Basic properties
| Modulus: | \(6044\) | |
| Conductor: | \(6044\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(302\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6044.k
\(\chi_{6044}(55,\cdot)\) \(\chi_{6044}(67,\cdot)\) \(\chi_{6044}(83,\cdot)\) \(\chi_{6044}(115,\cdot)\) \(\chi_{6044}(211,\cdot)\) \(\chi_{6044}(231,\cdot)\) \(\chi_{6044}(295,\cdot)\) \(\chi_{6044}(431,\cdot)\) \(\chi_{6044}(463,\cdot)\) \(\chi_{6044}(471,\cdot)\) \(\chi_{6044}(483,\cdot)\) \(\chi_{6044}(487,\cdot)\) \(\chi_{6044}(491,\cdot)\) \(\chi_{6044}(495,\cdot)\) \(\chi_{6044}(523,\cdot)\) \(\chi_{6044}(579,\cdot)\) \(\chi_{6044}(603,\cdot)\) \(\chi_{6044}(619,\cdot)\) \(\chi_{6044}(647,\cdot)\) \(\chi_{6044}(679,\cdot)\) \(\chi_{6044}(695,\cdot)\) \(\chi_{6044}(723,\cdot)\) \(\chi_{6044}(747,\cdot)\) \(\chi_{6044}(835,\cdot)\) \(\chi_{6044}(1007,\cdot)\) \(\chi_{6044}(1035,\cdot)\) \(\chi_{6044}(1151,\cdot)\) \(\chi_{6044}(1171,\cdot)\) \(\chi_{6044}(1223,\cdot)\) \(\chi_{6044}(1239,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{151})$ |
| Fixed field: | Number field defined by a degree 302 polynomial (not computed) |
Values on generators
\((3023,3033)\) → \((-1,e\left(\frac{225}{302}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 6044 }(55, a) \) | \(1\) | \(1\) | \(e\left(\frac{249}{302}\right)\) | \(e\left(\frac{63}{151}\right)\) | \(e\left(\frac{7}{302}\right)\) | \(e\left(\frac{98}{151}\right)\) | \(e\left(\frac{37}{151}\right)\) | \(e\left(\frac{121}{151}\right)\) | \(e\left(\frac{73}{302}\right)\) | \(e\left(\frac{150}{151}\right)\) | \(e\left(\frac{119}{302}\right)\) | \(e\left(\frac{128}{151}\right)\) |