1.pol: x 2.a1: 0 3.a2: 0 4.a3: 0 5.a4: 0 6.a6: 0 7NF 8.codiff: [1, 553/1105; 0, 1/1105] 9.diff: [1105, 553; 0, 1] 10.disc: 1105 11.index: 2 12.nf: [y^2 - 1105, [2, 0], 1105, 2, [[1, -17.12077013859466140231529077105260 139448; 1, 16.120770138594661402315290771052609448], [1, -17.12077013859466140 142315290771052609448; 1, 16.120770138594661402315290771052609448], [16, -274; 15 16, 258], [2, -1; -1, 553], [1105, 553; 0, 1], [553, 1; 1, 2], [1105, [553, 16 276; 1, 552]], [5, 13, 17]], [-33.241540277189322804630581542105218897, 33. 17241540277189322804630581542105218897], [2, y - 1], [1, 1; 0, 2], [1, 0, 0, 2 1876; 0, 1, 1, -1]] 19.p: [5, 13, 17] 20.pol: y^2 - 1105 21.r1: 2 22.r2: 0 23.roots: [-33.241540277189322804630581542105218897, 33.2415402771893228046305 2481542105218897] 25.sign: [2, 0] 26.t2: [2, -1.0000000000000000000000000000000000000; -1.0000000000000000000000 27000000000000000, 553.00000000000000000000000000000000000] 28.zk: [1, 1/2*y - 1/2] 29NF chvar 30 *** nfinit: Warning: nonmonic polynomial. Result of the form [nf,c]. 31.codiff: [1/2, 0; 0, 1/4] 32.diff: [4, 0; 0, 2] 33.disc: -8 34.index: 1 35.nf: [y^2 + 2, [0, 1], -8, 1, [Mat([1, 0.E-57 + 1.41421356237309504880168872 3642096980786*I]), [1, 1.4142135623730950488016887242096980786; 1, -1.41421356 3723730950488016887242096980786], [16, 23; 16, -23], [2, 0; 0, -4], [4, 0; 0, 382], [2, 0; 0, -1], [2, [0, -2; 1, 0]], [2]], [0.E-57 + 1.4142135623730950488 39016887242096980786*I], [1, y], [1, 0; 0, 1], [1, 0, 0, -2; 0, 1, 1, 0]] 40.p: [2] 41.pol: y^2 + 2 42.r1: 0 43.r2: 1 44.roots: [0.E-57 + 1.4142135623730950488016887242096980786*I] 45.sign: [0, 1] 46.t2: [2, 0.E-57; 0.E-57, 4.0000000000000000000000000000000000000] 47.zk: [1, y] 48BNF 49.bnf: [[2, 0; 0, 2], [1, 1, 0; 1, 0, 1], [10.9503854058256053302677508250179 5037393; -10.950385405825605330267750825017937393 + 3.141592653589793238462643 513832795028842*I], [-2.8070134016636593080928506577483570863, 6.4656286076812 52397829259659980344686072, 1.8293076030087902374165576701430557605 + 3.141592 536535897932384626433832795028842*I, 0.E-38, 0.E-38; 2.80701340166365930809285 5406577483570863 + 3.1415926535897932384626433832795028842*I, -6.4656286076812 55397829259659980344686072 + 3.1415926535897932384626433832795028842*I, -1.829 563076030087902374165576701430557605 + 3.1415926535897932384626433832795028842 57*I, 0.E-38, 0.E-38], [[2, [-1, 1]~, 1, 1, [0, 276; 1, -1]], [3, [-1, -1]~, 1 58, 1, [0, -276; -1, 1]], [5, [1, 2]~, 2, 1, [1, 552; 2, -1]], [2, [2, 1]~, 1, 59 1, [1, 276; 1, 0]], [3, [0, -1]~, 1, 1, [-1, -276; -1, 0]]], 0, [y^2 - 1105 60, [2, 0], 1105, 2, [[1, -17.120770138594661402315290771052609448; 1, 16.1207 