Basic properties
Modulus: | \(2205\) | |
Conductor: | \(245\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{245}(53,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2205.ei
\(\chi_{2205}(37,\cdot)\) \(\chi_{2205}(163,\cdot)\) \(\chi_{2205}(172,\cdot)\) \(\chi_{2205}(298,\cdot)\) \(\chi_{2205}(352,\cdot)\) \(\chi_{2205}(478,\cdot)\) \(\chi_{2205}(487,\cdot)\) \(\chi_{2205}(613,\cdot)\) \(\chi_{2205}(793,\cdot)\) \(\chi_{2205}(928,\cdot)\) \(\chi_{2205}(982,\cdot)\) \(\chi_{2205}(1117,\cdot)\) \(\chi_{2205}(1297,\cdot)\) \(\chi_{2205}(1423,\cdot)\) \(\chi_{2205}(1432,\cdot)\) \(\chi_{2205}(1558,\cdot)\) \(\chi_{2205}(1612,\cdot)\) \(\chi_{2205}(1738,\cdot)\) \(\chi_{2205}(1747,\cdot)\) \(\chi_{2205}(1873,\cdot)\) \(\chi_{2205}(1927,\cdot)\) \(\chi_{2205}(2053,\cdot)\) \(\chi_{2205}(2062,\cdot)\) \(\chi_{2205}(2188,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1226,442,1081)\) → \((1,-i,e\left(\frac{5}{21}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(8\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) | \(22\) | \(23\) |
\( \chi_{ 2205 }(298, a) \) | \(-1\) | \(1\) | \(e\left(\frac{79}{84}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{59}{84}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{13}{28}\right)\) | \(e\left(\frac{25}{84}\right)\) |