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 \(\chi_{539}(470,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2156.cd
\(\chi_{2156}(29,\cdot)\) \(\chi_{2156}(57,\cdot)\) \(\chi_{2156}(85,\cdot)\) \(\chi_{2156}(281,\cdot)\) \(\chi_{2156}(337,\cdot)\) \(\chi_{2156}(365,\cdot)\) \(\chi_{2156}(645,\cdot)\) \(\chi_{2156}(673,\cdot)\) \(\chi_{2156}(701,\cdot)\) \(\chi_{2156}(897,\cdot)\) \(\chi_{2156}(953,\cdot)\) \(\chi_{2156}(1009,\cdot)\) \(\chi_{2156}(1205,\cdot)\) \(\chi_{2156}(1261,\cdot)\) \(\chi_{2156}(1289,\cdot)\) \(\chi_{2156}(1317,\cdot)\) \(\chi_{2156}(1513,\cdot)\) \(\chi_{2156}(1597,\cdot)\) \(\chi_{2156}(1625,\cdot)\) \(\chi_{2156}(1821,\cdot)\) \(\chi_{2156}(1877,\cdot)\) \(\chi_{2156}(1905,\cdot)\) \(\chi_{2156}(1933,\cdot)\) \(\chi_{2156}(2129,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((1079,1277,981)\) → \((1,e\left(\frac{3}{7}\right),e\left(\frac{3}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 2156 }(1009, a) \) | \(-1\) | \(1\) | \(e\left(\frac{29}{35}\right)\) | \(e\left(\frac{22}{35}\right)\) | \(e\left(\frac{23}{35}\right)\) | \(e\left(\frac{31}{70}\right)\) | \(e\left(\frac{16}{35}\right)\) | \(e\left(\frac{29}{70}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{9}{35}\right)\) | \(e\left(\frac{17}{35}\right)\) |