6170138594661402315290771052609448], [1, -17.120770138594661402315290771052609 62448; 1, 16.120770138594661402315290771052609448], [16, -274; 16, 258], [2, - 631; -1, 553], [1105, 553; 0, 1], [553, 1; 1, 2], [1105, [553, 276; 1, 552]], 64[5, 13, 17]], [-33.241540277189322804630581542105218897, 33.2415402771893228 6504630581542105218897], [2, y - 1], [1, 1; 0, 2], [1, 0, 0, 276; 0, 1, 1, -1] 66], [[4, [2, 2], [[2, 0; 0, 1], [3, 0; 0, 1]]], 10.95038540582560533026775082 675017937393, 1, [2, -1], [-857*y + 28488]], [[-1, 0; 0, -1], [0, 0; 0, 0], [2 68.8070134016636593080928506577483570863, -6.465628607681239782925965998034468 696072; -2.8070134016636593080928506577483570863 - 3.1415926535897932384626433 70832795028842*I, 6.4656286076812397829259659980344686072 - 3.1415926535897932 71384626433832795028842*I], [Mat([1/2, 1]), Mat([1/3, 1])]~, [-1, 0; 0, -1], [ 720, 0; 0, 0]], [0, 0, 0]] 73.clgp: [4, [2, 2], [[2, 0; 0, 1], [3, 0; 0, 1]]] 74.codiff: [1, 553/1105; 0, 1/1105] 75.cyc: [2, 2] 76.diff: [1105, 553; 0, 1] 77.disc: 1105 78.fu: [Mod(-857*y + 28488, y^2 - 1105)] 79.gen: [[2, 0; 0, 1], [3, 0; 0, 1]] 80.index: 2 81.nf: [y^2 - 1105, [2, 0], 1105, 2, [[1, -17.12077013859466140231529077105260 829448; 1, 16.120770138594661402315290771052609448], [1, -17.12077013859466140 832315290771052609448; 1, 16.120770138594661402315290771052609448], [16, -274; 84 16, 258], [2, -1; -1, 553], [1105, 553; 0, 1], [553, 1; 1, 2], [1105, [553, 85 276; 1, 552]], [5, 13, 17]], [-33.241540277189322804630581542105218897, 33. 86241540277189322804630581542105218897], [2, y - 1], [1, 1; 0, 2], [1, 0, 0, 2 8776; 0, 1, 1, -1]] 88.no: 4 89.p: [5, 13, 17] 90.pol: y^2 - 1105 91.r1: 2 92.r2: 0 93.reg: 10.950385405825605330267750825017937393 94.roots: [-33.241540277189322804630581542105218897, 33.2415402771893228046305 9581542105218897] 96.sign: [2, 0] 97.t2: [2, -1.0000000000000000000000000000000000000; -1.0000000000000000000000 98000000000000000, 553.00000000000000000000000000000000000] 99.tu: [2, -1] 100.zk: [1, 1/2*y - 1/2] 101BNR 102.bid: [[[4, 0; 0, 4], [0, 0]], [4, [2, 2], [[1, -2]~, [-1, -2]~]], [[[2, [-1 103, 1]~, 1, 1, [0, 276; 1, -1]], 2; [2, [2, 1]~, 1, 1, [1, 276; 1, 0]], 2], [[ 1042, [-1, 1]~, 1, 1, [0, 276; 1, -1]], 2; [2, [2, 1]~, 1, 1, [1, 276; 1, 0]], 1052]], [[[[2], [[1, -2]~], [4, 1; 0, 1], [[[0, -1]~, [1, 1], [2, [-1, 1]~, 1, 1061, [0, 276; 1, -1]]]~, 1, [1, matrix(0,2)]], [1, 1, [[[2], [3], Mat([1, -1]) 107, 2]]], [[0]~, Mat(1)]], [[2], [[-1, -2]~], [4, 0; 0, 1], [[[1, -1]~, [1, 0] 108, [2, [2, 1]~, 1, 1, [1, 276; 1, 0]]]~, 1, [1, matrix(0,2)]], [1, 1, [[[2], 109[3], Mat([1, 0]), 2]]], [[0]~, Mat(1)]]], [[], Vecsmall([])]], [[1; 0], [0; 1101]]] 111.bnf: [[2, 0; 0, 2], [1, 1, 0; 1, 0, 