Global number field search results

Further refine search

Degree	Signature	Galois group	Class number	Class group
Regulator	Num. ramified primes	Ramified primes		Unramified primes
CM field	Discriminant		Root discriminant

Results (displaying matches 1-50 of 881)

Label	Polynomial	Discriminant	Galois group	Class group
32.0.1689856796077948861582881651286068022251129150390625.1	x^32 - x^31 + 8x^30 - 9x^29 + 44x^28 - 38x^27 + 192x^26 - 145x^25 + 766x^24 - 556x^23 + 2257x^22 - 1493x^21 + 5640x^20 - 2513x^19 + 11628x^18 - 4801x^17 + 21029x^16 - 8919x^15 + 26197x^14 - 7798x^13 + 27196x^12 - 90x^11 + 19367x^10 - 2094x^9 + 12428x^8 - 3657x^7 + 3055x^6 - 664x^5 + 741x^4 + 134x^3 + 26x^2 + 4x + 1	\( 5^{24}\cdot 17^{28} \)	$C_4\times C_8$ (as 32T43)	$[365]$ (GRH)
32.0.1267650600228229401496703205376000000000000000000000000.1	x^32 - 8x^30 + 44x^28 - 208x^26 + 910x^24 - 2800x^22 + 7440x^20 - 17664x^18 + 35492x^16 - 44096x^14 + 49952x^12 - 50240x^10 + 37432x^8 - 5696x^6 + 864x^4 - 128x^2 + 16	\( 2^{124}\cdot 5^{24} \)	$C_4\times C_8$ (as 32T43)	$[85]$ (GRH)
32.0.1267650600228229401496703205376000000000000000000000000.2	x^32 + 8x^30 + 44x^28 + 208x^26 + 910x^24 + 2800x^22 + 7440x^20 + 17664x^18 + 35492x^16 + 44096x^14 + 49952x^12 + 50240x^10 + 37432x^8 + 5696x^6 + 864x^4 + 128x^2 + 16	\( 2^{124}\cdot 5^{24} \)	$C_4\times C_8$ (as 32T43)	$[3, 615]$ (GRH)
32.32.20282409603651670423947251286016000000000000000000000000.1	x^32 - 32x^30 + 464x^28 - 4032x^26 + 23400x^24 - 95680x^22 + 283360x^20 - 615296x^18 + 980627x^16 - 1136944x^14 + 940472x^12 - 537120x^10 + 200892x^8 - 45024x^6 + 5104x^4 - 192x^2 + 1	\( 2^{128}\cdot 5^{24} \)	$C_4\times C_8$ (as 32T43)	Trivial (GRH)
32.0.20282409603651670423947251286016000000000000000000000000.1	x^32 + 32x^30 + 464x^28 + 4032x^26 + 23400x^24 + 95680x^22 + 283360x^20 + 615296x^18 + 980627x^16 + 1136944x^14 + 940472x^12 + 537120x^10 + 200892x^8 + 45024x^6 + 5104x^4 + 192x^2 + 1	\( 2^{128}\cdot 5^{24} \)	$C_4\times C_8$ (as 32T43)	$[3, 4182]$ (GRH)
32.32.72742794030721358896825924818930661340866148471832275390625.1	x^32 - 4x^31 - 57x^30 + 246x^29 + 1318x^28 - 6334x^27 - 15812x^26 + 89642x^25 + 102376x^24 - 771912x^23 - 299890x^22 + 4237982x^21 - 283286x^20 - 15130884x^19 + 5324168x^18 + 35220860x^17 - 18558598x^16 - 52954720x^15 + 32826914x^14 + 50625606x^13 - 32389886x^12 - 30305480x^11 + 17702718x^10 + 11166940x^9 - 5039008x^8 - 2410058x^7 + 624842x^6 + 256798x^5 - 16252x^4 - 6488x^3 + 67x^2 + 46x + 1	\( 3^{16}\cdot 5^{24}\cdot 17^{28} \)	$C_4\times C_8$ (as 32T43)	Trivial (GRH)
32.0.72742794030721358896825924818930661340866148471832275390625.1	x^32 - x^31 + x^30 - 2x^29 - 157x^28 + 136x^27 + 194x^26 + 123x^25 + 6029x^24 - 784x^23 - 15683x^22 - 28328x^21 - 43829x^20 - 60297x^19 + 259309x^18 + 488309x^17 + 580886x^16 + 27606x^15 - 197086x^14 - 6589011x^13 - 48880x^12 - 11329204x^11 + 10963461x^10 + 3190803x^9 + 31270930x^8 + 19525837x^7 + 28309424x^6 + 9007615x^5 + 7220745x^4 - 102743x^3 + 1319440x^2 + 211141x + 330991	\( 3^{16}\cdot 5^{24}\cdot 17^{28} \)	$C_4\times C_8$ (as 32T43)	$[2, 2482]$ (GRH)
