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.eo
\(\chi_{2205}(52,\cdot)\) \(\chi_{2205}(103,\cdot)\) \(\chi_{2205}(292,\cdot)\) \(\chi_{2205}(367,\cdot)\) \(\chi_{2205}(418,\cdot)\) \(\chi_{2205}(493,\cdot)\) \(\chi_{2205}(682,\cdot)\) \(\chi_{2205}(733,\cdot)\) \(\chi_{2205}(808,\cdot)\) \(\chi_{2205}(922,\cdot)\) \(\chi_{2205}(997,\cdot)\) \(\chi_{2205}(1123,\cdot)\) \(\chi_{2205}(1237,\cdot)\) \(\chi_{2205}(1312,\cdot)\) \(\chi_{2205}(1363,\cdot)\) \(\chi_{2205}(1438,\cdot)\) \(\chi_{2205}(1552,\cdot)\) \(\chi_{2205}(1627,\cdot)\) \(\chi_{2205}(1678,\cdot)\) \(\chi_{2205}(1753,\cdot)\) \(\chi_{2205}(1867,\cdot)\) \(\chi_{2205}(1993,\cdot)\) \(\chi_{2205}(2068,\cdot)\) \(\chi_{2205}(2182,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1226,442,1081)\) → \((e\left(\frac{1}{3}\right),i,e\left(\frac{11}{42}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(8\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) | \(22\) | \(23\) |
\( \chi_{ 2205 }(1237, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{28}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{5}{84}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{67}{84}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{17}{84}\right)\) | \(e\left(\frac{31}{84}\right)\) |