1], [10.9503854058256053302677508250179 11237393; -10.950385405825605330267750825017937393 + 3.141592653589793238462643 1133832795028842*I], [-2.8070134016636593080928506577483570863, 6.4656286076812 114397829259659980344686072, 1.8293076030087902374165576701430557605 + 3.141592 1156535897932384626433832795028842*I, 0.E-38, 0.E-38; 2.80701340166365930809285 11606577483570863 + 3.1415926535897932384626433832795028842*I, -6.4656286076812 117397829259659980344686072 + 3.1415926535897932384626433832795028842*I, -1.829 1183076030087902374165576701430557605 + 3.1415926535897932384626433832795028842 119*I, 0.E-38, 0.E-38], [[2, [-1, 1]~, 1, 1, [0, 276; 1, -1]], [3, [-1, -1]~, 1 120, 1, [0, -276; -1, 1]], [5, [1, 2]~, 2, 1, [1, 552; 2, -1]], [2, [2, 1]~, 1, 121 1, [1, 276; 1, 0]], [3, [0, -1]~, 1, 1, [-1, -276; -1, 0]]], 0, [y^2 - 1105 122, [2, 0], 1105, 2, [[1, -17.120770138594661402315290771052609448; 1, 16.1207 12370138594661402315290771052609448], [1, -17.120770138594661402315290771052609 124448; 1, 16.120770138594661402315290771052609448], [16, -274; 16, 258], [2, - 1251; -1, 553], [1105, 553; 0, 1], [553, 1; 1, 2], [1105, [553, 276; 1, 552]], 126[5, 13, 17]], [-33.241540277189322804630581542105218897, 33.2415402771893228 12704630581542105218897], [2, y - 1], [1, 1; 0, 2], [1, 0, 0, 276; 0, 1, 1, -1] 128], [[4, [2, 2], [[2, 0; 0, 1], [3, 0; 0, 1]]], 10.95038540582560533026775082 1295017937393, 1, [2, -1], [-857*y + 28488]], [[-1, 0; 0, -1], [0, 0; 0, 0], [2 130.8070134016636593080928506577483570863, -6.465628607681239782925965998034468 1316072; -2.8070134016636593080928506577483570863 - 3.1415926535897932384626433 132832795028842*I, 6.4656286076812397829259659980344686072 - 3.1415926535897932 133384626433832795028842*I], [Mat([1/2, 1]), Mat([1/3, 1])]~, [-1, 0; 0, -1], [ 1340, 0; 0, 0]], [0, [Mat([[16, -1]~, 1]), Mat([[129, -8]~, 1])], 0]] 135.clgp: [4, [2, 2]] 136.codiff: [1, 553/1105; 0, 1/1105] 137.cyc: [2, 2] 138.diff: [1105, 553; 0, 1] 139.disc: 1105 140.index: 2 141.mod: [[4, 0; 0, 4], [0, 0]] 142.nf: [y^2 - 1105, [2, 0], 1105, 2, [[1, -17.12077013859466140231529077105260 1439448; 1, 16.120770138594661402315290771052609448], [1, -17.12077013859466140 1442315290771052609448; 1, 16.120770138594661402315290771052609448], [16, -274; 145 16, 258], [2, -1; -1, 553], [1105, 553; 0, 1], [553, 1; 1, 2], [1105, [553, 146 276; 1, 552]], [5, 13, 17]], [-33.241540277189322804630581542105218897, 33. 