Basic properties
| Modulus: | \(6422\) | |
| Conductor: | \(169\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{169}(2,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6422.da
\(\chi_{6422}(115,\cdot)\) \(\chi_{6422}(267,\cdot)\) \(\chi_{6422}(305,\cdot)\) \(\chi_{6422}(457,\cdot)\) \(\chi_{6422}(609,\cdot)\) \(\chi_{6422}(761,\cdot)\) \(\chi_{6422}(799,\cdot)\) \(\chi_{6422}(951,\cdot)\) \(\chi_{6422}(1255,\cdot)\) \(\chi_{6422}(1293,\cdot)\) \(\chi_{6422}(1445,\cdot)\) \(\chi_{6422}(1597,\cdot)\) \(\chi_{6422}(1749,\cdot)\) \(\chi_{6422}(1787,\cdot)\) \(\chi_{6422}(2091,\cdot)\) \(\chi_{6422}(2243,\cdot)\) \(\chi_{6422}(2281,\cdot)\) \(\chi_{6422}(2433,\cdot)\) \(\chi_{6422}(2585,\cdot)\) \(\chi_{6422}(2737,\cdot)\) \(\chi_{6422}(2775,\cdot)\) \(\chi_{6422}(2927,\cdot)\) \(\chi_{6422}(3079,\cdot)\) \(\chi_{6422}(3231,\cdot)\) \(\chi_{6422}(3269,\cdot)\) \(\chi_{6422}(3421,\cdot)\) \(\chi_{6422}(3573,\cdot)\) \(\chi_{6422}(3725,\cdot)\) \(\chi_{6422}(3763,\cdot)\) \(\chi_{6422}(3915,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((4903,4733)\) → \((e\left(\frac{1}{156}\right),1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(21\) | \(23\) | \(25\) |
| \( \chi_{ 6422 }(4903, a) \) | \(-1\) | \(1\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{3}{52}\right)\) | \(e\left(\frac{107}{156}\right)\) | \(e\left(\frac{23}{39}\right)\) | \(e\left(\frac{103}{156}\right)\) | \(e\left(\frac{133}{156}\right)\) | \(e\left(\frac{73}{78}\right)\) | \(e\left(\frac{25}{52}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{3}{26}\right)\) |