Global number field search results

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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 168)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.6884340550074368.1	x^16 - 6x^15 + 22x^14 - 56x^13 + 110x^12 - 174x^11 + 232x^10 - 266x^9 + 259x^8 - 202x^7 + 112x^6 - 30x^5 - 14x^4 + 20x^3 - 6x^2 - 2x + 1	\( 2^{24}\cdot 17^{7} \)	$C_4.D_4:C_4$ (as 16T289)	Trivial
16.0.530117544460899393.1	x^16 - 4x^15 + 14x^14 - 39x^13 + 86x^12 - 162x^11 + 260x^10 - 360x^9 + 414x^8 - 369x^7 + 231x^6 - 70x^5 - 20x^4 + 27x^3 - 8x^2 - x + 1	\( 3^{8}\cdot 97^{7} \)	$C_4.D_4:C_4$ (as 16T289)	Trivial
16.0.1762391180819038208.2	x^16 - 2x^12 + 19x^8 - 34x^4 + 17	\( 2^{32}\cdot 17^{7} \)	$C_4.D_4:C_4$ (as 16T289)	Trivial
16.8.3267434519824695296.1	x^16 - 4x^15 + 8x^14 - 14x^13 + 20x^12 - 22x^11 + 7x^10 + 18x^9 - 53x^8 + 86x^7 - 119x^6 + 58x^5 + 68x^4 - 42x^3 - 16x^2 + 4x + 1	\( 2^{24}\cdot 41^{7} \)	$C_4.D_4:C_4$ (as 16T289)	Trivial
16.0.5871040516387428777.1	x^16 + 7x^14 - 7x^13 + 25x^12 - 33x^11 + 97x^10 - 87x^9 + 205x^8 - 233x^7 + 283x^6 - 241x^5 + 185x^4 - 109x^3 + 43x^2 - 10x + 1	\( 3^{12}\cdot 73^{7} \)	$C_4.D_4:C_4$ (as 16T289)	Trivial
16.0.6969012721055784593.1	x^16 - 5x^15 + 11x^14 - 4x^13 - 34x^12 + 86x^11 - 69x^10 - 72x^9 + 250x^8 - 275x^7 + 122x^6 + 39x^5 - 62x^4 + 14x^3 + 16x^2 - 8x + 1	\( 17^{7}\cdot 19^{8} \)	$C_4.D_4:C_4$ (as 16T289)	Trivial
16.8.836463237075121995776.2	x^16 + 2x^14 - 20x^13 - 13x^12 - 16x^11 + 114x^10 + 144x^9 + 24x^8 - 296x^7 - 306x^6 + 44x^5 + 258x^4 + 112x^3 - 68x^2 - 28x + 1	\( 2^{32}\cdot 41^{7} \)	$C_4.D_4:C_4$ (as 16T289)	Trivial
16.0.4796120591669025963473.1	x^16 - 7x^15 + 19x^14 - 7x^13 - 97x^12 + 260x^11 - 172x^10 - 428x^9 + 1109x^8 - 1096x^7 + 722x^6 - 692x^5 + 335x^4 + 73x^3 + 65x^2 - 7x + 1	\( 17^{7}\cdot 43^{8} \)	$C_4.D_4:C_4$ (as 16T289)	Trivial
16.0.9770691771209608583153.2	x^16 - 8x^15 + 30x^14 - 70x^13 + 101x^12 - 60x^11 - 115x^10 + 410x^9 - 658x^8 + 656x^7 - 231x^6 - 404x^5 + 1028x^4 - 1172x^3 + 996x^2 - 504x + 243	\( 17^{7}\cdot 47^{8} \)	$C_4.D_4:C_4$ (as 16T289)	$[5]$ (GRH)
16.16.17147496360040000913408.1	x^16 - 16x^14 + 94x^12 - 265x^10 + 391x^8 - 308x^6 + 128x^4 - 26x^2 + 2	\( 2^{31}\cdot 41^{8} \)	$C_4.D_4:C_4$ (as 16T289)	Trivial (GRH)
16.0.17319829847447971671553.1	x^16 - 5x^15 + 11x^14 - 23x^13 + 47x^12 - 59x^11 + 116x^10 - 345x^9 + 541x^8 - 768x^7 + 1388x^6 - 994x^5 + 32x^4 - 879x^3 + 459x^2 + 850x + 269	\( 11^{8}\cdot 97^{7} \)	$C_4.D_4:C_4$ (as 16T289)	Trivial
