Number field search results

Results (1-50 of 375 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
42.0.118...207.1	x^42 - x^35 + x^28 - x^21 + x^14 - x^7 + 1	$42$	[0,21]	$-\,7^{77}$	$1$	$35.4279812936$	✓	✓	✓	$C_{42}$ (as 42T1)	$[43]$	$98$	$20$	$1776855897760068.5$
42.0.938...043.1	x^42 - x^41 + x^40 - x^39 + x^38 - x^37 + x^36 - x^35 + x^34 - x^33 + x^32 - x^31 + x^30 - x^29 + x^28 - x^27 + x^26 - x^25 + x^24 - x^23 + x^22 - x^21 + x^20 - x^19 + x^18 - x^17 + x^16 - x^15 + x^14 - x^13 + x^12 - x^11 + x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1	$42$	[0,21]	$-\,43^{41}$	$1$	$39.3166357953$	✓	✓	✓	$C_{42}$ (as 42T1)	$[211]$	$86$	$20$	$2748021948787771.5$
42.0.148...423.1	x^42 - x + 1	$42$	[0,21]	$-\,250460976091\cdot 2191665374655671317777039\cdot 27\!\cdots\!27$	$3$	$41.9910966386$			✓	$S_{42}$ (as 42T9491)	not computed	$2$	$20$	$$
42.2.151...705.1	x^42 - x - 1	$42$	[2,20]	$5\cdot 3355730803775717\cdot 90\!\cdots\!73$	$3$	$42.0088266452$			✓	$S_{42}$ (as 42T9491)	trivial	$2$	$21$	$239179039607002720$
42.0.475...976.1	x^42 + 46x^40 + 825x^38 + 9020x^36 + 65490x^34 + 325184x^32 + 1115476x^30 + 2295041x^28 + 2315947x^26 - 2734559x^24 - 14848773x^22 - 6221636x^20 + 35462359x^18 - 4544065x^16 - 16428325x^14 + 5957296x^12 + 1133059x^10 - 497379x^8 - 50982x^6 + 12238x^4 + 1537x^2 + 29	$42$	[0,21]	$-\,2^{42}\cdot 29^{39}$	$2$	$45.60064585163551$		✓	not computed	$C_7\times S_3$ (as 42T6)	not computed	$2$	$20$	$$
42.0.157...864.1	x^42 - 2x^21 + 2	$42$	[0,21]	$-\,2^{62}\cdot 3^{42}\cdot 7^{42}$	$3$	$58.4247560083$			✓	$C_2\times S_3\times F_7$ (as 42T95)	trivial	$4$	$20$	$507894019142814700000$
42.0.176...003.1	x^42 + 21x^40 + 252x^38 + 2065x^36 - x^35 + 12789x^34 - 7x^33 + 62181x^32 + 7x^31 + 244265x^30 + 574x^29 + 784101x^28 + 5341x^27 + 2075577x^26 + 29988x^25 + 4529364x^24 + 118188x^23 + 8142834x^22 + 346087x^21 + 11951541x^20 + 767956x^19 + 14210490x^18 + 1288070x^17 + 13430361x^16 + 1624252x^15 + 9960725x^14 + 1486219x^13 + 5587183x^12 + 983626x^11 + 2322670x^10 + 429093x^9 + 648396x^8 + 121077x^7 + 117649x^6 + 14763x^5 + 7399x^4 + 56x^3 + 245x^2 + 14x + 1	$42$	[0,21]	$-\,3^{21}\cdot 7^{76}$	$2$	$58.5848944957$	✓	✓	not computed	$C_{42}$ (as 42T1)	$[136619]$	$6$	$20$	$1776855897760068.5$
42.42.123...021.1	x^42 - 42x^40 + 819x^38 - 9842x^36 - x^35 + 81585x^34 + 35x^33 - 494802x^32 - 560x^31 + 2272424x^30 + 5425x^29 - 8069424x^28 - 35525x^27 + 22428252x^26 + 166257x^25 - 49085400x^24 - 573300x^23 + 84672315x^22 + 1480051x^21 - 114717330x^20 - 2877896x^19 + 121090515x^18 + 4206314x^17 - 98285670x^16 - 4577216x^15 + 60174899x^14 + 3643150x^13 - 27041546x^12 - 2063243x^11 + 8580418x^10 + 798357x^9 - 1816836x^8 - 198948x^7 + 235249x^6 + 29211x^5 - 15974x^4 - 2170x^3 + 392x^2 + 56x + 1	$42$	[42,0]	$3^{21}\cdot 7^{77}$	$2$	$61.3630636101$		✓	✓	$C_{42}$ (as 42T1)	trivial	$2$	$41$	$1966641158581684500000000$
42.0.124...123.1	x^42 + 3	$42$	[0,21]	$-\,3^{83}\cdot 7^{42}$	$2$	$61.3734475287$				$S_3\times F_7$ (as 42T45)	trivial	$6$	$20$	$2625406827600082000000$
