Basic properties
Modulus: | \(4056\) | |
Conductor: | \(2028\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(156\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{2028}(71,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4056.dq
\(\chi_{4056}(71,\cdot)\) \(\chi_{4056}(119,\cdot)\) \(\chi_{4056}(167,\cdot)\) \(\chi_{4056}(215,\cdot)\) \(\chi_{4056}(383,\cdot)\) \(\chi_{4056}(431,\cdot)\) \(\chi_{4056}(479,\cdot)\) \(\chi_{4056}(527,\cdot)\) \(\chi_{4056}(743,\cdot)\) \(\chi_{4056}(791,\cdot)\) \(\chi_{4056}(839,\cdot)\) \(\chi_{4056}(1007,\cdot)\) \(\chi_{4056}(1055,\cdot)\) \(\chi_{4056}(1151,\cdot)\) \(\chi_{4056}(1319,\cdot)\) \(\chi_{4056}(1367,\cdot)\) \(\chi_{4056}(1415,\cdot)\) \(\chi_{4056}(1463,\cdot)\) \(\chi_{4056}(1631,\cdot)\) \(\chi_{4056}(1679,\cdot)\) \(\chi_{4056}(1727,\cdot)\) \(\chi_{4056}(1775,\cdot)\) \(\chi_{4056}(1943,\cdot)\) \(\chi_{4056}(1991,\cdot)\) \(\chi_{4056}(2039,\cdot)\) \(\chi_{4056}(2087,\cdot)\) \(\chi_{4056}(2255,\cdot)\) \(\chi_{4056}(2303,\cdot)\) \(\chi_{4056}(2351,\cdot)\) \(\chi_{4056}(2399,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{156})$ |
Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((1015,2029,2705,3889)\) → \((-1,1,-1,e\left(\frac{137}{156}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 4056 }(71, a) \) | \(-1\) | \(1\) | \(e\left(\frac{21}{52}\right)\) | \(e\left(\frac{73}{156}\right)\) | \(e\left(\frac{71}{156}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{49}{78}\right)\) | \(e\left(\frac{49}{52}\right)\) | \(e\left(\frac{34}{39}\right)\) |