Basic properties
| Modulus: | \(2156\) | |
| Conductor: | \(2156\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(70\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2156.ca
\(\chi_{2156}(15,\cdot)\) \(\chi_{2156}(71,\cdot)\) \(\chi_{2156}(267,\cdot)\) \(\chi_{2156}(323,\cdot)\) \(\chi_{2156}(379,\cdot)\) \(\chi_{2156}(575,\cdot)\) \(\chi_{2156}(603,\cdot)\) \(\chi_{2156}(631,\cdot)\) \(\chi_{2156}(911,\cdot)\) \(\chi_{2156}(939,\cdot)\) \(\chi_{2156}(995,\cdot)\) \(\chi_{2156}(1191,\cdot)\) \(\chi_{2156}(1219,\cdot)\) \(\chi_{2156}(1247,\cdot)\) \(\chi_{2156}(1303,\cdot)\) \(\chi_{2156}(1499,\cdot)\) \(\chi_{2156}(1527,\cdot)\) \(\chi_{2156}(1555,\cdot)\) \(\chi_{2156}(1611,\cdot)\) \(\chi_{2156}(1807,\cdot)\) \(\chi_{2156}(1835,\cdot)\) \(\chi_{2156}(1919,\cdot)\) \(\chi_{2156}(2115,\cdot)\) \(\chi_{2156}(2143,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((1079,1277,981)\) → \((-1,e\left(\frac{6}{7}\right),e\left(\frac{4}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 2156 }(2115, a) \) | \(-1\) | \(1\) | \(e\left(\frac{53}{70}\right)\) | \(e\left(\frac{2}{35}\right)\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{3}{35}\right)\) | \(e\left(\frac{57}{70}\right)\) | \(e\left(\frac{22}{35}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{4}{35}\right)\) | \(e\left(\frac{19}{70}\right)\) |