Basic properties
| Modulus: | \(243675\) | |
| Conductor: | \(243675\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1710\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 243675.bbn
\(\chi_{243675}(56,\cdot)\) \(\chi_{243675}(911,\cdot)\) \(\chi_{243675}(1481,\cdot)\) \(\chi_{243675}(1766,\cdot)\) \(\chi_{243675}(2336,\cdot)\) \(\chi_{243675}(2621,\cdot)\) \(\chi_{243675}(3191,\cdot)\) \(\chi_{243675}(4046,\cdot)\) \(\chi_{243675}(5186,\cdot)\) \(\chi_{243675}(5756,\cdot)\) \(\chi_{243675}(6041,\cdot)\) \(\chi_{243675}(6611,\cdot)\) \(\chi_{243675}(6896,\cdot)\) \(\chi_{243675}(7466,\cdot)\) \(\chi_{243675}(8321,\cdot)\) \(\chi_{243675}(8606,\cdot)\) \(\chi_{243675}(9461,\cdot)\) \(\chi_{243675}(10031,\cdot)\) \(\chi_{243675}(10316,\cdot)\) \(\chi_{243675}(10886,\cdot)\) \(\chi_{243675}(11171,\cdot)\) \(\chi_{243675}(11741,\cdot)\) \(\chi_{243675}(12596,\cdot)\) \(\chi_{243675}(12881,\cdot)\) \(\chi_{243675}(13736,\cdot)\) \(\chi_{243675}(14306,\cdot)\) \(\chi_{243675}(14591,\cdot)\) \(\chi_{243675}(15446,\cdot)\) \(\chi_{243675}(16016,\cdot)\) \(\chi_{243675}(16871,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{855})$ |
| Fixed field: | Number field defined by a degree 1710 polynomial (not computed) |
Values on generators
\((36101,77977,129601)\) → \((e\left(\frac{1}{18}\right),e\left(\frac{2}{5}\right),e\left(\frac{17}{38}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(22\) |
| \( \chi_{ 243675 }(56, a) \) | \(1\) | \(1\) | \(e\left(\frac{772}{855}\right)\) | \(e\left(\frac{689}{855}\right)\) | \(e\left(\frac{170}{171}\right)\) | \(e\left(\frac{202}{285}\right)\) | \(e\left(\frac{1289}{1710}\right)\) | \(e\left(\frac{391}{1710}\right)\) | \(e\left(\frac{767}{855}\right)\) | \(e\left(\frac{523}{855}\right)\) | \(e\left(\frac{79}{570}\right)\) | \(e\left(\frac{1123}{1710}\right)\) |