42.0.228...203.1	x^42 - x^41 + 21x^40 - 18x^39 + 248x^38 - 191x^37 + 1996x^36 - 1375x^35 + 12088x^34 - 7495x^33 + 57373x^32 - 31825x^31 + 219409x^30 - 108700x^29 + 684645x^28 - 300153x^27 + 1757705x^26 - 677756x^25 + 3715466x^24 - 1242500x^23 + 6455978x^22 - 1853597x^21 + 9148985x^20 - 2205194x^19 + 10469894x^18 - 2090336x^17 + 9505112x^16 - 1507895x^15 + 6709547x^14 - 839645x^13 + 3559478x^12 - 314951x^11 + 1368367x^10 - 93808x^9 + 355278x^8 - 10362x^7 + 58036x^6 - 2497x^5 + 4950x^4 + 165x^3 + 176x^2 - 11x + 1	$42$	[0,21]	$-\,3^{21}\cdot 43^{40}$	$2$	$62.2651259274$	✓	✓	not computed	$C_{42}$ (as 42T1)	$[179249]$	$6$	$20$	$2748021948787771.5$
42.0.742...504.1	x^42 + 42x^40 + 819x^38 + 9842x^36 + 81585x^34 + 494802x^32 + 2272424x^30 + 8069423x^28 + 22428224x^26 + 49085050x^24 + 84669739x^22 + 114704933x^20 + 121049551x^18 + 98190708x^16 + 60019861x^14 + 26865216x^12 + 8444436x^10 + 1749188x^8 + 215453x^6 + 13181x^4 + 294x^2 + 1	$42$	[0,21]	$-\,2^{42}\cdot 7^{76}$	$2$	$67.6480092151$	✓	✓	✓	$C_{42}$ (as 42T1)	$[1923461]$	$4$	$20$	$1776855897760068.5$
42.42.981...729.1	x^42 - x^41 - 42x^40 + 42x^39 + 818x^38 - 818x^37 - 9803x^36 + 9803x^35 + 80884x^34 - 80884x^33 - 487103x^32 + 487103x^31 + 2214673x^30 - 2214673x^29 - 7756167x^28 + 7756167x^27 + 21159269x^26 - 21159269x^25 - 45176143x^24 + 45176143x^23 + 75433697x^22 - 75433697x^21 - 97942948x^20 + 97942948x^19 + 97804877x^18 - 97804877x^17 - 73850908x^16 + 73850908x^15 + 41150012x^14 - 41150012x^13 - 16350448x^12 + 16350448x^11 + 4413607x^10 - 4413607x^9 - 753918x^8 + 753918x^7 + 72886x^6 - 72886x^5 - 3267x^4 + 3267x^3 + 44x^2 - 44x + 1	$42$	[42,0]	$3^{21}\cdot 43^{41}$	$2$	$68.0984107801$		✓	✓	$C_{42}$ (as 42T1)	trivial	$2$	$41$	$16535537450237775000000000$
42.42.519...528.1	x^42 - 42x^40 + 819x^38 - 9842x^36 + 81585x^34 - 494802x^32 + 2272424x^30 - 8069425x^28 + 22428280x^26 - 49085750x^24 + 84674891x^22 - 114729727x^20 + 121131479x^18 - 98380632x^16 + 60329941x^14 - 27217932x^12 + 8716708x^10 - 1885324x^8 + 256221x^6 - 19551x^4 + 686x^2 - 7	$42$	[42,0]	$2^{42}\cdot 7^{77}$	$2$	$70.8559625871$		✓	✓	$C_{42}$ (as 42T1)	trivial	$2$	$41$	$40972406918644810000000000$
42.0.959...104.1	x^42 + 41x^40 + 780x^38 + 9139x^36 + 73815x^34 + 435897x^32 + 1947792x^30 + 6724520x^28 + 18156204x^26 + 38567100x^24 + 64512240x^22 + 84672315x^20 + 86493225x^18 + 67863915x^16 + 40116600x^14 + 17383860x^12 + 5311735x^10 + 1081575x^8 + 134596x^6 + 8855x^4 + 231x^2 + 1	$42$	[0,21]	$-\,2^{42}\cdot 43^{40}$	$2$	$71.8975744306$	✓	✓	✓	$C_{42}$ (as 42T1)	$[2, 1878326]$	$4$	$20$	$2748021948787771.5$
42.2.585...728.1	x^42 - 2x - 1	$42$	[2,20]	$2^{43}\cdot 151\cdot 4132611804876851\cdot 111869437509421489132043\cdot 9532243245509920520310487$	$5$	$75.060981117$			✓	$S_{42}$ (as 42T9491)	not computed	$2$	$21$	$$
42.0.636...560.1	x^42 - 4x + 4	$42$	[0,21]	$-\,2^{42}\cdot 5\cdot 14815048403\cdot 223886382998191\cdot 87\!\cdots\!11$	$5$	$75.2119624159$			not computed	$S_{42}$ (as 42T9491)	not computed	$2$	$20$	$$
