{"label":"468.2.a","level":468,"weight":2,"dims":{"new":5,"cusp":73,"eisenstein":23,"modsym":169},"old":[[26,2,6],[36,1,2],[39,3,6],[52,1,3],[78,1,4],[117,5,3],[156,2,2],[234,5,2]],"T":[[5,1],[7,3],[11,5],[17,7],[19,9]],"status":"proven","checks":["dim M^+ at levels [1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 36, 39, 52, 78, 117, 156, 234, 468]: [0, 1, 1, 2, 3, 2, 5, 1, 5, 5, 9, 6, 10, 18, 16, 34, 46, 90] (certified at ell = 2147483629)","T = [(5, 1), (7, 3), (11, 5), (17, 7), (19, 9)]; h of degree 5 = 1 x 5 (phi(ord eps) x dim S_k^new); 2 primes, 0 rejected"],"newforms":[{"label":"468.2.a.a","letter":"a","dim":1,"charpoly":["-28","1"],"traces":["1","0","0","0","-4","0","4","0","0","0","4","0","-1","0","0","0","0","0","0","0","0","0","8","0","11","0","0","0","8","0","4","0","0","0","-16","0","6","0","0","0","-12","0","-8","0","0","0","4","0","9","0","0","0","0","0","-16","0","0","0","-4","0","-2","0","0","0","4","0","-8","0","0","0","4","0","-10","0","0","0","16","0","-4","0","0","0","-12","0","0","0","0","0","12","0","-4","0","0","0","0","0","14","0","0","0","-8","0","4","0","0","0","8","0","-14","0","0","0","8","0","-32","0","0","0","0","0","5","0","0","0","-24","0","4","0","0","0","8","0","0","0","0","0","-12","0","16","0","0","0","-4","0","-32","0","0","0","-12","0","-12","0","0","0","-16","0","14","0","0","0","32","0","-16","0","0","0","-12","0","1","0","0","0","8","0","44","0","0","0","0","0","-6","0","0","0","-24","0","0","0","0","0","16","0","2","0","0","0","12","0","20","0","0","0","32","0","48","0","0","0","0","0","-16","0","0","0","32","0","16","0","0","0","0","0","12","0","0","0","12","0","-6","0","0","0","-8","0","-16","0","0","0","-12","0","-18","0","0","0","-36","0","0","0","0","0","-24","0","32","0","0","0","-24","0","24","0","0","0","-24","0","0","0","0","0","24","0","-20","0","0","0","44","0","-6","0","0","0","4","0","16","0","0","0","-48","0","-17","0","0","0","4","0","16","0","0","0","-8","0","-32","0","0","0","8","0","8","0","0","0","-24","0","26","0","0","0","12","0","32","0","0","0","0","0","-11","0","0","0","16","0","8","0","0","0","32","0","14","0","0","0","16","0","8","0","0","0","0","0","-2","0","0","0","4","0","-16","0","0","0","-12","0","-19","0","0","0","40","0","-4","0","0","0","0","0","-10","0","0","0","-8","0","-32","0","0","0","-36","0","-64","0","0","0","0","0","0","0","0","0","16","0","14","0","0","0","12","0","-4","0","0","0","24","0","-26","0","0","0","-16","0","48","0","0","0","-24","0","-38","0","0","0","0","0","-8","0","0","0","-36","0","-14","0","0","0","0","0","20","0","0","0","24","0","-48","0","0","0","-20","0","-48","0","0","0","16","0","22","0","0","0","12","0","28","0","0","0","8","0","-32","0","0","0","-32","0","0","0","0","0","12","0","-6","0","0","0","-56","0","20","0","0","0","-8","0","0","0","0","0","16","0","40","0","0","0","-8","0","32","0","0","0","-20","0","-40","0","0","0","-16","0","16","0","0","0","-24","0","-24","0","0","0","0","0","41","0","0","0","12","0","-32","0","0","0","36","0","2","0","0","0","56","0","-8","0","0","0","0","0","-16","0","0","0","36","0","8","0","0","0","32","0","-32","0","0","0","-8","0","0","0","0","0","88","0","18","0","0","0","-48","0","0","0","0","0","-28","0","0","0","0","0","-4","0","0","0","0","0","-8","0","10","0","0","0","-20","0","-12","0","0","0","-4","0","38","0","0","0","4","0","-8","0","0","0","48","0","41","0","0","0","0","0","4","0","0","0","-16