16.0.60250206922566378206033.1	x^16 - 8x^15 + 24x^14 - 25x^13 - 9x^12 - 74x^11 + 490x^10 - 924x^9 + 910x^8 - 814x^7 + 1005x^6 - 908x^5 + 734x^4 - 272x^3 + 36x^2 - 4x + 1	\( 17^{7}\cdot 59^{8} \)	$C_4.D_4:C_4$ (as 16T289)	$[3]$ (GRH)
16.0.166625271956783950277393.2	x^16 - 8x^15 + 31x^14 - 77x^13 + 173x^12 - 371x^11 + 621x^10 - 836x^9 + 1463x^8 - 1828x^7 + 1237x^6 - 1805x^5 + 2223x^4 + 1361x^3 + 2339x^2 + 726x + 277	\( 17^{7}\cdot 67^{8} \)	$C_4.D_4:C_4$ (as 16T289)	$[5]$ (GRH)
16.16.214134588691231230918656.1	x^16 - 28x^14 + 234x^12 - 876x^10 + 1695x^8 - 1804x^6 + 1066x^4 - 328x^2 + 41	\( 2^{40}\cdot 41^{7} \)	$C_4.D_4:C_4$ (as 16T289)	Trivial (GRH)
16.0.214134588691231230918656.1	x^16 + 28x^14 + 234x^12 + 876x^10 + 1695x^8 + 1804x^6 + 1066x^4 + 328x^2 + 41	\( 2^{40}\cdot 41^{7} \)	$C_4.D_4:C_4$ (as 16T289)	$[3, 6]$
16.16.269966643649468994140625.1	x^16 - 3x^15 - 26x^14 + 82x^13 + 198x^12 - 718x^11 - 449x^10 + 2591x^9 - 507x^8 - 3558x^7 + 2259x^6 + 901x^5 - 687x^4 - 156x^3 + 56x^2 + 16x + 1	\( 5^{14}\cdot 89^{7} \)	$C_4.D_4:C_4$ (as 16T289)	Trivial (GRH)
16.0.269966643649468994140625.1	x^16 - x^15 - 9x^14 + 6x^13 + 123x^12 + 254x^11 + 229x^10 + 313x^9 + 1638x^8 + 3529x^7 + 4151x^6 + 3843x^5 + 5443x^4 + 6438x^3 + 5024x^2 + 2218x + 401	\( 5^{14}\cdot 89^{7} \)	$C_4.D_4:C_4$ (as 16T289)	$[2]$ (GRH)
16.0.363868615074348706640625.1	x^16 - 5x^15 + 3x^14 - 4x^13 + 80x^12 - 174x^11 + 334x^10 - 806x^9 + 912x^8 - 893x^7 + 3355x^6 - 5175x^5 + 3140x^4 - 1156x^3 + 2736x^2 - 1748x + 529	\( 3^{14}\cdot 5^{8}\cdot 41^{7} \)	$C_4.D_4:C_4$ (as 16T289)	$[2]$ (GRH)
16.0.582058911475300184991953.1	x^16 - 6x^15 + 12x^14 + x^13 - 40x^12 + 172x^11 - 25x^10 - 305x^9 + 752x^8 - 675x^7 + 154x^6 + 1113x^5 - 1623x^4 + 579x^3 + 629x^2 - 739x + 305	\( 17^{11}\cdot 19^{8} \)	$C_4.D_4:C_4$ (as 16T289)	$[2]$ (GRH)
16.0.924202605744142035432593.1	x^16 - 4x^15 - 7x^14 + 61x^13 - 32x^12 - 315x^11 + 492x^10 + 479x^9 - 1876x^8 + 1049x^7 + 2612x^6 - 2639x^5 - 461x^4 - 5376x^3 + 5666x^2 + 2330x + 3949	\( 17^{7}\cdot 83^{8} \)	$C_4.D_4:C_4$ (as 16T289)	$[3]$ (GRH)
16.8.37335818540463054882317561.1	x^16 - 4x^15 - 2x^14 + 30x^13 - 66x^12 - 28x^11 + 365x^10 + 339x^9 - 931x^8 - 4384x^7 - 102x^6 + 17058x^5 + 9547x^4 - 21072x^3 - 19007x^2 - 1092x + 1611	\( 41^{7}\cdot 61^{8} \)	$C_4.D_4:C_4$ (as 16T289)	Trivial (GRH)
16.0.46930925056608955875626433.1	x^16 - 5x^15 - 12x^14 + 171x^13 - 123x^12 - 2068x^11 + 3340x^10 + 13003x^9 - 22030x^8 - 79804x^7 + 142619x^6 + 372630x^5 - 1015471x^4 - 69749x^3 + 2505865x^2 - 2986939x + 1181299	\( 3^{8}\cdot 97^{11} \)	$C_4.D_4:C_4$ (as 16T289)	$[2]$ (GRH)
