Basic properties
| Modulus: | \(6034\) | |
| Conductor: | \(3017\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1290\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3017}(33,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6034.bd
\(\chi_{6034}(5,\cdot)\) \(\chi_{6034}(19,\cdot)\) \(\chi_{6034}(33,\cdot)\) \(\chi_{6034}(45,\cdot)\) \(\chi_{6034}(59,\cdot)\) \(\chi_{6034}(61,\cdot)\) \(\chi_{6034}(75,\cdot)\) \(\chi_{6034}(87,\cdot)\) \(\chi_{6034}(115,\cdot)\) \(\chi_{6034}(157,\cdot)\) \(\chi_{6034}(159,\cdot)\) \(\chi_{6034}(171,\cdot)\) \(\chi_{6034}(173,\cdot)\) \(\chi_{6034}(227,\cdot)\) \(\chi_{6034}(283,\cdot)\) \(\chi_{6034}(285,\cdot)\) \(\chi_{6034}(297,\cdot)\) \(\chi_{6034}(327,\cdot)\) \(\chi_{6034}(353,\cdot)\) \(\chi_{6034}(369,\cdot)\) \(\chi_{6034}(397,\cdot)\) \(\chi_{6034}(451,\cdot)\) \(\chi_{6034}(453,\cdot)\) \(\chi_{6034}(481,\cdot)\) \(\chi_{6034}(507,\cdot)\) \(\chi_{6034}(521,\cdot)\) \(\chi_{6034}(523,\cdot)\) \(\chi_{6034}(537,\cdot)\) \(\chi_{6034}(549,\cdot)\) \(\chi_{6034}(551,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{645})$ |
| Fixed field: | Number field defined by a degree 1290 polynomial (not computed) |
Values on generators
\((1725,869)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{134}{215}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 6034 }(33, a) \) | \(-1\) | \(1\) | \(e\left(\frac{89}{258}\right)\) | \(e\left(\frac{413}{1290}\right)\) | \(e\left(\frac{89}{129}\right)\) | \(e\left(\frac{551}{645}\right)\) | \(e\left(\frac{251}{430}\right)\) | \(e\left(\frac{143}{215}\right)\) | \(e\left(\frac{199}{1290}\right)\) | \(e\left(\frac{791}{1290}\right)\) | \(e\left(\frac{547}{645}\right)\) | \(e\left(\frac{413}{645}\right)\) |