Formats: - HTML - YAML - JSON - 2026-07-04T18:37:31.582600
Query: /api/lfunc_lfunctions/?_offset=0
Show schema

{'Lhash': '1083686761127362147183684064225', 'a10': [1.1784445922812923, 0.0], 'a2': [2.101399326171404, 0.0], 'a3': [0.0, 0.0], 'a4': [2.4158791280336303, 0.0], 'a5': [0.5607904112296125, 0.0], 'a6': [0.0, 0.0], 'a7': [1.0, 0.0], 'a8': [0.8739281194186218, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 63.888306657226465, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-1.0, 0]]], [127, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [3, 7, 127], 'central_character': '8001.1', 'coefficient_field': 'CDF', 'conductor': 8001, 'conductor_radical': 2667, 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.101399326171404, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.5607904112296125, 0], [5.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [5.809208811663187, 0], [11.0, 0]], [[1.0, 0], [0.5078388279257942, 0], [13.0, 0]], [[1.0, 0], [-0.4468234285968004, 0], [17.0, 0]], [[1.0, 0], [-5.4382950098369145, 0], [19.0, 0]], [[1.0, 0], [-5.142835933269496, 0], [23.0, 0]], [[1.0, 0], [-7.224664808233353, 0], [29.0, 0]], [[1.0, 0], [-9.146091932035677, 0], [31.0, 0]], [[1.0, 0], [-3.9824473494473853, 0], [37.0, 0]], [[1.0, 0], [4.973028254017182, 0], [41.0, 0]], [[1.0, 0], [1.0489132236991967, 0], [43.0, 0]], [[1.0, 0], [-7.687336616004535, 0], [47.0, 0]], [[1.0, 0], [-12.322082724319904, 0], [53.0, 0]], [[1.0, 0], [5.408220529354129, 0], [59.0, 0]], [[1.0, 0], [-7.997830697485237, 0], [61.0, 0]], [[1.0, 0], [5.650092727295937, 0], [67.0, 0]], [[1.0, 0], [12.663580012483074, 0], [71.0, 0]], [[1.0, 0], [-12.084275955884964, 0], [73.0, 0]], [[1.0, 0], [-14.94107431125004, 0], [79.0, 0]], [[1.0, 0], [-16.989763857262567, 0], [83.0, 0]], [[1.0, 0], [6.7772200638079525, 0], [89.0, 0]], [[1.0, 0], [-5.810574130554579, 0], [97.0, 0]], [[1.0, 0], [6.942728895936889, 0], [101.0, 0]], [[1.0, 0], [-14.288844317417123, 0], [103.0, 0]], [[1.0, 0], [-6.014233204708702, 0], [107.0, 0]], [[1.0, 0], [1.9059515367544786, 0], [109.0, 0]], [[1.0, 0], [13.775996321358566, 0], [113.0, 0]], [[1.0, 0], [1.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 21888980, 'index': 125, 'label': '2-8001-1.1-c1-0-125', 'leading_term': '4.79204180596833269402445734398', 'load_key': 'CMFs-workshop', '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': 'ModularForm/GL2/Q/holomorphic/8001/2/a/ba/1/33', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [4.792041805968332, 4.777794746724108, 4.734965043210892, 4.663297504180537, 4.562400781665909, 4.4317961172205065, 4.27098138383291, 4.079506688717267, 3.857057315264663, 3.6035396005299876, 3.319165431156773, 3.004531337019399, 2.6606886021385936, 2.289201335514576, 1.8921900019822755, 1.4723584722812557, 1.0330031944219118, 0.578003609045903, 0.11179343138341923, -0.3606870932078335, -0.8340573787216415, -1.3025800835079075, -1.7602605791248687, -2.200960338403868, -2.6185218413401348, -3.006902187022158, -3.3603122283443496, -3.67335772787218, -3.941178782771638, -4.159583598758642, -4.325172621034438, -4.435449065682387, -4.488912046870439, -4.4851287689761685, -4.424782650121087, -4.309694762004138, -4.142816603274522, -3.928192958265973, -3.6708944134454278, -3.3769199897977606, -3.0530712760558307, -2.7068003873622617, -2.346034996244629, -1.9789845557062957, -1.6139326252191106, -1.2590208874735906, -0.9220309767209098, -0.6101706012958786, -0.3298706105694338, -0.0865996126793603, 0.11529751710145833, 0.27273139032225735, 0.3839649895743162, 0.4486714755534684, 0.4679498229839417, 0.4442964646282142, 0.3815325189575057, 0.28468765323082473, 0.15984314092680407, 0.013938157925420908, -0.145455229416776, -0.31038165430078624, -0.4727687959711218, -0.6247018037704003, -0.7586965401206672, -0.8679621162813469, -0.9466432641716653, -0.9900335069879099, -0.9947508610365965, -0.9588689078392097, -0.8819974920607588, -0.7653089866289414, -0.6115079684193441, -0.4247442018292054, -0.21047096004941793, 0.02474715518918084, 0.2734706889989581, 0.5276580215485411, 0.7789645621121165, 1.0190574435935127, 1.2399338054396352, 1.4342302900925514, 1.595511395803912, 1.7185248450797244, 1.7994131417449197, 1.8358719783803965, 