Basic properties
| Modulus: | \(7448\) | |
| Conductor: | \(3724\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(126\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3724}(47,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7448.iz
\(\chi_{7448}(47,\cdot)\) \(\chi_{7448}(327,\cdot)\) \(\chi_{7448}(871,\cdot)\) \(\chi_{7448}(1111,\cdot)\) \(\chi_{7448}(1279,\cdot)\) \(\chi_{7448}(1487,\cdot)\) \(\chi_{7448}(1879,\cdot)\) \(\chi_{7448}(1935,\cdot)\) \(\chi_{7448}(2343,\cdot)\) \(\chi_{7448}(2455,\cdot)\) \(\chi_{7448}(2551,\cdot)\) \(\chi_{7448}(2943,\cdot)\) \(\chi_{7448}(2999,\cdot)\) \(\chi_{7448}(3239,\cdot)\) \(\chi_{7448}(3407,\cdot)\) \(\chi_{7448}(3519,\cdot)\) \(\chi_{7448}(3615,\cdot)\) \(\chi_{7448}(4007,\cdot)\) \(\chi_{7448}(4063,\cdot)\) \(\chi_{7448}(4303,\cdot)\) \(\chi_{7448}(4471,\cdot)\) \(\chi_{7448}(4583,\cdot)\) \(\chi_{7448}(4679,\cdot)\) \(\chi_{7448}(5071,\cdot)\) \(\chi_{7448}(5367,\cdot)\) \(\chi_{7448}(5535,\cdot)\) \(\chi_{7448}(5647,\cdot)\) \(\chi_{7448}(5743,\cdot)\) \(\chi_{7448}(6135,\cdot)\) \(\chi_{7448}(6191,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((1863,3725,3041,3137)\) → \((-1,1,e\left(\frac{5}{42}\right),e\left(\frac{4}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 7448 }(47, a) \) | \(1\) | \(1\) | \(e\left(\frac{25}{63}\right)\) | \(e\left(\frac{71}{126}\right)\) | \(e\left(\frac{50}{63}\right)\) | \(e\left(\frac{25}{42}\right)\) | \(e\left(\frac{19}{126}\right)\) | \(e\left(\frac{121}{126}\right)\) | \(e\left(\frac{53}{126}\right)\) | \(e\left(\frac{115}{126}\right)\) | \(e\left(\frac{8}{63}\right)\) | \(e\left(\frac{4}{21}\right)\) |