32.0.72742794030721358896825924818930661340866148471832275390625.3	x^32 - x^31 - 9x^30 + 8x^29 + 78x^28 + 81x^27 - 811x^26 - 417x^25 + 6444x^24 + 736x^23 - 208x^22 - 31498x^21 - 10544x^20 - 22352x^19 + 161874x^18 + 175569x^17 - 155159x^16 - 641829x^15 + 1310904x^14 - 657436x^13 + 1201420x^12 - 5443694x^11 + 4223756x^10 - 6671092x^9 + 16511370x^8 + 1917717x^7 + 1253609x^6 - 32655165x^5 + 45419760x^4 - 19509848x^3 - 39942885x^2 - 51358169x + 112550881	\( 3^{16}\cdot 5^{24}\cdot 17^{28} \)	$C_4\times C_8$ (as 32T43)	$[2, 170]$ (GRH)
32.0.7257879674078131427258907485712138496000000000000000000000000.1	x^32 - 17x^30 + 221x^28 - 2686x^26 + 32062x^24 - 145945x^22 + 525402x^20 - 1687182x^18 + 4815029x^16 - 9305222x^14 + 16320986x^12 - 25297037x^10 + 29310958x^8 - 7182806x^6 + 1753941x^4 - 417605x^2 + 83521	\( 2^{32}\cdot 5^{24}\cdot 17^{28} \)	$C_4\times C_8$ (as 32T43)	n/a
32.32.7257879674078131427258907485712138496000000000000000000000000.1	x^32 - 4x^31 - 62x^30 + 254x^29 + 1634x^28 - 6922x^27 - 23918x^26 + 106300x^25 + 212831x^24 - 1015754x^23 - 1179608x^22 + 6296568x^21 + 3963550x^20 - 25646062x^19 - 7114737x^18 + 68207746x^17 + 2809454x^16 - 115984606x^15 + 13245392x^14 + 121984038x^13 - 25600339x^12 - 75984420x^11 + 19655062x^10 + 26633854x^9 - 7358192x^8 - 4774168x^7 + 1309965x^6 + 357464x^5 - 89234x^4 - 7564x^3 + 1651x^2 - 74x + 1	\( 2^{32}\cdot 5^{24}\cdot 17^{28} \)	$C_4\times C_8$ (as 32T43)	Trivial (GRH)
32.0.7257879674078131427258907485712138496000000000000000000000000.2	x^32 - 7x^30 - 94x^28 + 739x^26 + 1632x^24 - 21915x^22 + 61832x^20 - 161567x^18 + 517344x^16 + 629743x^14 - 3440334x^12 - 4579907x^10 + 12169433x^8 + 32864424x^6 + 28638896x^4 + 6817920x^2 + 2027776	\( 2^{32}\cdot 5^{24}\cdot 17^{28} \)	$C_4\times C_8$ (as 32T43)	$[2, 2, 10, 730]$ (GRH)
32.32.8774238133649262699883985224531159760379882962200337418551296.1	x^32 - 60x^30 + 1542x^28 - 22360x^26 + 203404x^24 - 1224784x^22 + 5034128x^20 - 14374848x^18 + 28730096x^16 - 40097856x^14 + 38567232x^12 - 24884992x^10 + 10286208x^8 - 2526720x^6 + 327168x^4 - 18432x^2 + 256	\( 2^{88}\cdot 17^{28} \)	$C_4\times C_8$ (as 32T43)	Trivial (GRH)
32.0.8774238133649262699883985224531159760379882962200337418551296.1	x^32 + 60x^30 + 1542x^28 + 22360x^26 + 203404x^24 + 1224784x^22 + 5034128x^20 + 14374848x^18 + 28730096x^16 + 40097856x^14 + 38567232x^12 + 24884992x^10 + 10286208x^8 + 2526720x^6 + 327168x^4 + 18432x^2 + 256	\( 2^{88}\cdot 17^{28} \)	$C_4\times C_8$ (as 32T43)	$[8, 72488]$ (GRH)