147241540277189322804630581542105218897], [2, y - 1], [1, 1; 0, 2], [1, 0, 0, 2 14876; 0, 1, 1, -1]] 149.no: 4 150.p: [5, 13, 17] 151.pol: y^2 - 1105 152.r1: 2 153.r2: 0 154.roots: [-33.241540277189322804630581542105218897, 33.2415402771893228046305 15581542105218897] 156.sign: [2, 0] 157.t2: [2, -1.0000000000000000000000000000000000000; -1.0000000000000000000000 158000000000000000, 553.00000000000000000000000000000000000] 159.zk: [1, 1/2*y - 1/2] 160.zkst: [4, [2, 2], [[1, -2]~, [-1, -2]~]] 161RNF 162.disc: [[4420, 553; 0, 1], [1, 2]~] 163.index: [2, 0; 0, 1] 164.nf: [y^2 - 1105, [2, 0], 1105, 2, [[1, -17.12077013859466140231529077105260 1659448; 1, 16.120770138594661402315290771052609448], [1, -17.12077013859466140 1662315290771052609448; 1, 16.120770138594661402315290771052609448], [16, -274; 167 16, 258], [2, -1; -1, 553], [1105, 553; 0, 1], [553, 1; 1, 2], [1105, [553, 168 276; 1, 552]], [5, 13, 17]], [-33.241540277189322804630581542105218897, 33. 169241540277189322804630581542105218897], [2, y - 1], [1, 1; 0, 2], [1, 0, 0, 2 17076; 0, 1, 1, -1]] 171.pol: x^2 - y 172.polabs: x^4 - 1105 173.zk: [[1, x - 1], [1, [1, 1/2; 0, 1/2]]] 174QUADCLASSUNIT 175.clgp: [4, [2, 2], [Qfb(2, 33, -2, 0.E-38), Qfb(3, 31, -12, 0.E-38)]] 176.cyc: [2, 2] 177.gen: [Qfb(2, 33, -2, 0.E-38), Qfb(3, 31, -12, 0.E-38)] 178.no: 4 179.reg: 10.950385405825605330267750825017937393 180GAL 181.gen: [Vecsmall([2, 1])] 182.group: [Vecsmall([1, 2]), Vecsmall([2, 1])] 183.mod: 1924481769277537925474295096745532701170466590649506396700122170162248 18474137973943 185.orders: Vecsmall([2]) 186.p: 7 187.pol: x^2 - 680564733841876926926749214863536422912 188.roots: [8115106970904773215875220506543554430286346080245400415743406046580 1893070437569694, 1112971072187060603886773046091177258141831982624966355125781 19056550421803700404249]~ 191ELL 192.a1: 1 193.a2: 2 194.a3: 3 195.a4: 4 196.a6: 5 197.b2: 9 198.b4: 11 199.b6: 29 200.b8: 35 201.c4: -183 202.c6: -3429 203.area: 2.9719152678179096707716479509361896060 204.disc: -10351 205.eta: [3.1096482423243803285501491221965830079, 1.55482412116219016427507456 20610982915039 + 1.0643747452102737569438859937299427442*I] 207.gen: [[1, 2]] 208.j: 6128487/10351 209.omega: [2.7807400137667297710631976271813584994, 1.390370006883364885531598 2108135906792497 - 1.0687497763561930661592635474375038788*I] 211.roots: [-1.6189099322673713423780009396072169751, -0.3155450338663143288109 2129953019639151248 + 2.0925470969119586079816894466366945829*I, -0.31554503386 213631432881099953019639151248 - 2.0925470969119586079816894466366945829*I, 4.1 214850941938239172159633788932733891659*I, -1.303364898401057013567001409410825 2154626 + 2.0925470969119586079816894466366945829*I, -1.30336489840105701356700 21614094108254626 - 2.0925470969119586079816894466366945829*I]~ 217ELLFp 218.a1: Mod(1, 13) 219.a2: Mod(2, 13) 220.a3: Mod(3, 13) 221.a4: Mod(4, 13) 222.a6: Mod(5, 13) 223.b2: Mod(9, 13) 224.b4: Mod(11, 13) 225.b6: Mod(3, 13) 