Basic properties
| Modulus: | \(6422\) | |
| Conductor: | \(3211\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3211}(277,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6422.cn
\(\chi_{6422}(277,\cdot)\) \(\chi_{6422}(387,\cdot)\) \(\chi_{6422}(771,\cdot)\) \(\chi_{6422}(881,\cdot)\) \(\chi_{6422}(1265,\cdot)\) \(\chi_{6422}(1759,\cdot)\) \(\chi_{6422}(1869,\cdot)\) \(\chi_{6422}(2253,\cdot)\) \(\chi_{6422}(2363,\cdot)\) \(\chi_{6422}(2747,\cdot)\) \(\chi_{6422}(2857,\cdot)\) \(\chi_{6422}(3241,\cdot)\) \(\chi_{6422}(3351,\cdot)\) \(\chi_{6422}(3735,\cdot)\) \(\chi_{6422}(3845,\cdot)\) \(\chi_{6422}(4229,\cdot)\) \(\chi_{6422}(4339,\cdot)\) \(\chi_{6422}(4723,\cdot)\) \(\chi_{6422}(4833,\cdot)\) \(\chi_{6422}(5327,\cdot)\) \(\chi_{6422}(5711,\cdot)\) \(\chi_{6422}(5821,\cdot)\) \(\chi_{6422}(6205,\cdot)\) \(\chi_{6422}(6315,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((4903,4733)\) → \((e\left(\frac{31}{78}\right),e\left(\frac{2}{3}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(21\) | \(23\) | \(25\) |
| \( \chi_{ 6422 }(277, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{39}\right)\) | \(e\left(\frac{19}{78}\right)\) | \(e\left(\frac{41}{78}\right)\) | \(e\left(\frac{35}{39}\right)\) | \(e\left(\frac{73}{78}\right)\) | \(e\left(\frac{5}{26}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{37}{78}\right)\) | \(1\) | \(e\left(\frac{19}{39}\right)\) |