","0","-9","0","0","0","16","0","32","0","0","0","16","0","-16","0","0","0","-24","0","-32","0","0","0","-48","0","-10","0","0","0","0","0","64","0","0","0","-8","0","-14","0","0","0","0","0","56","0","0","0","-44","0","48","0","0","0","0","0","16","0","0","0","-64","0","0","0","0","0","-48","0","0","0","0","0","-32","0","26","0","0","0","32","0","16","0","0","0","8","0","16","0","0","0","88","0","28","0","0","0","0","0","2","0","0","0","-32","0","-24","0","0","0","-44","0","48","0","0","0","32","0","-36","0","0","0","48","0","42","0","0","0","36","0","-56","0","0","0","4","0","-30","0","0","0","20","0","44","0","0","0","0","0","16","0","0","0","-56","0","-16","0","0","0","32","0","2","0","0","0","0","0","0","0","0","0","-40","0","-128","0","0","0","24","0","-16","0","0","0","64","0","0","0","0","0","20","0","-36","0","0","0","-12","0","34","0","0","0","0","0","48","0","0","0","44","0","35","0","0","0","-4","0","20","0","0","0","48","0","22","0","0","0","-56","0","-40","0","0","0","28","0","-32","0","0","0","-16","0","8","0","0","0","-96","0","-18","0","0","0","24","0","-8","0","0","0","-32","0","16","0","0","0","0","0","0","0","0","0","32","0","0","0","0","0","24","0","-24","0","0","0","-48","0","-48","0","0","0","32","0","12","0","0","0","-4","0","66","0","0","0","-12","0","0","0","0","0","0","0","42","0","0","0","4","0","-96","0","0","0","12","0","10","0","0","0","56","0","-64","0","0","0","-48","0","-15","0","0","0","-8","0","-4","0","0","0","0","0","64","0","0","0","12","0","48","0","0","0","-4","0","-48","0","0","0","-64","0","12","0","0","0","-80","0","-10","0","0","0"],"lmfdb":"agrees","curve":{"cremona":"468b1","lmfdb":"468.a","ainvs":[0,0,0,-1512,23085],"rank":0,"torsion":2},"derived":{"al":[[2,null],[3,null],[13,1]],"fricke":null,"sign":null,"cm":null,"cmInert":0,"cmExact":0}},{"label":"468.2.a.b","letter":"b","dim":1,"charpoly":["94","1"],"traces":["1","0","0","0","-2","0","-2","0","0","0","2","0","-1","0","0","0","-6","0","-6","0","0","0","-8","0","-1","0","0","0","-2","0","10","0","0","0","4","0","-6","0","0","0","6","0","4","0","0","0","2","0","-3","0","0","0","-6","0","-4","0","0","0","10","0","-2","0","0","0","2","0","10","0","0","0","-10","0","2","0","0","0","-4","0","-4","0","0","0","6","0","12","0","0","0","6","0","2","0","0","0","12","0","2","0","0","0","2","0","-8","0","0","0","16","0","-14","0","0","0","-14","0","16","0","0","0","12","0","-7","0","0","0","12","0","-8","0","0","0","16","0","12","0","0","0","-18","0","16","0","0","0","-2","0","4","0","0","0","-18","0","6","0","0","0","-20","0","2","0","0","0","16","0","-10","0","0","0","-6","0","1","0","0","0","10","0","2","0","0","0","-12","0","-6","0","0","0","12","0","-12","0","0","0","-4","0","2","0","0","0","6","0","-16","0","0","0","4","0","-12","0","0","0","-12","0","8","0","0","0","-8","0","-20","0","0","0","6","0","-6","0","0","0","-18","0","18","0","0","0","-10","0","-4","0","0","0","-18","0","-6","0","0","0","6","0","6","0","0","0","-12","0","-16","0","0","0","-18","0","12","0","0","0","12","0","12","0","0","0","-18","0","-2","0","0","0","-2","0","30","0","0","0","14","0","4","0","0","0","-12","0","19","0","0","0","14","0","-20","0","0","0","8","0","-8","0","0","0","4","0","-34","0","0","0","0","0","-10","0","0","0","-18","0","-4","0","0","0","36","0","1","0","0","0","-4","0","-22","0","0","0","-20","0","-10","0","0","0","20","0","20","0","0","0","24","0","10","0","0","0","