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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': -1, 'A3': 1, 'A4': 1, 'A5': 0, 'A6': -1, 'A7': 4, 'A8': -1, 'A9': 1, 'Lhash': '2141463374892290401', 'a10': [0.0, 0], 'a2': [-0.7071067811865475, 0], 'a3': [0.5773502691896258, 0], 'a4': [0.5, 0], 'a5': [0.0, 0], 'a6': [-0.4082482904638631, 0], 'a7': [1.5118578920369088, 0], 'a8': [-0.35355339059327373, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 202.42076912394586, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1, -1]], [5, [1]], [13, [1]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '25350.1', 'coefficient_field': '1.1.1.1', 'conductor': 25350, 'conductor_radical': 390, 'degree': 2, 'euler_factors': [[1, 1], [1, -1], [1], [1, -4, 7], [1, 4, 11], [1], [1, 4, 17], [1, 7, 19], [1, -4, 23], [1, -5, 29], [1, 4, 31], [1, 9, 37], [1, -5, 41], [1, 10, 43], [1, 3, 47], [1, -9, 53], [1, -6, 59], [1, -4, 61], [1, -7, 67], [1, -15, 71], [1, 12, 73], [1, -7, 79], [1, 6, 83], [1, 14, 89], [1, -16, 97]], 'gamma_factors': [[], [0]], 'index': 11, 'label': '2-25350-1.1-c1-0-11', 'leading_term': '1.80191540876', '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/25350/bs', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [1.801915408758244, 1.400414870249558, 0.3015089365007196, -1.090138268632288, -2.065194566816303, -2.004350844816502, -0.9662040258121105, 0.1641985024004684, 0.3690926308144632, -0.4189312057125969, -0.9889640214800953, 0.02977306674769886, 2.455546387587785, 4.183145945600312, 3.082957773368766, -0.4829872237949318, -3.483649190823986, -3.193835220844598, -0.3247921864265184, 1.560024055084405, 0.2168473777074401, -2.312750111502607, -1.934376655257353, 2.32793993088883, 6.650747479932639, 6.741158082717294, 2.976564832240677, -0.2298827572536773, -0.005529118821222127, 1.83887737846946, 2.00103742541959, 0.2998504655805971, -0.7927279098988133, -0.3296930535467317, 0.01095001430980152, -0.6342119575723029, -0.441473335279499, 1.874046469126943, 4.053993483965616, 3.153614215716407, 0.2427062170935271, -0.9070115637800359, 0.4333354919464087, 1.120999926069529, -0.1500120427299607, -0.3275584956332836, 2.387071458932703, 4.155412000202318, 0.952975074315963, -4.149268837457856, -4.640193536701813, -0.5625822270902595, 1.353626320081657, -1.61869122942153, -3.921317459808257, -1.025429848800162, 3.101221758468199, 2.727525059077871, -0.414639997211582, -0.9043661923055022, 0.9893135175168556, 0.92707588151395, -0.719286386601615, 0.3727258156618759, 3.579791552815174, 3.352766903170079, -1.009877842668194, -3.52704112548625, -1.4102490078182, 0.8419753644627902, -0.07131072931233826, -1.13744082770537, 0.138441452223193, 1.01794736604907, -0.2652227767286131, -0.4988438624029088, 1.914308259406002, 3.134562493071716, 1.161483215940362, 0.005749512285183557, 1.988639984322255, 3.15294507602956, 1.07375945642833, -0.5165360383191411, 0.4412064666212596, 0.577080372605628, -0.2054997476814843, 3.362546257384737, 9.791200643945704, 8.566081906125, -2.651912222806038, -10.97688005775327, -7.261637163914158, 0.2693926546779886, 1.042289536351773, -1.755303180179348, -0.8764509828914377, 1.203028873912785, -0.3315965072869616, -2.180925422943072, -0.5224144487297258, 0.8045585932764695, -1.353517091579884, -2.813458877871367, -0.8930165036148237, 0.3642314545917421, -0.8963675351699315, -0.9199059937367906, 0.8389961073243951, 