Basic properties
| Modulus: | \(6034\) | |
| Conductor: | \(3017\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(430\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3017}(13,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6034.bb
\(\chi_{6034}(13,\cdot)\) \(\chi_{6034}(83,\cdot)\) \(\chi_{6034}(111,\cdot)\) \(\chi_{6034}(153,\cdot)\) \(\chi_{6034}(167,\cdot)\) \(\chi_{6034}(181,\cdot)\) \(\chi_{6034}(195,\cdot)\) \(\chi_{6034}(237,\cdot)\) \(\chi_{6034}(251,\cdot)\) \(\chi_{6034}(279,\cdot)\) \(\chi_{6034}(293,\cdot)\) \(\chi_{6034}(349,\cdot)\) \(\chi_{6034}(391,\cdot)\) \(\chi_{6034}(517,\cdot)\) \(\chi_{6034}(573,\cdot)\) \(\chi_{6034}(587,\cdot)\) \(\chi_{6034}(601,\cdot)\) \(\chi_{6034}(657,\cdot)\) \(\chi_{6034}(685,\cdot)\) \(\chi_{6034}(699,\cdot)\) \(\chi_{6034}(727,\cdot)\) \(\chi_{6034}(741,\cdot)\) \(\chi_{6034}(839,\cdot)\) \(\chi_{6034}(951,\cdot)\) \(\chi_{6034}(965,\cdot)\) \(\chi_{6034}(979,\cdot)\) \(\chi_{6034}(993,\cdot)\) \(\chi_{6034}(1049,\cdot)\) \(\chi_{6034}(1063,\cdot)\) \(\chi_{6034}(1119,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{215})$ |
| Fixed field: | Number field defined by a degree 430 polynomial (not computed) |
Values on generators
\((1725,869)\) → \((-1,e\left(\frac{167}{430}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 6034 }(13, a) \) | \(1\) | \(1\) | \(e\left(\frac{21}{86}\right)\) | \(e\left(\frac{139}{430}\right)\) | \(e\left(\frac{21}{43}\right)\) | \(e\left(\frac{73}{215}\right)\) | \(e\left(\frac{77}{215}\right)\) | \(e\left(\frac{122}{215}\right)\) | \(e\left(\frac{116}{215}\right)\) | \(e\left(\frac{33}{430}\right)\) | \(e\left(\frac{131}{215}\right)\) | \(e\left(\frac{139}{215}\right)\) |