Number field search results

Results (1-50 of 349 matches)

 

Label	Polynomial	Degree	Signature	Discriminant	Ram. prime count	Root discriminant	CM field	Galois	Monogenic	Galois group	Class group	Unit group torsion	Unit group rank	Regulator
44.0.488...561.1	x^44 - x^43 + x^41 - x^40 + x^38 - x^37 + x^35 - x^34 + x^32 - x^31 + x^29 - x^28 + x^26 - x^25 + x^23 - x^22 + x^21 - x^19 + x^18 - x^16 + x^15 - x^13 + x^12 - x^10 + x^9 - x^7 + x^6 - x^4 + x^3 - x + 1	$44$	[0,22]	$3^{22}\cdot 23^{42}$	$2$	$34.5455207339$	✓	✓	✓	$C_2\times C_{22}$ (as 44T2)	$[69]$	$138$	$21$	$5770465240890302.0$
44.0.274...664.1	x^44 - x^42 + x^40 - x^38 + x^36 - x^34 + x^32 - x^30 + x^28 - x^26 + x^24 - x^22 + x^20 - x^18 + x^16 - x^14 + x^12 - x^10 + x^8 - x^6 + x^4 - x^2 + 1	$44$	[0,22]	$2^{44}\cdot 23^{42}$	$2$	$39.8897313901$	✓	✓	✓	$C_2\times C_{22}$ (as 44T2)	$[201]$	$92$	$21$	$23864585134104340$
44.0.178...352.1	x^44 - 3x^22 + 3	$44$	[0,22]	$2^{44}\cdot 3^{43}\cdot 11^{36}$	$3$	$41.6251820652$			not computed	$C_{11}:(C_{10}\times D_4)$ (as 44T32)	not computed	$6$	$21$	$$
44.2.206...803.1	x^44 - x - 1	$44$	[2,21]	$-\,1752761753\cdot 4199398081\cdot 12798563620399\cdot 21\!\cdots\!29$	$4$	$44.0084224293$			✓	$S_{44}$ (as 44T2113)	not computed	$2$	$22$	$$
44.0.371...625.1	x^44 - x^43 + 2x^42 - 3x^41 + 5x^40 - 8x^39 + 13x^38 - 21x^37 + 34x^36 - 55x^35 + 89x^34 - 144x^33 + 233x^32 - 377x^31 + 610x^30 - 987x^29 + 1597x^28 - 2584x^27 + 4181x^26 - 6765x^25 + 10946x^24 - 17711x^23 + 28657x^22 + 17711x^21 + 10946x^20 + 6765x^19 + 4181x^18 + 2584x^17 + 1597x^16 + 987x^15 + 610x^14 + 377x^13 + 233x^12 + 144x^11 + 89x^10 + 55x^9 + 34x^8 + 21x^7 + 13x^6 + 8x^5 + 5x^4 + 3x^3 + 2x^2 + x + 1	$44$	[0,22]	$5^{22}\cdot 23^{42}$	$2$	$44.5980754962$	✓	✓	not computed	$C_2\times C_{22}$ (as 44T2)	not computed	$46$	$21$	$$
44.0.609...321.1	x^44 - x^43 - x^42 + 3x^41 - x^40 - 5x^39 + 7x^38 + 3x^37 - 17x^36 + 11x^35 + 23x^34 - 45x^33 - x^32 + 91x^31 - 89x^30 - 93x^29 + 271x^28 - 85x^27 - 457x^26 + 627x^25 + 287x^24 - 1541x^23 + 967x^22 - 3082x^21 + 1148x^20 + 5016x^19 - 7312x^18 - 2720x^17 + 17344x^16 - 11904x^15 - 22784x^14 + 46592x^13 - 1024x^12 - 92160x^11 + 94208x^10 + 90112x^9 - 278528x^8 + 98304x^7 + 458752x^6 - 655360x^5 - 262144x^4 + 1572864x^3 - 1048576x^2 - 2097152x + 4194304	$44$	[0,22]	$7^{22}\cdot 23^{42}$	$2$	$52.7691545617$	✓	✓	not computed	$C_2\times C_{22}$ (as 44T2)	not computed	$46$	$21$	$$
44.0.114...856.1	x^44 - 2x^42 + 4x^40 - 8x^38 + 16x^36 - 32x^34 + 64x^32 - 128x^30 + 256x^28 - 512x^26 + 1024x^24 - 2048x^22 + 4096x^20 - 8192x^18 + 16384x^16 - 32768x^14 + 65536x^12 - 131072x^10 + 262144x^8 - 524288x^6 + 1048576x^4 - 2097152x^2 + 4194304	$44$	[0,22]	$2^{66}\cdot 23^{42}$	$2$	$56.4125991313$	✓	✓	not computed	$C_2\times C_{22}$ (as 44T2)	not computed	$46$	$21$	$$
44.0.114...856.2	x^44 + 2x^42 + 4x^40 + 8x^38 + 16x^36 + 32x^34 + 64x^32 + 128x^30 + 256x^28 + 512x^26 + 1024x^24 + 2048x^22 + 4096x^20 + 8192x^18 + 16384x^16 + 32768x^14 + 65536x^12 + 131072x^10 + 262144x^8 + 524288x^6 + 1048576x^4 + 2097152x^2 + 4194304	$44$	[0,22]	$2^{66}\cdot 23^{42}$	$2$	$56.4125991313$	✓	✓	not computed	$C_2\times C_{22}$ (as 44T2)	not computed	$46$	$21$	$$