16.0.68912132671990843828028833.1	x^16 - x^15 + 9x^14 + 10x^13 - 65x^12 - 108x^11 + 329x^10 + 621x^9 - 438x^8 - 1692x^7 + 34x^6 + 3020x^5 + 2338x^4 - 1363x^3 - 1839x^2 + 926x + 1327	\( 31^{8}\cdot 97^{7} \)	$C_4.D_4:C_4$ (as 16T289)	$[3]$ (GRH)
16.0.138816876576378001590580409.2	x^16 - 3x^15 - 7x^14 + 37x^13 + 5x^12 - 276x^11 + 305x^10 + 635x^9 - 1264x^8 - 3454x^7 + 5416x^6 + 15875x^5 + 4819x^4 - 15664x^3 - 15620x^2 + 3696x + 8272	\( 11^{12}\cdot 89^{7} \)	$C_4.D_4:C_4$ (as 16T289)	Trivial (GRH)
16.0.166727223505134651779581257.1	x^16 - x^15 + 54x^14 - 159x^13 + 1505x^12 - 5493x^11 + 20123x^10 - 41890x^9 + 113688x^8 - 129668x^7 + 19031x^6 + 511794x^5 - 198259x^4 + 779238x^3 + 3313449x^2 + 1089775x + 96091	\( 3^{12}\cdot 73^{11} \)	$C_4.D_4:C_4$ (as 16T289)	$[2]$ (GRH)
16.0.168215025416361753462674417.1	x^16 - 4x^15 + 17x^14 - 21x^13 - 29x^12 + 49x^11 + 305x^10 + 826x^9 - 323x^8 - 1031x^7 + 2425x^6 + 2213x^5 - 3789x^4 - 2019x^3 + 3524x^2 + 2080x + 353	\( 17^{13}\cdot 19^{8} \)	$C_4.D_4:C_4$ (as 16T289)	$[4]$ (GRH)
16.0.168215025416361753462674417.2	x^16 - 4x^15 - 10x^14 + 74x^13 - 122x^12 - 118x^11 + 1316x^10 - 4138x^9 + 9760x^8 - 15630x^7 + 29961x^6 - 41377x^5 + 55145x^4 - 57267x^3 + 48763x^2 - 17956x + 4489	\( 17^{13}\cdot 19^{8} \)	$C_4.D_4:C_4$ (as 16T289)	$[4]$ (GRH)
16.0.400576787936788717495228433.1	x^16 - 2x^15 - 23x^14 + 75x^13 + 257x^12 - 1167x^11 - 975x^10 + 8314x^9 - 2631x^8 - 26244x^7 + 35757x^6 + 15701x^5 + 57683x^4 - 304085x^3 + 493567x^2 - 258800x + 78949	\( 17^{11}\cdot 43^{8} \)	$C_4.D_4:C_4$ (as 16T289)	$[2]$ (GRH)
16.0.816057947423197718473521713.4	x^16 - 4x^15 + 8x^14 - 29x^13 + 35x^12 - 82x^11 + 465x^10 + 1019x^9 + 424x^8 + 641x^7 - 3230x^6 - 17180x^5 + 1535x^4 + 63306x^3 - 20704x^2 - 70561x + 44357	\( 17^{11}\cdot 47^{8} \)	$C_4.D_4:C_4$ (as 16T289)	$[2, 10]$ (GRH)
16.0.944386531066764936008646913.3	x^16 - 5x^15 + 12x^14 - 32x^13 + 72x^12 + 90x^11 - 203x^10 - 298x^9 - 2060x^8 + 1226x^7 + 12621x^6 + 483x^5 - 28551x^4 + 42851x^3 + 228396x^2 + 275623x + 114563	\( 43^{8}\cdot 97^{7} \)	$C_4.D_4:C_4$ (as 16T289)	Trivial (GRH)
16.0.1923911113486862917838536993.2	x^16 - 3x^15 + 23x^13 + 123x^12 - 54x^11 - 860x^10 + 607x^9 + 202x^8 - 17395x^7 - 8350x^6 + 76302x^5 + 96796x^4 + 9928x^3 + 81135x^2 + 214956x + 122768	\( 47^{8}\cdot 97^{7} \)	$C_4.D_4:C_4$ (as 16T289)	$[5]$ (GRH)
16.0.4267966768632939662191535801.2	x^16 - 3x^15 - 26x^14 + 165x^13 + 184x^12 - 2943x^11 + 3213x^10 + 26164x^9 - 64784x^8 - 95606x^7 + 483073x^6 - 91475x^5 - 1637207x^4 + 1717890x^3 + 1643530x^2 - 3791354x + 2065061	\( 23^{12}\cdot 41^{7} \)	$C_4.D_4:C_4$ (as 16T289)	$[3]$ (GRH)