1.8272480766300623, 1.7745713325215997, 1.6805187161005715, 1.5493101422277822, 1.3865393778999753, 1.1989458632861196, 0.9941359776718057, 0.7802646580850302, 0.5656902647915604, 0.3586170834360701, 0.16674077476836283, -0.0030876324271384486, -0.1451639981609227, -0.2551854413112135, -0.33044441778177946, -0.36995244243909, -0.3744862601863685, -0.34655256223248354, -0.29027092408055394, -0.2111783620601654, -0.11596260267980363, -0.012134665052134641, 0.09234549604043822, 0.1894739082629658, 0.27161971019778586, 0.3319349418443316, 0.36473711315177426, 0.36584524343697994, 0.33285156466575716, 0.2653134734315911, 0.1648535257221026, 0.03515917958450971, -0.11812154986857393, -0.2875875368888661, -0.46438913355292044, -0.6386190437918364, -0.7997740396569409, -0.9372680296911224, -1.0409736972422705, -1.1017675779379112, -1.1120521928319311, -1.0662288043810284, -0.9610955716367121, -0.7961483468273824, -0.5737650160465856, -0.2992590206558944, 0.019206674694931765, 0.37084760543278095, 0.7426235675743187, 1.1197310744667825, 1.4862049074309214, 1.8256051451156672, 2.121760903517525, 2.3595380099746985, 2.525595212089873, 2.6090924728876796, 2.602315545890754, 2.501183401683315, 2.3056091531062575, 2.019690778600346, 1.651714970581479, 1.2139655615612803, 0.7223368638319294, 0.19576150673567808, -0.3445284576057381, -0.875879725296646, -1.375199988619456, -1.820002664260306, -2.189467817715523, -2.4654703159291924, -2.6335257697256997, -2.6836066823731395, -2.6107854051944757, -2.415666908179165, -2.1045827844914755, -1.6895279990574767, -1.1878332460154883, -0.6215779038425491, -0.016760920675140966, 0.5977410553050052, 1.1913879498072024, 1.7333130621263921, 2.1937250007783433, 2.5453123006425673, 2.7645859763785947, 2.8330959546790373, 2.738461062402551, 2.4751589520767583, 2.045031797918426, 1.457475431501945, 0.7292933165448113, -0.11578821032771174, -1.0479313604132061, -2.0322973690402613, -3.0304137450481274, -4.001742921769064, -4.905386105021025, -5.701848119762221, -6.354784361850843, -6.832649876958057, -7.110173259957056, -7.1695844607761146, -7.001535480116869, -6.605665947392317, -5.990781138755265, -5.1746274217324295, -4.1832686037492115, -3.0500853432702844, -1.8144377541120715, -0.5200477107486102, 0.786828680018896, 2.0593571606151353, 3.252121586536652, 4.323069044647547, 5.235313886751618, 5.958716473730894, 6.471162290016675, 6.759480657580776, 6.8199589361848405, 6.658427061449219, 6.289907636189385, 5.737847561794875, 5.032967349242428, 4.211782775132959, 3.3148695076718067, 2.38495389993617, 1.4649216745304425, 0.5958402446992159, -0.18491030310447124, -0.8453079965924596, -1.3600819115927187, -1.7117615829674713, -1.8913344942525583, -1.8984829689790699, -1.7413929565451425, -1.4361487407462437, -1.0057483902244209, -0.47879373994648056, 0.11207514638450718, 0.7319185764847213, 1.345318239743483, 1.918186520999418, 2.4194714803303974, 2.8226711735027132, 3.1070818040412806, 3.258718937257151, 3.270868875721043, 3.1442473310132524, 2.8867636457774517, 2.512909880602995, 2.042813941598127, 1.5010135110259313, 0.9150219037570145, 0.3137673327248245, -0.2740071257069876, -0.8212946207062305, -1.3042423525309073, -1.7033603852111043, -2.004458402961215, -2.1992634763313057, -2.2856904912422387, -2.2677568943803483, -2.155153678827299, -1.962503917756673, -1.708357547966571, -1.413985521924843, -1.1020470736433234, -0.7952100880311122, -0.5148060893530738, -0.27959811198978174, -0.10473190576179311], 'positive_zeros': ['0.854878119358957291267611150551272', '2.31577807302959132442359659123559', '2.76985241878973125631113419015919', '3.51084269193985671851277391979980', '4.54595353117878351521186345366750', '5.02101566155872761233050076919802', '5.49571077760068170551234288787665', '6.18482124076061158032390284439628', '7.00139521072681654063175126722027', '7.68877795807082726620583728475201'], 'prelabel': '2-8001-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.993016117663373, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.854878119358957291267611150551', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.31577807302959132442359659124', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.76985241878973125631113419016', 'prec': 103}}