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 \(\chi_{3724}(135,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7448.js
\(\chi_{7448}(135,\cdot)\) \(\chi_{7448}(319,\cdot)\) \(\chi_{7448}(431,\cdot)\) \(\chi_{7448}(527,\cdot)\) \(\chi_{7448}(599,\cdot)\) \(\chi_{7448}(1143,\cdot)\) \(\chi_{7448}(1199,\cdot)\) \(\chi_{7448}(1383,\cdot)\) \(\chi_{7448}(1495,\cdot)\) \(\chi_{7448}(1591,\cdot)\) \(\chi_{7448}(1663,\cdot)\) \(\chi_{7448}(2207,\cdot)\) \(\chi_{7448}(2263,\cdot)\) \(\chi_{7448}(2447,\cdot)\) \(\chi_{7448}(2559,\cdot)\) \(\chi_{7448}(2655,\cdot)\) \(\chi_{7448}(2727,\cdot)\) \(\chi_{7448}(3271,\cdot)\) \(\chi_{7448}(3327,\cdot)\) \(\chi_{7448}(3511,\cdot)\) \(\chi_{7448}(3623,\cdot)\) \(\chi_{7448}(3719,\cdot)\) \(\chi_{7448}(4335,\cdot)\) \(\chi_{7448}(4687,\cdot)\) \(\chi_{7448}(4855,\cdot)\) \(\chi_{7448}(5399,\cdot)\) \(\chi_{7448}(5455,\cdot)\) \(\chi_{7448}(5639,\cdot)\) \(\chi_{7448}(5847,\cdot)\) \(\chi_{7448}(5919,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{63})$ |
Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((1863,3725,3041,3137)\) → \((-1,1,e\left(\frac{16}{21}\right),e\left(\frac{1}{18}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(23\) | \(25\) | \(27\) |
\( \chi_{ 7448 }(135, a) \) | \(1\) | \(1\) | \(e\left(\frac{62}{63}\right)\) | \(e\left(\frac{62}{63}\right)\) | \(e\left(\frac{61}{63}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{53}{126}\right)\) | \(e\left(\frac{61}{63}\right)\) | \(e\left(\frac{38}{63}\right)\) | \(e\left(\frac{71}{126}\right)\) | \(e\left(\frac{61}{63}\right)\) | \(e\left(\frac{20}{21}\right)\) |