16.0.5032157532379666474146082193.1	x^16 - 2x^15 - 13x^14 + 13x^13 + 43x^12 + 371x^11 + 911x^10 - 2412x^9 - 9712x^8 - 21167x^7 - 2902x^6 + 137244x^5 + 452160x^4 + 926259x^3 + 1251998x^2 + 1086394x + 680627	\( 17^{11}\cdot 59^{8} \)	$C_4.D_4:C_4$ (as 16T289)	$[6]$ (GRH)
16.0.13916709339102552311118140753.4	x^16 - 7x^15 + 13x^14 + 44x^13 + 256x^12 - 535x^11 + 1005x^10 - 546x^9 + 5016x^8 + 7037x^7 + 16281x^6 + 32756x^5 + 38306x^4 + 30752x^3 + 22338x^2 + 10381x + 2803	\( 17^{11}\cdot 67^{8} \)	$C_4.D_4:C_4$ (as 16T289)	$[2, 10]$ (GRH)
16.0.24451371959186803441564976617.1	x^16 - 3x^15 - 4x^14 + 8x^13 - 187x^12 + 294x^11 + 1123x^10 - 730x^9 + 6731x^8 + 292x^7 - 18088x^6 - 15999x^5 + 349884x^4 + 341793x^3 + 1018387x^2 - 768343x + 2375353	\( 19^{12}\cdot 73^{7} \)	$C_4.D_4:C_4$ (as 16T289)	Trivial (GRH)
16.0.77190325834356486941365599953.1	x^16 - 6x^15 + 19x^14 - 43x^13 + 245x^12 - 837x^11 + 2250x^10 - 2227x^9 - 454x^8 + 17194x^7 + 13639x^6 - 65293x^5 + 388293x^4 - 718066x^3 + 1544858x^2 - 2274735x + 5689003	\( 17^{11}\cdot 83^{8} \)	$C_4.D_4:C_4$ (as 16T289)	$[6]$ (GRH)
16.0.115766691713731939356121017137.1	x^16 - 4x^15 - 13x^14 + 13x^13 - 208x^12 + 615x^11 + 3549x^10 + 3624x^9 + 24634x^8 + 49059x^7 + 68036x^6 + 110519x^5 + 190104x^4 + 506625x^3 + 856157x^2 + 651963x + 180323	\( 17^{13}\cdot 43^{8} \)	$C_4.D_4:C_4$ (as 16T289)	$[4]$ (GRH)
16.0.115766691713731939356121017137.2	x^16 - 8x^15 - 4x^14 + 168x^13 - 188x^12 - 1420x^11 + 3302x^10 + 1464x^9 - 6476x^8 - 7080x^7 + 131882x^6 - 340070x^5 + 426206x^4 - 309188x^3 - 373724x^2 + 475135x + 775541	\( 17^{13}\cdot 43^{8} \)	$C_4.D_4:C_4$ (as 16T289)	$[4]$ (GRH)
16.0.153400693519826106945591092441.1	x^16 - 5x^15 + 7x^14 + 99x^13 - 356x^12 - 1132x^11 + 3572x^10 + 8350x^9 - 14239x^8 - 36480x^7 - 11456x^6 + 96639x^5 + 329692x^4 - 182670x^3 - 1169950x^2 + 185500x + 1500625	\( 31^{12}\cdot 41^{7} \)	$C_4.D_4:C_4$ (as 16T289)	$[3]$ (GRH)
16.0.235840746805304140638847775057.4	x^16 - 8x^15 + 30x^14 - 70x^13 - 86x^12 + 1062x^11 - 3974x^10 + 9420x^9 - 4164x^8 - 27038x^7 + 174382x^6 - 401814x^5 + 919138x^4 - 1212534x^3 + 1711428x^2 - 1165773x + 1666681	\( 17^{13}\cdot 47^{8} \)	$C_4.D_4:C_4$ (as 16T289)	$[4, 20]$ (GRH)
16.0.235840746805304140638847775057.5	x^16 - 4x^15 - 22x^14 + 86x^13 + 184x^12 - 590x^11 - 223x^10 - 3842x^9 + 27319x^8 - 165022x^7 + 739945x^6 - 1832404x^5 + 3521479x^4 - 6214060x^3 + 7132469x^2 - 6444788x + 5564881	\( 17^{13}\cdot 47^{8} \)	$C_4.D_4:C_4$ (as 16T289)	$[4, 20]$ (GRH)