42.42.805...125.1	x^42 - 63x^40 + 1764x^38 - 29043x^36 - 29x^35 + 313845x^34 + 1295x^33 - 2356263x^32 - 24605x^31 + 12710649x^30 + 262360x^29 - 50338309x^28 - 1751015x^27 + 148468453x^26 + 7757582x^25 - 329114310x^24 - 23675820x^23 + 550880022x^22 + 50961633x^21 - 696364921x^20 - 78352652x^19 + 661675518x^18 + 86284422x^17 - 467756891x^16 - 67555180x^15 + 241883075x^14 + 36893815x^13 - 89215119x^12 - 13584956x^11 + 22638112x^10 + 3191321x^9 - 3752308x^8 - 437383x^7 + 374801x^6 + 29995x^5 - 19355x^4 - 798x^3 + 343x^2 + 14x - 1	$42$	[42,0]	$5^{21}\cdot 7^{76}$	$2$	$75.6327735738$		✓	not computed	$C_{42}$ (as 42T1)	trivial	$2$	$41$	$119589768703493500000000000$
42.42.412...472.1	x^42 - 43x^40 + 860x^38 - 10621x^36 + 90687x^34 - 567987x^32 + 2701776x^30 - 9970840x^28 + 28915436x^26 - 66335412x^24 + 120609840x^22 - 173376645x^20 + 195747825x^18 - 171655785x^16 + 115000920x^14 - 57500460x^12 + 20764055x^10 - 5167525x^8 + 826804x^6 - 76153x^4 + 3311x^2 - 43	$42$	[42,0]	$2^{42}\cdot 43^{41}$	$2$	$78.6332715905$		✓	✓	$C_{42}$ (as 42T1)	not computed	$2$	$41$	$$
42.0.563...875.1	x^42 + 42x^40 + 819x^38 + 9842x^36 - 29x^35 + 81585x^34 - 1015x^33 + 494802x^32 - 16240x^31 + 2272424x^30 - 157325x^29 + 8070266x^28 - 1030225x^27 + 22451828x^26 - 4821453x^25 + 49380100x^24 - 16625700x^23 + 86841307x^22 - 42945897x^21 + 125155604x^20 - 83971762x^19 + 155582203x^18 - 126598108x^17 + 178243674x^16 - 155985200x^15 + 191428385x^14 - 177440270x^13 + 185472266x^12 - 199822441x^11 + 177861992x^10 - 194249279x^9 + 208189352x^8 - 152082148x^7 + 226081541x^6 - 195873685x^5 + 141819720x^4 - 297986948x^3 + 34945918x^2 - 144775946x + 599786069	$42$	[0,21]	$-\,5^{21}\cdot 7^{77}$	$2$	$79.219374478$	✓	✓	not computed	$C_{42}$ (as 42T1)	not computed	$2$	$20$	$$
42.42.104...125.1	x^42 - x^41 - 61x^40 + 56x^39 + 1654x^38 - 1379x^37 - 26380x^36 + 19735x^35 + 276302x^34 - 183047x^33 - 2012061x^32 + 1164081x^31 + 10536175x^30 - 5248100x^29 - 40536685x^28 + 17139885x^27 + 116229751x^26 - 41141876x^25 - 250648402x^24 + 73243022x^23 + 408521488x^22 - 97102633x^21 - 503598537x^20 + 95768202x^19 + 467783098x^18 - 69790048x^17 - 324502952x^16 + 37071837x^15 + 165565463x^14 - 14037193x^13 - 60679502x^12 + 3661307x^11 + 15419833x^10 - 625768x^9 - 2575782x^8 + 66132x^7 + 260062x^6 - 4477x^5 - 13750x^4 + 275x^3 + 286x^2 - 11x - 1	$42$	[42,0]	$5^{21}\cdot 43^{40}$	$2$	$80.3839319221$		✓	not computed	$C_{42}$ (as 42T1)	not computed	$2$	$41$	$$
42.2.170...328.1	x^42 - 4x - 4	$42$	[2,20]	$2^{42}\cdot 37\cdot 479\cdot 22037\cdot 3375017\cdot 4905809483\cdot 799858695525167\cdot 7513694603813636232170428411$	$8$	$81.3401245086$			not computed	$S_{42}$ (as 42T9491)	not computed	$2$	$21$	$$
42.0.324...664.1	x^42 - 2x + 2	$42$	[0,21]	$-\,2^{42}\cdot 19\cdot 11483\cdot 457151\cdot 73\!\cdots\!33$	$5$	$82.5898982026$			✓	$S_{42}$ (as 42T9491)	not computed	$2$	$20$	$$
42.0.330...328.1	x^42 + 2	$42$	[0,21]	$-\,2^{83}\cdot 3^{42}\cdot 7^{42}$	$3$	$82.6250823253$			✓	$C_2\times S_3\times F_7$ (as 42T95)	not computed	$2$	$20$	$$
42.2.330...328.1	x^42 - 2	$42$	[2,20]	$2^{83}\cdot 3^{42}\cdot 7^{42}$	$3$	$82.6250823253$			✓	$C_2\times S_3\times F_7$ (as 42T95)	not computed	$2$	$21$	$$