14","0","20","0","0","0","-30","0","17","0","0","0","-4","0","-4","0","0","0","12","0","-22","0","0","0","2","0","10","0","0","0","-18","0","8","0","0","0","6","0","48","0","0","0","8","0","2","0","0","0","6","0","-10","0","0","0","-12","0","-14","0","0","0","-20","0","-12","0","0","0","-24","0","10","0","0","0","6","0","4","0","0","0","30","0","-14","0","0","0","48","0","-16","0","0","0","24","0","-12","0","0","0","38","0","12","0","0","0","-4","0","34","0","0","0","6","0","22","0","0","0","-20","0","-20","0","0","0","8","0","6","0","0","0","18","0","6","0","0","0","-4","0","2","0","0","0","20","0","12","0","0","0","20","0","-14","0","0","0","-28","0","-4","0","0","0","14","0","-4","0","0","0","16","0","4","0","0","0","-6","0","24","0","0","0","-60","0","41","0","0","0","-6","0","-32","0","0","0","-6","0","26","0","0","0","28","0","-32","0","0","0","12","0","8","0","0","0","-42","0","-4","0","0","0","4","0","28","0","0","0","-10","0","-12","0","0","0","8","0","-6","0","0","0","-12","0","-12","0","0","0","-26","0","-60","0","0","0","-26","0","-24","0","0","0","-4","0","-26","0","0","0","14","0","-12","0","0","0","-2","0","26","0","0","0","-34","0","-2","0","0","0","-12","0","-19","0","0","0","36","0","22","0","0","0","16","0","3","0","0","0","26","0","2","0","0","0","32","0","20","0","0","0","-18","0","-32","0","0","0","0","0","2","0","0","0","-24","0","16","0","0","0","-4","0","-26","0","0","0","-6","0","-4","0","0","0","2","0","36","0","0","0","6","0","34","0","0","0","-32","0","-36","0","0","0","-18","0","36","0","0","0","-4","0","-22","0","0","0","-80","0","4","0","0","0","40","0","16","0","0","0","2","0","-32","0","0","0","-24","0","26","0","0","0","20","0","6","0","0","0","14","0","36","0","0","0","-32","0","0","0","0","0","-12","0","-42","0","0","0","-18","0","28","0","0","0","-10","0","-54","0","0","0","46","0","-10","0","0","0","-36","0","-20","0","0","0","-4","0","38","0","0","0","28","0","2","0","0","0","-18","0","-12","0","0","0","4","0","-32","0","0","0","-6","0","-22","0","0","0","20","0","-24","0","0","0","-2","0","-24","0","0","0","-6","0","22","0","0","0","18","0","12","0","0","0","10","0","-25","0","0","0","-2","0","14","0","0","0","48","0","-38","0","0","0","38","0","8","0","0","0","-34","0","-20","0","0","0","-8","0","-10","0","0","0","-24","0","18","0","0","0","-18","0","28","0","0","0","-4","0","16","0","0","0","-12","0","24","0","0","0","-20","0","36","0","0","0","12","0","36","0","0","0","36","0","12","0","0","0","-32","0","-12","0","0","0","10","0","6","0","0","0","54","0","18","0","0","0","24","0","42","0","0","0","-10","0","-48","0","0","0","42","0","-2","0","0","0","-26","0","8","0","0","0","36","0","69","0","0","0","-4","0","50","0","0","0","48","0","-32","0","0","0","-18","0","12","0","0","0","-14","0","-12","0","0","0","-32","0","12","0","0","0","32","0","-58","0","0","0"],"lmfdb":"agrees","curve":{"cremona":"468c1","lmfdb":"468.b","ainvs":[0,0,0,-36,81],"rank":1,"torsion":2},"derived":{"al":[[2,null],[3,null],[13,1]],"fricke":null,"sign":null,"cm":null,"cmInert":0,"cmExact":0}},{"label":"468.2.a.c","letter":"c","dim":1,"charpoly":["-66","1"],"traces":["1","0","0","0","0","0","2","0","0","0","0","0","1","0","0","0","6","0","2","0","0","0","0","0","-5","0","0","0","6","0","2","0","0","0","0","0","2","0","0","0","12","0","-4","0","0","0","0","0","-3","0","0","0","-6","0","0","0","0","0","-12","0","2","0","0","0","0","0","-10","