Formats: - HTML - YAML - JSON - 2026-04-06T21:38:57.714722
Query: /api/lfunc_lfunctions/?_offset=0
Show schema

{'A10': 0, 'A2': 0, 'A3': 1, 'A4': 0, 'A5': 1, 'A6': 0, 'A7': 1, 'A8': 0, 'A9': 1, 'Lhash': '1220843165401529993', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 355.4939897987404, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [5, [1, -1]], [7, [1, -1]], [53, [1, -1]]], 'bad_primes': [2, 3, 5, 7, 53], 'central_character': '44520.1', 'coefficient_field': '1.1.1.1', 'conductor': 44520, 'conductor_radical': 11130, 'degree': 2, 'euler_factors': [[1], [1, -1], [1, -1], [1, -1], [1, -4, 11], [1, 6, 13], [1, -6, 17], [1, -8, 19], [1, -8, 23], [1, 2, 29], [1, 0, 31], [1, -2, 37], [1, 2, 41], [1, 8, 43], [1, -12, 47], [1, -1], [1, -4, 59], [1, -10, 61], [1, 12, 67], [1, 4, 71], [1, -10, 73], [1, 8, 79], [1, 4, 83], [1, 14, 89], [1, 6, 97]], 'gamma_factors': [[], [0]], 'id': 7845441, 'index': 12, 'label': '2-44520-1.1-c1-0-12', 'leading_term': '4.87138701445', '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/44520/x', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [4.871387014454131, 4.276660257663102, 2.668700725451634, 0.6960821168967859, -0.582327055946465, -0.3931152879597568, 0.9052030497000773, 1.866012066065202, 1.237095766685827, -0.6330905792474063, -1.955145496327979, -1.442144903517154, 0.02602520430498334, 0.2694128314212576, -1.4183897800386, -3.009301661317164, -2.069321992710882, 0.9055855453103346, 2.705991868997306, 1.457082778591574, -0.7686984594581736, -0.7630493028628317, 1.091988282496197, 1.071464971521665, -2.439530321956831, -6.01787513901353, -5.560346124174712, -1.972503397523593, 0.2831247831747736, -0.2671751963507067, -0.4817106036604696, 1.662595020446312, 3.362851292650226, 1.566006147257605, -1.642705743817073, -2.030736293577035, 0.140241886227449, 0.9556142176810537, -0.3729764322391775, -0.7238636527517491, 0.3938103592013706, -0.7645045979196855, -4.972918366760717, -6.879845603527618, -3.058201490824303, 1.760676880990522, 1.757383584388403, -0.9579818289497419, -0.8177247614285116, 1.275145443782802, 0.2657996892063506, -3.035592101737501, -2.913550641230162, 0.9084279128201352, 2.623519676573944, 0.4928239713793845, -0.9679737402892038, 0.06866087261981285, 0.3306270765257748, -0.7409446574047674, 0.141931338735168, 1.897275700920507, -0.5860956954193903, -5.970150636195496, -6.601225552989194, -1.418361293387578, 2.012941753014247, 0.7346413171834983, 0.1428788269194728, 1.995550710760808, 1.117221363460807, -2.888683747221653, -3.43560798250416, 0.3578127324041632, 1.576433288079981, -1.271494766788041, -1.983249909881091, 0.5987684292084279, 0.957962500970329, -1.128173904859842, -0.4734001733482243, 2.090774626184673, 1.532386343662824, -0.3308229040287008, 1.236871406060164, 3.203217896053137, 0.8769497535011384, -1.868958595631673, -0.7012748077155603, 0.01993610886759164, -2.445048685514513, -1.773363807619607, 3.942692025210438, 5.727244262939364, 0.3034752680316124, -3.008666109788059, 0.2417992322975969, 2.60465608269086, 0.5097405901662646, -0.711777873292328, 0.1487240996119765, -0.5289412202571341, -0.5300678196424354, 3.300447532375134, 5.462941663188048, 1.641264160176489, -1.959378225871577, -0.8498052672412475, 0.201234157856317, -0.1414888724987831, 2.908216016487181, 6.4863072216054, 3.453921691446388, -1.507852078954484, 0.2418876251247498, 3.830688157417802, 1.30146357318002, -2.149826504083725, -0.3268313578310732, 1.408735861448956, -0.4345513080316222], 'positive_zeros': ['0.8572199997483300', '1.338595670813115', '2.170498500831170', '2.994606317012510', '3.310734284897200', '4.177109063003918', '4.899363237408560', '5.357700189829622', '5.849360569769320', '6.933374507632336', '7.187474638510498', '7.580506345279594', '8.362808295880746', '8.983648952092934', '9.437603042524874', '9.904097338381138', '10.17609876414191', '11.13914934106461', '11.65267456577895', '12.09033320828886', '12.52124249695692', '13.19286055152792', '13.79896157031052', '14.23655888441262', '14.57707193732481', '14.98294748694677', '15.46940270591982', '16.31750569097798', '16.88001699865564', '16.96035227294837', '17.57428960463346', '18.22648746360523', '18.64963040149401', '19.19234552794358', '19.61250364947728'], 'prelabel': '2-44520-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 18.854548252311442, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1220843165401529993, 'z1': {'__RealLiteral__': 0, 'data': '0.8572199997483300', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.338595670813115', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.170498500831170', 'prec': 57}}