16.0.242099589496868228963210570137.1	x^16 - 6x^15 + 9x^14 + 76x^13 - 257x^12 + 72x^11 + 1069x^10 + 2288x^9 - 3048x^8 - 26060x^7 + 141119x^6 - 44446x^5 - 197231x^4 + 2236473x^3 - 148671x^2 - 11428128x + 15512391	\( 23^{12}\cdot 73^{7} \)	$C_4.D_4:C_4$ (as 16T289)	$[3]$ (GRH)
16.0.441573073857633665833769108097.1	x^16 - 2x^15 - 72x^14 + 35x^13 + 1730x^12 + 1148x^11 - 13574x^10 - 13264x^9 + 62090x^8 + 91739x^7 + 59197x^6 + 222822x^5 + 337044x^4 - 93725x^3 + 157928x^2 + 79985x + 87721	\( 3^{8}\cdot 97^{13} \)	$C_4.D_4:C_4$ (as 16T289)	$[4]$ (GRH)
16.0.441573073857633665833769108097.2	x^16 - 4x^15 + 33x^14 - 256x^13 + 1002x^12 - 3750x^11 + 19159x^10 - 60643x^9 + 129678x^8 - 385606x^7 + 1010979x^6 - 621919x^5 - 1198369x^4 - 3332401x^3 + 20600666x^2 - 29838288x + 14591551	\( 3^{8}\cdot 97^{13} \)	$C_4.D_4:C_4$ (as 16T289)	$[4]$ (GRH)
16.0.888489374058862559333388518553.1	x^16 - 3x^15 - 41x^14 + 151x^13 + 1726x^12 + 1245x^11 - 10904x^10 + 16035x^9 + 190159x^8 + 341342x^7 - 115337x^6 - 1549502x^5 - 1969087x^4 + 823765x^3 + 1279138x^2 + 2209756x + 7274677	\( 3^{12}\cdot 73^{13} \)	$C_4.D_4:C_4$ (as 16T289)	$[4]$ (GRH)
16.0.888489374058862559333388518553.2	x^16 - x^15 - 46x^14 + 201x^13 + 1710x^12 - 4394x^11 - 24509x^10 + 91982x^9 + 363862x^8 - 670143x^7 - 1709406x^6 + 16998374x^5 + 87471399x^4 + 193906446x^3 + 244084510x^2 + 171975278x + 52726789	\( 3^{12}\cdot 73^{13} \)	$C_4.D_4:C_4$ (as 16T289)	$[4]$ (GRH)
16.0.1454293526857723611028217753777.1	x^16 - 4x^15 - 7x^14 + 75x^13 - 229x^12 + 115x^11 + 1296x^10 - 2939x^9 + 5710x^8 - 13835x^7 + 111463x^6 - 274658x^5 + 587698x^4 - 745842x^3 + 1436059x^2 - 1312335x + 572661	\( 17^{13}\cdot 59^{8} \)	$C_4.D_4:C_4$ (as 16T289)	$[12]$ (GRH)
16.0.1454293526857723611028217753777.2	x^16 - 2x^15 - 34x^14 + 194x^13 - 132x^12 - 2562x^11 + 17177x^10 - 79564x^9 + 300789x^8 - 894616x^7 + 2128095x^6 - 4264318x^5 + 7120382x^4 - 9199270x^3 + 8457612x^2 - 4906712x + 1422185	\( 17^{13}\cdot 59^{8} \)	$C_4.D_4:C_4$ (as 16T289)	$[12]$ (GRH)
16.0.1533312083436908616990955243393.1	x^16 - 3x^15 + 32x^14 - 208x^13 + 2259x^12 - 4308x^11 + 4001x^10 - 43853x^9 + 101795x^8 - 25994x^7 + 97717x^6 - 564362x^5 + 610004x^4 - 130309x^3 + 129810x^2 - 328710x + 152441	\( 11^{8}\cdot 97^{11} \)	$C_4.D_4:C_4$ (as 16T289)	$[2]$ (GRH)
16.0.4021928999000637617913142677617.5	x^16 - 7x^15 + 15x^14 + 15x^13 + 702x^12 + 2439x^11 - 3698x^10 - 4348x^9 + 70051x^8 + 68003x^7 - 281102x^6 - 230649x^5 + 755793x^4 + 624720x^3 - 788730x^2 - 457257x + 444313	\( 17^{13}\cdot 67^{8} \)	$C_4.D_4:C_4$ (as 16T289)	$[4, 4]$ (GRH)