Basic properties
| Modulus: | \(8043\) | |
| Conductor: | \(1149\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(382\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1149}(155,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8043.u
\(\chi_{8043}(155,\cdot)\) \(\chi_{8043}(176,\cdot)\) \(\chi_{8043}(197,\cdot)\) \(\chi_{8043}(218,\cdot)\) \(\chi_{8043}(239,\cdot)\) \(\chi_{8043}(281,\cdot)\) \(\chi_{8043}(302,\cdot)\) \(\chi_{8043}(365,\cdot)\) \(\chi_{8043}(428,\cdot)\) \(\chi_{8043}(449,\cdot)\) \(\chi_{8043}(617,\cdot)\) \(\chi_{8043}(638,\cdot)\) \(\chi_{8043}(680,\cdot)\) \(\chi_{8043}(701,\cdot)\) \(\chi_{8043}(743,\cdot)\) \(\chi_{8043}(764,\cdot)\) \(\chi_{8043}(806,\cdot)\) \(\chi_{8043}(827,\cdot)\) \(\chi_{8043}(848,\cdot)\) \(\chi_{8043}(911,\cdot)\) \(\chi_{8043}(932,\cdot)\) \(\chi_{8043}(953,\cdot)\) \(\chi_{8043}(974,\cdot)\) \(\chi_{8043}(1016,\cdot)\) \(\chi_{8043}(1037,\cdot)\) \(\chi_{8043}(1100,\cdot)\) \(\chi_{8043}(1121,\cdot)\) \(\chi_{8043}(1142,\cdot)\) \(\chi_{8043}(1184,\cdot)\) \(\chi_{8043}(1226,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{191})$ |
| Fixed field: | Number field defined by a degree 382 polynomial (not computed) |
Values on generators
\((5363,2299,6133)\) → \((-1,1,e\left(\frac{33}{382}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 8043 }(155, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{382}\right)\) | \(e\left(\frac{29}{191}\right)\) | \(e\left(\frac{112}{191}\right)\) | \(e\left(\frac{87}{382}\right)\) | \(e\left(\frac{253}{382}\right)\) | \(e\left(\frac{169}{191}\right)\) | \(e\left(\frac{181}{382}\right)\) | \(e\left(\frac{58}{191}\right)\) | \(e\left(\frac{373}{382}\right)\) | \(e\left(\frac{44}{191}\right)\) |