Basic properties
| Modulus: | \(4028\) | |
| Conductor: | \(1007\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(234\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1007}(13,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4028.co
\(\chi_{4028}(13,\cdot)\) \(\chi_{4028}(89,\cdot)\) \(\chi_{4028}(97,\cdot)\) \(\chi_{4028}(205,\cdot)\) \(\chi_{4028}(261,\cdot)\) \(\chi_{4028}(281,\cdot)\) \(\chi_{4028}(333,\cdot)\) \(\chi_{4028}(413,\cdot)\) \(\chi_{4028}(545,\cdot)\) \(\chi_{4028}(629,\cdot)\) \(\chi_{4028}(649,\cdot)\) \(\chi_{4028}(705,\cdot)\) \(\chi_{4028}(713,\cdot)\) \(\chi_{4028}(717,\cdot)\) \(\chi_{4028}(725,\cdot)\) \(\chi_{4028}(789,\cdot)\) \(\chi_{4028}(925,\cdot)\) \(\chi_{4028}(945,\cdot)\) \(\chi_{4028}(1001,\cdot)\) \(\chi_{4028}(1017,\cdot)\) \(\chi_{4028}(1181,\cdot)\) \(\chi_{4028}(1229,\cdot)\) \(\chi_{4028}(1321,\cdot)\) \(\chi_{4028}(1473,\cdot)\) \(\chi_{4028}(1477,\cdot)\) \(\chi_{4028}(1497,\cdot)\) \(\chi_{4028}(1533,\cdot)\) \(\chi_{4028}(1553,\cdot)\) \(\chi_{4028}(1561,\cdot)\) \(\chi_{4028}(1573,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{117})$ |
| Fixed field: | Number field defined by a degree 234 polynomial (not computed) |
Values on generators
\((2015,2757,2281)\) → \((1,e\left(\frac{5}{18}\right),e\left(\frac{6}{13}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 4028 }(13, a) \) | \(-1\) | \(1\) | \(e\left(\frac{107}{234}\right)\) | \(e\left(\frac{16}{117}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{107}{117}\right)\) | \(e\left(\frac{4}{39}\right)\) | \(e\left(\frac{109}{234}\right)\) | \(e\left(\frac{139}{234}\right)\) | \(e\left(\frac{46}{117}\right)\) | \(e\left(\frac{137}{234}\right)\) | \(e\left(\frac{5}{9}\right)\) |