Basic properties
| Modulus: | \(2028\) | |
| Conductor: | \(507\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(52\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{507}(5,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2028.bi
\(\chi_{2028}(5,\cdot)\) \(\chi_{2028}(125,\cdot)\) \(\chi_{2028}(161,\cdot)\) \(\chi_{2028}(281,\cdot)\) \(\chi_{2028}(317,\cdot)\) \(\chi_{2028}(473,\cdot)\) \(\chi_{2028}(593,\cdot)\) \(\chi_{2028}(629,\cdot)\) \(\chi_{2028}(749,\cdot)\) \(\chi_{2028}(785,\cdot)\) \(\chi_{2028}(905,\cdot)\) \(\chi_{2028}(941,\cdot)\) \(\chi_{2028}(1061,\cdot)\) \(\chi_{2028}(1097,\cdot)\) \(\chi_{2028}(1217,\cdot)\) \(\chi_{2028}(1373,\cdot)\) \(\chi_{2028}(1409,\cdot)\) \(\chi_{2028}(1529,\cdot)\) \(\chi_{2028}(1565,\cdot)\) \(\chi_{2028}(1685,\cdot)\) \(\chi_{2028}(1721,\cdot)\) \(\chi_{2028}(1841,\cdot)\) \(\chi_{2028}(1877,\cdot)\) \(\chi_{2028}(1997,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{52})$ |
| Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((1015,677,1861)\) → \((1,-1,e\left(\frac{3}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 2028 }(5, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{52}\right)\) | \(e\left(\frac{9}{52}\right)\) | \(e\left(\frac{23}{52}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(-i\) | \(1\) | \(e\left(\frac{1}{26}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{11}{52}\right)\) | \(e\left(\frac{5}{26}\right)\) |