44.0.342...125.1	x^44 - x^43 + 11x^42 - 12x^41 + 77x^40 - 74x^39 + 424x^38 - 368x^37 + 2052x^36 - 1675x^35 + 8154x^34 - 6259x^33 + 27860x^32 - 18614x^31 + 82991x^30 - 50150x^29 + 218995x^28 - 122605x^27 + 487495x^26 - 239465x^25 + 942321x^24 - 367121x^23 + 1562162x^22 - 556097x^21 + 2230394x^20 - 742219x^19 + 2512113x^18 - 607127x^17 + 2369760x^16 - 263798x^15 + 1750478x^14 - 273124x^13 + 1076097x^12 - 237409x^11 + 402111x^10 - 41911x^9 + 123922x^8 + 19642x^7 + 17600x^6 + 1439x^5 + 2686x^4 - 361x^3 + 51x^2 - 6x + 1	$44$	[0,22]	$5^{33}\cdot 23^{40}$	$2$	$57.8311594663$	✓	✓	not computed	$C_{44}$ (as 44T1)	$[45013]$	$10$	$21$	$36326958556899850$
44.0.162...944.1	x^44 - 21x^42 + 251x^40 - 2052x^38 + 12691x^36 - 61778x^34 + 243629x^32 - 788303x^30 + 2113175x^28 - 4700059x^26 + 8677408x^24 - 13214290x^22 + 16492213x^20 - 16617826x^18 + 13339732x^16 - 8284333x^14 + 3900832x^12 - 1305733x^10 + 306592x^8 - 41184x^6 + 3641x^4 - 66x^2 + 1	$44$	[0,22]	$2^{44}\cdot 3^{22}\cdot 23^{40}$	$3$	$59.9135453394$	✓	✓	not computed	$C_2\times C_{22}$ (as 44T2)	not computed	$12$	$21$	$$
44.0.126...409.1	x^44 - x^43 - 2x^42 + 5x^41 + x^40 - 16x^39 + 13x^38 + 35x^37 - 74x^36 - 31x^35 + 253x^34 - 160x^33 - 599x^32 + 1079x^31 + 718x^30 - 3955x^29 + 1801x^28 + 10064x^27 - 15467x^26 - 14725x^25 + 61126x^24 - 16951x^23 - 166427x^22 - 50853x^21 + 550134x^20 - 397575x^19 - 1252827x^18 + 2445552x^17 + 1312929x^16 - 8649585x^15 + 4710798x^14 + 21237957x^13 - 35370351x^12 - 28343520x^11 + 134454573x^10 - 49424013x^9 - 353939706x^8 + 502211745x^7 + 559607373x^6 - 2066242608x^5 + 387420489x^4 + 5811307335x^3 - 6973568802x^2 - 10460353203x + 31381059609	$44$	[0,22]	$11^{22}\cdot 23^{42}$	$2$	$66.1496360045$	✓	✓	not computed	$C_2\times C_{22}$ (as 44T2)	not computed	$46$	$21$	$$
44.44.181...125.1	x^44 - x^43 - 44x^42 + 43x^41 + 902x^40 - 859x^39 - 11441x^38 + 10582x^37 + 100567x^36 - 89985x^35 - 650236x^34 + 560251x^33 + 3203650x^32 - 2643399x^31 - 12294569x^30 + 9651170x^29 + 37253225x^28 - 27602055x^27 - 89808680x^26 + 62206625x^25 + 172779011x^24 - 110572386x^23 - 265002643x^22 + 154430258x^21 + 322457859x^20 - 168027624x^19 - 308473797x^18 + 140446403x^17 + 228768475x^16 - 88323383x^15 - 128871012x^14 + 40552321x^13 + 53558102x^12 - 13016729x^11 - 15742859x^10 + 2742874x^9 + 3073662x^8 - 347233x^7 - 361455x^6 + 24089x^5 + 21786x^4 - 986x^3 - 504x^2 + 24x + 1	$44$	[44,0]	$5^{33}\cdot 23^{42}$	$2$	$66.6896778381$		✓	✓	$C_{44}$ (as 44T1)	trivial	$2$	$43$	$183282479706502550000000000$
44.0.220...625.1	x^44 - x^43 + 32x^42 - 21x^41 + 608x^40 - 302x^39 + 7441x^38 - 2334x^37 + 66293x^36 - 12644x^35 + 432280x^34 - 28161x^33 + 2141316x^32 + 33285x^31 + 8001765x^30 + 693375x^29 + 23077394x^28 + 2792911x^27 + 51292654x^26 + 7229970x^25 + 89635724x^24 + 12947356x^23 + 123068074x^22 + 17592284x^21 + 133953248x^20 + 17840654x^19 + 114270996x^18 + 13803865x^17 + 76240835x^16 + 7576064x^15 + 38619954x^14 + 2830121x^13 + 14698338x^12 + 489978x^11 + 3921204x^10 - 46901x^9 + 736586x^8 - 41505x^7 + 78482x^6 - 8849x^5 + 5761x^4 - 386x^3 + 117x^2 + 6x + 1	$44$	[0,22]	$3^{22}\cdot 5^{22}\cdot 23^{40}$	$3$	$66.985380076$	✓	✓	not computed	$C_2\times C_{22}$ (as 44T2)	not computed	$6$	$21$	$$
