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 \(\chi_{931}(89,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7448.jn
\(\chi_{7448}(89,\cdot)\) \(\chi_{7448}(185,\cdot)\) \(\chi_{7448}(257,\cdot)\) \(\chi_{7448}(801,\cdot)\) \(\chi_{7448}(857,\cdot)\) \(\chi_{7448}(1041,\cdot)\) \(\chi_{7448}(1153,\cdot)\) \(\chi_{7448}(1249,\cdot)\) \(\chi_{7448}(1321,\cdot)\) \(\chi_{7448}(1865,\cdot)\) \(\chi_{7448}(1921,\cdot)\) \(\chi_{7448}(2105,\cdot)\) \(\chi_{7448}(2217,\cdot)\) \(\chi_{7448}(2313,\cdot)\) \(\chi_{7448}(2385,\cdot)\) \(\chi_{7448}(2929,\cdot)\) \(\chi_{7448}(2985,\cdot)\) \(\chi_{7448}(3169,\cdot)\) \(\chi_{7448}(3281,\cdot)\) \(\chi_{7448}(3377,\cdot)\) \(\chi_{7448}(3993,\cdot)\) \(\chi_{7448}(4345,\cdot)\) \(\chi_{7448}(4513,\cdot)\) \(\chi_{7448}(5057,\cdot)\) \(\chi_{7448}(5113,\cdot)\) \(\chi_{7448}(5297,\cdot)\) \(\chi_{7448}(5505,\cdot)\) \(\chi_{7448}(5577,\cdot)\) \(\chi_{7448}(6121,\cdot)\) \(\chi_{7448}(6177,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{63})$ |
Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((1863,3725,3041,3137)\) → \((1,1,e\left(\frac{23}{42}\right),e\left(\frac{5}{18}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(23\) | \(25\) | \(27\) |
\( \chi_{ 7448 }(89, a) \) | \(1\) | \(1\) | \(e\left(\frac{10}{63}\right)\) | \(e\left(\frac{41}{126}\right)\) | \(e\left(\frac{20}{63}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{29}{63}\right)\) | \(e\left(\frac{61}{126}\right)\) | \(e\left(\frac{59}{126}\right)\) | \(e\left(\frac{23}{63}\right)\) | \(e\left(\frac{41}{63}\right)\) | \(e\left(\frac{10}{21}\right)\) |