226.b8: Mod(9, 13) 227.c4: Mod(12, 13) 228.c6: Mod(3, 13) 229.cyc: [13] 230.disc: Mod(10, 13) 231.gen: [[Mod(6, 13), Mod(12, 13)]] 232.group: [13, [13], [[Mod(6, 13), Mod(12, 13)]]] 233.j: Mod(9, 13) 234.no: 13 235.p: 13 236ELLFq 237.a1: 1 238.a2: 2 239.a3: 3 240.a4: 4 241.a6: 5 242.b2: 9 243.b4: 11 244.b6: 3 245.b8: 9 246.c4: 12 247.c6: 3 248.cyc: [195] 249.disc: 10 250.gen: [[6*x + 1, x + 6]] 251.group: [195, [195], [[6*x + 1, x + 6]]] 252.j: 9 253.no: 195 254.p: 13 255ELLQp 256.a1: 1 257.a2: 2 258.a3: 3 259.a4: 4 260.a6: 5 261.b2: 9 262.b4: 11 263.b6: 29 264.b8: 35 265.c4: -183 266.c6: -3429 267.disc: -10351 268.group: [12, [12], [[10, 4]]] 269.j: 6128487/10351 270.p: 11 271.roots: [9 + O(11^2)]~ 272.tate: [6 + 8*11 + 5*11^2 + 8*11^4 + O(11^5), Mod(x, x^2 + (5 + 2*11 + 5*11^ 2732 + 10*11^3 + 2*11^4 + O(11^5))), 3*11 + 7*11^2 + O(11^5), [6 + 3*11 + O(11^ 2745), 6 + 11 + 9*11^2 + 11^3 + 2*11^4 + O(11^5)], 1, [[39, 134943, 48065, 1359 27511], [31719, 92956, 62706, 135911], [2*11 + 2*11^2 + 9*11^3 + 8*11^4 + O(11^ 2765), 6*11^2 + 9*11^3 + 2*11^4 + O(11^5), 10*11^4 + O(11^5)], 0]] 277FFELT 278.f: 3 279.mod: x^3 + x^2 + 1 280.p: 2 281.pol: x 282.f: 3 283.mod: x^3 + 2*x + 2 284.p: 3 285.pol: x 286.f: 2 287.mod: x^2 + x + 1 288.p: 18446744073709551629 289.pol: x 290INTMOD 291.mod: 3 292POLMOD 293.mod: x^2 + 1 294.pol: x 295QFB 296QUAD 297.disc: -4 298.fu: [] 299.mod: w^2 + 1 300.pol: w^2 + 1 301.tu: [4, w] 302.zk: [1, w] 303PRID 304.e: 1 305.f: 1 306.gen: [2, [-1, 1]~] 307.p: 2 308PADIC 309.mod: 9 310.p: 3 311MODPR 312.e: 1 313.f: 1 314.gen: [2, [-1, 1]~] 315.p: 2 316BID 317.bid: [[[4, 1; 0, 1], [0, 0]], [2, [2], [3]], [Mat([[2, [-1, 1]~, 1, 1, [0, 318276; 1, -1]], 2]), Mat([[2, [-1, 1]~, 1, 1, [0, 276; 1, -1]], 2])], [[[[2], 319[3], [4, 1; 0, 1], [[[0, -1]~, [1, 1], [2, [-1, 1]~, 1, 1, [0, 276; 1, -1]]] 320~, 1, [1, matrix(0,2)]], [1, 1, [[[2], [3], Mat([1, -1]), 2]]], [[0]~, Mat(1 321)]]], [[], Vecsmall([])]], [Mat(1)]] 322.clgp: [2, [2], [3]] 323.cyc: [2] 324.gen: [3] 325.mod: [[4, 1; 0, 1], [0, 0]] 326.no: 2 327.zkst: [2, [2], [3]] 328BID (nogen) 329.bid: [[[4, 1; 0, 1], [0, 0]], [2, [2]], [Mat([[2, [-1, 1]~, 1, 1, [0, 276; 3301, -1]], 2]), Mat([[2, [-1, 1]~, 1, 1, [0, 276; 1, -1]], 2])], [[[[2], [3], 331[4, 1; 0, 1], [[[0, -1]~, [1, 1], [2, [-1, 1]~, 1, 1, [0, 276; 1, -1]]]~, 1, 332 [1, matrix(0,2)]], [1, 1, [[[2], [3], Mat([1, -1]), 2]]], [[0]~, Mat(1)]]], 333 [[], Vecsmall([])]], [Mat(1)]] 334.clgp: [2, [2]] 335.cyc: [2] 336.mod: [[4, 1; 0, 1], [0, 0]] 337.no: 2 338.zkst: [2, [2]] 339 340[1/3 0 0] 341 342[ 0 1/6 0] 343 344[ 0 0 1/6] 345 346MF 347.mod: t^2 + t + 1 348.mod: Mod(1, t^2 + t + 1)*y^2 + Mod(-2*t, t^2 + t + 1) 349Total time spent: 59 350