0","0","0","-12","0","14","0","0","0","0","0","8","0","0","0","-12","0","0","0","0","0","0","0","2","0","0","0","0","0","-10","0","0","0","-18","0","-16","0","0","0","12","0","14","0","0","0","-6","0","0","0","0","0","12","0","-11","0","0","0","0","0","-4","0","0","0","-12","0","4","0","0","0","12","0","-16","0","0","0","0","0","0","0","0","0","-12","0","-10","0","0","0","0","0","2","0","0","0","0","0","14","0","0","0","24","0","1","0","0","0","6","0","-10","0","0","0","-12","0","2","0","0","0","0","0","0","0","0","0","0","0","2","0","0","0","24","0","20","0","0","0","12","0","0","0","0","0","0","0","-4","0","0","0","0","0","4","0","0","0","6","0","26","0","0","0","-24","0","14","0","0","0","-6","0","0","0","0","0","12","0","-10","0","0","0","0","0","2","0","0","0","-12","0","0","0","0","0","-6","0","4","0","0","0","24","0","0","0","0","0","-18","0","26","0","0","0","0","0","-10","0","0","0","12","0","-16","0","0","0","24","0","19","0","0","0","12","0","0","0","0","0","0","0","-8","0","0","0","0","0","2","0","0","0","-24","0","-22","0","0","0","24","0","0","0","0","0","12","0","-5","0","0","0","0","0","-10","0","0","0","0","0","2","0","0","0","0","0","-20","0","0","0","12","0","-22","0","0","0","-12","0","0","0","0","0","24","0","-15","0","0","0","0","0","20","0","0","0","-12","0","14","0","0","0","6","0","26","0","0","0","-24","0","0","0","0","0","-30","0","0","0","0","0","0","0","-22","0","0","0","-24","0","2","0","0","0","0","0","-10","0","0","0","-24","0","0","0","0","0","12","0","-34","0","0","0","-30","0","4","0","0","0","-24","0","14","0","0","0","0","0","8","0","0","0","12","0","0","0","0","0","0","0","0","0","0","0","0","0","38","0","0","0","0","0","-22","0","0","0","-36","0","-20","0","0","0","0","0","-10","0","0","0","12","0","2","0","0","0","0","0","2","0","0","0","-12","0","36","0","0","0","-24","0","14","0","0","0","24","0","0","0","0","0","0","0","28","0","0","0","0","0","0","0","0","0","-30","0","-16","0","0","0","12","0","-23","0","0","0","12","0","0","0","0","0","0","0","-10","0","0","0","0","0","-16","0","0","0","12","0","16","0","0","0","12","0","-4","0","0","0","-12","0","0","0","0","0","18","0","-40","0","0","0","0","0","2","0","0","0","-24","0","0","0","0","0","12","0","4","0","0","0","0","0","0","0","0","0","48","0","26","0","0","0","0","0","-4","0","0","0","0","0","-22","0","0","0","36","0","-22","0","0","0","0","0","25","0","0","0","12","0","-10","0","0","0","0","0","-3","0","0","0","-18","0","14","0","0","0","24","0","0","0","0","0","30","0","0","0","0","0","36","0","2","0","0","0","0","0","0","0","0","0","0","0","-10","0","0","0","-6","0","-20","0","0","0","24","0","0","0","0","0","-6","0","14","0","0","0","0","0","72","0","0","0","42","0","4","0","0","0","-36","0","-10","0","0","0","0","0","0","0","0","0","0","0","-32","0","0","0","-30","0","44","0","0","0","-24","0","38","0","0","0","0","0","2","0","0","0","-12","0","0","0","0","0","24","0","32","0","0","0","0","0","2","0","0","0","12","0","28","0","0","0","-12","0","-22","0","0","0","-12","0","-10","0","0","0","24","0","0","0","0","0","0","0","26","0","0","0","-12","0","2","0","0","0","18","0","0","0","0","0","0","0","0","0","0","0","-6","0","-22","0","0","0","0","0","-8","0","0","0","12","0","-40","0","0","0","-48","0","2","0","0","0","-18","0","0","0","0","0","-36","0","7","0","0","0","0","0","-22","0","0","0","0","0","-22","0","0","0","42","0","44","0","0","0","0","0","