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lfunc_lfunctions • Show schema
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{'A10': -1, 'A2': -1, 'A3': -1, 'A4': 1, 'A5': 1, 'A6': 1, 'A7': 0, 'A8': -1, 'A9': 1, 'Lhash': '731351590513809259', 'a10': [-0.31622776601683794, 0], 'a2': [-0.7071067811865475, 0], 'a3': [-0.5773502691896258, 0], 'a4': [0.5, 0], 'a5': [0.4472135954999579, 0], 'a6': [0.4082482904638631, 0], 'a7': [0.0, 0], 'a8': [-0.35355339059327373, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 269.9742092339491, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1, 1]], [5, [1, -1]], [7, [1]], [23, [1, 1]]], 'bad_primes': [2, 3, 5, 7, 23], 'central_character': '33810.1', 'coefficient_field': '1.1.1.1', 'conductor': 33810, 'conductor_radical': 4830, 'degree': 2, 'euler_factors': [[1, 1], [1, 1], [1, -1], [1], [1, 2, 11], [1, -5, 13], [1, 0, 17], [1, 5, 19], [1, 1], [1, -5, 29], [1, 5, 31], [1, -4, 37], [1, 4, 41], [1, 2, 43], [1, 8, 47], [1, 3, 53], [1, -3, 59], [1, -7, 61], [1, 2, 67], [1, -14, 71], [1, 2, 73], [1, 2, 79], [1, 0, 83], [1, 1, 89], [1, -7, 97]], 'gamma_factors': [[], [0]], 'index': 38, 'label': '2-33810-1.1-c1-0-38', 'leading_term': '3.6639194405', 'load_key': 'Cremona', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'EllipticCurve/Q/33810/s', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 0.8357297532406147, 1.203740501108319, 0.7868991008986277, -0.2580031984145851, -1.160408889001522, -1.033126852784104, 0.1900853389645836, 1.325224389619925, 0.8327985827837135, -1.461952764433092, -3.637291125391165, -3.254555817024119, -0.1061540456388235, 2.933187548501933, 2.571617488108057, -1.144541986216853, -4.415920120158095, -3.722558122348521, 0.08480352638156542, 2.728081029817346, 1.632959827365379, -1.124127981438992, -1.867680998894061, -0.2262101889986596, 0.8617206778915578, -0.1243988569725806, -0.922476544092879, 0.8407361148710139, 3.511220420036299, 3.453337625436937, 0.5145107543114664, -1.553750997771287, -0.6734162731491031, 0.5833877986160158, -0.6164193197467249, -2.639565562866723, -2.075414442366675, 0.5263361431406168, 1.445054516473875, -0.1553141593396704, -1.133064354965625, 0.01836603854180425, 0.8004248877620006, -0.2443035891344461, -0.4812318471818466, 1.704373335744767, 2.835089478421078, -0.1255760939303106, -3.60217110618758, -2.507057255933243, 1.06383455639458, 1.192507903095698, -1.283636057468356, 0.1171923971310472, 5.476014574750419, 6.789591624175093, 1.146411731389123, -3.525894013216608, -0.9067777354422651, 3.8174048660295, 3.179432335628859, -0.6901341271750092, -1.384159962981713, 0.5308150725495081, 0.3264471221877739, -1.391602086168098, -0.8090425145883579, 0.9957074102821457, 0.4206584882927713, -1.308208591985084, -0.8827525448322575, 0.368644435875801, -0.2110374643494286, -0.7059182417652557, 0.8080262223768078, 0.9443322922132426, -2.346305243224393, -4.018520994156026, -0.6945103361572879, 2.017865280291563, -0.6472899464368927, -3.63853513345056, -1.789027656024419, 0.6633643505158515, -0.5281295972826108, -0.934073589547537, 2.307231849169979, 2.876125548135343, -2.286204229548827, -5.114362509025405, -0.7271807323179594, 3.403363684957193, 1.731129254497421, 0.0055178554037998, 1.935279696128287, 1.658949977106258, -2.681315026510641, -3.551213990182414, 1.156897941881071, 3.654111613871393, 1.229296741060943, -0.09824957180079864, 0.9478576421657754, -0.3258596969629172, -2.606726547213276, -0.8690880605512472, 