Basic properties
| Modulus: | \(2028\) | |
| Conductor: | \(507\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{507}(41,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2028.bu
\(\chi_{2028}(41,\cdot)\) \(\chi_{2028}(137,\cdot)\) \(\chi_{2028}(149,\cdot)\) \(\chi_{2028}(197,\cdot)\) \(\chi_{2028}(245,\cdot)\) \(\chi_{2028}(293,\cdot)\) \(\chi_{2028}(305,\cdot)\) \(\chi_{2028}(353,\cdot)\) \(\chi_{2028}(401,\cdot)\) \(\chi_{2028}(449,\cdot)\) \(\chi_{2028}(461,\cdot)\) \(\chi_{2028}(509,\cdot)\) \(\chi_{2028}(557,\cdot)\) \(\chi_{2028}(605,\cdot)\) \(\chi_{2028}(617,\cdot)\) \(\chi_{2028}(665,\cdot)\) \(\chi_{2028}(713,\cdot)\) \(\chi_{2028}(761,\cdot)\) \(\chi_{2028}(773,\cdot)\) \(\chi_{2028}(821,\cdot)\) \(\chi_{2028}(869,\cdot)\) \(\chi_{2028}(917,\cdot)\) \(\chi_{2028}(929,\cdot)\) \(\chi_{2028}(977,\cdot)\) \(\chi_{2028}(1025,\cdot)\) \(\chi_{2028}(1073,\cdot)\) \(\chi_{2028}(1085,\cdot)\) \(\chi_{2028}(1133,\cdot)\) \(\chi_{2028}(1181,\cdot)\) \(\chi_{2028}(1229,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((1015,677,1861)\) → \((1,-1,e\left(\frac{85}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 2028 }(41, a) \) | \(1\) | \(1\) | \(e\left(\frac{21}{52}\right)\) | \(e\left(\frac{47}{156}\right)\) | \(e\left(\frac{97}{156}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{23}{78}\right)\) | \(e\left(\frac{23}{52}\right)\) | \(e\left(\frac{55}{78}\right)\) |