Basic properties
Modulus: | \(6034\) | |
Conductor: | \(431\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(215\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{431}(169,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6034.v
\(\chi_{6034}(15,\cdot)\) \(\chi_{6034}(29,\cdot)\) \(\chi_{6034}(57,\cdot)\) \(\chi_{6034}(99,\cdot)\) \(\chi_{6034}(169,\cdot)\) \(\chi_{6034}(183,\cdot)\) \(\chi_{6034}(197,\cdot)\) \(\chi_{6034}(225,\cdot)\) \(\chi_{6034}(253,\cdot)\) \(\chi_{6034}(295,\cdot)\) \(\chi_{6034}(379,\cdot)\) \(\chi_{6034}(477,\cdot)\) \(\chi_{6034}(491,\cdot)\) \(\chi_{6034}(519,\cdot)\) \(\chi_{6034}(631,\cdot)\) \(\chi_{6034}(659,\cdot)\) \(\chi_{6034}(673,\cdot)\) \(\chi_{6034}(701,\cdot)\) \(\chi_{6034}(757,\cdot)\) \(\chi_{6034}(785,\cdot)\) \(\chi_{6034}(799,\cdot)\) \(\chi_{6034}(827,\cdot)\) \(\chi_{6034}(841,\cdot)\) \(\chi_{6034}(855,\cdot)\) \(\chi_{6034}(911,\cdot)\) \(\chi_{6034}(953,\cdot)\) \(\chi_{6034}(981,\cdot)\) \(\chi_{6034}(1009,\cdot)\) \(\chi_{6034}(1121,\cdot)\) \(\chi_{6034}(1135,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{215})$ |
Fixed field: | Number field defined by a degree 215 polynomial (not computed) |
Values on generators
\((1725,869)\) → \((1,e\left(\frac{167}{215}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
\( \chi_{ 6034 }(169, a) \) | \(1\) | \(1\) | \(e\left(\frac{21}{43}\right)\) | \(e\left(\frac{139}{215}\right)\) | \(e\left(\frac{42}{43}\right)\) | \(e\left(\frac{146}{215}\right)\) | \(e\left(\frac{154}{215}\right)\) | \(e\left(\frac{29}{215}\right)\) | \(e\left(\frac{17}{215}\right)\) | \(e\left(\frac{33}{215}\right)\) | \(e\left(\frac{47}{215}\right)\) | \(e\left(\frac{63}{215}\right)\) |