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 \(\chi_{735}(368,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2205.ee
\(\chi_{2205}(53,\cdot)\) \(\chi_{2205}(107,\cdot)\) \(\chi_{2205}(233,\cdot)\) \(\chi_{2205}(242,\cdot)\) \(\chi_{2205}(368,\cdot)\) \(\chi_{2205}(548,\cdot)\) \(\chi_{2205}(683,\cdot)\) \(\chi_{2205}(737,\cdot)\) \(\chi_{2205}(872,\cdot)\) \(\chi_{2205}(1052,\cdot)\) \(\chi_{2205}(1178,\cdot)\) \(\chi_{2205}(1187,\cdot)\) \(\chi_{2205}(1313,\cdot)\) \(\chi_{2205}(1367,\cdot)\) \(\chi_{2205}(1493,\cdot)\) \(\chi_{2205}(1502,\cdot)\) \(\chi_{2205}(1628,\cdot)\) \(\chi_{2205}(1682,\cdot)\) \(\chi_{2205}(1808,\cdot)\) \(\chi_{2205}(1817,\cdot)\) \(\chi_{2205}(1943,\cdot)\) \(\chi_{2205}(1997,\cdot)\) \(\chi_{2205}(2123,\cdot)\) \(\chi_{2205}(2132,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1226,442,1081)\) → \((-1,-i,e\left(\frac{8}{21}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(8\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) | \(22\) | \(23\) |
| \( \chi_{ 2205 }(368, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{84}\right)\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{13}{28}\right)\) | \(e\left(\frac{31}{42}\right)\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{65}{84}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{19}{84}\right)\) |