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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2156.cb
\(\chi_{2156}(27,\cdot)\) \(\chi_{2156}(223,\cdot)\) \(\chi_{2156}(251,\cdot)\) \(\chi_{2156}(279,\cdot)\) \(\chi_{2156}(335,\cdot)\) \(\chi_{2156}(531,\cdot)\) \(\chi_{2156}(559,\cdot)\) \(\chi_{2156}(643,\cdot)\) \(\chi_{2156}(839,\cdot)\) \(\chi_{2156}(867,\cdot)\) \(\chi_{2156}(895,\cdot)\) \(\chi_{2156}(951,\cdot)\) \(\chi_{2156}(1147,\cdot)\) \(\chi_{2156}(1203,\cdot)\) \(\chi_{2156}(1259,\cdot)\) \(\chi_{2156}(1455,\cdot)\) \(\chi_{2156}(1483,\cdot)\) \(\chi_{2156}(1511,\cdot)\) \(\chi_{2156}(1791,\cdot)\) \(\chi_{2156}(1819,\cdot)\) \(\chi_{2156}(1875,\cdot)\) \(\chi_{2156}(2071,\cdot)\) \(\chi_{2156}(2099,\cdot)\) \(\chi_{2156}(2127,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((1079,1277,981)\) → \((-1,e\left(\frac{1}{14}\right),e\left(\frac{1}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 2156 }(1203, a) \) | \(1\) | \(1\) | \(e\left(\frac{6}{35}\right)\) | \(e\left(\frac{61}{70}\right)\) | \(e\left(\frac{12}{35}\right)\) | \(e\left(\frac{39}{70}\right)\) | \(e\left(\frac{3}{70}\right)\) | \(e\left(\frac{41}{70}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{26}{35}\right)\) | \(e\left(\frac{18}{35}\right)\) |