Basic properties
| Modulus: | \(30492\) | |
| Conductor: | \(30492\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(330\) | 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 30492.lt
\(\chi_{30492}(103,\cdot)\) \(\chi_{30492}(115,\cdot)\) \(\chi_{30492}(355,\cdot)\) \(\chi_{30492}(367,\cdot)\) \(\chi_{30492}(619,\cdot)\) \(\chi_{30492}(1615,\cdot)\) \(\chi_{30492}(1879,\cdot)\) \(\chi_{30492}(2623,\cdot)\) \(\chi_{30492}(2875,\cdot)\) \(\chi_{30492}(2887,\cdot)\) \(\chi_{30492}(3127,\cdot)\) \(\chi_{30492}(3139,\cdot)\) \(\chi_{30492}(4387,\cdot)\) \(\chi_{30492}(4651,\cdot)\) \(\chi_{30492}(5395,\cdot)\) \(\chi_{30492}(5659,\cdot)\) \(\chi_{30492}(5899,\cdot)\) \(\chi_{30492}(5911,\cdot)\) \(\chi_{30492}(6163,\cdot)\) \(\chi_{30492}(7159,\cdot)\) \(\chi_{30492}(7423,\cdot)\) \(\chi_{30492}(8167,\cdot)\) \(\chi_{30492}(8419,\cdot)\) \(\chi_{30492}(8431,\cdot)\) \(\chi_{30492}(8671,\cdot)\) \(\chi_{30492}(8683,\cdot)\) \(\chi_{30492}(8935,\cdot)\) \(\chi_{30492}(10195,\cdot)\) \(\chi_{30492}(10939,\cdot)\) \(\chi_{30492}(11191,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{165})$ |
| Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
Values on generators
\((15247,23717,4357,27469)\) → \((-1,e\left(\frac{2}{3}\right),e\left(\frac{1}{6}\right),e\left(\frac{27}{55}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 30492 }(13975, a) \) | \(1\) | \(1\) | \(e\left(\frac{163}{330}\right)\) | \(e\left(\frac{137}{330}\right)\) | \(e\left(\frac{73}{330}\right)\) | \(e\left(\frac{13}{165}\right)\) | \(e\left(\frac{35}{66}\right)\) | \(e\left(\frac{163}{165}\right)\) | \(e\left(\frac{2}{165}\right)\) | \(e\left(\frac{12}{55}\right)\) | \(e\left(\frac{157}{165}\right)\) | \(e\left(\frac{41}{330}\right)\) |