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lfunc_lfunctions • Show schema
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{'A10': 1, 'A2': -1, 'A3': 0, 'A4': 1, 'A5': -1, 'A6': 0, 'A7': -5, 'A8': -1, 'A9': 0, 'Lhash': '712207304271900908', 'a10': [0.31622776601683794, 0], 'a2': [-0.7071067811865475, 0], 'a3': [0.0, 0], 'a4': [0.5, 0], 'a5': [-0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [-1.889822365046136, 0], 'a8': [-0.35355339059327373, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 2284.599852230854, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1]], [5, [1, 1]], [11, [1, -1]], [17, [1]]], 'bad_primes': [2, 3, 5, 11, 17], 'central_character': '286110.1', 'coefficient_field': '1.1.1.1', 'conductor': 286110, 'conductor_radical': 5610, 'degree': 2, 'euler_factors': [[1, 1], [1], [1, 1], [1, 5, 7], [1, -1], [1, 4, 13], [1], [1, 4, 19], [1, 3, 23], [1, -9, 29], [1, 5, 31], [1, 2, 37], [1, 0, 41], [1, -11, 43], [1, 0, 47], [1, 12, 53], [1, -6, 59], [1, 2, 61], [1, 4, 67], [1, 6, 71], [1, 2, 73], [1, 8, 79], [1, 12, 83], [1, 0, 89], [1, -7, 97]], 'gamma_factors': [[], [0]], 'index': 48, 'label': '2-286110-1.1-c1-0-48', 'leading_term': '2.39903130388', '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/286110/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 0.4112558566894749, -0.09945933969454993, -1.439208382905069, -2.105119496367372, -0.5463754124237672, 2.522790417736006, 4.105981545244932, 2.40661522234474, -0.4003498546359662, -0.7946930963879703, 0.973842326010721, 1.249607988436445, -0.8512599908132876, -1.430803426965708, 1.518585716144493, 3.588054064533197, 0.9044450677235067, -2.031897984567524, 1.39722698462068, 8.091453365482016, 8.628202292779378, 2.067673136464188, -2.684825440831857, -1.438861126520745, 0.1886098953303526, -1.383212771380953, -2.187117399279417, -0.4135436880299386, -0.1036455577169424, -1.682711384715536, -0.4067040631472216, 3.16612138185914, 3.183243992977023, 0.06948657993292913, -0.4042528606102411, 1.302802873189358, 0.5920902702101297, -1.027554781982554, -0.1287963609442287, 0.586279676192965, -0.711055470125955, 0.02489389342421598, 2.357060796193564, 0.110079102898265, -4.526812247355005, -3.265586674087356, 1.350435609799214, 1.051846312952472, -1.338623861130324, -0.183112515327384, 0.04506187519532293, -1.970160005190378, 2.131008929556267, 10.11814552327152, 8.843633328870336, 0.942819471231231, 0.6646209200644237, 4.976076225537867, 1.84817526050071, -3.594668204516578, -1.731768692765327, 1.537290342530754, 0.2672955998295279, -0.3440922927413787, 0.5327399943463261, -1.353094000235458, -2.494471195962216, -0.3428978606559209, -0.5495624247217554, -2.251199903835624, 0.8201278426377037, 3.724059209156444, 0.2870914292848851, -2.437618779291083, 0.02814590011333936, 1.259006364187732, 0.07549344492662341, 0.1306632891942158, -0.5619520697401115, -1.047307126565678, 2.146905233678775, 2.258356101115199, -3.388971396434484, -2.203006667815089, 6.4980594953855, 6.994169250661655, 0.6525302531340983, 0.2978786903297282, 0.9542976040373571, -2.990837620857946, -2.050236912572372, 2.446531431942885, 0.260833261175944, -1.287936476434851, 4.151823121883276, 4.736063366835337, -0.1916481122395355, 1.823633755011498, 5.766496810253667, 2.205096191203054, -1.004482768660008, 0.184732146192382, -0.3302922475406138, -0.1282653396913912, 2.705917744855573, 1.849692262052361, -0.4352762371131771, 0.6569667215809971, -0.2328239643035868, -2.432571429832665, 0.2007871493034769, 