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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': -3, 'A8': 1, 'A9': 1, 'Lhash': '711796263301849985', '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': [-1.1338934190276817, 0], 'a8': [0.35355339059327373, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 769.1989226709943, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1, 1]], [5, [1, 1]], [13, [1]], [19, [1, 1]]], 'bad_primes': [2, 3, 5, 13, 19], 'central_character': '96330.1', 'coefficient_field': '1.1.1.1', 'conductor': 96330, 'conductor_radical': 7410, 'degree': 2, 'euler_factors': [[1, -1], [1, 1], [1, 1], [1, 3, 7], [1, -6, 11], [1], [1, -4, 17], [1, 1], [1, 1, 23], [1, 0, 29], [1, -3, 31], [1, 6, 37], [1, 8, 41], [1, -12, 43], [1, -5, 47], [1, 1, 53], [1, -13, 59], [1, -7, 61], [1, -8, 67], [1, -9, 71], [1, 8, 73], [1, 1, 79], [1, -3, 83], [1, -4, 89], [1, 15, 97]], 'gamma_factors': [[], [0]], 'index': 20, 'label': '2-96330-1.1-c1-0-20', 'leading_term': '3.18289129218', '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/96330/by', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [3.182891292184283, 2.443660586872907, 0.6360656682606312, -1.02045277121456, -1.062586385931639, 0.8361401140622922, 2.99966400293884, 2.960235666760119, 0.1158503031130927, -3.113622566587843, -3.586680041665103, -1.009702050978449, 1.656576395589931, 1.838761933455629, 0.4124306706716373, -0.04475962920686881, 0.7242661647317133, 0.4742437640402704, -1.503598749124355, -2.66742812351198, -1.083540052802696, 1.155099951740697, 0.9393118056565538, -0.9516681462696512, -1.311483746910396, -0.01172769543906727, 0.1209869664069659, -1.082725009803688, -0.7034022945745271, 0.8680591358948128, -0.9951191494303376, -6.632231854928524, -8.911908752448712, -3.804094477164862, 1.762755987967472, -0.1240940682710431, -5.647947420231636, -5.651572486341059, -0.7349954224112984, 0.9020615705844834, -1.663371449525296, -1.423650537071802, 2.790888152262211, 4.2168120768077, 0.9232685805103277, -1.136182385226888, 0.4885960065590793, 1.479670693716018, 0.2667983598132729, 0.03102492128424301, 0.6460626693610197, -0.8020501611380336, -2.22647703058086, 0.1141321536276644, 2.9452510842905, 1.421146375468808, -1.157210487238587, 0.001965394017082592, 1.325293720552281, -1.280893707156789, -3.2477395471933, -0.7141569423910633, 1.254903218803787, -0.7069665341534214, -1.653883595444778, 0.33262019290197, 0.3857500713966562, -1.260035992348389, 0.3022385604576841, 2.047299912895969, -1.146906826837889, -2.362759222069501, 5.716005707477647, 13.54281387295692, 9.82895703001204, 1.618717395221601, -0.308888782498171, 0.2303232791222541, -1.875927903145796, -1.282195892204465, 3.001489950075951, 2.949168848638917, -0.7892701435929365, 0.4977213463723447, 4.540547755812056, 2.679325256678853, -2.002168342815698, -1.962268121855285, 0.08227366420031856, -0.2724780276371943, -0.3883178850332212, 0.4644585712681278, -0.3538279815913645, -0.5922303374415704, 1.430868562804188, 1.078030411926735, -1.546200076153487, -0.316086524318375, 2.389522662885135, 0.3284006674732474, -1.602451233786429, 1.386296185872485, 2.033526118511967, -1.228704626585126, 1.188289796051862, 6.416805943912179, 1.960826717491423, -6.459093265444306, -5.026405737643136, 0.3442639798466316, -0.8167046582528615, -1.915499583158302, 1.688302198892175, 1.580076188047037, -2.150344857198994, -0.7957557425009544, 