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.jc
\(\chi_{7448}(155,\cdot)\) \(\chi_{7448}(211,\cdot)\) \(\chi_{7448}(547,\cdot)\) \(\chi_{7448}(603,\cdot)\) \(\chi_{7448}(659,\cdot)\) \(\chi_{7448}(827,\cdot)\) \(\chi_{7448}(1219,\cdot)\) \(\chi_{7448}(1611,\cdot)\) \(\chi_{7448}(1723,\cdot)\) \(\chi_{7448}(1891,\cdot)\) \(\chi_{7448}(2283,\cdot)\) \(\chi_{7448}(2339,\cdot)\) \(\chi_{7448}(2675,\cdot)\) \(\chi_{7448}(2731,\cdot)\) \(\chi_{7448}(2787,\cdot)\) \(\chi_{7448}(2955,\cdot)\) \(\chi_{7448}(3347,\cdot)\) \(\chi_{7448}(3403,\cdot)\) \(\chi_{7448}(3739,\cdot)\) \(\chi_{7448}(3795,\cdot)\) \(\chi_{7448}(3851,\cdot)\) \(\chi_{7448}(4467,\cdot)\) \(\chi_{7448}(4859,\cdot)\) \(\chi_{7448}(4915,\cdot)\) \(\chi_{7448}(5083,\cdot)\) \(\chi_{7448}(5475,\cdot)\) \(\chi_{7448}(5531,\cdot)\) \(\chi_{7448}(5867,\cdot)\) \(\chi_{7448}(5923,\cdot)\) \(\chi_{7448}(6147,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((1863,3725,3041,3137)\) → \((-1,-1,e\left(\frac{6}{7}\right),e\left(\frac{13}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 7448 }(155, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{126}\right)\) | \(e\left(\frac{115}{126}\right)\) | \(e\left(\frac{31}{63}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{25}{63}\right)\) | \(e\left(\frac{10}{63}\right)\) | \(e\left(\frac{41}{63}\right)\) | \(e\left(\frac{65}{126}\right)\) | \(e\left(\frac{52}{63}\right)\) | \(e\left(\frac{31}{42}\right)\) |