1.732578432738933, -1.230432523510339, -0.857415425248266, 1.15849577554234, -0.6042884620236202, -0.7029062965712909, 0.5350240947211989, -1.298493936118675, 0.6031819358770117], 'positive_zeros': ['0.4756111545892521', '1.298020080008979', '2.205291578473418', '2.621091570042912', '3.158528883247662', '3.643671091145026', '4.303986737668335', '4.692041898278294', '5.576484727863437', '6.164136847961689', '6.318287703703526', '7.072048686471763', '7.227397445520979', '7.779350485323045', '8.507011108514295', '8.809276938422186', '9.321098397009920', '9.770103803484036', '10.12402790982669', '10.49746541623274', '11.00557866749278', '11.66241561353716', '12.08756821956467', '12.52486284790728', '12.75586275903351', '13.17530353908646', '14.05101144444803', '14.20663522111422', '14.81798327857116', '15.34836749994850', '15.78487218734336', '16.07332069067558', '16.36499285494600', '17.05665300084489', '17.16797542753520', '17.70650858257307', '18.26481023235787', '18.74767859744586', '19.28143571844537', '19.40588430433016', '19.63529407829614'], 'prelabel': '2-286110-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 47.79748792803712, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 712207304271900908, 'z1': {'__RealLiteral__': 0, 'data': '0.4756111545892521', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.298020080008979', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.205291578473418', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2284.599852230854, 'bad_primes': [2, 3, 5, 11, 17], 'central_character': '1.1', 'conductor': 286110, 'conductor_radical': 5610, 'degree': 2, 'dirichlet_coefficients': [1, -1, 0, 1, -1, 0, -5, -1, 0, 1, 1, 0, -4, 5, 0, 1, 0, 0, -4, -1, 0, -1, -3, 0, 1, 4, 0, -5, 9, 0, -5, -1, 0, 0, 5, 0, -2, 4, 0, 1, 0, 0, 11, 1, 0, 3, 0, 0, 18, -1, 0, -4, -12, 0, -1, 5, 0, -9, 6, 0, -2, 5, 0, 1, 4, 0, -4, 0, 0, -5, -6, 0, -2, 2, 0, -4, -5, 0, -8, -1, 0, 0, -12, 0, 0, -11, 0, -1, 0, 0, 20, -3, 0, 0, 4, 0, 7, -18, 0, 1], 'euler11': [1, -1, 0], 'euler13': [1, 4, 13], 'euler17': [1, 0, 0], 'euler19': [1, 4, 19], 'euler2': [1, 1, 0], 'euler23': [1, 3, 23], 'euler29': [1, -9, 29], 'euler3': [1, 0, 0], 'euler31': [1, 5, 31], 'euler37': [1, 2, 37], 'euler41': [1, 0, 41], 'euler43': [1, -11, 43], 'euler47': [1, 0, 47], 'euler5': [1, 1, 0], 'euler53': [1, 12, 53], 'euler59': [1, -6, 59], 'euler61': [1, 2, 61], 'euler67': [1, 4, 67], 'euler7': [1, 5, 7], 'euler71': [1, 6, 71], 'euler73': [1, 2, 73], 'euler79': [1, 8, 79], 'euler83': [1, 12, 83], 'euler89': [1, 0, 89], 'euler97': [1, -7, 97], 'euler_factors': [[1, 1, 0], [1, 0, 0], [1, 1, 0], [1, 5, 7], [1, -1, 0], [1, 4, 13], [1, 0, 0], [1, 4, 19], [1, 3, 23], [1, -9, 29], [1, 5, 31], [1, 2, 37], [1, 0, 41], [1, -11, 43], [1, 0, 47], [1, 12, 53], [1, -6, 59], [1, 2, 61], [1, 4, 67], [1, 6, 71], [1, 2, 73], [1, 8, 79], [1, 12, 83], [1, 0, 89], [1, -7, 97]], 'index': 48, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/286110/a'], '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': '2-286110-1.1-c1-0-48', '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': '2-286110-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 47.79748792803712, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 712207304271900908, 'z1': {'__RealLiteral__': 0, 'data': '0.4756111545892521', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '712207304271900908', 'Lhash_array': ['712207304271900908'], 'label': '2-286110-1.1-c1-0-48', 'type': 'ECQ', 'url': 'EllipticCurve/Q/286110/a'}