32.0.15388994837398808258189466602517183151497694747133163269152801.1	x^32 - 4x^31 - 9x^30 + 90x^29 - 46x^28 - 558x^27 + 1218x^26 + 1208x^25 - 1596x^24 + 6274x^23 - 6246x^22 + 55176x^21 + 119832x^20 - 5090x^19 + 698130x^18 + 815952x^17 + 1621632x^16 + 5502716x^15 + 2685146x^14 + 9810462x^13 + 10151814x^12 - 16856174x^11 + 13433300x^10 - 17714304x^9 + 33195458x^8 + 175428026x^7 + 842388x^6 - 165678188x^5 + 111572666x^4 + 47363710x^3 + 50770223x^2 - 14835712x + 34431289	\( 13^{24}\cdot 17^{28} \)	$C_4\times C_8$ (as 32T43)	$[2, 2, 2, 2, 6, 1020]$ (GRH)
32.32.54568201713507127370225565301626372096000000000000000000000000.1	x^32 - 56x^30 + 1316x^28 - 17104x^26 + 136570x^24 - 705040x^22 + 2417360x^20 - 5581792x^18 + 8730872x^16 - 9255712x^14 + 6621008x^12 - 3155840x^10 + 976032x^8 - 186432x^6 + 20096x^4 - 1024x^2 + 16	\( 2^{124}\cdot 3^{16}\cdot 5^{24} \)	$C_4\times C_8$ (as 32T43)	Trivial (GRH)
32.0.54568201713507127370225565301626372096000000000000000000000000.1	x^32 + 56x^30 + 1316x^28 + 17104x^26 + 136570x^24 + 705040x^22 + 2417360x^20 + 5581792x^18 + 8730872x^16 + 9255712x^14 + 6621008x^12 + 3155840x^10 + 976032x^8 + 186432x^6 + 20096x^4 + 1024x^2 + 16	\( 2^{124}\cdot 3^{16}\cdot 5^{24} \)	$C_4\times C_8$ (as 32T43)	$[3, 3, 42, 1722]$ (GRH)
32.32.54568201713507127370225565301626372096000000000000000000000000.2	x^32 - 8x^31 - 36x^30 + 440x^29 + 134x^28 - 9792x^27 + 11652x^26 + 113616x^25 - 240255x^24 - 732960x^23 + 2231260x^22 + 2495960x^21 - 11792220x^20 - 2751040x^19 + 37734684x^18 - 9662688x^17 - 73953556x^16 + 40994896x^15 + 87563076x^14 - 65186904x^13 - 61202386x^12 + 52549560x^11 + 25065416x^10 - 22254968x^9 - 6034148x^8 + 4705064x^7 + 803092x^6 - 427104x^5 - 38980x^4 + 16600x^3 + 376x^2 - 192x + 1	\( 2^{124}\cdot 3^{16}\cdot 5^{24} \)	$C_4\times C_8$ (as 32T43)	Trivial (GRH)
32.0.54568201713507127370225565301626372096000000000000000000000000.4	x^32 - 8x^31 + 28x^30 - 40x^29 + 54x^28 - 512x^27 + 2516x^26 - 5296x^25 + 3985x^24 - 2080x^23 + 37260x^22 - 153000x^21 + 294260x^20 - 227840x^19 - 382084x^18 + 1259168x^17 + 717500x^16 - 10742192x^15 + 22324164x^14 - 3197336x^13 - 76009730x^12 + 176356600x^11 - 141389160x^10 - 339377432x^9 + 1611662172x^8 - 3467919192x^7 + 4930199252x^6 - 5279972480x^5 + 4642269708x^4 - 2995482536x^3 + 970581784x^2 - 206749664x + 295089121	\( 2^{124}\cdot 3^{16}\cdot 5^{24} \)	$C_4\times C_8$ (as 32T43)	$[14, 21182]$ (GRH)
32.0.54568201713507127370225565301626372096000000000000000000000000.5	x^32 - 24x^30 + 396x^28 - 5616x^26 + 73710x^24 - 680400x^22 + 5423760x^20 - 38631168x^18 + 232863012x^16 - 867941568x^14 + 2949615648x^12 - 8899865280x^10 + 19892899512x^8 - 9081263808x^6 + 4132485216x^4 - 1836660096x^2 + 688747536	\( 2^{124}\cdot 3^{16}\cdot 5^{24} \)	$C_4\times C_8$ (as 32T43)	n/a
