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lfunc_lfunctions • Show schema
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{'A10': 2, 'A2': -1, 'A3': 0, 'A4': 1, 'A5': -2, 'A6': 0, 'A7': 0, 'A8': -1, 'A9': 0, 'Lhash': '171088897004721043', 'a10': [0.6324555320336759, 0], 'a2': [-0.7071067811865475, 0], 'a3': [0.0, 0], 'a4': [0.5, 0], 'a5': [-0.8944271909999159, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [-0.35355339059327373, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 1176.1485115322478, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1]], [7, [1]], [167, [1, -1]]], 'bad_primes': [2, 3, 7, 167], 'central_character': '147294.1', 'coefficient_field': '1.1.1.1', 'conductor': 147294, 'conductor_radical': 7014, 'degree': 2, 'euler_factors': [[1, 1], [1], [1, 2, 5], [1], [1, -2, 11], [1, 1, 13], [1, -3, 17], [1, -1, 19], [1, 0, 23], [1, -3, 29], [1, -9, 31], [1, 4, 37], [1, 7, 41], [1, -5, 43], [1, -8, 47], [1, -6, 53], [1, 10, 59], [1, -8, 61], [1, 7, 67], [1, 3, 71], [1, -5, 73], [1, 11, 79], [1, 12, 83], [1, 2, 89], [1, 16, 97]], 'gamma_factors': [[], [0]], 'index': 10, 'label': '2-147294-1.1-c1-0-10', 'leading_term': '1.18267081731', '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/147294/k', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [1.182670817309701, 0.681500589183556, -0.4315060223626055, -1.145844326824927, -0.6132683719911153, 0.6970341763563827, 0.9967397515283966, -0.8735950782803991, -3.512315504190039, -4.033513796233661, -1.705668060683895, 0.5491521814132362, -0.268736695346005, -2.858765119094621, -3.148809402743615, -0.4239071821783049, 1.140041896155046, -1.089106557771818, -3.332021071460411, -0.7816761981803353, 4.228650458777096, 4.887628269293126, 0.4405567146267395, -2.256515626543482, 0.5762052961774365, 3.936833047011644, 2.674606647201794, -0.3965724018375619, -0.3710307551243268, 1.25715543587389, 0.5337624523753203, -1.183616911315145, -0.5610238393973763, 0.7337537021448731, -0.2450556523897622, -1.185257418845849, 0.7800381713573077, 2.488779509323392, 0.5903950642850008, -1.479390854646033, -0.2360668287439174, 0.7418905869959102, -1.53921987951251, -2.686781270620386, 0.1875098951182026, 2.097776453649222, 0.1780492944222367, -0.8864639967562793, 0.5024621341940048, 0.01960662585647599, -0.5929423850160486, 5.072274534446757, 12.30276825712597, 9.9695192369923, 1.490430190404584, -0.1205495159878803, 3.977626089283835, 2.528858026120296, -2.866661076352513, -2.417113104313023, 1.608275016119998, 1.30479670052844, -0.5103838288455527, 1.068045410935718, 1.762181346986028, -0.6936448412858122, -0.7023399840182863, 1.972223623751724, 1.49729177018218, -0.5348565300396102, 0.5470955221231033, 0.7816616207827647, -3.035494836585211, -4.636867357890487, -1.51569303696416, 0.02337111102639807, -1.008201010321218, -0.1431305871862121, 0.6833070100719995, -0.9637679292328769, -0.7505941667297007, 0.9555472244343876, -1.591631276477332, -4.404121889098516, -1.181590778507606, 0.7429160365201662, -3.689727461927607, -3.799982066468422, 3.334376098125101, 4.6304437476784, -0.7795911441673279, -0.351618046869989, 3.758375575543443, 1.872801863493825, -0.1517269284839027, 3.549014965116699, 4.292756045766989, 0.1114997639094547, 0.05361913731786388, 2.073999834037992, -0.8021764013077968, -2.787603975057203, -0.1345235419081754, -0.5110084787012615, -3.667066451806832, -1.936500903359239, 1.292539070313046, 0.4379176067740106, -0.1037253803326137, 0.9664602625615629, -0.2781237225107363, -1.014931664418676, 