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 |
9.1.29510281.1 |
$ x^{9} - 2 x^{8} + 2 x^{7} - 3 x^{5} + 7 x^{4} - 8 x^{3} + 6 x^{2} + \cdots + 1 $ |
$9$ |
[1,4] |
$101\cdot 292181$ |
$2$ |
$6.76078364853$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$4$ |
$0.680531134278$ |
9.1.30073129.1 |
$ x^{9} - 2 x^{8} + 2 x^{7} - x^{5} + x^{3} + x^{2} - 2 x + 1 $ |
$9$ |
[1,4] |
$353\cdot 85193$ |
$2$ |
$6.77499119692$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$4$ |
$0.688991454074$ |
9.1.30450401.1 |
$ x^{9} - x^{8} - x^{7} + 3 x^{6} - x^{5} - 2 x^{4} + x^{3} - 1 $ |
$9$ |
[1,4] |
$31\cdot 982271$ |
$2$ |
$6.784382654590378$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$4$ |
$0.6943689096630966$ |
9.1.30453593.1 |
$ x^{9} - x^{7} - x^{6} + x^{4} - x^{3} + x + 1 $ |
$9$ |
[1,4] |
$137\cdot 222289$ |
$2$ |
$6.7844616710304475$ |
|
|
not computed |
$S_9$ (as 9T34) |
trivial |
$2$ |
$4$ |
$0.6951489854299296$ |
9.1.30544313.1 |
$ x^{9} - x^{8} + x^{6} - 3 x^{5} + 2 x^{4} - 2 x^{2} + 2 x - 1 $ |
$9$ |
[1,4] |
$47\cdot 649879$ |
$2$ |
$6.786704329211214$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$4$ |
$0.6960773498170069$ |
9.1.30626693.1 |
$ x^{9} - x^{6} - 2 x^{5} - x^{4} + 2 x^{2} + x + 1 $ |
$9$ |
[1,4] |
$30626693$ |
$1$ |
$6.78873569358$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$4$ |
$0.697791262451$ |
9.1.30861161.1 |
$ x^{9} - 3 x^{8} + 5 x^{7} - 5 x^{6} + 5 x^{5} - 5 x^{4} + 5 x^{3} + \cdots - 1 $ |
$9$ |
[1,4] |
$30861161$ |
$1$ |
$6.794490845023192$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$4$ |
$0.700663986552305$ |
9.1.31042889.1 |
$ x^{9} - 2 x^{8} + 3 x^{7} - 3 x^{6} + 2 x^{5} - 2 x^{4} + 3 x^{3} + \cdots - 1 $ |
$9$ |
[1,4] |
$37\cdot 47\cdot 17851$ |
$3$ |
$6.798924787991613$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$4$ |
$0.7037123132761675$ |
9.1.31508353.1 |
$ x^{9} - x^{8} - x^{7} + 3 x^{6} - x^{5} - 2 x^{4} + 2 x^{3} - x + 1 $ |
$9$ |
[1,4] |
$359\cdot 87767$ |
$2$ |
$6.8101771847288655$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$4$ |
$0.7109245176713707$ |
9.1.31638601.1 |
$ x^{9} - x^{8} - 2 x^{7} + 3 x^{6} + x^{5} - 2 x^{4} + 1 $ |
$9$ |
[1,4] |
$31638601$ |
$1$ |
$6.813299413387336$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$4$ |
$0.7125137165211469$ |
9.1.31759433.1 |
$ x^{9} - 3 x^{5} + 2 x - 1 $ |
$9$ |
[1,4] |
$179\cdot 177427$ |
$2$ |
$6.81618572777313$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$4$ |
$0.7139714909872039$ |
9.1.32029433.1 |
$ x^{9} - 2 x^{8} + 3 x^{6} - x^{5} - 3 x^{4} + 3 x^{3} + x^{2} - 2 x + 1 $ |
$9$ |
[1,4] |
$32029433$ |
$1$ |
$6.82260010718$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$4$ |
$0.7178935503824918$ |
9.1.32031161.1 |
$ x^{9} - 2 x^{8} + 2 x^{7} - 3 x^{6} + 4 x^{5} - 5 x^{4} + 5 x^{3} + \cdots - 1 $ |
$9$ |
[1,4] |
$61\cdot 525101$ |
$2$ |
