Basic properties
| Modulus: | \(87362\) | |
| Conductor: | \(43681\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1254\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{43681}(65,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 87362.cx
\(\chi_{87362}(65,\cdot)\) \(\chi_{87362}(373,\cdot)\) \(\chi_{87362}(901,\cdot)\) \(\chi_{87362}(1319,\cdot)\) \(\chi_{87362}(1627,\cdot)\) \(\chi_{87362}(2045,\cdot)\) \(\chi_{87362}(2155,\cdot)\) \(\chi_{87362}(2463,\cdot)\) \(\chi_{87362}(2573,\cdot)\) \(\chi_{87362}(2881,\cdot)\) \(\chi_{87362}(2991,\cdot)\) \(\chi_{87362}(3299,\cdot)\) \(\chi_{87362}(3409,\cdot)\) \(\chi_{87362}(3717,\cdot)\) \(\chi_{87362}(3827,\cdot)\) \(\chi_{87362}(4135,\cdot)\) \(\chi_{87362}(4245,\cdot)\) \(\chi_{87362}(4553,\cdot)\) \(\chi_{87362}(4663,\cdot)\) \(\chi_{87362}(4971,\cdot)\) \(\chi_{87362}(5389,\cdot)\) \(\chi_{87362}(5499,\cdot)\) \(\chi_{87362}(5917,\cdot)\) \(\chi_{87362}(6225,\cdot)\) \(\chi_{87362}(6335,\cdot)\) \(\chi_{87362}(6643,\cdot)\) \(\chi_{87362}(6753,\cdot)\) \(\chi_{87362}(7061,\cdot)\) \(\chi_{87362}(7171,\cdot)\) \(\chi_{87362}(7479,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{627})$ |
| Fixed field: | Number field defined by a degree 1254 polynomial (not computed) |
Values on generators
\((21661,22023)\) → \((e\left(\frac{13}{22}\right),e\left(\frac{73}{114}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) | \(25\) |
| \( \chi_{ 87362 }(65, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{114}\right)\) | \(e\left(\frac{181}{627}\right)\) | \(e\left(\frac{79}{418}\right)\) | \(e\left(\frac{1}{57}\right)\) | \(e\left(\frac{224}{627}\right)\) | \(e\left(\frac{373}{1254}\right)\) | \(e\left(\frac{845}{1254}\right)\) | \(e\left(\frac{124}{627}\right)\) | \(e\left(\frac{536}{627}\right)\) | \(e\left(\frac{362}{627}\right)\) |