0.5991032457982299, -0.9389624529772783, -0.1053513294916915, 0.8699106457811482, -1.677000483791513, -3.629301622836669, -0.5205626478971475, 2.50447692230753, 0.3686549255917972, -1.521474818702005, 1.560874170709415, 3.678417368593886], 'positive_zeros': ['0.5548480554930588', '1.703363722993133', '2.138737124194310', '2.746138847282986', '3.719227032964508', '4.527486613890115', '5.020340718520190', '5.632536752233184', '6.718398983434509', '7.000835618991253', '7.793215207825983', '8.391575339476529', '8.509513174277362', '9.066961987714363', '10.02455296995505', '10.43522093993666', '10.97420076428458', '11.29640308044221', '12.04368050986940', '12.78546281546932', '13.14437252445432', '13.80304474930754', '14.46142420013576', '14.87102947656113', '15.37739097491459', '15.71586524204238', '16.44661374998889', '17.11897805924184', '17.49000530056875', '17.98054654513083', '18.45738766386580', '18.81947722194549', '19.67107749254653', '19.74769734917899'], 'prelabel': '2-25350-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 14.227465309180896, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 2141463374892290401, 'z1': {'__RealLiteral__': 0, 'data': '0.5548480554930588', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.703363722993133', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.138737124194310', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 202.42076912394586, 'bad_primes': [2, 3, 5, 13], 'central_character': '1.1', 'conductor': 25350, 'conductor_radical': 390, 'degree': 2, 'dirichlet_coefficients': [1, -1, 1, 1, 0, -1, 4, -1, 1, 0, -4, 1, 0, -4, 0, 1, -4, -1, -7, 0, 4, 4, 4, -1, 0, 0, 1, 4, 5, 0, -4, -1, -4, 4, 0, 1, -9, 7, 0, 0, 5, -4, -10, -4, 0, -4, -3, 1, 9, 0, -4, 0, 9, -1, 0, -4, -7, -5, 6, 0, 4, 4, 4, 1, 0, 4, 7, -4, 4, 0, 15, -1, -12, 9, 0, -7, -16, 0, 7, 0, 1, -5, -6, 4, 0, 10, 5, 4, -14, 0, 0, 4, -4, 3, 0, -1, 16, -9, -4, 0], 'euler11': [1, 4, 11], 'euler13': [1, 0, 0], 'euler17': [1, 4, 17], 'euler19': [1, 7, 19], 'euler2': [1, 1, 0], 'euler23': [1, -4, 23], 'euler29': [1, -5, 29], 'euler3': [1, -1, 0], 'euler31': [1, 4, 31], 'euler37': [1, 9, 37], 'euler41': [1, -5, 41], 'euler43': [1, 10, 43], 'euler47': [1, 3, 47], 'euler5': [1, 0, 0], 'euler53': [1, -9, 53], 'euler59': [1, -6, 59], 'euler61': [1, -4, 61], 'euler67': [1, -7, 67], 'euler7': [1, -4, 7], 'euler71': [1, -15, 71], 'euler73': [1, 12, 73], 'euler79': [1, -7, 79], 'euler83': [1, 6, 83], 'euler89': [1, 14, 89], 'euler97': [1, -16, 97], 'euler_factors': [[1, 1, 0], [1, -1, 0], [1, 0, 0], [1, -4, 7], [1, 4, 11], [1, 0, 0], [1, 4, 17], [1, 7, 19], [1, -4, 23], [1, -5, 29], [1, 4, 31], [1, 9, 37], [1, -5, 41], [1, 10, 43], [1, 3, 47], [1, -9, 53], [1, -6, 59], [1, -4, 61], [1, -7, 67], [1, -15, 71], [1, 12, 73], [1, -7, 79], [1, 6, 83], [1, 14, 89], [1, -16, 97]], 'index': 11, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/25350/bs'], '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': '2-25350-1.1-c1-0-11', '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': '2-25350-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 14.227465309180896, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2141463374892290401, 'z1': {'__RealLiteral__': 0, 'data': '0.5548480554930588', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '2141463374892290401', 'Lhash_array': ['2141463374892290401'], 'factors': ['2-25350-1.1-c1-0-11'], 'label': '2-25350-1.1-c1-0-11', 'type': 'ECQ', 'url': 'EllipticCurve/Q/25350/bs'}