Basic properties
| Modulus: | \(8670\) | |
| Conductor: | \(1445\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(272\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1445}(7,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8670.cs
\(\chi_{8670}(7,\cdot)\) \(\chi_{8670}(73,\cdot)\) \(\chi_{8670}(133,\cdot)\) \(\chi_{8670}(343,\cdot)\) \(\chi_{8670}(367,\cdot)\) \(\chi_{8670}(397,\cdot)\) \(\chi_{8670}(403,\cdot)\) \(\chi_{8670}(487,\cdot)\) \(\chi_{8670}(517,\cdot)\) \(\chi_{8670}(583,\cdot)\) \(\chi_{8670}(853,\cdot)\) \(\chi_{8670}(877,\cdot)\) \(\chi_{8670}(913,\cdot)\) \(\chi_{8670}(997,\cdot)\) \(\chi_{8670}(1027,\cdot)\) \(\chi_{8670}(1093,\cdot)\) \(\chi_{8670}(1153,\cdot)\) \(\chi_{8670}(1363,\cdot)\) \(\chi_{8670}(1387,\cdot)\) \(\chi_{8670}(1417,\cdot)\) \(\chi_{8670}(1423,\cdot)\) \(\chi_{8670}(1507,\cdot)\) \(\chi_{8670}(1537,\cdot)\) \(\chi_{8670}(1663,\cdot)\) \(\chi_{8670}(1873,\cdot)\) \(\chi_{8670}(1897,\cdot)\) \(\chi_{8670}(1927,\cdot)\) \(\chi_{8670}(1933,\cdot)\) \(\chi_{8670}(2017,\cdot)\) \(\chi_{8670}(2047,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{272})$ |
| Fixed field: | Number field defined by a degree 272 polynomial (not computed) |
Values on generators
\((2891,6937,6361)\) → \((1,i,e\left(\frac{155}{272}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 8670 }(7, a) \) | \(1\) | \(1\) | \(e\left(\frac{157}{272}\right)\) | \(e\left(\frac{29}{272}\right)\) | \(e\left(\frac{15}{34}\right)\) | \(e\left(\frac{65}{136}\right)\) | \(e\left(\frac{225}{272}\right)\) | \(e\left(\frac{199}{272}\right)\) | \(e\left(\frac{35}{272}\right)\) | \(e\left(\frac{207}{272}\right)\) | \(e\left(\frac{121}{272}\right)\) | \(e\left(\frac{73}{136}\right)\) |