Basic properties
Modulus: | \(8043\) | |
Conductor: | \(8043\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(382\) | 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 8043.v
\(\chi_{8043}(62,\cdot)\) \(\chi_{8043}(146,\cdot)\) \(\chi_{8043}(251,\cdot)\) \(\chi_{8043}(272,\cdot)\) \(\chi_{8043}(293,\cdot)\) \(\chi_{8043}(419,\cdot)\) \(\chi_{8043}(440,\cdot)\) \(\chi_{8043}(545,\cdot)\) \(\chi_{8043}(587,\cdot)\) \(\chi_{8043}(608,\cdot)\) \(\chi_{8043}(671,\cdot)\) \(\chi_{8043}(692,\cdot)\) \(\chi_{8043}(713,\cdot)\) \(\chi_{8043}(755,\cdot)\) \(\chi_{8043}(797,\cdot)\) \(\chi_{8043}(839,\cdot)\) \(\chi_{8043}(902,\cdot)\) \(\chi_{8043}(986,\cdot)\) \(\chi_{8043}(1070,\cdot)\) \(\chi_{8043}(1112,\cdot)\) \(\chi_{8043}(1217,\cdot)\) \(\chi_{8043}(1259,\cdot)\) \(\chi_{8043}(1301,\cdot)\) \(\chi_{8043}(1322,\cdot)\) \(\chi_{8043}(1427,\cdot)\) \(\chi_{8043}(1553,\cdot)\) \(\chi_{8043}(1574,\cdot)\) \(\chi_{8043}(1595,\cdot)\) \(\chi_{8043}(1616,\cdot)\) \(\chi_{8043}(1658,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{191})$ |
Fixed field: | Number field defined by a degree 382 polynomial (not computed) |
Values on generators
\((5363,2299,6133)\) → \((-1,-1,e\left(\frac{83}{191}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 8043 }(62, a) \) | \(1\) | \(1\) | \(e\left(\frac{279}{382}\right)\) | \(e\left(\frac{88}{191}\right)\) | \(e\left(\frac{83}{191}\right)\) | \(e\left(\frac{73}{382}\right)\) | \(e\left(\frac{63}{382}\right)\) | \(e\left(\frac{97}{382}\right)\) | \(e\left(\frac{187}{382}\right)\) | \(e\left(\frac{176}{191}\right)\) | \(e\left(\frac{151}{191}\right)\) | \(e\left(\frac{379}{382}\right)\) |