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lfunc_lfunctions • Show schema
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{'A10': -2, 'A2': 1, 'A3': -1, 'A4': 1, 'A5': -2, 'A6': -1, 'A7': 1, 'A8': 1, 'A9': 1, 'Lhash': '249386957225005071', 'a10': [-0.6324555320336759, 0], 'a2': [0.7071067811865475, 0], 'a3': [-0.5773502691896258, 0], 'a4': [0.5, 0], 'a5': [-0.8944271909999159, 0], 'a6': [-0.4082482904638631, 0], 'a7': [0.3779644730092272, 0], 'a8': [0.35355339059327373, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 108.32505538206902, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1, 1]], [7, [1, -1]], [17, [1, 1]], [19, [1, 1]]], 'bad_primes': [2, 3, 7, 17, 19], 'central_character': '13566.1', 'coefficient_field': '1.1.1.1', 'conductor': 13566, 'conductor_radical': 13566, 'degree': 2, 'euler_factors': [[1, -1], [1, 1], [1, 2, 5], [1, -1], [1, 0, 11], [1, -6, 13], [1, 1], [1, 1], [1, 8, 23], [1, -6, 29], [1, 4, 31], [1, -10, 37], [1, 6, 41], [1, 4, 43], [1, 12, 47], [1, 10, 53], [1, -4, 59], [1, -14, 61], [1, 0, 67], [1, 8, 71], [1, -2, 73], [1, 8, 79], [1, 12, 83], [1, 14, 89], [1, -6, 97]], 'gamma_factors': [[], [0]], 'index': 13, 'label': '2-13566-1.1-c1-0-13', 'leading_term': '5.69850967647', '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/13566/m', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.362923497204014, 2.328751929314856, 2.459775332576989, 1.517915014481001, -0.1699100066732865, -1.64366418748088, -1.800664182999999, -0.2327077411008422, 2.247151440898219, 3.997104989260999, 3.763372163100323, 1.769695724329806, -0.3932689613760144, -1.159859611939972, -0.4223466051435693, 0.4737438219086399, 0.273036226384859, -0.7342729700959082, -1.053143856251556, 0.1450145618798435, 1.822718253593144, 2.175722833930347, 0.8791511768789001, -0.363183100747179, 0.05737237920911751, 1.395938142297876, 1.296243563338812, -1.028266403829123, -3.297175388156868, -2.793019381542178, -0.06525835602295953, 1.441049180323192, 0.002300435339884248, -1.480706735645983, 1.162421673758973, 7.442598199874914, 11.67778793032502, 9.424554391649002, 3.025998118965517, -1.065099234963899, 0.07262042456287397, 3.060713546109279, 3.455533288443601, 1.33439907387349, -0.138281273071132, 0.009415347129071529, -0.3035119658618533, -1.984236470039086, -2.868866410662294, -1.418865131289392, 0.2593164871459642, -0.4763056360712995, -2.348724062077009, -1.948339056098325, 0.6577752958825002, 1.677665269879448, -0.4083837775052973, -2.189594544761319, -0.6248870938032199, 2.110564618142401, 2.174813740261778, 0.1305894908491438, -0.543482282306627, 0.334413700477172, -0.2394915589098254, -2.124294188569668, -1.197171058878667, 3.338407813356573, 5.995613747768977, 2.905720415088158, -1.730238709009589, -2.018471149790949, 0.2653465033869377, -0.9713258034180721, -5.396525364066083, -6.359288277502145, -1.980807934296976, 1.51627464083036, -0.06340345075149532, -2.528717986000482, -1.144419254509459, 1.415180944572369, 0.514444501973719, -2.018134592269408, -1.472431503843928, 1.244334204365674, 1.626701049478223, -0.1852922828019752, -0.1707580446923915, 1.87228282224633, 2.261693053626008, 0.4592381617355624, -0.4452720735525605, 0.07935844010725178, -0.113873432907706, -0.2317513162696839, 2.179636191502797, 4.745316982763754, 2.861405279217314, -1.313791431960328, -1.215288251933572, 2.357174182637588, 1.769115798458167, -3.613716312954249, -5.13286679398743, 0.331228685874221, 4.558899628988699, 2.027884776052713, -1.313374694996671, 