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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2205.ej
\(\chi_{2205}(13,\cdot)\) \(\chi_{2205}(202,\cdot)\) \(\chi_{2205}(223,\cdot)\) \(\chi_{2205}(328,\cdot)\) \(\chi_{2205}(412,\cdot)\) \(\chi_{2205}(517,\cdot)\) \(\chi_{2205}(643,\cdot)\) \(\chi_{2205}(727,\cdot)\) \(\chi_{2205}(853,\cdot)\) \(\chi_{2205}(958,\cdot)\) \(\chi_{2205}(1042,\cdot)\) \(\chi_{2205}(1147,\cdot)\) \(\chi_{2205}(1168,\cdot)\) \(\chi_{2205}(1357,\cdot)\) \(\chi_{2205}(1462,\cdot)\) \(\chi_{2205}(1483,\cdot)\) \(\chi_{2205}(1588,\cdot)\) \(\chi_{2205}(1672,\cdot)\) \(\chi_{2205}(1777,\cdot)\) \(\chi_{2205}(1798,\cdot)\) \(\chi_{2205}(1903,\cdot)\) \(\chi_{2205}(1987,\cdot)\) \(\chi_{2205}(2092,\cdot)\) \(\chi_{2205}(2113,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1226,442,1081)\) → \((e\left(\frac{1}{3}\right),i,e\left(\frac{13}{14}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(8\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) | \(22\) | \(23\) |
\( \chi_{ 2205 }(1147, a) \) | \(1\) | \(1\) | \(e\left(\frac{61}{84}\right)\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{5}{84}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{13}{28}\right)\) | \(1\) | \(e\left(\frac{17}{84}\right)\) | \(e\left(\frac{59}{84}\right)\) |