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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': -1, 'A3': 0, 'A4': 1, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': -1, 'A9': 0, 'Lhash': '846905852748791748', 'a10': [0.0, 0], 'a2': [-0.7071067811865475, 0], 'a3': [0.0, 0], 'a4': [0.5, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [-0.35355339059327373, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 2288.9117739400035, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1]], [5, [1]], [7, [1]], [13, [1, -1]]], 'bad_primes': [2, 3, 5, 7, 13], 'central_character': '286650.1', 'coefficient_field': '1.1.1.1', 'conductor': 286650, 'conductor_radical': 2730, 'degree': 2, 'euler_factors': [[1, 1], [1], [1], [1], [1, -1, 11], [1, -1], [1, 3, 17], [1, -7, 19], [1, -4, 23], [1, 2, 29], [1, 3, 31], [1, -2, 37], [1, -6, 41], [1, -6, 43], [1, -4, 47], [1, 2, 53], [1, -4, 59], [1, 1, 61], [1, 11, 67], [1, -1, 71], [1, 14, 73], [1, -10, 79], [1, -7, 83], [1, 18, 89], [1, -12, 97]], 'gamma_factors': [[], [0]], 'index': 113, 'label': '2-286650-1.1-c1-0-113', 'leading_term': '2.05617878416', '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/286650/fh', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [2.056178784160716, 1.382613338228479, -0.07754852247827984, -0.967177053989977, -0.3634468037749122, 0.8535504443931824, 0.6703090681114732, -1.287994326256298, -2.599638443189322, -1.159417580916281, 1.245658130882008, 0.9861341841839734, -1.640845398884054, -2.166824944603432, 0.8802271999771868, 2.619226306719624, -0.6470435612338514, -4.421068524235851, -2.511161297504891, 2.370143051471213, 2.444286213149802, -2.168021087928706, -3.793582566927564, -0.6507238889993451, 0.6681154494198438, -2.120811650394547, -3.103097326762407, 0.06988439742538174, 1.988737424568843, 0.4408529247890536, -0.05696860477056791, 1.387047589931249, 0.1972202965736163, -3.17425468021094, -3.278181683542773, -0.5611957249789787, 0.1465693825573741, -0.1782703653466888, 1.635274498521391, 2.48839557966327, -0.06961510665699687, -1.080171341748235, 1.53732800637618, 2.040174346874858, -0.6133157684891156, -0.7760717078540482, 0.4959696454902454, -1.742255998842678, -2.986497688937305, 1.569035859836964, 4.190403576009729, 0.104510272193544, -1.193103540258214, 3.493919776934981, 3.335807960278454, -2.468329597891833, -2.415231848749286, 1.839478587773321, -0.3258697154889834, -4.416762862435003, -1.557803086678299, 1.677611166731506, -0.8650707599889828, -2.036478065280753, 0.3774091759348692, -0.2218178826157139, -1.886036661411981, 0.426354721324779, 1.559495027958151, -1.144483702378527, -1.281985842319511, 0.907246168135214, 0.2003186353052253, -0.1696789526350799, 1.929840496879253, 0.9519257680559821, -1.615185913063226, 0.1193002337426184, 1.729264366541061, -0.1982305529047966, 0.4984027568811225, 2.781329182941418, 0.5336724630392363, -1.068800696154093, 0.6023777755023239, -2.997875481280332, -8.372130725845834, -4.346625046510119, 1.267961235064128, -0.8040401165926832, -0.950390591425838, 2.167896977117513, -3.083039755809318, -9.634587493493584, -4.964843942905312, 0.4332383907087275, -1.504598012083478, -0.5144808322309428, 3.452295076175025, 1.808062548404057, -0.2790767480842843, 0.5967164156662097, -2.271403200385325, -5.157241644096248, -1.834172630067108, 0.6062889411247694, -0.2948631107031424, 1.072826908133042, 1.37016308106217, -1.20289473053529, -0.2348330071679646, 1.3561016012167, -1.146920656686355, -1.164703423167074, 