Basic properties
| Modulus: | \(9126\) | |
| Conductor: | \(4563\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(468\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4563}(1643,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9126.dp
\(\chi_{9126}(5,\cdot)\) \(\chi_{9126}(47,\cdot)\) \(\chi_{9126}(83,\cdot)\) \(\chi_{9126}(203,\cdot)\) \(\chi_{9126}(281,\cdot)\) \(\chi_{9126}(317,\cdot)\) \(\chi_{9126}(473,\cdot)\) \(\chi_{9126}(515,\cdot)\) \(\chi_{9126}(551,\cdot)\) \(\chi_{9126}(671,\cdot)\) \(\chi_{9126}(707,\cdot)\) \(\chi_{9126}(749,\cdot)\) \(\chi_{9126}(785,\cdot)\) \(\chi_{9126}(905,\cdot)\) \(\chi_{9126}(941,\cdot)\) \(\chi_{9126}(983,\cdot)\) \(\chi_{9126}(1019,\cdot)\) \(\chi_{9126}(1139,\cdot)\) \(\chi_{9126}(1175,\cdot)\) \(\chi_{9126}(1217,\cdot)\) \(\chi_{9126}(1373,\cdot)\) \(\chi_{9126}(1409,\cdot)\) \(\chi_{9126}(1487,\cdot)\) \(\chi_{9126}(1607,\cdot)\) \(\chi_{9126}(1643,\cdot)\) \(\chi_{9126}(1685,\cdot)\) \(\chi_{9126}(1721,\cdot)\) \(\chi_{9126}(1841,\cdot)\) \(\chi_{9126}(1877,\cdot)\) \(\chi_{9126}(1919,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{468})$ |
| Fixed field: | Number field defined by a degree 468 polynomial (not computed) |
Values on generators
\((677,3889)\) → \((e\left(\frac{11}{18}\right),e\left(\frac{47}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 9126 }(1643, a) \) | \(1\) | \(1\) | \(e\left(\frac{89}{468}\right)\) | \(e\left(\frac{229}{468}\right)\) | \(e\left(\frac{19}{468}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{89}{234}\right)\) | \(e\left(\frac{179}{234}\right)\) | \(e\left(\frac{95}{468}\right)\) | \(e\left(\frac{53}{78}\right)\) |