Basic properties
| Modulus: | \(4028\) | |
| Conductor: | \(1007\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(52\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1007}(569,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4028.bw
\(\chi_{4028}(569,\cdot)\) \(\chi_{4028}(721,\cdot)\) \(\chi_{4028}(797,\cdot)\) \(\chi_{4028}(949,\cdot)\) \(\chi_{4028}(1025,\cdot)\) \(\chi_{4028}(1101,\cdot)\) \(\chi_{4028}(1253,\cdot)\) \(\chi_{4028}(1405,\cdot)\) \(\chi_{4028}(1481,\cdot)\) \(\chi_{4028}(1557,\cdot)\) \(\chi_{4028}(2089,\cdot)\) \(\chi_{4028}(2165,\cdot)\) \(\chi_{4028}(2393,\cdot)\) \(\chi_{4028}(2469,\cdot)\) \(\chi_{4028}(3001,\cdot)\) \(\chi_{4028}(3077,\cdot)\) \(\chi_{4028}(3153,\cdot)\) \(\chi_{4028}(3305,\cdot)\) \(\chi_{4028}(3457,\cdot)\) \(\chi_{4028}(3533,\cdot)\) \(\chi_{4028}(3609,\cdot)\) \(\chi_{4028}(3761,\cdot)\) \(\chi_{4028}(3837,\cdot)\) \(\chi_{4028}(3989,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{52})$ |
| Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((2015,2757,2281)\) → \((1,-1,e\left(\frac{41}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 4028 }(569, a) \) | \(1\) | \(1\) | \(e\left(\frac{47}{52}\right)\) | \(e\left(\frac{3}{52}\right)\) | \(e\left(\frac{1}{26}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{19}{26}\right)\) | \(e\left(\frac{11}{26}\right)\) | \(e\left(\frac{25}{26}\right)\) | \(e\left(\frac{23}{26}\right)\) | \(e\left(\frac{49}{52}\right)\) | \(-i\) |