44.0.860...376.1	x^44 + 45x^42 + 944x^40 + 12258x^38 + 110332x^36 + 730456x^34 + 3683681x^32 + 14457937x^30 + 44741027x^28 + 109922933x^26 + 214871383x^24 + 333482657x^22 + 408408103x^20 + 390551177x^18 + 287137498x^16 + 158825372x^14 + 64156063x^12 + 18161627x^10 + 3397768x^8 + 384582x^6 + 22748x^4 + 528x^2 + 1	$44$	[0,22]	$2^{44}\cdot 3^{22}\cdot 23^{42}$	$3$	$69.0910414679$	✓	✓	✓	$C_2\times C_{22}$ (as 44T2)	not computed	$4$	$21$	$$
44.44.860...376.1	x^44 - 43x^42 + 860x^40 - 10622x^38 + 90724x^36 - 568616x^34 + 2708289x^32 - 10016751x^30 + 29148711x^28 - 67217827x^26 + 123140835x^24 - 178931535x^22 + 205096155x^20 - 183670815x^18 + 126676230x^16 - 65934180x^14 + 25178895x^12 - 6781005x^10 + 1216380x^8 - 133210x^6 + 7700x^4 - 176x^2 + 1	$44$	[44,0]	$2^{44}\cdot 3^{22}\cdot 23^{42}$	$3$	$69.0910414679$		✓	✓	$C_2\times C_{22}$ (as 44T2)	trivial	$2$	$43$	$396826934994876900000000000$
44.0.860...376.2	x^44 + 23x^42 + 299x^40 + 2668x^38 + 18055x^36 + 96646x^34 + 421245x^32 + 1516689x^30 + 4557519x^28 + 11467961x^26 + 24199128x^24 + 42662286x^22 + 62532561x^20 + 75392022x^18 + 73935156x^16 + 57768387x^14 + 35301228x^12 + 16195335x^10 + 5446584x^8 + 1210352x^6 + 180389x^4 + 11638x^2 + 529	$44$	[0,22]	$2^{44}\cdot 3^{22}\cdot 23^{42}$	$3$	$69.0910414679$	✓	✓	not computed	$C_2\times C_{22}$ (as 44T2)	not computed	$6$	$21$	$$
44.0.860...376.3	x^44 + 3x^42 + 9x^40 + 27x^38 + 81x^36 + 243x^34 + 729x^32 + 2187x^30 + 6561x^28 + 19683x^26 + 59049x^24 + 177147x^22 + 531441x^20 + 1594323x^18 + 4782969x^16 + 14348907x^14 + 43046721x^12 + 129140163x^10 + 387420489x^8 + 1162261467x^6 + 3486784401x^4 + 10460353203x^2 + 31381059609	$44$	[0,22]	$2^{44}\cdot 3^{22}\cdot 23^{42}$	$3$	$69.0910414679$	✓	✓	not computed	$C_2\times C_{22}$ (as 44T2)	not computed	$46$	$21$	$$
44.0.911...456.1	x^44 + 61x^40 + 1522x^36 + 20041x^32 + 150032x^28 + 642172x^24 + 1506232x^20 + 1760035x^16 + 860639x^12 + 127699x^8 + 2926x^4 + 1	$44$	[0,22]	$2^{88}\cdot 23^{40}$	$2$	$69.1822030597$	✓	✓	not computed	$C_2\times C_{22}$ (as 44T2)	not computed	$8$	$21$	$$
44.0.500...601.1	x^44 - x^43 + 4x^42 - 7x^41 + 19x^40 - 40x^39 + 97x^38 - 217x^37 + 508x^36 - 1159x^35 + 2683x^34 - 6160x^33 + 14209x^32 - 32689x^31 + 75316x^30 - 173383x^29 + 399331x^28 - 919480x^27 + 2117473x^26 - 4875913x^25 + 11228332x^24 - 25856071x^23 + 59541067x^22 + 77568213x^21 + 101054988x^20 + 131649651x^19 + 171515313x^18 + 223433640x^17 + 291112299x^16 + 379188621x^15 + 494148276x^14 + 643417587x^13 + 839027241x^12 + 1091225520x^11 + 1425856203x^10 + 1847820357x^9 + 2429748252x^8 + 3113712819x^7 + 4175531937x^6 + 5165606520x^5 + 7360989291x^4 + 8135830269x^3 + 13947137604x^2 + 10460353203x + 31381059609	$44$	[0,22]	$13^{22}\cdot 23^{42}$	$2$	$71.9122359457$	✓	✓	not computed	$C_2\times C_{22}$ (as 44T2)	not computed	$46$	$21$	$$
44.44.116...625.1	x^44 - x^43 - 67x^42 + 66x^41 + 2006x^40 - 1940x^39 - 35522x^38 + 33582x^37 + 415391x^36 - 381809x^35 - 3396482x^34 + 3014673x^33 + 20088042x^32 - 17073369x^31 - 87848856x^30 + 70775487x^29 + 288431096x^28 - 217655609x^27 - 718686410x^26 + 501030801x^25 + 1368730205x^24 - 867699404x^23 - 1999332041x^22 + 1131696716x^21 + 2238799988x^20 - 1107666220x^19 - 1911947202x^18 + 806431252x^17 + 1231950206x^16 - 430200535x^15 - 588270804x^14 + 164470157x^13 + 202516659x^12 - 43750410x^11 - 48240456x^10 + 7822102x^9 + 7480922x^8 - 908640x^7 - 688078x^6 + 65581x^5 + 31906x^4 - 2504x^3 - 504x^2 + 24x + 1	$44$	[44,0]	$3^{22}\cdot 5^{22}\cdot 23^{42}$	$3$	$77.2461326792$		✓	not computed	$C_2\times C_{22}$ (as 44T2)	trivial	$2$	$43$	$4751041378621857000000000000$