$6.822641004182137$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$4$ |
$0.7178415555973245$ |
9.1.32058553.1 |
$ x^{9} - 2 x^{8} + 3 x^{7} - 3 x^{6} + x^{5} - x^{4} + x^{3} - 2 x^{2} + \cdots - 1 $ |
$9$ |
[1,4] |
$32058553$ |
$1$ |
$6.823289035606978$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$4$ |
$0.7183654917840255$ |
9.1.32206049.1 |
$ x^{9} - 2 x^{8} + 4 x^{7} - 5 x^{6} + 6 x^{5} - 6 x^{4} + 5 x^{3} + \cdots - 1 $ |
$9$ |
[1,4] |
$23^{3}\cdot 2647$ |
$2$ |
$6.82677001293$ |
|
|
✓ |
$S_3\wr S_3$ (as 9T31) |
trivial |
$2$ |
$4$ |
$0.720252095298$ |
9.1.32344469.1 |
$ x^{9} - x^{7} - x^{6} + 2 x^{5} + 2 x^{4} - x^{3} - 2 x^{2} + 1 $ |
$9$ |
[1,4] |
$53\cdot 89\cdot 6857$ |
$3$ |
$6.83002392654$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$4$ |
$0.722703704685$ |
9.1.32652713.1 |
$ x^{9} - 2 x^{8} + 4 x^{6} - 3 x^{5} - 2 x^{4} + 4 x^{3} - 2 x + 1 $ |
$9$ |
[1,4] |
$32652713$ |
$1$ |
$6.837225741156748$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$4$ |
$0.7271831373870599$ |
9.1.32768213.1 |
$ x^{9} - 2 x^{7} - x^{6} + x^{5} + 2 x^{2} + x - 1 $ |
$9$ |
[1,4] |
$3413\cdot 9601$ |
$2$ |
$6.839908726808573$ |
|
|
not computed |
$S_9$ (as 9T34) |
trivial |
$2$ |
$4$ |
$0.7287627479094403$ |
9.1.32855993.1 |
$ x^{9} - 2 x^{8} + x^{7} + 2 x^{6} - 3 x^{5} + x^{4} + x^{3} - x^{2} + \cdots - 1 $ |
$9$ |
[1,4] |
$113\cdot 290761$ |
$2$ |
$6.841942179695031$ |
|
|
not computed |
$S_9$ (as 9T34) |
trivial |
$2$ |
$4$ |
$0.729608042282312$ |
9.1.32894473.1 |
$ x^{9} - 2 x^{8} + 4 x^{7} - 5 x^{6} + 5 x^{5} - 3 x^{4} + x^{3} + \cdots + 1 $ |
$9$ |
[1,4] |
$17\cdot 1934969$ |
$2$ |
$6.842832059610452$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$4$ |
$0.7304523946359703$ |
9.1.32923873.1 |
$ x^{9} - x^{8} + 3 x^{7} - 4 x^{6} + 5 x^{5} - 5 x^{4} + 5 x^{3} + \cdots - 1 $ |
$9$ |
[1,4] |
$809\cdot 40697$ |
$2$ |
$6.843511334119867$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$4$ |
$0.7306149370217431$ |
9.1.32987233.1 |
$ x^{9} - 2 x^{8} + 2 x^{7} - 2 x^{6} + x^{4} - 2 x^{3} + 2 x^{2} + \cdots + 1 $ |
$9$ |
[1,4] |
$32987233$ |
$1$ |
$6.844973408840747$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$4$ |
$0.7315932692727032$ |
9.1.33121433.1 |
$ x^{9} + x^{7} - x^{6} - 2 x^{5} - x^{3} + x^{2} + x - 1 $ |
$9$ |
[1,4] |
$1321\cdot 25073$ |
$2$ |
$6.848061939602068$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$4$ |
$0.7356771671046255$ |
9.1.33445561.1 |
$ x^{9} - 2 x^{8} + 2 x^{7} - 3 x^{4} + 5 x^{3} - 2 x^{2} - x + 1 $ |
$9$ |
[1,4] |
$449\cdot 74489$ |
$2$ |
$6.855475915810484$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$4$ |
$0.7400598322062453$ |
9.1.33571261.1 |
$ x^{9} - x^{8} + x^{6} + x^{5} - 2 x^{4} - 2 x^{3} + 3 x^{2} + x - 1 $ |
$9$ |
[1,4] |
$43\cdot 857\cdot 911$ |
$3$ |
$6.858333950961397$ |
|
|
not computed |
$S_9$ (as 9T34) |
trivial |
$2$ |
$4$ |
$0.7412699877661832$ |
9.1.33626161.1 |
