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.ie
\(\chi_{7448}(611,\cdot)\) \(\chi_{7448}(963,\cdot)\) \(\chi_{7448}(1131,\cdot)\) \(\chi_{7448}(1675,\cdot)\) \(\chi_{7448}(1731,\cdot)\) \(\chi_{7448}(1915,\cdot)\) \(\chi_{7448}(2123,\cdot)\) \(\chi_{7448}(2195,\cdot)\) \(\chi_{7448}(2739,\cdot)\) \(\chi_{7448}(2795,\cdot)\) \(\chi_{7448}(2979,\cdot)\) \(\chi_{7448}(3091,\cdot)\) \(\chi_{7448}(3187,\cdot)\) \(\chi_{7448}(3259,\cdot)\) \(\chi_{7448}(3859,\cdot)\) \(\chi_{7448}(4043,\cdot)\) \(\chi_{7448}(4155,\cdot)\) \(\chi_{7448}(4251,\cdot)\) \(\chi_{7448}(4323,\cdot)\) \(\chi_{7448}(4867,\cdot)\) \(\chi_{7448}(4923,\cdot)\) \(\chi_{7448}(5107,\cdot)\) \(\chi_{7448}(5219,\cdot)\) \(\chi_{7448}(5315,\cdot)\) \(\chi_{7448}(5387,\cdot)\) \(\chi_{7448}(5931,\cdot)\) \(\chi_{7448}(5987,\cdot)\) \(\chi_{7448}(6171,\cdot)\) \(\chi_{7448}(6283,\cdot)\) \(\chi_{7448}(6379,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((1863,3725,3041,3137)\) → \((-1,-1,e\left(\frac{19}{21}\right),e\left(\frac{13}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 7448 }(611, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{126}\right)\) | \(e\left(\frac{37}{126}\right)\) | \(e\left(\frac{37}{63}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{61}{63}\right)\) | \(e\left(\frac{37}{63}\right)\) | \(e\left(\frac{53}{63}\right)\) | \(e\left(\frac{41}{126}\right)\) | \(e\left(\frac{37}{63}\right)\) | \(e\left(\frac{37}{42}\right)\) |