Basic properties
| Modulus: | \(2205\) | |
| Conductor: | \(735\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{735}(152,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2205.ed
\(\chi_{2205}(17,\cdot)\) \(\chi_{2205}(143,\cdot)\) \(\chi_{2205}(152,\cdot)\) \(\chi_{2205}(278,\cdot)\) \(\chi_{2205}(332,\cdot)\) \(\chi_{2205}(458,\cdot)\) \(\chi_{2205}(467,\cdot)\) \(\chi_{2205}(593,\cdot)\) \(\chi_{2205}(647,\cdot)\) \(\chi_{2205}(773,\cdot)\) \(\chi_{2205}(782,\cdot)\) \(\chi_{2205}(908,\cdot)\) \(\chi_{2205}(1088,\cdot)\) \(\chi_{2205}(1223,\cdot)\) \(\chi_{2205}(1277,\cdot)\) \(\chi_{2205}(1412,\cdot)\) \(\chi_{2205}(1592,\cdot)\) \(\chi_{2205}(1718,\cdot)\) \(\chi_{2205}(1727,\cdot)\) \(\chi_{2205}(1853,\cdot)\) \(\chi_{2205}(1907,\cdot)\) \(\chi_{2205}(2033,\cdot)\) \(\chi_{2205}(2042,\cdot)\) \(\chi_{2205}(2168,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1226,442,1081)\) → \((-1,i,e\left(\frac{29}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(8\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) | \(22\) | \(23\) |
| \( \chi_{ 2205 }(152, a) \) | \(-1\) | \(1\) | \(e\left(\frac{59}{84}\right)\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{1}{84}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{41}{84}\right)\) |