$ x^{9} - 3 x^{8} + 6 x^{7} - 9 x^{6} + 12 x^{5} - 12 x^{4} + \cdots - 1 $ |
$9$ |
[1,4] |
$23\cdot 67\cdot 21821$ |
$3$ |
$6.859579226245459$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$4$ |
$0.7431092993530156$ |
9.1.33860761.1 |
$ x^{9} - 2 x^{8} + 2 x^{7} - 2 x^{5} + 2 x^{4} - x + 1 $ |
$9$ |
[1,4] |
$11^{2}\cdot 23^{4}$ |
$2$ |
$6.8648802879$ |
|
|
✓ |
$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T30) |
trivial |
$2$ |
$4$ |
$0.744153660637$ |
9.1.33984793.1 |
$ x^{9} - x^{8} - 2 x^{7} + 2 x^{6} + 2 x^{5} - 3 x^{4} + 2 x^{2} + \cdots - 1 $ |
$9$ |
[1,4] |
$33984793$ |
$1$ |
$6.867669756729682$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$4$ |
$0.74673838323778$ |
9.1.34090153.1 |
$ x^{9} - 2 x^{8} + 3 x^{7} - 2 x^{6} - x^{5} + 5 x^{4} - 6 x^{3} + \cdots + 1 $ |
$9$ |
[1,4] |
$71\cdot 480143$ |
$2$ |
$6.8700321945101726$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$4$ |
$0.7498544128110662$ |
9.1.34349041.1 |
$ x^{9} - x^{8} - x^{7} + 2 x^{6} - 2 x^{4} + x^{2} - 1 $ |
$9$ |
[1,4] |
$34349041$ |
$1$ |
$6.8758096673688$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$4$ |
$0.7514041293660256$ |
9.1.34405373.1 |
$ x^{9} - x^{8} + x^{6} - 2 x^{5} - x^{4} + 3 x^{3} + x^{2} - 2 x - 1 $ |
$9$ |
[1,4] |
$34405373$ |
$1$ |
$6.87706167089583$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$4$ |
$0.7526295068317561$ |
9.1.34573709.1 |
$ x^{9} - x^{8} - x^{7} + 2 x^{6} - 2 x^{4} + 2 x^{3} - x + 1 $ |
$9$ |
[1,4] |
$34573709$ |
$1$ |
$6.880792184488982$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$4$ |
$0.7549654984195712$ |
9.1.34590113.1 |
$ x^{9} - x^{8} + x^{7} + x^{6} - x^{4} + 2 x^{3} - 3 x^{2} + 2 x - 1 $ |
$9$ |
[1,4] |
$509\cdot 67957$ |
$2$ |
$6.881154851586754$ |
|
|
not computed |
$S_9$ (as 9T34) |
trivial |
$2$ |
$4$ |
$0.7592380312557747$ |
9.1.34628113.1 |
$ x^{9} - x^{6} - x^{5} + x^{4} + x^{3} + x^{2} - 1 $ |
$9$ |
[1,4] |
$13\cdot 2663701$ |
$2$ |
$6.881994385964947$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$4$ |
$0.7566233443489708$ |
9.1.35028793.1 |
$ x^{9} - 2 x^{8} + 4 x^{7} - 7 x^{6} + 10 x^{5} - 11 x^{4} + \cdots - 1 $ |
$9$ |
[1,4] |
$23^{3}\cdot 2879$ |
$2$ |
$6.89079712201$ |
|
|
✓ |
$S_3\wr S_3$ (as 9T31) |
trivial |
$2$ |
$4$ |
$0.760652964324$ |
9.1.35050633.1 |
$ x^{9} - x^{8} + x^{7} - 3 x^{6} + 3 x^{5} - 2 x^{4} + 4 x^{3} - 2 x^{2} + \cdots - 1 $ |
$9$ |
[1,4] |
$43\cdot 311\cdot 2621$ |
$3$ |
$6.891274359$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$4$ |
$0.7613732494747866$ |
9.1.35051893.1 |
$ x^{9} - x^{8} + 3 x^{7} - 3 x^{6} + 5 x^{5} - 5 x^{4} + 4 x^{3} + \cdots - 1 $ |
$9$ |
[1,4] |
$109\cdot 321577$ |
$2$ |
$6.891301883842185$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$4$ |
$0.7612088480089704$ |
9.1.35234033.1 |
$ x^{9} - 2 x^{8} + 4 x^{7} - 5 x^{6} + 5 x^{5} - 4 x^{4} + 3 x^{3} + \cdots - 1 $ |
$9$ |
[1,4] |
