Basic properties
| Modulus: | \(2205\) | |
| Conductor: | \(2205\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2205.eb
\(\chi_{2205}(142,\cdot)\) \(\chi_{2205}(193,\cdot)\) \(\chi_{2205}(268,\cdot)\) \(\chi_{2205}(382,\cdot)\) \(\chi_{2205}(457,\cdot)\) \(\chi_{2205}(583,\cdot)\) \(\chi_{2205}(697,\cdot)\) \(\chi_{2205}(772,\cdot)\) \(\chi_{2205}(823,\cdot)\) \(\chi_{2205}(898,\cdot)\) \(\chi_{2205}(1012,\cdot)\) \(\chi_{2205}(1087,\cdot)\) \(\chi_{2205}(1138,\cdot)\) \(\chi_{2205}(1213,\cdot)\) \(\chi_{2205}(1327,\cdot)\) \(\chi_{2205}(1453,\cdot)\) \(\chi_{2205}(1528,\cdot)\) \(\chi_{2205}(1642,\cdot)\) \(\chi_{2205}(1717,\cdot)\) \(\chi_{2205}(1768,\cdot)\) \(\chi_{2205}(1957,\cdot)\) \(\chi_{2205}(2032,\cdot)\) \(\chi_{2205}(2083,\cdot)\) \(\chi_{2205}(2158,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1226,442,1081)\) → \((e\left(\frac{1}{3}\right),i,e\left(\frac{2}{21}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(8\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) | \(22\) | \(23\) |
| \( \chi_{ 2205 }(1012, a) \) | \(-1\) | \(1\) | \(e\left(\frac{5}{84}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{47}{84}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{53}{84}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{17}{84}\right)\) | \(e\left(\frac{1}{28}\right)\) |