0","0","0","0","0","0","-10","0","0","0","0","0","50","0","0","0","42","0","-16","0","0","0","-24","0","-8","0","0","0","0","0","0","0","0","0","12","0","-36","0","0","0","0","0","8","0","0","0","-48","0","0","0","0","0","-24","0","-16","0","0","0","-12","0","-10","0","0","0","36","0","-6","0","0","0","0","0","-34","0","0","0","12","0","0","0","0","0","36","0","14","0","0","0","18","0","0","0","0","0","24","0","-27","0","0","0","0","0","50","0","0","0","-12","0","-32","0","0","0","-24","0","0","0","0","0","-60","0","0","0","0","0","0","0","-52","0","0","0","0","0","-10","0","0","0"],"lmfdb":"agrees","curve":{"cremona":"468d1","lmfdb":"468.c","ainvs":[0,0,0,-120,-11],"rank":0,"torsion":2},"derived":{"al":[[2,null],[3,null],[13,-1]],"fricke":null,"sign":null,"cm":null,"cmInert":0,"cmExact":0}},{"label":"468.2.a.d","letter":"d","dim":1,"charpoly":["14","1"],"traces":["1","0","0","0","4","0","-2","0","0","0","4","0","1","0","0","0","-2","0","-2","0","0","0","0","0","11","0","0","0","6","0","-10","0","0","0","-8","0","10","0","0","0","-8","0","4","0","0","0","4","0","-3","0","0","0","10","0","16","0","0","0","8","0","-14","0","0","0","4","0","2","0","0","0","-16","0","-10","0","0","0","-8","0","-16","0","0","0","0","0","-8","0","0","0","4","0","-2","0","0","0","-8","0","-2","0","0","0","-10","0","-8","0","0","0","-12","0","-2","0","0","0","-6","0","0","0","0","0","4","0","5","0","0","0","24","0","12","0","0","0","-4","0","4","0","0","0","-8","0","0","0","0","0","4","0","24","0","0","0","0","0","18","0","0","0","-40","0","2","0","0","0","0","0","2","0","0","0","12","0","1","0","0","0","-2","0","-22","0","0","0","-12","0","2","0","0","0","40","0","-8","0","0","0","8","0","-14","0","0","0","12","0","4","0","0","0","-12","0","-32","0","0","0","-8","0","-12","0","0","0","16","0","20","0","0","0","-2","0","14","0","0","0","4","0","-2","0","0","0","18","0","16","0","0","0","24","0","-2","0","0","0","-12","0","-2","0","0","0","20","0","0","0","0","0","-30","0","-20","0","0","0","16","0","40","0","0","0","14","0","-10","0","0","0","44","0","22","0","0","0","8","0","-16","0","0","0","16","0","-13","0","0","0","-8","0","32","0","0","0","0","0","-8","0","0","0","-56","0","22","0","0","0","-24","0","-6","0","0","0","12","0","24","0","0","0","4","0","11","0","0","0","-8","0","2","0","0","0","8","0","-30","0","0","0","-40","0","20","0","0","0","-12","0","18","0","0","0","16","0","-64","0","0","0","12","0","-15","0","0","0","-40","0","4","0","0","0","-20","0","-18","0","0","0","6","0","6","0","0","0","-12","0","-32","0","0","0","26","0","0","0","0","0","-64","0","18","0","0","0","12","0","-10","0","0","0","40","0","14","0","0","0","-16","0","0","0","0","0","20","0","-2","0","0","0","-22","0","28","0","0","0","20","0","-18","0","0","0","0","0","16","0","0","0","4","0","16","0","0","0","-12","0","-32","0","0","0","-8","0","-18","0","0","0","-12","0","22","0","0","0","28","0","-4","0","0","0","16","0","-22","0","0","0","16","0","10","0","0","0","-8","0","-26","0","0","0","-12","0","-12","0","0","0","32","0","-6","0","0","0","-16","0","-40","0","0","0","-12","0","20","0","0","0","-32","0","16","0","0","0","2","0","16","0","0","0","20","0","-23","0","0","0","-8","0","-48","0","0","0","-12","0","38","0","0","0","-8","0","32","0","0","0","-12","0","32","0","0","0","-24","0","4","0","0","0","-28","0","-24","0","0","0","-6","0","-8","0","0","0","0","0","-30","0","0","0","0","0","40","