$59\cdot 347\cdot 1721$ |
$3$ |
$6.895271529570494$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$4$ |
$0.7650177657725251$ |
9.1.35357129.1 |
$ x^{9} + x^{7} - 3 x^{6} + x^{5} - 3 x^{4} + 4 x^{3} - x^{2} + 2 x - 1 $ |
$9$ |
[1,4] |
$41\cdot 862369$ |
$2$ |
$6.897944025537414$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$4$ |
$0.7655906869400728$ |
9.1.35607973.1 |
$ x^{9} - 2 x^{7} + 4 x^{5} - 4 x^{3} - x^{2} + 2 x + 1 $ |
$9$ |
[1,4] |
$5501\cdot 6473$ |
$2$ |
$6.903364514047256$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$4$ |
$0.7698346623635847$ |
9.1.35666053.1 |
$ x^{9} - x^{8} - x^{7} + 3 x^{6} - x^{5} - 3 x^{4} + 4 x^{3} - 2 x + 1 $ |
$9$ |
[1,4] |
$787\cdot 45319$ |
$2$ |
$6.9046147242172875$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$4$ |
$0.7697638265558684$ |
9.1.35678113.1 |
$ x^{9} - x^{8} + 3 x^{6} - 3 x^{5} + 3 x^{3} - 2 x^{2} - x + 1 $ |
$9$ |
[1,4] |
$199\cdot 179287$ |
$2$ |
$6.904874096724272$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$4$ |
$0.7740357851599975$ |
9.1.35686793.1 |
$ x^{9} - 2 x^{7} - 2 x^{6} + 2 x^{5} + 4 x^{4} + 2 x^{3} - 2 x^{2} + \cdots - 1 $ |
$9$ |
[1,4] |
$35686793$ |
$1$ |
$6.905060727881392$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$4$ |
$0.7717632848146379$ |
9.1.35935321.1 |
$ x^{9} - 2 x^{7} - x^{6} + x^{5} + 2 x^{4} - x^{2} - 1 $ |
$9$ |
[1,4] |
$29\cdot 337\cdot 3677$ |
$3$ |
$6.910387355992345$ |
|
|
not computed |
$S_9$ (as 9T34) |
trivial |
$2$ |
$4$ |
$0.7750794614336419$ |
9.1.36055441.1 |
$ x^{9} - x^{8} - x^{7} + x^{6} + x^{5} + x^{4} - x^{3} - 2 x^{2} + x + 1 $ |
$9$ |
[1,4] |
$41\cdot 879401$ |
$2$ |
$6.912950124346879$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$4$ |
$0.7771849288158317$ |
9.1.36155633.1 |
$ x^{9} - x^{8} + x^{7} - x^{6} - x^{3} + x^{2} + 1 $ |
$9$ |
[1,4] |
$36155633$ |
$1$ |
$6.915081928897711$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$4$ |
$0.7789574842919698$ |
9.1.36722413.1 |
$ x^{9} - x^{8} + x^{6} - x^{4} + x^{3} + x^{2} - 2 x + 1 $ |
$9$ |
[1,4] |
$7^{2}\cdot 13\cdot 57649$ |
$3$ |
$6.927043458364813$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$4$ |
$0.7869155967978311$ |
9.1.36743849.1 |
$ x^{9} - 3 x^{8} + 6 x^{7} - 9 x^{6} + 13 x^{5} - 14 x^{4} + \cdots - 1 $ |
$9$ |
[1,4] |
$37\cdot 71^{2}\cdot 197$ |
$3$ |
$6.927492622732046$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$4$ |
$0.7848509470291687$ |
9.1.37009129.1 |
$ x^{9} - 2 x^{8} + x^{7} - x^{6} + x^{5} + x^{4} + x^{2} - 2 x + 1 $ |
$9$ |
[1,4] |
$839\cdot 44111$ |
$2$ |
$6.933032038439399$ |
|
|
not computed |
$S_9$ (as 9T34) |
trivial |
$2$ |
$4$ |
$0.7903392925308504$ |
9.1.37065113.1 |
$ x^{9} - x^{8} - x^{6} + x^{5} + 3 x^{4} - 2 x^{3} - 2 x^{2} + x + 1 $ |
$9$ |
[1,4] |
$5849\cdot 6337$ |
$2$ |
$6.934196550406416$ |
|
|
✓ |
$S_9$ (as 9T34) |
trivial |
$2$ |
$4$ |
$0.7932015302763461$ |