42.2.335...992.1	x^42 - 2x - 2	$42$	[2,20]	$2^{42}\cdot 13\cdot 43\cdot 7237697\cdot 7281116753\cdot 16009936396480001782447\cdot 161984247228508288433890361$	$7$	$82.6596626942$			✓	$S_{42}$ (as 42T9491)	not computed	$2$	$21$	$$
42.42.496...469.1	x^42 - x^41 - 67x^40 + 62x^39 + 1993x^38 - 1704x^37 - 34847x^36 + 27519x^35 + 399768x^34 - 291838x^33 - 3181854x^32 + 2151119x^31 + 18125561x^30 - 11376768x^29 - 75199314x^28 + 43948028x^27 + 229267037x^26 - 125109956x^25 - 515411960x^24 + 263200585x^23 + 854114535x^22 - 408541162x^21 - 1040280967x^20 + 465602383x^19 + 926307827x^18 - 386475878x^17 - 597992464x^16 + 230741151x^15 + 276295754x^14 - 97190872x^13 - 89602671x^12 + 28039534x^11 + 19807180x^10 - 5297092x^9 - 2853616x^8 + 611802x^7 + 248962x^6 - 38836x^5 - 11508x^4 + 1155x^3 + 217x^2 - 14x - 1	$42$	[42,0]	$7^{28}\cdot 29^{39}$	$2$	$83.4333518728$		✓	not computed	$C_{42}$ (as 42T1)	trivial	$2$	$41$	$1205750664686969300000000000$
42.0.447...375.1	x^42 - x^41 + 44x^40 - 44x^39 + 904x^38 - 904x^37 + 11525x^36 - 11525x^35 + 102212x^34 - 102212x^33 + 670199x^32 - 670199x^31 + 3371975x^30 - 3371975x^29 + 13342815x^28 - 13342815x^27 + 42258251x^26 - 42258251x^25 + 108593663x^24 - 108593663x^23 + 229203503x^22 - 229203503x^21 + 402580148x^20 - 402580148x^19 + 598327973x^18 - 598327973x^17 + 769983758x^16 - 769983758x^15 + 884984678x^14 - 884984678x^13 + 942485138x^12 - 942485138x^11 + 963249193x^10 - 963249193x^9 + 968416718x^8 - 968416718x^7 + 969243522x^6 - 969243522x^5 + 969319675x^4 - 969319675x^3 + 969322986x^2 - 969322986x + 969323029	$42$	[0,21]	$-\,5^{21}\cdot 43^{41}$	$2$	$87.9146702848$	✓	✓	not computed	$C_{42}$ (as 42T1)	not computed	$2$	$20$	$$
42.0.167...503.1	x^42 - x^41 + 13x^40 - 18x^39 + 139x^38 - 250x^37 + 1451x^36 + 321x^35 + 11819x^34 + 7069x^33 + 101147x^32 + 34723x^31 + 906407x^30 - 143662x^29 + 2718926x^28 - 434521x^27 + 7093735x^26 - 1731307x^25 + 17818760x^24 - 17036040x^23 + 50814721x^22 - 44435389x^21 + 124550915x^20 - 97201554x^19 + 258557330x^18 - 191477895x^17 + 222793332x^16 - 183429282x^15 + 205234539x^14 - 104619060x^13 + 150123312x^12 + 66144604x^11 + 21062459x^10 + 5929237x^9 + 1586736x^8 + 394344x^7 + 106707x^6 + 17635x^5 + 2858x^4 + 449x^3 + 67x^2 + 9x + 1	$42$	[0,21]	$-\,7^{35}\cdot 29^{36}$	$2$	$90.7261255722$	✓	✓	not computed	$C_{42}$ (as 42T1)	not computed	$14$	$20$	$$
42.0.506...267.1	x^42 - 16x^39 + 1066x^36 + 13384x^33 + 639480x^30 + 581064x^27 + 10535858x^24 - 25402305x^21 + 171805922x^18 - 184669454x^15 + 198189968x^12 + 3751640x^9 + 57337x^6 + 267x^3 + 1	$42$	[0,21]	$-\,3^{63}\cdot 29^{36}$	$2$	$93.1463583267$	✓	✓	not computed	$C_{42}$ (as 42T1)	not computed	$18$	$20$	$$
42.0.121...007.1	x^42 - x^41 + 62x^40 - 55x^39 + 1885x^38 - 1493x^37 + 36890x^36 - 26096x^35 + 516884x^34 - 325868x^33 + 5474760x^32 - 3063183x^31 + 45214327x^30 - 22319399x^29 + 296463014x^28 - 128129100x^27 + 1558565095x^26 - 584173775x^25 + 6595257074x^24 - 2118905803x^23 + 22443263173x^22 - 6093288301x^21 + 61089146298x^20 - 13772999112x^19 + 131703790552x^18 - 24134677936x^17 + 221581028128x^16 - 32118789120x^15 + 284876509184x^14 - 31567940608x^13 + 271846162432x^12 - 21964134400x^11 + 184905250816x^10 - 10296512512x^9 + 84546772992x^8 - 2848260096x^7 + 23814799360x^6 - 531300352x^5 + 3554017280x^4 + 28835840x^3 + 213385216x^2 - 11534336x + 2097152	$42$	[0,21]	$-\,7^{21}\cdot 43^{40}$	$2$	$95.1115509061$	✓	✓	not computed	$C_{42}$ (as 42T1)	not computed	$2$	$20$	$$