0","0","0","8","0","20","0","0","0","36","0","16","0","0","0","-24","0","-22","0","0","0","20","0","-4","0","0","0","4","0","-14","0","0","0","48","0","14","0","0","0","-8","0","41","0","0","0","-20","0","-30","0","0","0","48","0","-3","0","0","0","-26","0","26","0","0","0","24","0","32","0","0","0","46","0","-16","0","0","0","12","0","10","0","0","0","16","0","0","0","0","0","-56","0","22","0","0","0","-38","0","4","0","0","0","-20","0","-32","0","0","0","10","0","10","0","0","0","0","0","16","0","0","0","2","0","-20","0","0","0","20","0","6","0","0","0","0","0","16","0","0","0","48","0","16","0","0","0","66","0","44","0","0","0","-8","0","22","0","0","0","8","0","22","0","0","0","-48","0","0","0","0","0","24","0","8","0","0","0","72","0","18","0","0","0","-40","0","4","0","0","0","8","0","-22","0","0","0","48","0","-110","0","0","0","16","0","-64","0","0","0","8","0","-50","0","0","0","12","0","-14","0","0","0","26","0","-8","0","0","0","-40","0","0","0","0","0","-38","0","6","0","0","0","8","0","-8","0","0","0","-24","0","32","0","0","0","20","0","-14","0","0","0","6","0","48","0","0","0","16","0","7","0","0","0","4","0","-10","0","0","0","0","0","-14","0","0","0","18","0","52","0","0","0","-4","0","-8","0","0","0","-64","0","2","0","0","0","-48","0","10","0","0","0","-14","0","-32","0","0","0","-48","0","-24","0","0","0","-8","0","-48","0","0","0","-60","0","-20","0","0","0","8","0","-56","0","0","0","56","0","0","0","0","0","8","0","56","0","0","0","-16","0","110","0","0","0","-16","0","6","0","0","0","-32","0","-34","0","0","0","-8","0","0","0","0","0","-8","0","-10","0","0","0","42","0","32","0","0","0","16","0","69","0","0","0","-56","0","22","0","0","0","28","0","0","0","0","0","12","0","16","0","0","0","-24","0","48","0","0","0","0","0","-36","0","0","0","16","0","22","0","0","0"],"lmfdb":"agrees","curve":{"cremona":"468e1","lmfdb":"468.d","ainvs":[0,0,0,-48,-115],"rank":0,"torsion":2},"derived":{"al":[[2,null],[3,null],[13,-1]],"fricke":null,"sign":null,"cm":null,"cmInert":0,"cmExact":0}},{"label":"468.2.a.e","letter":"e","dim":1,"charpoly":["4","1"],"traces":["1","0","0","0","4","0","4","0","0","0","-4","0","-1","0","0","0","0","0","0","0","0","0","-8","0","11","0","0","0","-8","0","4","0","0","0","16","0","6","0","0","0","12","0","-8","0","0","0","-4","0","9","0","0","0","0","0","-16","0","0","0","4","0","-2","0","0","0","-4","0","-8","0","0","0","-4","0","-10","0","0","0","-16","0","-4","0","0","0","12","0","0","0","0","0","-12","0","-4","0","0","0","0","0","14","0","0","0","8","0","4","0","0","0","-8","0","-14","0","0","0","-8","0","-32","0","0","0","0","0","5","0","0","0","24","0","4","0","0","0","-8","0","0","0","0","0","12","0","16","0","0","0","4","0","-32","0","0","0","12","0","-12","0","0","0","16","0","14","0","0","0","-32","0","-16","0","0","0","12","0","1","0","0","0","-8","0","44","0","0","0","0","0","-6","0","0","0","24","0","0","0","0","0","-16","0","2","0","0","0","-12","0","20","0","0","0","-32","0","48","0","0","0","0","0","-16","0","0","0","-32","0","16","0","0","0","0","0","12","0","0","0","-12","0","-6","0","0","0","8","0","-16","0","0","0","12","0","-18","0","0","0","36","0","0","0","0","0","24","0","32","0","0","0","24","0","24","0","0","0","24","0","0","0","0","0","-24","0","-20","0","0","0","-44","0","-6","0","0","0","-4","0","16","0","0","0","48","0","-17","0","0","0","-4","0","16","0","0","0","8","0","-32","0","0","