44.0.116...625.1	x^44 - x^43 + 43x^42 - 39x^41 + 856x^40 - 700x^39 + 10478x^38 - 7678x^37 + 88356x^36 - 57644x^35 + 545008x^34 - 314432x^33 + 2548537x^32 - 1290809x^31 + 9238279x^30 - 4075043x^29 + 26320891x^28 - 10020719x^27 + 59401115x^26 - 19318239x^25 + 106508095x^24 - 29235139x^23 + 151556799x^22 - 34552164x^21 + 170215728x^20 - 30533255x^19 + 148629623x^18 - 11758433x^17 + 94928616x^16 + 36112685x^15 + 30135721x^14 + 126072207x^13 - 23633656x^12 + 220881720x^11 - 44029406x^10 + 233441302x^9 - 35764283x^8 + 155778230x^7 - 8938748x^6 + 18093321x^5 + 18069001x^4 + 120313546x^3 - 192566274x^2 - 256263936x + 1026529561	$44$	[0,22]	$3^{22}\cdot 5^{22}\cdot 23^{42}$	$3$	$77.2461326792$	✓	✓	not computed	$C_2\times C_{22}$ (as 44T2)	not computed	$2$	$21$	$$
44.0.116...625.2	x^44 - x^43 - 23x^42 + 24x^41 + 298x^40 - 322x^39 - 2644x^38 + 2966x^37 + 17733x^36 - 20699x^35 - 93680x^34 + 114379x^33 + 400546x^32 - 514925x^31 - 1402310x^30 + 1917235x^29 + 4042594x^28 - 5959829x^27 - 9550726x^26 + 15510555x^25 + 18239299x^24 - 33749854x^23 - 27151731x^22 + 60965664x^21 + 28718628x^20 - 92631926x^19 - 11478724x^18 + 118848820x^17 - 33434940x^16 - 1406311x^15 - 22927136x^14 - 576983889x^13 + 635212253x^12 + 643308528x^11 - 1294716116x^10 + 1724346364x^9 - 424183664x^8 - 3407721010x^7 + 3830694322x^6 + 209294181x^5 - 4039808114x^4 + 4041269764x^3 - 1473288x^2 - 4104644424x + 4106118241	$44$	[0,22]	$3^{22}\cdot 5^{22}\cdot 23^{42}$	$3$	$77.2461326792$	✓	✓	not computed	$C_2\times C_{22}$ (as 44T2)	not computed	$6$	$21$	$$
44.0.116...625.3	x^44 - x^43 - 3x^42 + 7x^41 + 5x^40 - 33x^39 + 13x^38 + 119x^37 - 171x^36 - 305x^35 + 989x^34 + 231x^33 - 4187x^32 + 3263x^31 + 13485x^30 - 26537x^29 - 27403x^28 + 133551x^27 - 23939x^26 - 510265x^25 + 606021x^24 + 1435039x^23 - 3859123x^22 + 5740156x^21 + 9696336x^20 - 32656960x^19 - 6128384x^18 + 136756224x^17 - 112242688x^16 - 434782208x^15 + 883752960x^14 + 855375872x^13 - 4390387712x^12 + 968884224x^11 + 16592666624x^10 - 20468203520x^9 - 45902462976x^8 + 127775277056x^7 + 55834574848x^6 - 566935683072x^5 + 343597383680x^4 + 1924145348608x^3 - 3298534883328x^2 - 4398046511104x + 17592186044416	$44$	[0,22]	$3^{22}\cdot 5^{22}\cdot 23^{42}$	$3$	$77.2461326792$	✓	✓	not computed	$C_2\times C_{22}$ (as 44T2)	not computed	$46$	$21$	$$
44.0.123...000.1	x^44 + 63x^42 + 1771x^40 + 29412x^38 + 322363x^36 + 2470134x^34 + 13694893x^32 + 56167749x^30 + 172989335x^28 + 404160705x^26 + 720751936x^24 + 983588334x^22 + 1025844301x^20 + 813203334x^18 + 484862836x^16 + 213849639x^14 + 68058536x^12 + 15071199x^10 + 2201056x^8 + 195624x^6 + 9361x^4 + 198x^2 + 1	$44$	[0,22]	$2^{44}\cdot 5^{22}\cdot 23^{40}$	$3$	$77.3480544373$	✓	✓	not computed	$C_2\times C_{22}$ (as 44T2)	not computed	$4$	$21$	$$
44.2.305...208.1	x^44 - 2x - 1	$44$	[2,21]	$-\,2^{44}\cdot 6849881\cdot 418859713\cdot 847100666339\cdot 26342648577937357\cdot 270892830308402529909668477$	$6$	$78.9540056094$			✓	$S_{44}$ (as 44T2113)	not computed	$2$	$22$	$$
