Basic properties
Modulus: | \(1225\) | |
Conductor: | \(245\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{245}(53,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1225.bm
\(\chi_{1225}(32,\cdot)\) \(\chi_{1225}(93,\cdot)\) \(\chi_{1225}(107,\cdot)\) \(\chi_{1225}(193,\cdot)\) \(\chi_{1225}(207,\cdot)\) \(\chi_{1225}(268,\cdot)\) \(\chi_{1225}(282,\cdot)\) \(\chi_{1225}(368,\cdot)\) \(\chi_{1225}(382,\cdot)\) \(\chi_{1225}(443,\cdot)\) \(\chi_{1225}(457,\cdot)\) \(\chi_{1225}(543,\cdot)\) \(\chi_{1225}(632,\cdot)\) \(\chi_{1225}(718,\cdot)\) \(\chi_{1225}(732,\cdot)\) \(\chi_{1225}(793,\cdot)\) \(\chi_{1225}(807,\cdot)\) \(\chi_{1225}(893,\cdot)\) \(\chi_{1225}(907,\cdot)\) \(\chi_{1225}(968,\cdot)\) \(\chi_{1225}(982,\cdot)\) \(\chi_{1225}(1068,\cdot)\) \(\chi_{1225}(1082,\cdot)\) \(\chi_{1225}(1143,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1177,101)\) → \((-i,e\left(\frac{5}{21}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
\( \chi_{ 1225 }(543, a) \) | \(-1\) | \(1\) | \(e\left(\frac{79}{84}\right)\) | \(e\left(\frac{41}{84}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{41}{42}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{31}{84}\right)\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{16}{21}\right)\) |