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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': -1, 'A8': 0, 'A9': 0, 'Lhash': '162698273663799982', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [-0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 373.6998814595924, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1]], [13, [1, 1]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '46800.1', 'coefficient_field': '1.1.1.1', 'conductor': 46800, 'conductor_radical': 390, 'degree': 2, 'euler_factors': [[1], [1], [1], [1, 1, 7], [1, -3, 11], [1, 1], [1, -3, 17], [1, -4, 19], [1, -6, 23], [1, -3, 29], [1, -1, 31], [1, 2, 37], [1, 0, 41], [1, 10, 43], [1, -3, 47], [1, -3, 53], [1, 15, 59], [1, 13, 61], [1, 13, 67], [1, 0, 71], [1, -10, 73], [1, -4, 79], [1, 15, 83], [1, 6, 89], [1, -4, 97]], 'gamma_factors': [[], [0]], 'index': 125, 'label': '2-46800-1.1-c1-0-125', 'leading_term': '6.5117955333', '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/46800/cg', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.510012250171013, 2.329239949199071, 1.976727091384468, 0.6581737006818243, -0.5216542367620322, -0.2632099146989921, 1.625688825869551, 3.662712692997606, 3.86162332102701, 1.811336538942642, -0.6298960224489369, -1.233039228481562, -0.02910448292807081, 0.6053736454660071, -1.052460710901671, -3.591155262276924, -4.039669239253052, -1.864632666762779, 0.01164984551866008, -0.9563638093618214, -3.284506491120712, -3.399417069123453, -0.8023545535314506, 1.059272381982855, -0.160194197102978, -2.164833112667929, -1.594885543006968, 0.6350940130970238, 0.8127246766081723, -1.328411005683071, -1.786030925065411, 1.231651094448719, 3.923347848728529, 2.639768011679199, -0.2832230180241928, -0.3603932438068507, 1.770977846148297, 1.921494350645782, -0.02853801959847628, 0.0349438071422337, 2.676193362921412, 3.25273601984203, 0.02453275711042619, -2.247252041521941, -0.2237884724282497, 2.294648821707163, 1.184396413909571, -0.9010116262732784, -0.03606619485504141, 1.313649932193708, -0.8920863581680422, -3.967035648004395, -2.892265066521825, 0.3583466820159751, 0.3470637386695307, -1.804991589132381, -0.9965428228687058, 1.650325536995573, 0.9189154148420686, -2.070521236615689, -1.838534394391862, 0.5780995717223707, -0.5404520277876229, -4.200886138208581, -4.230829822958433, -0.9237093204746429, 0.198257913583189, -0.3897010160704802, 1.969243153476445, 5.184567367226682, 3.627033192529684, -0.2498408470480116, 0.004494749325781596, 2.428792160289478, 0.933713392851684, -2.371915114359364, -1.84127937817788, 0.2180937730109981, -0.8172846763913117, -1.672657879250633, 1.364822202933045, 3.307277395347376, 0.1803605689900491, -2.294627643879095, -0.05078485211679976, 1.229600723675812, -1.681031243974114, -2.862367901961417, -0.01000347117160366, 0.9634121229630874, -1.042821131495769, -0.545695112826191, 1.408382741268784, -0.9257559347855627, -4.389091191844362, -2.15532542997603, 2.055478077231911, 1.368894343248489, -0.7931176411283108, 0.4528678167301262, 0.8589775850323472, -2.05223221328013, -2.241062636032899, 1.260523500956825, 1.150957764579114, -2.53019023334463, -2.343233524389708, 0.65764049382396, 0.2457947233996482, -0.6487363134053739, 2.56774821583276, 4.313869586301351, 0.6625753386656104, -1.492521237823855, 0.7846477797471602, 0.7919611238406402, -1.944153356702072, -0.8278036296066464, 2.11908736126464, 0.8133898165018395], 'positive_zeros': ['1.116896409377772', '1.548460694754005', '2.673481456207800', '3.255267646642553', '3.632469355240183', '4.745302859980027', '4.843731081848754', '5.823236823233250', '6.232377133413806', '6.922114649053482', '7.355962629850493', '7.917254318026098', '8.717585269156694', '9.047505431322494', '9.745593318097353', '9.995225406736726', '10.75161669284646', '11.26680885924296', '11.86593884504940', '12.25444187689223', '12.68530576000081', '13.46374565347974', '13.79030466393304', '14.33611570936798', '14.82416287075866', '15.42422141882850', '15.70589095704959', '16.60486456769409', '16.81426225657071', '17.08695534087836', '17.97656402049927', '18.24955206334833', '18.81241010017271', '19.45062807258740', '19.63885649729556'], 'prelabel': '2-46800-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 19.331318668409363, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 162698273663799982, 'z1': {'__RealLiteral__': 0, 'data': '1.116896409377772', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '1.548460694754005', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.673481456207800', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 373.6998814595924, 'bad_primes': [2, 3, 5, 13], 'central_character': '1.1', 'conductor': 46800, 'conductor_radical': 390, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 3, 0, -1, 0, 0, 0, 3, 0, 4, 0, 0, 0, 6, 0, 0, 0, 0, 0, 3, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -10, 0, 0, 0, 3, 0, -6, 0, 0, 0, 3, 0, 0, 0, 0, 0, -15, 0, -13, 0, 0, 0, 0, 0, -13, 0, 0, 0, 0, 0, 10, 0, 0, 0, -3, 0, 4, 0, 0, 0, -15, 0, 0, 0, 0, 0, -6, 0, 1, 0, 0, 0, 0, 0, 4, 0, 0, 0], 'euler11': [1, -3, 11], 'euler13': [1, 1, 0], 'euler17': [1, -3, 17], 'euler19': [1, -4, 19], 'euler2': [1, 0, 0], 'euler23': [1, -6, 23], 'euler29': [1, -3, 29], 'euler3': [1, 0, 0], 'euler31': [1, -1, 31], 'euler37': [1, 2, 37], 'euler41': [1, 0, 41], 'euler43': [1, 10, 43], 'euler47': [1, -3, 47], 'euler5': [1, 0, 0], 'euler53': [1, -3, 53], 'euler59': [1, 15, 59], 'euler61': [1, 13, 61], 'euler67': [1, 13, 67], 'euler7': [1, 1, 7], 'euler71': [1, 0, 71], 'euler73': [1, -10, 73], 'euler79': [1, -4, 79], 'euler83': [1, 15, 83], 'euler89': [1, 6, 89], 'euler97': [1, -4, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 0, 0], [1, 1, 7], [1, -3, 11], [1, 1, 0], [1, -3, 17], [1, -4, 19], [1, -6, 23], [1, -3, 29], [1, -1, 31], [1, 2, 37], [1, 0, 41], [1, 10, 43], [1, -3, 47], [1, -3, 53], [1, 15, 59], [1, 13, 61], [1, 13, 67], [1, 0, 71], [1, -10, 73], [1, -4, 79], [1, 15, 83], [1, 6, 89], [1, -4, 97]], 'index': 125, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/46800/cg'], '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': '2-46800-1.1-c1-0-125', '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': '2-46800-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 19.331318668409363, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 162698273663799982, 'z1': {'__RealLiteral__': 0, 'data': '1.116896409377772', 'prec': 57}}
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lfunc_instances • Show schema
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{'Lhash': '162698273663799982', 'Lhash_array': ['162698273663799982'], 'label': '2-46800-1.1-c1-0-125', 'type': 'ECQ', 'url': 'EllipticCurve/Q/46800/cg'}