44.0.361...241.1	x^44 - x^43 - 31x^42 + 18x^41 + 509x^40 - 128x^39 - 6323x^38 + 711x^37 + 64913x^36 - 2855x^35 - 548822x^34 - 30450x^33 + 3909507x^32 + 497028x^31 - 24053724x^30 - 3501489x^29 + 127000724x^28 + 22049413x^27 - 570173510x^26 - 120800376x^25 + 2191193723x^24 + 441547756x^23 - 7154579015x^22 - 1235011630x^21 + 19357719068x^20 + 3692553824x^19 - 42800540592x^18 - 8560769600x^17 + 77181753152x^16 + 8780862080x^15 - 109191557376x^14 - 4336701952x^13 + 115169783808x^12 + 13857435648x^11 - 86371995648x^10 - 18961448960x^9 + 47011856384x^8 + 1711374336x^7 - 14905901056x^6 + 3448373248x^5 + 3020947456x^4 - 373293056x^3 - 84934656x^2 - 12582912x + 4194304	$44$	[0,22]	$3^{22}\cdot 7^{22}\cdot 23^{40}$	$3$	$79.2581705662$	✓	✓	not computed	$C_2\times C_{22}$ (as 44T2)	not computed	$6$	$21$	$$
44.0.482...224.1	x^44 + 44x^42 + 901x^40 + 11400x^38 + 99790x^36 + 641208x^34 + 3131721x^32 + 11878176x^30 + 35442612x^28 + 83778736x^26 + 157236844x^24 + 233880352x^22 + 274130056x^20 + 250699168x^18 + 176290339x^16 + 93382192x^14 + 36217051x^12 + 9883588x^10 + 1792219x^8 + 197912x^6 + 11506x^4 + 264x^2 + 1	$44$	[0,22]	$2^{88}\cdot 23^{42}$	$2$	$79.7794627802$	✓	✓	✓	$C_2\times C_{22}$ (as 44T2)	not computed	$2$	$21$	$$
44.44.482...224.1	x^44 - 44x^42 + 901x^40 - 11400x^38 + 99790x^36 - 641208x^34 + 3131721x^32 - 11878176x^30 + 35442612x^28 - 83778736x^26 + 157236844x^24 - 233880352x^22 + 274130056x^20 - 250699168x^18 + 176290339x^16 - 93382192x^14 + 36217051x^12 - 9883588x^10 + 1792219x^8 - 197912x^6 + 11506x^4 - 264x^2 + 1	$44$	[44,0]	$2^{88}\cdot 23^{42}$	$2$	$79.7794627802$		✓	✓	$C_2\times C_{22}$ (as 44T2)	trivial	$2$	$43$	$8626989567142591000000000000$
44.0.482...224.2	x^44 + 69x^40 + 1978x^36 + 30521x^32 + 274712x^28 + 1463260x^24 + 4481688x^20 + 7339875x^16 + 5623799x^12 + 1588587x^8 + 104742x^4 + 529	$44$	[0,22]	$2^{88}\cdot 23^{42}$	$2$	$79.7794627802$	✓	✓	not computed	$C_2\times C_{22}$ (as 44T2)	not computed	$4$	$21$	$$
44.44.666...569.1	x^44 - x^43 - 43x^42 + 42x^41 + 861x^40 - 820x^39 - 10660x^38 + 9880x^37 + 91390x^36 - 82251x^35 - 575757x^34 + 501942x^33 + 2760681x^32 - 2324784x^31 - 10295472x^30 + 8347680x^29 + 30260340x^28 - 23535820x^27 - 70607460x^26 + 52451256x^25 + 131128140x^24 - 92561040x^23 - 193536720x^22 + 129024480x^21 + 225792840x^20 - 141120525x^19 - 206253075x^18 + 119759850x^17 + 145422675x^16 - 77558760x^15 - 77558760x^14 + 37442160x^13 + 30421755x^12 - 13037895x^11 - 8436285x^10 + 3124550x^9 + 1562275x^8 - 480700x^7 - 177100x^6 + 42504x^5 + 10626x^4 - 1771x^3 - 253x^2 + 22x + 1	$44$	[44,0]	$89^{43}$	$1$	$80.3684677251$		✓	✓	$C_{44}$ (as 44T1)	trivial	$2$	$43$	$9928065388501928000000000000$
44.0.182...881.1	x^44 - x^43 + 5x^42 - 9x^41 + 29x^40 - 65x^39 + 181x^38 - 441x^37 + 1165x^36 - 2929x^35 + 7589x^34 - 19305x^33 + 49661x^32 - 126881x^31 + 325525x^30 - 833049x^29 + 2135149x^28 - 5467345x^27 + 14007941x^26 - 35877321x^25 + 91909085x^24 - 235418369x^23 + 603054709x^22 + 941673476x^21 + 1470545360x^20 + 2296148544x^19 + 3586032896x^18 + 5598561280x^17 + 8745570304x^16 + 13648674816x^15 + 21333606400x^14 + 33261092864x^13 + 52073332736x^12 + 80971038720x^11 + 127322292224x^10 + 196561862656x^9 + 312727306240x^8 + 473520144384x^7 + 777389080576x^6 + 1116691496960x^5 + 1992864825344x^4 + 2473901162496x^3 + 5497558138880x^2 + 4398046511104x + 17592186044416	$44$	[0,22]	$17^{22}\cdot 23^{42}$	$2$	$82.2347879494$	✓	✓	not computed	$C_2\times C_{22}$ (as 44T2)	not computed	$46$	$21$	$$
