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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -1, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': 2, 'A8': 0, 'A9': 1, 'Lhash': '467637974837205418', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.7559289460184544, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 728.2356664340774, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [5, [1]], [19, [1, -1]]], 'bad_primes': [2, 3, 5, 19], 'central_character': '91200.1', 'coefficient_field': '1.1.1.1', 'conductor': 91200, 'conductor_radical': 570, 'degree': 2, 'euler_factors': [[1], [1, 1], [1], [1, -2, 7], [1, 4, 11], [1, -6, 13], [1, 4, 17], [1, -1], [1, 0, 23], [1, -10, 29], [1, -2, 31], [1, 2, 37], [1, -8, 41], [1, -8, 43], [1, 0, 47], [1, 6, 53], [1, 2, 59], [1, 2, 61], [1, 4, 67], [1, 0, 71], [1, -10, 73], [1, -2, 79], [1, -10, 83], [1, 12, 89], [1, -2, 97]], 'gamma_factors': [[], [0]], 'index': 191, 'label': '2-91200-1.1-c1-0-191', 'leading_term': '6.34319612939', '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/91200/dk', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.430544333173974, 1.996266420335814, 1.28263490991303, -0.1068872757503987, -0.68884771659643, 0.5341468451209637, 2.656691104207415, 3.390258953031939, 1.636529386188269, -0.7239121661221966, -0.6171586064769587, 2.331228481876562, 4.774136205370293, 3.573696295635253, -0.009197751512649718, -1.792980676144955, -0.2580810849972354, 1.599222776751893, 0.9811146133410177, -0.52398756531648, 0.150645106996836, 2.233734840792078, 2.317727309156994, 0.2958707928726506, -0.2507023254484706, 1.559936192643803, 1.825287284019776, -1.440348038777106, -4.104523906726364, -2.34062390482706, 0.8554980180934129, 0.8110940270553982, -0.7273080900216413, 0.7330986501224214, 3.428939399294735, 2.071968006763516, -1.846125143198035, -1.502829303012431, 3.436553222148108, 5.81000350545619, 2.922061422426954, 0.02274597818267821, 0.06104594814254679, -0.2474922214445145, -1.913278119706065, -1.355645198535091, 0.9921454685382433, 0.1235191385643252, -3.382841152541825, -3.486274128672167, -0.3580496705019446, -0.202132404916957, -2.852874907734308, -2.378197625526052, 0.2925005796186466, -0.6868188972647722, -2.897089156527523, 0.550343221621311, 6.401109478166282, 6.007739190092492, 1.119280624504296, -0.4239727499649424, 0.7169395348624382, -0.08027395239261316, -0.07461559378647314, 3.562969431760194, 5.024071312248396, 0.7768048630266047, -2.630272278909305, -1.175315394756524, 0.1810979958300811, -0.5140549453096424, 0.3545729436982124, 0.9288671216595268, -2.662750263365069, -5.100454108016277, -1.47639708273207, 0.6256960492481363, -4.480041386808477, -7.955533291486944, -3.454531739036373, 1.074316424919107, 0.4167363942515241, 0.2983085457555082, 1.935966281448006, 0.423667862814822, -1.138338769483725, 2.532434856506091, 5.540983515925829, 2.275534145992206, -0.9368409478757367, 0.054442414132713, -0.186589770452897, -2.256371351216792, -1.146075926879133, 0.5588672240084251, -0.6992194081223715, 0.6599110533336348, 5.665332968477094, 5.410015405678155, 0.4493403063264494, 0.8605299503027346, 4.346227371804312, 1.901671763810052, -1.783870885118898, 0.1405006176462637, 1.164782089007721, -2.191673464547808, -2.078156074556092, 1.693413662692232, 1.32377988256769, -0.9037036188429876, 0.4693283032043048, 