42.0.155...608.1	x^42 + 84x^40 + 3276x^38 + 78736x^36 + 1305360x^34 + 15833664x^32 + 145435136x^30 + 1032886144x^28 + 5741625344x^26 + 25131545600x^24 + 86701812736x^22 + 234915702784x^20 + 495818960896x^18 + 804378279936x^16 + 983365402624x^14 + 880319397888x^12 + 553414557696x^10 + 229269569536x^8 + 56479711232x^6 + 6910640128x^4 + 308281344x^2 + 2097152	$42$	[0,21]	$-\,2^{63}\cdot 7^{76}$	$2$	$95.6687320996$	✓	✓	not computed	$C_{42}$ (as 42T1)	not computed	$2$	$20$	$$
42.42.155...608.1	x^42 - 84x^40 + 3276x^38 - 78736x^36 + 1305360x^34 - 15833664x^32 + 145435136x^30 - 1032886144x^28 + 5741625344x^26 - 25131545600x^24 + 86701812736x^22 - 234915702784x^20 + 495818960896x^18 - 804378279936x^16 + 983365402624x^14 - 880319397888x^12 + 553414557696x^10 - 229269569536x^8 + 56479711232x^6 - 6910640128x^4 + 308281344x^2 - 2097152	$42$	[42,0]	$2^{63}\cdot 7^{76}$	$2$	$95.6687320996$		✓	not computed	$C_{42}$ (as 42T1)	trivial	$2$	$41$	$31575205777918616000000000000$
42.42.565...149.1	x^42 - 81x^40 - 4x^39 + 2925x^38 + 276x^37 - 62221x^36 - 8388x^35 + 868038x^34 + 148164x^33 - 8369604x^32 - 1690536x^31 + 57288192x^30 + 13101552x^29 - 281708427x^28 - 70649728x^27 + 997233012x^26 + 267447468x^25 - 2528669823x^24 - 709905600x^23 + 4548805662x^22 + 1311105276x^21 - 5738345406x^20 - 1666490856x^19 + 5023839240x^18 + 1442807064x^17 - 3028872840x^16 - 846440256x^15 + 1246931667x^14 + 334448784x^13 - 345422658x^12 - 87695253x^11 + 62698236x^10 + 14793089x^9 - 7127757x^8 - 1516980x^7 + 472108x^6 + 85806x^5 - 16338x^4 - 2275x^3 + 252x^2 + 21x - 1	$42$	[42,0]	$3^{56}\cdot 29^{39}$	$2$	$98.6512678279$		✓	not computed	$C_{42}$ (as 42T1)	trivial	$2$	$41$	$43619585644836630000000000000$
42.0.109...256.1	x^42 + 84x^40 + 3276x^38 + 78736x^36 + 1305360x^34 + 15833664x^32 + 145435136x^30 + 1032886400x^28 + 5741639680x^26 + 25131904000x^24 + 86707088384x^22 + 234966480896x^20 + 496154537984x^18 + 805934137344x^16 + 988445753344x^14 + 891877195776x^12 + 571258175488x^10 + 247113187328x^8 + 67166797824x^6 + 10250354688x^4 + 719323136x^2 + 14680064	$42$	[0,21]	$-\,2^{63}\cdot 7^{77}$	$2$	$100.205463266$	✓	✓	not computed	$C_{42}$ (as 42T1)	not computed	$2$	$20$	$$
42.42.109...256.1	x^42 - 84x^40 + 3276x^38 - 78736x^36 + 1305360x^34 - 15833664x^32 + 145435136x^30 - 1032886400x^28 + 5741639680x^26 - 25131904000x^24 + 86707088384x^22 - 234966480896x^20 + 496154537984x^18 - 805934137344x^16 + 988445753344x^14 - 891877195776x^12 + 571258175488x^10 - 247113187328x^8 + 67166797824x^6 - 10250354688x^4 + 719323136x^2 - 14680064	$42$	[42,0]	$2^{63}\cdot 7^{77}$	$2$	$100.205463266$		✓	not computed	$C_{42}$ (as 42T1)	not computed	$2$	$41$	$$
42.2.155...125.1	x^42 - 5	$42$	[2,20]	$3^{42}\cdot 5^{41}\cdot 7^{42}$	$3$	$101.052521836$				$C_2\times S_3\times F_7$ (as 42T95)	not computed	$2$	$21$	$$