1.236353726011895, -0.4266666169060077, -1.331445572173877, 0.3112545735817978, -1.888564416217716, -2.140603165202779, 3.458939714112642], 'positive_zeros': ['0.4865137407088737', '1.069874046951209', '1.601560454187838', '2.358188240315104', '2.850352552324271', '3.438688686295564', '3.966154962758666', '4.620716725611845', '5.138574659140320', '5.801735504638409', '6.082566171714595', '6.745188100360315', '7.319809979607634', '7.512716343128617', '8.015426090812834', '8.829812954445586', '9.054822124852549', '9.297020135192769', '9.994007135280862', '10.36999130961227', '10.93920016967189', '11.35871151830996', '11.60221892066144', '12.18068799602130', '12.75561510631051', '13.07689031596663', '13.64063243152891', '14.12500778422408', '14.48433580029643', '15.07931380388147', '15.43916051760829', '15.95436505718394', '16.22645305779952', '16.71638412061506', '17.15206158744961', '17.62916149077375', '18.03138657989723', '18.27600070083254', '18.82355602215216', '19.24040986397989', '19.72291576083929', '19.95084088589648'], 'prelabel': '2-286650-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 47.84257281898627, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 846905852748791748, 'z1': {'__RealLiteral__': 0, 'data': '0.4865137407088737', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.069874046951209', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.601560454187838', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2288.9117739400035, 'bad_primes': [2, 3, 5, 7, 13], 'central_character': '1.1', 'conductor': 286650, 'conductor_radical': 2730, 'degree': 2, 'dirichlet_coefficients': [1, -1, 0, 1, 0, 0, 0, -1, 0, 0, 1, 0, 1, 0, 0, 1, -3, 0, 7, 0, 0, -1, 4, 0, 0, -1, 0, 0, -2, 0, -3, -1, 0, 3, 0, 0, 2, -7, 0, 0, 6, 0, 6, 1, 0, -4, 4, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 2, 4, 0, -1, 3, 0, 1, 0, 0, -11, -3, 0, 0, 1, 0, -14, -2, 0, 7, 0, 0, 10, 0, 0, -6, 7, 0, 0, -6, 0, -1, -18, 0, 0, 4, 0, -4, 0, 0, 12, 0, 0, 0], 'euler11': [1, -1, 11], 'euler13': [1, -1, 0], 'euler17': [1, 3, 17], 'euler19': [1, -7, 19], 'euler2': [1, 1, 0], 'euler23': [1, -4, 23], 'euler29': [1, 2, 29], 'euler3': [1, 0, 0], 'euler31': [1, 3, 31], 'euler37': [1, -2, 37], 'euler41': [1, -6, 41], 'euler43': [1, -6, 43], 'euler47': [1, -4, 47], 'euler5': [1, 0, 0], 'euler53': [1, 2, 53], 'euler59': [1, -4, 59], 'euler61': [1, 1, 61], 'euler67': [1, 11, 67], 'euler7': [1, 0, 0], 'euler71': [1, -1, 71], 'euler73': [1, 14, 73], 'euler79': [1, -10, 79], 'euler83': [1, -7, 83], 'euler89': [1, 18, 89], 'euler97': [1, -12, 97], 'euler_factors': [[1, 1, 0], [1, 0, 0], [1, 0, 0], [1, 0, 0], [1, -1, 11], [1, -1, 0], [1, 3, 17], [1, -7, 19], [1, -4, 23], [1, 2, 29], [1, 3, 31], [1, -2, 37], [1, -6, 41], [1, -6, 43], [1, -4, 47], [1, 2, 53], [1, -4, 59], [1, 1, 61], [1, 11, 67], [1, -1, 71], [1, 14, 73], [1, -10, 79], [1, -7, 83], [1, 18, 89], [1, -12, 97]], 'index': 113, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/286650/fh'], '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': '2-286650-1.1-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': '2-286650-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 47.84257281898627, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 846905852748791748, 'z1': {'__RealLiteral__': 0, 'data': '0.4865137407088737', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '846905852748791748', 'Lhash_array': ['846905852748791748'], 'factors': ['2-286650-1.1-c1-0-113'], 'label': '2-286650-1.1-c1-0-113', 'type': 'ECQ', 'url': 'EllipticCurve/Q/286650/fh'}