44.2.314...432.1	x^44 - 3	$44$	[2,21]	$-\,2^{88}\cdot 3^{43}\cdot 11^{36}$	$3$	$83.2503641304$			not computed	$C_{11}:(C_{10}\times D_4)$ (as 44T32)	not computed	$2$	$22$	$$
44.0.681...976.1	x^44 - 42x^42 + 1004x^40 - 16416x^38 + 203056x^36 - 1976896x^34 + 15592256x^32 - 100902784x^30 + 540972800x^28 - 2406430208x^26 + 8885665792x^24 - 27062865920x^22 + 67552104448x^20 - 136133230592x^18 + 218558169088x^16 - 271461023744x^14 + 255644925952x^12 - 171145035776x^10 + 80371253248x^8 - 21592276992x^6 + 3817865216x^4 - 138412032x^2 + 4194304	$44$	[0,22]	$2^{66}\cdot 3^{22}\cdot 23^{40}$	$3$	$84.7305483889$	✓	✓	not computed	$C_2\times C_{22}$ (as 44T2)	not computed	$6$	$21$	$$
44.0.681...976.2	x^44 + 42x^42 + 1004x^40 + 16416x^38 + 203056x^36 + 1976896x^34 + 15592256x^32 + 100902784x^30 + 540972800x^28 + 2406430208x^26 + 8885665792x^24 + 27062865920x^22 + 67552104448x^20 + 136133230592x^18 + 218558169088x^16 + 271461023744x^14 + 255644925952x^12 + 171145035776x^10 + 80371253248x^8 + 21592276992x^6 + 3817865216x^4 + 138412032x^2 + 4194304	$44$	[0,22]	$2^{66}\cdot 3^{22}\cdot 23^{40}$	$3$	$84.7305483889$	✓	✓	not computed	$C_2\times C_{22}$ (as 44T2)	not computed	$6$	$21$	$$
44.2.932...696.1	x^44 - 4x - 4	$44$	[2,21]	$-\,2^{44}\cdot 24247\cdot 97990843\cdot 22\!\cdots\!11$	$4$	$85.3351326318$			not computed	$S_{44}$ (as 44T2113)	not computed	$2$	$22$	$$
44.0.180...061.1	x^44 - x + 2	$44$	[0,22]	$7\cdot 29\cdot 17117\cdot 330203\cdot 700658261310857\cdot 22\!\cdots\!41$	$6$	$86.6245679117$			✓	$S_{44}$ (as 44T2113)	not computed	$2$	$21$	$$
44.2.180...568.1	x^44 - 2	$44$	[2,21]	$-\,2^{131}\cdot 11^{44}$	$2$	$86.6245679117$			✓	$C_{11}:(C_{10}\times D_4)$ (as 44T32)	not computed	$2$	$22$	$$
44.0.180...568.1	x^44 + 2	$44$	[0,22]	$2^{131}\cdot 11^{44}$	$2$	$86.6245679117$			✓	$C_{11}:(C_{10}\times D_4)$ (as 44T32)	not computed	$2$	$21$	$$
44.2.183...480.1	x^44 - 2x - 2	$44$	[2,21]	$-\,2^{44}\cdot 3\cdot 5\cdot 677\cdot 1613\cdot 13103\cdot 37912031\cdot 8935109131219\cdot 14\!\cdots\!31$	$9$	$86.6575957175$			✓	$S_{44}$ (as 44T2113)	not computed	$2$	$22$	$$
44.0.211...969.1	x^44 - x^43 - 4x^42 + 9x^41 + 11x^40 - 56x^39 + x^38 + 279x^37 - 284x^36 - 1111x^35 + 2531x^34 + 3024x^33 - 15679x^32 + 559x^31 + 77836x^30 - 80631x^29 - 308549x^28 + 711704x^27 + 831041x^26 - 4389561x^25 + 234356x^24 + 21713449x^23 - 22885229x^22 + 108567245x^21 + 5858900x^20 - 548695125x^19 + 519400625x^18 + 2224075000x^17 - 4821078125x^16 - 6299296875x^15 + 30404687500x^14 + 1091796875x^13 - 153115234375x^12 + 147656250000x^11 + 617919921875x^10 - 1356201171875x^9 - 1733398437500x^8 + 8514404296875x^7 + 152587890625x^6 - 42724609375000x^5 + 41961669921875x^4 + 171661376953125x^3 - 381469726562500x^2 - 476837158203125x + 2384185791015625	$44$	[0,22]	$19^{22}\cdot 23^{42}$	$2$	$86.9376540072$	✓	✓	not computed	$C_2\times C_{22}$ (as 44T2)	not computed	$46$	$21$	$$
