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 \(\chi_{245}(102,\cdot)\) | 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
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
| \( \chi_{ 1225 }(1082, a) \) | \(-1\) | \(1\) | \(e\left(\frac{37}{84}\right)\) | \(e\left(\frac{83}{84}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{41}{42}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{73}{84}\right)\) | \(e\left(\frac{17}{28}\right)\) | \(e\left(\frac{16}{21}\right)\) |