Basic properties
| Modulus: | \(6034\) | |
| Conductor: | \(3017\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(645\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3017}(25,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6034.bc
\(\chi_{6034}(11,\cdot)\) \(\chi_{6034}(23,\cdot)\) \(\chi_{6034}(25,\cdot)\) \(\chi_{6034}(53,\cdot)\) \(\chi_{6034}(109,\cdot)\) \(\chi_{6034}(121,\cdot)\) \(\chi_{6034}(123,\cdot)\) \(\chi_{6034}(135,\cdot)\) \(\chi_{6034}(151,\cdot)\) \(\chi_{6034}(163,\cdot)\) \(\chi_{6034}(177,\cdot)\) \(\chi_{6034}(179,\cdot)\) \(\chi_{6034}(205,\cdot)\) \(\chi_{6034}(207,\cdot)\) \(\chi_{6034}(221,\cdot)\) \(\chi_{6034}(261,\cdot)\) \(\chi_{6034}(263,\cdot)\) \(\chi_{6034}(275,\cdot)\) \(\chi_{6034}(277,\cdot)\) \(\chi_{6034}(289,\cdot)\) \(\chi_{6034}(291,\cdot)\) \(\chi_{6034}(305,\cdot)\) \(\chi_{6034}(319,\cdot)\) \(\chi_{6034}(345,\cdot)\) \(\chi_{6034}(347,\cdot)\) \(\chi_{6034}(361,\cdot)\) \(\chi_{6034}(375,\cdot)\) \(\chi_{6034}(389,\cdot)\) \(\chi_{6034}(403,\cdot)\) \(\chi_{6034}(417,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{645})$ |
| Fixed field: | Number field defined by a degree 645 polynomial (not computed) |
Values on generators
\((1725,869)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{127}{215}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 6034 }(25, a) \) | \(1\) | \(1\) | \(e\left(\frac{8}{129}\right)\) | \(e\left(\frac{227}{645}\right)\) | \(e\left(\frac{16}{129}\right)\) | \(e\left(\frac{373}{645}\right)\) | \(e\left(\frac{139}{215}\right)\) | \(e\left(\frac{89}{215}\right)\) | \(e\left(\frac{631}{645}\right)\) | \(e\left(\frac{74}{645}\right)\) | \(e\left(\frac{581}{645}\right)\) | \(e\left(\frac{454}{645}\right)\) |