44.0.653...000.1	x^44 + 41x^42 + 784x^40 + 9282x^38 + 76180x^36 + 459888x^34 + 2114697x^32 + 7568133x^30 + 21358299x^28 + 47872465x^26 + 85431991x^24 + 121194085x^22 + 135920335x^20 + 119357605x^18 + 80900650x^16 + 41459620x^14 + 15683335x^12 + 3901015x^10 + 2054320x^8 - 6489250x^6 + 32853580x^4 - 164244624x^2 + 821223649	$44$	[0,22]	$2^{44}\cdot 5^{22}\cdot 23^{42}$	$3$	$89.1961509924$	✓	✓	not computed	$C_2\times C_{22}$ (as 44T2)	not computed	$2$	$21$	$$
44.44.653...000.1	x^44 - 69x^42 + 2139x^40 - 39468x^38 + 484495x^36 - 4193682x^34 + 26499197x^32 - 125010267x^30 + 447055439x^28 - 1224773115x^26 + 2588447416x^24 - 4235761650x^22 + 5369828745x^20 - 5258413410x^18 + 3950328660x^16 - 2250421545x^14 + 955257620x^12 - 294507525x^10 + 63543480x^8 - 9077640x^6 + 785565x^4 - 34914x^2 + 529	$44$	[44,0]	$2^{44}\cdot 5^{22}\cdot 23^{42}$	$3$	$89.1961509924$		✓	not computed	$C_2\times C_{22}$ (as 44T2)	trivial	$2$	$43$	$90452671457773850000000000000$
44.0.653...000.2	x^44 - 47x^42 + 1036x^40 - 14238x^38 + 136828x^36 - 977616x^34 + 5391753x^32 - 23533371x^30 + 82732335x^28 - 237396295x^26 + 562190611x^24 - 1110544651x^22 + 1852435411x^20 - 2651394691x^18 + 3329083366x^16 - 3775046236x^14 + 3998027671x^12 - 4080345361x^10 + 4101904756x^8 - 4105687106x^6 + 4106094436x^4 - 4106117712x^2 + 4106118241	$44$	[0,22]	$2^{44}\cdot 5^{22}\cdot 23^{42}$	$3$	$89.1961509924$	✓	✓	not computed	$C_2\times C_{22}$ (as 44T2)	not computed	$4$	$21$	$$
44.0.653...000.3	x^44 - 5x^42 + 25x^40 - 125x^38 + 625x^36 - 3125x^34 + 15625x^32 - 78125x^30 + 390625x^28 - 1953125x^26 + 9765625x^24 - 48828125x^22 + 244140625x^20 - 1220703125x^18 + 6103515625x^16 - 30517578125x^14 + 152587890625x^12 - 762939453125x^10 + 3814697265625x^8 - 19073486328125x^6 + 95367431640625x^4 - 476837158203125x^2 + 2384185791015625	$44$	[0,22]	$2^{44}\cdot 5^{22}\cdot 23^{42}$	$3$	$89.1961509924$	✓	✓	not computed	$C_2\times C_{22}$ (as 44T2)	not computed	$46$	$21$	$$
44.0.191...489.1	x^44 - x^43 + 46x^42 - 45x^41 + 1195x^40 - 1150x^39 + 21299x^38 - 20149x^37 + 287730x^36 - 267581x^35 + 3072523x^34 - 2804942x^33 + 26692099x^32 - 23887157x^31 + 191331250x^30 - 167444093x^29 + 1142837707x^28 - 975393614x^27 + 5704151939x^26 - 4728758325x^25 + 23804513458x^24 - 19075755133x^23 + 82643603403x^22 - 63567853467x^21 + 237057619920x^20 - 173490244577x^19 + 554044068881x^18 - 380558605544x^17 + 1037868132567x^16 - 657255020887x^15 + 1512341393536x^14 - 854306074281x^13 + 1655465958953x^12 - 799339188480x^11 + 1266628178647x^10 - 472858178519x^9 + 634019315968x^8 - 183040091689x^7 + 183593805097x^6 - 13681085952x^5 + 19238856919x^4 + 3193810729x^3 + 1973987328x^2 + 217790679x + 27008809	$44$	[0,22]	$3^{22}\cdot 7^{22}\cdot 23^{42}$	$3$	$91.3988567732$	✓	✓	not computed	$C_2\times C_{22}$ (as 44T2)	not computed	$6$	$21$	$$
44.44.191...489.1	x^44 - x^43 - 86x^42 + 81x^41 + 3445x^40 - 3040x^39 - 85351x^38 + 70151x^37 + 1464534x^36 - 1113779x^35 - 18468767x^34 + 12899872x^33 + 177261061x^32 - 112761701x^31 - 1323060098x^30 + 759251593x^29 + 7780382701x^28 - 3984124736x^27 - 36301909279x^26 + 16381285599x^25 + 134698547590x^24 - 52792119595x^23 - 396744216375x^22 + 132783613203x^21 + 922279857882x^20 - 258361552805x^19 - 1675313579545x^18 + 383501034280x^17 + 2343182319195x^16 - 425622641659x^15 - 2471777086526x^14 + 343273729047x^13 + 1911152162483x^12 - 192962821056x^11 - 1040820630209x^10 + 70437336577x^9 + 377125555258x^8 - 13999395253x^7 - 83413545257x^6 + 289196448x^5 + 9759539347x^4 + 438024589x^3 - 453637806x^2 - 49033617x - 368597	$44$	[44,0]	$3^{22}\cdot 7^{22}\cdot 23^{42}$	$3$	$91.3988567732$		✓	not computed	$C_2\times C_{22}$ (as 44T2)	not computed	$2$	$43$	$$
