# table of some fundamental units

Below, we tabulate the fundamental units $\eta$ of first real quadratic fields $\mathbb{Q}(\sqrt{d})$; the number $\omega$ is $\displaystyle\frac{1\!+\!\sqrt{d}}{2}$ for  $d\equiv 1\pmod{4}$  and $\sqrt{d}$ for  $d\not\equiv 1\pmod{4}$.

$d$ $\eta$ $d$ $\eta$

$2$
$1+\omega$ $47$ $48+7\omega$
$3$ $2+\omega$ $51$ $50+7\omega$
$5$ $\omega$ $53$ $3+\omega$
$6$ $5+2\omega$ $55$ $89+12\omega$
$7$ $8+3\omega$ $57$ $131+40\omega$
$10$ $3+\omega$ $58$ $99+13\omega$
$11$ $10+3\omega$ $59$ $530+69\omega$
$13$ $1+\omega$ $61$ $17+5\omega$
$14$ $15+4\omega$ $62$ $63+8\omega$
$15$ $4+\omega$ $65$ $7+2\omega$
$17$ $3+2\omega$ $66$ $65+8\omega$
$19$ $170+39\omega$ $67$ $48842+5967\omega$
$21$ $2+\omega$ $69$ $11+3\omega$
$22$ $197+42\omega$ $70$ $251+30\omega$
$23$ $24+5\omega$ $71$ $3480+413\omega$
$26$ $5+\omega$ $73$ $943+250\omega$
$29$ $2+\omega$ $74$ $43+5\omega$
$30$ $11+2\omega$ $77$ $4+\omega$
$31$ $1520+273\omega$ $78$ $53+6\omega$
$33$ $19+8\omega$ 79 $80+9\omega$
$34$ $35+6\omega$ $82$ $9+\omega$
$35$ $6+\omega$ $83$ $82+9\omega$
$37$ $5+2\omega$ $85$ $4+\omega$
$38$ $37+6\omega$ $86$ $10405+1122\omega$
$39$ $25+4\omega$ $87$ $28+3\omega$
$41$ $27+10\omega$ $89$ $447+106\omega$
$42$ $13+2\omega$ $91$ $1574+165\omega$
$43$ $3482+531\omega$ $93$ $13+3\omega$
$46$ $24335+3588\omega$ $94$ $2143295+221064\omega$

## References

• 1 S. Borewicz & I. Safarevic: Zahlentheorie.  Birkhäuser Verlag. Basel und Stuttgart (1966).
 Title table of some fundamental units Canonical name TableOfSomeFundamentalUnits Date of creation 2013-03-22 17:58:39 Last modified on 2013-03-22 17:58:39 Owner pahio (2872) Last modified by pahio (2872) Numerical id 9 Author pahio (2872) Entry type Result Classification msc 11R04 Classification msc 11R11 Classification msc 11R27 Related topic UnitsOfQuadraticFields Related topic QuadraticField Related topic IntegralBasisOfQuadraticField Related topic AlgebraicNumberTheory