32.0.54568201713507127370225565301626372096000000000000000000000000.6	x^32 + 24x^30 + 396x^28 + 5616x^26 + 73710x^24 + 680400x^22 + 5423760x^20 + 38631168x^18 + 232863012x^16 + 867941568x^14 + 2949615648x^12 + 8899865280x^10 + 19892899512x^8 + 9081263808x^6 + 4132485216x^4 + 1836660096x^2 + 688747536	\( 2^{124}\cdot 3^{16}\cdot 5^{24} \)	$C_4\times C_8$ (as 32T43)	n/a
32.0.85748808121891140298253320589821486779348249495029449462890625.1	x^32 - x^31 - 2x^30 - 6x^29 - 21x^28 - 406x^27 + 417x^26 + 1503x^25 + 2405x^24 + 5907x^23 + 51558x^22 - 80653x^21 - 292681x^20 - 304226x^19 - 38117x^18 - 2136490x^17 + 7115533x^16 + 17827751x^15 - 1285999x^14 - 34006613x^13 + 23039126x^12 + 24562491x^11 - 146418413x^10 - 215674134x^9 + 198051499x^8 + 330667302x^7 + 301645453x^6 + 191861363x^5 + 93574213x^4 + 82119327x^3 + 57690613x^2 + 32860640x + 12117361	\( 5^{24}\cdot 41^{28} \)	$C_4\times C_8$ (as 32T43)	$[24, 120]$ (GRH)
32.32.873091227416114037923609044826021953536000000000000000000000000.2	x^32 - 96x^30 + 4176x^28 - 108864x^26 + 1895400x^24 - 23250240x^22 + 206569440x^20 - 1345652352x^18 + 6433893747x^16 - 22378468752x^14 + 55533931128x^12 - 95149196640x^10 + 106762245372x^8 - 71782798752x^6 + 24412273776x^4 - 2754990144x^2 + 43046721	\( 2^{128}\cdot 3^{16}\cdot 5^{24} \)	$C_4\times C_8$ (as 32T43)	n/a
32.0.873091227416114037923609044826021953536000000000000000000000000.5	x^32 - 16x^30 + 56x^28 + 256x^26 - 1460x^24 - 1760x^22 + 12800x^20 + 10048x^18 + 12827x^16 + 536128x^14 + 2598488x^12 + 4206560x^10 + 8338152x^8 - 605472x^6 + 4540976x^4 - 921344x^2 + 34093921	\( 2^{128}\cdot 3^{16}\cdot 5^{24} \)	$C_4\times C_8$ (as 32T43)	$[2, 24, 1968]$ (GRH)
32.0.873091227416114037923609044826021953536000000000000000000000000.6	x^32 + 16x^30 + 56x^28 - 256x^26 - 1460x^24 + 1760x^22 + 12800x^20 - 10048x^18 + 12827x^16 - 536128x^14 + 2598488x^12 - 4206560x^10 + 8338152x^8 + 605472x^6 + 4540976x^4 + 921344x^2 + 34093921	\( 2^{128}\cdot 3^{16}\cdot 5^{24} \)	$C_4\times C_8$ (as 32T43)	n/a
32.0.873091227416114037923609044826021953536000000000000000000000000.7	x^32 + 96x^30 + 4176x^28 + 108864x^26 + 1895400x^24 + 23250240x^22 + 206569440x^20 + 1345652352x^18 + 6433893747x^16 + 22378468752x^14 + 55533931128x^12 + 95149196640x^10 + 106762245372x^8 + 71782798752x^6 + 24412273776x^4 + 2754990144x^2 + 43046721	\( 2^{128}\cdot 3^{16}\cdot 5^{24} \)	$C_4\times C_8$ (as 32T43)	n/a
32.0.873091227416114037923609044826021953536000000000000000000000000.10	x^32 - 48x^30 + 984x^28 - 11328x^26 + 81260x^24 - 382560x^22 + 1217920x^20 - 2670144x^18 + 4129467x^16 - 5233056x^14 + 14823352x^12 - 99845280x^10 + 479321832x^8 - 1275041376x^6 + 1668661744x^4 - 832092288x^2 + 779470561	\( 2^{128}\cdot 3^{16}\cdot 5^{24} \)	$C_4\times C_8$ (as 32T43)	$[2, 8, 272]$ (GRH)
32.0.873091227416114037923609044826021953536000000000000000000000000.11	x^32 + 48x^30 + 984x^28 + 11328x^26 + 81260x^24 + 382560x^22 + 1217920x^20 + 2670144x^18 + 4129467x^16 + 5233056x^14 + 14823352x^12 + 99845280x^10 + 479321832x^8 + 1275041376x^6 + 1668661744x^4 + 832092288x^2 + 779470561	\( 2^{128}\cdot 3^{16}\cdot 5^{24} \)	$C_4\times C_8$ (as 32T43)	n/a