2.1134514624107, 0.9066929203096888, -1.464624966743211, -0.276441186631931, 1.288596849600775, -0.06378593582309725, -0.8884964035463464, 0.3350903904549503, 0.004670989231430678, -1.272084439635615, 0.237945022002387, 1.691749582327509, -0.6671681582365921, -2.014405823949723], 'positive_zeros': ['0.9437129898980661', '1.717397484778948', '2.357133818656381', '3.257085355904469', '3.933265192319547', '4.744695522535968', '5.392284469113243', '6.030388742162324', '6.478950015268269', '6.918972646089799', '7.791507796797508', '8.348000766617438', '8.674296648171135', '9.447578471566836', '9.979799974995779', '10.49699724886424', '10.95357753466069', '11.32609198331235', '11.99269050271402', '12.66552485443180', '13.11373870340853', '13.49312738056412', '14.29223651223793', '14.79167984041537', '15.44856064095077', '15.92418439900121', '16.29558370408844', '16.84852143181280', '17.30426288059271', '17.89725255146244', '18.20440061110979', '18.63802567453732', '19.09105049953994', '19.79007905454564'], 'prelabel': '2-33810-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 16.430891918394117, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 731351590513809259, 'z1': {'__RealLiteral__': 0, 'data': '0.9437129898980661', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.717397484778948', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.357133818656381', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 269.9742092339491, 'bad_primes': [2, 3, 5, 7, 23], 'central_character': '1.1', 'conductor': 33810, 'conductor_radical': 4830, 'degree': 2, 'dirichlet_coefficients': [1, -1, -1, 1, 1, 1, 0, -1, 1, -1, -2, -1, 5, 0, -1, 1, 0, -1, -5, 1, 0, 2, -1, 1, 1, -5, -1, 0, 5, 1, -5, -1, 2, 0, 0, 1, 4, 5, -5, -1, -4, 0, -2, -2, 1, 1, -8, -1, 0, -1, 0, 5, -3, 1, -2, 0, 5, -5, 3, -1, 7, 5, 0, 1, 5, -2, -2, 0, 1, 0, 14, -1, -2, -4, -1, -5, 0, 5, -2, 1, 1, 4, 0, 0, 0, 2, -5, 2, -1, -1, 0, -1, 5, 8, -5, 1, 7, 0, -2, 1], 'euler11': [1, 2, 11], 'euler13': [1, -5, 13], 'euler17': [1, 0, 17], 'euler19': [1, 5, 19], 'euler2': [1, 1, 0], 'euler23': [1, 1, 0], 'euler29': [1, -5, 29], 'euler3': [1, 1, 0], 'euler31': [1, 5, 31], 'euler37': [1, -4, 37], 'euler41': [1, 4, 41], 'euler43': [1, 2, 43], 'euler47': [1, 8, 47], 'euler5': [1, -1, 0], 'euler53': [1, 3, 53], 'euler59': [1, -3, 59], 'euler61': [1, -7, 61], 'euler67': [1, 2, 67], 'euler7': [1, 0, 0], 'euler71': [1, -14, 71], 'euler73': [1, 2, 73], 'euler79': [1, 2, 79], 'euler83': [1, 0, 83], 'euler89': [1, 1, 89], 'euler97': [1, -7, 97], 'euler_factors': [[1, 1, 0], [1, 1, 0], [1, -1, 0], [1, 0, 0], [1, 2, 11], [1, -5, 13], [1, 0, 17], [1, 5, 19], [1, 1, 0], [1, -5, 29], [1, 5, 31], [1, -4, 37], [1, 4, 41], [1, 2, 43], [1, 8, 47], [1, 3, 53], [1, -3, 59], [1, -7, 61], [1, 2, 67], [1, -14, 71], [1, 2, 73], [1, 2, 79], [1, 0, 83], [1, 1, 89], [1, -7, 97]], 'index': 38, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/33810/s'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-33810-1.1-c1-0-38', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-33810-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 16.430891918394117, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 731351590513809259, 'z1': {'__RealLiteral__': 0, 'data': '0.9437129898980661', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '731351590513809259', 'Lhash_array': ['731351590513809259'], 'label': '2-33810-1.1-c1-0-38', 'type': 'ECQ', 'url': 'EllipticCurve/Q/33810/s'}