Basic properties
| Modulus: | \(3724\) | |
| Conductor: | \(3724\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(126\) | 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 3724.ek
\(\chi_{3724}(55,\cdot)\) \(\chi_{3724}(111,\cdot)\) \(\chi_{3724}(139,\cdot)\) \(\chi_{3724}(251,\cdot)\) \(\chi_{3724}(503,\cdot)\) \(\chi_{3724}(643,\cdot)\) \(\chi_{3724}(671,\cdot)\) \(\chi_{3724}(727,\cdot)\) \(\chi_{3724}(1035,\cdot)\) \(\chi_{3724}(1119,\cdot)\) \(\chi_{3724}(1203,\cdot)\) \(\chi_{3724}(1259,\cdot)\) \(\chi_{3724}(1315,\cdot)\) \(\chi_{3724}(1651,\cdot)\) \(\chi_{3724}(1707,\cdot)\) \(\chi_{3724}(1735,\cdot)\) \(\chi_{3724}(1791,\cdot)\) \(\chi_{3724}(1847,\cdot)\) \(\chi_{3724}(2099,\cdot)\) \(\chi_{3724}(2183,\cdot)\) \(\chi_{3724}(2239,\cdot)\) \(\chi_{3724}(2267,\cdot)\) \(\chi_{3724}(2323,\cdot)\) \(\chi_{3724}(2379,\cdot)\) \(\chi_{3724}(2631,\cdot)\) \(\chi_{3724}(2715,\cdot)\) \(\chi_{3724}(2771,\cdot)\) \(\chi_{3724}(2799,\cdot)\) \(\chi_{3724}(2855,\cdot)\) \(\chi_{3724}(2911,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((1863,3041,3137)\) → \((-1,e\left(\frac{9}{14}\right),e\left(\frac{5}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 3724 }(55, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{63}\right)\) | \(e\left(\frac{67}{126}\right)\) | \(e\left(\frac{46}{63}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{125}{126}\right)\) | \(e\left(\frac{113}{126}\right)\) | \(e\left(\frac{79}{126}\right)\) | \(e\left(\frac{5}{126}\right)\) | \(e\left(\frac{4}{63}\right)\) | \(e\left(\frac{2}{21}\right)\) |