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 \(\chi_{3017}(69,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6034.ba
\(\chi_{6034}(41,\cdot)\) \(\chi_{6034}(69,\cdot)\) \(\chi_{6034}(97,\cdot)\) \(\chi_{6034}(125,\cdot)\) \(\chi_{6034}(139,\cdot)\) \(\chi_{6034}(209,\cdot)\) \(\chi_{6034}(223,\cdot)\) \(\chi_{6034}(265,\cdot)\) \(\chi_{6034}(307,\cdot)\) \(\chi_{6034}(363,\cdot)\) \(\chi_{6034}(461,\cdot)\) \(\chi_{6034}(475,\cdot)\) \(\chi_{6034}(489,\cdot)\) \(\chi_{6034}(531,\cdot)\) \(\chi_{6034}(545,\cdot)\) \(\chi_{6034}(615,\cdot)\) \(\chi_{6034}(629,\cdot)\) \(\chi_{6034}(643,\cdot)\) \(\chi_{6034}(671,\cdot)\) \(\chi_{6034}(769,\cdot)\) \(\chi_{6034}(783,\cdot)\) \(\chi_{6034}(797,\cdot)\) \(\chi_{6034}(811,\cdot)\) \(\chi_{6034}(825,\cdot)\) \(\chi_{6034}(867,\cdot)\) \(\chi_{6034}(881,\cdot)\) \(\chi_{6034}(895,\cdot)\) \(\chi_{6034}(923,\cdot)\) \(\chi_{6034}(937,\cdot)\) \(\chi_{6034}(1021,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{215})$ |
| Fixed field: | Number field defined by a degree 430 polynomial (not computed) |
Values on generators
\((1725,869)\) → \((-1,e\left(\frac{88}{215}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 6034 }(69, a) \) | \(-1\) | \(1\) | \(e\left(\frac{9}{86}\right)\) | \(e\left(\frac{207}{430}\right)\) | \(e\left(\frac{9}{43}\right)\) | \(e\left(\frac{19}{215}\right)\) | \(e\left(\frac{367}{430}\right)\) | \(e\left(\frac{126}{215}\right)\) | \(e\left(\frac{81}{430}\right)\) | \(e\left(\frac{309}{430}\right)\) | \(e\left(\frac{93}{215}\right)\) | \(e\left(\frac{207}{215}\right)\) |