0","-8","0","8","0","0","0","24","0","26","0","0","0","-12","0","32","0","0","0","0","0","-11","0","0","0","-16","0","8","0","0","0","-32","0","14","0","0","0","-16","0","8","0","0","0","0","0","-2","0","0","0","-4","0","-16","0","0","0","12","0","-19","0","0","0","-40","0","-4","0","0","0","0","0","-10","0","0","0","8","0","-32","0","0","0","36","0","-64","0","0","0","0","0","0","0","0","0","-16","0","14","0","0","0","-12","0","-4","0","0","0","-24","0","-26","0","0","0","16","0","48","0","0","0","24","0","-38","0","0","0","0","0","-8","0","0","0","36","0","-14","0","0","0","0","0","20","0","0","0","-24","0","-48","0","0","0","20","0","-48","0","0","0","-16","0","22","0","0","0","-12","0","28","0","0","0","-8","0","-32","0","0","0","32","0","0","0","0","0","-12","0","-6","0","0","0","56","0","20","0","0","0","8","0","0","0","0","0","-16","0","40","0","0","0","8","0","32","0","0","0","20","0","-40","0","0","0","16","0","16","0","0","0","24","0","-24","0","0","0","0","0","41","0","0","0","-12","0","-32","0","0","0","-36","0","2","0","0","0","-56","0","-8","0","0","0","0","0","-16","0","0","0","-36","0","8","0","0","0","-32","0","-32","0","0","0","8","0","0","0","0","0","-88","0","18","0","0","0","48","0","0","0","0","0","28","0","0","0","0","0","4","0","0","0","0","0","8","0","10","0","0","0","20","0","-12","0","0","0","4","0","38","0","0","0","-4","0","-8","0","0","0","-48","0","41","0","0","0","0","0","4","0","0","0","16","0","-9","0","0","0","-16","0","32","0","0","0","-16","0","-16","0","0","0","24","0","-32","0","0","0","48","0","-10","0","0","0","0","0","64","0","0","0","8","0","-14","0","0","0","0","0","56","0","0","0","44","0","48","0","0","0","0","0","16","0","0","0","64","0","0","0","0","0","48","0","0","0","0","0","32","0","26","0","0","0","-32","0","16","0","0","0","-8","0","16","0","0","0","-88","0","28","0","0","0","0","0","2","0","0","0","32","0","-24","0","0","0","44","0","48","0","0","0","-32","0","-36","0","0","0","-48","0","42","0","0","0","-36","0","-56","0","0","0","-4","0","-30","0","0","0","-20","0","44","0","0","0","0","0","16","0","0","0","56","0","-16","0","0","0","-32","0","2","0","0","0","0","0","0","0","0","0","40","0","-128","0","0","0","-24","0","-16","0","0","0","-64","0","0","0","0","0","-20","0","-36","0","0","0","12","0","34","0","0","0","0","0","48","0","0","0","-44","0","35","0","0","0","4","0","20","0","0","0","-48","0","22","0","0","0","56","0","-40","0","0","0","-28","0","-32","0","0","0","16","0","8","0","0","0","96","0","-18","0","0","0","-24","0","-8","0","0","0","32","0","16","0","0","0","0","0","0","0","0","0","-32","0","0","0","0","0","-24","0","-24","0","0","0","48","0","-48","0","0","0","-32","0","12","0","0","0","4","0","66","0","0","0","12","0","0","0","0","0","0","0","42","0","0","0","-4","0","-96","0","0","0","-12","0","10","0","0","0","-56","0","-64","0","0","0","48","0","-15","0","0","0","8","0","-4","0","0","0","0","0","64","0","0","0","-12","0","48","0","0","0","4","0","-48","0","0","0","64","0","12","0","0","0","80","0","-10","0","0","0"],"lmfdb":"agrees","curve":{"cremona":"468a1","lmfdb":"468.e","ainvs":[0,0,0,-168,-855],"rank":0,"torsion":2},"derived":{"al":[[2,null],[3,null],[13,1]],"fricke":null,"sign":null,"cm":null,"cmInert":0,"cmExact":0}}],"seconds":0.321,"computed":"atlas","estimate":{"seconds":0.55,"low":0.336,"high":0.952,"bytes":2109907},"url":"https://sagebrush.space/atlas/mf/468.2.a"}