32.0.2246204962214211251170300217479976898657250038323286379149131776.2	x^32 - 8x^30 - 124x^28 + 736x^26 + 4997x^24 - 15672x^22 - 27588x^20 + 201200x^18 + 376952x^16 - 3438736x^14 + 6156800x^12 - 2082176x^10 + 382501x^8 - 16686272x^6 + 26615832x^4 - 10774256x^2 + 3243601	\( 2^{96}\cdot 17^{28} \)	$C_4\times C_8$ (as 32T43)	n/a
32.0.2246204962214211251170300217479976898657250038323286379149131776.3	x^32 + 8x^30 - 124x^28 - 736x^26 + 4997x^24 + 15672x^22 - 27588x^20 - 201200x^18 + 376952x^16 + 3438736x^14 + 6156800x^12 + 2082176x^10 + 382501x^8 + 16686272x^6 + 26615832x^4 + 10774256x^2 + 3243601	\( 2^{96}\cdot 17^{28} \)	$C_4\times C_8$ (as 32T43)	$[2, 2, 2, 6, 4182]$ (GRH)
32.0.11544095681843725705116280971624020302917345750478466341169790976.1	x^32 - 8x^31 + 76x^30 - 376x^29 + 1990x^28 - 7200x^27 + 27220x^26 - 78416x^25 + 230321x^24 - 549536x^23 + 1299116x^22 - 2640872x^21 + 5132100x^20 - 8981104x^19 + 14525436x^18 - 22097552x^17 + 30299804x^16 - 38582432x^15 + 45545668x^14 - 51444648x^13 + 48961614x^12 - 37727976x^11 + 45640456x^10 - 34775816x^9 - 15710452x^8 - 19426712x^7 + 45725380x^6 + 54746128x^5 - 17251700x^4 - 60652600x^3 - 26861080x^2 + 26719104x + 19747393	\( 2^{124}\cdot 13^{24} \)	$C_4\times C_8$ (as 32T43)	$[45, 45]$ (GRH)
32.0.11544095681843725705116280971624020302917345750478466341169790976.2	x^32 - 8x^31 + 12x^30 + 104x^29 - 426x^28 + 32x^27 + 2948x^26 - 5200x^25 - 351x^24 + 12896x^23 - 26884x^22 + 106392x^21 - 108044x^20 - 106160x^19 + 1069852x^18 - 1263952x^17 + 2202572x^16 + 2415456x^15 - 5967804x^14 + 18098136x^13 - 15688322x^12 - 17522856x^11 + 52305080x^10 - 101764328x^9 + 173545612x^8 + 103143400x^7 - 285976060x^6 - 53577424x^5 + 350995068x^4 - 163307832x^3 + 89896776x^2 - 55119136x + 58281889	\( 2^{124}\cdot 13^{24} \)	$C_4\times C_8$ (as 32T43)	$[5, 87965]$ (GRH)
32.32.56158893576626869963359344621945280012905849018156528472900390625.1	x^32 - 4x^31 - 97x^30 + 416x^29 + 3953x^28 - 18474x^27 - 87837x^26 + 461322x^25 + 1146281x^24 - 7186022x^23 - 8540945x^22 + 73242962x^21 + 26561229x^20 - 497884694x^19 + 105769163x^18 + 2251615110x^17 - 1474815293x^16 - 6592149900x^15 + 6946567999x^14 + 11614969466x^13 - 17900177751x^12 - 9777588040x^11 + 26279937053x^10 - 1494801150x^9 - 20290513343x^8 + 9449532252x^7 + 5947593437x^6 - 5889335682x^5 + 731994753x^4 + 828328332x^3 - 384738348x^2 + 63812896x - 3700304	\( 5^{24}\cdot 7^{16}\cdot 17^{28} \)	$C_4\times C_8$ (as 32T43)	Trivial (GRH)
