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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -2, 'A4': 0, 'A5': -1, 'A6': 0, 'A7': 1, 'A8': 0, 'A9': 1, 'Lhash': '2126503673800461214', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-1.1547005383792517, 0], 'a4': [0.0, 0], 'a5': [-0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 3022.8168189175917, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1, 1]], [7, [1, -1]], [13, [1]]], 'bad_primes': [2, 5, 7, 13], 'central_character': '378560.1', 'coefficient_field': '1.1.1.1', 'conductor': 378560, 'conductor_radical': 910, 'degree': 2, 'euler_factors': [[1], [1, 2, 3], [1, 1], [1, -1], [1, 2, 11], [1], [1, -6, 17], [1, 6, 19], [1, -6, 23], [1, -6, 29], [1, -6, 31], [1, -6, 37], [1, -10, 41], [1, -6, 43], [1, 0, 47], [1, 6, 53], [1, 10, 59], [1, 2, 61], [1, -8, 67], [1, -10, 71], [1, -14, 73], [1, 12, 79], [1, -12, 83], [1, -10, 89], [1, -2, 97]], 'gamma_factors': [[], [0]], 'index': 113, 'label': '2-378560-1.1-c1-0-113', 'leading_term': '2.08493304618', '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': 0, 'origin': 'EllipticCurve/Q/378560/x', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [2.084933046180748, 1.480236532171098, 0.3027725467296322, -0.04654808495108628, 0.9782892458180477, 1.698566956500667, -0.2694915120886508, -4.343316289200982, -6.422442977198438, -3.934715354005356, -0.1216106483772186, -0.09143369948554494, -3.105005612077684, -3.268016275860324, 1.14743710786653, 4.46561275412073, 2.510198823127963, -0.8965131808934216, -0.8859297444756588, 0.5962399302109698, -0.1557968776625846, -1.21538895645238, 0.2772727054912723, 1.57539547643255, -0.0176736128048888, -1.161584753987417, 0.3154806093710057, -0.004109444268064278, -3.753666540484698, -4.80023426610193, -1.043109408679319, 0.9219021916872013, -0.5957775190697941, 0.8807333363057689, 4.67810448444578, 2.559387255353349, -3.236895000430499, -2.229896132588551, 3.561728145225894, 3.233609434440474, -1.785079985170015, -2.237206686203007, 0.5143043997069845, 0.5015700843757234, 0.03124171735817475, 1.252863535133024, 0.2790503892162336, -2.004103211792993, -0.9952624696771619, 0.4619786528581591, -0.6169415618361964, 0.3475119790800628, 2.200496102713285, -2.547280806538862, -8.435613157288268, -4.636338375381386, 1.71486604379087, -0.2211129082260515, -2.804410535847428, 0.8279875799573477, 1.569324731660698, -2.846152222280166, -2.676276828375947, 0.666191778854496, -0.5477360191079192, -1.817859805484053, 0.8868802961323008, 1.441740625078682, -0.3878512684039381, 0.07835357567532358, -0.5086005195524294, -2.782659980826848, -0.6319610374077623, 2.298211491378293, 0.0004111984673580282, -0.8625905734515861, 1.632465185368418, -0.640459054537875, -3.116482955941247, 1.545499969004165, 2.181233349631321, -5.8270244002371, -7.277703169128593, -0.5667476618894669, 1.074826000324692, -0.3208703871940044, 1.051989519795838, -1.226935812101227, -5.06684870281951, -1.692886832344713, 2.526952210413646, 0.9494451396777055, -0.271628892593558, 0.1813055527135683, -0.05568171303958056, 2.101350499091235, 2.874058742320593, -1.407997420306157, -1.319822820485022, 2.607046883902911, -1.477890917768114, -6.017248192738767, -1.083760170312062, 0.915203757021841, -2.496524565752693, 2.129732709505686, 7.67908586221792, 2.564664847891565, -1.872356732828726, 0.05518906373551598, -0.1754073696618774, -0.5035168898587579, 1.523208024749255, 0.332824287366686, -0.5043437934317176, 1.633680155673763, 