Basic properties
| Modulus: | \(7448\) | |
| Conductor: | \(7448\) | 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 7448.jd
\(\chi_{7448}(139,\cdot)\) \(\chi_{7448}(251,\cdot)\) \(\chi_{7448}(643,\cdot)\) \(\chi_{7448}(1035,\cdot)\) \(\chi_{7448}(1203,\cdot)\) \(\chi_{7448}(1259,\cdot)\) \(\chi_{7448}(1315,\cdot)\) \(\chi_{7448}(1651,\cdot)\) \(\chi_{7448}(1707,\cdot)\) \(\chi_{7448}(2099,\cdot)\) \(\chi_{7448}(2267,\cdot)\) \(\chi_{7448}(2323,\cdot)\) \(\chi_{7448}(2379,\cdot)\) \(\chi_{7448}(2715,\cdot)\) \(\chi_{7448}(2771,\cdot)\) \(\chi_{7448}(3163,\cdot)\) \(\chi_{7448}(3387,\cdot)\) \(\chi_{7448}(3443,\cdot)\) \(\chi_{7448}(3779,\cdot)\) \(\chi_{7448}(3835,\cdot)\) \(\chi_{7448}(4227,\cdot)\) \(\chi_{7448}(4395,\cdot)\) \(\chi_{7448}(4451,\cdot)\) \(\chi_{7448}(4843,\cdot)\) \(\chi_{7448}(5459,\cdot)\) \(\chi_{7448}(5515,\cdot)\) \(\chi_{7448}(5571,\cdot)\) \(\chi_{7448}(5907,\cdot)\) \(\chi_{7448}(5963,\cdot)\) \(\chi_{7448}(6355,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((1863,3725,3041,3137)\) → \((-1,-1,e\left(\frac{11}{14}\right),e\left(\frac{7}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 7448 }(2267, a) \) | \(1\) | \(1\) | \(e\left(\frac{113}{126}\right)\) | \(e\left(\frac{46}{63}\right)\) | \(e\left(\frac{50}{63}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{20}{63}\right)\) | \(e\left(\frac{79}{126}\right)\) | \(e\left(\frac{53}{126}\right)\) | \(e\left(\frac{115}{126}\right)\) | \(e\left(\frac{29}{63}\right)\) | \(e\left(\frac{29}{42}\right)\) |