32.0.56158893576626869963359344621945280012905849018156528472900390625.2	x^32 - x^31 - 6x^30 + 5x^29 - 546x^28 + 556x^27 + 4802x^26 - 4187x^25 + 57950x^24 + 71120x^23 - 710547x^22 - 1199025x^21 + 81720x^20 - 12009033x^19 + 32840498x^18 + 115457045x^17 + 148502093x^16 + 90690253x^15 + 77390757x^14 - 4980292302x^13 - 6297437270x^12 - 14252605152x^11 + 651843825x^10 + 45573354048x^9 + 154455067964x^8 + 270487093719x^7 + 331005058977x^6 + 207815025774x^5 + 32016319033x^4 - 98707729302x^3 - 79785142736x^2 + 5111337362x + 18479977261	\( 5^{24}\cdot 7^{16}\cdot 17^{28} \)	$C_4\times C_8$ (as 32T43)	n/a
32.0.56158893576626869963359344621945280012905849018156528472900390625.3	x^32 - x^31 - 26x^30 + 25x^29 + 554x^28 + 166x^27 - 12048x^26 - 2967x^25 + 243900x^24 - 34760x^23 - 1239627x^22 - 566845x^21 + 4462190x^20 - 23080013x^19 + 12321838x^18 + 133745895x^17 + 71438063x^16 - 731908967x^15 + 958307527x^14 + 715528798x^13 - 3048724550x^12 - 8181879192x^11 + 18801912335x^10 - 5205488012x^9 - 6043816216x^8 + 13428234259x^7 + 130340525677x^6 - 276022878046x^5 + 163663111613x^4 - 110147425102x^3 + 183684061184x^2 - 1310299091478x + 1791981145201	\( 5^{24}\cdot 7^{16}\cdot 17^{28} \)	$C_4\times C_8$ (as 32T43)	n/a
32.32.184705530909499611281860495545984324846677532007655461458716655616.1	x^32 - 80x^30 + 2744x^28 - 53120x^26 + 644748x^24 - 5172960x^22 + 28278912x^20 - 107218880x^18 + 283997723x^16 - 523451648x^14 + 659656088x^12 - 548056352x^10 + 280891560x^8 - 78474144x^6 + 9153840x^4 - 160256x^2 + 1	\( 2^{128}\cdot 13^{24} \)	$C_4\times C_8$ (as 32T43)	Trivial (GRH)
32.0.184705530909499611281860495545984324846677532007655461458716655616.1	x^32 + 80x^30 + 2744x^28 + 53120x^26 + 644748x^24 + 5172960x^22 + 28278912x^20 + 107218880x^18 + 283997723x^16 + 523451648x^14 + 659656088x^12 + 548056352x^10 + 280891560x^8 + 78474144x^6 + 9153840x^4 + 160256x^2 + 1	\( 2^{128}\cdot 13^{24} \)	$C_4\times C_8$ (as 32T43)	n/a
32.0.475652402320384421216839760983630708473856000000000000000000000000.1	x^32 + 14x^30 - 376x^28 - 5912x^26 + 26112x^24 + 701280x^22 + 3957248x^20 + 20680576x^18 + 132440064x^16 - 322428416x^14 - 3522902016x^12 + 9379649536x^10 + 49845997568x^8 - 269225361408x^6 + 469219672064x^4 - 223409602560x^2 + 132892327936	\( 2^{48}\cdot 5^{24}\cdot 17^{28} \)	$C_4\times C_8$ (as 32T43)	n/a
32.32.475652402320384421216839760983630708473856000000000000000000000000.1	x^32 - 4x^31 - 102x^30 + 404x^29 + 4549x^28 - 17812x^27 - 117028x^26 + 451980x^25 + 1929761x^24 - 7327884x^23 - 21441958x^22 + 79690868x^21 + 164374860x^20 - 594024912x^19 - 876219412x^18 + 3049830256x^17 + 3236345879x^16 - 10699434056x^15 - 8173761298x^14 + 25146964908x^13 + 13793063056x^12 - 38328647620x^11 - 14997610308x^10 + 36075446764x^9 + 9895657258x^8 - 19452177308x^7 - 3540548500x^6 + 5285519244x^5 + 538535816x^4 - 555932464x^3 - 5956104x^2 + 14755336x - 522239	\( 2^{48}\cdot 5^{24}\cdot 17^{28} \)	$C_4\times C_8$ (as 32T43)	n/a
