Basic properties
Modulus: | \(2061\) | |
Conductor: | \(229\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(76\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{229}(21,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2061.bn
\(\chi_{2061}(109,\cdot)\) \(\chi_{2061}(136,\cdot)\) \(\chi_{2061}(145,\cdot)\) \(\chi_{2061}(199,\cdot)\) \(\chi_{2061}(208,\cdot)\) \(\chi_{2061}(343,\cdot)\) \(\chi_{2061}(352,\cdot)\) \(\chi_{2061}(370,\cdot)\) \(\chi_{2061}(406,\cdot)\) \(\chi_{2061}(424,\cdot)\) \(\chi_{2061}(460,\cdot)\) \(\chi_{2061}(559,\cdot)\) \(\chi_{2061}(586,\cdot)\) \(\chi_{2061}(685,\cdot)\) \(\chi_{2061}(721,\cdot)\) \(\chi_{2061}(739,\cdot)\) \(\chi_{2061}(775,\cdot)\) \(\chi_{2061}(793,\cdot)\) \(\chi_{2061}(802,\cdot)\) \(\chi_{2061}(937,\cdot)\) \(\chi_{2061}(946,\cdot)\) \(\chi_{2061}(1000,\cdot)\) \(\chi_{2061}(1009,\cdot)\) \(\chi_{2061}(1036,\cdot)\) \(\chi_{2061}(1153,\cdot)\) \(\chi_{2061}(1288,\cdot)\) \(\chi_{2061}(1342,\cdot)\) \(\chi_{2061}(1387,\cdot)\) \(\chi_{2061}(1396,\cdot)\) \(\chi_{2061}(1549,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{76})$ |
Fixed field: | Number field defined by a degree 76 polynomial |
Values on generators
\((1604,235)\) → \((1,e\left(\frac{29}{76}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 2061 }(937, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1}{76}\right)\) | \(e\left(\frac{1}{38}\right)\) | \(e\left(\frac{15}{38}\right)\) | \(e\left(\frac{63}{76}\right)\) | \(e\left(\frac{3}{76}\right)\) | \(e\left(\frac{31}{76}\right)\) | \(e\left(\frac{31}{38}\right)\) | \(e\left(\frac{49}{76}\right)\) | \(e\left(\frac{16}{19}\right)\) | \(e\left(\frac{1}{19}\right)\) |