Basic properties
| Modulus: | \(6044\) | |
| Conductor: | \(1511\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(151\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1511}(9,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6044.i
\(\chi_{6044}(9,\cdot)\) \(\chi_{6044}(81,\cdot)\) \(\chi_{6044}(89,\cdot)\) \(\chi_{6044}(101,\cdot)\) \(\chi_{6044}(221,\cdot)\) \(\chi_{6044}(281,\cdot)\) \(\chi_{6044}(309,\cdot)\) \(\chi_{6044}(389,\cdot)\) \(\chi_{6044}(425,\cdot)\) \(\chi_{6044}(473,\cdot)\) \(\chi_{6044}(489,\cdot)\) \(\chi_{6044}(517,\cdot)\) \(\chi_{6044}(617,\cdot)\) \(\chi_{6044}(729,\cdot)\) \(\chi_{6044}(781,\cdot)\) \(\chi_{6044}(801,\cdot)\) \(\chi_{6044}(833,\cdot)\) \(\chi_{6044}(845,\cdot)\) \(\chi_{6044}(853,\cdot)\) \(\chi_{6044}(909,\cdot)\) \(\chi_{6044}(937,\cdot)\) \(\chi_{6044}(969,\cdot)\) \(\chi_{6044}(985,\cdot)\) \(\chi_{6044}(989,\cdot)\) \(\chi_{6044}(1037,\cdot)\) \(\chi_{6044}(1041,\cdot)\) \(\chi_{6044}(1081,\cdot)\) \(\chi_{6044}(1101,\cdot)\) \(\chi_{6044}(1137,\cdot)\) \(\chi_{6044}(1149,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{151})$ |
| Fixed field: | Number field defined by a degree 151 polynomial (not computed) |
Values on generators
\((3023,3033)\) → \((1,e\left(\frac{148}{151}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 6044 }(9, a) \) | \(1\) | \(1\) | \(e\left(\frac{45}{151}\right)\) | \(e\left(\frac{101}{151}\right)\) | \(e\left(\frac{14}{151}\right)\) | \(e\left(\frac{90}{151}\right)\) | \(e\left(\frac{148}{151}\right)\) | \(e\left(\frac{31}{151}\right)\) | \(e\left(\frac{146}{151}\right)\) | \(e\left(\frac{147}{151}\right)\) | \(e\left(\frac{87}{151}\right)\) | \(e\left(\frac{59}{151}\right)\) |