0.3367261810829495, -0.7472621527692491, 2.252237501762131, 1.30937619433873, -0.7749188921279814], 'positive_zeros': ['0.5960766309539369', '0.7735644209932395', '1.480169834371493', '2.512861795007310', '2.739658058099180', '3.444489420234348', '4.165818849101759', '4.626215796487772', '4.976045556861618', '5.468686424033955', '5.998022622854349', '6.453541851714907', '6.749602382870974', '7.571444037868464', '7.905229995522238', '8.185030248633611', '8.851609222133533', '9.342819518043096', '9.904243941621624', '10.44108361888210', '10.87679210190896', '10.98834468675849', '11.52658803539761', '12.11591949694781', '12.38182166553240', '12.71613544396206', '13.15876787034940', '13.90397670380536', '14.23806620738000', '14.70287624279628', '15.09465567723991', '15.67827854698381', '15.95002436572021', '16.42731204901686', '16.92789730878709', '17.23010925371939', '17.43429468778230', '18.03717880734464', '18.50003193116775', '18.83301731921576', '19.21394731466705', '19.68313913638486'], 'prelabel': '2-378560-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 54.980149316981596, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 2126503673800461214, 'z1': {'__RealLiteral__': 0, 'data': '0.5960766309539369', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '0.7735644209932395', 'prec': 60}, 'z3': {'__RealLiteral__': 0, 'data': '1.480169834371493', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3022.8168189175917, 'bad_primes': [2, 5, 7, 13], 'central_character': '1.1', 'conductor': 378560, 'conductor_radical': 910, 'degree': 2, 'dirichlet_coefficients': [1, 0, -2, 0, -1, 0, 1, 0, 1, 0, -2, 0, 0, 0, 2, 0, 6, 0, -6, 0, -2, 0, 6, 0, 1, 0, 4, 0, 6, 0, 6, 0, 4, 0, -1, 0, 6, 0, 0, 0, 10, 0, 6, 0, -1, 0, 0, 0, 1, 0, -12, 0, -6, 0, 2, 0, 12, 0, -10, 0, -2, 0, 1, 0, 0, 0, 8, 0, -12, 0, 10, 0, 14, 0, -2, 0, -2, 0, -12, 0, -11, 0, 12, 0, -6, 0, -12, 0, 10, 0, 0, 0, -12, 0, 6, 0, 2, 0, -2, 0], 'euler11': [1, 2, 11], 'euler13': [1, 0, 0], 'euler17': [1, -6, 17], 'euler19': [1, 6, 19], 'euler2': [1, 0, 0], 'euler23': [1, -6, 23], 'euler29': [1, -6, 29], 'euler3': [1, 2, 3], 'euler31': [1, -6, 31], 'euler37': [1, -6, 37], 'euler41': [1, -10, 41], 'euler43': [1, -6, 43], 'euler47': [1, 0, 47], 'euler5': [1, 1, 0], 'euler53': [1, 6, 53], 'euler59': [1, 10, 59], 'euler61': [1, 2, 61], 'euler67': [1, -8, 67], 'euler7': [1, -1, 0], 'euler71': [1, -10, 71], 'euler73': [1, -14, 73], 'euler79': [1, 12, 79], 'euler83': [1, -12, 83], 'euler89': [1, -10, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, 0, 0], [1, 2, 3], [1, 1, 0], [1, -1, 0], [1, 2, 11], [1, 0, 0], [1, -6, 17], [1, 6, 19], [1, -6, 23], [1, -6, 29], [1, -6, 31], [1, -6, 37], [1, -10, 41], [1, -6, 43], [1, 0, 47], [1, 6, 53], [1, 10, 59], [1, 2, 61], [1, -8, 67], [1, -10, 71], [1, -14, 73], [1, 12, 79], [1, -12, 83], [1, -10, 89], [1, -2, 97]], 'index': 113, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/378560/x'], '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': '2-378560-1.1-c1-0-113', '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': '2-378560-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 54.980149316981596, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2126503673800461214, 'z1': {'__RealLiteral__': 0, 'data': '0.5960766309539369', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '2126503673800461214', 'Lhash_array': ['2126503673800461214'], 'label': '2-378560-1.1-c1-0-113', 'type': 'ECQ', 'url': 'EllipticCurve/Q/378560/x'}