2.203136248195594, 0.1330301766212501, -1.48292744782223, 0.5871943374089157, 0.5948912252874105], 'positive_zeros': ['0.5818334745039002', '1.160627729499868', '2.007963720758391', '2.829309495140900', '3.606455886613850', '3.773083214906407', '4.324084096425796', '5.104777420100257', '5.623777041618059', '6.252577088050380', '6.529715599734428', '7.098096412443080', '7.435048755794214', '8.392111822473319', '8.744154866995794', '9.545410559565274', '9.852585130594953', '10.34417965761810', '11.06610677264028', '11.44458264470363', '12.06647888538770', '12.23879652273719', '12.65560752888130', '13.24230666325878', '13.85953806995720', '14.24979637807274', '14.65800967269102', '15.30320964138944', '15.68250987710595', '16.20836443773053', '16.55198893546412', '16.97419479204751', '17.43403394420152', '17.85306544767245', '18.84892040803075', '19.07036035504009', '19.29439565086732', '19.82850903064831'], 'prelabel': '2-96330-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 27.734435683298017, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 711796263301849985, 'z1': {'__RealLiteral__': 0, 'data': '0.5818334745039002', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.160627729499868', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.007963720758391', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 769.1989226709943, 'bad_primes': [2, 3, 5, 13, 19], 'central_character': '1.1', 'conductor': 96330, 'conductor_radical': 7410, 'degree': 2, 'dirichlet_coefficients': [1, 1, -1, 1, -1, -1, -3, 1, 1, -1, 6, -1, 0, -3, 1, 1, 4, 1, -1, -1, 3, 6, -1, -1, 1, 0, -1, -3, 0, 1, 3, 1, -6, 4, 3, 1, -6, -1, 0, -1, -8, 3, 12, 6, -1, -1, 5, -1, 2, 1, -4, 0, -1, -1, -6, -3, 1, 0, 13, 1, 7, 3, -3, 1, 0, -6, 8, 4, 1, 3, 9, 1, -8, -6, -1, -1, -18, 0, -1, -1, 1, -8, 3, 3, -4, 12, 0, 6, 4, -1, 0, -1, -3, 5, 1, -1, -15, 2, 6, 1], 'euler11': [1, -6, 11], 'euler13': [1, 0, 0], 'euler17': [1, -4, 17], 'euler19': [1, 1, 0], 'euler2': [1, -1, 0], 'euler23': [1, 1, 23], 'euler29': [1, 0, 29], 'euler3': [1, 1, 0], 'euler31': [1, -3, 31], 'euler37': [1, 6, 37], 'euler41': [1, 8, 41], 'euler43': [1, -12, 43], 'euler47': [1, -5, 47], 'euler5': [1, 1, 0], 'euler53': [1, 1, 53], 'euler59': [1, -13, 59], 'euler61': [1, -7, 61], 'euler67': [1, -8, 67], 'euler7': [1, 3, 7], 'euler71': [1, -9, 71], 'euler73': [1, 8, 73], 'euler79': [1, 1, 79], 'euler83': [1, -3, 83], 'euler89': [1, -4, 89], 'euler97': [1, 15, 97], 'euler_factors': [[1, -1, 0], [1, 1, 0], [1, 1, 0], [1, 3, 7], [1, -6, 11], [1, 0, 0], [1, -4, 17], [1, 1, 0], [1, 1, 23], [1, 0, 29], [1, -3, 31], [1, 6, 37], [1, 8, 41], [1, -12, 43], [1, -5, 47], [1, 1, 53], [1, -13, 59], [1, -7, 61], [1, -8, 67], [1, -9, 71], [1, 8, 73], [1, 1, 79], [1, -3, 83], [1, -4, 89], [1, 15, 97]], 'index': 20, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/96330/by'], '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': '2-96330-1.1-c1-0-20', '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': '2-96330-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 27.734435683298017, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 711796263301849985, 'z1': {'__RealLiteral__': 0, 'data': '0.5818334745039002', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '711796263301849985', 'Lhash_array': ['711796263301849985'], 'factors': ['2-96330-1.1-c1-0-20'], 'label': '2-96330-1.1-c1-0-20', 'type': 'ECQ', 'url': 'EllipticCurve/Q/96330/by'}