32.0.475652402320384421216839760983630708473856000000000000000000000000.2	x^32 - 14x^30 - 376x^28 + 5912x^26 + 26112x^24 - 701280x^22 + 3957248x^20 - 20680576x^18 + 132440064x^16 + 322428416x^14 - 3522902016x^12 - 9379649536x^10 + 49845997568x^8 + 269225361408x^6 + 469219672064x^4 + 223409602560x^2 + 132892327936	\( 2^{48}\cdot 5^{24}\cdot 17^{28} \)	$C_4\times C_8$ (as 32T43)	n/a
32.0.475652402320384421216839760983630708473856000000000000000000000000.3	x^32 - 4x^31 + 58x^30 - 196x^29 + 1769x^28 - 5332x^27 + 36592x^26 - 99500x^25 + 565421x^24 - 1397804x^23 + 6873202x^22 - 15497652x^21 + 67844200x^20 - 139719472x^19 + 555470148x^18 - 1043995424x^17 + 3821729999x^16 - 6530125576x^15 + 22197557342x^14 - 34192038852x^13 + 108414578156x^12 - 148455171060x^11 + 440639227972x^10 - 525717928076x^9 + 1465891189858x^8 - 1474785975388x^7 + 3846333624060x^6 - 3081196575196x^5 + 7536247963216x^4 - 4320797259664x^3 + 9841464291016x^2 - 3060156463304x + 6460791592081	\( 2^{48}\cdot 5^{24}\cdot 17^{28} \)	$C_4\times C_8$ (as 32T43)	n/a
32.0.475652402320384421216839760983630708473856000000000000000000000000.5	x^32 - 34x^30 + 884x^28 - 21488x^26 + 512992x^24 - 4670240x^22 + 33625728x^20 - 215959296x^18 + 1232647424x^16 - 4764273664x^14 + 16712689664x^12 - 51808331776x^10 + 120057683968x^8 - 58841546752x^6 + 28736569344x^4 - 13684080640x^2 + 5473632256	\( 2^{48}\cdot 5^{24}\cdot 17^{28} \)	$C_4\times C_8$ (as 32T43)	n/a
32.0.475652402320384421216839760983630708473856000000000000000000000000.6	x^32 + 34x^30 + 884x^28 + 21488x^26 + 512992x^24 + 4670240x^22 + 33625728x^20 + 215959296x^18 + 1232647424x^16 + 4764273664x^14 + 16712689664x^12 + 51808331776x^10 + 120057683968x^8 + 58841546752x^6 + 28736569344x^4 + 13684080640x^2 + 5473632256	\( 2^{48}\cdot 5^{24}\cdot 17^{28} \)	$C_4\times C_8$ (as 32T43)	n/a
32.32.7219274832693987941813796201388115200494782171469796274056657371136.1	x^32 - 8x^31 - 52x^30 + 528x^29 + 942x^28 - 14808x^27 - 4040x^26 + 232952x^25 - 101787x^24 - 2290952x^23 + 1894744x^22 + 14880024x^21 - 15740682x^20 - 65768208x^19 + 78677084x^18 + 200834584x^17 - 255633450x^16 - 425796088x^15 + 553415588x^14 + 624757920x^13 - 797607810x^12 - 627979512x^11 + 749016552x^10 + 424971976x^9 - 437179375x^8 - 187713208x^7 + 144420248x^6 + 50201368x^5 - 21676018x^4 - 6390976x^3 + 552740x^2 + 49768x - 2753	\( 2^{124}\cdot 17^{24} \)	$C_4\times C_8$ (as 32T43)	Trivial (GRH)
32.0.7219274832693987941813796201388115200494782171469796274056657371136.1	x^32 - 8x^31 + 12x^30 + 48x^29 + 30x^28 - 984x^27 + 1096x^26 + 2456x^25 + 2917x^24 - 10632x^23 + 6216x^22 - 151880x^21 + 49206x^20 + 562864x^19 + 734604x^18 + 1498456x^17 + 539142x^16 - 23901944x^15 - 28776348x^14 - 9443456x^13 - 11820722x^12 + 421923464x^11 + 905081912x^10 + 1134683112x^9 + 3831594961x^8 + 442166472x^7 + 6109266600x^6 - 781734536x^5 + 4368859022x^4 - 1030498048x^3 + 646464852x^2 + 118091240x + 449086927	\( 2^{124}\cdot 17^{24} \)	$C_4\times C_8$ (as 32T43)	$[2, 4, 180, 7380]$ (GRH)