1.098381359684413, -0.805384802451741, 0.06901335226805871, 1.184437828065726, -2.295935369249383, -3.367883629459431, 1.901852021733852], 'positive_zeros': ['0.9792364189863016', '1.426652768040919', '2.408111980604780', '2.818637144466461', '3.749312266437701', '4.276777248528444', '4.891119854239197', '5.229532151057199', '6.043013066348774', '6.299550366090333', '6.908641602235698', '7.666186078191138', '8.108900712898232', '8.432858535949461', '9.124630923265917', '9.586952511658339', '10.50471369152610', '10.72386722902527', '10.94760769485248', '11.63336697893056', '12.00983595715022', '12.79109971386621', '12.97430877981146', '13.70935884529227', '13.93337541121858', '14.47741735465478', '15.33619843394814', '15.58996018129584', '15.98586860072087', '16.25850630782901', '17.03750789655296', '17.65292408582854', '17.83605501499942', '18.19625760706772', '18.59387915740905', '19.33664800642461', '19.55521016838743'], 'prelabel': '2-91200-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 26.98584196266771, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 467637974837205418, 'z1': {'__RealLiteral__': 0, 'data': '0.9792364189863016', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.426652768040919', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.408111980604780', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 728.2356664340774, 'bad_primes': [2, 3, 5, 19], 'central_character': '1.1', 'conductor': 91200, 'conductor_radical': 570, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, 0, 0, 2, 0, 1, 0, -4, 0, 6, 0, 0, 0, -4, 0, 1, 0, -2, 0, 0, 0, 0, 0, -1, 0, 10, 0, 2, 0, 4, 0, 0, 0, -2, 0, -6, 0, 8, 0, 8, 0, 0, 0, 0, 0, -3, 0, 4, 0, -6, 0, 0, 0, -1, 0, -2, 0, -2, 0, 2, 0, 0, 0, -4, 0, 0, 0, 0, 0, 10, 0, 0, 0, -8, 0, 2, 0, 1, 0, 10, 0, 0, 0, -10, 0, -12, 0, 12, 0, -2, 0, 0, 0, 2, 0, -4, 0], 'euler11': [1, 4, 11], 'euler13': [1, -6, 13], 'euler17': [1, 4, 17], 'euler19': [1, -1, 0], 'euler2': [1, 0, 0], 'euler23': [1, 0, 23], 'euler29': [1, -10, 29], 'euler3': [1, 1, 0], 'euler31': [1, -2, 31], 'euler37': [1, 2, 37], 'euler41': [1, -8, 41], 'euler43': [1, -8, 43], 'euler47': [1, 0, 47], 'euler5': [1, 0, 0], 'euler53': [1, 6, 53], 'euler59': [1, 2, 59], 'euler61': [1, 2, 61], 'euler67': [1, 4, 67], 'euler7': [1, -2, 7], 'euler71': [1, 0, 71], 'euler73': [1, -10, 73], 'euler79': [1, -2, 79], 'euler83': [1, -10, 83], 'euler89': [1, 12, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, 0, 0], [1, -2, 7], [1, 4, 11], [1, -6, 13], [1, 4, 17], [1, -1, 0], [1, 0, 23], [1, -10, 29], [1, -2, 31], [1, 2, 37], [1, -8, 41], [1, -8, 43], [1, 0, 47], [1, 6, 53], [1, 2, 59], [1, 2, 61], [1, 4, 67], [1, 0, 71], [1, -10, 73], [1, -2, 79], [1, -10, 83], [1, 12, 89], [1, -2, 97]], 'index': 191, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/91200/dk'], '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': '2-91200-1.1-c1-0-191', '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': '2-91200-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 26.98584196266771, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 467637974837205418, 'z1': {'__RealLiteral__': 0, 'data': '0.9792364189863016', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '467637974837205418', 'Lhash_array': ['467637974837205418'], 'label': '2-91200-1.1-c1-0-191', 'type': 'ECQ', 'url': 'EllipticCurve/Q/91200/dk'}