0.3563700514595008, -1.246915250478017, -3.312978295527901, -0.6954598135144, -0.05589858106764316, -4.038810851134204, -3.13317676295818, 1.513865792496683, 0.7825517713399878], 'positive_zeros': ['0.4066287557131318', '1.117755304327842', '1.662462707593865', '2.660254338550877', '2.969390933011863', '3.786730500496721', '4.163057156985168', '4.788554860575675', '5.523053079958867', '5.966717356838089', '6.705805413779287', '7.052119098452377', '7.565764459556073', '8.082124576763183', '8.464294985485283', '8.928115140921150', '9.549929143124009', '10.02847580359400', '10.36139154964691', '10.98682948980828', '11.51844073415334', '11.91146897906695', '12.25282657056484', '12.55306619605816', '13.57027425278183', '13.75933874072491', '14.35863541609105', '14.88717015789102', '15.38596000237809', '15.63119403010496', '16.18177878495576', '16.56687565688718', '17.15339128880380', '17.42809216301566', '17.81837159664896', '18.67343167009026', '18.76042797693804', '19.27063913157363', '19.62210381281223'], 'prelabel': '2-147294-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 34.29502167271873, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 171088897004721043, 'z1': {'__RealLiteral__': 0, 'data': '0.4066287557131318', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.117755304327842', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.662462707593865', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1176.1485115322478, 'bad_primes': [2, 3, 7, 167], 'central_character': '1.1', 'conductor': 147294, 'conductor_radical': 7014, 'degree': 2, 'dirichlet_coefficients': [1, -1, 0, 1, -2, 0, 0, -1, 0, 2, 2, 0, -1, 0, 0, 1, 3, 0, 1, -2, 0, -2, 0, 0, -1, 1, 0, 0, 3, 0, 9, -1, 0, -3, 0, 0, -4, -1, 0, 2, -7, 0, 5, 2, 0, 0, 8, 0, 0, 1, 0, -1, 6, 0, -4, 0, 0, -3, -10, 0, 8, -9, 0, 1, 2, 0, -7, 3, 0, 0, -3, 0, 5, 4, 0, 1, 0, 0, -11, -2, 0, 7, -12, 0, -6, -5, 0, -2, -2, 0, 0, 0, 0, -8, -2, 0, -16, 0, 0, -1], 'euler11': [1, -2, 11], 'euler13': [1, 1, 13], 'euler17': [1, -3, 17], 'euler19': [1, -1, 19], 'euler2': [1, 1, 0], 'euler23': [1, 0, 23], 'euler29': [1, -3, 29], 'euler3': [1, 0, 0], 'euler31': [1, -9, 31], 'euler37': [1, 4, 37], 'euler41': [1, 7, 41], 'euler43': [1, -5, 43], 'euler47': [1, -8, 47], 'euler5': [1, 2, 5], 'euler53': [1, -6, 53], 'euler59': [1, 10, 59], 'euler61': [1, -8, 61], 'euler67': [1, 7, 67], 'euler7': [1, 0, 0], 'euler71': [1, 3, 71], 'euler73': [1, -5, 73], 'euler79': [1, 11, 79], 'euler83': [1, 12, 83], 'euler89': [1, 2, 89], 'euler97': [1, 16, 97], 'euler_factors': [[1, 1, 0], [1, 0, 0], [1, 2, 5], [1, 0, 0], [1, -2, 11], [1, 1, 13], [1, -3, 17], [1, -1, 19], [1, 0, 23], [1, -3, 29], [1, -9, 31], [1, 4, 37], [1, 7, 41], [1, -5, 43], [1, -8, 47], [1, -6, 53], [1, 10, 59], [1, -8, 61], [1, 7, 67], [1, 3, 71], [1, -5, 73], [1, 11, 79], [1, 12, 83], [1, 2, 89], [1, 16, 97]], 'index': 10, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/147294/k'], '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': '2-147294-1.1-c1-0-10', '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': '2-147294-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 34.29502167271873, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 171088897004721043, 'z1': {'__RealLiteral__': 0, 'data': '0.4066287557131318', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '171088897004721043', 'Lhash_array': ['171088897004721043'], 'label': '2-147294-1.1-c1-0-10', 'type': 'ECQ', 'url': 'EllipticCurve/Q/147294/k'}