Basic properties
Modulus: | \(2415\) | |
Conductor: | \(805\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(132\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{805}(18,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2415.dp
\(\chi_{2415}(58,\cdot)\) \(\chi_{2415}(142,\cdot)\) \(\chi_{2415}(163,\cdot)\) \(\chi_{2415}(193,\cdot)\) \(\chi_{2415}(403,\cdot)\) \(\chi_{2415}(478,\cdot)\) \(\chi_{2415}(487,\cdot)\) \(\chi_{2415}(508,\cdot)\) \(\chi_{2415}(583,\cdot)\) \(\chi_{2415}(772,\cdot)\) \(\chi_{2415}(823,\cdot)\) \(\chi_{2415}(877,\cdot)\) \(\chi_{2415}(928,\cdot)\) \(\chi_{2415}(982,\cdot)\) \(\chi_{2415}(1087,\cdot)\) \(\chi_{2415}(1108,\cdot)\) \(\chi_{2415}(1117,\cdot)\) \(\chi_{2415}(1222,\cdot)\) \(\chi_{2415}(1297,\cdot)\) \(\chi_{2415}(1327,\cdot)\) \(\chi_{2415}(1432,\cdot)\) \(\chi_{2415}(1453,\cdot)\) \(\chi_{2415}(1507,\cdot)\) \(\chi_{2415}(1612,\cdot)\) \(\chi_{2415}(1642,\cdot)\) \(\chi_{2415}(1738,\cdot)\) \(\chi_{2415}(1843,\cdot)\) \(\chi_{2415}(1852,\cdot)\) \(\chi_{2415}(1927,\cdot)\) \(\chi_{2415}(1948,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{132})$ |
Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((806,967,346,1891)\) → \((1,-i,e\left(\frac{2}{3}\right),e\left(\frac{6}{11}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(8\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) | \(22\) | \(26\) |
\( \chi_{ 2415 }(823, a) \) | \(-1\) | \(1\) | \(e\left(\frac{23}{132}\right)\) | \(e\left(\frac{23}{66}\right)\) | \(e\left(\frac{23}{44}\right)\) | \(e\left(\frac{19}{33}\right)\) | \(e\left(\frac{39}{44}\right)\) | \(e\left(\frac{23}{33}\right)\) | \(e\left(\frac{31}{132}\right)\) | \(e\left(\frac{1}{66}\right)\) | \(-i\) | \(e\left(\frac{2}{33}\right)\) |