42.0.201...808.1	x^42 + 82x^40 + 3120x^38 + 73112x^36 + 1181040x^34 + 13948704x^32 + 124658688x^30 + 860738560x^28 + 4647988224x^26 + 19746355200x^24 + 66060533760x^22 + 173408901120x^20 + 354276249600x^18 + 555941191680x^16 + 657270374400x^14 + 569634324480x^12 + 348109864960x^10 + 141764198400x^8 + 35283533824x^6 + 4642570240x^4 + 242221056x^2 + 2097152	$42$	[0,21]	$-\,2^{63}\cdot 43^{40}$	$2$	$101.678524861$	✓	✓	not computed	$C_{42}$ (as 42T1)	not computed	$2$	$20$	$$
42.42.201...808.1	x^42 - 82x^40 + 3120x^38 - 73112x^36 + 1181040x^34 - 13948704x^32 + 124658688x^30 - 860738560x^28 + 4647988224x^26 - 19746355200x^24 + 66060533760x^22 - 173408901120x^20 + 354276249600x^18 - 555941191680x^16 + 657270374400x^14 - 569634324480x^12 + 348109864960x^10 - 141764198400x^8 + 35283533824x^6 - 4642570240x^4 + 242221056x^2 - 2097152	$42$	[42,0]	$2^{63}\cdot 43^{40}$	$2$	$101.678524861$		✓	not computed	$C_{42}$ (as 42T1)	not computed	$2$	$41$	$$
42.42.523...301.1	x^42 - x^41 - 85x^40 + 85x^39 + 3355x^38 - 3355x^37 - 81613x^36 + 81613x^35 + 1369379x^34 - 1369379x^33 - 16806205x^32 + 16806205x^31 + 156107459x^30 - 156107459x^29 - 1120160061x^28 + 1120160061x^27 + 6282191555x^26 - 6282191555x^25 - 27681539389x^24 + 27681539389x^23 + 95822936771x^22 - 95822936771x^21 - 259252432189x^20 + 259252432189x^19 + 542530659011x^18 - 542530659011x^17 - 863673531709x^16 + 863673531709x^15 + 1020501541571x^14 - 1020501541571x^13 - 863673531709x^12 + 863673531709x^11 + 497119576771x^10 - 497119576771x^9 - 180198260029x^8 + 180198260029x^7 + 36543447747x^6 - 36543447747x^5 - 3382656317x^4 + 3382656317x^3 + 89178819x^2 - 89178819x - 998717	$42$	[42,0]	$7^{21}\cdot 43^{41}$	$2$	$104.022040702$		✓	not computed	$C_{42}$ (as 42T1)	not computed	$2$	$41$	$$
42.0.865...744.1	x^42 + 86x^40 + 3440x^38 + 84968x^36 + 1450992x^34 + 18175584x^32 + 172913664x^30 + 1276267520x^28 + 7402351616x^26 + 33963730944x^24 + 123504476160x^22 + 355075368960x^20 + 801783091200x^18 + 1406204190720x^16 + 1884175073280x^14 + 1884175073280x^12 + 1360793108480x^10 + 677317836800x^8 + 216741707776x^6 + 39926104064x^4 + 3471835136x^2 + 90177536	$42$	[0,21]	$-\,2^{63}\cdot 43^{41}$	$2$	$111.204239137$	✓	✓	not computed	$C_{42}$ (as 42T1)	not computed	$2$	$20$	$$
42.42.865...744.1	x^42 - 86x^40 + 3440x^38 - 84968x^36 + 1450992x^34 - 18175584x^32 + 172913664x^30 - 1276267520x^28 + 7402351616x^26 - 33963730944x^24 + 123504476160x^22 - 355075368960x^20 + 801783091200x^18 - 1406204190720x^16 + 1884175073280x^14 - 1884175073280x^12 + 1360793108480x^10 - 677317836800x^8 + 216741707776x^6 - 39926104064x^4 + 3471835136x^2 - 90177536	$42$	[42,0]	$2^{63}\cdot 43^{41}$	$2$	$111.204239137$		✓	not computed	$C_{42}$ (as 42T1)	not computed	$2$	$41$	$$
