Basic properties
| Modulus: | \(2156\) | |
| Conductor: | \(539\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(70\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{539}(251,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2156.bx
\(\chi_{2156}(69,\cdot)\) \(\chi_{2156}(125,\cdot)\) \(\chi_{2156}(181,\cdot)\) \(\chi_{2156}(377,\cdot)\) \(\chi_{2156}(405,\cdot)\) \(\chi_{2156}(433,\cdot)\) \(\chi_{2156}(713,\cdot)\) \(\chi_{2156}(741,\cdot)\) \(\chi_{2156}(797,\cdot)\) \(\chi_{2156}(993,\cdot)\) \(\chi_{2156}(1021,\cdot)\) \(\chi_{2156}(1049,\cdot)\) \(\chi_{2156}(1105,\cdot)\) \(\chi_{2156}(1301,\cdot)\) \(\chi_{2156}(1329,\cdot)\) \(\chi_{2156}(1357,\cdot)\) \(\chi_{2156}(1413,\cdot)\) \(\chi_{2156}(1609,\cdot)\) \(\chi_{2156}(1637,\cdot)\) \(\chi_{2156}(1721,\cdot)\) \(\chi_{2156}(1917,\cdot)\) \(\chi_{2156}(1945,\cdot)\) \(\chi_{2156}(1973,\cdot)\) \(\chi_{2156}(2029,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((1079,1277,981)\) → \((1,e\left(\frac{9}{14}\right),e\left(\frac{3}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 2156 }(1329, a) \) | \(-1\) | \(1\) | \(e\left(\frac{31}{70}\right)\) | \(e\left(\frac{3}{70}\right)\) | \(e\left(\frac{31}{35}\right)\) | \(e\left(\frac{57}{70}\right)\) | \(e\left(\frac{17}{35}\right)\) | \(e\left(\frac{33}{70}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{3}{35}\right)\) | \(e\left(\frac{23}{70}\right)\) |