Basic properties
| Modulus: | \(7448\) | |
| Conductor: | \(931\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(126\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{931}(808,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7448.ih
\(\chi_{7448}(33,\cdot)\) \(\chi_{7448}(241,\cdot)\) \(\chi_{7448}(409,\cdot)\) \(\chi_{7448}(649,\cdot)\) \(\chi_{7448}(1193,\cdot)\) \(\chi_{7448}(1473,\cdot)\) \(\chi_{7448}(1713,\cdot)\) \(\chi_{7448}(1769,\cdot)\) \(\chi_{7448}(2161,\cdot)\) \(\chi_{7448}(2257,\cdot)\) \(\chi_{7448}(2369,\cdot)\) \(\chi_{7448}(2537,\cdot)\) \(\chi_{7448}(2777,\cdot)\) \(\chi_{7448}(2833,\cdot)\) \(\chi_{7448}(3225,\cdot)\) \(\chi_{7448}(3321,\cdot)\) \(\chi_{7448}(3433,\cdot)\) \(\chi_{7448}(3601,\cdot)\) \(\chi_{7448}(3897,\cdot)\) \(\chi_{7448}(4289,\cdot)\) \(\chi_{7448}(4385,\cdot)\) \(\chi_{7448}(4497,\cdot)\) \(\chi_{7448}(4665,\cdot)\) \(\chi_{7448}(4905,\cdot)\) \(\chi_{7448}(4961,\cdot)\) \(\chi_{7448}(5353,\cdot)\) \(\chi_{7448}(5449,\cdot)\) \(\chi_{7448}(5561,\cdot)\) \(\chi_{7448}(5729,\cdot)\) \(\chi_{7448}(5969,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((1863,3725,3041,3137)\) → \((1,1,e\left(\frac{37}{42}\right),e\left(\frac{17}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 7448 }(3601, a) \) | \(1\) | \(1\) | \(e\left(\frac{10}{63}\right)\) | \(e\left(\frac{83}{126}\right)\) | \(e\left(\frac{20}{63}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{50}{63}\right)\) | \(e\left(\frac{103}{126}\right)\) | \(e\left(\frac{59}{126}\right)\) | \(e\left(\frac{23}{63}\right)\) | \(e\left(\frac{20}{63}\right)\) | \(e\left(\frac{10}{21}\right)\) |