44.0.191...489.2	x^44 - 20x^43 + 189x^42 - 1124x^41 + 4865x^40 - 17456x^39 + 58421x^38 - 190050x^37 + 582353x^36 - 1651670x^35 + 4443991x^34 - 11616036x^33 + 29347307x^32 - 70941366x^31 + 165084544x^30 - 373261630x^29 + 819539932x^28 - 1741244694x^27 + 3587123034x^26 - 7185027240x^25 + 13992949317x^24 - 26465017896x^23 + 48644839484x^22 - 86902148486x^21 + 150906753803x^20 - 254398639764x^19 + 416538699753x^18 - 661207715179x^17 + 1018298320297x^16 - 1516385399452x^15 + 2187310150678x^14 - 3038199352295x^13 + 4080627086016x^12 - 5240849624589x^11 + 6499724444701x^10 - 7615237158361x^9 + 8625505710097x^8 - 9008819848319x^7 + 9179431123587x^6 - 8198182177669x^5 + 7374297175226x^4 - 5145387322896x^3 + 3993217874024x^2 - 1687064084492x + 1104623059513	$44$	[0,22]	$3^{22}\cdot 7^{22}\cdot 23^{42}$	$3$	$91.3988567732$	✓	✓	not computed	$C_2\times C_{22}$ (as 44T2)	not computed	$2$	$21$	$$
44.0.191...489.3	x^44 - x^43 + 6x^42 - 11x^41 + 41x^40 - 96x^39 + 301x^38 - 781x^37 + 2286x^36 - 6191x^35 + 17621x^34 - 48576x^33 + 136681x^32 - 379561x^31 + 1062966x^30 - 2960771x^29 + 8275601x^28 - 23079456x^27 + 64457461x^26 - 179854741x^25 + 502142046x^24 - 1401415751x^23 + 3912125981x^22 + 7007078755x^21 + 12553551150x^20 + 22481842625x^19 + 40285913125x^18 + 72123300000x^17 + 129306265625x^16 + 231310234375x^15 + 415221093750x^14 + 741330078125x^13 + 1334775390625x^12 + 2371875000000x^11 + 4302001953125x^10 + 7557373046875x^9 + 13952636718750x^8 + 23834228515625x^7 + 45928955078125x^6 + 73242187500000x^5 + 156402587890625x^4 + 209808349609375x^3 + 572204589843750x^2 + 476837158203125x + 2384185791015625	$44$	[0,22]	$3^{22}\cdot 7^{22}\cdot 23^{42}$	$3$	$91.3988567732$	✓	✓	not computed	$C_2\times C_{22}$ (as 44T2)	not computed	$46$	$21$	$$
44.0.202...984.1	x^44 - 63x^42 + 1954x^40 - 39159x^38 + 564136x^36 - 6171204x^34 + 52905976x^32 - 362220741x^30 + 2002105655x^28 - 8980281297x^26 + 32710198942x^24 - 96439370415x^22 + 228524812948x^20 - 430395212448x^18 + 634098522688x^16 - 714985491456x^14 + 598979244032x^12 - 357650202624x^10 + 143735308288x^8 - 35340484608x^6 + 4755030016x^4 - 207618048x^2 + 4194304	$44$	[0,22]	$2^{44}\cdot 7^{22}\cdot 23^{40}$	$3$	$91.5194522237$	✓	✓	not computed	$C_2\times C_{22}$ (as 44T2)	not computed	$4$	$21$	$$
44.0.155...001.1	x^44 - x^43 - x^42 - 82x^41 + 77x^40 + 73x^39 + 2795x^38 - 2452x^37 - 2193x^36 - 51847x^35 + 42213x^34 + 35713x^33 + 576416x^32 - 432884x^31 - 345487x^30 - 3995639x^29 + 2790104x^28 + 2010938x^27 + 17436469x^26 - 11948291x^25 - 6590980x^24 - 47156450x^23 + 36319435x^22 + 9637447x^21 + 76421426x^20 - 81395780x^19 + 4175237x^18 - 78460015x^17 + 124870243x^16 - 45435254x^15 + 82436729x^14 - 106904257x^13 + 95684734x^12 - 78566744x^11 + 62868338x^10 - 89632848x^9 + 65796469x^8 - 36457247x^7 + 9020998x^6 - 24902176x^5 + 25739321x^4 + 13163316x^3 - 5336842x^2 + 199578x + 1151329	$44$	[0,22]	$3^{22}\cdot 67^{42}$	$2$	$95.8588092539$	✓	✓		$C_2\times C_{22}$ (as 44T2)	not computed	$6$	$21$	$$