942739416335, 'bad_primes': [2, 7], 'central_character': '1.1', 'conductor': 1404928, 'conductor_radical': 14, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, -1, 0, -4, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 1, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, -4, 0, 0, 0, 4, 0, 0, 0, 0, 0, -6, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0], 'euler11': [1, -6, 30, -66, 121], 'euler13': [1, 0, -6, 0, 169], 'euler17': [1, 0, 26, 0, 289], 'euler19': [1, 0, -20, 0, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 2, 22, 46, 529], 'euler29': [1, -6, 58, -174, 841], 'euler3': [1, 0, 4, 0, 9], 'euler31': [1, 0, 34, 0, 961], 'euler37': [1, -6, 34, -222, 1369], 'euler41': [1, 0, 50, 0, 1681], 'euler43': [1, -14, 126, -602, 1849], 'euler47': [1, 0, 70, 0, 2209], 'euler5': [1, 0, -2, 0, 25], 'euler53': [1, -4, 94, -212, 2809], 'euler59': [1, 0, 68, 0, 3481], 'euler61': [1, 0, 14, 0, 3721], 'euler67': [1, 4, 134, 268, 4489], 'euler7': [1, 1, 0, 0, 0], 'euler71': [1, -4, 46, -284, 5041], 'euler73': [1, 0, 86, 0, 5329], 'euler79': [1, 0, -98, 0, 6241], 'euler83': [1, 0, -68, 0, 6889], 'euler89': [1, 0, -162, 0, 7921], 'euler97': [1, 0, 106, 0, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 4, 0, 9], [1, 0, -2, 0, 25], [1, 1, 0, 0, 0], [1, -6, 30, -66, 121], [1, 0, -6, 0, 169], [1, 0, 26, 0, 289], [1, 0, -20, 0, 361], [1, 2, 22, 46, 529], [1, -6, 58, -174, 841], [1, 0, 34, 0, 961], [1, -6, 34, -222, 1369], [1, 0, 50, 0, 1681], [1, -14, 126, -602, 1849], [1, 0, 70, 0, 2209], [1, -4, 94, -212, 2809], [1, 0, 68, 0, 3481], [1, 0, 14, 0, 3721], [1, 4, 134, 268, 4489], [1, -4, 46, -284, 5041], [1, 0, 86, 0, 5329], [1, 0, -98, 0, 6241], [1, 0, -68, 0, 6889], [1, 0, -162, 0, 7921], [1, 0, 106, 0, 9409]], 'index': 3, 'instance_types': ['BMF', 'BMF', 'ECNF', 'ECNF'], 'instance_urls': ['ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/28672.6/b', 'ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/28672.8/b', 'EllipticCurve/2.0.7.1/28672.8/b', 'EllipticCurve/2.0.7.1/28672.6/b'], 'is_instance_Artin': False, 'is_instance_BMF': True, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': True, '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': '4-112e3-1.1-c1e2-0-3', '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': 0, 'prelabel': '4-112e3-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.076465650952455, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1588359829701072412, 'z1': {'__RealLiteral__': 0, 'data': '0.66605993241860822215856807505572', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9620405
{'Lhash': '844331273118422623721075654687', 'Lhash_array': ['844331273118422623721075654687'], 'label': '4-112e3-1.1-c1e2-0-3', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.7.1/28672.6/b'}
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id: 9620298
{'Lhash': '844331273118422623721075654687', 'Lhash_array': ['844331273118422623721075654687'], 'label': '4-112e3-1.1-c1e2-0-3', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.7.1/28672.8/b'}
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id: 9620284
{'Lhash': '844331273118422623721075654687', 'Lhash_array': ['844331273118422623721075654687'], 'label': '4-112e3-1.1-c1e2-0-3', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/28672.8/b'}
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id: 9619971
{'Lhash': '844331273118422623721075654687', 'Lhash_array': ['844331273118422623721075654687'], 'label': '4-112e3-1.1-c1e2-0-3', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/28672.6/b'}