Basic properties
| Modulus: | \(6422\) | |
| Conductor: | \(3211\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(52\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3211}(151,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6422.cf
\(\chi_{6422}(151,\cdot)\) \(\chi_{6422}(265,\cdot)\) \(\chi_{6422}(645,\cdot)\) \(\chi_{6422}(759,\cdot)\) \(\chi_{6422}(1139,\cdot)\) \(\chi_{6422}(1633,\cdot)\) \(\chi_{6422}(1747,\cdot)\) \(\chi_{6422}(2241,\cdot)\) \(\chi_{6422}(2621,\cdot)\) \(\chi_{6422}(2735,\cdot)\) \(\chi_{6422}(3115,\cdot)\) \(\chi_{6422}(3229,\cdot)\) \(\chi_{6422}(3609,\cdot)\) \(\chi_{6422}(3723,\cdot)\) \(\chi_{6422}(4103,\cdot)\) \(\chi_{6422}(4217,\cdot)\) \(\chi_{6422}(4597,\cdot)\) \(\chi_{6422}(4711,\cdot)\) \(\chi_{6422}(5091,\cdot)\) \(\chi_{6422}(5205,\cdot)\) \(\chi_{6422}(5585,\cdot)\) \(\chi_{6422}(5699,\cdot)\) \(\chi_{6422}(6079,\cdot)\) \(\chi_{6422}(6193,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{52})$ |
| Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((4903,4733)\) → \((e\left(\frac{5}{52}\right),-1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(21\) | \(23\) | \(25\) |
| \( \chi_{ 6422 }(151, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{26}\right)\) | \(e\left(\frac{45}{52}\right)\) | \(e\left(\frac{15}{52}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{47}{52}\right)\) | \(e\left(\frac{15}{52}\right)\) | \(e\left(\frac{1}{26}\right)\) | \(e\left(\frac{37}{52}\right)\) | \(-1\) | \(e\left(\frac{19}{26}\right)\) |