Basic properties
Modulus: | \(6010\) | |
Conductor: | \(601\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(75\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{601}(81,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6010.ce
\(\chi_{6010}(81,\cdot)\) \(\chi_{6010}(141,\cdot)\) \(\chi_{6010}(201,\cdot)\) \(\chi_{6010}(211,\cdot)\) \(\chi_{6010}(341,\cdot)\) \(\chi_{6010}(371,\cdot)\) \(\chi_{6010}(401,\cdot)\) \(\chi_{6010}(471,\cdot)\) \(\chi_{6010}(501,\cdot)\) \(\chi_{6010}(551,\cdot)\) \(\chi_{6010}(1211,\cdot)\) \(\chi_{6010}(1851,\cdot)\) \(\chi_{6010}(1991,\cdot)\) \(\chi_{6010}(2071,\cdot)\) \(\chi_{6010}(2091,\cdot)\) \(\chi_{6010}(2451,\cdot)\) \(\chi_{6010}(2471,\cdot)\) \(\chi_{6010}(2931,\cdot)\) \(\chi_{6010}(3011,\cdot)\) \(\chi_{6010}(3041,\cdot)\) \(\chi_{6010}(3101,\cdot)\) \(\chi_{6010}(3381,\cdot)\) \(\chi_{6010}(3411,\cdot)\) \(\chi_{6010}(3491,\cdot)\) \(\chi_{6010}(3911,\cdot)\) \(\chi_{6010}(4301,\cdot)\) \(\chi_{6010}(4341,\cdot)\) \(\chi_{6010}(4351,\cdot)\) \(\chi_{6010}(4541,\cdot)\) \(\chi_{6010}(4591,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{75})$ |
Fixed field: | Number field defined by a degree 75 polynomial |
Values on generators
\((3607,2411)\) → \((1,e\left(\frac{2}{75}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
\( \chi_{ 6010 }(81, a) \) | \(1\) | \(1\) | \(e\left(\frac{8}{75}\right)\) | \(e\left(\frac{2}{75}\right)\) | \(e\left(\frac{16}{75}\right)\) | \(e\left(\frac{14}{75}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{32}{75}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{29}{75}\right)\) | \(e\left(\frac{8}{25}\right)\) |