42.0.124...811.1	x^42 - 21x^41 + 231x^40 - 1750x^39 + 10395x^38 - 52269x^37 + 233611x^36 - 952918x^35 + 3599785x^34 - 12710201x^33 + 42287014x^32 - 133370664x^31 + 400618099x^30 - 1149584975x^29 + 3160451592x^28 - 8341179427x^27 + 21174580693x^26 - 51755274760x^25 + 121953514697x^24 - 277155797093x^23 + 608007380806x^22 - 1287295716241x^21 + 2631847521996x^20 - 5192066875520x^19 + 9886990587068x^18 - 18146977046303x^17 + 32112635555588x^16 - 54655115299659x^15 + 89504829240548x^14 - 140479267770793x^13 + 211514505374151x^12 - 303526580264439x^11 + 416119886096880x^10 - 538840804150264x^9 + 662937764461147x^8 - 758558920220686x^7 + 819087800747125x^6 - 798550011094073x^5 + 729734808064227x^4 - 562691756062212x^3 + 407486767661645x^2 - 201294019183845x + 99519182315771	$42$	[0,21]	$-\,7^{76}\cdot 11^{21}$	$2$	$112.181532191$	✓	✓	not computed	$C_{42}$ (as 42T1)	not computed	$2$	$20$	$$
42.2.145...905.1	x^42 - 3x + 1	$42$	[2,20]	$3^{42}\cdot 5\cdot 277\cdot 9883\cdot 24851\cdot 5267491\cdot 28880594132963764921\cdot 25718507492700353234963282659$	$8$	$112.591471675$			✓	$S_{42}$ (as 42T9491)	not computed	$2$	$21$	$$
42.0.180...927.1	x^42 - x^41 + 2x^40 + 80x^39 - 73x^38 + 139x^37 + 2635x^36 - 2181x^35 + 3934x^34 + 46702x^33 - 34779x^32 + 59013x^31 + 489577x^30 - 325107x^29 + 514966x^28 + 3148122x^27 - 1839378x^26 + 2684924x^25 + 12529404x^24 - 6257436x^23 + 8056643x^22 + 30745048x^21 - 12383236x^20 + 11933159x^19 + 46384476x^18 - 13840937x^17 + 3649186x^16 + 41025120x^15 - 8138959x^14 - 9679906x^13 + 28379769x^12 - 8357477x^11 + 3513515x^10 + 45545418x^9 - 12952087x^8 + 8843411x^7 + 29858262x^6 - 8807791x^5 + 14296232x^4 - 4154414x^3 - 181830x^2 + 2389098x + 733913	$42$	[0,21]	$-\,127^{41}$	$1$	$113.165267975$	✓	✓		$C_{42}$ (as 42T1)	$[1528865]$	$2$	$20$	$418513668789608050000$
42.0.213...363.1	x^42 - 4x^41 + 62x^40 - 200x^39 + 2132x^38 - 6208x^37 + 46584x^36 - 115568x^35 + 701352x^34 - 1537594x^33 + 7769821x^32 - 14875116x^31 + 64656220x^30 - 109927490x^29 + 414171141x^28 - 618138014x^27 + 2041345075x^26 - 2683015728x^25 + 7816607585x^24 - 8902561137x^23 + 22976431713x^22 - 22760113866x^21 + 52536783259x^20 - 45434427911x^19 + 92226880868x^18 - 71336683352x^17 + 125874997329x^16 - 89801104142x^15 + 131144820279x^14 - 89289000509x^13 + 106600416700x^12 - 67935846970x^11 + 65774842016x^10 - 38731708226x^9 + 30551737937x^8 - 15767508635x^7 + 9878705051x^6 - 4297296085x^5 + 2147704850x^4 - 731044046x^3 + 251922248x^2 - 47762400x + 8082649	$42$	[0,21]	$-\,3^{21}\cdot 7^{28}\cdot 29^{36}$	$3$	$113.617000298$	✓	✓	not computed	$C_{42}$ (as 42T1)	not computed	$6$	$20$	$$
42.0.409...667.1	x^42 - x^41 + 20x^40 - 25x^39 - 8x^38 - 138x^37 - 2077x^36 + 839x^35 - 7305x^34 + 8805x^33 + 67596x^32 - 12107x^31 + 444232x^30 - 141646x^29 + 238560x^28 + 2150502x^27 - 3285732x^26 + 14361861x^25 - 708679x^24 + 4004385x^23 + 63920534x^22 - 73366557x^21 + 232544983x^20 + 114300646x^19 + 134380032x^18 + 644451241x^17 - 110366019x^16 + 50739485x^15 + 3000292231x^14 - 3874326960x^13 + 7531027885x^12 - 11845394651x^11 + 8115584321x^10 - 10398559445x^9 + 11442787794x^8 - 3901741530x^7 + 3575301015x^6 - 3614499453x^5 - 715331685x^4 + 331663193x^3 + 2507361126x^2 - 1452650295x + 649728353	$42$	[0,21]	$-\,7^{35}\cdot 29^{39}$	$2$	$115.395630586$	✓	✓		$C_{42}$ (as 42T1)	not computed	$2$	$20$	$$