32.32.42127744383897781264481528176959874165374976000000000000000000000000.1	x^32 - 96x^30 + 3696x^28 - 75184x^26 + 899720x^24 - 6660000x^22 + 31193320x^20 - 93050912x^18 + 175529272x^16 - 205236512x^14 + 144210848x^12 - 58587840x^10 + 13396712x^8 - 1684032x^6 + 108576x^4 - 2944x^2 + 16	\( 2^{124}\cdot 5^{24}\cdot 7^{16} \)	$C_4\times C_8$ (as 32T43)	Trivial (GRH)
32.32.42127744383897781264481528176959874165374976000000000000000000000000.2	x^32 - 8x^31 - 76x^30 + 760x^29 + 1954x^28 - 30352x^27 - 7628x^26 + 666456x^25 - 634585x^24 - 8827760x^23 + 15632420x^22 + 72455680x^21 - 182544660x^20 - 357343720x^19 + 1267393024x^18 + 888389032x^17 - 5510095721x^16 + 176836216x^15 + 14927443376x^14 - 8043244424x^13 - 23836615436x^12 + 23589054160x^11 + 18807108516x^10 - 31998194928x^9 - 1328020573x^8 + 20765809224x^7 - 7738765748x^6 - 4658045344x^5 + 3842975350x^4 - 498020920x^3 - 286773844x^2 + 103141288x - 9793409	\( 2^{124}\cdot 5^{24}\cdot 7^{16} \)	$C_4\times C_8$ (as 32T43)	n/a
32.0.42127744383897781264481528176959874165374976000000000000000000000000.2	x^32 - 8x^31 - 12x^30 + 280x^29 - 206x^28 - 5712x^27 + 12196x^26 + 71064x^25 - 240585x^24 - 567280x^23 + 2902260x^22 + 2536640x^21 - 22883300x^20 - 4950760x^19 + 120802336x^18 + 38552968x^17 - 478813865x^16 - 813999752x^15 + 2360618384x^14 + 6386853784x^13 - 14042867340x^12 - 20749097200x^11 + 38583306500x^10 + 52356953808x^9 + 54615249427x^8 - 483652890552x^7 + 223883790332x^6 + 456373127360x^5 + 603312953478x^4 - 1277065516216x^3 - 954628846756x^2 + 858240692296x + 1117847129071	\( 2^{124}\cdot 5^{24}\cdot 7^{16} \)	$C_4\times C_8$ (as 32T43)	n/a
32.0.42127744383897781264481528176959874165374976000000000000000000000000.3	x^32 + 96x^30 + 3696x^28 + 75184x^26 + 899720x^24 + 6660000x^22 + 31193320x^20 + 93050912x^18 + 175529272x^16 + 205236512x^14 + 144210848x^12 + 58587840x^10 + 13396712x^8 + 1684032x^6 + 108576x^4 + 2944x^2 + 16	\( 2^{124}\cdot 5^{24}\cdot 7^{16} \)	$C_4\times C_8$ (as 32T43)	n/a
32.0.42127744383897781264481528176959874165374976000000000000000000000000.4	x^32 - 56x^30 + 2156x^28 - 71344x^26 + 2184910x^24 - 47059600x^22 + 875308560x^20 - 14547063552x^18 + 204604317092x^16 - 1779432654272x^14 + 14110203638048x^12 - 99340895568320x^10 + 518107062507832x^8 - 551879803278272x^6 + 585984734941536x^4 - 607687873272704x^2 + 531726889113616	\( 2^{124}\cdot 5^{24}\cdot 7^{16} \)	$C_4\times C_8$ (as 32T43)	n/a
32.0.42127744383897781264481528176959874165374976000000000000000000000000.5	x^32 + 56x^30 + 2156x^28 + 71344x^26 + 2184910x^24 + 47059600x^22 + 875308560x^20 + 14547063552x^18 + 204604317092x^16 + 1779432654272x^14 + 14110203638048x^12 + 99340895568320x^10 + 518107062507832x^8 + 551879803278272x^6 + 585984734941536x^4 + 607687873272704x^2 + 531726889113616	\( 2^{124}\cdot 5^{24}\cdot 7^{16} \)	$C_4\times C_8$ (as 32T43)	n/a