0.3256653355424233, 2.756466648674894, 1.073420440350426, -1.145364629814543, -0.03201303198823011, 0.3568595466459506, -3.52117704213063, -6.606599686881645, -4.078060901066491, -0.2350015371099951, -0.4165787044313325], 'positive_zeros': ['1.226214823793492', '2.025217528239841', '3.195222694046241', '3.847438931713403', '4.324290915119967', '4.978968676312469', '5.897274382756004', '6.238035965484654', '6.907512902541461', '7.756020106677459', '8.250254149425815', '8.685834172434827', '9.896834959631980', '10.24384494008712', '11.19922167794424', '11.49300966601184', '11.65720429374522', '12.68566940389491', '12.92698106954521', '13.68817545006649', '14.21272665298899', '14.80195475360249', '15.51850310534038', '15.90284249313282', '16.21261537436746', '16.82793351974720', '17.64075404925263', '18.20884166729437', '18.41866853496657', '19.35364171252085', '19.74502048597239'], 'prelabel': '2-13566-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 10.407932329817918, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 249386957225005071, 'z1': {'__RealLiteral__': 0, 'data': '1.226214823793492', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '2.025217528239841', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '3.195222694046241', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 108.32505538206902, 'bad_primes': [2, 3, 7, 17, 19], 'central_character': '1.1', 'conductor': 13566, 'conductor_radical': 13566, 'degree': 2, 'dirichlet_coefficients': [1, 1, -1, 1, -2, -1, 1, 1, 1, -2, 0, -1, 6, 1, 2, 1, -1, 1, -1, -2, -1, 0, -8, -1, -1, 6, -1, 1, 6, 2, -4, 1, 0, -1, -2, 1, 10, -1, -6, -2, -6, -1, -4, 0, -2, -8, -12, -1, 1, -1, 1, 6, -10, -1, 0, 1, 1, 6, 4, 2, 14, -4, 1, 1, -12, 0, 0, -1, 8, -2, -8, 1, 2, 10, 1, -1, 0, -6, -8, -2, 1, -6, -12, -1, 2, -4, -6, 0, -14, -2, 6, -8, 4, -12, 2, -1, 6, 1, 0, -1], 'euler11': [1, 0, 11], 'euler13': [1, -6, 13], 'euler17': [1, 1, 0], 'euler19': [1, 1, 0], 'euler2': [1, -1, 0], 'euler23': [1, 8, 23], 'euler29': [1, -6, 29], 'euler3': [1, 1, 0], 'euler31': [1, 4, 31], 'euler37': [1, -10, 37], 'euler41': [1, 6, 41], 'euler43': [1, 4, 43], 'euler47': [1, 12, 47], 'euler5': [1, 2, 5], 'euler53': [1, 10, 53], 'euler59': [1, -4, 59], 'euler61': [1, -14, 61], 'euler67': [1, 0, 67], 'euler7': [1, -1, 0], 'euler71': [1, 8, 71], 'euler73': [1, -2, 73], 'euler79': [1, 8, 79], 'euler83': [1, 12, 83], 'euler89': [1, 14, 89], 'euler97': [1, -6, 97], 'euler_factors': [[1, -1, 0], [1, 1, 0], [1, 2, 5], [1, -1, 0], [1, 0, 11], [1, -6, 13], [1, 1, 0], [1, 1, 0], [1, 8, 23], [1, -6, 29], [1, 4, 31], [1, -10, 37], [1, 6, 41], [1, 4, 43], [1, 12, 47], [1, 10, 53], [1, -4, 59], [1, -14, 61], [1, 0, 67], [1, 8, 71], [1, -2, 73], [1, 8, 79], [1, 12, 83], [1, 14, 89], [1, -6, 97]], 'index': 13, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/13566/m'], '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': '2-13566-1.1-c1-0-13', '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': '2-13566-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 10.407932329817918, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 249386957225005071, 'z1': {'__RealLiteral__': 0, 'data': '1.226214823793492', 'prec': 57}}
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lfunc_instances • Show schema
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{'Lhash': '249386957225005071', 'Lhash_array': ['249386957225005071'], 'label': '2-13566-1.1-c1-0-13', 'type': 'ECQ', 'url': 'EllipticCurve/Q/13566/m'}