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 \(\chi_{4563}(281,\cdot)\) | 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
\((677,3889)\) → \((e\left(\frac{13}{18}\right),e\left(\frac{37}{52}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 9126 }(281, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{468}\right)\) | \(e\left(\frac{323}{468}\right)\) | \(e\left(\frac{317}{468}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{7}{234}\right)\) | \(e\left(\frac{43}{234}\right)\) | \(e\left(\frac{181}{468}\right)\) | \(e\left(\frac{55}{78}\right)\) |