Basic properties
| Modulus: | \(2805\) | |
| Conductor: | \(2805\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(80\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2805.fb
\(\chi_{2805}(62,\cdot)\) \(\chi_{2805}(173,\cdot)\) \(\chi_{2805}(227,\cdot)\) \(\chi_{2805}(233,\cdot)\) \(\chi_{2805}(347,\cdot)\) \(\chi_{2805}(413,\cdot)\) \(\chi_{2805}(602,\cdot)\) \(\chi_{2805}(668,\cdot)\) \(\chi_{2805}(728,\cdot)\) \(\chi_{2805}(743,\cdot)\) \(\chi_{2805}(827,\cdot)\) \(\chi_{2805}(992,\cdot)\) \(\chi_{2805}(998,\cdot)\) \(\chi_{2805}(1217,\cdot)\) \(\chi_{2805}(1238,\cdot)\) \(\chi_{2805}(1337,\cdot)\) \(\chi_{2805}(1448,\cdot)\) \(\chi_{2805}(1493,\cdot)\) \(\chi_{2805}(1502,\cdot)\) \(\chi_{2805}(1592,\cdot)\) \(\chi_{2805}(1757,\cdot)\) \(\chi_{2805}(1877,\cdot)\) \(\chi_{2805}(1943,\cdot)\) \(\chi_{2805}(1982,\cdot)\) \(\chi_{2805}(2213,\cdot)\) \(\chi_{2805}(2273,\cdot)\) \(\chi_{2805}(2492,\cdot)\) \(\chi_{2805}(2642,\cdot)\) \(\chi_{2805}(2708,\cdot)\) \(\chi_{2805}(2723,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((1871,562,1531,496)\) → \((-1,i,e\left(\frac{7}{10}\right),e\left(\frac{7}{16}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(13\) | \(14\) | \(16\) | \(19\) | \(23\) | \(26\) |
| \( \chi_{ 2805 }(62, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{77}{80}\right)\) | \(e\left(\frac{29}{40}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{43}{80}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{29}{40}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{31}{40}\right)\) |