Basic properties
| Modulus: | \(4028\) | |
| Conductor: | \(4028\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(234\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4028.cl
\(\chi_{4028}(43,\cdot)\) \(\chi_{4028}(123,\cdot)\) \(\chi_{4028}(131,\cdot)\) \(\chi_{4028}(199,\cdot)\) \(\chi_{4028}(271,\cdot)\) \(\chi_{4028}(327,\cdot)\) \(\chi_{4028}(347,\cdot)\) \(\chi_{4028}(435,\cdot)\) \(\chi_{4028}(555,\cdot)\) \(\chi_{4028}(567,\cdot)\) \(\chi_{4028}(587,\cdot)\) \(\chi_{4028}(643,\cdot)\) \(\chi_{4028}(727,\cdot)\) \(\chi_{4028}(859,\cdot)\) \(\chi_{4028}(891,\cdot)\) \(\chi_{4028}(1011,\cdot)\) \(\chi_{4028}(1119,\cdot)\) \(\chi_{4028}(1175,\cdot)\) \(\chi_{4028}(1183,\cdot)\) \(\chi_{4028}(1195,\cdot)\) \(\chi_{4028}(1203,\cdot)\) \(\chi_{4028}(1259,\cdot)\) \(\chi_{4028}(1279,\cdot)\) \(\chi_{4028}(1315,\cdot)\) \(\chi_{4028}(1403,\cdot)\) \(\chi_{4028}(1415,\cdot)\) \(\chi_{4028}(1491,\cdot)\) \(\chi_{4028}(1543,\cdot)\) \(\chi_{4028}(1575,\cdot)\) \(\chi_{4028}(1619,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{117})$ |
| Fixed field: | Number field defined by a degree 234 polynomial (not computed) |
Values on generators
\((2015,2757,2281)\) → \((-1,e\left(\frac{8}{9}\right),e\left(\frac{11}{26}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 4028 }(43, a) \) | \(-1\) | \(1\) | \(e\left(\frac{29}{117}\right)\) | \(e\left(\frac{25}{234}\right)\) | \(e\left(\frac{59}{78}\right)\) | \(e\left(\frac{58}{117}\right)\) | \(e\left(\frac{55}{78}\right)\) | \(e\left(\frac{70}{117}\right)\) | \(e\left(\frac{83}{234}\right)\) | \(e\left(\frac{14}{117}\right)\) | \(e\left(\frac{1}{234}\right)\) | \(e\left(\frac{7}{9}\right)\) |