42.42.776...312.1	x^42 - 105x^40 + 4977x^38 - 140819x^36 - 2x^35 + 2650095x^34 + 28x^33 - 34991649x^32 + 3416x^31 + 333300632x^30 - 147910x^29 - 2319579309x^28 + 2698850x^27 + 11820066804x^26 - 26976474x^25 - 43812582639x^24 + 153194076x^23 + 116368453593x^22 - 445815310x^21 - 216225058245x^20 + 272316800x^19 + 271556250546x^18 + 1986860386x^17 - 220004406804x^16 - 5445985720x^15 + 108239023559x^14 + 5365080098x^13 - 29954210552x^12 - 2176838734x^11 + 4303639312x^10 + 340937478x^9 - 323375283x^8 - 25471098x^7 + 12576760x^6 + 955878x^5 - 232127x^4 - 16898x^3 + 1505x^2 + 112x + 1	$42$	[42,0]	$2^{42}\cdot 3^{21}\cdot 7^{76}$	$3$	$117.169788991$		✓	not computed	$C_{42}$ (as 42T1)	not computed	$2$	$41$	$$
42.42.874...677.1	x^42 - 126x^40 + 7371x^38 - 265734x^36 - 83x^35 + 6608385x^34 + 8715x^33 - 120236886x^32 - 418320x^31 + 1656597096x^30 + 12157425x^29 - 17647825586x^28 - 238834575x^27 + 147151366404x^26 + 3353237433x^25 - 966133116900x^24 - 34688663100x^23 + 4999488494931x^22 + 268659947305x^21 - 20317109311296x^20 - 1567171092690x^19 + 64305659489211x^18 + 6871145069880x^17 - 156373597496214x^16 - 22423210892208x^15 + 286220369519701x^14 + 53473028777910x^13 - 382576512454206x^12 - 90465142642875x^11 + 356767740698292x^10 + 103652112041415x^9 - 215794576784304x^8 - 74585905238228x^7 + 74443140953685x^6 + 29468446974645x^5 - 11170399688028x^4 - 4811855646528x^3 + 319923920106x^2 + 140495689782x - 11523307067	$42$	[42,0]	$7^{77}\cdot 11^{21}$	$2$	$117.501321031$		✓	not computed	$C_{42}$ (as 42T1)	not computed	$2$	$41$	$$
42.0.123...863.1	x^42 + 6x^40 - 4x^39 - 207x^38 - 72x^37 - 857x^36 + 225x^35 + 13524x^34 + 4498x^33 + 47646x^32 - 1779x^31 - 319728x^30 + 56511x^29 - 873558x^28 + 1268358x^27 + 3182931x^26 - 287550x^25 + 12585242x^24 - 25238916x^23 + 37767705x^22 + 35532417x^21 + 14671665x^20 + 387146580x^19 - 33604015x^18 + 83426931x^17 + 893018691x^16 - 978644267x^15 + 2536898589x^14 + 320653281x^13 + 1627927205x^12 + 1198131426x^11 - 1595121042x^10 - 2227675498x^9 - 1701355491x^8 - 2415610293x^7 - 905477771x^6 + 53305794x^5 + 1490523864x^4 + 2070850257x^3 + 1799361396x^2 + 662562267x + 198529417	$42$	[0,21]	$-\,3^{63}\cdot 29^{39}$	$2$	$118.473953209$	✓	✓		$C_{42}$ (as 42T1)	not computed	$2$	$20$	$$
42.0.161...211.1	x^42 - 19x^41 + 193x^40 - 1368x^39 + 7730x^38 - 37504x^37 + 163424x^36 - 653089x^35 + 2424227x^34 - 8429227x^33 + 27684879x^32 - 86328882x^31 + 256735509x^30 - 730024655x^29 + 1991090346x^28 - 5216701163x^27 + 13158377790x^26 - 31970357867x^25 + 74948907297x^24 - 169511696295x^23 + 370383530887x^22 - 781186383780x^21 + 1592472532020x^20 - 3132457376500x^19 + 5954059663605x^18 - 10905928130092x^17 + 19286342092183x^16 - 32785066852903x^15 + 53727191837034x^14 - 84287557742257x^13 + 127210697307990x^12 - 182579457912758x^11 + 251464793643596x^10 - 325756069207898x^9 + 403964380869043x^8 - 462110196994188x^7 + 505689982566923x^6 - 491465579236069x^5 + 459935510967285x^4 - 350571727520514x^3 + 266244504765895x^2 - 126760076648507x + 70799148954451	$42$	[0,21]	$-\,11^{21}\cdot 43^{40}$	$2$	$119.228638861$	✓	✓	not computed	$C_{42}$ (as 42T1)	not computed	$2$	$20$	$$