Basic properties
| Modulus: | \(2156\) | |
| Conductor: | \(2156\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(210\) | 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.cj
\(\chi_{2156}(135,\cdot)\) \(\chi_{2156}(163,\cdot)\) \(\chi_{2156}(179,\cdot)\) \(\chi_{2156}(191,\cdot)\) \(\chi_{2156}(207,\cdot)\) \(\chi_{2156}(235,\cdot)\) \(\chi_{2156}(247,\cdot)\) \(\chi_{2156}(291,\cdot)\) \(\chi_{2156}(443,\cdot)\) \(\chi_{2156}(487,\cdot)\) \(\chi_{2156}(499,\cdot)\) \(\chi_{2156}(515,\cdot)\) \(\chi_{2156}(543,\cdot)\) \(\chi_{2156}(555,\cdot)\) \(\chi_{2156}(599,\cdot)\) \(\chi_{2156}(751,\cdot)\) \(\chi_{2156}(779,\cdot)\) \(\chi_{2156}(795,\cdot)\) \(\chi_{2156}(807,\cdot)\) \(\chi_{2156}(823,\cdot)\) \(\chi_{2156}(907,\cdot)\) \(\chi_{2156}(1087,\cdot)\) \(\chi_{2156}(1103,\cdot)\) \(\chi_{2156}(1115,\cdot)\) \(\chi_{2156}(1131,\cdot)\) \(\chi_{2156}(1159,\cdot)\) \(\chi_{2156}(1171,\cdot)\) \(\chi_{2156}(1215,\cdot)\) \(\chi_{2156}(1367,\cdot)\) \(\chi_{2156}(1395,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((1079,1277,981)\) → \((-1,e\left(\frac{10}{21}\right),e\left(\frac{4}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 2156 }(751, a) \) | \(-1\) | \(1\) | \(e\left(\frac{79}{210}\right)\) | \(e\left(\frac{1}{105}\right)\) | \(e\left(\frac{79}{105}\right)\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{27}{70}\right)\) | \(e\left(\frac{11}{105}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{25}{42}\right)\) | \(e\left(\frac{2}{105}\right)\) | \(e\left(\frac{9}{70}\right)\) |