Basic properties
| Modulus: | \(405\) | |
| Conductor: | \(405\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(108\) | 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 405.x
\(\chi_{405}(2,\cdot)\) \(\chi_{405}(23,\cdot)\) \(\chi_{405}(32,\cdot)\) \(\chi_{405}(38,\cdot)\) \(\chi_{405}(47,\cdot)\) \(\chi_{405}(68,\cdot)\) \(\chi_{405}(77,\cdot)\) \(\chi_{405}(83,\cdot)\) \(\chi_{405}(92,\cdot)\) \(\chi_{405}(113,\cdot)\) \(\chi_{405}(122,\cdot)\) \(\chi_{405}(128,\cdot)\) \(\chi_{405}(137,\cdot)\) \(\chi_{405}(158,\cdot)\) \(\chi_{405}(167,\cdot)\) \(\chi_{405}(173,\cdot)\) \(\chi_{405}(182,\cdot)\) \(\chi_{405}(203,\cdot)\) \(\chi_{405}(212,\cdot)\) \(\chi_{405}(218,\cdot)\) \(\chi_{405}(227,\cdot)\) \(\chi_{405}(248,\cdot)\) \(\chi_{405}(257,\cdot)\) \(\chi_{405}(263,\cdot)\) \(\chi_{405}(272,\cdot)\) \(\chi_{405}(293,\cdot)\) \(\chi_{405}(302,\cdot)\) \(\chi_{405}(308,\cdot)\) \(\chi_{405}(317,\cdot)\) \(\chi_{405}(338,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{108})$ |
| Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((326,82)\) → \((e\left(\frac{19}{54}\right),-i)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 405 }(218, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{108}\right)\) | \(e\left(\frac{11}{54}\right)\) | \(e\left(\frac{41}{108}\right)\) | \(e\left(\frac{11}{36}\right)\) | \(e\left(\frac{31}{54}\right)\) | \(e\left(\frac{7}{108}\right)\) | \(e\left(\frac{13}{27}\right)\) | \(e\left(\frac{11}{27}\right)\) | \(e\left(\frac{13}{36}\right)\) | \(e\left(\frac{7}{18}\right)\) |