Basic properties
Modulus: | \(9408\) | |
Conductor: | \(784\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{784}(75,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9408.fb
\(\chi_{9408}(271,\cdot)\) \(\chi_{9408}(367,\cdot)\) \(\chi_{9408}(943,\cdot)\) \(\chi_{9408}(1039,\cdot)\) \(\chi_{9408}(1615,\cdot)\) \(\chi_{9408}(1711,\cdot)\) \(\chi_{9408}(2287,\cdot)\) \(\chi_{9408}(3055,\cdot)\) \(\chi_{9408}(3631,\cdot)\) \(\chi_{9408}(3727,\cdot)\) \(\chi_{9408}(4303,\cdot)\) \(\chi_{9408}(4399,\cdot)\) \(\chi_{9408}(4975,\cdot)\) \(\chi_{9408}(5071,\cdot)\) \(\chi_{9408}(5647,\cdot)\) \(\chi_{9408}(5743,\cdot)\) \(\chi_{9408}(6319,\cdot)\) \(\chi_{9408}(6415,\cdot)\) \(\chi_{9408}(6991,\cdot)\) \(\chi_{9408}(7759,\cdot)\) \(\chi_{9408}(8335,\cdot)\) \(\chi_{9408}(8431,\cdot)\) \(\chi_{9408}(9007,\cdot)\) \(\chi_{9408}(9103,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1471,6469,3137,4609)\) → \((-1,i,1,e\left(\frac{17}{42}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
\( \chi_{ 9408 }(271, a) \) | \(1\) | \(1\) | \(e\left(\frac{83}{84}\right)\) | \(e\left(\frac{79}{84}\right)\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{41}{42}\right)\) | \(e\left(\frac{1}{28}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{17}{84}\right)\) |